dormbr.c

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/* dormbr.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;
static integer c__2 = 2;

/* Subroutine */ int dormbr_(char *vect, char *side, char *trans, integer *m, 
        integer *n, integer *k, doublereal *a, integer *lda, doublereal *tau, 
        doublereal *c__, integer *ldc, doublereal *work, integer *lwork, 
        integer *info)
{
    /* System generated locals */
    address a__1[2];
    integer a_dim1, a_offset, c_dim1, c_offset, i__1, i__2, i__3[2];
    char ch__1[2];

    /* Builtin functions */
    /* Subroutine */ int s_cat(char *, char **, integer *, integer *, ftnlen);

    /* Local variables */
    integer i1, i2, nb, mi, ni, nq, nw;
    logical left;
    extern logical lsame_(char *, char *);
    integer iinfo;
    extern /* Subroutine */ int xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int dormlq_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, integer *);
    logical notran;
    extern /* Subroutine */ int dormqr_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, integer *);
    logical applyq;
    char transt[1];
    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 */
/*  ======= */

/*  If VECT = 'Q', DORMBR overwrites the general real M-by-N matrix C */
/*  with */
/*                  SIDE = 'L'     SIDE = 'R' */
/*  TRANS = 'N':      Q * C          C * Q */
/*  TRANS = 'T':      Q**T * C       C * Q**T */

/*  If VECT = 'P', DORMBR overwrites the general real M-by-N matrix C */
/*  with */
/*                  SIDE = 'L'     SIDE = 'R' */
/*  TRANS = 'N':      P * C          C * P */
/*  TRANS = 'T':      P**T * C       C * P**T */

/*  Here Q and P**T are the orthogonal matrices 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) and G(i) */
/*  respectively. */

/*  Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the */
/*  order of the orthogonal matrix Q or P**T that is applied. */

/*  If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: */
/*  if nq >= k, Q = H(1) H(2) . . . H(k); */
/*  if nq < k, Q = H(1) H(2) . . . H(nq-1). */

/*  If VECT = 'P', A is assumed to have been a K-by-NQ matrix: */
/*  if k < nq, P = G(1) G(2) . . . G(k); */
/*  if k >= nq, P = G(1) G(2) . . . G(nq-1). */

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

/*  VECT    (input) CHARACTER*1 */
/*          = 'Q': apply Q or Q**T; */
/*          = 'P': apply P or P**T. */

/*  SIDE    (input) CHARACTER*1 */
/*          = 'L': apply Q, Q**T, P or P**T from the Left; */
/*          = 'R': apply Q, Q**T, P or P**T from the Right. */

/*  TRANS   (input) CHARACTER*1 */
/*          = 'N':  No transpose, apply Q  or P; */
/*          = 'T':  Transpose, apply Q**T or P**T. */

/*  M       (input) INTEGER */
/*          The number of rows of the matrix C. M >= 0. */

/*  N       (input) INTEGER */
/*          The number of columns of the matrix C. N >= 0. */

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

/*  A       (input) DOUBLE PRECISION array, dimension */
/*                                (LDA,min(nq,K)) if VECT = 'Q' */
/*                                (LDA,nq)        if VECT = 'P' */
/*          The vectors which define the elementary reflectors H(i) and */
/*          G(i), whose products determine the matrices Q and P, as */
/*          returned by DGEBRD. */

/*  LDA     (input) INTEGER */
/*          The leading dimension of the array A. */
/*          If VECT = 'Q', LDA >= max(1,nq); */
/*          if VECT = 'P', LDA >= max(1,min(nq,K)). */

/*  TAU     (input) DOUBLE PRECISION array, dimension (min(nq,K)) */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i) or G(i) which determines Q or P, as returned */
/*          by DGEBRD in the array argument TAUQ or TAUP. */

/*  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N) */
/*          On entry, the M-by-N matrix C. */
/*          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q */
/*          or P*C or P**T*C or C*P or C*P**T. */

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

/*  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. */
/*          If SIDE = 'L', LWORK >= max(1,N); */
/*          if SIDE = 'R', LWORK >= max(1,M). */
/*          For optimum performance LWORK >= N*NB if SIDE = 'L', and */
/*          LWORK >= M*NB if SIDE = 'R', 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 */

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

/*     .. 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;
    c_dim1 = *ldc;
    c_offset = 1 + c_dim1;
    c__ -= c_offset;
    --work;

    /* Function Body */
    *info = 0;
    applyq = lsame_(vect, "Q");
    left = lsame_(side, "L");
    notran = lsame_(trans, "N");
    lquery = *lwork == -1;

