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opencv/3rdparty/lapack/dlarfb.c

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/* dlarfb.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 "clapack.h"
/* Table of constant values */
static integer c__1 = 1;
static doublereal c_b14 = 1.;
static doublereal c_b25 = -1.;
/* Subroutine */ int dlarfb_(char *side, char *trans, char *direct, char *
storev, integer *m, integer *n, integer *k, doublereal *v, integer *
ldv, doublereal *t, integer *ldt, doublereal *c__, integer *ldc,
doublereal *work, integer *ldwork)
{
/* System generated locals */
integer c_dim1, c_offset, t_dim1, t_offset, v_dim1, v_offset, work_dim1,
work_offset, i__1, i__2;
/* Local variables */
integer i__, j;
extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern logical lsame_(char *, char *);
integer lastc;
extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *,
doublereal *, integer *), dtrmm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *);
integer lastv;
extern integer iladlc_(integer *, integer *, doublereal *, integer *),
iladlr_(integer *, integer *, doublereal *, integer *);
char transt[1];
/* -- LAPACK auxiliary routine (version 3.2) -- */
/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/* November 2006 */
/* .. Scalar Arguments .. */
/* .. */
/* .. Array Arguments .. */
/* .. */
/* Purpose */
/* ======= */
/* DLARFB applies a real block reflector H or its transpose H' to a */
/* real 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) */
/* = 'T': apply H' (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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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. LDA >= max(1,M). */
/* WORK (workspace) DOUBLE PRECISION 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). */
/* ===================================================================== */
/* .. Parameters .. */
/* .. */
/* .. Local Scalars .. */
/* .. */
/* .. External Functions .. */
/* .. */
/* .. External Subroutines .. */
/* .. */
/* .. Executable Statements .. */
/* Quick return if possible */
/* Parameter adjustments */
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 = 'T';
} 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 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlr_(m, k, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
/* W := C1' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ 1], &c__1);
/* L10: */
}
/* W := W * V1 */
dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
if (lastv > *k) {
/* W := W + C2'*V2 */
i__1 = lastv - *k;
dgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
c_b14, &c__[*k + 1 + c_dim1], ldc, &v[*k + 1 +
v_dim1], ldv, &c_b14, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
dtrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (lastv > *k) {
/* C2 := C2 - V2 * W' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
c_b25, &v[*k + 1 + v_dim1], ldv, &work[
work_offset], ldwork, &c_b14, &c__[*k + 1 +
c_dim1], ldc);
}
/* W := W * V1' */
dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
/* L20: */
}
/* L30: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlr_(n, k, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
/* W := C1 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L40: */
}
/* W := W * V1 */
dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
if (lastv > *k) {
/* W := W + C2 * V2 */
i__1 = lastv - *k;
dgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[*k +
1 + v_dim1], ldv, &c_b14, &work[work_offset],
ldwork);
}
/* W := W * T or W * T' */
dtrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
&t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (lastv > *k) {
/* C2 := C2 - W * V2' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
c_b25, &work[work_offset], ldwork, &v[*k + 1 +
v_dim1], ldv, &c_b14, &c__[(*k + 1) * c_dim1 + 1],
ldc);
}
/* W := W * V1' */
dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
/* 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 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlr_(m, k, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
/* W := C' * V = (C1'*V1 + C2'*V2) (stored in WORK) */
/* W := C2' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
j * work_dim1 + 1], &c__1);
/* L70: */
}
/* W := W * V2 */
dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
if (lastv > *k) {
/* W := W + C1'*V1 */
i__1 = lastv - *k;
dgemm_("Transpose", "No transpose", &lastc, k, &i__1, &
c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b14, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
dtrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V * W' */
if (lastv > *k) {
/* C1 := C1 - V1 * W' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &i__1, &lastc, k, &
c_b25, &v[v_offset], ldv, &work[work_offset],
ldwork, &c_b14, &c__[c_offset], ldc);
}
/* W := W * V2' */
dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
work_dim1];
/* L80: */
}
/* L90: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlr_(n, k, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
/* W := C * V = (C1*V1 + C2*V2) (stored in WORK) */
/* W := C2 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[(*n - *k + j) * c_dim1 + 1], &c__1, &
work[j * work_dim1 + 1], &c__1);
/* L100: */
}
/* W := W * V2 */
dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
if (lastv > *k) {
/* W := W + C1 * V1 */
i__1 = lastv - *k;
dgemm_("No transpose", "No transpose", &lastc, k, &i__1, &
c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b14, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
dtrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
