225 lines
6.2 KiB
C
225 lines
6.2 KiB
C
#include "blaswrap.h"
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#ifdef _cpluscplus
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extern "C" {
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#endif
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#include "f2c.h"
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/* Subroutine */ int dtrtri_(char *uplo, char *diag, integer *n, doublereal *
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a, integer *lda, integer *info)
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{
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/* -- LAPACK routine (version 3.0) --
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Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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Courant Institute, Argonne National Lab, and Rice University
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March 31, 1993
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Purpose
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=======
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DTRTRI computes the inverse of a real upper or lower triangular
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matrix A.
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This is the Level 3 BLAS version of the algorithm.
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Arguments
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=========
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UPLO (input) CHARACTER*1
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= 'U': A is upper triangular;
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= 'L': A is lower triangular.
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DIAG (input) CHARACTER*1
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= 'N': A is non-unit triangular;
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= 'U': A is unit triangular.
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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 triangular matrix A. If UPLO = 'U', the
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leading N-by-N upper triangular part of the array A contains
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the upper triangular matrix, and the strictly lower
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triangular part of A is not referenced. If UPLO = 'L', the
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leading N-by-N lower triangular part of the array A contains
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the lower triangular matrix, and the strictly upper
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triangular part of A is not referenced. If DIAG = 'U', the
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diagonal elements of A are also not referenced and are
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assumed to be 1.
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On exit, the (triangular) inverse of the original matrix, in
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the same storage format.
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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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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, A(i,i) is exactly zero. The triangular
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matrix is singular and its inverse can not be computed.
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=====================================================================
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Test the input parameters.
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Parameter adjustments */
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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_b18 = 1.;
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static doublereal c_b22 = -1.;
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/* System generated locals */
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address a__1[2];
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integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5;
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char ch__1[2];
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/* Builtin functions
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Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);
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/* Local variables */
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static integer j;
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extern logical lsame_(char *, char *);
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extern /* Subroutine */ int dtrmm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *), dtrsm_(
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char *, char *, char *, char *, integer *, integer *, doublereal *
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, doublereal *, integer *, doublereal *, integer *);
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static logical upper;
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extern /* Subroutine */ int dtrti2_(char *, char *, integer *, doublereal
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*, integer *, integer *);
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static integer jb, nb, nn;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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extern integer ilaenv_(integer *, char *, char *, integer *, integer *,
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integer *, integer *, ftnlen, ftnlen);
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static logical nounit;
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#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
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a_dim1 = *lda;
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a_offset = 1 + a_dim1 * 1;
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a -= a_offset;
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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, "U");
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nounit = lsame_(diag, "N");
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if (! upper && ! lsame_(uplo, "L")) {
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*info = -1;
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} else if (! nounit && ! lsame_(diag, "U")) {
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*info = -2;
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} else if (*n < 0) {
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*info = -3;
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} else if (*lda < max(1,*n)) {
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*info = -5;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_("DTRTRI", &i__1);
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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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/* Check for singularity if non-unit. */
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if (nounit) {
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i__1 = *n;
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for (*info = 1; *info <= i__1; ++(*info)) {
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if (a_ref(*info, *info) == 0.) {
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return 0;
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}
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/* L10: */
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}
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*info = 0;
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}
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/* Determine the block size for this environment.
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Writing concatenation */
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i__2[0] = 1, a__1[0] = uplo;
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i__2[1] = 1, a__1[1] = diag;
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s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
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nb = ilaenv_(&c__1, "DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
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ftnlen)2);
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if (nb <= 1 || nb >= *n) {
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/* Use unblocked code */
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dtrti2_(uplo, diag, n, &a[a_offset], lda, info);
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} else {
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/* Use blocked code */
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if (upper) {
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/* Compute inverse of upper triangular matrix */
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i__1 = *n;
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i__3 = nb;
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for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
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/* Computing MIN */
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i__4 = nb, i__5 = *n - j + 1;
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jb = min(i__4,i__5);
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/* Compute rows 1:j-1 of current block column */
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i__4 = j - 1;
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dtrmm_("Left", "Upper", "No transpose", diag, &i__4, &jb, &
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c_b18, &a[a_offset], lda, &a_ref(1, j), lda);
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i__4 = j - 1;
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dtrsm_("Right", "Upper", "No transpose", diag, &i__4, &jb, &
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c_b22, &a_ref(j, j), lda, &a_ref(1, j), lda);
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/* Compute inverse of current diagonal block */
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dtrti2_("Upper", diag, &jb, &a_ref(j, j), lda, info);
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/* L20: */
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}
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} else {
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/* Compute inverse of lower triangular matrix */
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nn = (*n - 1) / nb * nb + 1;
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i__3 = -nb;
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for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) {
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/* Computing MIN */
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i__1 = nb, i__4 = *n - j + 1;
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jb = min(i__1,i__4);
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if (j + jb <= *n) {
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/* Compute rows j+jb:n of current block column */
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i__1 = *n - j - jb + 1;
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dtrmm_("Left", "Lower", "No transpose", diag, &i__1, &jb,
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&c_b18, &a_ref(j + jb, j + jb), lda, &a_ref(j +
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jb, j), lda);
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i__1 = *n - j - jb + 1;
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dtrsm_("Right", "Lower", "No transpose", diag, &i__1, &jb,
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&c_b22, &a_ref(j, j), lda, &a_ref(j + jb, j),
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lda);
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}
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/* Compute inverse of current diagonal block */
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dtrti2_("Lower", diag, &jb, &a_ref(j, j), lda, info);
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/* L30: */
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}
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}
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}
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return 0;
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/* End of DTRTRI */
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} /* dtrtri_ */
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#undef a_ref
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#ifdef _cpluscplus
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}
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#endif
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