1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656
|
/* lapack/single/sggsvp.f -- translated by f2c (version 20050501).
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
*/
#ifdef __cplusplus
extern "C" {
#endif
#include "v3p_netlib.h"
/* Table of constant values */
static real c_b12 = (float)0.;
static real c_b22 = (float)1.;
/*< >*/
/* Subroutine */ int sggsvp_(const char *jobu, const char *jobv, const char *jobq, integer *m,
integer *p, integer *n, real *a, integer *lda, real *b, integer *ldb,
real *tola, real *tolb, integer *k, integer *l, real *u, integer *ldu,
real *v, integer *ldv, real *q, integer *ldq, integer *iwork, real *
tau, real *work, integer *info, ftnlen jobu_len, ftnlen jobv_len,
ftnlen jobq_len)
{
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, q_dim1, q_offset, u_dim1,
u_offset, v_dim1, v_offset, i__1, i__2, i__3;
real r__1;
/* Local variables */
integer i__, j;
extern logical lsame_(const char *, const char *, ftnlen, ftnlen);
logical wantq, wantu, wantv;
extern /* Subroutine */ int sgeqr2_(integer *, integer *, real *, integer
*, real *, real *, integer *), sgerq2_(integer *, integer *, real
*, integer *, real *, real *, integer *), sorg2r_(integer *,
integer *, integer *, real *, integer *, real *, real *, integer *
), sorm2r_(char *, char *, integer *, integer *, integer *, real *
, integer *, real *, real *, integer *, real *, integer *, ftnlen,
ftnlen), sormr2_(char *, char *, integer *, integer *, integer *,
real *, integer *, real *, real *, integer *, real *, integer *,
ftnlen, ftnlen), xerbla_(char *, integer *, ftnlen), sgeqpf_(
integer *, integer *, real *, integer *, integer *, real *, real *
, integer *), slacpy_(char *, integer *, integer *, real *,
integer *, real *, integer *, ftnlen), slaset_(char *, integer *,
integer *, real *, real *, real *, integer *, ftnlen), slapmt_(
logical *, integer *, integer *, real *, integer *, integer *);
logical forwrd;
(void)jobu_len;
(void)jobv_len;
(void)jobq_len;
/* -- LAPACK routine (version 3.0) -- */
/* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., */
/* Courant Institute, Argonne National Lab, and Rice University */
/* September 30, 1994 */
/* .. Scalar Arguments .. */
/*< CHARACTER JOBQ, JOBU, JOBV >*/
/*< INTEGER INFO, K, L, LDA, LDB, LDQ, LDU, LDV, M, N, P >*/
/*< REAL TOLA, TOLB >*/
/* .. */
/* .. Array Arguments .. */
/*< INTEGER IWORK( * ) >*/
/*< >*/
/* .. */
/* Purpose */
/* ======= */
/* SGGSVP computes orthogonal matrices U, V and Q such that */
/* N-K-L K L */
/* U'*A*Q = K ( 0 A12 A13 ) if M-K-L >= 0; */
/* L ( 0 0 A23 ) */
/* M-K-L ( 0 0 0 ) */
/* N-K-L K L */
/* = K ( 0 A12 A13 ) if M-K-L < 0; */
/* M-K ( 0 0 A23 ) */
/* N-K-L K L */
/* V'*B*Q = L ( 0 0 B13 ) */
/* P-L ( 0 0 0 ) */
