Chris@202: /* dgetri.f -- translated by f2c (version 20061008).
Chris@202:    You must link the resulting object file with libf2c:
Chris@202: 	on Microsoft Windows system, link with libf2c.lib;
Chris@202: 	on Linux or Unix systems, link with .../path/to/libf2c.a -lm
Chris@202: 	or, if you install libf2c.a in a standard place, with -lf2c -lm
Chris@202: 	-- in that order, at the end of the command line, as in
Chris@202: 		cc *.o -lf2c -lm
Chris@202: 	Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
Chris@202: 
Chris@202: 		http://www.netlib.org/f2c/libf2c.zip
Chris@202: */
Chris@202: 
Chris@202: #include "f2c.h"
Chris@202: #include "blaswrap.h"
Chris@202: 
Chris@202: /* Table of constant values */
Chris@202: 
Chris@202: static integer c__1 = 1;
Chris@202: static integer c_n1 = -1;
Chris@202: static integer c__2 = 2;
Chris@202: static doublereal c_b20 = -1.;
Chris@202: static doublereal c_b22 = 1.;
Chris@202: 
Chris@202: /* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer 
Chris@202: 	*ipiv, doublereal *work, integer *lwork, integer *info)
Chris@202: {
Chris@202:     /* System generated locals */
Chris@202:     integer a_dim1, a_offset, i__1, i__2, i__3;
Chris@202: 
Chris@202:     /* Local variables */
Chris@202:     integer i__, j, jb, nb, jj, jp, nn, iws;
Chris@202:     extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
Chris@202: 	    integer *, doublereal *, doublereal *, integer *, doublereal *, 
Chris@202: 	    integer *, doublereal *, doublereal *, integer *),
Chris@202: 	     dgemv_(char *, integer *, integer *, doublereal *, doublereal *, 
Chris@202: 	    integer *, doublereal *, integer *, doublereal *, doublereal *, 
Chris@202: 	    integer *);
Chris@202:     integer nbmin;
Chris@202:     extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
Chris@202: 	    doublereal *, integer *), dtrsm_(char *, char *, char *, char *, 
Chris@202: 	    integer *, integer *, doublereal *, doublereal *, integer *, 
Chris@202: 	    doublereal *, integer *), xerbla_(
Chris@202: 	    char *, integer *);
Chris@202:     extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
Chris@202: 	    integer *, integer *);
Chris@202:     integer ldwork;
Chris@202:     extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal 
Chris@202: 	    *, integer *, integer *);
Chris@202:     integer lwkopt;
Chris@202:     logical lquery;
Chris@202: 
Chris@202: 
Chris@202: /*  -- LAPACK routine (version 3.2) -- */
Chris@202: /*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
Chris@202: /*     November 2006 */
Chris@202: 
Chris@202: /*     .. Scalar Arguments .. */
Chris@202: /*     .. */
Chris@202: /*     .. Array Arguments .. */
Chris@202: /*     .. */
Chris@202: 
Chris@202: /*  Purpose */
Chris@202: /*  ======= */
Chris@202: 
Chris@202: /*  DGETRI computes the inverse of a matrix using the LU factorization */
Chris@202: /*  computed by DGETRF. */
Chris@202: 
Chris@202: /*  This method inverts U and then computes inv(A) by solving the system */
Chris@202: /*  inv(A)*L = inv(U) for inv(A). */
Chris@202: 
Chris@202: /*  Arguments */
Chris@202: /*  ========= */
Chris@202: 
Chris@202: /*  N       (input) INTEGER */
Chris@202: /*          The order of the matrix A.  N >= 0. */
Chris@202: 
Chris@202: /*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
Chris@202: /*          On entry, the factors L and U from the factorization */
Chris@202: /*          A = P*L*U as computed by DGETRF. */
Chris@202: /*          On exit, if INFO = 0, the inverse of the original matrix A. */
Chris@202: 
Chris@202: /*  LDA     (input) INTEGER */
Chris@202: /*          The leading dimension of the array A.  LDA >= max(1,N). */
Chris@202: 
Chris@202: /*  IPIV    (input) INTEGER array, dimension (N) */
Chris@202: /*          The pivot indices from DGETRF; for 1<=i<=N, row i of the */
Chris@202: /*          matrix was interchanged with row IPIV(i). */
Chris@202: 
Chris@202: /*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
Chris@202: /*          On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
Chris@202: 
Chris@202: /*  LWORK   (input) INTEGER */
Chris@202: /*          The dimension of the array WORK.  LWORK >= max(1,N). */
Chris@202: /*          For optimal performance LWORK >= N*NB, where NB is */
Chris@202: /*          the optimal blocksize returned by ILAENV. */
Chris@202: 
Chris@202: /*          If LWORK = -1, then a workspace query is assumed; the routine */
Chris@202: /*          only calculates the optimal size of the WORK array, returns */
Chris@202: /*          this value as the first entry of the WORK array, and no error */
Chris@202: /*          message related to LWORK is issued by XERBLA. */
Chris@202: 
Chris@202: /*  INFO    (output) INTEGER */
Chris@202: /*          = 0:  successful exit */
Chris@202: /*          < 0:  if INFO = -i, the i-th argument had an illegal value */
Chris@202: /*          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is */
Chris@202: /*                singular and its inverse could not be computed. */
Chris@202: 
Chris@202: /*  ===================================================================== */
