#include "blaswrap.h"
#include "f2c.h"
/* Subroutine */ int clarfb_(char *side, char *trans, char *direct, char *
storev, integer *m, integer *n, integer *k, complex *v, integer *ldv,
complex *t, integer *ldt, complex *c__, integer *ldc, complex *work,
integer *ldwork)
{
/* -- LAPACK auxiliary routine (version 3.1) --
Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
November 2006
Purpose
=======
CLARFB 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 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 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 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 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 */
/* Table of constant values */
static complex c_b1 = {1.f,0.f};
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;
complex q__1, q__2;
/* Builtin functions */
void r_cnjg(complex *, complex *);
/* Local variables */
static integer i__, j;
extern /* Subroutine */ int cgemm_(char *, char *, integer *, integer *,
integer *, complex *, complex *, integer *, complex *, integer *,
complex *, complex *, integer *);
extern logical lsame_(char *, char *);
extern /* Subroutine */ int ccopy_(integer *, complex *, integer *,
complex *, integer *), ctrmm_(char *, char *, char *, char *,
integer *, integer *, complex *, complex *, integer *, complex *,
integer *), clacgv_(integer *,
complex *, integer *);
static char transt[1];
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
t_dim1 = *ldt;
t_offset = 1 + t_dim1;
t -= t_offset;
c_dim1 = *ldc;
c_offset = 1 + c_dim1;
c__ -= c_offset;
work_dim1 = *ldwork;
work_offset = 1 + work_dim1;
work -= work_offset;
/* Function Body */
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 <= i__1; ++j) {
ccopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
&c__1);
clacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L10: */
}
/* W := W * V1 */
ctrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1,
&v[v_offset], ldv, &work[work_offset], ldwork);
if (*m > *k) {
/* W := W + C2'*V2 */
i__1 = *m - *k;
cgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b1, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ctrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C2 := C2 - V2 * W' */
i__1 = *m - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&q__1, &v[*k + 1 + v_dim1], ldv, &work[
work_offset], ldwork, &c_b1, &c__[*k + 1 + c_dim1]
, ldc);
}
/* W := W * V1' */
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * c_dim1;
i__4 = j + i__ * c_dim1;
r_cnjg(&q__2, &work[i__ + j * work_dim1]);
q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
q__2.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__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 WORK)
W := C1 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L40: */
}
/* W := W * V1 */
ctrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1,
&v[v_offset], ldv, &work[work_offset], ldwork);
if (*n > *k) {
/* W := W + C2 * V2 */
i__1 = *n - *k;
cgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
&c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k + 1 +
v_dim1], ldv, &c_b1, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
ctrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (*n > *k) {
/* C2 := C2 - W * V2' */
i__1 = *n - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
&q__1, &work[work_offset], ldwork, &v[*k + 1 +
v_dim1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
ldc);
}
/* W := W * V1' */
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * work_dim1;
q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__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 <= i__1; ++j) {
ccopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
work_dim1 + 1], &c__1);
clacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L70: */
}
/* W := W * V2 */
ctrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1,
&v[*m - *k + 1 + v_dim1], ldv, &work[work_offset],
ldwork);
if (*m > *k) {
/* W := W + C1'*V1 */
i__1 = *m - *k;
cgemm_("Conjugate transpose", "No transpose", n, k, &i__1,
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b1, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ctrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (*m > *k) {
/* C1 := C1 - V1 * W' */
i__1 = *m - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", &i__1, n, k,
&q__1, &v[v_offset], ldv, &work[work_offset],
ldwork, &c_b1, &c__[c_offset], ldc);
}
/* W := W * V2' */
ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
&c_b1, &v[*m - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = *m - *k + j + i__ * c_dim1;
i__4 = *m - *k + j + i__ * c_dim1;
r_cnjg(&q__2, &work[i__ + j * work_dim1]);
q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
q__2.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__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 WORK)
W := C2 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
j * work_dim1 + 1], &c__1);
/* L100: */
}
/* W := W * V2 */
ctrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1,
&v[*n - *k + 1 + v_dim1], ldv, &work[work_offset],
ldwork);
if (*n > *k) {
/* W := W + C1 * V1 */
i__1 = *n - *k;
cgemm_("No transpose", "No transpose", m, k, &i__1, &c_b1,
&c__[c_offset], ldc, &v[v_offset], ldv, &c_b1, &
work[work_offset], ldwork)
;
}
/* W := W * T or W * T' */
ctrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (*n > *k) {
/* C1 := C1 - W * V1' */
i__1 = *n - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "Conjugate transpose", m, &i__1, k,
&q__1, &work[work_offset], ldwork, &v[v_offset],
ldv, &c_b1, &c__[c_offset], ldc);
}
/* W := W * V2' */
ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
&c_b1, &v[*n - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (*n - *k + j) * c_dim1;