/* where the K-by-K matrix A12 and L-by-L matrix B13 are nonsingular */
/* upper triangular; A23 is L-by-L upper triangular if M-K-L >= 0, */
/* otherwise A23 is (M-K)-by-L upper trapezoidal. K+L = the effective */
/* numerical rank of the (M+P)-by-N matrix (A',B')'. Z' denotes the */
/* transpose of Z. */
/* This decomposition is the preprocessing step for computing the */
/* Generalized Singular Value Decomposition (GSVD), see subroutine */
/* SGGSVD. */
/* Arguments */
/* ========= */
/* JOBU (input) CHARACTER*1 */
/* = 'U': Orthogonal matrix U is computed; */
/* = 'N': U is not computed. */
/* JOBV (input) CHARACTER*1 */
/* = 'V': Orthogonal matrix V is computed; */
/* = 'N': V is not computed. */
/* JOBQ (input) CHARACTER*1 */
/* = 'Q': Orthogonal matrix Q is computed; */
/* = 'N': Q is not computed. */
/* M (input) INTEGER */
/* The number of rows of the matrix A. M >= 0. */
/* P (input) INTEGER */
/* The number of rows of the matrix B. P >= 0. */
/* N (input) INTEGER */
/* The number of columns of the matrices A and B. N >= 0. */
/* A (input/output) REAL array, dimension (LDA,N) */
/* On entry, the M-by-N matrix A. */
/* On exit, A contains the triangular (or trapezoidal) matrix */
/* described in the Purpose section. */
/* LDA (input) INTEGER */
/* The leading dimension of the array A. LDA >= max(1,M). */
/* B (input/output) REAL array, dimension (LDB,N) */
/* On entry, the P-by-N matrix B. */
/* On exit, B contains the triangular matrix described in */
/* the Purpose section. */
/* LDB (input) INTEGER */
/* The leading dimension of the array B. LDB >= max(1,P). */
/* TOLA (input) REAL */
/* TOLB (input) REAL */
/* TOLA and TOLB are the thresholds to determine the effective */
/* numerical rank of matrix B and a subblock of A. Generally, */
/* they are set to */
/* TOLA = MAX(M,N)*norm(A)*MACHEPS, */
/* TOLB = MAX(P,N)*norm(B)*MACHEPS. */
/* The size of TOLA and TOLB may affect the size of backward */
/* errors of the decomposition. */
/* K (output) INTEGER */
/* L (output) INTEGER */
/* On exit, K and L specify the dimension of the subblocks */
/* described in Purpose. */
/* K + L = effective numerical rank of (A',B')'. */
/* U (output) REAL array, dimension (LDU,M) */
/* If JOBU = 'U', U contains the orthogonal matrix U. */
/* If JOBU = 'N', U is not referenced. */
/* LDU (input) INTEGER */
/* The leading dimension of the array U. LDU >= max(1,M) if */
/* JOBU = 'U'; LDU >= 1 otherwise. */
/* V (output) REAL array, dimension (LDV,M) */
/* If JOBV = 'V', V contains the orthogonal matrix V. */
/* If JOBV = 'N', V is not referenced. */
/* LDV (input) INTEGER */
/* The leading dimension of the array V. LDV >= max(1,P) if */
/* JOBV = 'V'; LDV >= 1 otherwise. */
/* Q (output) REAL array, dimension (LDQ,N) */
