Mercurial > hg > qm-dsp
changeset 242:6060110dc3c6
* Build PCA and HMM
| author | Chris Cannam <c.cannam@qmul.ac.uk> |
|---|---|
| date | Wed, 09 Jan 2008 10:37:06 +0000 |
| parents | a98dd8ec96f8 |
| children | dc30e3864ceb |
| files | hmm/HMM.c hmm/HMM.h hmm/hmm.c hmm/hmm.h include/cblas.h include/clapack.h maths/pca/PCA.c maths/pca/PCA.h maths/pca/pca.c maths/pca/pca.h qm-dsp.pro |
| diffstat | 11 files changed, 7191 insertions(+), 1214 deletions(-) [+] |
line wrap: on
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/hmm/HMM.c Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,800 @@ +/* + * hmm.c + * soundbite + * + * Created by Mark Levy on 12/02/2006. + * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. + * + */ + +#include <stdio.h> +#include <math.h> +#include <stdlib.h> +#include <float.h> +#include <time.h> /* to seed random number generator */ +#include <clapack.h> /* LAPACK for matrix inversion */ +#ifdef _MAC_OS_X +#include <vecLib/cblas.h> +#else +#include <cblas.h> /* BLAS for matrix multiplication */ +#endif + +#include "HMM.h" + +model_t* hmm_init(double** x, int T, int L, int N) +{ + int i, j, d, e, t; + double s, ss; + + model_t* model; + model = (model_t*) malloc(sizeof(model_t)); + model->N = N; + model->L = L; + model->p0 = (double*) malloc(N*sizeof(double)); + model->a = (double**) malloc(N*sizeof(double*)); + model->mu = (double**) malloc(N*sizeof(double*)); + for (i = 0; i < N; i++) + { + model->a[i] = (double*) malloc(N*sizeof(double)); + model->mu[i] = (double*) malloc(L*sizeof(double)); + } + model->cov = (double**) malloc(L*sizeof(double*)); + for (i = 0; i < L; i++) + model->cov[i] = (double*) malloc(L*sizeof(double)); + + srand(time(0)); + double* global_mean = (double*) malloc(L*sizeof(double)); + + /* find global mean */ + for (d = 0; d < L; d++) + { + global_mean[d] = 0; + for (t = 0; t < T; t++) + global_mean[d] += x[t][d]; + global_mean[d] /= T; + } + + /* calculate global diagonal covariance */ + for (d = 0; d < L; d++) + { + for (e = 0; e < L; e++) + model->cov[d][e] = 0; + for (t = 0; t < T; t++) + model->cov[d][d] += (x[t][d] - global_mean[d]) * (x[t][d] - global_mean[d]); + model->cov[d][d] /= T-1; + } + + /* set all means close to global mean */ + for (i = 0; i < N; i++) + { + for (d = 0; d < L; d++) + { + /* add some random noise related to covariance */ + /* ideally the random number would be Gaussian(0,1), as a hack we make it uniform on [-0.25,0.25] */ + model->mu[i][d] = global_mean[d] + (0.5 * rand() / (double) RAND_MAX - 0.25) * sqrt(model->cov[d][d]); + } + } + + /* random intial and transition probs */ + s = 0; + for (i = 0; i < N; i++) + { + model->p0[i] = 1 + rand() / (double) RAND_MAX; + s += model->p0[i]; + ss = 0; + for (j = 0; j < N; j++) + { + model->a[i][j] = 1 + rand() / (double) RAND_MAX; + ss += model->a[i][j]; + } + for (j = 0; j < N; j++) + { + model->a[i][j] /= ss; + } + } + for (i = 0; i < N; i++) + model->p0[i] /= s; + + free(global_mean); + + return model; +} + +void hmm_close(model_t* model) +{ + int i; + + for (i = 0; i < model->N; i++) + { + free(model->a[i]); + free(model->mu[i]); + } + free(model->a); + free(model->mu); + for (i = 0; i < model->L; i++) + free(model->cov[i]); + free(model->cov); + free(model); +} + +void hmm_train(double** x, int T, model_t* model) +{ + int i, t; + double loglik; /* overall log-likelihood at each iteration */ + + int N = model->N; + int L = model->L; + double* p0 = model->p0; + double** a = model->a; + double** mu = model->mu; + double** cov = model->cov; + + /* allocate memory */ + double** gamma = (double**) malloc(T*sizeof(double*)); + double*** xi = (double***) malloc(T*sizeof(double**)); + for (t = 0; t < T; t++) + { + gamma[t] = (double*) malloc(N*sizeof(double)); + xi[t] = (double**) malloc(N*sizeof(double*)); + for (i = 0; i < N; i++) + xi[t][i] = (double*) malloc(N*sizeof(double)); + } + + /* temporary memory */ + double* gauss_y = (double*) malloc(L*sizeof(double)); + double* gauss_z = (double*) malloc(L*sizeof(double)); + + /* obs probs P(j|{x}) */ + double** b = (double**) malloc(T*sizeof(double*)); + for (t = 0; t < T; t++) + b[t] = (double*) malloc(N*sizeof(double)); + + /* inverse covariance and its determinant */ + double** icov = (double**) malloc(L*sizeof(double*)); + for (i = 0; i < L; i++) + icov[i] = (double*) malloc(L*sizeof(double)); + double detcov; + + double thresh = 0.0001; + int niter = 50; + int iter = 0; + double loglik1, loglik2; + while(iter < niter && !(iter > 1 && (loglik - loglik1) < thresh * (loglik1 - loglik2))) + { + ++iter; + + fprintf(stderr, "calculating obsprobs...\n"); + fflush(stderr); + + /* precalculate obs probs */ + invert(cov, L, icov, &detcov); + + for (t = 0; t < T; t++) + { + //int allzero = 1; + for (i = 0; i < N; i++) + { + b[t][i] = exp(loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z)); + + //if (b[t][i] != 0) + // allzero = 0; + } + /* + if (allzero) + { + printf("all the b[t][i] were zero for t = %d, correcting...\n", t); + for (i = 0; i < N; i++) + { + b[t][i] = 0.00001; + } + } + */ + } + + fprintf(stderr, "forwards-backwards...\n"); + fflush(stderr); + + forward_backwards(xi, gamma, &loglik, &loglik1, &loglik2, iter, N, T, p0, a, b); + + fprintf(stderr, "iteration %d: loglik = %f\n", iter, loglik); + fprintf(stderr, "re-estimation...\n"); + fflush(stderr); + + baum_welch(p0, a, mu, cov, N, T, L, x, xi, gamma); + + /* + printf("a:\n"); + for (i = 0; i < model->N; i++) + { + for (j = 0; j < model->N; j++) + printf("%f ", model->a[i][j]); + printf("\n"); + } + printf("\n\n"); + */ + //hmm_print(model); + } + + /* deallocate memory */ + for (t = 0; t < T; t++) + { + free(gamma[t]); + free(b[t]); + for (i = 0; i < N; i++) + free(xi[t][i]); + free(xi[t]); + } + free(gamma); + free(xi); + free(b); + + for (i = 0; i < L; i++) + free(icov[i]); + free(icov); + + free(gauss_y); + free(gauss_z); +} + +void mlss_reestimate(double* p0, double** a, double** mu, double** cov, int N, int T, int L, int* q, double** x) +{ + /* fit a single Gaussian to observations in each state */ + + /* calculate the mean observation in each state */ + + /* calculate the overall covariance */ + + /* count transitions */ + + /* estimate initial probs from transitions (???) */ +} + +void baum_welch(double* p0, double** a, double** mu, double** cov, int N, int T, int L, double** x, double*** xi, double** gamma) +{ + int i, j, t; + + double* sum_gamma = (double*) malloc(N*sizeof(double)); + + /* temporary memory */ + double* u = (double*) malloc(L*L*sizeof(double)); + double* yy = (double*) malloc(T*L*sizeof(double)); + double* yy2 = (double*) malloc(T*L*sizeof(double)); + + /* re-estimate transition probs */ + for (i = 0; i < N; i++) + { + sum_gamma[i] = 0; + for (t = 0; t < T-1; t++) + sum_gamma[i] += gamma[t][i]; + } + + for (i = 0; i < N; i++) + { + if (sum_gamma[i] == 0) + { + fprintf(stderr, "sum_gamma[%d] was zero...\n", i); + } + //double s = 0; + for (j = 0; j < N; j++) + { + a[i][j] = 0; + for (t = 0; t < T-1; t++) + a[i][j] += xi[t][i][j]; + //s += a[i][j]; + a[i][j] /= sum_gamma[i]; + } + /* + for (j = 0; j < N; j++) + { + a[i][j] /= s; + } + */ + } + + /* NB: now we need to sum gamma over all t */ + for (i = 0; i < N; i++) + sum_gamma[i] += gamma[T-1][i]; + + /* re-estimate initial probs */ + for (i = 0; i < N; i++) + p0[i] = gamma[0][i]; + + /* re-estimate covariance */ + int d, e; + double sum_sum_gamma = 0; + for (i = 0; i < N; i++) + sum_sum_gamma += sum_gamma[i]; + + /* + for (d = 0; d < L; d++) + { + for (e = d; e < L; e++) + { + cov[d][e] = 0; + for (t = 0; t < T; t++) + for (j = 0; j < N; j++) + cov[d][e] += gamma[t][j] * (x[t][d] - mu[j][d]) * (x[t][e] - mu[j][e]); + + cov[d][e] /= sum_sum_gamma; + + if (isnan(cov[d][e])) + { + printf("cov[%d][%d] was nan\n", d, e); + for (j = 0; j < N; j++) + for (i = 0; i < L; i++) + if (isnan(mu[j][i])) + printf("mu[%d][%d] was nan\n", j, i); + for (t = 0; t < T; t++) + for (j = 0; j < N; j++) + if (isnan(gamma[t][j])) + printf("gamma[%d][%d] was nan\n", t, j); + exit(-1); + } + } + } + for (d = 0; d < L; d++) + for (e = 0; e < d; e++) + cov[d][e] = cov[e][d]; + */ + + /* using BLAS */ + for (d = 0; d < L; d++) + for (e = 0; e < L; e++) + cov[d][e] = 0; + + for (j = 0; j < N; j++) + { + for (d = 0; d < L; d++) + for (t = 0; t < T; t++) + { + yy[d*T+t] = x[t][d] - mu[j][d]; + yy2[d*T+t] = gamma[t][j] * (x[t][d] - mu[j][d]); + } + + cblas_dgemm(CblasColMajor, CblasTrans, CblasNoTrans, L, L, T, 1.0, yy, T, yy2, T, 0, u, L); + + for (e = 0; e < L; e++) + for (d = 0; d < L; d++) + cov[d][e] += u[e*L+d]; + } + + for (d = 0; d < L; d++) + for (e = 0; e < L; e++) + cov[d][e] /= T; /* sum_sum_gamma; */ + + //printf("sum_sum_gamma = %f\n", sum_sum_gamma); /* fine, = T IS THIS ALWAYS TRUE with pooled cov?? */ + + /* re-estimate means */ + for (j = 0; j < N; j++) + { + for (d = 0; d < L; d++) + { + mu[j][d] = 0; + for (t = 0; t < T; t++) + mu[j][d] += gamma[t][j] * x[t][d]; + mu[j][d] /= sum_gamma[j]; + } + } + + /* deallocate memory */ + free(sum_gamma); + free(yy); + free(yy2); + free(u); +} + +void forward_backwards(double*** xi, double** gamma, double* loglik, double* loglik1, double* loglik2, int iter, int N, int T, double* p0, double** a, double** b) +{ + /* forwards-backwards with scaling */ + int i, j, t; + + double** alpha = (double**) malloc(T*sizeof(double*)); + double** beta = (double**) malloc(T*sizeof(double*)); + for (t = 0; t < T; t++) + { + alpha[t] = (double*) malloc(N*sizeof(double)); + beta[t] = (double*) malloc(N*sizeof(double)); + } + + /* scaling coefficients */ + double* c = (double*) malloc(T*sizeof(double)); + + /* calculate forward probs and scale coefficients */ + c[0] = 0; + for (i = 0; i < N; i++) + { + alpha[0][i] = p0[i] * b[0][i]; + c[0] += alpha[0][i]; + + //printf("p0[%d] = %f, b[0][%d] = %f\n", i, p0[i], i, b[0][i]); + } + c[0] = 1 / c[0]; + for (i = 0; i < N; i++) + { + alpha[0][i] *= c[0]; + + //printf("alpha[0][%d] = %f\n", i, alpha[0][i]); /* OK agrees with Matlab */ + } + + *loglik1 = *loglik; + *loglik = -log(c[0]); + if (iter == 2) + *loglik2 = *loglik; + + for (t = 1; t < T; t++) + { + c[t] = 0; + for (j = 0; j < N; j++) + { + alpha[t][j] = 0; + for (i = 0; i < N; i++) + alpha[t][j] += alpha[t-1][i] * a[i][j]; + alpha[t][j] *= b[t][j]; + + c[t] += alpha[t][j]; + } + + /* + if (c[t] == 0) + { + printf("c[%d] = 0, going to blow up so exiting\n", t); + for (i = 0; i < N; i++) + if (b[t][i] == 0) + fprintf(stderr, "b[%d][%d] was zero\n", t, i); + fprintf(stderr, "x[t] was \n"); + for (i = 0; i < L; i++) + fprintf(stderr, "%f ", x[t][i]); + fprintf(stderr, "\n\n"); + exit(-1); + } + */ + + c[t] = 1 / c[t]; + for (j = 0; j < N; j++) + alpha[t][j] *= c[t]; + + //printf("c[%d] = %e\n", t, c[t]); + + *loglik -= log(c[t]); + } + + /* calculate backwards probs using same coefficients */ + for (i = 0; i < N; i++) + beta[T-1][i] = 1; + t = T - 1; + while (1) + { + for (i = 0; i < N; i++) + beta[t][i] *= c[t]; + + if (t == 0) + break; + + for (i = 0; i < N; i++) + { + beta[t-1][i] = 0; + for (j = 0; j < N; j++) + beta[t-1][i] += a[i][j] * b[t][j] * beta[t][j]; + } + + t--; + } + + /* + printf("alpha:\n"); + for (t = 0; t < T; t++) + { + for (i = 0; i < N; i++) + printf("%4.4e\t\t", alpha[t][i]); + printf("\n"); + } + printf("\n\n");printf("beta:\n"); + for (t = 0; t < T; t++) + { + for (i = 0; i < N; i++) + printf("%4.4e\t\t", beta[t][i]); + printf("\n"); + } + printf("\n\n"); + */ + + /* calculate posterior probs */ + double tot; + for (t = 0; t < T; t++) + { + tot = 0; + for (i = 0; i < N; i++) + { + gamma[t][i] = alpha[t][i] * beta[t][i]; + tot += gamma[t][i]; + } + for (i = 0; i < N; i++) + { + gamma[t][i] /= tot; + + //printf("gamma[%d][%d] = %f\n", t, i, gamma[t][i]); + } + } + + for (t = 0; t < T-1; t++) + { + tot = 0; + for (i = 0; i < N; i++) + { + for (j = 0; j < N; j++) + { + xi[t][i][j] = alpha[t][i] * a[i][j] * b[t+1][j] * beta[t+1][j]; + tot += xi[t][i][j]; + } + } + for (i = 0; i < N; i++) + for (j = 0; j < N; j++) + xi[t][i][j] /= tot; + } + + /* + // CHECK - fine + // gamma[t][i] = \sum_j{xi[t][i][j]} + tot = 0; + for (j = 0; j < N; j++) + tot += xi[3][1][j]; + printf("gamma[3][1] = %f, sum_j(xi[3][1][j]) = %f\n", gamma[3][1], tot); + */ + + for (t = 0; t < T; t++) + { + free(alpha[t]); + free(beta[t]); + } + free(alpha); + free(beta); + free(c); +} + +void viterbi_decode(double** x, int T, model_t* model, int* q) +{ + int i, j, t; + double max; + + int N = model->N; + int L = model->L; + double* p0 = model->p0; + double** a = model->a; + double** mu = model->mu; + double** cov = model->cov; + + /* inverse covariance and its determinant */ + double** icov = (double**) malloc(L*sizeof(double*)); + for (i = 0; i < L; i++) + icov[i] = (double*) malloc(L*sizeof(double)); + double detcov; + + double** logb = (double**) malloc(T*sizeof(double*)); + double** phi = (double**) malloc(T*sizeof(double*)); + int** psi = (int**) malloc(T*sizeof(int*)); + for (t = 0; t < T; t++) + { + logb[t] = (double*) malloc(N*sizeof(double)); + phi[t] = (double*) malloc(N*sizeof(double)); + psi[t] = (int*) malloc(N*sizeof(int)); + } + + /* temporary memory */ + double* gauss_y = (double*) malloc(L*sizeof(double)); + double* gauss_z = (double*) malloc(L*sizeof(double)); + + /* calculate observation logprobs */ + invert(cov, L, icov, &detcov); + for (t = 0; t < T; t++) + for (i = 0; i < N; i++) + logb[t][i] = loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z); + + /* initialise */ + for (i = 0; i < N; i++) + { + phi[0][i] = log(p0[i]) + logb[0][i]; + psi[0][i] = 0; + } + + for (t = 1; t < T; t++) + { + for (j = 0; j < N; j++) + { + max = -1000000; // TODO: what should this be?? = smallest possible sumlogprob + psi[t][j] = 0; + for (i = 0; i < N; i++) + { + if (phi[t-1][i] + log(a[i][j]) > max) + { + max = phi[t-1][i] + log(a[i][j]); + phi[t][j] = max + logb[t][j]; + psi[t][j] = i; + } + } + } + } + + /* find maximising state at time T-1 */ + max = phi[T-1][0]; + q[T-1] = 0; + for (i = 1; i < N; i++) + { + if (phi[T-1][i] > max) + { + max = phi[T-1][i]; + q[T-1] = i; + } + } + + + /* track back */ + t = T - 2; + while (t >= 0) + { + q[t] = psi[t+1][q[t+1]]; + t--; + } + + /* de-allocate memory */ + for (i = 0; i < L; i++) + free(icov[i]); + free(icov); + for (t = 0; t < T; t++) + { + free(logb[t]); + free(phi[t]); + free(psi[t]); + } + free(logb); + free(phi); + free(psi); + + free(gauss_y); + free(gauss_z); +} + +/* invert matrix and calculate determinant using LAPACK */ +void invert(double** cov, int L, double** icov, double* detcov) +{ + /* copy square matrix into a vector in column-major order */ + double* a = (double*) malloc(L*L*sizeof(double)); + int i, j; + for(j=0; j < L; j++) + for (i=0; i < L; i++) + a[j*L+i] = cov[i][j]; + + long M = (long) L; + long* ipiv = (long*) malloc(L*L*sizeof(int)); + long ret; + + /* LU decomposition */ + ret = dgetrf_(&M, &M, a, &M, ipiv, &ret); /* ret should be zero, negative if cov is singular */ + if (ret < 0) + { + fprintf(stderr, "Covariance matrix was singular, couldn't invert\n"); + exit(-1); + } + + /* find determinant */ + double det = 1; + for(i = 0; i < L; i++) + det *= a[i*L+i]; + // TODO: get this to work!!! If detcov < 0 then cov is bad anyway... + /* + int sign = 1; + for (i = 0; i < L; i++) + if (ipiv[i] != i) + sign = -sign; + det *= sign; + */ + if (det < 0) + det = -det; + *detcov = det; + + /* allocate required working storage */ + long lwork = -1; + double lwbest; + dgetri_(&M, a, &M, ipiv, &lwbest, &lwork, &ret); + lwork = (long) lwbest; + double* work = (double*) malloc(lwork*sizeof(double)); + + /* find inverse */ + dgetri_(&M, a, &M, ipiv, work, &lwork, &ret); + + for(j=0; j < L; j++) + for (i=0; i < L; i++) + icov[i][j] = a[j*L+i]; + + free(work); + free(a); +} + +/* probability of multivariate Gaussian given mean, inverse and determinant of covariance */ +double gauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z) +{ + int i, j; + double s = 0; + for (i = 0; i < L; i++) + y[i] = x[i] - mu[i]; + for (i = 0; i < L; i++) + { + //z[i] = 0; + //for (j = 0; j < L; j++) + // z[i] += icov[i][j] * y[j]; + z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1); + } + s = cblas_ddot(L, z, 1, y, 1); + //for (i = 0; i < L; i++) + // s += z[i] * y[i]; + + return exp(-s/2.0) / (pow(2*PI, L/2.0) * sqrt(detcov)); +} + +/* log probability of multivariate Gaussian given mean, inverse and determinant of covariance */ +double loggauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z) +{ + int i, j; + double s = 0; + double ret; + for (i = 0; i < L; i++) + y[i] = x[i] - mu[i]; + for (i = 0; i < L; i++) + { + //z[i] = 0; + //for (j = 0; j < L; j++) + // z[i] += icov[i][j] * y[j]; + z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1); + } + s = cblas_ddot(L, z, 1, y, 1); + //for (i = 0; i < L; i++) + // s += z[i] * y[i]; + + ret = -0.5 * (s + L * log(2*PI) + log(detcov)); + + /* + // TEST + if (isinf(ret) > 0) + printf("loggauss returning infinity\n"); + if (isinf(ret) < 0) + printf("loggauss returning -infinity\n"); + if (isnan(ret)) + printf("loggauss returning nan\n"); + */ + + return ret; +} + +void hmm_print(model_t* model) +{ + int i, j; + printf("p0:\n"); + for (i = 0; i < model->N; i++) + printf("%f ", model->p0[i]); + printf("\n\n"); + printf("a:\n"); + for (i = 0; i < model->N; i++) + { + for (j = 0; j < model->N; j++) + printf("%f ", model->a[i][j]); + printf("\n"); + } + printf("\n\n"); + printf("mu:\n"); + for (i = 0; i < model->N; i++) + { + for (j = 0; j < model->L; j++) + printf("%f ", model->mu[i][j]); + printf("\n"); + } + printf("\n\n"); + printf("cov:\n"); + for (i = 0; i < model->L; i++) + { + for (j = 0; j < model->L; j++) + printf("%f ", model->cov[i][j]); + printf("\n"); + } + printf("\n\n"); +} + +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/hmm/HMM.h Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,39 @@ +#ifndef _HMM_H +#define _HMM_H + +/* + * hmm.h + * soundbite + * + * Created by Mark Levy on 12/02/2006. + * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. + * + */ + +#ifndef PI +#define PI 3.14159265358979323846264338327950288 +#endif + +typedef struct _model_t { + int N; /* number of states */ + double* p0; /* initial probs */ + double** a; /* transition probs */ + int L; /* dimensionality of data */ + double** mu; /* state means */ + double** cov; /* covariance, tied between all states */ +} model_t; + +void hmm_train(double** x, int T, model_t* model); /* with scaling */ +void forward_backwards(double*** xi, double** gamma, double* loglik, double* loglik1, double* loglik2, int iter, + int N, int T, double* p0, double** a, double** b); +void baum_welch(double* p0, double** a, double** mu, double** cov, int N, int T, int L, double** x, double*** xi, double** gamma); +void viterbi_decode(double** x, int T, model_t* model, int* q); /* using logs */ +model_t* hmm_init(double** x, int T, int L, int N); +void hmm_close(model_t* model); +void invert(double** cov, int L, double** icov, double* detcov); /* uses LAPACK (included with Mac OSX) */ +double gauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z); +double loggauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z); +void hmm_print(model_t* model); + +#endif +
--- a/hmm/hmm.c Wed Jan 09 10:31:29 2008 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,800 +0,0 @@ -/* - * hmm.c - * soundbite - * - * Created by Mark Levy on 12/02/2006. - * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. - * - */ - -#include <stdio.h> -#include <math.h> -#include <stdlib.h> -#include <float.h> -#include <time.h> /* to seed random number generator */ -#include "clapack.h" /* LAPACK for matrix inversion */ -#ifdef _MAC_OS_X -#include <vecLib/cblas.h> -#else -#include <cblas.h> /* BLAS for matrix multiplication */ -#endif - -#include "hmm.h" - -model_t* hmm_init(double** x, int T, int L, int N) -{ - int i, j, d, e, t; - double s, ss; - - model_t* model; - model = (model_t*) malloc(sizeof(model_t)); - model->N = N; - model->L = L; - model->p0 = (double*) malloc(N*sizeof(double)); - model->a = (double**) malloc(N*sizeof(double*)); - model->mu = (double**) malloc(N*sizeof(double*)); - for (i = 0; i < N; i++) - { - model->a[i] = (double*) malloc(N*sizeof(double)); - model->mu[i] = (double*) malloc(L*sizeof(double)); - } - model->cov = (double**) malloc(L*sizeof(double*)); - for (i = 0; i < L; i++) - model->cov[i] = (double*) malloc(L*sizeof(double)); - - srand(time(0)); - double* global_mean = (double*) malloc(L*sizeof(double)); - - /* find global mean */ - for (d = 0; d < L; d++) - { - global_mean[d] = 0; - for (t = 0; t < T; t++) - global_mean[d] += x[t][d]; - global_mean[d] /= T; - } - - /* calculate global diagonal covariance */ - for (d = 0; d < L; d++) - { - for (e = 0; e < L; e++) - model->cov[d][e] = 0; - for (t = 0; t < T; t++) - model->cov[d][d] += (x[t][d] - global_mean[d]) * (x[t][d] - global_mean[d]); - model->cov[d][d] /= T-1; - } - - /* set all means close to global mean */ - for (i = 0; i < N; i++) - { - for (d = 0; d < L; d++) - { - /* add some random noise related to covariance */ - /* ideally the random number would be Gaussian(0,1), as a hack we make it uniform on [-0.25,0.25] */ - model->mu[i][d] = global_mean[d] + (0.5 * rand() / (double) RAND_MAX - 0.25) * sqrt(model->cov[d][d]); - } - } - - /* random intial and transition probs */ - s = 0; - for (i = 0; i < N; i++) - { - model->p0[i] = 1 + rand() / (double) RAND_MAX; - s += model->p0[i]; - ss = 0; - for (j = 0; j < N; j++) - { - model->a[i][j] = 1 + rand() / (double) RAND_MAX; - ss += model->a[i][j]; - } - for (j = 0; j < N; j++) - { - model->a[i][j] /= ss; - } - } - for (i = 0; i < N; i++) - model->p0[i] /= s; - - free(global_mean); - - return model; -} - -void hmm_close(model_t* model) -{ - int i; - - for (i = 0; i < model->N; i++) - { - free(model->a[i]); - free(model->mu[i]); - } - free(model->a); - free(model->mu); - for (i = 0; i < model->L; i++) - free(model->cov[i]); - free(model->cov); - free(model); -} - -void hmm_train(double** x, int T, model_t* model) -{ - int i, t; - double loglik; /* overall log-likelihood at each iteration */ - - int N = model->N; - int L = model->L; - double* p0 = model->p0; - double** a = model->a; - double** mu = model->mu; - double** cov = model->cov; - - /* allocate memory */ - double** gamma = (double**) malloc(T*sizeof(double*)); - double*** xi = (double***) malloc(T*sizeof(double**)); - for (t = 0; t < T; t++) - { - gamma[t] = (double*) malloc(N*sizeof(double)); - xi[t] = (double**) malloc(N*sizeof(double*)); - for (i = 0; i < N; i++) - xi[t][i] = (double*) malloc(N*sizeof(double)); - } - - /* temporary memory */ - double* gauss_y = (double*) malloc(L*sizeof(double)); - double* gauss_z = (double*) malloc(L*sizeof(double)); - - /* obs probs P(j|{x}) */ - double** b = (double**) malloc(T*sizeof(double*)); - for (t = 0; t < T; t++) - b[t] = (double*) malloc(N*sizeof(double)); - - /* inverse covariance and its determinant */ - double** icov = (double**) malloc(L*sizeof(double*)); - for (i = 0; i < L; i++) - icov[i] = (double*) malloc(L*sizeof(double)); - double detcov; - - double thresh = 0.0001; - int niter = 50; - int iter = 0; - double loglik1, loglik2; - while(iter < niter && !(iter > 1 && (loglik - loglik1) < thresh * (loglik1 - loglik2))) - { - ++iter; - - fprintf(stderr, "calculating obsprobs...\n"); - fflush(stderr); - - /* precalculate obs probs */ - invert(cov, L, icov, &detcov); - - for (t = 0; t < T; t++) - { - //int allzero = 1; - for (i = 0; i < N; i++) - { - b[t][i] = exp(loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z)); - - //if (b[t][i] != 0) - // allzero = 0; - } - /* - if (allzero) - { - printf("all the b[t][i] were zero for t = %d, correcting...\n", t); - for (i = 0; i < N; i++) - { - b[t][i] = 0.00001; - } - } - */ - } - - fprintf(stderr, "forwards-backwards...\n"); - fflush(stderr); - - forward_backwards(xi, gamma, &loglik, &loglik1, &loglik2, iter, N, T, p0, a, b); - - fprintf(stderr, "iteration %d: loglik = %f\n", iter, loglik); - fprintf(stderr, "re-estimation...\n"); - fflush(stderr); - - baum_welch(p0, a, mu, cov, N, T, L, x, xi, gamma); - - /* - printf("a:\n"); - for (i = 0; i < model->N; i++) - { - for (j = 0; j < model->N; j++) - printf("%f ", model->a[i][j]); - printf("\n"); - } - printf("\n\n"); - */ - //hmm_print(model); - } - - /* deallocate memory */ - for (t = 0; t < T; t++) - { - free(gamma[t]); - free(b[t]); - for (i = 0; i < N; i++) - free(xi[t][i]); - free(xi[t]); - } - free(gamma); - free(xi); - free(b); - - for (i = 0; i < L; i++) - free(icov[i]); - free(icov); - - free(gauss_y); - free(gauss_z); -} - -void mlss_reestimate(double* p0, double** a, double** mu, double** cov, int N, int T, int L, int* q, double** x) -{ - /* fit a single Gaussian to observations in each state */ - - /* calculate the mean observation in each state */ - - /* calculate the overall covariance */ - - /* count transitions */ - - /* estimate initial probs from transitions (???) */ -} - -void baum_welch(double* p0, double** a, double** mu, double** cov, int N, int T, int L, double** x, double*** xi, double** gamma) -{ - int i, j, t; - - double* sum_gamma = (double*) malloc(N*sizeof(double)); - - /* temporary memory */ - double* u = (double*) malloc(L*L*sizeof(double)); - double* yy = (double*) malloc(T*L*sizeof(double)); - double* yy2 = (double*) malloc(T*L*sizeof(double)); - - /* re-estimate transition probs */ - for (i = 0; i < N; i++) - { - sum_gamma[i] = 0; - for (t = 0; t < T-1; t++) - sum_gamma[i] += gamma[t][i]; - } - - for (i = 0; i < N; i++) - { - if (sum_gamma[i] == 0) - { - fprintf(stderr, "sum_gamma[%d] was zero...\n", i); - } - //double s = 0; - for (j = 0; j < N; j++) - { - a[i][j] = 0; - for (t = 0; t < T-1; t++) - a[i][j] += xi[t][i][j]; - //s += a[i][j]; - a[i][j] /= sum_gamma[i]; - } - /* - for (j = 0; j < N; j++) - { - a[i][j] /= s; - } - */ - } - - /* NB: now we need to sum gamma over all t */ - for (i = 0; i < N; i++) - sum_gamma[i] += gamma[T-1][i]; - - /* re-estimate initial probs */ - for (i = 0; i < N; i++) - p0[i] = gamma[0][i]; - - /* re-estimate covariance */ - int d, e; - double sum_sum_gamma = 0; - for (i = 0; i < N; i++) - sum_sum_gamma += sum_gamma[i]; - - /* - for (d = 0; d < L; d++) - { - for (e = d; e < L; e++) - { - cov[d][e] = 0; - for (t = 0; t < T; t++) - for (j = 0; j < N; j++) - cov[d][e] += gamma[t][j] * (x[t][d] - mu[j][d]) * (x[t][e] - mu[j][e]); - - cov[d][e] /= sum_sum_gamma; - - if (isnan(cov[d][e])) - { - printf("cov[%d][%d] was nan\n", d, e); - for (j = 0; j < N; j++) - for (i = 0; i < L; i++) - if (isnan(mu[j][i])) - printf("mu[%d][%d] was nan\n", j, i); - for (t = 0; t < T; t++) - for (j = 0; j < N; j++) - if (isnan(gamma[t][j])) - printf("gamma[%d][%d] was nan\n", t, j); - exit(-1); - } - } - } - for (d = 0; d < L; d++) - for (e = 0; e < d; e++) - cov[d][e] = cov[e][d]; - */ - - /* using BLAS */ - for (d = 0; d < L; d++) - for (e = 0; e < L; e++) - cov[d][e] = 0; - - for (j = 0; j < N; j++) - { - for (d = 0; d < L; d++) - for (t = 0; t < T; t++) - { - yy[d*T+t] = x[t][d] - mu[j][d]; - yy2[d*T+t] = gamma[t][j] * (x[t][d] - mu[j][d]); - } - - cblas_dgemm(CblasColMajor, CblasTrans, CblasNoTrans, L, L, T, 1.0, yy, T, yy2, T, 0, u, L); - - for (e = 0; e < L; e++) - for (d = 0; d < L; d++) - cov[d][e] += u[e*L+d]; - } - - for (d = 0; d < L; d++) - for (e = 0; e < L; e++) - cov[d][e] /= T; /* sum_sum_gamma; */ - - //printf("sum_sum_gamma = %f\n", sum_sum_gamma); /* fine, = T IS THIS ALWAYS TRUE with pooled cov?? */ - - /* re-estimate means */ - for (j = 0; j < N; j++) - { - for (d = 0; d < L; d++) - { - mu[j][d] = 0; - for (t = 0; t < T; t++) - mu[j][d] += gamma[t][j] * x[t][d]; - mu[j][d] /= sum_gamma[j]; - } - } - - /* deallocate memory */ - free(sum_gamma); - free(yy); - free(yy2); - free(u); -} - -void forward_backwards(double*** xi, double** gamma, double* loglik, double* loglik1, double* loglik2, int iter, int N, int T, double* p0, double** a, double** b) -{ - /* forwards-backwards with scaling */ - int i, j, t; - - double** alpha = (double**) malloc(T*sizeof(double*)); - double** beta = (double**) malloc(T*sizeof(double*)); - for (t = 0; t < T; t++) - { - alpha[t] = (double*) malloc(N*sizeof(double)); - beta[t] = (double*) malloc(N*sizeof(double)); - } - - /* scaling coefficients */ - double* c = (double*) malloc(T*sizeof(double)); - - /* calculate forward probs and scale coefficients */ - c[0] = 0; - for (i = 0; i < N; i++) - { - alpha[0][i] = p0[i] * b[0][i]; - c[0] += alpha[0][i]; - - //printf("p0[%d] = %f, b[0][%d] = %f\n", i, p0[i], i, b[0][i]); - } - c[0] = 1 / c[0]; - for (i = 0; i < N; i++) - { - alpha[0][i] *= c[0]; - - //printf("alpha[0][%d] = %f\n", i, alpha[0][i]); /* OK agrees with Matlab */ - } - - *loglik1 = *loglik; - *loglik = -log(c[0]); - if (iter == 2) - *loglik2 = *loglik; - - for (t = 1; t < T; t++) - { - c[t] = 0; - for (j = 0; j < N; j++) - { - alpha[t][j] = 0; - for (i = 0; i < N; i++) - alpha[t][j] += alpha[t-1][i] * a[i][j]; - alpha[t][j] *= b[t][j]; - - c[t] += alpha[t][j]; - } - - /* - if (c[t] == 0) - { - printf("c[%d] = 0, going to blow up so exiting\n", t); - for (i = 0; i < N; i++) - if (b[t][i] == 0) - fprintf(stderr, "b[%d][%d] was zero\n", t, i); - fprintf(stderr, "x[t] was \n"); - for (i = 0; i < L; i++) - fprintf(stderr, "%f ", x[t][i]); - fprintf(stderr, "\n\n"); - exit(-1); - } - */ - - c[t] = 1 / c[t]; - for (j = 0; j < N; j++) - alpha[t][j] *= c[t]; - - //printf("c[%d] = %e\n", t, c[t]); - - *loglik -= log(c[t]); - } - - /* calculate backwards probs using same coefficients */ - for (i = 0; i < N; i++) - beta[T-1][i] = 1; - t = T - 1; - while (1) - { - for (i = 0; i < N; i++) - beta[t][i] *= c[t]; - - if (t == 0) - break; - - for (i = 0; i < N; i++) - { - beta[t-1][i] = 0; - for (j = 0; j < N; j++) - beta[t-1][i] += a[i][j] * b[t][j] * beta[t][j]; - } - - t--; - } - - /* - printf("alpha:\n"); - for (t = 0; t < T; t++) - { - for (i = 0; i < N; i++) - printf("%4.4e\t\t", alpha[t][i]); - printf("\n"); - } - printf("\n\n");printf("beta:\n"); - for (t = 0; t < T; t++) - { - for (i = 0; i < N; i++) - printf("%4.4e\t\t", beta[t][i]); - printf("\n"); - } - printf("\n\n"); - */ - - /* calculate posterior probs */ - double tot; - for (t = 0; t < T; t++) - { - tot = 0; - for (i = 0; i < N; i++) - { - gamma[t][i] = alpha[t][i] * beta[t][i]; - tot += gamma[t][i]; - } - for (i = 0; i < N; i++) - { - gamma[t][i] /= tot; - - //printf("gamma[%d][%d] = %f\n", t, i, gamma[t][i]); - } - } - - for (t = 0; t < T-1; t++) - { - tot = 0; - for (i = 0; i < N; i++) - { - for (j = 0; j < N; j++) - { - xi[t][i][j] = alpha[t][i] * a[i][j] * b[t+1][j] * beta[t+1][j]; - tot += xi[t][i][j]; - } - } - for (i = 0; i < N; i++) - for (j = 0; j < N; j++) - xi[t][i][j] /= tot; - } - - /* - // CHECK - fine - // gamma[t][i] = \sum_j{xi[t][i][j]} - tot = 0; - for (j = 0; j < N; j++) - tot += xi[3][1][j]; - printf("gamma[3][1] = %f, sum_j(xi[3][1][j]) = %f\n", gamma[3][1], tot); - */ - - for (t = 0; t < T; t++) - { - free(alpha[t]); - free(beta[t]); - } - free(alpha); - free(beta); - free(c); -} - -void viterbi_decode(double** x, int T, model_t* model, int* q) -{ - int i, j, t; - double max; - - int N = model->N; - int L = model->L; - double* p0 = model->p0; - double** a = model->a; - double** mu = model->mu; - double** cov = model->cov; - - /* inverse covariance and its determinant */ - double** icov = (double**) malloc(L*sizeof(double*)); - for (i = 0; i < L; i++) - icov[i] = (double*) malloc(L*sizeof(double)); - double detcov; - - double** logb = (double**) malloc(T*sizeof(double*)); - double** phi = (double**) malloc(T*sizeof(double*)); - int** psi = (int**) malloc(T*sizeof(int*)); - for (t = 0; t < T; t++) - { - logb[t] = (double*) malloc(N*sizeof(double)); - phi[t] = (double*) malloc(N*sizeof(double)); - psi[t] = (int*) malloc(N*sizeof(int)); - } - - /* temporary memory */ - double* gauss_y = (double*) malloc(L*sizeof(double)); - double* gauss_z = (double*) malloc(L*sizeof(double)); - - /* calculate observation logprobs */ - invert(cov, L, icov, &detcov); - for (t = 0; t < T; t++) - for (i = 0; i < N; i++) - logb[t][i] = loggauss(x[t], L, mu[i], icov, detcov, gauss_y, gauss_z); - - /* initialise */ - for (i = 0; i < N; i++) - { - phi[0][i] = log(p0[i]) + logb[0][i]; - psi[0][i] = 0; - } - - for (t = 1; t < T; t++) - { - for (j = 0; j < N; j++) - { - max = -1000000; // TODO: what should this be?? = smallest possible sumlogprob - psi[t][j] = 0; - for (i = 0; i < N; i++) - { - if (phi[t-1][i] + log(a[i][j]) > max) - { - max = phi[t-1][i] + log(a[i][j]); - phi[t][j] = max + logb[t][j]; - psi[t][j] = i; - } - } - } - } - - /* find maximising state at time T-1 */ - max = phi[T-1][0]; - q[T-1] = 0; - for (i = 1; i < N; i++) - { - if (phi[T-1][i] > max) - { - max = phi[T-1][i]; - q[T-1] = i; - } - } - - - /* track back */ - t = T - 2; - while (t >= 0) - { - q[t] = psi[t+1][q[t+1]]; - t--; - } - - /* de-allocate memory */ - for (i = 0; i < L; i++) - free(icov[i]); - free(icov); - for (t = 0; t < T; t++) - { - free(logb[t]); - free(phi[t]); - free(psi[t]); - } - free(logb); - free(phi); - free(psi); - - free(gauss_y); - free(gauss_z); -} - -/* invert matrix and calculate determinant using LAPACK */ -void invert(double** cov, int L, double** icov, double* detcov) -{ - /* copy square matrix into a vector in column-major order */ - double* a = (double*) malloc(L*L*sizeof(double)); - int i, j; - for(j=0; j < L; j++) - for (i=0; i < L; i++) - a[j*L+i] = cov[i][j]; - - long M = (long) L; - long* ipiv = (long*) malloc(L*L*sizeof(int)); - long ret; - - /* LU decomposition */ - ret = dgetrf_(&M, &M, a, &M, ipiv, &ret); /* ret should be zero, negative if cov is singular */ - if (ret < 0) - { - fprintf(stderr, "Covariance matrix was singular, couldn't invert\n"); - exit(-1); - } - - /* find determinant */ - double det = 1; - for(i = 0; i < L; i++) - det *= a[i*L+i]; - // TODO: get this to work!!! If detcov < 0 then cov is bad anyway... - /* - int sign = 1; - for (i = 0; i < L; i++) - if (ipiv[i] != i) - sign = -sign; - det *= sign; - */ - if (det < 0) - det = -det; - *detcov = det; - - /* allocate required working storage */ - long lwork = -1; - double lwbest; - dgetri_(&M, a, &M, ipiv, &lwbest, &lwork, &ret); - lwork = (long) lwbest; - double* work = (double*) malloc(lwork*sizeof(double)); - - /* find inverse */ - dgetri_(&M, a, &M, ipiv, work, &lwork, &ret); - - for(j=0; j < L; j++) - for (i=0; i < L; i++) - icov[i][j] = a[j*L+i]; - - free(work); - free(a); -} - -/* probability of multivariate Gaussian given mean, inverse and determinant of covariance */ -double gauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z) -{ - int i, j; - double s = 0; - for (i = 0; i < L; i++) - y[i] = x[i] - mu[i]; - for (i = 0; i < L; i++) - { - //z[i] = 0; - //for (j = 0; j < L; j++) - // z[i] += icov[i][j] * y[j]; - z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1); - } - s = cblas_ddot(L, z, 1, y, 1); - //for (i = 0; i < L; i++) - // s += z[i] * y[i]; - - return exp(-s/2.0) / (pow(2*PI, L/2.0) * sqrt(detcov)); -} - -/* log probability of multivariate Gaussian given mean, inverse and determinant of covariance */ -double loggauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z) -{ - int i, j; - double s = 0; - double ret; - for (i = 0; i < L; i++) - y[i] = x[i] - mu[i]; - for (i = 0; i < L; i++) - { - //z[i] = 0; - //for (j = 0; j < L; j++) - // z[i] += icov[i][j] * y[j]; - z[i] = cblas_ddot(L, &icov[i][0], 1, y, 1); - } - s = cblas_ddot(L, z, 1, y, 1); - //for (i = 0; i < L; i++) - // s += z[i] * y[i]; - - ret = -0.5 * (s + L * log(2*PI) + log(detcov)); - - /* - // TEST - if (isinf(ret) > 0) - printf("loggauss returning infinity\n"); - if (isinf(ret) < 0) - printf("loggauss returning -infinity\n"); - if (isnan(ret)) - printf("loggauss returning nan\n"); - */ - - return ret; -} - -void hmm_print(model_t* model) -{ - int i, j; - printf("p0:\n"); - for (i = 0; i < model->N; i++) - printf("%f ", model->p0[i]); - printf("\n\n"); - printf("a:\n"); - for (i = 0; i < model->N; i++) - { - for (j = 0; j < model->N; j++) - printf("%f ", model->a[i][j]); - printf("\n"); - } - printf("\n\n"); - printf("mu:\n"); - for (i = 0; i < model->N; i++) - { - for (j = 0; j < model->L; j++) - printf("%f ", model->mu[i][j]); - printf("\n"); - } - printf("\n\n"); - printf("cov:\n"); - for (i = 0; i < model->L; i++) - { - for (j = 0; j < model->L; j++) - printf("%f ", model->cov[i][j]); - printf("\n"); - } - printf("\n\n"); -} - -
