You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
405 lines
11 KiB
405 lines
11 KiB
#include "blaswrap.h"
|
|
#include "f2c.h"
|
|
|
|
/* Subroutine */ int dtrsm_(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 */
|
|
static integer info;
|
|
static doublereal temp;
|
|
static integer i__, j, k;
|
|
static logical lside;
|
|
extern logical lsame_(char *, char *);
|
|
static integer nrowa;
|
|
static logical upper;
|
|
extern /* Subroutine */ int xerbla_(char *, integer *);
|
|
static logical nounit;
|
|
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
|
|
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
|
|
/* Purpose
|
|
=======
|
|
DTRSM solves one of the matrix equations
|
|
op( A )*X = alpha*B, or X*op( A ) = alpha*B,
|
|
where alpha is a scalar, X and B are m by n matrices, 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'.
|
|
The matrix X is overwritten on B.
|
|
Parameters
|
|
==========
|
|
SIDE - CHARACTER*1.
|
|
On entry, SIDE specifies whether op( A ) appears on the left
|
|
or right of X as follows:
|
|
SIDE = 'L' or 'l' op( A )*X = alpha*B.
|
|
SIDE = 'R' or 'r' X*op( A ) = alpha*B.
|
|
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 right-hand side matrix B, and on exit is
|
|
overwritten by the solution matrix X.
|
|
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.
|
|
Test the input parameters.
|
|
Parameter adjustments */
|
|
a_dim1 = *lda;
|
|
a_offset = 1 + a_dim1 * 1;
|
|
a -= a_offset;
|
|
b_dim1 = *ldb;
|
|
b_offset = 1 + b_dim1 * 1;
|
|
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_("DTRSM ", &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_ref(i__, j) = 0.;
|
|
/* L10: */
|
|
}
|
|
/* L20: */
|
|
}
|
|
return 0;
|
|
}
|
|
/* Start the operations. */
|
|
if (lside) {
|
|
if (lsame_(transa, "N")) {
|
|
/* Form B := alpha*inv( A )*B. */
|
|
if (upper) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (*alpha != 1.) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = *alpha * b_ref(i__, j);
|
|
/* L30: */
|
|
}
|
|
}
|
|
for (k = *m; k >= 1; --k) {
|
|
if (b_ref(k, j) != 0.) {
|
|
if (nounit) {
|
|
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
|
|
}
|
|
i__2 = k - 1;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
|
|
a_ref(i__, k);
|
|
/* L40: */
|
|
}
|
|
}
|
|
/* L50: */
|
|
}
|
|
/* L60: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (*alpha != 1.) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = *alpha * b_ref(i__, j);
|
|
/* L70: */
|
|
}
|
|
}
|
|
i__2 = *m;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
if (b_ref(k, j) != 0.) {
|
|
if (nounit) {
|
|
b_ref(k, j) = b_ref(k, j) / a_ref(k, k);
|
|
}
|
|
i__3 = *m;
|
|
for (i__ = k + 1; i__ <= i__3; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - b_ref(k, j) *
|
|
a_ref(i__, k);
|
|
/* L80: */
|
|
}
|
|
}
|
|
/* L90: */
|
|
}
|
|
/* L100: */
|
|
}
|
|
}
|
|
} else {
|
|
/* Form B := alpha*inv( A' )*B. */
|
|
if (upper) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
temp = *alpha * b_ref(i__, j);
|
|
i__3 = i__ - 1;
|
|
for (k = 1; k <= i__3; ++k) {
|
|
temp -= a_ref(k, i__) * b_ref(k, j);
|
|
/* L110: */
|
|
}
|
|
if (nounit) {
|
|
temp /= a_ref(i__, i__);
