412 lines
13 KiB
C++
412 lines
13 KiB
C++
/* fortran/dtrsv.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* > \brief \b DTRSV */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DTRSV(UPLO,TRANS,DIAG,N,A,LDA,X,INCX) */
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/* .. Scalar Arguments .. */
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/* INTEGER INCX,LDA,N */
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/* CHARACTER DIAG,TRANS,UPLO */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION A(LDA,*),X(*) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DTRSV solves one of the systems of equations */
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/* > */
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/* > A*x = b, or A**T*x = b, */
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/* > */
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/* > where b and x are n element vectors and A is an n by n unit, or */
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/* > non-unit, upper or lower triangular matrix. */
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/* > */
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/* > No test for singularity or near-singularity is included in this */
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/* > routine. Such tests must be performed before calling this routine. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > On entry, UPLO specifies whether the matrix is an upper or */
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/* > lower triangular matrix as follows: */
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/* > */
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/* > UPLO = 'U' or 'u' A is an upper triangular matrix. */
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/* > */
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/* > UPLO = 'L' or 'l' A is a lower triangular matrix. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] TRANS */
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/* > \verbatim */
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/* > TRANS is CHARACTER*1 */
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/* > On entry, TRANS specifies the equations to be solved as */
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/* > follows: */
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/* > */
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/* > TRANS = 'N' or 'n' A*x = b. */
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/* > */
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/* > TRANS = 'T' or 't' A**T*x = b. */
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/* > */
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/* > TRANS = 'C' or 'c' A**T*x = b. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] DIAG */
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/* > \verbatim */
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/* > DIAG is CHARACTER*1 */
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/* > On entry, DIAG specifies whether or not A is unit */
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/* > triangular as follows: */
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/* > */
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/* > DIAG = 'U' or 'u' A is assumed to be unit triangular. */
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/* > */
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/* > DIAG = 'N' or 'n' A is not assumed to be unit */
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/* > triangular. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > On entry, N specifies the order of the matrix A. */
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/* > N must be at least zero. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension ( LDA, N ) */
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/* > Before entry with UPLO = 'U' or 'u', the leading n by n */
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/* > upper triangular part of the array A must contain the upper */
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/* > triangular matrix and the strictly lower triangular part of */
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/* > A is not referenced. */
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/* > Before entry with UPLO = 'L' or 'l', the leading n by n */
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/* > lower triangular part of the array A must contain the lower */
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/* > triangular matrix and the strictly upper triangular part of */
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/* > A is not referenced. */
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/* > Note that when DIAG = 'U' or 'u', the diagonal elements of */
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/* > A are not referenced either, but are assumed to be unity. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > On entry, LDA specifies the first dimension of A as declared */
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/* > in the calling (sub) program. LDA must be at least */
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/* > max( 1, n ). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] X */
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/* > \verbatim */
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/* > X is DOUBLE PRECISION array, dimension at least */
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/* > ( 1 + ( n - 1 )*abs( INCX ) ). */
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/* > Before entry, the incremented array X must contain the n */
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/* > element right-hand side vector b. On exit, X is overwritten */
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/* > with the solution vector x. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] INCX */
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/* > \verbatim */
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/* > INCX is INTEGER */
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/* > On entry, INCX specifies the increment for the elements of */
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/* > X. INCX must not be zero. */
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/* > */
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/* > Level 2 Blas routine. */
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/* > */
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/* > -- Written on 22-October-1986. */
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/* > Jack Dongarra, Argonne National Lab. */
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/* > Jeremy Du Croz, Nag Central Office. */
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/* > Sven Hammarling, Nag Central Office. */
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/* > Richard Hanson, Sandia National Labs. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup double_blas_level1 */
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/* ===================================================================== */
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/* Subroutine */ int dtrsv_(char *uplo, char *trans, char *diag, integer *n,
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doublereal *a, integer *lda, doublereal *x, integer *incx, ftnlen
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uplo_len, ftnlen trans_len, ftnlen diag_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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/* Local variables */
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integer i__, j, ix, jx, kx, info;
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doublereal temp;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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logical nounit;
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/* -- Reference BLAS level1 routine -- */
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/* -- Reference BLAS is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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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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/* 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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--x;
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/* Function Body */
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info = 0;
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if (! lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(uplo, (char *)"L", (
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ftnlen)1, (ftnlen)1)) {
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info = 1;
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} else if (! lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1) && ! lsame_(trans,
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(char *)"T", (ftnlen)1, (ftnlen)1) && ! lsame_(trans, (char *)"C", (ftnlen)1, (
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ftnlen)1)) {
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info = 2;
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} else if (! lsame_(diag, (char *)"U", (ftnlen)1, (ftnlen)1) && ! lsame_(diag,
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(char *)"N", (ftnlen)1, (ftnlen)1)) {
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info = 3;
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} else if (*n < 0) {
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info = 4;
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} else if (*lda < max(1,*n)) {
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info = 6;
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} else if (*incx == 0) {
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info = 8;
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}
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if (info != 0) {
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xerbla_((char *)"DTRSV ", &info, (ftnlen)6);
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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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nounit = lsame_(diag, (char *)"N", (ftnlen)1, (ftnlen)1);
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/* Set up the start point in X if the increment is not unity. This */
