zlarfb.c
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C
736 行
#include "f2c.h"
/* Subroutine */ int zlarfb_(char *side, char *trans, char *direct, char *
storev, integer *m, integer *n, integer *k, doublecomplex *v, integer
*ldv, doublecomplex *t, integer *ldt, doublecomplex *c, integer *ldc,
doublecomplex *work, integer *ldwork)
{
/* -- LAPACK auxiliary routine (version 2.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
September 30, 1994
Purpose
=======
ZLARFB applies a complex block reflector H or its transpose H' to a
complex M-by-N matrix C, from either the left or the right.
Arguments
=========
SIDE (input) CHARACTER*1
= 'L': apply H or H' from the Left
= 'R': apply H or H' from the Right
TRANS (input) CHARACTER*1
= 'N': apply H (No transpose)
= 'C': apply H' (Conjugate transpose)
DIRECT (input) CHARACTER*1
Indicates how H is formed from a product of elementary
reflectors
= 'F': H = H(1) H(2) . . . H(k) (Forward)
= 'B': H = H(k) . . . H(2) H(1) (Backward)
STOREV (input) CHARACTER*1
Indicates how the vectors which define the elementary
reflectors are stored:
= 'C': Columnwise
= 'R': Rowwise
M (input) INTEGER
The number of rows of the matrix C.
N (input) INTEGER
The number of columns of the matrix C.
K (input) INTEGER
The order of the matrix T (= the number of elementary
reflectors whose product defines the block reflector).
V (input) COMPLEX*16 array, dimension
(LDV,K) if STOREV = 'C'
(LDV,M) if STOREV = 'R' and SIDE = 'L'
(LDV,N) if STOREV = 'R' and SIDE = 'R'
The matrix V. See further details.
LDV (input) INTEGER
The leading dimension of the array V.
If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
if STOREV = 'R', LDV >= K.
T (input) COMPLEX*16 array, dimension (LDT,K)
The triangular K-by-K matrix T in the representation of the
block reflector.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= K.
C (input/output) COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by H*C or H'*C or C*H or C*H'.
LDC (input) INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK (workspace) COMPLEX*16 array, dimension (LDWORK,K)
LDWORK (input) INTEGER
The leading dimension of the array WORK.
If SIDE = 'L', LDWORK >= max(1,N);
if SIDE = 'R', LDWORK >= max(1,M).
=====================================================================
Quick return if possible
Parameter adjustments
Function Body */
/* Table of constant values */
static doublecomplex c_b1 = {1.,0.};
static integer c__1 = 1;
/* System generated locals */
integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
work_offset, i__1, i__2, i__3, i__4, i__5;
doublecomplex z__1, z__2;
/* Builtin functions */
void d_cnjg(doublecomplex *, doublecomplex *);
/* Local variables */
static integer i, j;
extern logical lsame_(char *, char *);
extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *,
integer *, doublecomplex *, doublecomplex *, integer *,
doublecomplex *, integer *, doublecomplex *, doublecomplex *,
integer *), zcopy_(integer *, doublecomplex *,
integer *, doublecomplex *, integer *), ztrmm_(char *, char *,
char *, char *, integer *, integer *, doublecomplex *,
doublecomplex *, integer *, doublecomplex *, integer *), zlacgv_(integer *, doublecomplex *,
integer *);
static char transt[1];
#define V(I,J) v[(I)-1 + ((J)-1)* ( *ldv)]
#define T(I,J) t[(I)-1 + ((J)-1)* ( *ldt)]
#define C(I,J) c[(I)-1 + ((J)-1)* ( *ldc)]
#define WORK(I,J) work[(I)-1 + ((J)-1)* ( *ldwork)]
if (*m <= 0 || *n <= 0) {
return 0;
}
if (lsame_(trans, "N")) {
*(unsigned char *)transt = 'C';
} else {
*(unsigned char *)transt = 'N';
}
if (lsame_(storev, "C")) {
if (lsame_(direct, "F")) {
/* Let V = ( V1 ) (first K rows)
( V2 )
where V1 is unit lower triangular. */
if (lsame_(side, "L")) {
/* Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V = (C1'*V1 + C2'*V2) (stored in
WORK)
W := C1' */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