--- a/hmm/hmm.h Wed Jan 09 10:31:29 2008 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,39 +0,0 @@ -#ifndef _HMM_H -#define _HMM_H - -/* - * hmm.h - * soundbite - * - * Created by Mark Levy on 12/02/2006. - * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. - * - */ - -#ifndef PI -#define PI 3.14159265358979323846264338327950288 -#endif - -typedef struct _model_t { - int N; /* number of states */ - double* p0; /* initial probs */ - double** a; /* transition probs */ - int L; /* dimensionality of data */ - double** mu; /* state means */ - double** cov; /* covariance, tied between all states */ -} model_t; - -void hmm_train(double** x, int T, model_t* model); /* with scaling */ -void forward_backwards(double*** xi, double** gamma, double* loglik, double* loglik1, double* loglik2, int iter, - int N, int T, double* p0, double** a, double** b); -void baum_welch(double* p0, double** a, double** mu, double** cov, int N, int T, int L, double** x, double*** xi, double** gamma); -void viterbi_decode(double** x, int T, model_t* model, int* q); /* using logs */ -model_t* hmm_init(double** x, int T, int L, int N); -void hmm_close(model_t* model); -void invert(double** cov, int L, double** icov, double* detcov); /* uses LAPACK (included with Mac OSX) */ -double gauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z); -double loggauss(double* x, int L, double* mu, double** icov, double detcov, double* y, double* z); -void hmm_print(model_t* model); - -#endif -
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/include/cblas.h Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,578 @@ +#ifndef CBLAS_H +#define CBLAS_H +#include <stddef.h> + +/* Allow the use in C++ code. */ +#ifdef __cplusplus +extern "C" +{ +#endif + +/* + * Enumerated and derived types + */ +#define CBLAS_INDEX size_t /* this may vary between platforms */ + +enum CBLAS_ORDER {CblasRowMajor=101, CblasColMajor=102}; +enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113}; +enum CBLAS_UPLO {CblasUpper=121, CblasLower=122}; +enum CBLAS_DIAG {CblasNonUnit=131, CblasUnit=132}; +enum CBLAS_SIDE {CblasLeft=141, CblasRight=142}; + +/* + * =========================================================================== + * Prototypes for level 1 BLAS functions (complex are recast as routines) + * =========================================================================== + */ +float cblas_sdsdot(const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY); +double cblas_dsdot(const int N, const float *X, const int incX, const float *Y, + const int incY); +float cblas_sdot(const int N, const float *X, const int incX, + const float *Y, const int incY); +double cblas_ddot(const int N, const double *X, const int incX, + const double *Y, const int incY); + +/* + * Functions having prefixes Z and C only + */ +void cblas_cdotu_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotu); +void cblas_cdotc_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotc); + +void cblas_zdotu_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotu); +void cblas_zdotc_sub(const int N, const void *X, const int incX, + const void *Y, const int incY, void *dotc); + + +/* + * Functions having prefixes S D SC DZ + */ +float cblas_snrm2(const int N, const float *X, const int incX); +float cblas_sasum(const int N, const float *X, const int incX); + +double cblas_dnrm2(const int N, const double *X, const int incX); +double cblas_dasum(const int N, const double *X, const int incX); + +float cblas_scnrm2(const int N, const void *X, const int incX); +float cblas_scasum(const int N, const void *X, const int incX); + +double cblas_dznrm2(const int N, const void *X, const int incX); +double cblas_dzasum(const int N, const void *X, const int incX); + + +/* + * Functions having standard 4 prefixes (S D C Z) + */ +CBLAS_INDEX cblas_isamax(const int N, const float *X, const int incX); +CBLAS_INDEX cblas_idamax(const int N, const double *X, const int incX); +CBLAS_INDEX cblas_icamax(const int N, const void *X, const int incX); +CBLAS_INDEX cblas_izamax(const int N, const void *X, const int incX); + +/* + * =========================================================================== + * Prototypes for level 1 BLAS routines + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (s, d, c, z) + */ +void cblas_sswap(const int N, float *X, const int incX, + float *Y, const int incY); +void cblas_scopy(const int N, const float *X, const int incX, + float *Y, const int incY); +void cblas_saxpy(const int N, const float alpha, const float *X, + const int incX, float *Y, const int incY); + +void cblas_dswap(const int N, double *X, const int incX, + double *Y, const int incY); +void cblas_dcopy(const int N, const double *X, const int incX, + double *Y, const int incY); +void cblas_daxpy(const int N, const double alpha, const double *X, + const int incX, double *Y, const int incY); + +void cblas_cswap(const int N, void *X, const int incX, + void *Y, const int incY); +void cblas_ccopy(const int N, const void *X, const int incX, + void *Y, const int incY); +void cblas_caxpy(const int N, const void *alpha, const void *X, + const int incX, void *Y, const int incY); + +void cblas_zswap(const int N, void *X, const int incX, + void *Y, const int incY); +void cblas_zcopy(const int N, const void *X, const int incX, + void *Y, const int incY); +void cblas_zaxpy(const int N, const void *alpha, const void *X, + const int incX, void *Y, const int incY); + + +/* + * Routines with S and D prefix only + */ +void cblas_srotg(float *a, float *b, float *c, float *s); +void cblas_srotmg(float *d1, float *d2, float *b1, const float b2, float *P); +void cblas_srot(const int N, float *X, const int incX, + float *Y, const int incY, const float c, const float s); +void cblas_srotm(const int N, float *X, const int incX, + float *Y, const int incY, const float *P); + +void cblas_drotg(double *a, double *b, double *c, double *s); +void cblas_drotmg(double *d1, double *d2, double *b1, const double b2, double *P); +void cblas_drot(const int N, double *X, const int incX, + double *Y, const int incY, const double c, const double s); +void cblas_drotm(const int N, double *X, const int incX, + double *Y, const int incY, const double *P); + + +/* + * Routines with S D C Z CS and ZD prefixes + */ +void cblas_sscal(const int N, const float alpha, float *X, const int incX); +void cblas_dscal(const int N, const double alpha, double *X, const int incX); +void cblas_cscal(const int N, const void *alpha, void *X, const int incX); +void cblas_zscal(const int N, const void *alpha, void *X, const int incX); +void cblas_csscal(const int N, const float alpha, void *X, const int incX); +void cblas_zdscal(const int N, const double alpha, void *X, const int incX); + +/* + * =========================================================================== + * Prototypes for level 2 BLAS + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (S, D, C, Z) + */ +void cblas_sgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const float alpha, const float *A, const int lda, + const float *X, const int incX, const float beta, + float *Y, const int incY); +void cblas_sgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const float alpha, + const float *A, const int lda, const float *X, + const int incX, const float beta, float *Y, const int incY); +void cblas_strmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *A, const int lda, + float *X, const int incX); +void cblas_stbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const float *A, const int lda, + float *X, const int incX); +void cblas_stpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *Ap, float *X, const int incX); +void cblas_strsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *A, const int lda, float *X, + const int incX); +void cblas_stbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const float *A, const int lda, + float *X, const int incX); +void cblas_stpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const float *Ap, float *X, const int incX); + +void cblas_dgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const double alpha, const double *A, const int lda, + const double *X, const int incX, const double beta, + double *Y, const int incY); +void cblas_dgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const double alpha, + const double *A, const int lda, const double *X, + const int incX, const double beta, double *Y, const int incY); +void cblas_dtrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *A, const int lda, + double *X, const int incX); +void cblas_dtbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const double *A, const int lda, + double *X, const int incX); +void cblas_dtpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *Ap, double *X, const int incX); +void cblas_dtrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *A, const int lda, double *X, + const int incX); +void cblas_dtbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const double *A, const int lda, + double *X, const int incX); +void cblas_dtpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const double *Ap, double *X, const int incX); + +void cblas_cgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *X, const int incX, const void *beta, + void *Y, const int incY); +void cblas_cgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const void *alpha, + const void *A, const int lda, const void *X, + const int incX, const void *beta, void *Y, const int incY); +void cblas_ctrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, + void *X, const int incX); +void cblas_ctbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ctpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); +void cblas_ctrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, void *X, + const int incX); +void cblas_ctbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ctpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); + +void cblas_zgemv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *X, const int incX, const void *beta, + void *Y, const int incY); +void cblas_zgbmv(const enum CBLAS_ORDER order, + const enum CBLAS_TRANSPOSE TransA, const int M, const int N, + const int KL, const int KU, const void *alpha, + const void *A, const int lda, const void *X, + const int incX, const void *beta, void *Y, const int incY); +void cblas_ztrmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, + void *X, const int incX); +void cblas_ztbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ztpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); +void cblas_ztrsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *A, const int lda, void *X, + const int incX); +void cblas_ztbsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const int K, const void *A, const int lda, + void *X, const int incX); +void cblas_ztpsv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_DIAG Diag, + const int N, const void *Ap, void *X, const int incX); + + +/* + * Routines with S and D prefixes only + */ +void cblas_ssymv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *A, + const int lda, const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_ssbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const float alpha, const float *A, + const int lda, const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_sspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *Ap, + const float *X, const int incX, + const float beta, float *Y, const int incY); +void cblas_sger(const enum CBLAS_ORDER order, const int M, const int N, + const float alpha, const float *X, const int incX, + const float *Y, const int incY, float *A, const int lda); +void cblas_ssyr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, float *A, const int lda); +void cblas_sspr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, float *Ap); +void cblas_ssyr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY, float *A, + const int lda); +void cblas_sspr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const float *X, + const int incX, const float *Y, const int incY, float *A); + +void cblas_dsymv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *A, + const int lda, const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dsbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const double alpha, const double *A, + const int lda, const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dspmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *Ap, + const double *X, const int incX, + const double beta, double *Y, const int incY); +void cblas_dger(const enum CBLAS_ORDER order, const int M, const int N, + const double alpha, const double *X, const int incX, + const double *Y, const int incY, double *A, const int lda); +void cblas_dsyr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, double *A, const int lda); +void cblas_dspr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, double *Ap); +void cblas_dsyr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, const double *Y, const int incY, double *A, + const int lda); +void cblas_dspr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const double *X, + const int incX, const double *Y, const int incY, double *A); + + +/* + * Routines with C and Z prefixes only + */ +void cblas_chemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_chbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_chpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *Ap, + const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_cgeru(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_cgerc(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_cher(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const void *X, const int incX, + void *A, const int lda); +void cblas_chpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const float alpha, const void *X, + const int incX, void *A); +void cblas_cher2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_chpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *Ap); + +void cblas_zhemv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zhbmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const int K, const void *alpha, const void *A, + const int lda, const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zhpmv(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const void *alpha, const void *Ap, + const void *X, const int incX, + const void *beta, void *Y, const int incY); +void cblas_zgeru(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zgerc(const enum CBLAS_ORDER order, const int M, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zher(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const void *X, const int incX, + void *A, const int lda); +void cblas_zhpr(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, + const int N, const double alpha, const void *X, + const int incX, void *A); +void cblas_zher2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *A, const int lda); +void cblas_zhpr2(const enum CBLAS_ORDER order, const enum CBLAS_UPLO Uplo, const int N, + const void *alpha, const void *X, const int incX, + const void *Y, const int incY, void *Ap); + +/* + * =========================================================================== + * Prototypes for level 3 BLAS + * =========================================================================== + */ + +/* + * Routines with standard 4 prefixes (S, D, C, Z) + */ +void cblas_sgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const float alpha, const float *A, + const int lda, const float *B, const int ldb, + const float beta, float *C, const int ldc); +void cblas_ssymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const float alpha, const float *A, const int lda, + const float *B, const int ldb, const float beta, + float *C, const int ldc); +void cblas_ssyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const float *A, const int lda, + const float beta, float *C, const int ldc); +void cblas_ssyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const float *A, const int lda, + const float *B, const int ldb, const float beta, + float *C, const int ldc); +void cblas_strmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const float alpha, const float *A, const int lda, + float *B, const int ldb); +void cblas_strsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const float alpha, const float *A, const int lda, + float *B, const int ldb); + +void cblas_dgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const double alpha, const double *A, + const int lda, const double *B, const int ldb, + const double beta, double *C, const int ldc); +void cblas_dsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const double alpha, const double *A, const int lda, + const double *B, const int ldb, const double beta, + double *C, const int ldc); +void cblas_dsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const double *A, const int lda, + const double beta, double *C, const int ldc); +void cblas_dsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const double *A, const int lda, + const double *B, const int ldb, const double beta, + double *C, const int ldc); +void cblas_dtrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const double alpha, const double *A, const int lda, + double *B, const int ldb); +void cblas_dtrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const double alpha, const double *A, const int lda, + double *B, const int ldb); + +void cblas_cgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const void *alpha, const void *A, + const int lda, const void *B, const int ldb, + const void *beta, void *C, const int ldc); +void cblas_csymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_csyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *beta, void *C, const int ldc); +void cblas_csyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_ctrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); +void cblas_ctrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); + +void cblas_zgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_TRANSPOSE TransB, const int M, const int N, + const int K, const void *alpha, const void *A, + const int lda, const void *B, const int ldb, + const void *beta, void *C, const int ldc); +void cblas_zsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_zsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *beta, void *C, const int ldc); +void cblas_zsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_ztrmm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); +void cblas_ztrsm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE TransA, + const enum CBLAS_DIAG Diag, const int M, const int N, + const void *alpha, const void *A, const int lda, + void *B, const int ldb); + + +/* + * Routines with prefixes C and Z only + */ +void cblas_chemm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_cherk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const float alpha, const void *A, const int lda, + const float beta, void *C, const int ldc); +void cblas_cher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const float beta, + void *C, const int ldc); + +void cblas_zhemm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, + const enum CBLAS_UPLO Uplo, const int M, const int N, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const void *beta, + void *C, const int ldc); +void cblas_zherk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const double alpha, const void *A, const int lda, + const double beta, void *C, const int ldc); +void cblas_zher2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, + const enum CBLAS_TRANSPOSE Trans, const int N, const int K, + const void *alpha, const void *A, const int lda, + const void *B, const int ldb, const double beta, + void *C, const int ldc); + +void cblas_xerbla(int p, const char *rout, const char *form, ...); + +#ifdef __cplusplus +} +#endif + +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/include/clapack.h Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,5394 @@ +/* + ================================================================================================= + Definitions and prototypes for LAPACK as provided Apple Computer. + + Documentation of the LAPACK interfaces, including reference implementations, can be found on the web + starting from the LAPACK FAQ page at this URL (verified live as of April 2002): + http://netlib.org/lapack/faq.html + + A hardcopy maanual is: + LAPACK Users' Guide, Third Edition. + @BOOK{laug, + AUTHOR = {Anderson, E. and Bai, Z. and Bischof, C. and + Blackford, S. and Demmel, J. and Dongarra, J. and + Du Croz, J. and Greenbaum, A. and Hammarling, S. and + McKenney, A. and Sorensen, D.}, + TITLE = {{LAPACK} Users' Guide}, + EDITION = {Third}, + PUBLISHER = {Society for Industrial and Applied Mathematics}, + YEAR = {1999}, + ADDRESS = {Philadelphia, PA}, + ISBN = {0-89871-447-8 (paperback)} } + + ================================================================================================= +*/ +#ifndef __CLAPACK_H +#define __CLAPACK_H + +#ifdef __cplusplus +extern "C" { +#endif + + +#if defined(__LP64__) /* In LP64 match sizes with the 32 bit ABI */ +typedef int __CLPK_integer; +typedef int __CLPK_logical; +typedef float __CLPK_real; +typedef double __CLPK_doublereal; +typedef __CLPK_logical (*__CLPK_L_fp)(); +typedef int __CLPK_ftnlen; +#else +typedef long int __CLPK_integer; +typedef long int __CLPK_logical; +typedef float __CLPK_real; +typedef double __CLPK_doublereal; +typedef __CLPK_logical (*__CLPK_L_fp)(); +typedef long int __CLPK_ftnlen; +#endif + +typedef struct { __CLPK_real r, i; } __CLPK_complex; +typedef struct { __CLPK_doublereal r, i; } __CLPK_doublecomplex; + +/* Subroutine */ int cbdsqr_(char *uplo, __CLPK_integer *n, __CLPK_integer *ncvt, __CLPK_integer * + nru, __CLPK_integer *ncc, __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *vt, __CLPK_integer *ldvt, + __CLPK_complex *u, __CLPK_integer *ldu, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cgbbrd_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *ncc, + __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *d__, + __CLPK_real *e, __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *pt, __CLPK_integer *ldpt, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgbcon_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgbequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real + *colcnd, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int cgbrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *afb, __CLPK_integer * + ldafb, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer * + ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer * + info); + +/* Subroutine */ int cgbsv_(__CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_integer * + nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int cgbsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer *kl, + __CLPK_integer *ku, __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *afb, + __CLPK_integer *ldafb, __CLPK_integer *ipiv, char *equed, __CLPK_real *r__, __CLPK_real *c__, + __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real + *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgbtf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int cgbtrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int cgbtrs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_complex + *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cgebak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_real *scale, __CLPK_integer *m, __CLPK_complex *v, __CLPK_integer *ldv, + __CLPK_integer *info); + +/* Subroutine */ int cgebal_(char *job, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *scale, __CLPK_integer *info); + +/* Subroutine */ int cgebd2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *tauq, __CLPK_complex *taup, __CLPK_complex *work, + __CLPK_integer *info); + +/* Subroutine */ int cgebrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *tauq, __CLPK_complex *taup, __CLPK_complex *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgecon_(char *norm, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgeequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real *colcnd, __CLPK_real *amax, + __CLPK_integer *info); + +/* Subroutine */ int cgees_(char *jobvs, char *sort, __CLPK_L_fp select, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_complex *w, __CLPK_complex *vs, + __CLPK_integer *ldvs, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_logical * + bwork, __CLPK_integer *info); + +/* Subroutine */ int cgeesx_(char *jobvs, char *sort, __CLPK_L_fp select, char * + sense, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_complex * + w, __CLPK_complex *vs, __CLPK_integer *ldvs, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_complex * + work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int cgeev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *w, __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex *vr, + __CLPK_integer *ldvr, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer * + info); + +/* Subroutine */ int cgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *w, __CLPK_complex *vl, + __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_real *scale, __CLPK_real *abnrm, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_complex *work, + __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgegs_(char *jobvsl, char *jobvsr, __CLPK_integer *n, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *alpha, __CLPK_complex * + beta, __CLPK_complex *vsl, __CLPK_integer *ldvsl, __CLPK_complex *vsr, __CLPK_integer *ldvsr, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgegv_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *alpha, __CLPK_complex *beta, + __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_complex * + work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgehd2_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgehrd_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer + *info); + +/* Subroutine */ int cgelq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgelqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgels_(char *trans, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgelsx_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *jpvt, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgelsy_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *jpvt, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer * + info); + +/* Subroutine */ int cgeql2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgeqlf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgeqp3_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *jpvt, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real * + rwork, __CLPK_integer *info); + +/* Subroutine */ int cgeqpf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *jpvt, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer * + info); + +/* Subroutine */ int cgeqr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgeqrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgerfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, __CLPK_complex * + b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgerq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgerqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgesc2_(__CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex * + rhs, __CLPK_integer *ipiv, __CLPK_integer *jpiv, __CLPK_real *scale); + +/* Subroutine */ int cgesv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cgesvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer * + ipiv, char *equed, __CLPK_real *r__, __CLPK_real *c__, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgetc2_(__CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer * + ipiv, __CLPK_integer *jpiv, __CLPK_integer *info); + +/* Subroutine */ int cgetf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int cgetrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int cgetri_(__CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer * + ipiv, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgetrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int cggbak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_real *lscale, __CLPK_real *rscale, __CLPK_integer *m, __CLPK_complex *v, + __CLPK_integer *ldv, __CLPK_integer *info); + +/* Subroutine */ int cggbal_(char *job, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *lscale, + __CLPK_real *rscale, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int cgges_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + selctg, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer * + ldb, __CLPK_integer *sdim, __CLPK_complex *alpha, __CLPK_complex *beta, __CLPK_complex *vsl, + __CLPK_integer *ldvsl, __CLPK_complex *vsr, __CLPK_integer *ldvsr, __CLPK_complex *work, __CLPK_integer * + lwork, __CLPK_real *rwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int cggesx_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + selctg, char *sense, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_complex *alpha, __CLPK_complex *beta, __CLPK_complex * + vsl, __CLPK_integer *ldvsl, __CLPK_complex *vsr, __CLPK_integer *ldvsr, __CLPK_real *rconde, __CLPK_real + *rcondv, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int cggev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *alpha, __CLPK_complex *beta, + __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_complex * + work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *alpha, __CLPK_complex *beta, __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex * + vr, __CLPK_integer *ldvr, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *lscale, __CLPK_real * + rscale, __CLPK_real *abnrm, __CLPK_real *bbnrm, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_complex + *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_logical *bwork, + __CLPK_integer *info); + +/* Subroutine */ int cggglm_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *d__, __CLPK_complex *x, + __CLPK_complex *y, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cgghrd_(char *compq, char *compz, __CLPK_integer *n, __CLPK_integer * + ilo, __CLPK_integer *ihi, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *info); + +/* Subroutine */ int cgglse_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *p, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *c__, __CLPK_complex *d__, + __CLPK_complex *x, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cggqrf_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *taua, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *taub, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cggrqf_(__CLPK_integer *m, __CLPK_integer *p, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *taua, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *taub, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cggsvd_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *p, __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *a, __CLPK_integer * + lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *alpha, __CLPK_real *beta, __CLPK_complex *u, + __CLPK_integer *ldu, __CLPK_complex *v, __CLPK_integer *ldv, __CLPK_complex *q, __CLPK_integer *ldq, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int cggsvp_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer + *ldb, __CLPK_real *tola, __CLPK_real *tolb, __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *u, + __CLPK_integer *ldu, __CLPK_complex *v, __CLPK_integer *ldv, __CLPK_complex *q, __CLPK_integer *ldq, + __CLPK_integer *iwork, __CLPK_real *rwork, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer * + info); + +/* Subroutine */ int cgtcon_(char *norm, __CLPK_integer *n, __CLPK_complex *dl, __CLPK_complex * + d__, __CLPK_complex *du, __CLPK_complex *du2, __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real * + rcond, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cgtrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + dl, __CLPK_complex *d__, __CLPK_complex *du, __CLPK_complex *dlf, __CLPK_complex *df, __CLPK_complex * + duf, __CLPK_complex *du2, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex * + x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cgtsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex *dl, __CLPK_complex * + d__, __CLPK_complex *du, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cgtsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *dl, __CLPK_complex *d__, __CLPK_complex *du, __CLPK_complex *dlf, __CLPK_complex * + df, __CLPK_complex *duf, __CLPK_complex *du2, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer * + ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cgttrf_(__CLPK_integer *n, __CLPK_complex *dl, __CLPK_complex *d__, __CLPK_complex * + du, __CLPK_complex *du2, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int cgttrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + dl, __CLPK_complex *d__, __CLPK_complex *du, __CLPK_complex *du2, __CLPK_integer *ipiv, __CLPK_complex * + b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cgtts2_(__CLPK_integer *itrans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_complex *dl, __CLPK_complex *d__, __CLPK_complex *du, __CLPK_complex *du2, __CLPK_integer *ipiv, + __CLPK_complex *b, __CLPK_integer *ldb); + +/* Subroutine */ int chbev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chbevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *lrwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int chbevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *q, __CLPK_integer *ldq, + __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer * + m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int chbgst_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *bb, __CLPK_integer *ldbb, + __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chbgv_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *bb, __CLPK_integer *ldbb, + __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int chbgvx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *ka, __CLPK_integer *kb, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *bb, + __CLPK_integer *ldbb, __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer * + il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_complex *z__, + __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_integer * + ifail, __CLPK_integer *info); + +/* Subroutine */ int chbtrd_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *q, __CLPK_integer * + ldq, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int checon_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_integer * + info); + +/* Subroutine */ int cheev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *w, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cheevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *w, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, + __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int cheevr_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer * + iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_integer *isuppz, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer * + lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int cheevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer * + iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_integer * + ifail, __CLPK_integer *info); + +/* Subroutine */ int chegs2_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int chegst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int chegv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *w, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chegvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *w, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *lrwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int chegvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer * + m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int cherfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, __CLPK_complex * + b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chesv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int chesvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer * + ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int chetf2_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int chetrd_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int chetrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int chetri_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int chetrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int chgeqz_(char *job, char *compq, char *compz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_complex *alpha, __CLPK_complex *beta, __CLPK_complex *q, __CLPK_integer *ldq, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real * + rwork, __CLPK_integer *info); + +/* Subroutine */ int chpcon_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int chpev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_complex *ap, + __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int chpevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_complex *ap, + __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_real *rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int chpevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_complex *ap, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real * + abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex * + work, __CLPK_real *rwork, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int chpgst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_complex * + ap, __CLPK_complex *bp, __CLPK_integer *info); + +/* Subroutine */ int chpgv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_complex *ap, __CLPK_complex *bp, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chpgvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_complex *ap, __CLPK_complex *bp, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *lrwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int chpgvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_complex *bp, __CLPK_real *vl, __CLPK_real *vu, + __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_complex * + z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int chprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_complex *afp, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, + __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int chpsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int chpsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *ap, __CLPK_complex *afp, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer * + ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int chptrd_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_real *d__, + __CLPK_real *e, __CLPK_complex *tau, __CLPK_integer *info); + +/* Subroutine */ int chptrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_integer *info); + +/* Subroutine */ int chptri_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int chptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int chsein_(char *side, char *eigsrc, char *initv, __CLPK_logical * + select, __CLPK_integer *n, __CLPK_complex *h__, __CLPK_integer *ldh, __CLPK_complex *w, __CLPK_complex * + vl, __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer * + m, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *ifaill, __CLPK_integer *ifailr, + __CLPK_integer *info); + +/* Subroutine */ int chseqr_(char *job, char *compz, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_complex *h__, __CLPK_integer *ldh, __CLPK_complex *w, __CLPK_complex *z__, + __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int clabrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *tauq, __CLPK_complex *taup, + __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_complex *y, __CLPK_integer *ldy); + +/* Subroutine */ int clacgv_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_integer *incx); + +/* Subroutine */ int clacon_(__CLPK_integer *n, __CLPK_complex *v, __CLPK_complex *x, __CLPK_real *est, + __CLPK_integer *kase); + +/* Subroutine */ int clacp2_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb); + +/* Subroutine */ int clacpy_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb); + +/* Subroutine */ int clacrm_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_real *rwork); + +/* Subroutine */ int clacrt_(__CLPK_integer *n, __CLPK_complex *cx, __CLPK_integer *incx, __CLPK_complex * + cy, __CLPK_integer *incy, __CLPK_complex *c__, __CLPK_complex *s); + +/* Subroutine */ int claed0_(__CLPK_integer *qsiz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *qstore, __CLPK_integer *ldqs, __CLPK_real *rwork, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int claed7_(__CLPK_integer *n, __CLPK_integer *cutpnt, __CLPK_integer *qsiz, + __CLPK_integer *tlvls, __CLPK_integer *curlvl, __CLPK_integer *curpbm, __CLPK_real *d__, __CLPK_complex * + q, __CLPK_integer *ldq, __CLPK_real *rho, __CLPK_integer *indxq, __CLPK_real *qstore, __CLPK_integer * + qptr, __CLPK_integer *prmptr, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer * + givcol, __CLPK_real *givnum, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int claed8_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *qsiz, __CLPK_complex * + q, __CLPK_integer *ldq, __CLPK_real *d__, __CLPK_real *rho, __CLPK_integer *cutpnt, __CLPK_real *z__, + __CLPK_real *dlamda, __CLPK_complex *q2, __CLPK_integer *ldq2, __CLPK_real *w, __CLPK_integer *indxp, + __CLPK_integer *indx, __CLPK_integer *indxq, __CLPK_integer *perm, __CLPK_integer *givptr, + __CLPK_integer *givcol, __CLPK_real *givnum, __CLPK_integer *info); + +/* Subroutine */ int claein_(__CLPK_logical *rightv, __CLPK_logical *noinit, __CLPK_integer *n, + __CLPK_complex *h__, __CLPK_integer *ldh, __CLPK_complex *w, __CLPK_complex *v, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_real *rwork, __CLPK_real *eps3, __CLPK_real *smlnum, __CLPK_integer *info); + +/* Subroutine */ int claesy_(__CLPK_complex *a, __CLPK_complex *b, __CLPK_complex *c__, __CLPK_complex * + rt1, __CLPK_complex *rt2, __CLPK_complex *evscal, __CLPK_complex *cs1, __CLPK_complex *sn1); + +/* Subroutine */ int claev2_(__CLPK_complex *a, __CLPK_complex *b, __CLPK_complex *c__, __CLPK_real *rt1, + __CLPK_real *rt2, __CLPK_real *cs1, __CLPK_complex *sn1); + +/* Subroutine */ int clags2_(__CLPK_logical *upper, __CLPK_real *a1, __CLPK_complex *a2, __CLPK_real *a3, + __CLPK_real *b1, __CLPK_complex *b2, __CLPK_real *b3, __CLPK_real *csu, __CLPK_complex *snu, __CLPK_real *csv, + __CLPK_complex *snv, __CLPK_real *csq, __CLPK_complex *snq); + +/* Subroutine */ int clagtm_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real * + alpha, __CLPK_complex *dl, __CLPK_complex *d__, __CLPK_complex *du, __CLPK_complex *x, __CLPK_integer * + ldx, __CLPK_real *beta, __CLPK_complex *b, __CLPK_integer *ldb); + +/* Subroutine */ int clahef_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *w, __CLPK_integer *ldw, + __CLPK_integer *info); + +/* Subroutine */ int clahqr_(__CLPK_logical *wantt, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex *h__, __CLPK_integer *ldh, __CLPK_complex *w, + __CLPK_integer *iloz, __CLPK_integer *ihiz, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer * + info); + +/* Subroutine */ int clahrd_(__CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *nb, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *y, + __CLPK_integer *ldy); + +/* Subroutine */ int claic1_(__CLPK_integer *job, __CLPK_integer *j, __CLPK_complex *x, __CLPK_real *sest, + __CLPK_complex *w, __CLPK_complex *gamma, __CLPK_real *sestpr, __CLPK_complex *s, __CLPK_complex *c__); + +/* Subroutine */ int clals0_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *nrhs, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *bx, + __CLPK_integer *ldbx, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_integer *ldgcol, __CLPK_real *givnum, __CLPK_integer *ldgnum, __CLPK_real *poles, __CLPK_real * + difl, __CLPK_real *difr, __CLPK_real *z__, __CLPK_integer *k, __CLPK_real *c__, __CLPK_real *s, __CLPK_real * + rwork, __CLPK_integer *info); + +/* Subroutine */ int clalsa_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *bx, __CLPK_integer *ldbx, + __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, __CLPK_integer *k, __CLPK_real *difl, __CLPK_real *difr, + __CLPK_real *z__, __CLPK_real *poles, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer * + ldgcol, __CLPK_integer *perm, __CLPK_real *givnum, __CLPK_real *c__, __CLPK_real *s, __CLPK_real *rwork, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int clapll_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_complex * + y, __CLPK_integer *incy, __CLPK_real *ssmin); + +/* Subroutine */ int clapmt_(__CLPK_logical *forwrd, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex + *x, __CLPK_integer *ldx, __CLPK_integer *k); + +/* Subroutine */ int claqgb_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real + *colcnd, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqge_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real *colcnd, __CLPK_real *amax, char * + equed); + +/* Subroutine */ int claqhb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqhe_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqhp_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_real *s, + __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqp2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_complex + *a, __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_complex *tau, __CLPK_real *vn1, __CLPK_real *vn2, + __CLPK_complex *work); + +/* Subroutine */ int claqps_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_integer + *nb, __CLPK_integer *kb, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_complex * + tau, __CLPK_real *vn1, __CLPK_real *vn2, __CLPK_complex *auxv, __CLPK_complex *f, __CLPK_integer *ldf); + +/* Subroutine */ int claqsb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqsp_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_real *s, + __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int claqsy_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int clar1v_(__CLPK_integer *n, __CLPK_integer *b1, __CLPK_integer *bn, __CLPK_real * + sigma, __CLPK_real *d__, __CLPK_real *l, __CLPK_real *ld, __CLPK_real *lld, __CLPK_real *gersch, __CLPK_complex + *z__, __CLPK_real *ztz, __CLPK_real *mingma, __CLPK_integer *r__, __CLPK_integer *isuppz, __CLPK_real * + work); + +/* Subroutine */ int clar2v_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_complex *y, __CLPK_complex *z__, + __CLPK_integer *incx, __CLPK_real *c__, __CLPK_complex *s, __CLPK_integer *incc); + +/* Subroutine */ int clarcm_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_real *rwork); + +/* Subroutine */ int clarf_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *v, + __CLPK_integer *incv, __CLPK_complex *tau, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex * + work); + +/* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *v, __CLPK_integer *ldv, + __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, + __CLPK_integer *ldwork); + +/* Subroutine */ int clarfg_(__CLPK_integer *n, __CLPK_complex *alpha, __CLPK_complex *x, __CLPK_integer * + incx, __CLPK_complex *tau); + +/* Subroutine */ int clarft_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_complex *v, __CLPK_integer *ldv, __CLPK_complex *tau, __CLPK_complex *t, __CLPK_integer *ldt); + +/* Subroutine */ int clarfx_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *v, + __CLPK_complex *tau, __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work); + +/* Subroutine */ int clargv_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_complex * + y, __CLPK_integer *incy, __CLPK_real *c__, __CLPK_integer *incc); + +/* Subroutine */ int clarnv_(__CLPK_integer *idist, __CLPK_integer *iseed, __CLPK_integer *n, + __CLPK_complex *x); + +/* Subroutine */ int clarrv_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *l, __CLPK_integer *isplit, + __CLPK_integer *m, __CLPK_real *w, __CLPK_integer *iblock, __CLPK_real *gersch, __CLPK_real *tol, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_real *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int clartg_(__CLPK_complex *f, __CLPK_complex *g, __CLPK_real *cs, __CLPK_complex *sn, + __CLPK_complex *r__); + +/* Subroutine */ int clartv_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_complex * + y, __CLPK_integer *incy, __CLPK_real *c__, __CLPK_complex *s, __CLPK_integer *incc); + +/* Subroutine */ int clarz_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, + __CLPK_complex *v, __CLPK_integer *incv, __CLPK_complex *tau, __CLPK_complex *c__, __CLPK_integer *ldc, + __CLPK_complex *work); + +/* Subroutine */ int clarzb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *v, + __CLPK_integer *ldv, __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *c__, __CLPK_integer *ldc, + __CLPK_complex *work, __CLPK_integer *ldwork); + +/* Subroutine */ int clarzt_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_complex *v, __CLPK_integer *ldv, __CLPK_complex *tau, __CLPK_complex *t, __CLPK_integer *ldt); + +/* Subroutine */ int clascl_(char *type__, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_real * + cfrom, __CLPK_real *cto, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int claset_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex * + alpha, __CLPK_complex *beta, __CLPK_complex *a, __CLPK_integer *lda); + +/* Subroutine */ int clasr_(char *side, char *pivot, char *direct, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_real *c__, __CLPK_real *s, __CLPK_complex *a, __CLPK_integer *lda); + +/* Subroutine */ int classq_(__CLPK_integer *n, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_real * + scale, __CLPK_real *sumsq); + +/* Subroutine */ int claswp_(__CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer * + k1, __CLPK_integer *k2, __CLPK_integer *ipiv, __CLPK_integer *incx); + +/* Subroutine */ int clasyf_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *w, __CLPK_integer *ldw, + __CLPK_integer *info); + +/* Subroutine */ int clatbs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex * + x, __CLPK_real *scale, __CLPK_real *cnorm, __CLPK_integer *info); + +/* Subroutine */ int clatdf_(__CLPK_integer *ijob, __CLPK_integer *n, __CLPK_complex *z__, __CLPK_integer + *ldz, __CLPK_complex *rhs, __CLPK_real *rdsum, __CLPK_real *rdscal, __CLPK_integer *ipiv, __CLPK_integer + *jpiv); + +/* Subroutine */ int clatps_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_complex *x, __CLPK_real *scale, __CLPK_real *cnorm, + __CLPK_integer *info); + +/* Subroutine */ int clatrd_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *e, __CLPK_complex *tau, __CLPK_complex *w, __CLPK_integer *ldw); + +/* Subroutine */ int clatrs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *x, __CLPK_real *scale, + __CLPK_real *cnorm, __CLPK_integer *info); + +/* Subroutine */ int clatrz_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work); + +/* Subroutine */ int clatzm_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *v, + __CLPK_integer *incv, __CLPK_complex *tau, __CLPK_complex *c1, __CLPK_complex *c2, __CLPK_integer *ldc, + __CLPK_complex *work); + +/* Subroutine */ int clauu2_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int clauum_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int cpbcon_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cpbequ_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int cpbrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *afb, __CLPK_integer *ldafb, + __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real * + berr, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cpbstf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int cpbsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int cpbsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *afb, __CLPK_integer * + ldafb, char *equed, __CLPK_real *s, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, + __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, + __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cpbtf2_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int cpbtrf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_complex *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int cpbtrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int cpocon_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cpoequ_(__CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *s, + __CLPK_real *scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int cporfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, + __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cposv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cposvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, char * + equed, __CLPK_real *s, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, + __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cpotf2_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int cpotrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int cpotri_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int cpotrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cppcon_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_real *anorm, + __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cppequ_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_real *s, + __CLPK_real *scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int cpprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_complex *afp, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cppsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cppsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *ap, __CLPK_complex *afp, char *equed, __CLPK_real *s, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real + *berr, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cpptrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + info); + +/* Subroutine */ int cpptri_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + info); + +/* Subroutine */ int cpptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cptcon_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_complex *e, __CLPK_real *anorm, + __CLPK_real *rcond, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cptrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, + __CLPK_complex *e, __CLPK_real *df, __CLPK_complex *ef, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex + *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cptsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, __CLPK_complex *e, + __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cptsvx_(char *fact, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, + __CLPK_complex *e, __CLPK_real *df, __CLPK_complex *ef, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex + *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, + __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int cpttrf_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_complex *e, __CLPK_integer *info); + +/* Subroutine */ int cpttrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, + __CLPK_complex *e, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cptts2_(__CLPK_integer *iuplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real * + d__, __CLPK_complex *e, __CLPK_complex *b, __CLPK_integer *ldb); + +/* Subroutine */ int crot_(__CLPK_integer *n, __CLPK_complex *cx, __CLPK_integer *incx, __CLPK_complex * + cy, __CLPK_integer *incy, __CLPK_real *c__, __CLPK_complex *s); + +/* Subroutine */ int cspcon_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cspmv_(char *uplo, __CLPK_integer *n, __CLPK_complex *alpha, __CLPK_complex * + ap, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_complex *beta, __CLPK_complex *y, __CLPK_integer * + incy); + +/* Subroutine */ int cspr_(char *uplo, __CLPK_integer *n, __CLPK_complex *alpha, __CLPK_complex *x, + __CLPK_integer *incx, __CLPK_complex *ap); + +/* Subroutine */ int csprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_complex *afp, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, + __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int cspsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int cspsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *ap, __CLPK_complex *afp, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer * + ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int csptrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_integer *info); + +/* Subroutine */ int csptri_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_integer * + ipiv, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int csptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + ap, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int csrot_(__CLPK_integer *n, __CLPK_complex *cx, __CLPK_integer *incx, __CLPK_complex * + cy, __CLPK_integer *incy, __CLPK_real *c__, __CLPK_real *s); + +/* Subroutine */ int csrscl_(__CLPK_integer *n, __CLPK_real *sa, __CLPK_complex *sx, __CLPK_integer *incx); + +/* Subroutine */ int cstedc_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real * + rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer * + info); + +/* Subroutine */ int cstein_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_integer *m, __CLPK_real + *w, __CLPK_integer *iblock, __CLPK_integer *isplit, __CLPK_complex *z__, __CLPK_integer *ldz, + __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int csteqr_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int csycon_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_integer * + info); + +/* Subroutine */ int csymv_(char *uplo, __CLPK_integer *n, __CLPK_complex *alpha, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *x, __CLPK_integer *incx, __CLPK_complex *beta, __CLPK_complex *y, + __CLPK_integer *incy); + +/* Subroutine */ int csyr_(char *uplo, __CLPK_integer *n, __CLPK_complex *alpha, __CLPK_complex *x, + __CLPK_integer *incx, __CLPK_complex *a, __CLPK_integer *lda); + +/* Subroutine */ int csyrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, __CLPK_complex * + b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int csysv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int csysvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *af, __CLPK_integer *ldaf, __CLPK_integer * + ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *rcond, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int csytf2_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int csytrf_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int csytri_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int csytrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int ctbcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *rcond, __CLPK_complex *work, + __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctbrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, + __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctbtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ctgevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, + __CLPK_integer *m, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctgex2_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *q, + __CLPK_integer *ldq, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *j1, __CLPK_integer *info); + +/* Subroutine */ int ctgexc_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *q, + __CLPK_integer *ldq, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *ifst, __CLPK_integer * + ilst, __CLPK_integer *info); + +/* Subroutine */ int ctgsen_(__CLPK_integer *ijob, __CLPK_logical *wantq, __CLPK_logical *wantz, + __CLPK_logical *select, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, + __CLPK_integer *ldb, __CLPK_complex *alpha, __CLPK_complex *beta, __CLPK_complex *q, __CLPK_integer *ldq, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *m, __CLPK_real *pl, __CLPK_real *pr, __CLPK_real * + dif, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int ctgsja_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *a, __CLPK_integer * + lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *tola, __CLPK_real *tolb, __CLPK_real *alpha, + __CLPK_real *beta, __CLPK_complex *u, __CLPK_integer *ldu, __CLPK_complex *v, __CLPK_integer *ldv, + __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *work, __CLPK_integer *ncycle, __CLPK_integer * + info); + +/* Subroutine */ int ctgsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *vl, __CLPK_integer *ldvl, __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_real *s, __CLPK_real + *dif, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer + *iwork, __CLPK_integer *info); + +/* Subroutine */ int ctgsy2_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *d__, __CLPK_integer *ldd, __CLPK_complex *e, __CLPK_integer *lde, + __CLPK_complex *f, __CLPK_integer *ldf, __CLPK_real *scale, __CLPK_real *rdsum, __CLPK_real *rdscal, + __CLPK_integer *info); + +/* Subroutine */ int ctgsyl_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *d__, __CLPK_integer *ldd, __CLPK_complex *e, __CLPK_integer *lde, + __CLPK_complex *f, __CLPK_integer *ldf, __CLPK_real *scale, __CLPK_real *dif, __CLPK_complex *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int ctpcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_complex *ap, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctprfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_complex *ap, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_complex *x, + __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int ctptri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_complex *ap, + __CLPK_integer *info); + +/* Subroutine */ int ctptrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_complex *ap, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ctrcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *rcond, __CLPK_complex *work, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int ctrevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *vl, __CLPK_integer *ldvl, + __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_complex *work, + __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctrexc_(char *compq, __CLPK_integer *n, __CLPK_complex *t, __CLPK_integer * + ldt, __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_integer *ifst, __CLPK_integer *ilst, __CLPK_integer * + info); + +/* Subroutine */ int ctrrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_complex *work, __CLPK_real + *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctrsen_(char *job, char *compq, __CLPK_logical *select, __CLPK_integer + *n, __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *w, + __CLPK_integer *m, __CLPK_real *s, __CLPK_real *sep, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int ctrsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_complex *t, __CLPK_integer *ldt, __CLPK_complex *vl, __CLPK_integer *ldvl, + __CLPK_complex *vr, __CLPK_integer *ldvr, __CLPK_real *s, __CLPK_real *sep, __CLPK_integer *mm, __CLPK_integer * + m, __CLPK_complex *work, __CLPK_integer *ldwork, __CLPK_real *rwork, __CLPK_integer *info); + +/* Subroutine */ int ctrsyl_(char *trana, char *tranb, __CLPK_integer *isgn, __CLPK_integer + *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_real *scale, __CLPK_integer *info); + +/* Subroutine */ int ctrti2_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int ctrtri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int ctrtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int ctzrqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_integer *info); + +/* Subroutine */ int ctzrzf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cung2l_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cung2r_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cungbr_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int cunghr_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer + *info); + +/* Subroutine */ int cungl2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunglq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cungql_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cungqr_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cungr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cungrq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cungtr_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_complex *tau, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cunm2l_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunm2r_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunmbr_(char *vect, char *side, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cunmhr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cunml2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunmlq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cunmql_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cunmqr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cunmr2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunmr3_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cunmrq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cunmrz_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, + __CLPK_complex *c__, __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int cunmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_complex *tau, __CLPK_complex *c__, + __CLPK_integer *ldc, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int cupgtr_(char *uplo, __CLPK_integer *n, __CLPK_complex *ap, __CLPK_complex * + tau, __CLPK_complex *q, __CLPK_integer *ldq, __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int cupmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_complex *ap, __CLPK_complex *tau, __CLPK_complex *c__, __CLPK_integer *ldc, + __CLPK_complex *work, __CLPK_integer *info); + +/* Subroutine */ int dbdsdc_(char *uplo, char *compq, __CLPK_integer *n, __CLPK_doublereal * + d__, __CLPK_doublereal *e, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *vt, + __CLPK_integer *ldvt, __CLPK_doublereal *q, __CLPK_integer *iq, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dbdsqr_(char *uplo, __CLPK_integer *n, __CLPK_integer *ncvt, __CLPK_integer * + nru, __CLPK_integer *ncc, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *vt, + __CLPK_integer *ldvt, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *c__, __CLPK_integer * + ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int ddisna_(char *job, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + d__, __CLPK_doublereal *sep, __CLPK_integer *info); + +/* Subroutine */ int dgbbrd_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *ncc, + __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal * + d__, __CLPK_doublereal *e, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *pt, + __CLPK_integer *ldpt, __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dgbcon_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_doublereal *anorm, + __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgbequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublereal *rowcnd, __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, __CLPK_integer * + info); + +/* Subroutine */ int dgbrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *afb, + __CLPK_integer *ldafb, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgbsv_(__CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_integer * + nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dgbsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer *kl, + __CLPK_integer *ku, __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, + __CLPK_doublereal *afb, __CLPK_integer *ldafb, __CLPK_integer *ipiv, char *equed, + __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgbtf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dgbtrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dgbtrs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dgebak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublereal *scale, __CLPK_integer *m, __CLPK_doublereal *v, __CLPK_integer * + ldv, __CLPK_integer *info); + +/* Subroutine */ int dgebal_(char *job, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *scale, __CLPK_integer *info); + +/* Subroutine */ int dgebd2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tauq, __CLPK_doublereal * + taup, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgebrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tauq, __CLPK_doublereal * + taup, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgecon_(char *norm, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dgeequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublereal *rowcnd, __CLPK_doublereal + *colcnd, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int dgees_(char *jobvs, char *sort, __CLPK_L_fp select, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_doublereal *wr, + __CLPK_doublereal *wi, __CLPK_doublereal *vs, __CLPK_integer *ldvs, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int dgeesx_(char *jobvs, char *sort, __CLPK_L_fp select, char * + sense, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *sdim, + __CLPK_doublereal *wr, __CLPK_doublereal *wi, __CLPK_doublereal *vs, __CLPK_integer *ldvs, + __CLPK_doublereal *rconde, __CLPK_doublereal *rcondv, __CLPK_doublereal *work, __CLPK_integer * + lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int dgeev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *wr, __CLPK_doublereal *wi, __CLPK_doublereal *vl, + __CLPK_integer *ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *wr, + __CLPK_doublereal *wi, __CLPK_doublereal *vl, __CLPK_integer *ldvl, __CLPK_doublereal *vr, + __CLPK_integer *ldvr, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *scale, + __CLPK_doublereal *abnrm, __CLPK_doublereal *rconde, __CLPK_doublereal *rcondv, __CLPK_doublereal + *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgegs_(char *jobvsl, char *jobvsr, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + alphar, __CLPK_doublereal *alphai, __CLPK_doublereal *beta, __CLPK_doublereal *vsl, + __CLPK_integer *ldvsl, __CLPK_doublereal *vsr, __CLPK_integer *ldvsr, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgegv_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *alphar, + __CLPK_doublereal *alphai, __CLPK_doublereal *beta, __CLPK_doublereal *vl, __CLPK_integer *ldvl, + __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dgehd2_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dgehrd_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgelq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgelqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgels_(char *trans, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgelsd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + s, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgelss_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + s, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dgelsx_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + jpvt, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublereal *work, __CLPK_integer * + info); + +/* Subroutine */ int dgelsy_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + jpvt, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublereal *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int dgeql2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgeqlf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgeqp3_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *jpvt, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dgeqpf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *jpvt, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgeqr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgeqrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgerfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, __CLPK_integer * + ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dgerq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgerqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgesc2_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, + __CLPK_doublereal *rhs, __CLPK_integer *ipiv, __CLPK_integer *jpiv, __CLPK_doublereal *scale); + +/* Subroutine */ int dgesdd_(char *jobz, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublereal *u, __CLPK_integer *ldu, + __CLPK_doublereal *vt, __CLPK_integer *ldvt, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dgesv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *a, __CLPK_integer + *lda, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dgesvd_(char *jobu, char *jobvt, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublereal *u, __CLPK_integer * + ldu, __CLPK_doublereal *vt, __CLPK_integer *ldvt, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dgesvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, + __CLPK_integer *ipiv, char *equed, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dgetc2_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer + *ipiv, __CLPK_integer *jpiv, __CLPK_integer *info); + +/* Subroutine */ int dgetf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dgetrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dgetri_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer + *ipiv, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dgetrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int dggbak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, __CLPK_integer *m, + __CLPK_doublereal *v, __CLPK_integer *ldv, __CLPK_integer *info); + +/* Subroutine */ int dggbal_(char *job, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, __CLPK_doublereal *work, __CLPK_integer * + info); + +/* Subroutine */ int dgges_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + delctg, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_doublereal *alphar, __CLPK_doublereal *alphai, + __CLPK_doublereal *beta, __CLPK_doublereal *vsl, __CLPK_integer *ldvsl, __CLPK_doublereal *vsr, + __CLPK_integer *ldvsr, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_logical *bwork, + __CLPK_integer *info); + +/* Subroutine */ int dggesx_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + delctg, char *sense, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_doublereal *alphar, + __CLPK_doublereal *alphai, __CLPK_doublereal *beta, __CLPK_doublereal *vsl, __CLPK_integer *ldvsl, + __CLPK_doublereal *vsr, __CLPK_integer *ldvsr, __CLPK_doublereal *rconde, __CLPK_doublereal * + rcondv, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer * + liwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int dggev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *alphar, + __CLPK_doublereal *alphai, __CLPK_doublereal *beta, __CLPK_doublereal *vl, __CLPK_integer *ldvl, + __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *alphar, __CLPK_doublereal *alphai, __CLPK_doublereal * + beta, __CLPK_doublereal *vl, __CLPK_integer *ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, + __CLPK_doublereal *abnrm, __CLPK_doublereal *bbnrm, __CLPK_doublereal *rconde, __CLPK_doublereal * + rcondv, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_logical * + bwork, __CLPK_integer *info); + +/* Subroutine */ int dggglm_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *d__, + __CLPK_doublereal *x, __CLPK_doublereal *y, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dgghrd_(char *compq, char *compz, __CLPK_integer *n, __CLPK_integer * + ilo, __CLPK_integer *ihi, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *z__, __CLPK_integer * + ldz, __CLPK_integer *info); + +/* Subroutine */ int dgglse_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *p, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *c__, + __CLPK_doublereal *d__, __CLPK_doublereal *x, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dggqrf_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *taua, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *taub, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dggrqf_(__CLPK_integer *m, __CLPK_integer *p, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *taua, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *taub, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dggsvd_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *p, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublereal *a, + __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *alpha, + __CLPK_doublereal *beta, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *v, __CLPK_integer + *ldv, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dggsvp_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *tola, __CLPK_doublereal *tolb, __CLPK_integer *k, __CLPK_integer + *l, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *v, __CLPK_integer *ldv, + __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *iwork, __CLPK_doublereal *tau, + __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dgtcon_(char *norm, __CLPK_integer *n, __CLPK_doublereal *dl, + __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal *du2, __CLPK_integer *ipiv, + __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dgtrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *dl, __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal *dlf, + __CLPK_doublereal *df, __CLPK_doublereal *duf, __CLPK_doublereal *du2, __CLPK_integer *ipiv, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int dgtsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *dl, + __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer + *info); + +/* Subroutine */ int dgtsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *dl, __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal * + dlf, __CLPK_doublereal *df, __CLPK_doublereal *duf, __CLPK_doublereal *du2, __CLPK_integer *ipiv, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dgttrf_(__CLPK_integer *n, __CLPK_doublereal *dl, __CLPK_doublereal *d__, + __CLPK_doublereal *du, __CLPK_doublereal *du2, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dgttrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *dl, __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal *du2, + __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dgtts2_(__CLPK_integer *itrans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *dl, __CLPK_doublereal *d__, __CLPK_doublereal *du, __CLPK_doublereal *du2, + __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb); + +/* Subroutine */ int dhgeqz_(char *job, char *compq, char *compz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal * + b, __CLPK_integer *ldb, __CLPK_doublereal *alphar, __CLPK_doublereal *alphai, __CLPK_doublereal * + beta, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *z__, __CLPK_integer *ldz, + __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dhsein_(char *side, char *eigsrc, char *initv, __CLPK_logical * + select, __CLPK_integer *n, __CLPK_doublereal *h__, __CLPK_integer *ldh, __CLPK_doublereal *wr, + __CLPK_doublereal *wi, __CLPK_doublereal *vl, __CLPK_integer *ldvl, __CLPK_doublereal *vr, + __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublereal *work, __CLPK_integer * + ifaill, __CLPK_integer *ifailr, __CLPK_integer *info); + +/* Subroutine */ int dhseqr_(char *job, char *compz, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublereal *h__, __CLPK_integer *ldh, __CLPK_doublereal *wr, + __CLPK_doublereal *wi, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dlabad_(__CLPK_doublereal *small, __CLPK_doublereal *large); + +/* Subroutine */ int dlabrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tauq, + __CLPK_doublereal *taup, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *y, __CLPK_integer + *ldy); + +/* Subroutine */ int dlacon_(__CLPK_integer *n, __CLPK_doublereal *v, __CLPK_doublereal *x, + __CLPK_integer *isgn, __CLPK_doublereal *est, __CLPK_integer *kase); + +/* Subroutine */ int dlacpy_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb); + +/* Subroutine */ int dladiv_(__CLPK_doublereal *a, __CLPK_doublereal *b, __CLPK_doublereal *c__, + __CLPK_doublereal *d__, __CLPK_doublereal *p, __CLPK_doublereal *q); + +/* Subroutine */ int dlae2_(__CLPK_doublereal *a, __CLPK_doublereal *b, __CLPK_doublereal *c__, + __CLPK_doublereal *rt1, __CLPK_doublereal *rt2); + +/* Subroutine */ int dlaebz_(__CLPK_integer *ijob, __CLPK_integer *nitmax, __CLPK_integer *n, + __CLPK_integer *mmax, __CLPK_integer *minp, __CLPK_integer *nbmin, __CLPK_doublereal *abstol, + __CLPK_doublereal *reltol, __CLPK_doublereal *pivmin, __CLPK_doublereal *d__, __CLPK_doublereal * + e, __CLPK_doublereal *e2, __CLPK_integer *nval, __CLPK_doublereal *ab, __CLPK_doublereal *c__, + __CLPK_integer *mout, __CLPK_integer *nab, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dlaed0_(__CLPK_integer *icompq, __CLPK_integer *qsiz, __CLPK_integer *n, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *q, __CLPK_integer *ldq, + __CLPK_doublereal *qstore, __CLPK_integer *ldqs, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dlaed1_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *q, + __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_doublereal *rho, __CLPK_integer *cutpnt, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlaed2_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *n1, __CLPK_doublereal * + d__, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_doublereal *rho, + __CLPK_doublereal *z__, __CLPK_doublereal *dlamda, __CLPK_doublereal *w, __CLPK_doublereal *q2, + __CLPK_integer *indx, __CLPK_integer *indxc, __CLPK_integer *indxp, __CLPK_integer *coltyp, + __CLPK_integer *info); + +/* Subroutine */ int dlaed3_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *n1, __CLPK_doublereal * + d__, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *rho, __CLPK_doublereal *dlamda, + __CLPK_doublereal *q2, __CLPK_integer *indx, __CLPK_integer *ctot, __CLPK_doublereal *w, + __CLPK_doublereal *s, __CLPK_integer *info); + +/* Subroutine */ int dlaed4_(__CLPK_integer *n, __CLPK_integer *i__, __CLPK_doublereal *d__, + __CLPK_doublereal *z__, __CLPK_doublereal *delta, __CLPK_doublereal *rho, __CLPK_doublereal *dlam, + __CLPK_integer *info); + +/* Subroutine */ int dlaed5_(__CLPK_integer *i__, __CLPK_doublereal *d__, __CLPK_doublereal *z__, + __CLPK_doublereal *delta, __CLPK_doublereal *rho, __CLPK_doublereal *dlam); + +/* Subroutine */ int dlaed6_(__CLPK_integer *kniter, __CLPK_logical *orgati, __CLPK_doublereal * + rho, __CLPK_doublereal *d__, __CLPK_doublereal *z__, __CLPK_doublereal *finit, __CLPK_doublereal * + tau, __CLPK_integer *info); + +/* Subroutine */ int dlaed7_(__CLPK_integer *icompq, __CLPK_integer *n, __CLPK_integer *qsiz, + __CLPK_integer *tlvls, __CLPK_integer *curlvl, __CLPK_integer *curpbm, __CLPK_doublereal *d__, + __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_doublereal *rho, __CLPK_integer + *cutpnt, __CLPK_doublereal *qstore, __CLPK_integer *qptr, __CLPK_integer *prmptr, __CLPK_integer * + perm, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_doublereal *givnum, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlaed8_(__CLPK_integer *icompq, __CLPK_integer *k, __CLPK_integer *n, __CLPK_integer + *qsiz, __CLPK_doublereal *d__, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *indxq, + __CLPK_doublereal *rho, __CLPK_integer *cutpnt, __CLPK_doublereal *z__, __CLPK_doublereal *dlamda, + __CLPK_doublereal *q2, __CLPK_integer *ldq2, __CLPK_doublereal *w, __CLPK_integer *perm, __CLPK_integer + *givptr, __CLPK_integer *givcol, __CLPK_doublereal *givnum, __CLPK_integer *indxp, __CLPK_integer + *indx, __CLPK_integer *info); + +/* Subroutine */ int dlaed9_(__CLPK_integer *k, __CLPK_integer *kstart, __CLPK_integer *kstop, + __CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal * + rho, __CLPK_doublereal *dlamda, __CLPK_doublereal *w, __CLPK_doublereal *s, __CLPK_integer *lds, + __CLPK_integer *info); + +/* Subroutine */ int dlaeda_(__CLPK_integer *n, __CLPK_integer *tlvls, __CLPK_integer *curlvl, + __CLPK_integer *curpbm, __CLPK_integer *prmptr, __CLPK_integer *perm, __CLPK_integer *givptr, + __CLPK_integer *givcol, __CLPK_doublereal *givnum, __CLPK_doublereal *q, __CLPK_integer *qptr, + __CLPK_doublereal *z__, __CLPK_doublereal *ztemp, __CLPK_integer *info); + +/* Subroutine */ int dlaein_(__CLPK_logical *rightv, __CLPK_logical *noinit, __CLPK_integer *n, + __CLPK_doublereal *h__, __CLPK_integer *ldh, __CLPK_doublereal *wr, __CLPK_doublereal *wi, + __CLPK_doublereal *vr, __CLPK_doublereal *vi, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *work, __CLPK_doublereal *eps3, __CLPK_doublereal *smlnum, __CLPK_doublereal * + bignum, __CLPK_integer *info); + +/* Subroutine */ int dlaev2_(__CLPK_doublereal *a, __CLPK_doublereal *b, __CLPK_doublereal *c__, + __CLPK_doublereal *rt1, __CLPK_doublereal *rt2, __CLPK_doublereal *cs1, __CLPK_doublereal *sn1); + +/* Subroutine */ int dlaexc_(__CLPK_logical *wantq, __CLPK_integer *n, __CLPK_doublereal *t, + __CLPK_integer *ldt, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *j1, __CLPK_integer *n1, + __CLPK_integer *n2, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlag2_(__CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *safmin, __CLPK_doublereal *scale1, __CLPK_doublereal * + scale2, __CLPK_doublereal *wr1, __CLPK_doublereal *wr2, __CLPK_doublereal *wi); + +/* Subroutine */ int dlags2_(__CLPK_logical *upper, __CLPK_doublereal *a1, __CLPK_doublereal *a2, + __CLPK_doublereal *a3, __CLPK_doublereal *b1, __CLPK_doublereal *b2, __CLPK_doublereal *b3, + __CLPK_doublereal *csu, __CLPK_doublereal *snu, __CLPK_doublereal *csv, __CLPK_doublereal *snv, + __CLPK_doublereal *csq, __CLPK_doublereal *snq); + +/* Subroutine */ int dlagtf_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_doublereal *lambda, + __CLPK_doublereal *b, __CLPK_doublereal *c__, __CLPK_doublereal *tol, __CLPK_doublereal *d__, + __CLPK_integer *in, __CLPK_integer *info); + +/* Subroutine */ int dlagtm_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *alpha, __CLPK_doublereal *dl, __CLPK_doublereal *d__, __CLPK_doublereal *du, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *beta, __CLPK_doublereal *b, __CLPK_integer + *ldb); + +/* Subroutine */ int dlagts_(__CLPK_integer *job, __CLPK_integer *n, __CLPK_doublereal *a, + __CLPK_doublereal *b, __CLPK_doublereal *c__, __CLPK_doublereal *d__, __CLPK_integer *in, + __CLPK_doublereal *y, __CLPK_doublereal *tol, __CLPK_integer *info); + +/* Subroutine */ int dlagv2_(__CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *alphar, __CLPK_doublereal *alphai, __CLPK_doublereal * + beta, __CLPK_doublereal *csl, __CLPK_doublereal *snl, __CLPK_doublereal *csr, __CLPK_doublereal * + snr); + +/* Subroutine */ int dlahqr_(__CLPK_logical *wantt, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *h__, __CLPK_integer *ldh, __CLPK_doublereal + *wr, __CLPK_doublereal *wi, __CLPK_integer *iloz, __CLPK_integer *ihiz, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_integer *info); + +/* Subroutine */ int dlahrd_(__CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *nb, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *t, __CLPK_integer *ldt, + __CLPK_doublereal *y, __CLPK_integer *ldy); + +/* Subroutine */ int dlaic1_(__CLPK_integer *job, __CLPK_integer *j, __CLPK_doublereal *x, + __CLPK_doublereal *sest, __CLPK_doublereal *w, __CLPK_doublereal *gamma, __CLPK_doublereal * + sestpr, __CLPK_doublereal *s, __CLPK_doublereal *c__); + +/* Subroutine */ int dlaln2_(__CLPK_logical *ltrans, __CLPK_integer *na, __CLPK_integer *nw, + __CLPK_doublereal *smin, __CLPK_doublereal *ca, __CLPK_doublereal *a, __CLPK_integer *lda, + __CLPK_doublereal *d1, __CLPK_doublereal *d2, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *wr, __CLPK_doublereal *wi, __CLPK_doublereal *x, __CLPK_integer *ldx, + __CLPK_doublereal *scale, __CLPK_doublereal *xnorm, __CLPK_integer *info); + +/* Subroutine */ int dlals0_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *nrhs, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal + *bx, __CLPK_integer *ldbx, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_integer *ldgcol, __CLPK_doublereal *givnum, __CLPK_integer *ldgnum, __CLPK_doublereal * + poles, __CLPK_doublereal *difl, __CLPK_doublereal *difr, __CLPK_doublereal *z__, __CLPK_integer * + k, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlalsa_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *bx, __CLPK_integer * + ldbx, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *vt, __CLPK_integer *k, + __CLPK_doublereal *difl, __CLPK_doublereal *difr, __CLPK_doublereal *z__, __CLPK_doublereal * + poles, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_integer * + perm, __CLPK_doublereal *givnum, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublereal * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlalsd_(char *uplo, __CLPK_integer *smlsiz, __CLPK_integer *n, __CLPK_integer + *nrhs, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dlamc1_(__CLPK_integer *beta, __CLPK_integer *t, __CLPK_logical *rnd, __CLPK_logical + *ieee1); + +/* Subroutine */ int dlamc2_(__CLPK_integer *beta, __CLPK_integer *t, __CLPK_logical *rnd, + __CLPK_doublereal *eps, __CLPK_integer *emin, __CLPK_doublereal *rmin, __CLPK_integer *emax, + __CLPK_doublereal *rmax); + +/* Subroutine */ int dlamc4_(__CLPK_integer *emin, __CLPK_doublereal *start, __CLPK_integer *base); + +/* Subroutine */ int dlamc5_(__CLPK_integer *beta, __CLPK_integer *p, __CLPK_integer *emin, + __CLPK_logical *ieee, __CLPK_integer *emax, __CLPK_doublereal *rmax); + +/* Subroutine */ int dlamrg_(__CLPK_integer *n1, __CLPK_integer *n2, __CLPK_doublereal *a, __CLPK_integer + *dtrd1, __CLPK_integer *dtrd2, __CLPK_integer *index); + +/* Subroutine */ int dlanv2_(__CLPK_doublereal *a, __CLPK_doublereal *b, __CLPK_doublereal *c__, + __CLPK_doublereal *d__, __CLPK_doublereal *rt1r, __CLPK_doublereal *rt1i, __CLPK_doublereal *rt2r, + __CLPK_doublereal *rt2i, __CLPK_doublereal *cs, __CLPK_doublereal *sn); + +/* Subroutine */ int dlapll_(__CLPK_integer *n, __CLPK_doublereal *x, __CLPK_integer *incx, + __CLPK_doublereal *y, __CLPK_integer *incy, __CLPK_doublereal *ssmin); + +/* Subroutine */ int dlapmt_(__CLPK_logical *forwrd, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_integer *k); + +/* Subroutine */ int dlaqgb_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublereal *rowcnd, __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int dlaqge_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublereal *rowcnd, __CLPK_doublereal + *colcnd, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int dlaqp2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_doublereal *tau, + __CLPK_doublereal *vn1, __CLPK_doublereal *vn2, __CLPK_doublereal *work); + +/* Subroutine */ int dlaqps_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_integer + *nb, __CLPK_integer *kb, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *jpvt, + __CLPK_doublereal *tau, __CLPK_doublereal *vn1, __CLPK_doublereal *vn2, __CLPK_doublereal *auxv, + __CLPK_doublereal *f, __CLPK_integer *ldf); + +/* Subroutine */ int dlaqsb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, + char *equed); + +/* Subroutine */ int dlaqsp_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int dlaqsy_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int dlaqtr_(__CLPK_logical *ltran, __CLPK_logical *lreal, __CLPK_integer *n, + __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *b, __CLPK_doublereal *w, __CLPK_doublereal + *scale, __CLPK_doublereal *x, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlar1v_(__CLPK_integer *n, __CLPK_integer *b1, __CLPK_integer *bn, __CLPK_doublereal + *sigma, __CLPK_doublereal *d__, __CLPK_doublereal *l, __CLPK_doublereal *ld, __CLPK_doublereal * + lld, __CLPK_doublereal *gersch, __CLPK_doublereal *z__, __CLPK_doublereal *ztz, __CLPK_doublereal + *mingma, __CLPK_integer *r__, __CLPK_integer *isuppz, __CLPK_doublereal *work); + +/* Subroutine */ int dlar2v_(__CLPK_integer *n, __CLPK_doublereal *x, __CLPK_doublereal *y, + __CLPK_doublereal *z__, __CLPK_integer *incx, __CLPK_doublereal *c__, __CLPK_doublereal *s, + __CLPK_integer *incc); + +/* Subroutine */ int dlarf_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *v, + __CLPK_integer *incv, __CLPK_doublereal *tau, __CLPK_doublereal *c__, __CLPK_integer *ldc, + __CLPK_doublereal *work); + +/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal *v, __CLPK_integer * + ldv, __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *c__, __CLPK_integer *ldc, + __CLPK_doublereal *work, __CLPK_integer *ldwork); + +/* Subroutine */ int dlarfg_(__CLPK_integer *n, __CLPK_doublereal *alpha, __CLPK_doublereal *x, + __CLPK_integer *incx, __CLPK_doublereal *tau); + +/* Subroutine */ int dlarft_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_doublereal *v, __CLPK_integer *ldv, __CLPK_doublereal *tau, __CLPK_doublereal *t, + __CLPK_integer *ldt); + +/* Subroutine */ int dlarfx_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + v, __CLPK_doublereal *tau, __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work); + +/* Subroutine */ int dlargv_(__CLPK_integer *n, __CLPK_doublereal *x, __CLPK_integer *incx, + __CLPK_doublereal *y, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_integer *incc); + +/* Subroutine */ int dlarnv_(__CLPK_integer *idist, __CLPK_integer *iseed, __CLPK_integer *n, + __CLPK_doublereal *x); + +/* Subroutine */ int dlarrb_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *l, + __CLPK_doublereal *ld, __CLPK_doublereal *lld, __CLPK_integer *ifirst, __CLPK_integer *ilast, + __CLPK_doublereal *sigma, __CLPK_doublereal *reltol, __CLPK_doublereal *w, __CLPK_doublereal * + wgap, __CLPK_doublereal *werr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int dlarre_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublereal *tol, __CLPK_integer *nsplit, __CLPK_integer *isplit, __CLPK_integer *m, + __CLPK_doublereal *w, __CLPK_doublereal *woff, __CLPK_doublereal *gersch, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dlarrf_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *l, + __CLPK_doublereal *ld, __CLPK_doublereal *lld, __CLPK_integer *ifirst, __CLPK_integer *ilast, + __CLPK_doublereal *w, __CLPK_doublereal *dplus, __CLPK_doublereal *lplus, __CLPK_doublereal *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlarrv_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *l, + __CLPK_integer *isplit, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_integer *iblock, + __CLPK_doublereal *gersch, __CLPK_doublereal *tol, __CLPK_doublereal *z__, __CLPK_integer *ldz, + __CLPK_integer *isuppz, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlartg_(__CLPK_doublereal *f, __CLPK_doublereal *g, __CLPK_doublereal *cs, + __CLPK_doublereal *sn, __CLPK_doublereal *r__); + +/* Subroutine */ int dlartv_(__CLPK_integer *n, __CLPK_doublereal *x, __CLPK_integer *incx, + __CLPK_doublereal *y, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_integer + *incc); + +/* Subroutine */ int dlaruv_(__CLPK_integer *iseed, __CLPK_integer *n, __CLPK_doublereal *x); + +/* Subroutine */ int dlarz_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, + __CLPK_doublereal *v, __CLPK_integer *incv, __CLPK_doublereal *tau, __CLPK_doublereal *c__, + __CLPK_integer *ldc, __CLPK_doublereal *work); + +/* Subroutine */ int dlarzb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublereal *v, + __CLPK_integer *ldv, __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *c__, __CLPK_integer * + ldc, __CLPK_doublereal *work, __CLPK_integer *ldwork); + +/* Subroutine */ int dlarzt_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_doublereal *v, __CLPK_integer *ldv, __CLPK_doublereal *tau, __CLPK_doublereal *t, + __CLPK_integer *ldt); + +/* Subroutine */ int dlas2_(__CLPK_doublereal *f, __CLPK_doublereal *g, __CLPK_doublereal *h__, + __CLPK_doublereal *ssmin, __CLPK_doublereal *ssmax); + +/* Subroutine */ int dlascl_(char *type__, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *cfrom, __CLPK_doublereal *cto, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int dlasd0_(__CLPK_integer *n, __CLPK_integer *sqre, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *vt, __CLPK_integer * + ldvt, __CLPK_integer *smlsiz, __CLPK_integer *iwork, __CLPK_doublereal *work, __CLPK_integer * + info); + +/* Subroutine */ int dlasd1_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, + __CLPK_doublereal *d__, __CLPK_doublereal *alpha, __CLPK_doublereal *beta, __CLPK_doublereal *u, + __CLPK_integer *ldu, __CLPK_doublereal *vt, __CLPK_integer *ldvt, __CLPK_integer *idxq, __CLPK_integer * + iwork, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlasd2_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, __CLPK_integer + *k, __CLPK_doublereal *d__, __CLPK_doublereal *z__, __CLPK_doublereal *alpha, __CLPK_doublereal * + beta, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *vt, __CLPK_integer *ldvt, + __CLPK_doublereal *dsigma, __CLPK_doublereal *u2, __CLPK_integer *ldu2, __CLPK_doublereal *vt2, + __CLPK_integer *ldvt2, __CLPK_integer *idxp, __CLPK_integer *idx, __CLPK_integer *idxc, __CLPK_integer * + idxq, __CLPK_integer *coltyp, __CLPK_integer *info); + +/* Subroutine */ int dlasd3_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, __CLPK_integer + *k, __CLPK_doublereal *d__, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *dsigma, + __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *u2, __CLPK_integer *ldu2, + __CLPK_doublereal *vt, __CLPK_integer *ldvt, __CLPK_doublereal *vt2, __CLPK_integer *ldvt2, + __CLPK_integer *idxc, __CLPK_integer *ctot, __CLPK_doublereal *z__, __CLPK_integer *info); + +/* Subroutine */ int dlasd4_(__CLPK_integer *n, __CLPK_integer *i__, __CLPK_doublereal *d__, + __CLPK_doublereal *z__, __CLPK_doublereal *delta, __CLPK_doublereal *rho, __CLPK_doublereal * + sigma, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlasd5_(__CLPK_integer *i__, __CLPK_doublereal *d__, __CLPK_doublereal *z__, + __CLPK_doublereal *delta, __CLPK_doublereal *rho, __CLPK_doublereal *dsigma, __CLPK_doublereal * + work); + +/* Subroutine */ int dlasd6_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_doublereal *d__, __CLPK_doublereal *vf, __CLPK_doublereal *vl, + __CLPK_doublereal *alpha, __CLPK_doublereal *beta, __CLPK_integer *idxq, __CLPK_integer *perm, + __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_doublereal *givnum, + __CLPK_integer *ldgnum, __CLPK_doublereal *poles, __CLPK_doublereal *difl, __CLPK_doublereal * + difr, __CLPK_doublereal *z__, __CLPK_integer *k, __CLPK_doublereal *c__, __CLPK_doublereal *s, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlasd7_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *k, __CLPK_doublereal *d__, __CLPK_doublereal *z__, + __CLPK_doublereal *zw, __CLPK_doublereal *vf, __CLPK_doublereal *vfw, __CLPK_doublereal *vl, + __CLPK_doublereal *vlw, __CLPK_doublereal *alpha, __CLPK_doublereal *beta, __CLPK_doublereal * + dsigma, __CLPK_integer *idx, __CLPK_integer *idxp, __CLPK_integer *idxq, __CLPK_integer *perm, + __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_doublereal *givnum, + __CLPK_integer *ldgnum, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_integer *info); + +/* Subroutine */ int dlasd8_(__CLPK_integer *icompq, __CLPK_integer *k, __CLPK_doublereal *d__, + __CLPK_doublereal *z__, __CLPK_doublereal *vf, __CLPK_doublereal *vl, __CLPK_doublereal *difl, + __CLPK_doublereal *difr, __CLPK_integer *lddifr, __CLPK_doublereal *dsigma, __CLPK_doublereal * + work, __CLPK_integer *info); + +/* Subroutine */ int dlasd9_(__CLPK_integer *icompq, __CLPK_integer *ldu, __CLPK_integer *k, + __CLPK_doublereal *d__, __CLPK_doublereal *z__, __CLPK_doublereal *vf, __CLPK_doublereal *vl, + __CLPK_doublereal *difl, __CLPK_doublereal *difr, __CLPK_doublereal *dsigma, __CLPK_doublereal * + work, __CLPK_integer *info); + +/* Subroutine */ int dlasda_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *sqre, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *u, __CLPK_integer + *ldu, __CLPK_doublereal *vt, __CLPK_integer *k, __CLPK_doublereal *difl, __CLPK_doublereal *difr, + __CLPK_doublereal *z__, __CLPK_doublereal *poles, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_integer *ldgcol, __CLPK_integer *perm, __CLPK_doublereal *givnum, __CLPK_doublereal *c__, + __CLPK_doublereal *s, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dlasdq_(char *uplo, __CLPK_integer *sqre, __CLPK_integer *n, __CLPK_integer * + ncvt, __CLPK_integer *nru, __CLPK_integer *ncc, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublereal *vt, __CLPK_integer *ldvt, __CLPK_doublereal *u, __CLPK_integer *ldu, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlasdt_(__CLPK_integer *n, __CLPK_integer *lvl, __CLPK_integer *nd, __CLPK_integer * + inode, __CLPK_integer *ndiml, __CLPK_integer *ndimr, __CLPK_integer *msub); + +/* Subroutine */ int dlaset_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + alpha, __CLPK_doublereal *beta, __CLPK_doublereal *a, __CLPK_integer *lda); + +/* Subroutine */ int dlasq1_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dlasq2_(__CLPK_integer *n, __CLPK_doublereal *z__, __CLPK_integer *info); + +/* Subroutine */ int dlasq3_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_doublereal *z__, + __CLPK_integer *pp, __CLPK_doublereal *dmin__, __CLPK_doublereal *sigma, __CLPK_doublereal *desig, + __CLPK_doublereal *qmax, __CLPK_integer *nfail, __CLPK_integer *iter, __CLPK_integer *ndiv, + __CLPK_logical *ieee); + +/* Subroutine */ int dlasq4_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_doublereal *z__, + __CLPK_integer *pp, __CLPK_integer *n0in, __CLPK_doublereal *dmin__, __CLPK_doublereal *dmin1, + __CLPK_doublereal *dmin2, __CLPK_doublereal *dn, __CLPK_doublereal *dn1, __CLPK_doublereal *dn2, + __CLPK_doublereal *tau, __CLPK_integer *ttype); + +/* Subroutine */ int dlasq5_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_doublereal *z__, + __CLPK_integer *pp, __CLPK_doublereal *tau, __CLPK_doublereal *dmin__, __CLPK_doublereal *dmin1, + __CLPK_doublereal *dmin2, __CLPK_doublereal *dn, __CLPK_doublereal *dnm1, __CLPK_doublereal *dnm2, + __CLPK_logical *ieee); + +/* Subroutine */ int dlasq6_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_doublereal *z__, + __CLPK_integer *pp, __CLPK_doublereal *dmin__, __CLPK_doublereal *dmin1, __CLPK_doublereal *dmin2, + __CLPK_doublereal *dn, __CLPK_doublereal *dnm1, __CLPK_doublereal *dnm2); + +/* Subroutine */ int dlasr_(char *side, char *pivot, char *direct, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublereal *a, __CLPK_integer * + lda); + +/* Subroutine */ int dlasrt_(char *id, __CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_integer * + info); + +/* Subroutine */ int dlassq_(__CLPK_integer *n, __CLPK_doublereal *x, __CLPK_integer *incx, + __CLPK_doublereal *scale, __CLPK_doublereal *sumsq); + +/* Subroutine */ int dlasv2_(__CLPK_doublereal *f, __CLPK_doublereal *g, __CLPK_doublereal *h__, + __CLPK_doublereal *ssmin, __CLPK_doublereal *ssmax, __CLPK_doublereal *snr, __CLPK_doublereal * + csr, __CLPK_doublereal *snl, __CLPK_doublereal *csl); + +/* Subroutine */ int dlaswp_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer + *k1, __CLPK_integer *k2, __CLPK_integer *ipiv, __CLPK_integer *incx); + +/* Subroutine */ int dlasy2_(__CLPK_logical *ltranl, __CLPK_logical *ltranr, __CLPK_integer *isgn, + __CLPK_integer *n1, __CLPK_integer *n2, __CLPK_doublereal *tl, __CLPK_integer *ldtl, __CLPK_doublereal * + tr, __CLPK_integer *ldtr, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *scale, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *xnorm, __CLPK_integer *info); + +/* Subroutine */ int dlasyf_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *w, __CLPK_integer * + ldw, __CLPK_integer *info); + +/* Subroutine */ int dlatbs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal *ab, __CLPK_integer *ldab, + __CLPK_doublereal *x, __CLPK_doublereal *scale, __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int dlatdf_(__CLPK_integer *ijob, __CLPK_integer *n, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *rhs, __CLPK_doublereal *rdsum, __CLPK_doublereal *rdscal, + __CLPK_integer *ipiv, __CLPK_integer *jpiv); + +/* Subroutine */ int dlatps_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_doublereal *x, __CLPK_doublereal *scale, + __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int dlatrd_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *e, __CLPK_doublereal *tau, __CLPK_doublereal *w, + __CLPK_integer *ldw); + +/* Subroutine */ int dlatrs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *x, + __CLPK_doublereal *scale, __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int dlatrz_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work); + +/* Subroutine */ int dlatzm_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + v, __CLPK_integer *incv, __CLPK_doublereal *tau, __CLPK_doublereal *c1, __CLPK_doublereal *c2, + __CLPK_integer *ldc, __CLPK_doublereal *work); + +/* Subroutine */ int dlauu2_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *info); + +/* Subroutine */ int dlauum_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *info); + +/* Subroutine */ int dopgtr_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *tau, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dopmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_doublereal *tau, __CLPK_doublereal *c__, __CLPK_integer + *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorg2l_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorg2r_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorgbr_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dorghr_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dorgl2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorglq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dorgql_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dorgqr_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dorgr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorgrq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dorgtr_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dorm2l_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dorm2r_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dormhr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal * + tau, __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dorml2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dormlq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dormql_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dormqr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dormr2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dormr3_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dormrq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dormrz_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dormtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *tau, __CLPK_doublereal * + c__, __CLPK_integer *ldc, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dpbcon_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dpbequ_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, + __CLPK_integer *info); + +/* Subroutine */ int dpbrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *afb, __CLPK_integer *ldafb, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int dpbstf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int dpbsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int dpbsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *afb, + __CLPK_integer *ldafb, char *equed, __CLPK_doublereal *s, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dpbtf2_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int dpbtrf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublereal * + ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int dpbtrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int dpocon_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dpoequ_(__CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int dporfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int dposv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal + *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dposvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, + char *equed, __CLPK_doublereal *s, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal * + berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dpotf2_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *info); + +/* Subroutine */ int dpotrf_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *info); + +/* Subroutine */ int dpotri_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *info); + +/* Subroutine */ int dpotrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int dppcon_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dppequ_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int dpprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *ap, __CLPK_doublereal *afp, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dppsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal + *ap, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dppsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *ap, __CLPK_doublereal *afp, char *equed, __CLPK_doublereal *s, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dpptrf_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_integer * + info); + +/* Subroutine */ int dpptri_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_integer * + info); + +/* Subroutine */ int dpptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *ap, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dptcon_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dpteqr_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dptrfs_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *df, __CLPK_doublereal *ef, __CLPK_doublereal *b, __CLPK_integer + *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dptsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dptsvx_(char *fact, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *df, __CLPK_doublereal *ef, + __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal * + rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer * + info); + +/* Subroutine */ int dpttrf_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_integer *info); + +/* Subroutine */ int dpttrs_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dptts2_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *b, __CLPK_integer *ldb); + +/* Subroutine */ int drscl_(__CLPK_integer *n, __CLPK_doublereal *sa, __CLPK_doublereal *sx, + __CLPK_integer *incx); + +/* Subroutine */ int dsbev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dsbevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dsbevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *q, __CLPK_integer * + ldq, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, + __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *ifail, + __CLPK_integer *info); + +/* Subroutine */ int dsbgst_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *bb, __CLPK_integer * + ldbb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dsbgv_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *bb, __CLPK_integer * + ldbb, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dsbgvd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *bb, __CLPK_integer * + ldbb, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dsbgvx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *ka, __CLPK_integer *kb, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal * + bb, __CLPK_integer *ldbb, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *vl, + __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer + *m, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsbtrd_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dspcon_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_integer * + ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer + *iwork, __CLPK_integer *info); + +/* Subroutine */ int dspev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublereal * + ap, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dspevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublereal * + ap, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dspevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *ap, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer * + iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *ifail, + __CLPK_integer *info); + +/* Subroutine */ int dspgst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *ap, __CLPK_doublereal *bp, __CLPK_integer *info); + +/* Subroutine */ int dspgv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublereal *ap, __CLPK_doublereal *bp, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dspgvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublereal *ap, __CLPK_doublereal *bp, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dspgvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_doublereal *bp, __CLPK_doublereal *vl, + __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer + *m, __CLPK_doublereal *w, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *ap, __CLPK_doublereal *afp, __CLPK_integer *ipiv, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dspsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal + *ap, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dspsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *ap, __CLPK_doublereal *afp, __CLPK_integer *ipiv, __CLPK_doublereal *b, + __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dsptrd_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tau, __CLPK_integer *info); + +/* Subroutine */ int dsptrf_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_integer * + ipiv, __CLPK_integer *info); + +/* Subroutine */ int dsptri_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, __CLPK_integer * + ipiv, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dsptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *ap, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int dstebz_(char *range, char *order, __CLPK_integer *n, __CLPK_doublereal + *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_integer *m, __CLPK_integer *nsplit, + __CLPK_doublereal *w, __CLPK_integer *iblock, __CLPK_integer *isplit, __CLPK_doublereal *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dstedc_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dstegr_(char *jobz, char *range, __CLPK_integer *n, __CLPK_doublereal * + d__, __CLPK_doublereal *e, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, + __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dstein_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_integer *iblock, __CLPK_integer *isplit, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsteqr_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dsterf_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_integer *info); + +/* Subroutine */ int dstev_(char *jobz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int dstevd_(char *jobz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dstevr_(char *jobz, char *range, __CLPK_integer *n, __CLPK_doublereal * + d__, __CLPK_doublereal *e, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, + __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dstevx_(char *jobz, char *range, __CLPK_integer *n, __CLPK_doublereal * + d__, __CLPK_doublereal *e, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, + __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsycon_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dsyev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, + __CLPK_integer *lda, __CLPK_doublereal *w, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int dsyevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublereal *w, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dsyevr_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer * + il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dsyevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer * + il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *lwork, + __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsygs2_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int dsygst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int dsygv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *w, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dsygvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *w, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int dsygvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer + *ldb, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, + __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublereal *z__, + __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int dsyrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, __CLPK_integer * + ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dsysv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal + *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dsysvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *af, __CLPK_integer *ldaf, + __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer * + ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dsytd2_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tau, __CLPK_integer *info); + +/* Subroutine */ int dsytf2_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int dsytrd_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *tau, __CLPK_doublereal * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dsytrf_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dsytri_(char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_integer *ipiv, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dsytrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int dtbcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *rcond, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtbrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal + *b, __CLPK_integer *ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtbtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal + *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int dtgevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *vl, __CLPK_integer *ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_integer + *mm, __CLPK_integer *m, __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dtgex2_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + q, __CLPK_integer *ldq, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_integer *j1, __CLPK_integer * + n1, __CLPK_integer *n2, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dtgexc_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal * + q, __CLPK_integer *ldq, __CLPK_doublereal *z__, __CLPK_integer *ldz, __CLPK_integer *ifst, + __CLPK_integer *ilst, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int dtgsen_(__CLPK_integer *ijob, __CLPK_logical *wantq, __CLPK_logical *wantz, + __CLPK_logical *select, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal * + b, __CLPK_integer *ldb, __CLPK_doublereal *alphar, __CLPK_doublereal *alphai, __CLPK_doublereal * + beta, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_doublereal *z__, __CLPK_integer *ldz, + __CLPK_integer *m, __CLPK_doublereal *pl, __CLPK_doublereal *pr, __CLPK_doublereal *dif, + __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int dtgsja_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublereal *a, + __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublereal *tola, + __CLPK_doublereal *tolb, __CLPK_doublereal *alpha, __CLPK_doublereal *beta, __CLPK_doublereal *u, + __CLPK_integer *ldu, __CLPK_doublereal *v, __CLPK_integer *ldv, __CLPK_doublereal *q, __CLPK_integer * + ldq, __CLPK_doublereal *work, __CLPK_integer *ncycle, __CLPK_integer *info); + +/* Subroutine */ int dtgsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *vl, __CLPK_integer *ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, + __CLPK_doublereal *s, __CLPK_doublereal *dif, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublereal * + work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtgsy2_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *d__, __CLPK_integer *ldd, + __CLPK_doublereal *e, __CLPK_integer *lde, __CLPK_doublereal *f, __CLPK_integer *ldf, __CLPK_doublereal * + scale, __CLPK_doublereal *rdsum, __CLPK_doublereal *rdscal, __CLPK_integer *iwork, __CLPK_integer + *pq, __CLPK_integer *info); + +/* Subroutine */ int dtgsyl_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *d__, __CLPK_integer *ldd, + __CLPK_doublereal *e, __CLPK_integer *lde, __CLPK_doublereal *f, __CLPK_integer *ldf, __CLPK_doublereal * + scale, __CLPK_doublereal *dif, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dtpcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublereal *ap, __CLPK_doublereal *rcond, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int dtprfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublereal *ap, __CLPK_doublereal *b, __CLPK_integer *ldb, + __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtptri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_doublereal * + ap, __CLPK_integer *info); + +/* Subroutine */ int dtptrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublereal *ap, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int dtrcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *rcond, __CLPK_doublereal *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtrevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *vl, __CLPK_integer * + ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, + __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dtrexc_(char *compq, __CLPK_integer *n, __CLPK_doublereal *t, __CLPK_integer * + ldt, __CLPK_doublereal *q, __CLPK_integer *ldq, __CLPK_integer *ifst, __CLPK_integer *ilst, + __CLPK_doublereal *work, __CLPK_integer *info); + +/* Subroutine */ int dtrrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_doublereal *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int dtrsen_(char *job, char *compq, __CLPK_logical *select, __CLPK_integer + *n, __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *q, __CLPK_integer *ldq, + __CLPK_doublereal *wr, __CLPK_doublereal *wi, __CLPK_integer *m, __CLPK_doublereal *s, __CLPK_doublereal + *sep, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer * + liwork, __CLPK_integer *info); + +/* Subroutine */ int dtrsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublereal *t, __CLPK_integer *ldt, __CLPK_doublereal *vl, __CLPK_integer * + ldvl, __CLPK_doublereal *vr, __CLPK_integer *ldvr, __CLPK_doublereal *s, __CLPK_doublereal *sep, + __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublereal *work, __CLPK_integer *ldwork, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int dtrsyl_(char *trana, char *tranb, __CLPK_integer *isgn, __CLPK_integer + *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_doublereal *c__, __CLPK_integer *ldc, __CLPK_doublereal *scale, __CLPK_integer *info); + +/* Subroutine */ int dtrti2_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int dtrtri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int dtrtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int dtzrqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_integer *info); + +/* Subroutine */ int dtzrzf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info); + +__CLPK_integer icmax1_(__CLPK_integer *n, __CLPK_complex *cx, __CLPK_integer *incx); + +__CLPK_integer ieeeck_(__CLPK_integer *ispec, __CLPK_real *zero, __CLPK_real *one); + +__CLPK_integer ilaenv_(__CLPK_integer *ispec, char *name__, char *opts, __CLPK_integer *n1, + __CLPK_integer *n2, __CLPK_integer *n3, __CLPK_integer *n4, __CLPK_ftnlen name_len, __CLPK_ftnlen + opts_len); + +__CLPK_integer izmax1_(__CLPK_integer *n, __CLPK_doublecomplex *cx, __CLPK_integer *incx); + +/* Subroutine */ int sbdsdc_(char *uplo, char *compq, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, __CLPK_integer *ldvt, __CLPK_real *q, + __CLPK_integer *iq, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sbdsqr_(char *uplo, __CLPK_integer *n, __CLPK_integer *ncvt, __CLPK_integer * + nru, __CLPK_integer *ncc, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *vt, __CLPK_integer *ldvt, __CLPK_real * + u, __CLPK_integer *ldu, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sdisna_(char *job, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *sep, __CLPK_integer *info); + +/* Subroutine */ int sgbbrd_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *ncc, + __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *d__, __CLPK_real * + e, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *pt, __CLPK_integer *ldpt, __CLPK_real *c__, __CLPK_integer + *ldc, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgbcon_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, + __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgbequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real * + colcnd, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int sgbrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *afb, __CLPK_integer *ldafb, + __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real * + ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgbsv_(__CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_integer * + nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int sgbsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer *kl, + __CLPK_integer *ku, __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *afb, + __CLPK_integer *ldafb, __CLPK_integer *ipiv, char *equed, __CLPK_real *r__, __CLPK_real *c__, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, + __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgbtf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int sgbtrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int sgbtrs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sgebak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_real *scale, __CLPK_integer *m, __CLPK_real *v, __CLPK_integer *ldv, __CLPK_integer + *info); + +/* Subroutine */ int sgebal_(char *job, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *scale, __CLPK_integer *info); + +/* Subroutine */ int sgebd2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tauq, __CLPK_real *taup, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgebrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tauq, __CLPK_real *taup, __CLPK_real *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int sgecon_(char *norm, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgeequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real *colcnd, __CLPK_real *amax, __CLPK_integer + *info); + +/* Subroutine */ int sgees_(char *jobvs, char *sort, __CLPK_L_fp select, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real *vs, + __CLPK_integer *ldvs, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_logical *bwork, __CLPK_integer * + info); + +/* Subroutine */ int sgeesx_(char *jobvs, char *sort, __CLPK_L_fp select, char * + sense, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_real *wr, + __CLPK_real *wi, __CLPK_real *vs, __CLPK_integer *ldvs, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_logical *bwork, + __CLPK_integer *info); + +/* Subroutine */ int sgeev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, + __CLPK_integer *ldvr, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real * + vl, __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_integer *ilo, __CLPK_integer * + ihi, __CLPK_real *scale, __CLPK_real *abnrm, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgegs_(char *jobvsl, char *jobvsr, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real + *beta, __CLPK_real *vsl, __CLPK_integer *ldvsl, __CLPK_real *vsr, __CLPK_integer *ldvsr, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgegv_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real + *beta, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgehd2_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgehrd_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgelq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgelqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgels_(char *trans, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgelsd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *s, __CLPK_real *rcond, __CLPK_integer * + rank, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgelss_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *s, __CLPK_real *rcond, __CLPK_integer * + rank, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgelsx_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *jpvt, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgelsy_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *jpvt, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgeql2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgeqlf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgeqp3_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *jpvt, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgeqpf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *jpvt, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgeqr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgeqrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgerfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgerq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgerqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgesc2_(__CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *rhs, + __CLPK_integer *ipiv, __CLPK_integer *jpiv, __CLPK_real *scale); + +/* Subroutine */ int sgesdd_(char *jobz, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *s, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, __CLPK_integer *ldvt, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgesv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sgesvd_(char *jobu, char *jobvt, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *s, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, + __CLPK_integer *ldvt, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgesvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, + char *equed, __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, + __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgetc2_(__CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *ipiv, + __CLPK_integer *jpiv, __CLPK_integer *info); + +/* Subroutine */ int sgetf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int sgetrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int sgetri_(__CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *ipiv, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgetrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sggbak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_real *lscale, __CLPK_real *rscale, __CLPK_integer *m, __CLPK_real *v, + __CLPK_integer *ldv, __CLPK_integer *info); + +/* Subroutine */ int sggbal_(char *job, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *lscale, __CLPK_real + *rscale, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgges_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + selctg, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_integer *sdim, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real *beta, __CLPK_real *vsl, + __CLPK_integer *ldvsl, __CLPK_real *vsr, __CLPK_integer *ldvsr, __CLPK_real *work, __CLPK_integer *lwork, + __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int sggesx_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + selctg, char *sense, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real *beta, + __CLPK_real *vsl, __CLPK_integer *ldvsl, __CLPK_real *vsr, __CLPK_integer *ldvsr, __CLPK_real *rconde, + __CLPK_real *rcondv, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer * + liwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int sggev_(char *jobvl, char *jobvr, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real + *beta, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real + *alphar, __CLPK_real *alphai, __CLPK_real *beta, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, + __CLPK_integer *ldvr, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *lscale, __CLPK_real *rscale, + __CLPK_real *abnrm, __CLPK_real *bbnrm, __CLPK_real *rconde, __CLPK_real *rcondv, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int sggglm_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *d__, __CLPK_real *x, __CLPK_real *y, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sgghrd_(char *compq, char *compz, __CLPK_integer *n, __CLPK_integer * + ilo, __CLPK_integer *ihi, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real + *q, __CLPK_integer *ldq, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer *info); + +/* Subroutine */ int sgglse_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *p, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *c__, __CLPK_real *d__, __CLPK_real *x, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sggqrf_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *taua, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *taub, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sggrqf_(__CLPK_integer *m, __CLPK_integer *p, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *taua, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *taub, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sggsvd_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *p, __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *alpha, __CLPK_real *beta, __CLPK_real *u, __CLPK_integer * + ldu, __CLPK_real *v, __CLPK_integer *ldv, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sggsvp_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_real *tola, __CLPK_real *tolb, __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *u, __CLPK_integer *ldu, + __CLPK_real *v, __CLPK_integer *ldv, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_integer *iwork, __CLPK_real * + tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sgtcon_(char *norm, __CLPK_integer *n, __CLPK_real *dl, __CLPK_real *d__, + __CLPK_real *du, __CLPK_real *du2, __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgtrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *dl, + __CLPK_real *d__, __CLPK_real *du, __CLPK_real *dlf, __CLPK_real *df, __CLPK_real *duf, __CLPK_real *du2, + __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real * + ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sgtsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *dl, __CLPK_real *d__, + __CLPK_real *du, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sgtsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *dl, __CLPK_real *d__, __CLPK_real *du, __CLPK_real *dlf, __CLPK_real *df, __CLPK_real *duf, + __CLPK_real *du2, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer * + ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int sgttrf_(__CLPK_integer *n, __CLPK_real *dl, __CLPK_real *d__, __CLPK_real *du, __CLPK_real * + du2, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int sgttrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *dl, + __CLPK_real *d__, __CLPK_real *du, __CLPK_real *du2, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int sgtts2_(__CLPK_integer *itrans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real + *dl, __CLPK_real *d__, __CLPK_real *du, __CLPK_real *du2, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer * + ldb); + +/* Subroutine */ int shgeqz_(char *job, char *compq, char *compz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer * + ldb, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real *beta, __CLPK_real *q, __CLPK_integer *ldq, + __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int shsein_(char *side, char *eigsrc, char *initv, __CLPK_logical * + select, __CLPK_integer *n, __CLPK_real *h__, __CLPK_integer *ldh, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real + *vl, __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, + __CLPK_real *work, __CLPK_integer *ifaill, __CLPK_integer *ifailr, __CLPK_integer *info); + +/* Subroutine */ int shseqr_(char *job, char *compz, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_real *h__, __CLPK_integer *ldh, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real *z__, + __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int slabad_(__CLPK_real *small, __CLPK_real *large); + +/* Subroutine */ int slabrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tauq, __CLPK_real *taup, __CLPK_real *x, + __CLPK_integer *ldx, __CLPK_real *y, __CLPK_integer *ldy); + +/* Subroutine */ int slacon_(__CLPK_integer *n, __CLPK_real *v, __CLPK_real *x, __CLPK_integer *isgn, + __CLPK_real *est, __CLPK_integer *kase); + +/* Subroutine */ int slacpy_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb); + +/* Subroutine */ int sladiv_(__CLPK_real *a, __CLPK_real *b, __CLPK_real *c__, __CLPK_real *d__, __CLPK_real *p, + __CLPK_real *q); + +/* Subroutine */ int slae2_(__CLPK_real *a, __CLPK_real *b, __CLPK_real *c__, __CLPK_real *rt1, __CLPK_real *rt2); + +/* Subroutine */ int slaebz_(__CLPK_integer *ijob, __CLPK_integer *nitmax, __CLPK_integer *n, + __CLPK_integer *mmax, __CLPK_integer *minp, __CLPK_integer *nbmin, __CLPK_real *abstol, __CLPK_real * + reltol, __CLPK_real *pivmin, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *e2, __CLPK_integer *nval, + __CLPK_real *ab, __CLPK_real *c__, __CLPK_integer *mout, __CLPK_integer *nab, __CLPK_real *work, __CLPK_integer + *iwork, __CLPK_integer *info); + +/* Subroutine */ int slaed0_(__CLPK_integer *icompq, __CLPK_integer *qsiz, __CLPK_integer *n, __CLPK_real + *d__, __CLPK_real *e, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *qstore, __CLPK_integer *ldqs, + __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slaed1_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *q, __CLPK_integer *ldq, + __CLPK_integer *indxq, __CLPK_real *rho, __CLPK_integer *cutpnt, __CLPK_real *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int slaed2_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *n1, __CLPK_real *d__, + __CLPK_real *q, __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_real *rho, __CLPK_real *z__, __CLPK_real * + dlamda, __CLPK_real *w, __CLPK_real *q2, __CLPK_integer *indx, __CLPK_integer *indxc, __CLPK_integer * + indxp, __CLPK_integer *coltyp, __CLPK_integer *info); + +/* Subroutine */ int slaed3_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *n1, __CLPK_real *d__, + __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *rho, __CLPK_real *dlamda, __CLPK_real *q2, __CLPK_integer * + indx, __CLPK_integer *ctot, __CLPK_real *w, __CLPK_real *s, __CLPK_integer *info); + +/* Subroutine */ int slaed4_(__CLPK_integer *n, __CLPK_integer *i__, __CLPK_real *d__, __CLPK_real *z__, + __CLPK_real *delta, __CLPK_real *rho, __CLPK_real *dlam, __CLPK_integer *info); + +/* Subroutine */ int slaed5_(__CLPK_integer *i__, __CLPK_real *d__, __CLPK_real *z__, __CLPK_real *delta, + __CLPK_real *rho, __CLPK_real *dlam); + +/* Subroutine */ int slaed6_(__CLPK_integer *kniter, __CLPK_logical *orgati, __CLPK_real *rho, + __CLPK_real *d__, __CLPK_real *z__, __CLPK_real *finit, __CLPK_real *tau, __CLPK_integer *info); + +/* Subroutine */ int slaed7_(__CLPK_integer *icompq, __CLPK_integer *n, __CLPK_integer *qsiz, + __CLPK_integer *tlvls, __CLPK_integer *curlvl, __CLPK_integer *curpbm, __CLPK_real *d__, __CLPK_real *q, + __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_real *rho, __CLPK_integer *cutpnt, __CLPK_real * + qstore, __CLPK_integer *qptr, __CLPK_integer *prmptr, __CLPK_integer *perm, __CLPK_integer * + givptr, __CLPK_integer *givcol, __CLPK_real *givnum, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int slaed8_(__CLPK_integer *icompq, __CLPK_integer *k, __CLPK_integer *n, __CLPK_integer + *qsiz, __CLPK_real *d__, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_integer *indxq, __CLPK_real *rho, + __CLPK_integer *cutpnt, __CLPK_real *z__, __CLPK_real *dlamda, __CLPK_real *q2, __CLPK_integer *ldq2, + __CLPK_real *w, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_real * + givnum, __CLPK_integer *indxp, __CLPK_integer *indx, __CLPK_integer *info); + +/* Subroutine */ int slaed9_(__CLPK_integer *k, __CLPK_integer *kstart, __CLPK_integer *kstop, + __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *rho, __CLPK_real *dlamda, + __CLPK_real *w, __CLPK_real *s, __CLPK_integer *lds, __CLPK_integer *info); + +/* Subroutine */ int slaeda_(__CLPK_integer *n, __CLPK_integer *tlvls, __CLPK_integer *curlvl, + __CLPK_integer *curpbm, __CLPK_integer *prmptr, __CLPK_integer *perm, __CLPK_integer *givptr, + __CLPK_integer *givcol, __CLPK_real *givnum, __CLPK_real *q, __CLPK_integer *qptr, __CLPK_real *z__, + __CLPK_real *ztemp, __CLPK_integer *info); + +/* Subroutine */ int slaein_(__CLPK_logical *rightv, __CLPK_logical *noinit, __CLPK_integer *n, + __CLPK_real *h__, __CLPK_integer *ldh, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real *vr, __CLPK_real *vi, __CLPK_real + *b, __CLPK_integer *ldb, __CLPK_real *work, __CLPK_real *eps3, __CLPK_real *smlnum, __CLPK_real *bignum, + __CLPK_integer *info); + +/* Subroutine */ int slaev2_(__CLPK_real *a, __CLPK_real *b, __CLPK_real *c__, __CLPK_real *rt1, __CLPK_real * + rt2, __CLPK_real *cs1, __CLPK_real *sn1); + +/* Subroutine */ int slaexc_(__CLPK_logical *wantq, __CLPK_integer *n, __CLPK_real *t, __CLPK_integer * + ldt, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_integer *j1, __CLPK_integer *n1, __CLPK_integer *n2, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slag2_(__CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_real *safmin, __CLPK_real *scale1, __CLPK_real *scale2, __CLPK_real *wr1, __CLPK_real *wr2, __CLPK_real * + wi); + +/* Subroutine */ int slags2_(__CLPK_logical *upper, __CLPK_real *a1, __CLPK_real *a2, __CLPK_real *a3, + __CLPK_real *b1, __CLPK_real *b2, __CLPK_real *b3, __CLPK_real *csu, __CLPK_real *snu, __CLPK_real *csv, __CLPK_real * + snv, __CLPK_real *csq, __CLPK_real *snq); + +/* Subroutine */ int slagtf_(__CLPK_integer *n, __CLPK_real *a, __CLPK_real *lambda, __CLPK_real *b, __CLPK_real + *c__, __CLPK_real *tol, __CLPK_real *d__, __CLPK_integer *in, __CLPK_integer *info); + +/* Subroutine */ int slagtm_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real * + alpha, __CLPK_real *dl, __CLPK_real *d__, __CLPK_real *du, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real * + beta, __CLPK_real *b, __CLPK_integer *ldb); + +/* Subroutine */ int slagts_(__CLPK_integer *job, __CLPK_integer *n, __CLPK_real *a, __CLPK_real *b, __CLPK_real + *c__, __CLPK_real *d__, __CLPK_integer *in, __CLPK_real *y, __CLPK_real *tol, __CLPK_integer *info); + +/* Subroutine */ int slagv2_(__CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, + __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real *beta, __CLPK_real *csl, __CLPK_real *snl, __CLPK_real * + csr, __CLPK_real *snr); + +/* Subroutine */ int slahqr_(__CLPK_logical *wantt, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *h__, __CLPK_integer *ldh, __CLPK_real *wr, __CLPK_real * + wi, __CLPK_integer *iloz, __CLPK_integer *ihiz, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer * + info); + +/* Subroutine */ int slahrd_(__CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *nb, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *y, __CLPK_integer *ldy); + +/* Subroutine */ int slaic1_(__CLPK_integer *job, __CLPK_integer *j, __CLPK_real *x, __CLPK_real *sest, + __CLPK_real *w, __CLPK_real *gamma, __CLPK_real *sestpr, __CLPK_real *s, __CLPK_real *c__); + +/* Subroutine */ int slaln2_(__CLPK_logical *ltrans, __CLPK_integer *na, __CLPK_integer *nw, __CLPK_real * + smin, __CLPK_real *ca, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *d1, __CLPK_real *d2, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_real *wr, __CLPK_real *wi, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *scale, + __CLPK_real *xnorm, __CLPK_integer *info); + +/* Subroutine */ int slals0_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *nrhs, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *bx, + __CLPK_integer *ldbx, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_integer *ldgcol, __CLPK_real *givnum, __CLPK_integer *ldgnum, __CLPK_real *poles, __CLPK_real * + difl, __CLPK_real *difr, __CLPK_real *z__, __CLPK_integer *k, __CLPK_real *c__, __CLPK_real *s, __CLPK_real * + work, __CLPK_integer *info); + +/* Subroutine */ int slalsa_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *bx, __CLPK_integer *ldbx, __CLPK_real * + u, __CLPK_integer *ldu, __CLPK_real *vt, __CLPK_integer *k, __CLPK_real *difl, __CLPK_real *difr, __CLPK_real * + z__, __CLPK_real *poles, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, + __CLPK_integer *perm, __CLPK_real *givnum, __CLPK_real *c__, __CLPK_real *s, __CLPK_real *work, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int slalsd_(char *uplo, __CLPK_integer *smlsiz, __CLPK_integer *n, __CLPK_integer + *nrhs, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slamc1_(__CLPK_integer *beta, __CLPK_integer *t, __CLPK_logical *rnd, __CLPK_logical + *ieee1); + +/* Subroutine */ int slamc2_(__CLPK_integer *beta, __CLPK_integer *t, __CLPK_logical *rnd, __CLPK_real * + eps, __CLPK_integer *emin, __CLPK_real *rmin, __CLPK_integer *emax, __CLPK_real *rmax); + +/* Subroutine */ int slamc4_(__CLPK_integer *emin, __CLPK_real *start, __CLPK_integer *base); + +/* Subroutine */ int slamc5_(__CLPK_integer *beta, __CLPK_integer *p, __CLPK_integer *emin, + __CLPK_logical *ieee, __CLPK_integer *emax, __CLPK_real *rmax); + +/* Subroutine */ int slamrg_(__CLPK_integer *n1, __CLPK_integer *n2, __CLPK_real *a, __CLPK_integer * + strd1, __CLPK_integer *strd2, __CLPK_integer *index); + +/* Subroutine */ int slanv2_(__CLPK_real *a, __CLPK_real *b, __CLPK_real *c__, __CLPK_real *d__, __CLPK_real * + rt1r, __CLPK_real *rt1i, __CLPK_real *rt2r, __CLPK_real *rt2i, __CLPK_real *cs, __CLPK_real *sn); + +/* Subroutine */ int slapll_(__CLPK_integer *n, __CLPK_real *x, __CLPK_integer *incx, __CLPK_real *y, + __CLPK_integer *incy, __CLPK_real *ssmin); + +/* Subroutine */ int slapmt_(__CLPK_logical *forwrd, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *x, + __CLPK_integer *ldx, __CLPK_integer *k); + +/* Subroutine */ int slaqgb_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real * + colcnd, __CLPK_real *amax, char *equed); + +/* Subroutine */ int slaqge_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *r__, __CLPK_real *c__, __CLPK_real *rowcnd, __CLPK_real *colcnd, __CLPK_real *amax, char * + equed); + +/* Subroutine */ int slaqp2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_real *tau, __CLPK_real *vn1, __CLPK_real *vn2, __CLPK_real * + work); + +/* Subroutine */ int slaqps_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_integer + *nb, __CLPK_integer *kb, __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_real *tau, + __CLPK_real *vn1, __CLPK_real *vn2, __CLPK_real *auxv, __CLPK_real *f, __CLPK_integer *ldf); + +/* Subroutine */ int slaqsb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int slaqsp_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *s, __CLPK_real * + scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int