Chris@202: 
Chris@202: /*     .. Parameters .. */
Chris@202: /*     .. */
Chris@202: /*     .. Local Scalars .. */
Chris@202: /*     .. */
Chris@202: /*     .. External Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. External Subroutines .. */
Chris@202: /*     .. */
Chris@202: /*     .. Intrinsic Functions .. */
Chris@202: /*     .. */
Chris@202: /*     .. Executable Statements .. */
Chris@202: 
Chris@202: /*     Test the input parameters. */
Chris@202: 
Chris@202:     /* Parameter adjustments */
Chris@202:     a_dim1 = *lda;
Chris@202:     a_offset = 1 + a_dim1;
Chris@202:     a -= a_offset;
Chris@202:     --ipiv;
Chris@202:     --work;
Chris@202: 
Chris@202:     /* Function Body */
Chris@202:     *info = 0;
Chris@202:     nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1);
Chris@202:     lwkopt = *n * nb;
Chris@202:     work[1] = (doublereal) lwkopt;
Chris@202:     lquery = *lwork == -1;
Chris@202:     if (*n < 0) {
Chris@202: 	*info = -1;
Chris@202:     } else if (*lda < max(1,*n)) {
Chris@202: 	*info = -3;
Chris@202:     } else if (*lwork < max(1,*n) && ! lquery) {
Chris@202: 	*info = -6;
Chris@202:     }
Chris@202:     if (*info != 0) {
Chris@202: 	i__1 = -(*info);
Chris@202: 	xerbla_("DGETRI", &i__1);
Chris@202: 	return 0;
Chris@202:     } else if (lquery) {
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Quick return if possible */
Chris@202: 
Chris@202:     if (*n == 0) {
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202: /*     Form inv(U).  If INFO > 0 from DTRTRI, then U is singular, */
Chris@202: /*     and the inverse is not computed. */
Chris@202: 
Chris@202:     dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
Chris@202:     if (*info > 0) {
Chris@202: 	return 0;
Chris@202:     }
Chris@202: 
Chris@202:     nbmin = 2;
Chris@202:     ldwork = *n;
Chris@202:     if (nb > 1 && nb < *n) {
Chris@202: /* Computing MAX */
Chris@202: 	i__1 = ldwork * nb;
Chris@202: 	iws = max(i__1,1);
Chris@202: 	if (*lwork < iws) {
Chris@202: 	    nb = *lwork / ldwork;
Chris@202: /* Computing MAX */
Chris@202: 	    i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, &
Chris@202: 		    c_n1);
Chris@202: 	    nbmin = max(i__1,i__2);
Chris@202: 	}
Chris@202:     } else {
Chris@202: 	iws = *n;
Chris@202:     }
Chris@202: 
Chris@202: /*     Solve the equation inv(A)*L = inv(U) for inv(A). */
Chris@202: 
Chris@202:     if (nb < nbmin || nb >= *n) {
Chris@202: 
Chris@202: /*        Use unblocked code. */
Chris@202: 
Chris@202: 	for (j = *n; j >= 1; --j) {
Chris@202: 
Chris@202: /*           Copy current column of L to WORK and replace with zeros. */
Chris@202: 
Chris@202: 	    i__1 = *n;
Chris@202: 	    for (i__ = j + 1; i__ <= i__1; ++i__) {
Chris@202: 		work[i__] = a[i__ + j * a_dim1];
Chris@202: 		a[i__ + j * a_dim1] = 0.;
Chris@202: /* L10: */
Chris@202: 	    }
Chris@202: 
Chris@202: /*           Compute current column of inv(A). */
Chris@202: 
Chris@202: 	    if (j < *n) {
Chris@202: 		i__1 = *n - j;
Chris@202: 		dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1 
Chris@202: 			+ 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1 
Chris@202: 			+ 1], &c__1);
Chris@202: 	    }
Chris@202: /* L20: */
Chris@202: 	}
Chris@202:     } else {
Chris@202: 
Chris@202: /*        Use blocked code. */
Chris@202: 
Chris@202: 	nn = (*n - 1) / nb * nb + 1;
Chris@202: 	i__1 = -nb;
Chris@202: 	for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
Chris@202: /* Computing MIN */
Chris@202: 	    i__2 = nb, i__3 = *n - j + 1;
Chris@202: 	    jb = min(i__2,i__3);
Chris@202: 
Chris@202: /*           Copy current block column of L to WORK and replace with */
Chris@202: /*           zeros. */
Chris@202: 
Chris@202: 	    i__2 = j + jb - 1;
Chris@202: 	    for (jj = j; jj <= i__2; ++jj) {
Chris@202: 		i__3 = *n;
Chris@202: 		for (i__ = jj + 1; i__ <= i__3; ++i__) {
Chris@202: 		    work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1];
Chris@202: 		    a[i__ + jj * a_dim1] = 0.;
Chris@202: /* L30: */
Chris@202: 		}
Chris@202: /* L40: */
Chris@202: 	    }
Chris@202: 
Chris@202: /*           Compute current block column of inv(A). */
Chris@202: 
Chris@202: 	    if (j + jb <= *n) {
Chris@202: 		i__2 = *n - j - jb + 1;
Chris@202: 		dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20, 
Chris@202: 			&a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &
Chris@202: 			ldwork, &c_b22, &a[j * a_dim1 + 1], lda);
Chris@202: 	    }
Chris@202: 	    dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, &
Chris@202: 		    work[j], &ldwork, &a[j * a_dim1 + 1], lda);
Chris@202: /* L50: */
Chris@202: 	}
Chris@202:     }
Chris@202: 
Chris@202: /*     Apply column interchanges. */
Chris@202: 
Chris@202:     for (j = *n - 1; j >= 1; --j) {
Chris@202: 	jp = ipiv[j];
Chris@202: 	if (jp != j) {
Chris@202: 	    dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
Chris@202: 	}
Chris@202: /* L60: */
Chris@202:     }
Chris@202: 
Chris@202:     work[1] = (doublereal) iws;
Chris@202:     return 0;
Chris@202: 
Chris@202: /*     End of DGETRI */
Chris@202: 
Chris@202: } /* dgetri_ */