/* If JOBQ = 'Q', Q contains the orthogonal matrix Q. */
/* If JOBQ = 'N', Q is not referenced. */
/* LDQ (input) INTEGER */
/* The leading dimension of the array Q. LDQ >= max(1,N) if */
/* JOBQ = 'Q'; LDQ >= 1 otherwise. */
/* IWORK (workspace) INTEGER array, dimension (N) */
/* TAU (workspace) REAL array, dimension (N) */
/* WORK (workspace) REAL array, dimension (max(3*N,M,P)) */
/* INFO (output) INTEGER */
/* = 0: successful exit */
/* < 0: if INFO = -i, the i-th argument had an illegal value. */
/* Further Details */
/* =============== */
/* The subroutine uses LAPACK subroutine SGEQPF for the QR factorization */
/* with column pivoting to detect the effective numerical rank of the */
/* a matrix. It may be replaced by a better rank determination strategy. */
/* ===================================================================== */
/* .. Parameters .. */
/*< REAL ZERO, ONE >*/
/*< PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) >*/
/* .. */
/* .. Local Scalars .. */
/*< LOGICAL FORWRD, WANTQ, WANTU, WANTV >*/
/*< INTEGER I, J >*/
/* .. */
/* .. External Functions .. */
/*< LOGICAL LSAME >*/
/*< EXTERNAL LSAME >*/
/* .. */
/* .. External Subroutines .. */
/*< >*/
/* .. */
/* .. Intrinsic Functions .. */
/*< INTRINSIC ABS, MAX, MIN >*/
/* .. */
/* .. Executable Statements .. */
/* Test the input parameters */
/*< WANTU = LSAME( JOBU, 'U' ) >*/
/* Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1;
b -= b_offset;
u_dim1 = *ldu;
u_offset = 1 + u_dim1;
u -= u_offset;
v_dim1 = *ldv;
v_offset = 1 + v_dim1;
v -= v_offset;
q_dim1 = *ldq;
q_offset = 1 + q_dim1;
q -= q_offset;
--iwork;
--tau;
--work;
/* Function Body */
wantu = lsame_(jobu, "U", (ftnlen)1, (ftnlen)1);
/*< WANTV = LSAME( JOBV, 'V' ) >*/
wantv = lsame_(jobv, "V", (ftnlen)1, (ftnlen)1);
/*< WANTQ = LSAME( JOBQ, 'Q' ) >*/
wantq = lsame_(jobq, "Q", (ftnlen)1, (ftnlen)1);
/*< FORWRD = .TRUE. >*/
forwrd = TRUE_;
/*< INFO = 0 >*/
*info = 0;
/*< IF( .NOT.( WANTU .OR. LSAME( JOBU, 'N' ) ) ) THEN >*/
if (! (wantu || lsame_(jobu, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -1 >*/
*info = -1;
/*< ELSE IF( .NOT.( WANTV .OR. LSAME( JOBV, 'N' ) ) ) THEN >*/
} else if (! (wantv || lsame_(jobv, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -2 >*/
*info = -2;
/*< ELSE IF( .NOT.( WANTQ .OR. LSAME( JOBQ, 'N' ) ) ) THEN >*/
} else if (! (wantq || lsame_(jobq, "N", (ftnlen)1, (ftnlen)1))) {
/*< INFO = -3 >*/
*info = -3;
/*< ELSE IF( M.LT.0 ) THEN >*/
} else if (*m < 0) {
/*< INFO = -4 >*/
*info = -4;
/*< ELSE IF( P.LT.0 ) THEN >*/
} else if (*p < 0) {
/*< INFO = -5 >*/
*info = -5;
/*< ELSE IF( N.LT.0 ) THEN >*/
} else if (*n < 0) {
/*< INFO = -6 >*/
*info = -6;
/*< ELSE IF( LDA.LT.MAX( 1, M ) ) THEN >*/