slaqsy_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, char *equed); + +/* Subroutine */ int slaqtr_(__CLPK_logical *ltran, __CLPK_logical *lreal, __CLPK_integer *n, __CLPK_real + *t, __CLPK_integer *ldt, __CLPK_real *b, __CLPK_real *w, __CLPK_real *scale, __CLPK_real *x, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int slar1v_(__CLPK_integer *n, __CLPK_integer *b1, __CLPK_integer *bn, __CLPK_real * + sigma, __CLPK_real *d__, __CLPK_real *l, __CLPK_real *ld, __CLPK_real *lld, __CLPK_real *gersch, __CLPK_real * + z__, __CLPK_real *ztz, __CLPK_real *mingma, __CLPK_integer *r__, __CLPK_integer *isuppz, __CLPK_real * + work); + +/* Subroutine */ int slar2v_(__CLPK_integer *n, __CLPK_real *x, __CLPK_real *y, __CLPK_real *z__, __CLPK_integer + *incx, __CLPK_real *c__, __CLPK_real *s, __CLPK_integer *incc); + +/* Subroutine */ int slarf_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *v, + __CLPK_integer *incv, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real *work); + +/* Subroutine */ int slarfb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *v, __CLPK_integer *ldv, + __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer * + ldwork); + +/* Subroutine */ int slarfg_(__CLPK_integer *n, __CLPK_real *alpha, __CLPK_real *x, __CLPK_integer *incx, + __CLPK_real *tau); + +/* Subroutine */ int slarft_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_real *v, __CLPK_integer *ldv, __CLPK_real *tau, __CLPK_real *t, __CLPK_integer *ldt); + +/* Subroutine */ int slarfx_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *v, + __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real *work); + +/* Subroutine */ int slargv_(__CLPK_integer *n, __CLPK_real *x, __CLPK_integer *incx, __CLPK_real *y, + __CLPK_integer *incy, __CLPK_real *c__, __CLPK_integer *incc); + +/* Subroutine */ int slarnv_(__CLPK_integer *idist, __CLPK_integer *iseed, __CLPK_integer *n, __CLPK_real + *x); + +/* Subroutine */ int slarrb_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *l, __CLPK_real *ld, __CLPK_real * + lld, __CLPK_integer *ifirst, __CLPK_integer *ilast, __CLPK_real *sigma, __CLPK_real *reltol, __CLPK_real + *w, __CLPK_real *wgap, __CLPK_real *werr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slarre_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tol, + __CLPK_integer *nsplit, __CLPK_integer *isplit, __CLPK_integer *m, __CLPK_real *w, __CLPK_real *woff, + __CLPK_real *gersch, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slarrf_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *l, __CLPK_real *ld, __CLPK_real * + lld, __CLPK_integer *ifirst, __CLPK_integer *ilast, __CLPK_real *w, __CLPK_real *dplus, __CLPK_real * + lplus, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slarrv_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *l, __CLPK_integer *isplit, + __CLPK_integer *m, __CLPK_real *w, __CLPK_integer *iblock, __CLPK_real *gersch, __CLPK_real *tol, __CLPK_real * + z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int slartg_(__CLPK_real *f, __CLPK_real *g, __CLPK_real *cs, __CLPK_real *sn, __CLPK_real *r__); + +/* Subroutine */ int slartv_(__CLPK_integer *n, __CLPK_real *x, __CLPK_integer *incx, __CLPK_real *y, + __CLPK_integer *incy, __CLPK_real *c__, __CLPK_real *s, __CLPK_integer *incc); + +/* Subroutine */ int slaruv_(__CLPK_integer *iseed, __CLPK_integer *n, __CLPK_real *x); + +/* Subroutine */ int slarz_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, + __CLPK_real *v, __CLPK_integer *incv, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real * + work); + +/* Subroutine */ int slarzb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *v, + __CLPK_integer *ldv, __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real * + work, __CLPK_integer *ldwork); + +/* Subroutine */ int slarzt_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_real *v, __CLPK_integer *ldv, __CLPK_real *tau, __CLPK_real *t, __CLPK_integer *ldt); + +/* Subroutine */ int slas2_(__CLPK_real *f, __CLPK_real *g, __CLPK_real *h__, __CLPK_real *ssmin, __CLPK_real * + ssmax); + +/* Subroutine */ int slascl_(char *type__, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_real * + cfrom, __CLPK_real *cto, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int slasd0_(__CLPK_integer *n, __CLPK_integer *sqre, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, __CLPK_integer *ldvt, __CLPK_integer *smlsiz, + __CLPK_integer *iwork, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slasd1_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, __CLPK_real * + d__, __CLPK_real *alpha, __CLPK_real *beta, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, + __CLPK_integer *ldvt, __CLPK_integer *idxq, __CLPK_integer *iwork, __CLPK_real *work, __CLPK_integer * + info); + +/* Subroutine */ int slasd2_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, __CLPK_integer + *k, __CLPK_real *d__, __CLPK_real *z__, __CLPK_real *alpha, __CLPK_real *beta, __CLPK_real *u, __CLPK_integer * + ldu, __CLPK_real *vt, __CLPK_integer *ldvt, __CLPK_real *dsigma, __CLPK_real *u2, __CLPK_integer *ldu2, + __CLPK_real *vt2, __CLPK_integer *ldvt2, __CLPK_integer *idxp, __CLPK_integer *idx, __CLPK_integer *idxc, + __CLPK_integer *idxq, __CLPK_integer *coltyp, __CLPK_integer *info); + +/* Subroutine */ int slasd3_(__CLPK_integer *nl, __CLPK_integer *nr, __CLPK_integer *sqre, __CLPK_integer + *k, __CLPK_real *d__, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *dsigma, __CLPK_real *u, __CLPK_integer * + ldu, __CLPK_real *u2, __CLPK_integer *ldu2, __CLPK_real *vt, __CLPK_integer *ldvt, __CLPK_real *vt2, + __CLPK_integer *ldvt2, __CLPK_integer *idxc, __CLPK_integer *ctot, __CLPK_real *z__, __CLPK_integer * + info); + +/* Subroutine */ int slasd4_(__CLPK_integer *n, __CLPK_integer *i__, __CLPK_real *d__, __CLPK_real *z__, + __CLPK_real *delta, __CLPK_real *rho, __CLPK_real *sigma, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slasd5_(__CLPK_integer *i__, __CLPK_real *d__, __CLPK_real *z__, __CLPK_real *delta, + __CLPK_real *rho, __CLPK_real *dsigma, __CLPK_real *work); + +/* Subroutine */ int slasd6_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_real *d__, __CLPK_real *vf, __CLPK_real *vl, __CLPK_real *alpha, __CLPK_real *beta, + __CLPK_integer *idxq, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_integer *ldgcol, __CLPK_real *givnum, __CLPK_integer *ldgnum, __CLPK_real *poles, __CLPK_real * + difl, __CLPK_real *difr, __CLPK_real *z__, __CLPK_integer *k, __CLPK_real *c__, __CLPK_real *s, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slasd7_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *k, __CLPK_real *d__, __CLPK_real *z__, __CLPK_real *zw, __CLPK_real *vf, + __CLPK_real *vfw, __CLPK_real *vl, __CLPK_real *vlw, __CLPK_real *alpha, __CLPK_real *beta, __CLPK_real *dsigma, + __CLPK_integer *idx, __CLPK_integer *idxp, __CLPK_integer *idxq, __CLPK_integer *perm, __CLPK_integer * + givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_real *givnum, __CLPK_integer * + ldgnum, __CLPK_real *c__, __CLPK_real *s, __CLPK_integer *info); + +/* Subroutine */ int slasd8_(__CLPK_integer *icompq, __CLPK_integer *k, __CLPK_real *d__, __CLPK_real * + z__, __CLPK_real *vf, __CLPK_real *vl, __CLPK_real *difl, __CLPK_real *difr, __CLPK_integer *lddifr, + __CLPK_real *dsigma, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slasd9_(__CLPK_integer *icompq, __CLPK_integer *ldu, __CLPK_integer *k, __CLPK_real * + d__, __CLPK_real *z__, __CLPK_real *vf, __CLPK_real *vl, __CLPK_real *difl, __CLPK_real *difr, __CLPK_real * + dsigma, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int slasda_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *sqre, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *vt, + __CLPK_integer *k, __CLPK_real *difl, __CLPK_real *difr, __CLPK_real *z__, __CLPK_real *poles, __CLPK_integer * + givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_integer *perm, __CLPK_real *givnum, + __CLPK_real *c__, __CLPK_real *s, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int slasdq_(char *uplo, __CLPK_integer *sqre, __CLPK_integer *n, __CLPK_integer * + ncvt, __CLPK_integer *nru, __CLPK_integer *ncc, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *vt, + __CLPK_integer *ldvt, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real * + work, __CLPK_integer *info); + +/* Subroutine */ int slasdt_(__CLPK_integer *n, __CLPK_integer *lvl, __CLPK_integer *nd, __CLPK_integer * + inode, __CLPK_integer *ndiml, __CLPK_integer *ndimr, __CLPK_integer *msub); + +/* Subroutine */ int slaset_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *alpha, + __CLPK_real *beta, __CLPK_real *a, __CLPK_integer *lda); + +/* Subroutine */ int slasq1_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int slasq2_(__CLPK_integer *n, __CLPK_real *z__, __CLPK_integer *info); + +/* Subroutine */ int slasq3_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_real *z__, __CLPK_integer *pp, + __CLPK_real *dmin__, __CLPK_real *sigma, __CLPK_real *desig, __CLPK_real *qmax, __CLPK_integer *nfail, + __CLPK_integer *iter, __CLPK_integer *ndiv, __CLPK_logical *ieee); + +/* Subroutine */ int slasq4_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_real *z__, __CLPK_integer *pp, + __CLPK_integer *n0in, __CLPK_real *dmin__, __CLPK_real *dmin1, __CLPK_real *dmin2, __CLPK_real *dn, + __CLPK_real *dn1, __CLPK_real *dn2, __CLPK_real *tau, __CLPK_integer *ttype); + +/* Subroutine */ int slasq5_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_real *z__, __CLPK_integer *pp, + __CLPK_real *tau, __CLPK_real *dmin__, __CLPK_real *dmin1, __CLPK_real *dmin2, __CLPK_real *dn, __CLPK_real * + dnm1, __CLPK_real *dnm2, __CLPK_logical *ieee); + +/* Subroutine */ int slasq6_(__CLPK_integer *i0, __CLPK_integer *n0, __CLPK_real *z__, __CLPK_integer *pp, + __CLPK_real *dmin__, __CLPK_real *dmin1, __CLPK_real *dmin2, __CLPK_real *dn, __CLPK_real *dnm1, __CLPK_real * + dnm2); + +/* Subroutine */ int slasr_(char *side, char *pivot, char *direct, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_real *c__, __CLPK_real *s, __CLPK_real *a, __CLPK_integer *lda); + +/* Subroutine */ int slasrt_(char *id, __CLPK_integer *n, __CLPK_real *d__, __CLPK_integer *info); + +/* Subroutine */ int slassq_(__CLPK_integer *n, __CLPK_real *x, __CLPK_integer *incx, __CLPK_real *scale, + __CLPK_real *sumsq); + +/* Subroutine */ int slasv2_(__CLPK_real *f, __CLPK_real *g, __CLPK_real *h__, __CLPK_real *ssmin, __CLPK_real * + ssmax, __CLPK_real *snr, __CLPK_real *csr, __CLPK_real *snl, __CLPK_real *csl); + +/* Subroutine */ int slaswp_(__CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *k1, + __CLPK_integer *k2, __CLPK_integer *ipiv, __CLPK_integer *incx); + +/* Subroutine */ int slasy2_(__CLPK_logical *ltranl, __CLPK_logical *ltranr, __CLPK_integer *isgn, + __CLPK_integer *n1, __CLPK_integer *n2, __CLPK_real *tl, __CLPK_integer *ldtl, __CLPK_real *tr, __CLPK_integer * + ldtr, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *scale, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real + *xnorm, __CLPK_integer *info); + +/* Subroutine */ int slasyf_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_real *w, __CLPK_integer *ldw, __CLPK_integer + *info); + +/* Subroutine */ int slatbs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *x, + __CLPK_real *scale, __CLPK_real *cnorm, __CLPK_integer *info); + +/* Subroutine */ int slatdf_(__CLPK_integer *ijob, __CLPK_integer *n, __CLPK_real *z__, __CLPK_integer * + ldz, __CLPK_real *rhs, __CLPK_real *rdsum, __CLPK_real *rdscal, __CLPK_integer *ipiv, __CLPK_integer * + jpiv); + +/* Subroutine */ int slatps_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *x, __CLPK_real *scale, __CLPK_real *cnorm, + __CLPK_integer *info); + +/* Subroutine */ int slatrd_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *e, __CLPK_real *tau, __CLPK_real *w, __CLPK_integer *ldw); + +/* Subroutine */ int slatrs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *x, __CLPK_real *scale, __CLPK_real + *cnorm, __CLPK_integer *info); + +/* Subroutine */ int slatrz_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work); + +/* Subroutine */ int slatzm_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *v, + __CLPK_integer *incv, __CLPK_real *tau, __CLPK_real *c1, __CLPK_real *c2, __CLPK_integer *ldc, __CLPK_real * + work); + +/* Subroutine */ int slauu2_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int slauum_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int sopgtr_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *tau, + __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sopmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int sorg2l_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sorg2r_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sorgbr_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer + *info); + +/* Subroutine */ int sorghr_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorgl2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sorglq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorgql_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorgqr_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorgr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sorgrq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorgtr_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorm2l_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sorm2r_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sormbr_(char *vect, char *side, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, + __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormhr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real * + c__, __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sorml2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sormlq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormql_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormqr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormr2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sormr3_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, + __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sormrq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormrz_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, + __CLPK_integer *ldc, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int sormtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *tau, __CLPK_real *c__, __CLPK_integer *ldc, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int spbcon_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int spbequ_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_real *s, __CLPK_real *scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int spbrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *afb, __CLPK_integer *ldafb, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int spbstf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int spbsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int spbsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *afb, __CLPK_integer *ldafb, + char *equed, __CLPK_real *s, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, + __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int spbtf2_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int spbtrf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int spbtrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int spocon_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int spoequ_(__CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *s, __CLPK_real + *scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int sporfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, + __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int sposv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sposvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, char *equed, + __CLPK_real *s, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *rcond, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int spotf2_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int spotrf_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int spotri_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *info); + +/* Subroutine */ int spotrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sppcon_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *anorm, + __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sppequ_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *s, __CLPK_real * + scond, __CLPK_real *amax, __CLPK_integer *info); + +/* Subroutine */ int spprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_real *afp, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *ferr, + __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sppsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sppsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *ap, __CLPK_real *afp, char *equed, __CLPK_real *s, __CLPK_real *b, __CLPK_integer * + ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real + *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int spptrf_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_integer *info); + +/* Subroutine */ int spptri_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_integer *info); + +/* Subroutine */ int spptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sptcon_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *anorm, + __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int spteqr_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sptrfs_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *df, __CLPK_real *ef, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sptsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sptsvx_(char *fact, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *df, __CLPK_real *ef, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer + *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int spttrf_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_integer *info); + +/* Subroutine */ int spttrs_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sptts2_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *b, __CLPK_integer *ldb); + +/* Subroutine */ int srscl_(__CLPK_integer *n, __CLPK_real *sa, __CLPK_real *sx, __CLPK_integer *incx); + +/* Subroutine */ int ssbev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int ssbevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int ssbevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *vl, + __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real * + w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer * + ifail, __CLPK_integer *info); + +/* Subroutine */ int ssbgst_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *bb, __CLPK_integer *ldbb, __CLPK_real * + x, __CLPK_integer *ldx, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int ssbgv_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *bb, __CLPK_integer *ldbb, __CLPK_real * + w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int ssbgvd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *bb, __CLPK_integer *ldbb, __CLPK_real * + w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int ssbgvx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *ka, __CLPK_integer *kb, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *bb, __CLPK_integer * + ldbb, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer + *iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real + *work, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssbtrd_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *d__, __CLPK_real *e, __CLPK_real *q, __CLPK_integer *ldq, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sspcon_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_integer *ipiv, + __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sspev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_real *ap, + __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sspevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_real *ap, + __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer + *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sspevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_real *ap, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, + __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer * + iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int sspgst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_real *ap, + __CLPK_real *bp, __CLPK_integer *info); + +/* Subroutine */ int sspgv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_real *ap, __CLPK_real *bp, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int sspgvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_real *ap, __CLPK_real *bp, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sspgvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *bp, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, + __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer * + ldz, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_real *afp, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer * + ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int sspsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sspsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *ap, __CLPK_real *afp, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real + *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int ssptrd_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *tau, __CLPK_integer *info); + +/* Subroutine */ int ssptrf_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_integer *ipiv, + __CLPK_integer *info); + +/* Subroutine */ int ssptri_(char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_integer *ipiv, + __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int ssptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *ap, + __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int sstebz_(char *range, char *order, __CLPK_integer *n, __CLPK_real *vl, + __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_real *d__, __CLPK_real *e, + __CLPK_integer *m, __CLPK_integer *nsplit, __CLPK_real *w, __CLPK_integer *iblock, __CLPK_integer * + isplit, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int sstedc_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sstegr_(char *jobz, char *range, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, + __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sstein_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_integer *m, __CLPK_real + *w, __CLPK_integer *iblock, __CLPK_integer *isplit, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssteqr_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int ssterf_(__CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_integer *info); + +/* Subroutine */ int sstev_(char *jobz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_real * + z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int sstevd_(char *jobz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, __CLPK_real + *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sstevr_(char *jobz, char *range, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, + __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int sstevx_(char *jobz, char *range, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, + __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer * + iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssycon_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *anorm, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int ssyev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *w, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int ssyevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *w, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int ssyevr_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, + __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer * + isuppz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int ssyevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, + __CLPK_real *abstol, __CLPK_integer *m, __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real * + work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssygs2_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ssygst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ssygv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *w, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int ssygvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *w, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int ssygvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real * + vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, __CLPK_integer *m, + __CLPK_real *w, __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer + *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int ssyrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, __CLPK_real *b, + __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real * + work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int ssysv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int ssysvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *af, __CLPK_integer *ldaf, __CLPK_integer *ipiv, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *rcond, __CLPK_real *ferr, + __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int ssytd2_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tau, __CLPK_integer *info); + +/* Subroutine */ int ssytf2_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int ssytrd_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int ssytrf_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int ssytri_(char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int ssytrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int stbcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *rcond, __CLPK_real *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int stbrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *b, __CLPK_integer + *ldb, __CLPK_real *x, __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, + __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int stbtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *b, __CLPK_integer + *ldb, __CLPK_integer *info); + +/* Subroutine */ int stgevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *vl, + __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_real + *work, __CLPK_integer *info); + +/* Subroutine */ int stgex2_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, __CLPK_real + *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real * + z__, __CLPK_integer *ldz, __CLPK_integer *j1, __CLPK_integer *n1, __CLPK_integer *n2, __CLPK_real *work, + __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int stgexc_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, __CLPK_real + *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real * + z__, __CLPK_integer *ldz, __CLPK_integer *ifst, __CLPK_integer *ilst, __CLPK_real *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int stgsen_(__CLPK_integer *ijob, __CLPK_logical *wantq, __CLPK_logical *wantz, + __CLPK_logical *select, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer * + ldb, __CLPK_real *alphar, __CLPK_real *alphai, __CLPK_real *beta, __CLPK_real *q, __CLPK_integer *ldq, + __CLPK_real *z__, __CLPK_integer *ldz, __CLPK_integer *m, __CLPK_real *pl, __CLPK_real *pr, __CLPK_real *dif, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer * + info); + +/* Subroutine */ int stgsja_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *tola, __CLPK_real *tolb, __CLPK_real *alpha, __CLPK_real * + beta, __CLPK_real *u, __CLPK_integer *ldu, __CLPK_real *v, __CLPK_integer *ldv, __CLPK_real *q, __CLPK_integer * + ldq, __CLPK_real *work, __CLPK_integer *ncycle, __CLPK_integer *info); + +/* Subroutine */ int stgsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *vl, + __CLPK_integer *ldvl, __CLPK_real *vr, __CLPK_integer *ldvr, __CLPK_real *s, __CLPK_real *dif, __CLPK_integer * + mm, __CLPK_integer *m, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer * + info); + +/* Subroutine */ int stgsy2_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *c__, __CLPK_integer * + ldc, __CLPK_real *d__, __CLPK_integer *ldd, __CLPK_real *e, __CLPK_integer *lde, __CLPK_real *f, __CLPK_integer + *ldf, __CLPK_real *scale, __CLPK_real *rdsum, __CLPK_real *rdscal, __CLPK_integer *iwork, __CLPK_integer + *pq, __CLPK_integer *info); + +/* Subroutine */ int stgsyl_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *c__, __CLPK_integer * + ldc, __CLPK_real *d__, __CLPK_integer *ldd, __CLPK_real *e, __CLPK_integer *lde, __CLPK_real *f, __CLPK_integer + *ldf, __CLPK_real *scale, __CLPK_real *dif, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int stpcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_real *ap, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int stprfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_real *ap, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, __CLPK_integer *ldx, + __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int stptri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_real *ap, + __CLPK_integer *info); + +/* Subroutine */ int stptrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_real *ap, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int strcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *rcond, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int strevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, + __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int strexc_(char *compq, __CLPK_integer *n, __CLPK_real *t, __CLPK_integer *ldt, + __CLPK_real *q, __CLPK_integer *ldq, __CLPK_integer *ifst, __CLPK_integer *ilst, __CLPK_real *work, + __CLPK_integer *info); + +/* Subroutine */ int strrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real *x, + __CLPK_integer *ldx, __CLPK_real *ferr, __CLPK_real *berr, __CLPK_real *work, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int strsen_(char *job, char *compq, __CLPK_logical *select, __CLPK_integer + *n, __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *q, __CLPK_integer *ldq, __CLPK_real *wr, __CLPK_real *wi, + __CLPK_integer *m, __CLPK_real *s, __CLPK_real *sep, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int strsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_real *t, __CLPK_integer *ldt, __CLPK_real *vl, __CLPK_integer *ldvl, __CLPK_real *vr, + __CLPK_integer *ldvr, __CLPK_real *s, __CLPK_real *sep, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_real * + work, __CLPK_integer *ldwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int strsyl_(char *trana, char *tranb, __CLPK_integer *isgn, __CLPK_integer + *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_real * + c__, __CLPK_integer *ldc, __CLPK_real *scale, __CLPK_integer *info); + +/* Subroutine */ int strti2_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int strtri_(char *uplo, char *diag, __CLPK_integer *n, __CLPK_real *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int strtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int stzrqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_integer *info); + +/* Subroutine */ int stzrzf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *tau, __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int xerbla_(char *srname, __CLPK_integer *info); + +/* Subroutine */ int zbdsqr_(char *uplo, __CLPK_integer *n, __CLPK_integer *ncvt, __CLPK_integer * + nru, __CLPK_integer *ncc, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *vt, + __CLPK_integer *ldvt, __CLPK_doublecomplex *u, __CLPK_integer *ldu, __CLPK_doublecomplex *c__, + __CLPK_integer *ldc, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zdrot_(__CLPK_integer *n, __CLPK_doublecomplex *cx, __CLPK_integer *incx, + __CLPK_doublecomplex *cy, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_doublereal *s); + +/* Subroutine */ int zdrscl_(__CLPK_integer *n, __CLPK_doublereal *sa, __CLPK_doublecomplex *sx, + __CLPK_integer *incx); + +/* Subroutine */ int zgbbrd_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *ncc, + __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *q, __CLPK_integer *ldq, + __CLPK_doublecomplex *pt, __CLPK_integer *ldpt, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgbcon_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_doublereal *anorm, + __CLPK_doublereal *rcond, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zgbequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublereal *rowcnd, __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, __CLPK_integer * + info); + +/* Subroutine */ int zgbrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex * + afb, __CLPK_integer *ldafb, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgbsv_(__CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_doublecomplex * + b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zgbsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer *kl, + __CLPK_integer *ku, __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublecomplex *afb, __CLPK_integer *ldafb, __CLPK_integer *ipiv, char *equed, + __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zgbtf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zgbtrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zgbtrs_(char *trans, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer * + ku, __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *ipiv, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zgebak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublereal *scale, __CLPK_integer *m, __CLPK_doublecomplex *v, + __CLPK_integer *ldv, __CLPK_integer *info); + +/* Subroutine */ int zgebal_(char *job, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer + *lda, __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *scale, __CLPK_integer *info); + +/* Subroutine */ int zgebd2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *tauq, + __CLPK_doublecomplex *taup, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgebrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *tauq, + __CLPK_doublecomplex *taup, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer * + info); + +/* Subroutine */ int zgecon_(char *norm, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgeequ_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublereal *rowcnd, + __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int zgees_(char *jobvs, char *sort, __CLPK_L_fp select, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *sdim, __CLPK_doublecomplex *w, + __CLPK_doublecomplex *vs, __CLPK_integer *ldvs, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_doublereal *rwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int zgeesx_(char *jobvs, char *sort, __CLPK_L_fp select, char * + sense, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *sdim, + __CLPK_doublecomplex *w, __CLPK_doublecomplex *vs, __CLPK_integer *ldvs, __CLPK_doublereal * + rconde, __CLPK_doublereal *rcondv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_doublereal *rwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int zgeev_(char *jobvl, char *jobvr, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *w, __CLPK_doublecomplex *vl, + __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgeevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *w, + __CLPK_doublecomplex *vl, __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *scale, __CLPK_doublereal *abnrm, + __CLPK_doublereal *rconde, __CLPK_doublereal *rcondv, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgegs_(char *jobvsl, char *jobvsr, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *alpha, __CLPK_doublecomplex *beta, __CLPK_doublecomplex *vsl, + __CLPK_integer *ldvsl, __CLPK_doublecomplex *vsr, __CLPK_integer *ldvsr, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgegv_(char *jobvl, char *jobvr, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *alpha, __CLPK_doublecomplex *beta, __CLPK_doublecomplex *vl, __CLPK_integer + *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, __CLPK_doublecomplex *work, __CLPK_integer + *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgehd2_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zgehrd_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zgelq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgelqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zgels_(char *trans, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zgelsx_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *jpvt, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgelsy_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *jpvt, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgeql2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgeqlf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zgeqp3_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgeqpf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgeqr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgeqrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zgerfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer *ldaf, + __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, + __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgerq2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgerqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zgesc2_(__CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublecomplex *rhs, __CLPK_integer *ipiv, __CLPK_integer *jpiv, __CLPK_doublereal *scale); + +/* Subroutine */ int zgesv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer * + info); + +/* Subroutine */ int zgesvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer * + ldaf, __CLPK_integer *ipiv, char *equed, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgetc2_(__CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_integer *jpiv, __CLPK_integer *info); + +/* Subroutine */ int zgetf2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zgetrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zgetri_(__CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zgetrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zggbak_(char *job, char *side, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, __CLPK_integer *m, + __CLPK_doublecomplex *v, __CLPK_integer *ldv, __CLPK_integer *info); + +/* Subroutine */ int zggbal_(char *job, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer + *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, __CLPK_doublereal *work, __CLPK_integer * + info); + +/* Subroutine */ int zgges_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + delctg, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_doublecomplex *alpha, __CLPK_doublecomplex * + beta, __CLPK_doublecomplex *vsl, __CLPK_integer *ldvsl, __CLPK_doublecomplex *vsr, __CLPK_integer + *ldvsr, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int zggesx_(char *jobvsl, char *jobvsr, char *sort, __CLPK_L_fp + delctg, char *sense, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *sdim, __CLPK_doublecomplex *alpha, + __CLPK_doublecomplex *beta, __CLPK_doublecomplex *vsl, __CLPK_integer *ldvsl, + __CLPK_doublecomplex *vsr, __CLPK_integer *ldvsr, __CLPK_doublereal *rconde, __CLPK_doublereal * + rcondv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int zggev_(char *jobvl, char *jobvr, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *alpha, __CLPK_doublecomplex *beta, __CLPK_doublecomplex *vl, __CLPK_integer + *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, __CLPK_doublecomplex *work, __CLPK_integer + *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zggevx_(char *balanc, char *jobvl, char *jobvr, char * + sense, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *alpha, __CLPK_doublecomplex *beta, + __CLPK_doublecomplex *vl, __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublereal *lscale, __CLPK_doublereal *rscale, + __CLPK_doublereal *abnrm, __CLPK_doublereal *bbnrm, __CLPK_doublereal *rconde, __CLPK_doublereal * + rcondv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *iwork, __CLPK_logical *bwork, __CLPK_integer *info); + +/* Subroutine */ int zggglm_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *d__, __CLPK_doublecomplex *x, __CLPK_doublecomplex *y, __CLPK_doublecomplex + *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zgghrd_(char *compq, char *compz, __CLPK_integer *n, __CLPK_integer * + ilo, __CLPK_integer *ihi, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_integer *info); + +/* Subroutine */ int zgglse_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *p, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *c__, __CLPK_doublecomplex *d__, __CLPK_doublecomplex *x, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zggqrf_(__CLPK_integer *n, __CLPK_integer *m, __CLPK_integer *p, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *taua, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *taub, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int zggrqf_(__CLPK_integer *m, __CLPK_integer *p, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *taua, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *taub, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int zggsvd_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *p, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublereal *alpha, + __CLPK_doublereal *beta, __CLPK_doublecomplex *u, __CLPK_integer *ldu, __CLPK_doublecomplex *v, + __CLPK_integer *ldv, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zggsvp_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex + *b, __CLPK_integer *ldb, __CLPK_doublereal *tola, __CLPK_doublereal *tolb, __CLPK_integer *k, + __CLPK_integer *l, __CLPK_doublecomplex *u, __CLPK_integer *ldu, __CLPK_doublecomplex *v, __CLPK_integer + *ldv, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_integer *iwork, __CLPK_doublereal * + rwork, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zgtcon_(char *norm, __CLPK_integer *n, __CLPK_doublecomplex *dl, + __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, __CLPK_doublecomplex *du2, __CLPK_integer * + ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex *work, + __CLPK_integer *info); + +/* Subroutine */ int zgtrfs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *dl, __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, + __CLPK_doublecomplex *dlf, __CLPK_doublecomplex *df, __CLPK_doublecomplex *duf, + __CLPK_doublecomplex *du2, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zgtsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublecomplex *dl, + __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zgtsvx_(char *fact, char *trans, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *dl, __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, + __CLPK_doublecomplex *dlf, __CLPK_doublecomplex *df, __CLPK_doublecomplex *duf, + __CLPK_doublecomplex *du2, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zgttrf_(__CLPK_integer *n, __CLPK_doublecomplex *dl, __CLPK_doublecomplex * + d__, __CLPK_doublecomplex *du, __CLPK_doublecomplex *du2, __CLPK_integer *ipiv, __CLPK_integer * + info); + +/* Subroutine */ int zgttrs_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *dl, __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, + __CLPK_doublecomplex *du2, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zgtts2_(__CLPK_integer *itrans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *dl, __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du, + __CLPK_doublecomplex *du2, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb); + +/* Subroutine */ int zhbev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhbevd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zhbevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *q, + __CLPK_integer *ldq, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer * + iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int zhbgst_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *bb, + __CLPK_integer *ldbb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhbgv_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *bb, + __CLPK_integer *ldbb, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhbgvx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_integer *ka, __CLPK_integer *kb, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublecomplex *bb, __CLPK_integer *ldbb, __CLPK_doublecomplex *q, __CLPK_integer *ldq, + __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal * + abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer * + ifail, __CLPK_integer *info); + +/* Subroutine */ int zhbtrd_(char *vect, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zhecon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, + __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zheev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex + *a, __CLPK_integer *lda, __CLPK_doublereal *w, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zheevd_(char *jobz, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *w, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zheevr_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *vl, __CLPK_doublereal *vu, + __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal * + w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *lrwork, __CLPK_integer * + iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zheevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *vl, __CLPK_doublereal *vu, + __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal * + w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer * + info); + +/* Subroutine */ int zhegs2_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zhegst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zhegv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublereal *w, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *info); + +/* Subroutine */ int zhegvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublereal *w, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zhegvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer * + iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int zherfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer *ldaf, + __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, + __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhesv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zhesvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer * + ldaf, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, + __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhetf2_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zhetrd_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zhetrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zhetri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zhetrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zhgeqz_(char *job, char *compq, char *compz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *alpha, __CLPK_doublecomplex * + beta, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *z__, __CLPK_integer * + ldz, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zhpcon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zhpev_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex + *ap, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhpevd_(char *jobz, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer * + lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zhpevx_(char *jobz, char *range, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_doublereal *vl, __CLPK_doublereal *vu, __CLPK_integer *il, + __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_doublereal * + rwork, __CLPK_integer *iwork, __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int zhpgst_(__CLPK_integer *itype, char *uplo, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *bp, __CLPK_integer *info); + +/* Subroutine */ int zhpgv_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *bp, __CLPK_doublereal *w, __CLPK_doublecomplex + *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zhpgvd_(__CLPK_integer *itype, char *jobz, char *uplo, __CLPK_integer * + n, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *bp, __CLPK_doublereal *w, __CLPK_doublecomplex + *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal * + rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer * + info); + +/* Subroutine */ int zhpgvx_(__CLPK_integer *itype, char *jobz, char *range, char * + uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *bp, __CLPK_doublereal * + vl, __CLPK_doublereal *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, + __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer * + ifail, __CLPK_integer *info); + +/* Subroutine */ int zhprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, __CLPK_integer *ipiv, __CLPK_doublecomplex * + b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zhpsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zhpsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, __CLPK_integer *ipiv, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhptrd_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *tau, __CLPK_integer *info); + +/* Subroutine */ int zhptrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zhptri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zhptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zhsein_(char *side, char *eigsrc, char *initv, __CLPK_logical * + select, __CLPK_integer *n, __CLPK_doublecomplex *h__, __CLPK_integer *ldh, __CLPK_doublecomplex * + w, __CLPK_doublecomplex *vl, __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, + __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, + __CLPK_integer *ifaill, __CLPK_integer *ifailr, __CLPK_integer *info); + +/* Subroutine */ int zhseqr_(char *job, char *compz, __CLPK_integer *n, __CLPK_integer *ilo, + __CLPK_integer *ihi, __CLPK_doublecomplex *h__, __CLPK_integer *ldh, __CLPK_doublecomplex *w, + __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zlabrd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nb, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_doublecomplex *tauq, __CLPK_doublecomplex *taup, __CLPK_doublecomplex *x, __CLPK_integer * + ldx, __CLPK_doublecomplex *y, __CLPK_integer *ldy); + +/* Subroutine */ int zlacgv_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_integer *incx); + +/* Subroutine */ int zlacon_(__CLPK_integer *n, __CLPK_doublecomplex *v, __CLPK_doublecomplex *x, + __CLPK_doublereal *est, __CLPK_integer *kase); + +/* Subroutine */ int zlacp2_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal * + a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb); + +/* Subroutine */ int zlacpy_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb); + +/* Subroutine */ int zlacrm_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *b, __CLPK_integer *ldb, __CLPK_doublecomplex *c__, + __CLPK_integer *ldc, __CLPK_doublereal *rwork); + +/* Subroutine */ int zlacrt_(__CLPK_integer *n, __CLPK_doublecomplex *cx, __CLPK_integer *incx, + __CLPK_doublecomplex *cy, __CLPK_integer *incy, __CLPK_doublecomplex *c__, __CLPK_doublecomplex * + s); + +/* Subroutine */ int zlaed0_(__CLPK_integer *qsiz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *qstore, + __CLPK_integer *ldqs, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zlaed7_(__CLPK_integer *n, __CLPK_integer *cutpnt, __CLPK_integer *qsiz, + __CLPK_integer *tlvls, __CLPK_integer *curlvl, __CLPK_integer *curpbm, __CLPK_doublereal *d__, + __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublereal *rho, __CLPK_integer *indxq, + __CLPK_doublereal *qstore, __CLPK_integer *qptr, __CLPK_integer *prmptr, __CLPK_integer *perm, + __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_doublereal *givnum, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zlaed8_(__CLPK_integer *k, __CLPK_integer *n, __CLPK_integer *qsiz, + __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublereal *d__, __CLPK_doublereal *rho, + __CLPK_integer *cutpnt, __CLPK_doublereal *z__, __CLPK_doublereal *dlamda, __CLPK_doublecomplex * + q2, __CLPK_integer *ldq2, __CLPK_doublereal *w, __CLPK_integer *indxp, __CLPK_integer *indx, + __CLPK_integer *indxq, __CLPK_integer *perm, __CLPK_integer *givptr, __CLPK_integer *givcol, + __CLPK_doublereal *givnum, __CLPK_integer *info); + +/* Subroutine */ int zlaein_(__CLPK_logical *rightv, __CLPK_logical *noinit, __CLPK_integer *n, + __CLPK_doublecomplex *h__, __CLPK_integer *ldh, __CLPK_doublecomplex *w, __CLPK_doublecomplex *v, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublereal *rwork, __CLPK_doublereal *eps3, + __CLPK_doublereal *smlnum, __CLPK_integer *info); + +/* Subroutine */ int zlaesy_(__CLPK_doublecomplex *a, __CLPK_doublecomplex *b, + __CLPK_doublecomplex *c__, __CLPK_doublecomplex *rt1, __CLPK_doublecomplex *rt2, + __CLPK_doublecomplex *evscal, __CLPK_doublecomplex *cs1, __CLPK_doublecomplex *sn1); + +/* Subroutine */ int zlaev2_(__CLPK_doublecomplex *a, __CLPK_doublecomplex *b, + __CLPK_doublecomplex *c__, __CLPK_doublereal *rt1, __CLPK_doublereal *rt2, __CLPK_doublereal *cs1, + __CLPK_doublecomplex *sn1); + +/* Subroutine */ int zlags2_(__CLPK_logical *upper, __CLPK_doublereal *a1, __CLPK_doublecomplex * + a2, __CLPK_doublereal *a3, __CLPK_doublereal *b1, __CLPK_doublecomplex *b2, __CLPK_doublereal *b3, + __CLPK_doublereal *csu, __CLPK_doublecomplex *snu, __CLPK_doublereal *csv, __CLPK_doublecomplex * + snv, __CLPK_doublereal *csq, __CLPK_doublecomplex *snq); + +/* Subroutine */ int zlagtm_(char *trans, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *alpha, __CLPK_doublecomplex *dl, __CLPK_doublecomplex *d__, + __CLPK_doublecomplex *du, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *beta, + __CLPK_doublecomplex *b, __CLPK_integer *ldb); + +/* Subroutine */ int zlahef_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *w, + __CLPK_integer *ldw, __CLPK_integer *info); + +/* Subroutine */ int zlahqr_(__CLPK_logical *wantt, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublecomplex *h__, __CLPK_integer *ldh, + __CLPK_doublecomplex *w, __CLPK_integer *iloz, __CLPK_integer *ihiz, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_integer *info); + +/* Subroutine */ int zlahrd_(__CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *nb, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *t, + __CLPK_integer *ldt, __CLPK_doublecomplex *y, __CLPK_integer *ldy); + +/* Subroutine */ int zlaic1_(__CLPK_integer *job, __CLPK_integer *j, __CLPK_doublecomplex *x, + __CLPK_doublereal *sest, __CLPK_doublecomplex *w, __CLPK_doublecomplex *gamma, __CLPK_doublereal * + sestpr, __CLPK_doublecomplex *s, __CLPK_doublecomplex *c__); + +/* Subroutine */ int zlals0_(__CLPK_integer *icompq, __CLPK_integer *nl, __CLPK_integer *nr, + __CLPK_integer *sqre, __CLPK_integer *nrhs, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *bx, __CLPK_integer *ldbx, __CLPK_integer *perm, __CLPK_integer *givptr, + __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_doublereal *givnum, __CLPK_integer *ldgnum, + __CLPK_doublereal *poles, __CLPK_doublereal *difl, __CLPK_doublereal *difr, __CLPK_doublereal * + z__, __CLPK_integer *k, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublereal *rwork, + __CLPK_integer *info); + +/* Subroutine */ int zlalsa_(__CLPK_integer *icompq, __CLPK_integer *smlsiz, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *bx, + __CLPK_integer *ldbx, __CLPK_doublereal *u, __CLPK_integer *ldu, __CLPK_doublereal *vt, __CLPK_integer * + k, __CLPK_doublereal *difl, __CLPK_doublereal *difr, __CLPK_doublereal *z__, __CLPK_doublereal * + poles, __CLPK_integer *givptr, __CLPK_integer *givcol, __CLPK_integer *ldgcol, __CLPK_integer * + perm, __CLPK_doublereal *givnum, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublereal * + rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zlapll_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_integer *incx, + __CLPK_doublecomplex *y, __CLPK_integer *incy, __CLPK_doublereal *ssmin); + +/* Subroutine */ int zlapmt_(__CLPK_logical *forwrd, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_integer *k); + +/* Subroutine */ int zlaqgb_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *r__, __CLPK_doublereal *c__, + __CLPK_doublereal *rowcnd, __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqge_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *r__, __CLPK_doublereal *c__, __CLPK_doublereal *rowcnd, + __CLPK_doublereal *colcnd, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqhb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *s, __CLPK_doublereal *scond, + __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqhe_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, + char *equed); + +/* Subroutine */ int zlaqhp_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqp2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *jpvt, __CLPK_doublecomplex *tau, + __CLPK_doublereal *vn1, __CLPK_doublereal *vn2, __CLPK_doublecomplex *work); + +/* Subroutine */ int zlaqps_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *offset, __CLPK_integer + *nb, __CLPK_integer *kb, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *jpvt, + __CLPK_doublecomplex *tau, __CLPK_doublereal *vn1, __CLPK_doublereal *vn2, __CLPK_doublecomplex * + auxv, __CLPK_doublecomplex *f, __CLPK_integer *ldf); + +/* Subroutine */ int zlaqsb_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *s, __CLPK_doublereal *scond, + __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqsp_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, char *equed); + +/* Subroutine */ int zlaqsy_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, + char *equed); + +/* Subroutine */ int zlar1v_(__CLPK_integer *n, __CLPK_integer *b1, __CLPK_integer *bn, __CLPK_doublereal + *sigma, __CLPK_doublereal *d__, __CLPK_doublereal *l, __CLPK_doublereal *ld, __CLPK_doublereal * + lld, __CLPK_doublereal *gersch, __CLPK_doublecomplex *z__, __CLPK_doublereal *ztz, + __CLPK_doublereal *mingma, __CLPK_integer *r__, __CLPK_integer *isuppz, __CLPK_doublereal *work); + +/* Subroutine */ int zlar2v_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_doublecomplex *y, + __CLPK_doublecomplex *z__, __CLPK_integer *incx, __CLPK_doublereal *c__, __CLPK_doublecomplex *s, + __CLPK_integer *incc); + +/* Subroutine */ int zlarcm_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer * + lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, + __CLPK_doublereal *rwork); + +/* Subroutine */ int zlarf_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex + *v, __CLPK_integer *incv, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *c__, __CLPK_integer * + ldc, __CLPK_doublecomplex *work); + +/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublecomplex *v, __CLPK_integer + *ldv, __CLPK_doublecomplex *t, __CLPK_integer *ldt, __CLPK_doublecomplex *c__, __CLPK_integer * + ldc, __CLPK_doublecomplex *work, __CLPK_integer *ldwork); + +/* Subroutine */ int zlarfg_(__CLPK_integer *n, __CLPK_doublecomplex *alpha, __CLPK_doublecomplex * + x, __CLPK_integer *incx, __CLPK_doublecomplex *tau); + +/* Subroutine */ int zlarft_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_doublecomplex *v, __CLPK_integer *ldv, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + t, __CLPK_integer *ldt); + +/* Subroutine */ int zlarfx_(char *side, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *v, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *c__, __CLPK_integer * + ldc, __CLPK_doublecomplex *work); + +/* Subroutine */ int zlargv_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_integer *incx, + __CLPK_doublecomplex *y, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_integer *incc); + +/* Subroutine */ int zlarnv_(__CLPK_integer *idist, __CLPK_integer *iseed, __CLPK_integer *n, + __CLPK_doublecomplex *x); + +/* Subroutine */ int zlarrv_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *l, + __CLPK_integer *isplit, __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_integer *iblock, + __CLPK_doublereal *gersch, __CLPK_doublereal *tol, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_integer *isuppz, __CLPK_doublereal *work, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zlartg_(__CLPK_doublecomplex *f, __CLPK_doublecomplex *g, __CLPK_doublereal * + cs, __CLPK_doublecomplex *sn, __CLPK_doublecomplex *r__); + +/* Subroutine */ int zlartv_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_integer *incx, + __CLPK_doublecomplex *y, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_doublecomplex *s, + __CLPK_integer *incc); + +/* Subroutine */ int zlarz_(char *side, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, + __CLPK_doublecomplex *v, __CLPK_integer *incv, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work); + +/* Subroutine */ int zlarzb_(char *side, char *trans, char *direct, char * + storev, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublecomplex + *v, __CLPK_integer *ldv, __CLPK_doublecomplex *t, __CLPK_integer *ldt, __CLPK_doublecomplex *c__, + __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *ldwork); + +/* Subroutine */ int zlarzt_(char *direct, char *storev, __CLPK_integer *n, __CLPK_integer * + k, __CLPK_doublecomplex *v, __CLPK_integer *ldv, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + t, __CLPK_integer *ldt); + +/* Subroutine */ int zlascl_(char *type__, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *cfrom, __CLPK_doublereal *cto, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zlaset_(char *uplo, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *alpha, __CLPK_doublecomplex *beta, __CLPK_doublecomplex *a, __CLPK_integer * + lda); + +/* Subroutine */ int zlasr_(char *side, char *pivot, char *direct, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublereal *c__, __CLPK_doublereal *s, __CLPK_doublecomplex *a, + __CLPK_integer *lda); + +/* Subroutine */ int zlassq_(__CLPK_integer *n, __CLPK_doublecomplex *x, __CLPK_integer *incx, + __CLPK_doublereal *scale, __CLPK_doublereal *sumsq); + +/* Subroutine */ int zlaswp_(__CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_integer *k1, __CLPK_integer *k2, __CLPK_integer *ipiv, __CLPK_integer *incx); + +/* Subroutine */ int zlasyf_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, __CLPK_integer *kb, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *w, + __CLPK_integer *ldw, __CLPK_integer *info); + +/* Subroutine */ int zlatbs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublecomplex *x, __CLPK_doublereal *scale, __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int zlatdf_(__CLPK_integer *ijob, __CLPK_integer *n, __CLPK_doublecomplex *z__, + __CLPK_integer *ldz, __CLPK_doublecomplex *rhs, __CLPK_doublereal *rdsum, __CLPK_doublereal * + rdscal, __CLPK_integer *ipiv, __CLPK_integer *jpiv); + +/* Subroutine */ int zlatps_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *x, __CLPK_doublereal * + scale, __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int zlatrd_(char *uplo, __CLPK_integer *n, __CLPK_integer *nb, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *e, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *w, __CLPK_integer *ldw); + +/* Subroutine */ int zlatrs_(char *uplo, char *trans, char *diag, char * + normin, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *x, + __CLPK_doublereal *scale, __CLPK_doublereal *cnorm, __CLPK_integer *info); + +/* Subroutine */ int zlatrz_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *l, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work); + +/* Subroutine */ int zlatzm_(char *side, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *v, __CLPK_integer *incv, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + c1, __CLPK_doublecomplex *c2, __CLPK_integer *ldc, __CLPK_doublecomplex *work); + +/* Subroutine */ int zlauu2_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zlauum_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zpbcon_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *anorm, __CLPK_doublereal * + rcond, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zpbequ_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *s, __CLPK_doublereal *scond, + __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int zpbrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *afb, __CLPK_integer * + ldafb, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal * + rwork, __CLPK_integer *info); + +/* Subroutine */ int zpbstf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int zpbsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int zpbsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *afb, + __CLPK_integer *ldafb, char *equed, __CLPK_doublereal *s, __CLPK_doublecomplex *b, __CLPK_integer + *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal * + ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, + __CLPK_integer *info); + +/* Subroutine */ int zpbtf2_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int zpbtrf_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_integer *info); + +/* Subroutine */ int zpbtrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *kd, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *b, __CLPK_integer * + ldb, __CLPK_integer *info); + +/* Subroutine */ int zpocon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zpoequ_(__CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int zporfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer *ldaf, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal * + rwork, __CLPK_integer *info); + +/* Subroutine */ int zposv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zposvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer * + ldaf, char *equed, __CLPK_doublereal *s, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zpotf2_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zpotrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zpotri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int zpotrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zppcon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex *work, __CLPK_doublereal + *rwork, __CLPK_integer *info); + +/* Subroutine */ int zppequ_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *s, __CLPK_doublereal *scond, __CLPK_doublereal *amax, __CLPK_integer *info); + +/* Subroutine */ int zpprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zppsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zppsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, char *equed, __CLPK_doublereal * + s, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zpptrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *info); + +/* Subroutine */ int zpptri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *info); + +/* Subroutine */ int zpptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zptcon_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublecomplex *e, + __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zptrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *d__, __CLPK_doublecomplex *e, __CLPK_doublereal *df, __CLPK_doublecomplex *ef, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal * + rwork, __CLPK_integer *info); + +/* Subroutine */ int zptsv_(__CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_doublereal *d__, + __CLPK_doublecomplex *e, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int zptsvx_(char *fact, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *d__, __CLPK_doublecomplex *e, __CLPK_doublereal *df, __CLPK_doublecomplex *ef, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zpttrf_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublecomplex *e, + __CLPK_integer *info); + +/* Subroutine */ int zpttrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *d__, __CLPK_doublecomplex *e, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zptts2_(__CLPK_integer *iuplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublereal *d__, __CLPK_doublecomplex *e, __CLPK_doublecomplex *b, __CLPK_integer *ldb); + +/* Subroutine */ int zrot_(__CLPK_integer *n, __CLPK_doublecomplex *cx, __CLPK_integer *incx, + __CLPK_doublecomplex *cy, __CLPK_integer *incy, __CLPK_doublereal *c__, __CLPK_doublecomplex *s); + +/* Subroutine */ int zspcon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zspmv_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *alpha, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *x, __CLPK_integer *incx, __CLPK_doublecomplex * + beta, __CLPK_doublecomplex *y, __CLPK_integer *incy); + +/* Subroutine */ int zspr_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *alpha, + __CLPK_doublecomplex *x, __CLPK_integer *incx, __CLPK_doublecomplex *ap); + +/* Subroutine */ int zsprfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, __CLPK_integer *ipiv, __CLPK_doublecomplex * + b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int zspsv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zspsvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *afp, __CLPK_integer *ipiv, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zsptrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zsptri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zsptrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *ap, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int zstedc_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, + __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zstein_(__CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e, + __CLPK_integer *m, __CLPK_doublereal *w, __CLPK_integer *iblock, __CLPK_integer *isplit, + __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, __CLPK_integer *iwork, + __CLPK_integer *ifail, __CLPK_integer *info); + +/* Subroutine */ int zsteqr_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int zsycon_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublereal *anorm, __CLPK_doublereal *rcond, + __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zsymv_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *alpha, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *x, __CLPK_integer *incx, + __CLPK_doublecomplex *beta, __CLPK_doublecomplex *y, __CLPK_integer *incy); + +/* Subroutine */ int zsyr_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *alpha, + __CLPK_doublecomplex *x, __CLPK_integer *incx, __CLPK_doublecomplex *a, __CLPK_integer *lda); + +/* Subroutine */ int zsyrfs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer *ldaf, + __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, + __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zsysv_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zsysvx_(char *fact, char *uplo, __CLPK_integer *n, __CLPK_integer * + nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *af, __CLPK_integer * + ldaf, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, + __CLPK_integer *ldx, __CLPK_doublereal *rcond, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zsytf2_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_integer *info); + +/* Subroutine */ int zsytrf_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zsytri_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zsytrs_(char *uplo, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *ipiv, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ztbcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *rcond, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztbrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, + __CLPK_doublereal *ferr, __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal * + rwork, __CLPK_integer *info); + +/* Subroutine */ int ztbtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *kd, __CLPK_integer *nrhs, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ztgevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer + *ldb, __CLPK_doublecomplex *vl, __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer * + ldvr, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, + __CLPK_integer *info); + +/* Subroutine */ int ztgex2_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_integer *j1, __CLPK_integer *info); + +/* Subroutine */ int ztgexc_(__CLPK_logical *wantq, __CLPK_logical *wantz, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_integer *ifst, __CLPK_integer *ilst, __CLPK_integer *info); + +/* Subroutine */ int ztgsen_(__CLPK_integer *ijob, __CLPK_logical *wantq, __CLPK_logical *wantz, + __CLPK_logical *select, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublecomplex *alpha, __CLPK_doublecomplex * + beta, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex *z__, __CLPK_integer * + ldz, __CLPK_integer *m, __CLPK_doublereal *pl, __CLPK_doublereal *pr, __CLPK_doublereal *dif, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int ztgsja_(char *jobu, char *jobv, char *jobq, __CLPK_integer *m, + __CLPK_integer *p, __CLPK_integer *n, __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, __CLPK_doublereal *tola, + __CLPK_doublereal *tolb, __CLPK_doublereal *alpha, __CLPK_doublereal *beta, __CLPK_doublecomplex * + u, __CLPK_integer *ldu, __CLPK_doublecomplex *v, __CLPK_integer *ldv, __CLPK_doublecomplex *q, + __CLPK_integer *ldq, __CLPK_doublecomplex *work, __CLPK_integer *ncycle, __CLPK_integer *info); + +/* Subroutine */ int ztgsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer + *ldb, __CLPK_doublecomplex *vl, __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer * + ldvr, __CLPK_doublereal *s, __CLPK_doublereal *dif, __CLPK_integer *mm, __CLPK_integer *m, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int