441 lines
11 KiB
C
441 lines
11 KiB
C
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#include "clapack.h"
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/* Subroutine */ int dtrmm_(char *side, char *uplo, char *transa, char *diag,
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integer *m, integer *n, doublereal *alpha, doublereal *a, integer *
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lda, doublereal *b, integer *ldb)
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{
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/* System generated locals */
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integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
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/* Local variables */
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integer i__, j, k, info;
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doublereal temp;
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logical lside;
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extern logical lsame_(char *, char *);
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integer nrowa;
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logical upper;
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extern /* Subroutine */ int xerbla_(char *, integer *);
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logical nounit;
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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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/* DTRMM performs one of the matrix-matrix operations */
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/* B := alpha*op( A )*B, or B := alpha*B*op( A ), */
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/* where alpha is a scalar, B is an m by n matrix, A is a unit, or */
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/* non-unit, upper or lower triangular matrix and op( A ) is one of */
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/* op( A ) = A or op( A ) = A'. */
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/* Arguments */
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/* ========== */
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/* SIDE - CHARACTER*1. */
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/* On entry, SIDE specifies whether op( A ) multiplies B from */
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/* the left or right as follows: */
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/* SIDE = 'L' or 'l' B := alpha*op( A )*B. */
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/* SIDE = 'R' or 'r' B := alpha*B*op( A ). */
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/* Unchanged on exit. */
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/* UPLO - CHARACTER*1. */
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/* On entry, UPLO specifies whether the matrix A 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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/* TRANSA - CHARACTER*1. */
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/* On entry, TRANSA specifies the form of op( A ) to be used in */
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/* the matrix multiplication as follows: */
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/* TRANSA = 'N' or 'n' op( A ) = A. */
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/* TRANSA = 'T' or 't' op( A ) = A'. */
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/* TRANSA = 'C' or 'c' op( A ) = A'. */
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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 triangular */
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/* 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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/* M - INTEGER. */
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/* On entry, M specifies the number of rows of B. M must be at */
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/* least zero. */
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/* Unchanged on exit. */
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/* N - INTEGER. */
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/* On entry, N specifies the number of columns of B. N must be */
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/* at least zero. */
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/* Unchanged on exit. */
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/* ALPHA - DOUBLE PRECISION. */
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/* On entry, ALPHA specifies the scalar alpha. When alpha is */
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/* zero then A is not referenced and B need not be set before */
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/* entry. */
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/* Unchanged on exit. */
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/* A - DOUBLE PRECISION array of DIMENSION ( LDA, k ), where k is m */
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/* when SIDE = 'L' or 'l' and is n when SIDE = 'R' or 'r'. */
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/* Before entry with UPLO = 'U' or 'u', the leading k by k */
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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 k by k */
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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. When SIDE = 'L' or 'l' then */
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/* LDA must be at least max( 1, m ), when SIDE = 'R' or 'r' */
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/* then LDA must be at least max( 1, n ). */
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/* Unchanged on exit. */
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/* B - DOUBLE PRECISION array of DIMENSION ( LDB, n ). */
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/* Before entry, the leading m by n part of the array B must */
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/* contain the matrix B, and on exit is overwritten by the */
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/* transformed matrix. */
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/* LDB - INTEGER. */
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/* On entry, LDB specifies the first dimension of B as declared */
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/* in the calling (sub) program. LDB must be at least */
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/* max( 1, m ). */
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/* Unchanged on exit. */
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/* Level 3 Blas routine. */
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/* -- Written on 8-February-1989. */
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/* Jack Dongarra, Argonne National Laboratory. */
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/* Iain Duff, AERE Harwell. */
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/* Jeremy Du Croz, Numerical Algorithms Group Ltd. */
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/* Sven Hammarling, Numerical Algorithms Group Ltd. */
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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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/* .. Local Scalars .. */
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/* .. */
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/* .. Parameters .. */
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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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b_dim1 = *ldb;
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b_offset = 1 + b_dim1;
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b -= b_offset;
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/* Function Body */
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lside = lsame_(side, "L");
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if (lside) {
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nrowa = *m;
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} else {
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nrowa = *n;
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}
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nounit = lsame_(diag, "N");
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upper = lsame_(uplo, "U");
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info = 0;
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if (! lside && ! lsame_(side, "R")) {
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info = 1;
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} else if (! upper && ! lsame_(uplo, "L")) {
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info = 2;
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} else if (! lsame_(transa, "N") && ! lsame_(transa,
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"T") && ! lsame_(transa, "C")) {
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info = 3;
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} else if (! lsame_(diag, "U") && ! lsame_(diag,
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"N")) {
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info = 4;
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} else if (*m < 0) {
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info = 5;
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} else if (*n < 0) {
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info = 6;
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} else if (*lda < max(1,nrowa)) {
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info = 9;
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} else if (*ldb < max(1,*m)) {
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info = 11;
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}
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if (info != 0) {
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xerbla_("DTRMM ", &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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/* And when alpha.eq.zero. */
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if (*alpha == 0.) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = 0.;
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/* L10: */
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}
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/* L20: */
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}
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return 0;
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}
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/* Start the operations. */
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if (lside) {
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if (lsame_(transa, "N")) {
