comparison ext/clapack/src/dgetri.c @ 430:335af74a25b6

Merge from branch clapack-included

+/* dgetri.f -- translated by f2c (version 20061008).
+   You must link the resulting object file with libf2c:
+	on Microsoft Windows system, link with libf2c.lib;
+	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
+	or, if you install libf2c.a in a standard place, with -lf2c -lm
+	-- in that order, at the end of the command line, as in
+		cc *.o -lf2c -lm
+	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
+
+		http://www.netlib.org/f2c/libf2c.zip
+*/
+
+#include "f2c.h"
+#include "blaswrap.h"
+
+/* Table of constant values */
+
+static integer c__1 = 1;
+static integer c_n1 = -1;
+static integer c__2 = 2;
+static doublereal c_b20 = -1.;
+static doublereal c_b22 = 1.;
+
+/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer 
+	*ipiv, doublereal *work, integer *lwork, integer *info)
+{
+    /* System generated locals */
+    integer a_dim1, a_offset, i__1, i__2, i__3;
+
+    /* Local variables */
+    integer i__, j, jb, nb, jj, jp, nn, iws;
+    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
+	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
+	    integer *, doublereal *, doublereal *, integer *),
+	     dgemv_(char *, integer *, integer *, doublereal *, doublereal *, 
+	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
+	    integer *);
+    integer nbmin;
+    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
+	    doublereal *, integer *), dtrsm_(char *, char *, char *, char *, 
+	    integer *, integer *, doublereal *, doublereal *, integer *, 
+	    doublereal *, integer *), xerbla_(
+	    char *, integer *);
+    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
+	    integer *, integer *);
+    integer ldwork;
+    extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal 
+	    *, integer *, integer *);
+    integer lwkopt;
+    logical lquery;
+
+
+/*  -- LAPACK routine (version 3.2) -- */
+/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
+/*     November 2006 */
+
+/*     .. Scalar Arguments .. */
+/*     .. */
+/*     .. Array Arguments .. */
+/*     .. */
+
+/*  Purpose */
+/*  ======= */
+
+/*  DGETRI computes the inverse of a matrix using the LU factorization */
+/*  computed by DGETRF. */
+
+/*  This method inverts U and then computes inv(A) by solving the system */
+/*  inv(A)*L = inv(U) for inv(A). */
+
+/*  Arguments */
+/*  ========= */
+
+/*  N       (input) INTEGER */
+/*          The order of the matrix A.  N >= 0. */
+
+/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
+/*          On entry, the factors L and U from the factorization */
+/*          A = P*L*U as computed by DGETRF. */
+/*          On exit, if INFO = 0, the inverse of the original matrix A. */
+
+/*  LDA     (input) INTEGER */
+/*          The leading dimension of the array A.  LDA >= max(1,N). */
+
+/*  IPIV    (input) INTEGER array, dimension (N) */
+/*          The pivot indices from DGETRF; for 1<=i<=N, row i of the */
+/*          matrix was interchanged with row IPIV(i). */
+
+/*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
+/*          On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
+
+/*  LWORK   (input) INTEGER */
+/*          The dimension of the array WORK.  LWORK >= max(1,N). */
+/*          For optimal performance LWORK >= N*NB, where NB is */
+/*          the optimal blocksize returned by ILAENV. */
+
+/*          If LWORK = -1, then a workspace query is assumed; the routine */
+/*          only calculates the optimal size of the WORK array, returns */
+/*          this value as the first entry of the WORK array, and no error */
+/*          message related to LWORK is issued by XERBLA. */
+
+/*  INFO    (output) INTEGER */
+/*          = 0:  successful exit */