ztgsy2_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *d__, __CLPK_integer *ldd, + __CLPK_doublecomplex *e, __CLPK_integer *lde, __CLPK_doublecomplex *f, __CLPK_integer *ldf, + __CLPK_doublereal *scale, __CLPK_doublereal *rdsum, __CLPK_doublereal *rdscal, __CLPK_integer * + info); + +/* Subroutine */ int ztgsyl_(char *trans, __CLPK_integer *ijob, __CLPK_integer *m, __CLPK_integer * + n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *d__, __CLPK_integer *ldd, + __CLPK_doublecomplex *e, __CLPK_integer *lde, __CLPK_doublecomplex *f, __CLPK_integer *ldf, + __CLPK_doublereal *scale, __CLPK_doublereal *dif, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int ztpcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_doublereal *rcond, __CLPK_doublecomplex *work, __CLPK_doublereal + *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztprfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, __CLPK_doublereal *berr, + __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztptri_(char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_integer *info); + +/* Subroutine */ int ztptrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_integer *info); + +/* Subroutine */ int ztrcon_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *rcond, __CLPK_doublecomplex * + work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztrevc_(char *side, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublecomplex *t, __CLPK_integer *ldt, __CLPK_doublecomplex *vl, + __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, __CLPK_integer *mm, __CLPK_integer + *m, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztrexc_(char *compq, __CLPK_integer *n, __CLPK_doublecomplex *t, + __CLPK_integer *ldt, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_integer *ifst, __CLPK_integer * + ilst, __CLPK_integer *info); + +/* Subroutine */ int ztrrfs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *x, __CLPK_integer *ldx, __CLPK_doublereal *ferr, + __CLPK_doublereal *berr, __CLPK_doublecomplex *work, __CLPK_doublereal *rwork, __CLPK_integer * + info); + +/* Subroutine */ int ztrsen_(char *job, char *compq, __CLPK_logical *select, __CLPK_integer + *n, __CLPK_doublecomplex *t, __CLPK_integer *ldt, __CLPK_doublecomplex *q, __CLPK_integer *ldq, + __CLPK_doublecomplex *w, __CLPK_integer *m, __CLPK_doublereal *s, __CLPK_doublereal *sep, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int ztrsna_(char *job, char *howmny, __CLPK_logical *select, + __CLPK_integer *n, __CLPK_doublecomplex *t, __CLPK_integer *ldt, __CLPK_doublecomplex *vl, + __CLPK_integer *ldvl, __CLPK_doublecomplex *vr, __CLPK_integer *ldvr, __CLPK_doublereal *s, + __CLPK_doublereal *sep, __CLPK_integer *mm, __CLPK_integer *m, __CLPK_doublecomplex *work, + __CLPK_integer *ldwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int ztrsyl_(char *trana, char *tranb, __CLPK_integer *isgn, __CLPK_integer + *m, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublereal *scale, + __CLPK_integer *info); + +/* Subroutine */ int ztrti2_(char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int ztrtri_(char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_integer *info); + +/* Subroutine */ int ztrtrs_(char *uplo, char *trans, char *diag, __CLPK_integer *n, + __CLPK_integer *nrhs, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, + __CLPK_integer *ldb, __CLPK_integer *info); + +/* Subroutine */ int ztzrqf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_integer *info); + +/* Subroutine */ int ztzrzf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zung2l_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zung2r_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zungbr_(char *vect, __CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zunghr_(__CLPK_integer *n, __CLPK_integer *ilo, __CLPK_integer *ihi, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zungl2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zunglq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zungql_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zungqr_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zungr2_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zungrq_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zungtr_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zunm2l_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zunm2r_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zunmbr_(char *vect, char *side, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex + *tau, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int zunmhr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *ilo, __CLPK_integer *ihi, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublecomplex *tau, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex * + work, __CLPK_integer *lwork, __CLPK_integer *info); + +/* Subroutine */ int zunml2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zunmlq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zunmql_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zunmqr_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zunmr2_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* Subroutine */ int zunmr3_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex + *tau, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer * + info); + +/* Subroutine */ int zunmrq_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zunmrz_(char *side, char *trans, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_integer *l, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex + *tau, __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer * + lwork, __CLPK_integer *info); + +/* Subroutine */ int zunmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *tau, + __CLPK_doublecomplex *c__, __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *lwork, + __CLPK_integer *info); + +/* Subroutine */ int zupgtr_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublecomplex *tau, __CLPK_doublecomplex *q, __CLPK_integer *ldq, __CLPK_doublecomplex * + work, __CLPK_integer *info); + +/* Subroutine */ int zupmtr_(char *side, char *uplo, char *trans, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_doublecomplex *ap, __CLPK_doublecomplex *tau, __CLPK_doublecomplex *c__, + __CLPK_integer *ldc, __CLPK_doublecomplex *work, __CLPK_integer *info); + +/* + The following prototypes are not present in the reference clapack.h distributed via netlib. + Nevertheless, the supporting code has always been present in the library. +*/ + +/* Subroutine */ int cgelsd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *s, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer * + iwork, __CLPK_integer *info); + +/* Subroutine */ int cgelss_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, __CLPK_complex * + a, __CLPK_integer *lda, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *s, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer * + info); + +/* Subroutine */ int cgesdd_(char *jobz, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *s, __CLPK_complex *u, __CLPK_integer *ldu, __CLPK_complex *vt, __CLPK_integer + *ldvt, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, __CLPK_integer *iwork, + __CLPK_integer *info); + +/* Subroutine */ int cgesvd_(char *jobu, char *jobvt, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *s, __CLPK_complex *u, __CLPK_integer *ldu, __CLPK_complex * + vt, __CLPK_integer *ldvt, __CLPK_complex *work, __CLPK_integer *lwork, __CLPK_real *rwork, + __CLPK_integer *info); + +/* Subroutine */ int chbgvd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_complex *bb, __CLPK_integer *ldbb, + __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_complex *work, __CLPK_integer *lwork, + __CLPK_real *rwork, __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +/* Subroutine */ int chetd2_(char *uplo, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *tau, __CLPK_integer *info); + +/* Complex */ void cladiv_(__CLPK_complex * ret_val, __CLPK_complex *x, __CLPK_complex *y); + +/* Subroutine */ int clalsd_(char *uplo, __CLPK_integer *smlsiz, __CLPK_integer *n, __CLPK_integer + *nrhs, __CLPK_real *d__, __CLPK_real *e, __CLPK_complex *b, __CLPK_integer *ldb, __CLPK_real *rcond, + __CLPK_integer *rank, __CLPK_complex *work, __CLPK_real *rwork, __CLPK_integer *iwork, + __CLPK_integer *info); + +__CLPK_doublereal clangb_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal clange_(char *norm, __CLPK_integer *m, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *work); + +__CLPK_doublereal clangt_(char *norm, __CLPK_integer *n, __CLPK_complex *dl, __CLPK_complex *d__, + __CLPK_complex *du); + +__CLPK_doublereal clanhb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal clanhe_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *work); + +__CLPK_doublereal clanhp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_complex *ap, + __CLPK_real *work); + +__CLPK_doublereal clanhs_(char *norm, __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, + __CLPK_real *work); + +__CLPK_doublereal clanht_(char *norm, __CLPK_integer *n, __CLPK_real *d__, __CLPK_complex *e); + +__CLPK_doublereal clansb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal clansp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_complex *ap, + __CLPK_real *work); + +__CLPK_doublereal clansy_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_complex *a, + __CLPK_integer *lda, __CLPK_real *work); + +__CLPK_doublereal clantb_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_integer *k, __CLPK_complex *ab, __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal clantp_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_complex *ap, __CLPK_real *work); + +__CLPK_doublereal clantr_(char *norm, char *uplo, char *diag, __CLPK_integer *m, + __CLPK_integer *n, __CLPK_complex *a, __CLPK_integer *lda, __CLPK_real *work); + +/* Subroutine */ int cpteqr_(char *compz, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e, + __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_real *work, __CLPK_integer *info); + +/* Subroutine */ int cstegr_(char *jobz, char *range, __CLPK_integer *n, __CLPK_real *d__, + __CLPK_real *e, __CLPK_real *vl, __CLPK_real *vu, __CLPK_integer *il, __CLPK_integer *iu, __CLPK_real *abstol, + __CLPK_integer *m, __CLPK_real *w, __CLPK_complex *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, + __CLPK_real *work, __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, + __CLPK_integer *info); + +__CLPK_doublereal dlamc3_(__CLPK_doublereal *a, __CLPK_doublereal *b); + +__CLPK_doublereal dlamch_(char *cmach); + +__CLPK_doublereal dlangb_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal dlange_(char *norm, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, + __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal dlangt_(char *norm, __CLPK_integer *n, __CLPK_doublereal *dl, __CLPK_doublereal *d__, + __CLPK_doublereal *du); + +__CLPK_doublereal dlanhs_(char *norm, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *lda, + __CLPK_doublereal *work); + +__CLPK_doublereal dlansb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal dlansp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublereal *ap, + __CLPK_doublereal *work); + +__CLPK_doublereal dlanst_(char *norm, __CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublereal *e); + +__CLPK_doublereal dlansy_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublereal *a, + __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal dlantb_(char *norm, char *uplo, char *diag, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublereal *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal dlantp_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublereal *ap, __CLPK_doublereal *work); + +__CLPK_doublereal dlantr_(char *norm, char *uplo, char *diag, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublereal *a, __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal dlapy2_(__CLPK_doublereal *x, __CLPK_doublereal *y); + +__CLPK_doublereal dlapy3_(__CLPK_doublereal *x, __CLPK_doublereal *y, __CLPK_doublereal *z__); + +__CLPK_doublereal dsecnd_(); + +__CLPK_doublereal dzsum1_(__CLPK_integer *n, __CLPK_doublecomplex *cx, __CLPK_integer *incx); + +__CLPK_logical lsame_(char *ca, char *cb); + +__CLPK_logical lsamen_(__CLPK_integer *n, char *ca, char *cb); + +__CLPK_doublereal scsum1_(__CLPK_integer *n, __CLPK_complex *cx, __CLPK_integer *incx); + +__CLPK_doublereal second_(); + +__CLPK_doublereal slamc3_(__CLPK_real *a, __CLPK_real *b); + +__CLPK_doublereal slamch_(char *cmach); + +__CLPK_doublereal slangb_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal slange_(char *norm, __CLPK_integer *m, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *work); + +__CLPK_doublereal slangt_(char *norm, __CLPK_integer *n, __CLPK_real *dl, __CLPK_real *d__, __CLPK_real *du); + +__CLPK_doublereal slanhs_(char *norm, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *work); + +__CLPK_doublereal slansb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, __CLPK_real *ab, + __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal slansp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_real *ap, __CLPK_real *work); + +__CLPK_doublereal slanst_(char *norm, __CLPK_integer *n, __CLPK_real *d__, __CLPK_real *e); + +__CLPK_doublereal slansy_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_real *a, __CLPK_integer *lda, + __CLPK_real *work); + +__CLPK_doublereal slantb_(char *norm, char *uplo, char *diag, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_real *ab, __CLPK_integer *ldab, __CLPK_real *work); + +__CLPK_doublereal slantp_(char *norm, char *uplo, char *diag, __CLPK_integer *n, __CLPK_real *ap, + __CLPK_real *work); + +__CLPK_doublereal slantr_(char *norm, char *uplo, char *diag, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_real *a, __CLPK_integer *lda, __CLPK_real *work); + +__CLPK_doublereal slapy2_(__CLPK_real *x, __CLPK_real *y); + +__CLPK_doublereal slapy3_(__CLPK_real *x, __CLPK_real *y, __CLPK_real *z__); + +/* Subroutine */ int zgelsd_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_integer *nrhs, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublereal *s, __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zgesdd_(char *jobz, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublecomplex *u, + __CLPK_integer *ldu, __CLPK_doublecomplex *vt, __CLPK_integer *ldvt, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +/* Subroutine */ int zgesvd_(char *jobu, char *jobvt, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *s, __CLPK_doublecomplex *u, + __CLPK_integer *ldu, __CLPK_doublecomplex *vt, __CLPK_integer *ldvt, __CLPK_doublecomplex *work, + __CLPK_integer *lwork, __CLPK_doublereal *rwork, __CLPK_integer *info); + +/* Subroutine */ int zhbgvd_(char *jobz, char *uplo, __CLPK_integer *n, __CLPK_integer *ka, + __CLPK_integer *kb, __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublecomplex *bb, + __CLPK_integer *ldbb, __CLPK_doublereal *w, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, + __CLPK_doublecomplex *work, __CLPK_integer *lwork, __CLPK_doublereal *rwork, + __CLPK_integer *lrwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +/* Subroutine */ int zhetd2_(char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *tau, + __CLPK_integer *info); + +/* Double Complex */ void zladiv_(__CLPK_doublecomplex * ret_val, __CLPK_doublecomplex *x, + __CLPK_doublecomplex *y); + +/* Subroutine */ int zlalsd_(char *uplo, __CLPK_integer *smlsiz, __CLPK_integer *n, __CLPK_integer + *nrhs, __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublecomplex *b, __CLPK_integer *ldb, + __CLPK_doublereal *rcond, __CLPK_integer *rank, __CLPK_doublecomplex *work, + __CLPK_doublereal *rwork, __CLPK_integer *iwork, __CLPK_integer *info); + +__CLPK_doublereal zlangb_(char *norm, __CLPK_integer *n, __CLPK_integer *kl, __CLPK_integer *ku, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal zlange_(char *norm, __CLPK_integer *m, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal zlangt_(char *norm, __CLPK_integer *n, __CLPK_doublecomplex *dl, + __CLPK_doublecomplex *d__, __CLPK_doublecomplex *du); + +__CLPK_doublereal zlanhb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal zlanhe_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal zlanhp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *work); + +__CLPK_doublereal zlanhs_(char *norm, __CLPK_integer *n, __CLPK_doublecomplex *a, __CLPK_integer *lda, + __CLPK_doublereal *work); + +__CLPK_doublereal zlanht_(char *norm, __CLPK_integer *n, __CLPK_doublereal *d__, __CLPK_doublecomplex *e); + +__CLPK_doublereal zlansb_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal zlansp_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *ap, + __CLPK_doublereal *work); + +__CLPK_doublereal zlansy_(char *norm, char *uplo, __CLPK_integer *n, __CLPK_doublecomplex *a, + __CLPK_integer *lda, __CLPK_doublereal *work); + +__CLPK_doublereal zlantb_(char *norm, char *uplo, char *diag, __CLPK_integer *n, __CLPK_integer *k, + __CLPK_doublecomplex *ab, __CLPK_integer *ldab, __CLPK_doublereal *work); + +__CLPK_doublereal zlantp_(char *norm, char *uplo, char *diag, __CLPK_integer *n, + __CLPK_doublecomplex *ap, __CLPK_doublereal *work); + +__CLPK_doublereal zlantr_(char *norm, char *uplo, char *diag, __CLPK_integer *m, __CLPK_integer *n, + __CLPK_doublecomplex *a, __CLPK_integer *lda, __CLPK_doublereal *work); + +/* Subroutine */ int zpteqr_(char *compz, __CLPK_integer *n, __CLPK_doublereal *d__, + __CLPK_doublereal *e, __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_doublereal *work, + __CLPK_integer *info); + +/* Subroutine */ int zstegr_(char *jobz, char *range, __CLPK_integer *n, + __CLPK_doublereal *d__, __CLPK_doublereal *e, __CLPK_doublereal *vl, __CLPK_doublereal *vu, + __CLPK_integer *il, __CLPK_integer *iu, __CLPK_doublereal *abstol, __CLPK_integer *m, __CLPK_doublereal *w, + __CLPK_doublecomplex *z__, __CLPK_integer *ldz, __CLPK_integer *isuppz, __CLPK_doublereal *work, + __CLPK_integer *lwork, __CLPK_integer *iwork, __CLPK_integer *liwork, __CLPK_integer *info); + +#ifdef __cplusplus +} +#endif +#endif /* __CLAPACK_H */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/maths/pca/PCA.c Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,356 @@ +/*********************************/ +/* Principal Components Analysis */ +/*********************************/ + +/*********************************************************************/ +/* Principal Components Analysis or the Karhunen-Loeve expansion is a + classical method for dimensionality reduction or exploratory data + analysis. One reference among many is: F. Murtagh and A. Heck, + Multivariate Data Analysis, Kluwer Academic, Dordrecht, 1987. + + Author: + F. Murtagh + Phone: + 49 89 32006298 (work) + + 49 89 965307 (home) + Earn/Bitnet: fionn@dgaeso51, fim@dgaipp1s, murtagh@stsci + Span: esomc1::fionn + Internet: murtagh@scivax.stsci.edu + + F. Murtagh, Munich, 6 June 1989 */ +/*********************************************************************/ + +#include <stdio.h> +#include <stdlib.h> +#include <math.h> + +#include "PCA.h" + +#define SIGN(a, b) ( (b) < 0 ? -fabs(a) : fabs(a) ) + +/** Variance-covariance matrix: creation *****************************/ + +/* Create m * m covariance matrix from given n * m data matrix. */ +void covcol(double** data, int n, int m, double** symmat) +{ +double *mean; +int i, j, j1, j2; + +/* Allocate storage for mean vector */ + +mean = (double*) malloc(m*sizeof(double)); + +/* Determine mean of column vectors of input data matrix */ + +for (j = 0; j < m; j++) + { + mean[j] = 0.0; + for (i = 0; i < n; i++) + { + mean[j] += data[i][j]; + } + mean[j] /= (double)n; + } + +/* +printf("\nMeans of column vectors:\n"); +for (j = 0; j < m; j++) { + printf("%12.1f",mean[j]); } printf("\n"); + */ + +/* Center the column vectors. */ + +for (i = 0; i < n; i++) + { + for (j = 0; j < m; j++) + { + data[i][j] -= mean[j]; + } + } + +/* Calculate the m * m covariance matrix. */ +for (j1 = 0; j1 < m; j1++) + { + for (j2 = j1; j2 < m; j2++) + { + symmat[j1][j2] = 0.0; + for (i = 0; i < n; i++) + { + symmat[j1][j2] += data[i][j1] * data[i][j2]; + } + symmat[j2][j1] = symmat[j1][j2]; + } + } + +free(mean); + +return; + +} + +/** Error handler **************************************************/ + +void erhand(char* err_msg) +{ + fprintf(stderr,"Run-time error:\n"); + fprintf(stderr,"%s\n", err_msg); + fprintf(stderr,"Exiting to system.\n"); + exit(1); +} + + +/** Reduce a real, symmetric matrix to a symmetric, tridiag. matrix. */ + +/* Householder reduction of matrix a to tridiagonal form. +Algorithm: Martin et al., Num. Math. 11, 181-195, 1968. +Ref: Smith et al., Matrix Eigensystem Routines -- EISPACK Guide +Springer-Verlag, 1976, pp. 489-494. +W H Press et al., Numerical Recipes in C, Cambridge U P, +1988, pp. 373-374. */ +void tred2(double** a, int n, double* d, double* e) +{ + int l, k, j, i; + double scale, hh, h, g, f; + + for (i = n-1; i >= 1; i--) + { + l = i - 1; + h = scale = 0.0; + if (l > 0) + { + for (k = 0; k <= l; k++) + scale += fabs(a[i][k]); + if (scale == 0.0) + e[i] = a[i][l]; + else + { + for (k = 0; k <= l; k++) + { + a[i][k] /= scale; + h += a[i][k] * a[i][k]; + } + f = a[i][l]; + g = f>0 ? -sqrt(h) : sqrt(h); + e[i] = scale * g; + h -= f * g; + a[i][l] = f - g; + f = 0.0; + for (j = 0; j <= l; j++) + { + a[j][i] = a[i][j]/h; + g = 0.0; + for (k = 0; k <= j; k++) + g += a[j][k] * a[i][k]; + for (k = j+1; k <= l; k++) + g += a[k][j] * a[i][k]; + e[j] = g / h; + f += e[j] * a[i][j]; + } + hh = f / (h + h); + for (j = 0; j <= l; j++) + { + f = a[i][j]; + e[j] = g = e[j] - hh * f; + for (k = 0; k <= j; k++) + a[j][k] -= (f * e[k] + g * a[i][k]); + } + } + } + else + e[i] = a[i][l]; + d[i] = h; + } + d[0] = 0.0; + e[0] = 0.0; + for (i = 0; i < n; i++) + { + l = i - 1; + if (d[i]) + { + for (j = 0; j <= l; j++) + { + g = 0.0; + for (k = 0; k <= l; k++) + g += a[i][k] * a[k][j]; + for (k = 0; k <= l; k++) + a[k][j] -= g * a[k][i]; + } + } + d[i] = a[i][i]; + a[i][i] = 1.0; + for (j = 0; j <= l; j++) + a[j][i] = a[i][j] = 0.0; + } +} + +/** Tridiagonal QL algorithm -- Implicit **********************/ + +void tqli(double* d, double* e, int n, double** z) +{ + int m, l, iter, i, k; + double s, r, p, g, f, dd, c, b; + + for (i = 1; i < n; i++) + e[i-1] = e[i]; + e[n-1] = 0.0; + for (l = 0; l < n; l++) + { + iter = 0; + do + { + for (m = l; m < n-1; m++) + { + dd = fabs(d[m]) + fabs(d[m+1]); + if (fabs(e[m]) + dd == dd) break; + } + if (m != l) + { + if (iter++ == 30) erhand("No convergence in TLQI."); + g = (d[l+1] - d[l]) / (2.0 * e[l]); + r = sqrt((g * g) + 1.0); + g = d[m] - d[l] + e[l] / (g + SIGN(r, g)); + s = c = 1.0; + p = 0.0; + for (i = m-1; i >= l; i--) + { + f = s * e[i]; + b = c * e[i]; + if (fabs(f) >= fabs(g)) + { + c = g / f; + r = sqrt((c * c) + 1.0); + e[i+1] = f * r; + c *= (s = 1.0/r); + } + else + { + s = f / g; + r = sqrt((s * s) + 1.0); + e[i+1] = g * r; + s *= (c = 1.0/r); + } + g = d[i+1] - p; + r = (d[i] - g) * s + 2.0 * c * b; + p = s * r; + d[i+1] = g + p; + g = c * r - b; + for (k = 0; k < n; k++) + { + f = z[k][i+1]; + z[k][i+1] = s * z[k][i] + c * f; + z[k][i] = c * z[k][i] - s * f; + } + } + d[l] = d[l] - p; + e[l] = g; + e[m] = 0.0; + } + } while (m != l); + } +} + +/* In place projection onto basis vectors */ +void pca_project(double** data, int n, int m, int ncomponents) +{ + int i, j, k, k2; + double **symmat, **symmat2, *evals, *interm; + + //TODO: assert ncomponents < m + + symmat = (double**) malloc(m*sizeof(double*)); + for (i = 0; i < m; i++) + symmat[i] = (double*) malloc(m*sizeof(double)); + + covcol(data, n, m, symmat); + + /********************************************************************* + Eigen-reduction + **********************************************************************/ + + /* Allocate storage for dummy and new vectors. */ + evals = (double*) malloc(m*sizeof(double)); /* Storage alloc. for vector of eigenvalues */ + interm = (double*) malloc(m*sizeof(double)); /* Storage alloc. for 'intermediate' vector */ + //MALLOC_ARRAY(symmat2,m,m,double); + //for (i = 0; i < m; i++) { + // for (j = 0; j < m; j++) { + // symmat2[i][j] = symmat[i][j]; /* Needed below for col. projections */ + // } + //} + tred2(symmat, m, evals, interm); /* Triangular decomposition */ +tqli(evals, interm, m, symmat); /* Reduction of sym. trid. matrix */ +/* evals now contains the eigenvalues, +columns of symmat now contain the associated eigenvectors. */ + +/* + printf("\nEigenvalues:\n"); + for (j = m-1; j >= 0; j--) { + printf("%18.5f\n", evals[j]); } + printf("\n(Eigenvalues should be strictly positive; limited\n"); + printf("precision machine arithmetic may affect this.\n"); + printf("Eigenvalues are often expressed as cumulative\n"); + printf("percentages, representing the 'percentage variance\n"); + printf("explained' by the associated axis or principal component.)\n"); + + printf("\nEigenvectors:\n"); + printf("(First three; their definition in terms of original vbes.)\n"); + for (j = 0; j < m; j++) { + for (i = 1; i <= 3; i++) { + printf("%12.4f", symmat[j][m-i]); } + printf("\n"); } + */ + +/* Form projections of row-points on prin. components. */ +/* Store in 'data', overwriting original data. */ +for (i = 0; i < n; i++) { + for (j = 0; j < m; j++) { + interm[j] = data[i][j]; } /* data[i][j] will be overwritten */ + for (k = 0; k < ncomponents; k++) { + data[i][k] = 0.0; + for (k2 = 0; k2 < m; k2++) { + data[i][k] += interm[k2] * symmat[k2][m-k-1]; } + } +} + +/* +printf("\nProjections of row-points on first 3 prin. comps.:\n"); + for (i = 0; i < n; i++) { + for (j = 0; j < 3; j++) { + printf("%12.4f", data[i][j]); } + printf("\n"); } + */ + +/* Form projections of col.-points on first three prin. components. */ +/* Store in 'symmat2', overwriting what was stored in this. */ +//for (j = 0; j < m; j++) { +// for (k = 0; k < m; k++) { +// interm[k] = symmat2[j][k]; } /*symmat2[j][k] will be overwritten*/ +// for (i = 0; i < 3; i++) { +// symmat2[j][i] = 0.0; +// for (k2 = 0; k2 < m; k2++) { +// symmat2[j][i] += interm[k2] * symmat[k2][m-i-1]; } +// if (evals[m-i-1] > 0.0005) /* Guard against zero eigenvalue */ +// symmat2[j][i] /= sqrt(evals[m-i-1]); /* Rescale */ +// else +// symmat2[j][i] = 0.0; /* Standard kludge */ +// } +// } + +/* + printf("\nProjections of column-points on first 3 prin. comps.:\n"); + for (j = 0; j < m; j++) { + for (k = 0; k < 3; k++) { + printf("%12.4f", symmat2[j][k]); } + printf("\n"); } + */ + + +for (i = 0; i < m; i++) + free(symmat[i]); +free(symmat); +//FREE_ARRAY(symmat2,m); +free(evals); +free(interm); + +} + + +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/maths/pca/PCA.h Wed Jan 09 10:37:06 2008 +0000 @@ -0,0 +1,17 @@ +#ifndef _PCA_H +#define _PCA_H + +/* + * pca.h + * soundbite + * + * Created by Mark Levy on 08/02/2006. + * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. + * + */ + +void pca_project(double** data, int n, int m, int ncomponents); + + +#endif +
--- a/maths/pca/pca.c Wed Jan 09 10:31:29 2008 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,356 +0,0 @@ -/*********************************/ -/* Principal Components Analysis */ -/*********************************/ - -/*********************************************************************/ -/* Principal Components Analysis or the Karhunen-Loeve expansion is a - classical method for dimensionality reduction or exploratory data - analysis. One reference among many is: F. Murtagh and A. Heck, - Multivariate Data Analysis, Kluwer Academic, Dordrecht, 1987. - - Author: - F. Murtagh - Phone: + 49 89 32006298 (work) - + 49 89 965307 (home) - Earn/Bitnet: fionn@dgaeso51, fim@dgaipp1s, murtagh@stsci - Span: esomc1::fionn - Internet: murtagh@scivax.stsci.edu - - F. Murtagh, Munich, 6 June 1989 */ -/*********************************************************************/ - -#include <stdio.h> -#include <stdlib.h> -#include <math.h> - -#include "pca.h" - -#define SIGN(a, b) ( (b) < 0 ? -fabs(a) : fabs(a) ) - -/** Variance-covariance matrix: creation *****************************/ - -/* Create m * m covariance matrix from given n * m data matrix. */ -void covcol(double** data, int n, int m, double** symmat) -{ -double *mean; -int i, j, j1, j2; - -/* Allocate storage for mean vector */ - -mean = (double*) malloc(m*sizeof(double)); - -/* Determine mean of column vectors of input data matrix */ - -for (j = 0; j < m; j++) - { - mean[j] = 0.0; - for (i = 0; i < n; i++) - { - mean[j] += data[i][j]; - } - mean[j] /= (double)n; - } - -/* -printf("\nMeans of column vectors:\n"); -for (j = 0; j < m; j++) { - printf("%12.1f",mean[j]); } printf("\n"); - */ - -/* Center the column vectors. */ - -for (i = 0; i < n; i++) - { - for (j = 0; j < m; j++) - { - data[i][j] -= mean[j]; - } - } - -/* Calculate the m * m covariance matrix. */ -for (j1 = 0; j1 < m; j1++) - { - for (j2 = j1; j2 < m; j2++) - { - symmat[j1][j2] = 0.0; - for (i = 0; i < n; i++) - { - symmat[j1][j2] += data[i][j1] * data[i][j2]; - } - symmat[j2][j1] = symmat[j1][j2]; - } - } - -free(mean); - -return; - -} - -/** Error handler **************************************************/ - -void erhand(char* err_msg) -{ - fprintf(stderr,"Run-time error:\n"); - fprintf(stderr,"%s\n", err_msg); - fprintf(stderr,"Exiting to system.\n"); - exit(1); -} - - -/** Reduce a real, symmetric matrix to a symmetric, tridiag. matrix. */ - -/* Householder reduction of matrix a to tridiagonal form. -Algorithm: Martin et al., Num. Math. 11, 181-195, 1968. -Ref: Smith et al., Matrix Eigensystem Routines -- EISPACK Guide -Springer-Verlag, 1976, pp. 489-494. -W H Press et al., Numerical Recipes in C, Cambridge U P, -1988, pp. 373-374. */ -void tred2(double** a, int n, double* d, double* e) -{ - int l, k, j, i; - double scale, hh, h, g, f; - - for (i = n-1; i >= 1; i--) - { - l = i - 1; - h = scale = 0.0; - if (l > 0) - { - for (k = 0; k <= l; k++) - scale += fabs(a[i][k]); - if (scale == 0.0) - e[i] = a[i][l]; - else - { - for (k = 0; k <= l; k++) - { - a[i][k] /= scale; - h += a[i][k] * a[i][k]; - } - f = a[i][l]; - g = f>0 ? -sqrt(h) : sqrt(h); - e[i] = scale * g; - h -= f * g; - a[i][l] = f - g; - f = 0.0; - for (j = 0; j <= l; j++) - { - a[j][i] = a[i][j]/h; - g = 0.0; - for (k = 0; k <= j; k++) - g += a[j][k] * a[i][k]; - for (k = j+1; k <= l; k++) - g += a[k][j] * a[i][k]; - e[j] = g / h; - f += e[j] * a[i][j]; - } - hh = f / (h + h); - for (j = 0; j <= l; j++) - { - f = a[i][j]; - e[j] = g = e[j] - hh * f; - for (k = 0; k <= j; k++) - a[j][k] -= (f * e[k] + g * a[i][k]); - } - } - } - else - e[i] = a[i][l]; - d[i] = h; - } - d[0] = 0.0; - e[0] = 0.0; - for (i = 0; i < n; i++) - { - l = i - 1; - if (d[i]) - { - for (j = 0; j <= l; j++) - { - g = 0.0; - for (k = 0; k <= l; k++) - g += a[i][k] * a[k][j]; - for (k = 0; k <= l; k++) - a[k][j] -= g * a[k][i]; - } - } - d[i] = a[i][i]; - a[i][i] = 1.0; - for (j = 0; j <= l; j++) - a[j][i] = a[i][j] = 0.0; - } -} - -/** Tridiagonal QL algorithm -- Implicit **********************/ - -void tqli(double* d, double* e, int n, double** z) -{ - int m, l, iter, i, k; - double s, r, p, g, f, dd, c, b; - - for (i = 1; i < n; i++) - e[i-1] = e[i]; - e[n-1] = 0.0; - for (l = 0; l < n; l++) - { - iter = 0; - do - { - for (m = l; m < n-1; m++) - { - dd = fabs(d[m]) + fabs(d[m+1]); - if (fabs(e[m]) + dd == dd) break; - } - if (m != l) - { - if (iter++ == 30) erhand("No convergence in TLQI."); - g = (d[l+1] - d[l]) / (2.0 * e[l]); - r = sqrt((g * g) + 1.0); - g = d[m] - d[l] + e[l] / (g + SIGN(r, g)); - s = c = 1.0; - p = 0.0; - for (i = m-1; i >= l; i--) - { - f = s * e[i]; - b = c * e[i]; - if (fabs(f) >= fabs(g)) - { - c = g / f; - r = sqrt((c * c) + 1.0); - e[i+1] = f * r; - c *= (s = 1.0/r); - } - else - { - s = f / g; - r = sqrt((s * s) + 1.0); - e[i+1] = g * r; - s *= (c = 1.0/r); - } - g = d[i+1] - p; - r = (d[i] - g) * s + 2.0 * c * b; - p = s * r; - d[i+1] = g + p; - g = c * r - b; - for (k = 0; k < n; k++) - { - f = z[k][i+1]; - z[k][i+1] = s * z[k][i] + c * f; - z[k][i] = c * z[k][i] - s * f; - } - } - d[l] = d[l] - p; - e[l] = g; - e[m] = 0.0; - } - } while (m != l); - } -} - -/* In place projection onto basis vectors */ -void pca_project(double** data, int n, int m, int ncomponents) -{ - int i, j, k, k2; - double **symmat, **symmat2, *evals, *interm; - - //TODO: assert ncomponents < m - - symmat = (double**) malloc(m*sizeof(double*)); - for (i = 0; i < m; i++) - symmat[i] = (double*) malloc(m*sizeof(double)); - - covcol(data, n, m, symmat); - - /********************************************************************* - Eigen-reduction - **********************************************************************/ - - /* Allocate storage for dummy and new vectors. */ - evals = (double*) malloc(m*sizeof(double)); /* Storage alloc. for vector of eigenvalues */ - interm = (double*) malloc(m*sizeof(double)); /* Storage alloc. for 'intermediate' vector */ - //MALLOC_ARRAY(symmat2,m,m,double); - //for (i = 0; i < m; i++) { - // for (j = 0; j < m; j++) { - // symmat2[i][j] = symmat[i][j]; /* Needed below for col. projections */ - // } - //} - tred2(symmat, m, evals, interm); /* Triangular decomposition */ -tqli(evals, interm, m, symmat); /* Reduction of sym. trid. matrix */ -/* evals now contains the eigenvalues, -columns of symmat now contain the associated eigenvectors. */ - -/* - printf("\nEigenvalues:\n"); - for (j = m-1; j >= 0; j--) { - printf("%18.5f\n", evals[j]); } - printf("\n(Eigenvalues should be strictly positive; limited\n"); - printf("precision machine arithmetic may affect this.\n"); - printf("Eigenvalues are often expressed as cumulative\n"); - printf("percentages, representing the 'percentage variance\n"); - printf("explained' by the associated axis or principal component.)\n"); - - printf("\nEigenvectors:\n"); - printf("(First three; their definition in terms of original vbes.)\n"); - for (j = 0; j < m; j++) { - for (i = 1; i <= 3; i++) { - printf("%12.4f", symmat[j][m-i]); } - printf("\n"); } - */ - -/* Form projections of row-points on prin. components. */ -/* Store in 'data', overwriting original data. */ -for (i = 0; i < n; i++) { - for (j = 0; j < m; j++) { - interm[j] = data[i][j]; } /* data[i][j] will be overwritten */ - for (k = 0; k < ncomponents; k++) { - data[i][k] = 0.0; - for (k2 = 0; k2 < m; k2++) { - data[i][k] += interm[k2] * symmat[k2][m-k-1]; } - } -} - -/* -printf("\nProjections of row-points on first 3 prin. comps.:\n"); - for (i = 0; i < n; i++) { - for (j = 0; j < 3; j++) { - printf("%12.4f", data[i][j]); } - printf("\n"); } - */ - -/* Form projections of col.-points on first three prin. components. */ -/* Store in 'symmat2', overwriting what was stored in this. */ -//for (j = 0; j < m; j++) { -// for (k = 0; k < m; k++) { -// interm[k] = symmat2[j][k]; } /*symmat2[j][k] will be overwritten*/ -// for (i = 0; i < 3; i++) { -// symmat2[j][i] = 0.0; -// for (k2 = 0; k2 < m; k2++) { -// symmat2[j][i] += interm[k2] * symmat[k2][m-i-1]; } -// if (evals[m-i-1] > 0.0005) /* Guard against zero eigenvalue */ -// symmat2[j][i] /= sqrt(evals[m-i-1]); /* Rescale */ -// else -// symmat2[j][i] = 0.0; /* Standard kludge */ -// } -// } - -/* - printf("\nProjections of column-points on first 3 prin. comps.:\n"); - for (j = 0; j < m; j++) { - for (k = 0; k < 3; k++) { - printf("%12.4f", symmat2[j][k]); } - printf("\n"); } - */ - - -for (i = 0; i < m; i++) - free(symmat[i]); -free(symmat); -//FREE_ARRAY(symmat2,m); -free(evals); -free(interm); - -} - - -
--- a/maths/pca/pca.h Wed Jan 09 10:31:29 2008 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -#ifndef _PCA_H -#define _PCA_H - -/* - * pca.h - * soundbite - * - * Created by Mark Levy on 08/02/2006. - * Copyright 2006 Centre for Digital Music, Queen Mary, University of London. All rights reserved. - * - */ - -void pca_project(double** data, int n, int m, int ncomponents); - - -#endif \ No newline at end of file
--- a/qm-dsp.pro Wed Jan 09 10:31:29 2008 +0000 +++ b/qm-dsp.pro Wed Jan 09 10:37:06 2008 +0000 @@ -15,7 +15,7 @@ # dsp/tempotracking \ # dsp/tonal \ # dsp/transforms -INCLUDEPATH += . +INCLUDEPATH += . include # Input HEADERS += base/Pitch.h \ @@ -37,11 +37,13 @@ dsp/tonal/TCSgram.h \ dsp/tonal/TonalEstimator.h \ dsp/transforms/FFT.h \ + hmm/HMM.h \ maths/Correlation.h \ maths/Histogram.h \ maths/MathAliases.h \ maths/MathUtilities.h \ - maths/Polyfit.h + maths/Polyfit.h \ + maths/pca/PCA.h SOURCES += base/Pitch.cpp \ dsp/chromagram/Chromagram.cpp \ dsp/chromagram/ChromaProcess.cpp \ @@ -60,5 +62,7 @@ dsp/tonal/TCSgram.cpp \ dsp/tonal/TonalEstimator.cpp \ dsp/transforms/FFT.cpp \ + hmm/HMM.c \ maths/Correlation.cpp \ - maths/MathUtilities.cpp + maths/MathUtilities.cpp \ + maths/pca/PCA.c