&t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V' */
if (lastv > *k) {
/* C1 := C1 - W * V1' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &lastc, &i__1, k, &
c_b25, &work[work_offset], ldwork, &v[v_offset],
ldv, &c_b14, &c__[c_offset], ldc);
}
/* W := W * V2' */
dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
c_b14, &v[lastv - *k + 1 + v_dim1], ldv, &work[
work_offset], ldwork);
/* C2 := C2 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
work_dim1];
/* 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 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlc_(k, m, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
/* W := C1' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[j + c_dim1], ldc, &work[j * work_dim1
+ 1], &c__1);
/* L130: */
}
/* W := W * V1' */
dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
if (lastv > *k) {
/* W := W + C2'*V2' */
i__1 = lastv - *k;
dgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
&c__[*k + 1 + c_dim1], ldc, &v[(*k + 1) * v_dim1
+ 1], ldv, &c_b14, &work[work_offset], ldwork);
}
/* W := W * T' or W * T */
dtrmm_("Right", "Upper", transt, "Non-unit", &lastc, k, &
c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (lastv > *k) {
/* C2 := C2 - V2' * W' */
i__1 = lastv - *k;
dgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
&v[(*k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork, &c_b14, &c__[*k + 1 +
c_dim1], ldc);
}
/* W := W * V1 */
dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[j + i__ * c_dim1] -= work[i__ + j * work_dim1];
/* L140: */
}
/* L150: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlc_(k, n, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
/* W := C1 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[j * c_dim1 + 1], &c__1, &work[j *
work_dim1 + 1], &c__1);
/* L160: */
}
/* W := W * V1' */
dtrmm_("Right", "Upper", "Transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
if (lastv > *k) {
/* W := W + C2 * V2' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
c_b14, &c__[(*k + 1) * c_dim1 + 1], ldc, &v[(*k +
1) * v_dim1 + 1], ldv, &c_b14, &work[work_offset],
ldwork);
}
/* W := W * T or W * T' */
dtrmm_("Right", "Upper", trans, "Non-unit", &lastc, k, &c_b14,
&t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (lastv > *k) {
/* C2 := C2 - W * V2 */
i__1 = lastv - *k;
dgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
c_b25, &work[work_offset], ldwork, &v[(*k + 1) *
v_dim1 + 1], ldv, &c_b14, &c__[(*k + 1) * c_dim1
+ 1], ldc);
}
/* W := W * V1 */
dtrmm_("Right", "Upper", "No transpose", "Unit", &lastc, k, &
c_b14, &v[v_offset], ldv, &work[work_offset], ldwork);
/* C1 := C1 - W */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
i__2 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + j * c_dim1] -= work[i__ + j * work_dim1];
/* 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 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlc_(k, m, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlc_(&lastv, n, &c__[c_offset], ldc);
/* W := C' * V' = (C1'*V1' + C2'*V2') (stored in WORK) */
/* W := C2' */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[lastv - *k + j + c_dim1], ldc, &work[
j * work_dim1 + 1], &c__1);
/* L190: */
}
/* W := W * V2' */
dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (lastv > *k) {
/* W := W + C1'*V1' */
i__1 = lastv - *k;
dgemm_("Transpose", "Transpose", &lastc, k, &i__1, &c_b14,
&c__[c_offset], ldc, &v[v_offset], ldv, &c_b14, &
work[work_offset], ldwork);
}
/* W := W * T' or W * T */
dtrmm_("Right", "Lower", transt, "Non-unit", &lastc, k, &
c_b14, &t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - V' * W' */
if (lastv > *k) {
/* C1 := C1 - V1' * W' */
i__1 = lastv - *k;
dgemm_("Transpose", "Transpose", &i__1, &lastc, k, &c_b25,
&v[v_offset], ldv, &work[work_offset], ldwork, &
c_b14, &c__[c_offset], ldc);
}
/* W := W * V2 */
dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
c_b14, &v[(lastv - *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 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[lastv - *k + j + i__ * c_dim1] -= work[i__ + j *
work_dim1];
/* L200: */
}
/* L210: */
}
} else if (lsame_(side, "R")) {
/* Form C * H or C * H' where C = ( C1 C2 ) */
/* Computing MAX */
i__1 = *k, i__2 = iladlc_(k, n, &v[v_offset], ldv);
lastv = max(i__1,i__2);
lastc = iladlr_(m, &lastv, &c__[c_offset], ldc);
/* W := C * V' = (C1*V1' + C2*V2') (stored in WORK) */
/* W := C2 */
i__1 = *k;
for (j = 1; j <= i__1; ++j) {
dcopy_(&lastc, &c__[(lastv - *k + j) * c_dim1 + 1], &c__1,
&work[j * work_dim1 + 1], &c__1);
/* L220: */
}
/* W := W * V2' */
dtrmm_("Right", "Lower", "Transpose", "Unit", &lastc, k, &
c_b14, &v[(lastv - *k + 1) * v_dim1 + 1], ldv, &work[
work_offset], ldwork);
if (lastv > *k) {
/* W := W + C1 * V1' */
i__1 = lastv - *k;
dgemm_("No transpose", "Transpose", &lastc, k, &i__1, &
c_b14, &c__[c_offset], ldc, &v[v_offset], ldv, &
c_b14, &work[work_offset], ldwork);
}
/* W := W * T or W * T' */
dtrmm_("Right", "Lower", trans, "Non-unit", &lastc, k, &c_b14,
&t[t_offset], ldt, &work[work_offset], ldwork);
/* C := C - W * V */
if (lastv > *k) {
/* C1 := C1 - W * V1 */
i__1 = lastv - *k;
dgemm_("No transpose", "No transpose", &lastc, &i__1, k, &
c_b25, &work[work_offset], ldwork, &v[v_offset],
ldv, &c_b14, &c__[c_offset], ldc);
}
/* W := W * V2 */
dtrmm_("Right", "Lower", "No transpose", "Unit", &lastc, k, &
c_b14, &v[(lastv - *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 = lastc;
for (i__ = 1; i__ <= i__2; ++i__) {
c__[i__ + (lastv - *k + j) * c_dim1] -= work[i__ + j *
work_dim1];
/* L230: */
}
/* L240: */
}
}
}
}
return 0;
/* End of DLARFB */
} /* dlarfb_ */