dorgbr.c

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/* dorgbr.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 "f2c.h"
#include "blaswrap.h"

/* Table of constant values */

static integer c__1 = 1;
static integer c_n1 = -1;

/* Subroutine */ int dorgbr_(char *vect, integer *m, integer *n, integer *k, 
        doublereal *a, integer *lda, doublereal *tau, doublereal *work, 
        integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer i__, j, nb, mn;
    extern logical lsame_(char *, char *);
    integer iinfo;
    logical wantq;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int dorglq_(integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            integer *), dorgqr_(integer *, integer *, integer *, doublereal *, 
             integer *, doublereal *, doublereal *, integer *, integer *);
    integer lwkopt;
    logical lquery;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  DORGBR generates one of the real orthogonal matrices Q or P**T */
/*  determined by DGEBRD when reducing a real matrix A to bidiagonal */
/*  form: A = Q * B * P**T.  Q and P**T are defined as products of */
/*  elementary reflectors H(i) or G(i) respectively. */

/*  If VECT = 'Q', A is assumed to have been an M-by-K matrix, and Q */
/*  is of order M: */
/*  if m >= k, Q = H(1) H(2) . . . H(k) and DORGBR returns the first n */
/*  columns of Q, where m >= n >= k; */
/*  if m < k, Q = H(1) H(2) . . . H(m-1) and DORGBR returns Q as an */
/*  M-by-M matrix. */

/*  If VECT = 'P', A is assumed to have been a K-by-N matrix, and P**T */
/*  is of order N: */
/*  if k < n, P**T = G(k) . . . G(2) G(1) and DORGBR returns the first m */
/*  rows of P**T, where n >= m >= k; */
/*  if k >= n, P**T = G(n-1) . . . G(2) G(1) and DORGBR returns P**T as */
/*  an N-by-N matrix. */

/*  Arguments */
/*  ========= */

/*  VECT    (input) CHARACTER*1 */
/*          Specifies whether the matrix Q or the matrix P**T is */
/*          required, as defined in the transformation applied by DGEBRD: */
/*          = 'Q':  generate Q; */
/*          = 'P':  generate P**T. */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix Q or P**T to be returned. */
/*          M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix Q or P**T to be returned. */
/*          N >= 0. */
/*          If VECT = 'Q', M >= N >= min(M,K); */
/*          if VECT = 'P', N >= M >= min(N,K). */

/*  K       (input) INTEGER */
/*          If VECT = 'Q', the number of columns in the original M-by-K */
/*          matrix reduced by DGEBRD. */
/*          If VECT = 'P', the number of rows in the original K-by-N */
/*          matrix reduced by DGEBRD. */
/*          K >= 0. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the vectors which define the elementary reflectors, */
/*          as returned by DGEBRD. */
/*          On exit, the M-by-N matrix Q or P**T. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. LDA >= max(1,M). */

/*  TAU     (input) DOUBLE PRECISION array, dimension */
/*                                (min(M,K)) if VECT = 'Q' */
/*                                (min(N,K)) if VECT = 'P' */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i) or G(i), which determines Q or P**T, as */
/*          returned by DGEBRD in its array argument TAUQ or TAUP. */

/*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) */
/*          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */

/*  LWORK   (input) INTEGER */
/*          The dimension of the array WORK. LWORK >= max(1,min(M,N)). */
/*          For optimum performance LWORK >= min(M,N)*NB, where NB */
/*          is the optimal blocksize. */

/*          If LWORK = -1, then a workspace query is assumed; the routine */
/*          only calculates the optimal size of the WORK array, returns */
/*          this value as the first entry of the WORK array, and no error */
/*          message related to LWORK is issued by XERBLA. */

/*  INFO    (output) INTEGER */
/*          = 0:  successful exit */
/*          < 0:  if INFO = -i, the i-th argument had an illegal value */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --tau;
    --work;

    /* Function Body */
    *info = 0;
    wantq = lsame_(vect, "Q");
    mn = min(*m,*n);
    lquery = *lwork == -1;
    if (! wantq && ! lsame_(vect, "P")) {
        *info = -1;
    } else if (*m < 0) {
        *info = -2;
    } else if (*n < 0 || wantq && (*n > *m || *n < min(*m,*k)) || ! wantq && (
            *m > *n || *m < min(*n,*k))) {
        *info = -3;
    } else if (*k < 0) {
        *info = -4;
    } else if (*lda < max(1,*m)) {
        *info = -6;
    } else if (*lwork < max(1,mn) && ! lquery) {
        *info = -9;
    }

    if (*info == 0) {
        if (wantq) {
            nb = ilaenv_(&c__1, "DORGQR", " ", m, n, k, &c_n1);
        } else {
            nb = ilaenv_(&c__1, "DORGLQ", " ", m, n, k, &c_n1);
        }
        lwkopt = max(1,mn) * nb;
        work[1] = (doublereal) lwkopt;
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DORGBR", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
        work[1] = 1.;
        return 0;
    }

    if (wantq) {

/*        Form Q, determined by a call to DGEBRD to reduce an m-by-k */
/*        matrix */

        if (*m >= *k) {

/*           If m >= k, assume m >= n >= k */

            dorgqr_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
                    iinfo);

        } else {

/*           If m < k, assume m = n */

/*           Shift the vectors which define the elementary reflectors one */
/*           column to the right, and set the first row and column of Q */
/*           to those of the unit matrix */

            for (j = *m; j >= 2; --j) {
                a[j * a_dim1 + 1] = 0.;
                i__1 = *m;
                for (i__ = j + 1; i__ <= i__1; ++i__) {
                    a[i__ + j * a_dim1] = a[i__ + (j - 1) * a_dim1];
/* L10: */
                }
/* L20: */
            }
            a[a_dim1 + 1] = 1.;
            i__1 = *m;
            for (i__ = 2; i__ <= i__1; ++i__) {
                a[i__ + a_dim1] = 0.;
/* L30: */
            }
            if (*m > 1) {

/*              Form Q(2:m,2:m) */

                i__1 = *m - 1;
                i__2 = *m - 1;
                i__3 = *m - 1;
                dorgqr_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
                        1], &work[1], lwork, &iinfo);
            }
        }
    } else {

/*        Form P', determined by a call to DGEBRD to reduce a k-by-n */
/*        matrix */

        if (*k < *n) {

/*           If k < n, assume k <= m <= n */

            dorglq_(m, n, k, &a[a_offset], lda, &tau[1], &work[1], lwork, &
                    iinfo);

        } else {

/*           If k >= n, assume m = n */

/*           Shift the vectors which define the elementary reflectors one */
/*           row downward, and set the first row and column of P' to */
/*           those of the unit matrix */

            a[a_dim1 + 1] = 1.;
            i__1 = *n;
            for (i__ = 2; i__ <= i__1; ++i__) {
                a[i__ + a_dim1] = 0.;
/* L40: */
            }
            i__1 = *n;
            for (j = 2; j <= i__1; ++j) {
                for (i__ = j - 1; i__ >= 2; --i__) {
                    a[i__ + j * a_dim1] = a[i__ - 1 + j * a_dim1];
/* L50: */
                }
                a[j * a_dim1 + 1] = 0.;
/* L60: */
            }
            if (*n > 1) {

/*              Form P'(2:n,2:n) */

                i__1 = *n - 1;
                i__2 = *n - 1;
                i__3 = *n - 1;
                dorglq_(&i__1, &i__2, &i__3, &a[(a_dim1 << 1) + 2], lda, &tau[
                        1], &work[1], lwork, &iinfo);
            }
        }
    }
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DORGBR */

} /* dorgbr_ */