zcopy_(n, &C(j,1), ldc, &WORK(1,j), &
c__1);
zlacgv_(n, &WORK(1,j), &c__1);
/* L10: */
}
/* W := W * V1 */
ztrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1,
&V(1,1), ldv, &WORK(1,1), ldwork);
if (*m > *k) {
/* W := W + C2'*V2 */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b1, &C(*k+1,1), ldc, &V(*k+1,1), ldv, &c_b1, &WORK(1,1), ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &T(1,1), ldt, &WORK(1,1), ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C2 := C2 - V2 * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = 0.;
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&z__1, &V(*k+1,1), ldv, &WORK(1,1), ldwork, &c_b1, &C(*k+1,1),
ldc);
}
/* W := W * V1' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
&c_b1, &V(1,1), ldv, &WORK(1,1), ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__3 = j + i * c_dim1;
i__4 = j + i * c_dim1;
d_cnjg(&z__2, &WORK(i,j));
z__1.r = C(j,i).r - z__2.r, z__1.i = C(j,i).i -
z__2.i;
C(j,i).r = z__1.r, C(j,i).i = z__1.i;
/* L20: */
}
/* L30: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 )
W := C * V = (C1*V1 + C2*V2) (stored in WOR
K)
W := C1 */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
zcopy_(m, &C(1,j), &c__1, &WORK(1,j), &c__1);
/* L40: */
}
/* W := W * V1 */
ztrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1,
&V(1,1), ldv, &WORK(1,1), ldwork);
if (*n > *k) {
/* W := W + C2 * V2 */
i__1 = *n - *k;
zgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
&C(1,*k+1), ldc, &V(*k+1,1), ldv, &c_b1, &WORK(1,1), ldwork);
}
/* W := W * T or W * T' */
ztrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &T(1,1), ldt, &WORK(1,1), ldwork);
/* C := C - W * V' */
if (*n > *k) {
/* C2 := C2 - W * V2' */
i__1 = *n - *k;
z__1.r = -1., z__1.i = 0.;
zgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
&z__1, &WORK(1,1), ldwork, &V(*k+1,1), ldv, &c_b1, &C(1,*k+1),
ldc);
}
/* W := W * V1' */
ztrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
&c_b1, &V(1,1), ldv, &WORK(1,1), ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
i__2 = *m;
for (i = 1; i <= *m; ++i) {
i__3 = i + j * c_dim1;
i__4 = i + j * c_dim1;
i__5 = i + j * work_dim1;
z__1.r = C(i,j).r - WORK(i,j).r, z__1.i = C(i,j).i
- WORK(i,j).i;
C(i,j).r = z__1.r, C(i,j).i = z__1.i;
/* L50: */
}
/* L60: */
}
}
} else {
/* Let V = ( V1 )
( V2 ) (last K rows)
where V2 is unit upper triangular. */
if (lsame_(side, "L")) {
/* Form H * C or H' * C where C = ( C1 )
( C2 )
W := C' * V = (C1'*V1 + C2'*V2) (stored in
WORK)
W := C2' */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
zcopy_(n, &C(*m-*k+j,1), ldc, &WORK(1,j), &c__1);
zlacgv_(n, &WORK(1,j), &c__1);
/* L70: */
}
/* W := W * V2 */
ztrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1,
&V(*m-*k+1,1), ldv, &WORK(1,1),
ldwork);
if (*m > *k) {
/* W := W + C1'*V1 */
i__1 = *m - *k;
zgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b1, &C(1,1), ldc, &V(1,1), ldv, &
c_b1, &WORK(1,1), ldwork);
}
/* W := W * T' or W * T */
ztrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &T(1,1), ldt, &WORK(1,1), ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C1 := C1 - V1 * W' */
i__1 = *m - *k;
z__1.r = -1., z__1.i = 0.;
zgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&z__1, &V(1,1), ldv, &WORK(1,1),
ldwork, &c_b1, &C(1,1), ldc);
}
/* W := W * V2' */
ztrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
&c_b1, &V(*m-*k+1,1), ldv, &WORK(1,1), ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= *k; ++j) {
i__2 = *n;
for (i = 1; i <= *n; ++i) {
i__3 = *m - *k + j + i * c_dim1;
i__4 = *m - *k + j + i * c_dim1;
d_cnjg(&z__2, &WORK(i,j));
z__1.r = C(*m-*k+j,i).r - z__2.r, z__1.i = C(*m-*k+j,i).i -
z__2.i;
C(*m-*k+j,i).r = z__1.r, C(*m-*k+j,i).i = z__1.i;
/* L80: */
}
/* L90: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 )
W := C * V = (C1*V1 + C2*V2) (stored in WOR
K)
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