/* ztrsm.f -- translated by f2c (version 20061008).
You must link the resulting object file with libf2c:
on Microsoft Windows system, link with libf2c.lib;
on Linux or Unix systems, link with .../path/to/libf2c.a -lm
or, if you install libf2c.a in a standard place, with -lf2c -lm
-- in that order, at the end of the command line, as in
cc *.o -lf2c -lm
Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
http://www.netlib.org/f2c/libf2c.zip
*/
#include "f2c.h"
#include "blaswrap.h"
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
/* Subroutine */ int ztrsm_(char *side, char *uplo, char *transa, char *diag,
integer *m, integer *n, doublecomplex *alpha, doublecomplex *a,
integer *lda, doublecomplex *b, integer *ldb)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3, i__4, i__5,
i__6, i__7;
doublecomplex z__1, z__2, z__3;
/* Builtin functions */
void z_div(doublecomplex *, doublecomplex *, doublecomplex *), d_cnjg(
doublecomplex *, doublecomplex *);
/* Local variables */
integer i__, j, k, info;
doublecomplex temp;
logical lside;
extern logical lsame_(char *, char *);
integer nrowa;
logical upper;
extern /* Subroutine */ int xerbla_(char *, integer *);
logical noconj, nounit;
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* ZTRSM 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' or op( A ) = conjg( A' ). */
/* The matrix X is overwritten on B. */
/* Arguments */
/* ========== */
/* 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 ) = conjg( 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 - COMPLEX*16 . */
/* 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 - COMPLEX*16 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 - COMPLEX*16 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. */
/* .. 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;
}
noconj = lsame_(transa, "T");
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_("ZTRSM ", &info);
return 0;
}
/* Quick return if possible. */
if (*m == 0 || *n == 0) {
return 0;
}
/* And when alpha.eq.zero. */
if (alpha->r == 0. && alpha->i == 0.) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
b[i__3].r = 0., b[i__3].i = 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->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L30: */
}
}
for (k = *m; k >= 1; --k) {
i__2 = k + j * b_dim1;
if (b[i__2].r != 0. || b[i__2].i != 0.) {
if (nounit) {
i__2 = k + j * b_dim1;
z_div(&z__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
}
i__2 = k - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * b_dim1;
i__6 = i__ + k * a_dim1;
z__2.r = b[i__5].r * a[i__6].r - b[i__5].i *
a[i__6].i, z__2.i = b[i__5].r * a[
i__6].i + b[i__5].i * a[i__6].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L40: */
}
}
/* L50: */
}
/* L60: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L70: */
}
}
i__2 = *m;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * b_dim1;
if (b[i__3].r != 0. || b[i__3].i != 0.) {
if (nounit) {
i__3 = k + j * b_dim1;
z_div(&z__1, &b[k + j * b_dim1], &a[k + k *
a_dim1]);
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
}
i__3 = *m;
for (i__ = k + 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * b_dim1;
i__7 = i__ + k * a_dim1;
z__2.r = b[i__6].r * a[i__7].r - b[i__6].i *
a[i__7].i, z__2.i = b[i__6].r * a[
i__7].i + b[i__6].i * a[i__7].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L80: */
}
}
/* L90: */
}
/* L100: */
}
}
} else {
/* Form B := alpha*inv( A' )*B */
/* or B := alpha*inv( conjg( A' ) )*B. */
if (upper) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3].i,
z__1.i = alpha->r * b[i__3].i + alpha->i * b[
i__3].r;
temp.r = z__1.r, temp.i = z__1.i;
if (noconj) {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
i__4 = k + i__ * a_dim1;
i__5 = k + j * b_dim1;
z__2.r = a[i__4].r * b[i__5].r - a[i__4].i *
b[i__5].i, z__2.i = a[i__4].r * b[
i__5].i + a[i__4].i * b[i__5].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L110: */
}
if (nounit) {
z_div(&z__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__3 = i__ - 1;
for (k = 1; k <= i__3; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__4 = k + j * b_dim1;
z__2.r = z__3.r * b[i__4].r - z__3.i * b[i__4]
.i, z__2.i = z__3.r * b[i__4].i +
z__3.i * b[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L120: */
}
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__3 = i__ + j * b_dim1;
b[i__3].r = temp.r, b[i__3].i = temp.i;
/* L130: */
}
/* L140: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
for (i__ = *m; i__ >= 1; --i__) {
i__2 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__2].r - alpha->i * b[i__2].i,
z__1.i = alpha->r * b[i__2].i + alpha->i * b[
i__2].r;
temp.r = z__1.r, temp.i = z__1.i;
if (noconj) {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
i__3 = k + i__ * a_dim1;
i__4 = k + j * b_dim1;
z__2.r = a[i__3].r * b[i__4].r - a[i__3].i *
b[i__4].i, z__2.i = a[i__3].r * b[