|
|
}
|
|
b_ref(i__, j) = temp;
|
|
/* L120: */
|
|
}
|
|
/* L130: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
for (i__ = *m; i__ >= 1; --i__) {
|
|
temp = *alpha * b_ref(i__, j);
|
|
i__2 = *m;
|
|
for (k = i__ + 1; k <= i__2; ++k) {
|
|
temp -= a_ref(k, i__) * b_ref(k, j);
|
|
/* L140: */
|
|
}
|
|
if (nounit) {
|
|
temp /= a_ref(i__, i__);
|
|
}
|
|
b_ref(i__, j) = temp;
|
|
/* L150: */
|
|
}
|
|
/* L160: */
|
|
}
|
|
}
|
|
}
|
|
} else {
|
|
if (lsame_(transa, "N")) {
|
|
/* Form B := alpha*B*inv( A ). */
|
|
if (upper) {
|
|
i__1 = *n;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (*alpha != 1.) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = *alpha * b_ref(i__, j);
|
|
/* L170: */
|
|
}
|
|
}
|
|
i__2 = j - 1;
|
|
for (k = 1; k <= i__2; ++k) {
|
|
if (a_ref(k, j) != 0.) {
|
|
i__3 = *m;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
|
|
b_ref(i__, k);
|
|
/* L180: */
|
|
}
|
|
}
|
|
/* L190: */
|
|
}
|
|
if (nounit) {
|
|
temp = 1. / a_ref(j, j);
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = temp * b_ref(i__, j);
|
|
/* L200: */
|
|
}
|
|
}
|
|
/* L210: */
|
|
}
|
|
} else {
|
|
for (j = *n; j >= 1; --j) {
|
|
if (*alpha != 1.) {
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
b_ref(i__, j) = *alpha * b_ref(i__, j);
|
|
/* L220: */
|
|
}
|
|
}
|
|
i__1 = *n;
|
|
for (k = j + 1; k <= i__1; ++k) {
|
|
if (a_ref(k, j) != 0.) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - a_ref(k, j) *
|
|
b_ref(i__, k);
|
|
/* L230: */
|
|
}
|
|
}
|
|
/* L240: */
|
|
}
|
|
if (nounit) {
|
|
temp = 1. / a_ref(j, j);
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
b_ref(i__, j) = temp * b_ref(i__, j);
|
|
/* L250: */
|
|
}
|
|
}
|
|
/* L260: */
|
|
}
|
|
}
|
|
} else {
|
|
/* Form B := alpha*B*inv( A' ). */
|
|
if (upper) {
|
|
for (k = *n; k >= 1; --k) {
|
|
if (nounit) {
|
|
temp = 1. / a_ref(k, k);
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
b_ref(i__, k) = temp * b_ref(i__, k);
|
|
/* L270: */
|
|
}
|
|
}
|
|
i__1 = k - 1;
|
|
for (j = 1; j <= i__1; ++j) {
|
|
if (a_ref(j, k) != 0.) {
|
|
temp = a_ref(j, k);
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
|
|
i__, k);
|
|
/* L280: */
|
|
}
|
|
}
|
|
/* L290: */
|
|
}
|
|
if (*alpha != 1.) {
|
|
i__1 = *m;
|
|
for (i__ = 1; i__ <= i__1; ++i__) {
|
|
b_ref(i__, k) = *alpha * b_ref(i__, k);
|
|
/* L300: */
|
|
}
|
|
}
|
|
/* L310: */
|
|
}
|
|
} else {
|
|
i__1 = *n;
|
|
for (k = 1; k <= i__1; ++k) {
|
|
if (nounit) {
|
|
temp = 1. / a_ref(k, k);
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, k) = temp * b_ref(i__, k);
|
|
/* L320: */
|
|
}
|
|
}
|
|
i__2 = *n;
|
|
for (j = k + 1; j <= i__2; ++j) {
|
|
if (a_ref(j, k) != 0.) {
|
|
temp = a_ref(j, k);
|
|
i__3 = *m;
|
|
for (i__ = 1; i__ <= i__3; ++i__) {
|
|
b_ref(i__, j) = b_ref(i__, j) - temp * b_ref(
|
|
i__, k);
|
|
/* L330: */
|
|
}
|
|
}
|
|
/* L340: */
|
|
}
|
|
if (*alpha != 1.) {
|
|
i__2 = *m;
|
|
for (i__ = 1; i__ <= i__2; ++i__) {
|
|
b_ref(i__, k) = *alpha * b_ref(i__, k);
|
|
/* L350: */
|
|
}
|
|
}
|
|
/* L360: */
|
|
}
|
|
}
|
|
}
|
|
}
|
|
return 0;
|
|
/* End of DTRSM . */
|
|
} /* dtrsm_ */
|
|
#undef b_ref
|
|
#undef a_ref
|
|
|