} else if (*lda < max(1,*m)) {
/*< INFO = -8 >*/
*info = -8;
/*< ELSE IF( LDB.LT.MAX( 1, P ) ) THEN >*/
} else if (*ldb < max(1,*p)) {
/*< INFO = -10 >*/
*info = -10;
/*< ELSE IF( LDU.LT.1 .OR. ( WANTU .AND. LDU.LT.M ) ) THEN >*/
} else if (*ldu < 1 || (wantu && *ldu < *m)) {
/*< INFO = -16 >*/
*info = -16;
/*< ELSE IF( LDV.LT.1 .OR. ( WANTV .AND. LDV.LT.P ) ) THEN >*/
} else if (*ldv < 1 || (wantv && *ldv < *p)) {
/*< INFO = -18 >*/
*info = -18;
/*< ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.N ) ) THEN >*/
} else if (*ldq < 1 || (wantq && *ldq < *n)) {
/*< INFO = -20 >*/
*info = -20;
/*< END IF >*/
}
/*< IF( INFO.NE.0 ) THEN >*/
if (*info != 0) {
/*< CALL XERBLA( 'SGGSVP', -INFO ) >*/
i__1 = -(*info);
xerbla_("SGGSVP", &i__1, (ftnlen)6);
/*< RETURN >*/
return 0;
/*< END IF >*/
}
/* QR with column pivoting of B: B*P = V*( S11 S12 ) */
/* ( 0 0 ) */
/*< DO 10 I = 1, N >*/
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IWORK( I ) = 0 >*/
iwork[i__] = 0;
/*< 10 CONTINUE >*/
/* L10: */
}
/*< CALL SGEQPF( P, N, B, LDB, IWORK, TAU, WORK, INFO ) >*/
sgeqpf_(p, n, &b[b_offset], ldb, &iwork[1], &tau[1], &work[1], info);
/* Update A := A*P */
/*< CALL SLAPMT( FORWRD, M, N, A, LDA, IWORK ) >*/
slapmt_(&forwrd, m, n, &a[a_offset], lda, &iwork[1]);
/* Determine the effective rank of matrix B. */
/*< L = 0 >*/
*l = 0;
/*< DO 20 I = 1, MIN( P, N ) >*/
i__1 = min(*p,*n);
for (i__ = 1; i__ <= i__1; ++i__) {
/*< >*/
if ((r__1 = b[i__ + i__ * b_dim1], dabs(r__1)) > *tolb) {
++(*l);
}
/*< 20 CONTINUE >*/
/* L20: */
}
/*< IF( WANTV ) THEN >*/
if (wantv) {
/* Copy the details of V, and form V. */
/*< CALL SLASET( 'Full', P, P, ZERO, ZERO, V, LDV ) >*/
slaset_("Full", p, p, &c_b12, &c_b12, &v[v_offset], ldv, (ftnlen)4);
/*< >*/
if (*p > 1) {
i__1 = *p - 1;
slacpy_("Lower", &i__1, n, &b[b_dim1 + 2], ldb, &v[v_dim1 + 2],
ldv, (ftnlen)5);
}
/*< CALL SORG2R( P, P, MIN( P, N ), V, LDV, TAU, WORK, INFO ) >*/
i__1 = min(*p,*n);
sorg2r_(p, p, &i__1, &v[v_offset], ldv, &tau[1], &work[1], info);
/*< END IF >*/
}
/* Clean up B */
/*< DO 40 J = 1, L - 1 >*/
i__1 = *l - 1;
for (j = 1; j <= i__1; ++j) {
/*< DO 30 I = J + 1, L >*/
i__2 = *l;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/*< B( I, J ) = ZERO >*/
b[i__ + j * b_dim1] = (float)0.;
/*< 30 CONTINUE >*/
/* L30: */
}
/*< 40 CONTINUE >*/
/* L40: */
}
/*< >*/
if (*p > *l) {
i__1 = *p - *l;
slaset_("Full", &i__1, n, &c_b12, &c_b12, &b[*l + 1 + b_dim1], ldb, (
ftnlen)4);
}
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Set Q = I and Update Q := Q*P */
/*< CALL SLASET( 'Full', N, N, ZERO, ONE, Q, LDQ ) >*/
slaset_("Full", n, n, &c_b12, &c_b22, &q[q_offset], ldq, (ftnlen)4);
/*< CALL SLAPMT( FORWRD, N, N, Q, LDQ, IWORK ) >*/
slapmt_(&forwrd, n, n, &q[q_offset], ldq, &iwork[1]);