i__4].i + a[i__3].i * b[i__4].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L150: */
}
if (nounit) {
z_div(&z__1, &temp, &a[i__ + i__ * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
} else {
i__2 = *m;
for (k = i__ + 1; k <= i__2; ++k) {
d_cnjg(&z__3, &a[k + i__ * a_dim1]);
i__3 = k + j * b_dim1;
z__2.r = z__3.r * b[i__3].r - z__3.i * b[i__3]
.i, z__2.i = z__3.r * b[i__3].i +
z__3.i * b[i__3].r;
z__1.r = temp.r - z__2.r, z__1.i = temp.i -
z__2.i;
temp.r = z__1.r, temp.i = z__1.i;
/* L160: */
}
if (nounit) {
d_cnjg(&z__2, &a[i__ + i__ * a_dim1]);
z_div(&z__1, &temp, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
}
i__2 = i__ + j * b_dim1;
b[i__2].r = temp.r, b[i__2].i = temp.i;
/* L170: */
}
/* L180: */
}
}
}
} 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->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L190: */
}
}
i__2 = j - 1;
for (k = 1; k <= i__2; ++k) {
i__3 = k + j * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = k + j * a_dim1;
i__7 = i__ + k * b_dim1;
z__2.r = a[i__6].r * b[i__7].r - a[i__6].i *
b[i__7].i, z__2.i = a[i__6].r * b[
i__7].i + a[i__6].i * b[i__7].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L200: */
}
}
/* L210: */
}
if (nounit) {
z_div(&z__1, &c_b1, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L220: */
}
}
/* L230: */
}
} else {
for (j = *n; j >= 1; --j) {
if (alpha->r != 1. || alpha->i != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, z__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L240: */
}
}
i__1 = *n;
for (k = j + 1; k <= i__1; ++k) {
i__2 = k + j * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = k + j * a_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = a[i__5].r * b[i__6].r - a[i__5].i *
b[i__6].i, z__2.i = a[i__5].r * b[
i__6].i + a[i__5].i * b[i__6].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L250: */
}
}
/* L260: */
}
if (nounit) {
z_div(&z__1, &c_b1, &a[j + j * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + j * b_dim1;
i__3 = i__ + j * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L270: */
}
}
/* L280: */
}
}
} else {
/* Form B := alpha*B*inv( A' ) */
/* or B := alpha*B*inv( conjg( A' ) ). */
if (upper) {
for (k = *n; k >= 1; --k) {
if (nounit) {
if (noconj) {
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z_div(&z__1, &c_b1, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__3].r - temp.i * b[i__3].i,
z__1.i = temp.r * b[i__3].i + temp.i * b[
i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L290: */
}
}
i__1 = k - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = j + k * a_dim1;
if (a[i__2].r != 0. || a[i__2].i != 0.) {
if (noconj) {
i__2 = j + k * a_dim1;
temp.r = a[i__2].r, temp.i = a[i__2].i;
} else {
d_cnjg(&z__1, &a[j + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * b_dim1;
i__4 = i__ + j * b_dim1;
i__5 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__5].r - temp.i * b[i__5]
.i, z__2.i = temp.r * b[i__5].i +
temp.i * b[i__5].r;
z__1.r = b[i__4].r - z__2.r, z__1.i = b[i__4]
.i - z__2.i;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L300: */
}
}
/* L310: */
}
if (alpha->r != 1. || alpha->i != 0.) {
i__1 = *m;
for (i__ = 1; i__ <= i__1; ++i__) {
i__2 = i__ + k * b_dim1;
i__3 = i__ + k * b_dim1;
z__1.r = alpha->r * b[i__3].r - alpha->i * b[i__3]
.i, z__1.i = alpha->r * b[i__3].i +
alpha->i * b[i__3].r;
b[i__2].r = z__1.r, b[i__2].i = z__1.i;
/* L320: */
}
}
/* L330: */
}
} else {
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
if (nounit) {
if (noconj) {
z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
} else {
d_cnjg(&z__2, &a[k + k * a_dim1]);
z_div(&z__1, &c_b1, &z__2);
temp.r = z__1.r, temp.i = z__1.i;
}
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
z__1.r = temp.r * b[i__4].r - temp.i * b[i__4].i,
z__1.i = temp.r * b[i__4].i + temp.i * b[
i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L340: */
}
}
i__2 = *n;
for (j = k + 1; j <= i__2; ++j) {
i__3 = j + k * a_dim1;
if (a[i__3].r != 0. || a[i__3].i != 0.) {
if (noconj) {
i__3 = j + k * a_dim1;
temp.r = a[i__3].r, temp.i = a[i__3].i;
} else {
d_cnjg(&z__1, &a[j + k * a_dim1]);
temp.r = z__1.r, temp.i = z__1.i;
}
i__3 = *m;
for (i__ = 1; i__ <= i__3; ++i__) {
i__4 = i__ + j * b_dim1;
i__5 = i__ + j * b_dim1;
i__6 = i__ + k * b_dim1;
z__2.r = temp.r * b[i__6].r - temp.i * b[i__6]
.i, z__2.i = temp.r * b[i__6].i +
temp.i * b[i__6].r;
z__1.r = b[i__5].r - z__2.r, z__1.i = b[i__5]
.i - z__2.i;
b[i__4].r = z__1.r, b[i__4].i = z__1.i;
/* L350: */
}
}
/* L360: */
}
if (alpha->r != 1. || alpha->i != 0.) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + k * b_dim1;
i__4 = i__ + k * b_dim1;
z__1.r = alpha->r * b[i__4].r - alpha->i * b[i__4]
.i, z__1.i = alpha->r * b[i__4].i +
alpha->i * b[i__4].r;
b[i__3].r = z__1.r, b[i__3].i = z__1.i;
/* L370: */
}
}
/* L380: */
}
}
}
}
return 0;
/* End of ZTRSM . */
} /* ztrsm_ */