252 lines
6.8 KiB
C
252 lines
6.8 KiB
C
#include "clapack.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static integer c_n1 = -1;
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static integer c__2 = 2;
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static doublereal c_b20 = -1.;
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static doublereal c_b22 = 1.;
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/* Subroutine */ int dgetri_(integer *n, doublereal *a, integer *lda, integer
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*ipiv, doublereal *work, integer *lwork, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, jb, nb, jj, jp, nn, iws;
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extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
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integer *, doublereal *, doublereal *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, integer *),
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dgemv_(char *, integer *, integer *, doublereal *, doublereal *,
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integer *, doublereal *, integer *, doublereal *, doublereal *,
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integer *);
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integer nbmin;
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extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *,
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doublereal *, integer *), dtrsm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *), xerbla_(
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char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *);
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integer ldwork;
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extern /* Subroutine */ int dtrtri_(char *, char *, integer *, doublereal
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*, integer *, integer *);
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integer lwkopt;
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logical lquery;
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/* -- LAPACK routine (version 3.1) -- */
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
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/* November 2006 */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* Purpose */
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/* ======= */
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/* DGETRI computes the inverse of a matrix using the LU factorization */
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/* computed by DGETRF. */
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/* This method inverts U and then computes inv(A) by solving the system */
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/* inv(A)*L = inv(U) for inv(A). */
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/* Arguments */
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/* ========= */
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/* N (input) INTEGER */
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/* The order of the matrix A. N >= 0. */
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/* A (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
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/* On entry, the factors L and U from the factorization */
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/* A = P*L*U as computed by DGETRF. */
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/* On exit, if INFO = 0, the inverse of the original matrix A. */
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/* LDA (input) INTEGER */
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/* The leading dimension of the array A. LDA >= max(1,N). */
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/* IPIV (input) INTEGER array, dimension (N) */
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/* The pivot indices from DGETRF; for 1<=i<=N, row i of the */
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/* matrix was interchanged with row IPIV(i). */
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/* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
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/* On exit, if INFO=0, then WORK(1) returns the optimal LWORK. */
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/* LWORK (input) INTEGER */
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/* The dimension of the array WORK. LWORK >= max(1,N). */
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/* For optimal performance LWORK >= N*NB, where NB is */
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/* the optimal blocksize returned by ILAENV. */
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/* If LWORK = -1, then a workspace query is assumed; the routine */
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/* only calculates the optimal size of the WORK array, returns */
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/* this value as the first entry of the WORK array, and no error */
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/* message related to LWORK is issued by XERBLA. */
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/* INFO (output) INTEGER */
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/* = 0: successful exit */
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/* < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > 0: if INFO = i, U(i,i) is exactly zero; the matrix is */
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/* singular and its inverse could not be computed. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters. */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--ipiv;
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--work;
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/* Function Body */
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*info = 0;
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nb = ilaenv_(&c__1, "DGETRI", " ", n, &c_n1, &c_n1, &c_n1);
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lwkopt = *n * nb;
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work[1] = (doublereal) lwkopt;
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lquery = *lwork == -1;
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if (*n < 0) {
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*info = -1;
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} else if (*lda < max(1,*n)) {
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*info = -3;
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} else if (*lwork < max(1,*n) && ! lquery) {
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*info = -6;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DGETRI", &i__1);
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return 0;
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} else if (lquery) {
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return 0;
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}
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/* Quick return if possible */
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if (*n == 0) {
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return 0;
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}
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/* Form inv(U). If INFO > 0 from DTRTRI, then U is singular, */
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/* and the inverse is not computed. */
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dtrtri_("Upper", "Non-unit", n, &a[a_offset], lda, info);
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if (*info > 0) {
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return 0;
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}
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nbmin = 2;
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ldwork = *n;
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if (nb > 1 && nb < *n) {
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/* Computing MAX */
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i__1 = ldwork * nb;
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iws = max(i__1,1);
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if (*lwork < iws) {
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nb = *lwork / ldwork;
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/* Computing MAX */
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i__1 = 2, i__2 = ilaenv_(&c__2, "DGETRI", " ", n, &c_n1, &c_n1, &
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c_n1);
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nbmin = max(i__1,i__2);
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}
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} else {
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iws = *n;
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}
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/* Solve the equation inv(A)*L = inv(U) for inv(A). */
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if (nb < nbmin || nb >= *n) {
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/* Use unblocked code. */
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for (j = *n; j >= 1; --j) {
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/* Copy current column of L to WORK and replace with zeros. */
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i__1 = *n;
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for (i__ = j + 1; i__ <= i__1; ++i__) {
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work[i__] = a[i__ + j * a_dim1];
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a[i__ + j * a_dim1] = 0.;
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/* L10: */
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}
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/* Compute current column of inv(A). */
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if (j < *n) {
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i__1 = *n - j;
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dgemv_("No transpose", n, &i__1, &c_b20, &a[(j + 1) * a_dim1
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+ 1], lda, &work[j + 1], &c__1, &c_b22, &a[j * a_dim1
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+ 1], &c__1);
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}
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/* L20: */
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}
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} else {
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/* Use blocked code. */
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nn = (*n - 1) / nb * nb + 1;
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i__1 = -nb;
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for (j = nn; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) {
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/* Computing MIN */
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i__2 = nb, i__3 = *n - j + 1;
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jb = min(i__2,i__3);
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/* Copy current block column of L to WORK and replace with */
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/* zeros. */
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i__2 = j + jb - 1;
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for (jj = j; jj <= i__2; ++jj) {
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i__3 = *n;
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for (i__ = jj + 1; i__ <= i__3; ++i__) {
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work[i__ + (jj - j) * ldwork] = a[i__ + jj * a_dim1];
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a[i__ + jj * a_dim1] = 0.;
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/* L30: */
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}
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/* L40: */
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}
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/* Compute current block column of inv(A). */
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if (j + jb <= *n) {
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i__2 = *n - j - jb + 1;
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dgemm_("No transpose", "No transpose", n, &jb, &i__2, &c_b20,
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&a[(j + jb) * a_dim1 + 1], lda, &work[j + jb], &
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ldwork, &c_b22, &a[j * a_dim1 + 1], lda);
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}
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dtrsm_("Right", "Lower", "No transpose", "Unit", n, &jb, &c_b22, &
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work[j], &ldwork, &a[j * a_dim1 + 1], lda);
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/* L50: */
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}
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}
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/* Apply column interchanges. */
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for (j = *n - 1; j >= 1; --j) {
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jp = ipiv[j];
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if (jp != j) {
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dswap_(n, &a[j * a_dim1 + 1], &c__1, &a[jp * a_dim1 + 1], &c__1);
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}
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/* L60: */
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}
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work[1] = (doublereal) iws;
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return 0;
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/* End of DGETRI */
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} /* dgetri_ */
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