/*< END IF >*/
}
/*< IF( P.GE.L .AND. N.NE.L ) THEN >*/
if (*p >= *l && *n != *l) {
/* RQ factorization of (S11 S12): ( S11 S12 ) = ( 0 S12 )*Z */
/*< CALL SGERQ2( L, N, B, LDB, TAU, WORK, INFO ) >*/
sgerq2_(l, n, &b[b_offset], ldb, &tau[1], &work[1], info);
/* Update A := A*Z' */
/*< >*/
sormr2_("Right", "Transpose", m, n, l, &b[b_offset], ldb, &tau[1], &a[
a_offset], lda, &work[1], info, (ftnlen)5, (ftnlen)9);
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q := Q*Z' */
/*< >*/
sormr2_("Right", "Transpose", n, n, l, &b[b_offset], ldb, &tau[1],
&q[q_offset], ldq, &work[1], info, (ftnlen)5, (ftnlen)9);
/*< END IF >*/
}
/* Clean up B */
/*< CALL SLASET( 'Full', L, N-L, ZERO, ZERO, B, LDB ) >*/
i__1 = *n - *l;
slaset_("Full", l, &i__1, &c_b12, &c_b12, &b[b_offset], ldb, (ftnlen)
4);
/*< DO 60 J = N - L + 1, N >*/
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
/*< DO 50 I = J - N + L + 1, L >*/
i__2 = *l;
for (i__ = j - *n + *l + 1; i__ <= i__2; ++i__) {
/*< B( I, J ) = ZERO >*/
b[i__ + j * b_dim1] = (float)0.;
/*< 50 CONTINUE >*/
/* L50: */
}
/*< 60 CONTINUE >*/
/* L60: */
}
/*< END IF >*/
}
/* Let N-L L */
/* A = ( A11 A12 ) M, */
/* then the following does the complete QR decomposition of A11: */
/* A11 = U*( 0 T12 )*P1' */
/* ( 0 0 ) */
/*< DO 70 I = 1, N - L >*/
i__1 = *n - *l;
for (i__ = 1; i__ <= i__1; ++i__) {
/*< IWORK( I ) = 0 >*/
iwork[i__] = 0;
/*< 70 CONTINUE >*/
/* L70: */
}
/*< CALL SGEQPF( M, N-L, A, LDA, IWORK, TAU, WORK, INFO ) >*/
i__1 = *n - *l;
sgeqpf_(m, &i__1, &a[a_offset], lda, &iwork[1], &tau[1], &work[1], info);
/* Determine the effective rank of A11 */
/*< K = 0 >*/
*k = 0;
/*< DO 80 I = 1, MIN( M, N-L ) >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
for (i__ = 1; i__ <= i__1; ++i__) {
/*< >*/
if ((r__1 = a[i__ + i__ * a_dim1], dabs(r__1)) > *tola) {
++(*k);
}
/*< 80 CONTINUE >*/
/* L80: */
}
/* Update A12 := U'*A12, where A12 = A( 1:M, N-L+1:N ) */
/*< >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorm2r_("Left", "Transpose", m, l, &i__1, &a[a_offset], lda, &tau[1], &a[(
*n - *l + 1) * a_dim1 + 1], lda, &work[1], info, (ftnlen)4, (
ftnlen)9);
/*< IF( WANTU ) THEN >*/
if (wantu) {
/* Copy the details of U, and form U */
/*< CALL SLASET( 'Full', M, M, ZERO, ZERO, U, LDU ) >*/
slaset_("Full", m, m, &c_b12, &c_b12, &u[u_offset], ldu, (ftnlen)4);
/*< >*/
if (*m > 1) {
i__1 = *m - 1;
i__2 = *n - *l;
slacpy_("Lower", &i__1, &i__2, &a[a_dim1 + 2], lda, &u[u_dim1 + 2]
, ldu, (ftnlen)5);
}
/*< CALL SORG2R( M, M, MIN( M, N-L ), U, LDU, TAU, WORK, INFO ) >*/
/* Computing MIN */
i__2 = *m, i__3 = *n - *l;
i__1 = min(i__2,i__3);
sorg2r_(m, m, &i__1, &u[u_offset], ldu, &tau[1], &work[1], info);
/*< END IF >*/
}
