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