+/*          < 0:  if INFO = -i, the i-th argument had an illegal value */
+/*          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is */
+/*                singular and its inverse could not be computed. */
+
+/*  ===================================================================== */
+
+/*     .. Parameters .. */
+/*     .. */
+/*     .. Local Scalars .. */
+/*     .. */
+/*     .. External Functions .. */
+/*     .. */
+/*     .. External Subroutines .. */
+/*     .. */
+/*     .. Intrinsic Functions .. */
+/*     .. */
+/*     .. Executable Statements .. */
+
+/*     Test the input parameters. */
+
+    /* Parameter adjustments */
+    a_dim1 = *lda;
+    a_offset = 1 + a_dim1;
+    a -= a_offset;
+    --ipiv;
+    --work;
+
+    /* Function Body */
+    *info = 0;
+    nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1);
+    lwkopt = *n * nb;
+    work[1] = (doublereal) lwkopt;
+    lquery = *lwork == -1;
+    if (*n < 0) {
+	*info = -1;
+    } else if (*lda < max(1,*n)) {
+	*info = -3;
+    } else if (*lwork < max(1,*n) && ! lquery) {
+	*info = -6;
+    }
+    if (*info != 0) {
+	i__1 = -(*info);
+	xerbla_("DGETRI", &i__1);
+	return 0;
+    } else if (lquery) {
+	return 0;
+    }
+
+/*     Quick return if possible */
+
+    if (*n == 0) {
+	return 0;
+    }
+
+/*     Form inv(U).  If INFO > 0 from DTRTRI, then U is singular, */
+/*     and the inverse is not computed. */
+
+    dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
+    if (*info > 0) {
+	return 0;
+    }
+
+    nbmin = 2;
+    ldwork = *n;
+    if (nb > 1 && nb < *n) {
+/* Computing MAX */
+	i__1 = ldwork * nb;
+	iws = max(i__1,1);
+	if (*lwork < iws) {
+	    nb = *lwork / ldwork;
+/* Computing MAX */
+	    i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, &
+		    c_n1);
+	    nbmin = max(i__1,i__2);
+	}
+    } else {
+	iws = *n;
+    }
+
+/*     Solve the equation inv(A)*L = inv(U) for inv(A). */
+
+    if (nb < nbmin || nb >= *n) {
+
+/*        Use unblocked code. */
+
+	for (j = *n; j >= 1; --j) {
+
+/*           Copy current column of L to WORK and replace with zeros. */
+
+	    i__1 = *n;
+	    for (i__ = j + 1; i__ <= i__1; ++i__) {
+		work[i__] = a[i__ + j * a_dim1];
+		a[i__ + j * a_dim1] = 0.;
+/* L10: */
+	    }
+
+/*           Compute current column of inv(A). */
+
+	    if (j < *n) {
+		i__1 = *n - j;
+		dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 
+			+ 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 
+			+ 1], &c__1);
+	    }
+/* L20: */
+	}
+    } else {
+
+/*        Use blocked code. */
+
+	nn = (*n - 1) / nb * nb + 1;
+	i__1 = -nb;
+	for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
+/* Computing MIN */
+	    i__2 = nb, i__3 = *n - j + 1;
+	    jb = min(i__2,i__3);
+
+/*           Copy current block column of L to WORK and replace with */
+/*           zeros. */
+
+	    i__2 = j + jb - 1;
+	    for (jj = j; jj <= i__2; ++jj) {
+		i__3 = *n;
+		for (i__ = jj + 1; i__ <= i__3; ++i__) {
+		    work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1];
+		    a[i__ + jj * a_dim1] = 0.;
+/* L30: */
+		}
+/* L40: */
+	    }
+
+/*           Compute current block column of inv(A). */
+
+	    if (j + jb <= *n) {
+		i__2 = *n - j - jb + 1;
+		dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20, 
+			&a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &
+			ldwork, &c_b22, &a[j * a_dim1 + 1], lda);
+	    }
+	    dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, &
+		    work[j], &ldwork, &a[j * a_dim1 + 1], lda);
+/* L50: */
+	}
+    }
+
+/*     Apply column interchanges. */
+
+    for (j = *n - 1; j >= 1; --j) {
+	jp = ipiv[j];
+	if (jp != j) {
+	    dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
+	}
+/* L60: */
+    }
+
+    work[1] = (doublereal) iws;
+    return 0;
+
+/*     End of DGETRI */
+
+} /* dgetri_ */