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q( 1:N, 1:N-L ) = Q( 1:N, 1:N-L )*P1 */
/*< CALL SLAPMT( FORWRD, N, N-L, Q, LDQ, IWORK ) >*/
i__1 = *n - *l;
slapmt_(&forwrd, n, &i__1, &q[q_offset], ldq, &iwork[1]);
/*< END IF >*/
}
/* Clean up A: set the strictly lower triangular part of */
/* A(1:K, 1:K) = 0, and A( K+1:M, 1:N-L ) = 0. */
/*< DO 100 J = 1, K - 1 >*/
i__1 = *k - 1;
for (j = 1; j <= i__1; ++j) {
/*< DO 90 I = J + 1, K >*/
i__2 = *k;
for (i__ = j + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 90 CONTINUE >*/
/* L90: */
}
/*< 100 CONTINUE >*/
/* L100: */
}
/*< >*/
if (*m > *k) {
i__1 = *m - *k;
i__2 = *n - *l;
slaset_("Full", &i__1, &i__2, &c_b12, &c_b12, &a[*k + 1 + a_dim1],
lda, (ftnlen)4);
}
/*< IF( N-L.GT.K ) THEN >*/
if (*n - *l > *k) {
/* RQ factorization of ( T11 T12 ) = ( 0 T12 )*Z1 */
/*< CALL SGERQ2( K, N-L, A, LDA, TAU, WORK, INFO ) >*/
i__1 = *n - *l;
sgerq2_(k, &i__1, &a[a_offset], lda, &tau[1], &work[1], info);
/*< IF( WANTQ ) THEN >*/
if (wantq) {
/* Update Q( 1:N,1:N-L ) = Q( 1:N,1:N-L )*Z1' */
/*< >*/
i__1 = *n - *l;
sormr2_("Right", "Transpose", n, &i__1, k, &a[a_offset], lda, &
tau[1], &q[q_offset], ldq, &work[1], info, (ftnlen)5, (
ftnlen)9);
/*< END IF >*/
}
/* Clean up A */
/*< CALL SLASET( 'Full', K, N-L-K, ZERO, ZERO, A, LDA ) >*/
i__1 = *n - *l - *k;
slaset_("Full", k, &i__1, &c_b12, &c_b12, &a[a_offset], lda, (ftnlen)
4);
/*< DO 120 J = N - L - K + 1, N - L >*/
i__1 = *n - *l;
for (j = *n - *l - *k + 1; j <= i__1; ++j) {
/*< DO 110 I = J - N + L + K + 1, K >*/
i__2 = *k;
for (i__ = j - *n + *l + *k + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 110 CONTINUE >*/
/* L110: */
}
/*< 120 CONTINUE >*/
/* L120: */
}
/*< END IF >*/
}
/*< IF( M.GT.K ) THEN >*/
if (*m > *k) {
/* QR factorization of A( K+1:M,N-L+1:N ) */
/*< CALL SGEQR2( M-K, L, A( K+1, N-L+1 ), LDA, TAU, WORK, INFO ) >*/
i__1 = *m - *k;
sgeqr2_(&i__1, l, &a[*k + 1 + (*n - *l + 1) * a_dim1], lda, &tau[1], &
work[1], info);
/*< IF( WANTU ) THEN >*/
if (wantu) {
/* Update U(:,K+1:M) := U(:,K+1:M)*U1 */
/*< >*/
i__1 = *m - *k;
/* Computing MIN */
i__3 = *m - *k;
i__2 = min(i__3,*l);
sorm2r_("Right", "No transpose", m, &i__1, &i__2, &a[*k + 1 + (*n
- *l + 1) * a_dim1], lda, &tau[1], &u[(*k + 1) * u_dim1 +
1], ldu, &work[1], info, (ftnlen)5, (ftnlen)12);
/*< END IF >*/
}
/* Clean up */
/*< DO 140 J = N - L + 1, N >*/
i__1 = *n;
for (j = *n - *l + 1; j <= i__1; ++j) {
/*< DO 130 I = J - N + K + L + 1, M >*/
i__2 = *m;
for (i__ = j - *n + *k + *l + 1; i__ <= i__2; ++i__) {
/*< A( I, J ) = ZERO >*/
a[i__ + j * a_dim1] = (float)0.;
/*< 130 CONTINUE >*/
/* L130: */
}
/*< 140 CONTINUE >*/
/* L140: */
}
/*< END IF >*/
}
/*< RETURN >*/
return 0;
/* End of SGGSVP */
/*< END >*/
} /* sggsvp_ */
#ifdef __cplusplus
}
#endif
|