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/* will be ( N - 1 )*INCX too small for descending loops. */
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if (*incx <= 0) {
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kx = 1 - (*n - 1) * *incx;
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} else if (*incx != 1) {
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kx = 1;
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}
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/* Start the operations. In this version the elements of A are */
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/* accessed sequentially with one pass through A. */
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if (lsame_(trans, (char *)"N", (ftnlen)1, (ftnlen)1)) {
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/* Form x := inv( A )*x. */
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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if (x[j] != 0.) {
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if (nounit) {
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x[j] /= a[j + j * a_dim1];
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}
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temp = x[j];
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for (i__ = j - 1; i__ >= 1; --i__) {
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x[i__] -= temp * a[i__ + j * a_dim1];
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/* L10: */
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}
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}
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/* L20: */
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}
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} else {
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jx = kx + (*n - 1) * *incx;
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for (j = *n; j >= 1; --j) {
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if (x[jx] != 0.) {
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if (nounit) {
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x[jx] /= a[j + j * a_dim1];
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}
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temp = x[jx];
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ix = jx;
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for (i__ = j - 1; i__ >= 1; --i__) {
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ix -= *incx;
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x[ix] -= temp * a[i__ + j * a_dim1];
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/* L30: */
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}
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}
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jx -= *incx;
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/* L40: */
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}
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}
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} else {
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if (*incx == 1) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (x[j] != 0.) {
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if (nounit) {
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x[j] /= a[j + j * a_dim1];
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}
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temp = x[j];
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i__2 = *n;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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x[i__] -= temp * a[i__ + j * a_dim1];
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/* L50: */
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}
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}
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/* L60: */
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}
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} else {
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jx = kx;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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if (x[jx] != 0.) {
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if (nounit) {
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x[jx] /= a[j + j * a_dim1];
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}
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temp = x[jx];
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ix = jx;
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i__2 = *n;
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for (i__ = j + 1; i__ <= i__2; ++i__) {
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ix += *incx;
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x[ix] -= temp * a[i__ + j * a_dim1];
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/* L70: */
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}
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}
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jx += *incx;
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/* L80: */
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}
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}
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}
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} else {
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/* Form x := inv( A**T )*x. */
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if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) {
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if (*incx == 1) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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temp = x[j];
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp -= a[i__ + j * a_dim1] * x[i__];
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/* L90: */
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}
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if (nounit) {
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temp /= a[j + j * a_dim1];
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}
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x[j] = temp;
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/* L100: */
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}
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} else {
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jx = kx;
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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temp = x[jx];
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ix = kx;
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i__2 = j - 1;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp -= a[i__ + j * a_dim1] * x[ix];
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ix += *incx;
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/* L110: */
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}
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if (nounit) {
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temp /= a[j + j * a_dim1];
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}
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x[jx] = temp;
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jx += *incx;
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/* L120: */
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}
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}
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} else {
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if (*incx == 1) {
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for (j = *n; j >= 1; --j) {
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temp = x[j];
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i__1 = j + 1;
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for (i__ = *n; i__ >= i__1; --i__) {
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temp -= a[i__ + j * a_dim1] * x[i__];
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/* L130: */
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}
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if (nounit) {
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temp /= a[j + j * a_dim1];
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}
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x[j] = temp;
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/* L140: */
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}
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} else {
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kx += (*n - 1) * *incx;
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jx = kx;
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for (j = *n; j >= 1; --j) {
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temp = x[jx];
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ix = kx;
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i__1 = j + 1;
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for (i__ = *n; i__ >= i__1; --i__) {
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temp -= a[i__ + j * a_dim1] * x[ix];
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ix -= *incx;
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/* L150: */
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}
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if (nounit) {
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temp /= a[j + j * a_dim1];
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}
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x[jx] = temp;
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jx -= *incx;
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/* L160: */
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}
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}
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}
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}
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return 0;
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/* End of DTRSV */
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} /* dtrsv_ */
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#ifdef __cplusplus
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}
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#endif
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