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/* Form B := alpha*A*B. */
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if (upper) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (k = 1; k <= i__2; ++k) {
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if (b[k + j * b_dim1] != 0.) {
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temp = *alpha * b[k + j * b_dim1];
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i__3 = k - 1;
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for (i__ = 1; i__ <= i__3; ++i__) {
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b[i__ + j * b_dim1] += temp * a[i__ + k *
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a_dim1];
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/* L30: */
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}
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if (nounit) {
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temp *= a[k + k * a_dim1];
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}
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b[k + j * b_dim1] = temp;
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}
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/* L40: */
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}
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/* L50: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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for (k = *m; k >= 1; --k) {
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if (b[k + j * b_dim1] != 0.) {
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temp = *alpha * b[k + j * b_dim1];
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b[k + j * b_dim1] = temp;
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if (nounit) {
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b[k + j * b_dim1] *= a[k + k * a_dim1];
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}
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i__2 = *m;
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for (i__ = k + 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] += temp * a[i__ + k *
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a_dim1];
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/* L60: */
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}
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}
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/* L70: */
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}
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/* L80: */
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}
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}
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} else {
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/* Form B := alpha*A'*B. */
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if (upper) {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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for (i__ = *m; i__ >= 1; --i__) {
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temp = b[i__ + j * b_dim1];
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if (nounit) {
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temp *= a[i__ + i__ * a_dim1];
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}
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i__2 = i__ - 1;
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for (k = 1; k <= i__2; ++k) {
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temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
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/* L90: */
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}
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b[i__ + j * b_dim1] = *alpha * temp;
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/* L100: */
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}
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/* L110: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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temp = b[i__ + j * b_dim1];
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if (nounit) {
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temp *= a[i__ + i__ * a_dim1];
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}
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i__3 = *m;
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for (k = i__ + 1; k <= i__3; ++k) {
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temp += a[k + i__ * a_dim1] * b[k + j * b_dim1];
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/* L120: */
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}
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b[i__ + j * b_dim1] = *alpha * temp;
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/* L130: */
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}
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/* L140: */
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}
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}
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}
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} else {
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if (lsame_(transa, "N")) {
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/* Form B := alpha*B*A. */
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if (upper) {
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for (j = *n; j >= 1; --j) {
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temp = *alpha;
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if (nounit) {
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temp *= a[j + j * a_dim1];
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}
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i__1 = *m;
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for (i__ = 1; i__ <= i__1; ++i__) {
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b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
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/* L150: */
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}
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i__1 = j - 1;
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for (k = 1; k <= i__1; ++k) {
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if (a[k + j * a_dim1] != 0.) {
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temp = *alpha * a[k + j * a_dim1];
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] += temp * b[i__ + k *
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b_dim1];
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/* L160: */
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}
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}
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/* L170: */
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}
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/* L180: */
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}
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} else {
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i__1 = *n;
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for (j = 1; j <= i__1; ++j) {
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temp = *alpha;
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if (nounit) {
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temp *= a[j + j * a_dim1];
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}
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i__2 = *m;
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for (i__ = 1; i__ <= i__2; ++i__) {
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b[i__ + j * b_dim1] = temp * b[i__ + j * b_dim1];
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/* L190: */
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}
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i__2 = *n;
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for (k = j + 1; k <= i__2; ++k) {
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if (a[k + j * a_dim1] != 0.) {
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temp = *alpha * a[k + j * a_dim1];
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i__3 = *m;
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for (i__ = 1; i__ <= i__3; ++i__) {
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b[i__ + j * b_dim1] += temp * b[i__ + k *
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b_dim1];
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/* L200: */
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}
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}
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/* L210: */
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}
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/* L220: */
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}
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}
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} else {
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/* Form B := alpha*B*A'. */
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if (upper) {
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||
|
|
i__1 = *n;
|
||
|
|
for (k = 1; k <= i__1; ++k) {
|
||
|
|
i__2 = k - 1;
|
||
|
|
for (j = 1; j <= i__2; ++j) {
|
||
|
|
if (a[j + k * a_dim1] != 0.) {
|
||
|
|
temp = *alpha * a[j + k * a_dim1];
|
||
|
|
i__3 = *m;
|
||
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
||
|
|
b[i__ + j * b_dim1] += temp * b[i__ + k *
|
||
|
|
b_dim1];
|
||
|
|
/* L230: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L240: */
|
||
|
|
}
|
||
|
|
temp = *alpha;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[k + k * a_dim1];
|
||
|
|
}
|
||
|
|
if (temp != 1.) {
|
||
|
|
i__2 = *m;
|
||
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
||
|
|
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
|
||
|
|
/* L250: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L260: */
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
for (k = *n; k >= 1; --k) {
|
||
|
|
i__1 = *n;
|
||
|
|
for (j = k + 1; j <= i__1; ++j) {
|
||
|
|
if (a[j + k * a_dim1] != 0.) {
|
||
|
|
temp = *alpha * a[j + k * a_dim1];
|
||
|
|
i__2 = *m;
|
||
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
||
|
|
b[i__ + j * b_dim1] += temp * b[i__ + k *
|
||
|
|
b_dim1];
|
||
|
|
/* L270: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L280: */
|
||
|
|
}
|
||
|
|
temp = *alpha;
|
||
|
|
if (nounit) {
|
||
|
|
temp *= a[k + k * a_dim1];
|
||
|
|
}
|
||
|
|
if (temp != 1.) {
|
||
|
|
i__1 = *m;
|
||
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
||
|
|
b[i__ + k * b_dim1] = temp * b[i__ + k * b_dim1];
|
||
|
|
/* L290: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
/* L300: */
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
return 0;
|
||
|
|
|
||
|
|
/* End of DTRMM . */
|
||
|
|
|
||
|
|
} /* dtrmm_ */
|