285 lines
7.7 KiB
C
285 lines
7.7 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 dtrsv_(char *uplo, char *trans, char *diag, integer *n,
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doublereal *a, integer *lda, doublereal *x, integer *incx)
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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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static integer info;
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static doublereal temp;
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static integer i__, j;
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extern logical lsame_(char *, char *);
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static integer ix, jx, kx;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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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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/* Purpose
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=======
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DTRSV solves one of the systems of equations
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A*x = b, or A'*x = b,
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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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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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Parameters
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==========
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UPLO - 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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UPLO = 'U' or 'u' A is an upper triangular matrix.
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UPLO = 'L' or 'l' A is a lower triangular matrix.
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Unchanged on exit.
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TRANS - 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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TRANS = 'N' or 'n' A*x = b.
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TRANS = 'T' or 't' A'*x = b.
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TRANS = 'C' or 'c' A'*x = b.
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Unchanged on exit.
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DIAG - 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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DIAG = 'U' or 'u' A is assumed to be unit triangular.
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DIAG = 'N' or 'n' A is not assumed to be unit
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triangular.
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Unchanged on exit.
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N - 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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Unchanged on exit.
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A - DOUBLE PRECISION array of 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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Unchanged on exit.
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LDA - 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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Unchanged on exit.
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X - DOUBLE PRECISION array of 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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INCX - 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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Unchanged on exit.
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Level 2 Blas routine.
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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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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 * 1;
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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, "U") && ! lsame_(uplo, "L")) {
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info = 1;
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} else if (! lsame_(trans, "N") && ! lsame_(trans,
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"T") && ! lsame_(trans, "C")) {
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info = 2;
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} else if (! lsame_(diag, "U") && ! lsame_(diag,
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"N")) {
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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_("DTRSV ", &info);
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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, "N");
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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, "N")) {
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/* Form x := inv( A )*x. */
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if (lsame_(uplo, "U")) {
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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_ref(j, j);
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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_ref(i__, j);
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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_ref(j, j);
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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_ref(i__, j);
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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_ref(j, j);
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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_ref(i__, j);
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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_ref(j, j);
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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_ref(i__, j);
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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' )*x. */
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if (lsame_(uplo, "U")) {
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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_ref(i__, j) * x[i__];
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/* L90: */
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}
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if (nounit) {
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temp /= a_ref(j, j);
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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_ref(i__, j) * 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_ref(j, j);
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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_ref(i__, j) * x[i__];
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/* L130: */
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}
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if (nounit) {
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temp /= a_ref(j, j);
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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_ref(i__, j) * 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_ref(j, j);
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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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#undef a_ref
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#ifdef _cpluscplus
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}
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#endif
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