i__4 = i__ + (*n - *k + j) * c_dim1;
i__5 = i__ + j * work_dim1;
q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L110: */
}
/* L120: */
}
}
}
} else if (lsame_(storev, "R")) {
if (lsame_(direct, "F")) {
/* Let V = ( V1 V2 ) (V1: first K columns)
where V1 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 := C1' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(n, &c__[j + c_dim1], ldc, &work[j * work_dim1 + 1],
&c__1);
clacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L130: */
}
/* W := W * V1' */
ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", n, k,
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
if (*m > *k) {
/* W := W + C2'*V2' */
i__1 = *m - *k;
cgemm_("Conjugate transpose", "Conjugate transpose", n, k,
&i__1, &c_b1, &c__[*k + 1 + c_dim1], ldc, &v[(*k
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
, ldwork);
}
/* W := W * T' or W * T */
ctrmm_("Right", "Upper", transt, "Non-unit", n, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (*m > *k) {
/* C2 := C2 - V2' * W' */
i__1 = *m - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("Conjugate transpose", "Conjugate transpose", &
i__1, n, k, &q__1, &v[(*k + 1) * v_dim1 + 1], ldv,
&work[work_offset], ldwork, &c_b1, &c__[*k + 1 +
c_dim1], ldc);
}
/* W := W * V1 */
ctrmm_("Right", "Upper", "No transpose", "Unit", n, k, &c_b1,
&v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = j + i__ * c_dim1;
i__4 = j + i__ * c_dim1;
r_cnjg(&q__2, &work[i__ + j * work_dim1]);
q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
q__2.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L140: */
}
/* L150: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 )
W := C * V' = (C1*V1' + C2*V2') (stored in WORK)
W := C1 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(m, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L160: */
}
/* W := W * V1' */
ctrmm_("Right", "Upper", "Conjugate transpose", "Unit", m, k,
&c_b1, &v[v_offset], ldv, &work[work_offset], ldwork);
if (*n > *k) {
/* W := W + C2 * V2' */
i__1 = *n - *k;
cgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
&c_b1, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k
+ 1) * v_dim1 + 1], ldv, &c_b1, &work[work_offset]
, ldwork);
}
/* W := W * T or W * T' */
ctrmm_("Right", "Upper", trans, "Non-unit", m, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (*n > *k) {
/* C2 := C2 - W * V2 */
i__1 = *n - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "No transpose", m, &i__1, k, &q__1,
&work[work_offset], ldwork, &v[(*k + 1) * v_dim1
+ 1], ldv, &c_b1, &c__[(*k + 1) * c_dim1 + 1],
ldc);
}
/* W := W * V1 */
ctrmm_("Right", "Upper", "No transpose", "Unit", m, k, &c_b1,
&v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + j * c_dim1;
i__4 = i__ + j * c_dim1;
i__5 = i__ + j * work_dim1;
q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L170: */
}
/* L180: */
}
}
} else {
/* Let V = ( V1 V2 ) (V2: last K columns)
where V2 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 := C2' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(n, &c__[*m - *k + j + c_dim1], ldc, &work[j *
work_dim1 + 1], &c__1);
clacgv_(n, &work[j * work_dim1 + 1], &c__1);
/* L190: */
}
/* W := W * V2' */
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", n, k,
&c_b1, &v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (*m > *k) {
/* W := W + C1'*V1' */
i__1 = *m - *k;
cgemm_("Conjugate transpose", "Conjugate transpose", n, k,
&i__1, &c_b1, &c__[c_offset], ldc, &v[v_offset],
ldv, &c_b1, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
ctrmm_("Right", "Lower", transt, "Non-unit", n, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (*m > *k) {
/* C1 := C1 - V1' * W' */
i__1 = *m - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("Conjugate transpose", "Conjugate transpose", &
i__1, n, k, &q__1, &v[v_offset], ldv, &work[
work_offset], ldwork, &c_b1, &c__[c_offset], ldc);
}
/* W := W * V2 */
ctrmm_("Right", "Lower", "No transpose", "Unit", n, k, &c_b1,
&v[(*m - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = *m - *k + j + i__ * c_dim1;
i__4 = *m - *k + j + i__ * c_dim1;
r_cnjg(&q__2, &work[i__ + j * work_dim1]);
q__1.r = c__[i__4].r - q__2.r, q__1.i = c__[i__4].i -
q__2.i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L200: */
}
/* L210: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 )
W := C * V' = (C1*V1' + C2*V2') (stored in WORK)
W := C2 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
ccopy_(m, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &work[
j * work_dim1 + 1], &c__1);
/* L220: */
}
/* W := W * V2' */
ctrmm_("Right", "Lower", "Conjugate transpose", "Unit", m, k,
&c_b1, &v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (*n > *k) {
/* W := W + C1 * V1' */
i__1 = *n - *k;
cgemm_("No transpose", "Conjugate transpose", m, k, &i__1,
&c_b1, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b1, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
ctrmm_("Right", "Lower", trans, "Non-unit", m, k, &c_b1, &t[
t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (*n > *k) {
/* C1 := C1 - W * V1 */
i__1 = *n - *k;
q__1.r = -1.f, q__1.i = -0.f;
cgemm_("No transpose", "No transpose", m, &i__1, k, &q__1,
&work[work_offset], ldwork, &v[v_offset], ldv, &
c_b1, &c__[c_offset], ldc)
;
}
/* W := W * V2 */
ctrmm_("Right", "Lower", "No transpose", "Unit", m, k, &c_b1,
&v[(*n - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = *m;
for (i__ = 1; i__ <= i__2; ++i__) {
i__3 = i__ + (*n - *k + j) * c_dim1;
i__4 = i__ + (*n - *k + j) * c_dim1;
i__5 = i__ + j * work_dim1;
q__1.r = c__[i__4].r - work[i__5].r, q__1.i = c__[
i__4].i - work[i__5].i;
c__[i__3].r = q__1.r, c__[i__3].i = q__1.i;
/* L230: */
}
/* L240: */
}
}
}
}
return 0;
/* End of CLARFB */
} /* clarfb_ */