/*     NQ is the order of Q or P and NW is the minimum dimension of WORK */

    if (left) {
        nq = *m;
        nw = *n;
    } else {
        nq = *n;
        nw = *m;
    }
    if (! applyq && ! lsame_(vect, "P")) {
        *info = -1;
    } else if (! left && ! lsame_(side, "R")) {
        *info = -2;
    } else if (! notran && ! lsame_(trans, "T")) {
        *info = -3;
    } else if (*m < 0) {
        *info = -4;
    } else if (*n < 0) {
        *info = -5;
    } else if (*k < 0) {
        *info = -6;
    } else /* if(complicated condition) */ {
/* Computing MAX */
        i__1 = 1, i__2 = min(nq,*k);
        if (applyq && *lda < max(1,nq) || ! applyq && *lda < max(i__1,i__2)) {
            *info = -8;
        } else if (*ldc < max(1,*m)) {
            *info = -11;
        } else if (*lwork < max(1,nw) && ! lquery) {
            *info = -13;
        }
    }

    if (*info == 0) {
        if (applyq) {
            if (left) {
/* Writing concatenation */
                i__3[0] = 1, a__1[0] = side;
                i__3[1] = 1, a__1[1] = trans;
                s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
                i__1 = *m - 1;
                i__2 = *m - 1;
                nb = ilaenv_(&c__1, "DORMQR", ch__1, &i__1, n, &i__2, &c_n1);
            } else {
/* Writing concatenation */
                i__3[0] = 1, a__1[0] = side;
                i__3[1] = 1, a__1[1] = trans;
                s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
                i__1 = *n - 1;
                i__2 = *n - 1;
                nb = ilaenv_(&c__1, "DORMQR", ch__1, m, &i__1, &i__2, &c_n1);
            }
        } else {
            if (left) {
/* Writing concatenation */
                i__3[0] = 1, a__1[0] = side;
                i__3[1] = 1, a__1[1] = trans;
                s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
                i__1 = *m - 1;
                i__2 = *m - 1;
                nb = ilaenv_(&c__1, "DORMLQ", ch__1, &i__1, n, &i__2, &c_n1);
            } else {
/* Writing concatenation */
                i__3[0] = 1, a__1[0] = side;
                i__3[1] = 1, a__1[1] = trans;
                s_cat(ch__1, a__1, i__3, &c__2, (ftnlen)2);
                i__1 = *n - 1;
                i__2 = *n - 1;
                nb = ilaenv_(&c__1, "DORMLQ", ch__1, m, &i__1, &i__2, &c_n1);
            }
        }
        lwkopt = max(1,nw) * nb;
        work[1] = (doublereal) lwkopt;
    }

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

/*     Quick return if possible */

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

    if (applyq) {

/*        Apply Q */

        if (nq >= *k) {

/*           Q was determined by a call to DGEBRD with nq >= k */

            dormqr_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
                    c_offset], ldc, &work[1], lwork, &iinfo);
        } else if (nq > 1) {

/*           Q was determined by a call to DGEBRD with nq < k */

            if (left) {
                mi = *m - 1;
                ni = *n;
                i1 = 2;
                i2 = 1;
            } else {
                mi = *m;
                ni = *n - 1;
                i1 = 1;
                i2 = 2;
            }
            i__1 = nq - 1;
            dormqr_(side, trans, &mi, &ni, &i__1, &a[a_dim1 + 2], lda, &tau[1]
, &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &iinfo);
        }
    } else {

/*        Apply P */

        if (notran) {
            *(unsigned char *)transt = 'T';
        } else {
            *(unsigned char *)transt = 'N';
        }
        if (nq > *k) {

/*           P was determined by a call to DGEBRD with nq > k */

            dormlq_(side, transt, m, n, k, &a[a_offset], lda, &tau[1], &c__[
                    c_offset], ldc, &work[1], lwork, &iinfo);
        } else if (nq > 1) {

/*           P was determined by a call to DGEBRD with nq <= k */

            if (left) {
                mi = *m - 1;
                ni = *n;
                i1 = 2;
                i2 = 1;
            } else {
                mi = *m;
                ni = *n - 1;
                i1 = 1;
                i2 = 2;
            }
            i__1 = nq - 1;
            dormlq_(side, transt, &mi, &ni, &i__1, &a[(a_dim1 << 1) + 1], lda, 
                     &tau[1], &c__[i1 + i2 * c_dim1], ldc, &work[1], lwork, &
                    iinfo);
        }
    }
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DORMBR */

} /* dormbr_ */