sggsvp.c

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/* 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_(char *jobu, char *jobv, 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_(char *, 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]);