dormrq.c

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/* dormrq.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;
static integer c__65 = 65;

/* Subroutine */ int dormrq_(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], i__4, 
            i__5;
    char ch__1[2];

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

    /* Local variables */
    integer i__;
    doublereal t[4160]  /* was [65][64] */;
    integer i1, i2, i3, ib, nb, mi, ni, nq, nw, iws;
    logical left;
    extern logical lsame_(char *, char *);
    integer nbmin, iinfo;
    extern /* Subroutine */ int dormr2_(char *, char *, integer *, integer *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *), dlarfb_(char 
            *, char *, char *, char *, integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, integer *), dlarft_(char *, char *, integer *, integer *, doublereal 
            *, integer *, doublereal *, doublereal *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    logical notran;
    integer ldwork;
    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 */
/*  ======= */

/*  DORMRQ 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 */

/*  where Q is a real orthogonal matrix defined as the product of k */
/*  elementary reflectors */

/*        Q = H(1) H(2) . . . H(k) */

/*  as returned by DGERQF. Q is of order M if SIDE = 'L' and of order N */
/*  if SIDE = 'R'. */

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

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

/*  TRANS   (input) CHARACTER*1 */
/*          = 'N':  No transpose, apply Q; */
/*          = 'T':  Transpose, apply Q**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 */
/*          The number of elementary reflectors whose product defines */
/*          the matrix Q. */
/*          If SIDE = 'L', M >= K >= 0; */
/*          if SIDE = 'R', N >= K >= 0. */

/*  A       (input) DOUBLE PRECISION array, dimension */
/*                               (LDA,M) if SIDE = 'L', */
/*                               (LDA,N) if SIDE = 'R' */
/*          The i-th row must contain the vector which defines the */
/*          elementary reflector H(i), for i = 1,2,...,k, as returned by */
/*          DGERQF in the last k rows of its array argument A. */
/*          A is modified by the routine but restored on exit. */

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

/*  TAU     (input) DOUBLE PRECISION array, dimension (K) */
/*          TAU(i) must contain the scalar factor of the elementary */
/*          reflector H(i), as returned by DGERQF. */

/*  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. */

/*  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 */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. Local Arrays .. */
/*     .. */
/*     .. 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;
    left = lsame_(side, "L");
    notran = lsame_(trans, "N");
    lquery = *lwork == -1;

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

    if (left) {
        nq = *m;
        nw = max(1,*n);
    } else {
        nq = *n;
        nw = max(1,*m);
    }
    if (! left && ! lsame_(side, "R")) {
        *info = -1;
    } else if (! notran && ! lsame_(trans, "T")) {
        *info = -2;
    } else if (*m < 0) {
        *info = -3;
    } else if (*n < 0) {
        *info = -4;
    } else if (*k < 0 || *k > nq) {
        *info = -5;
    } else if (*lda < max(1,*k)) {
        *info = -7;
    } else if (*ldc < max(1,*m)) {
        *info = -10;
    }

    if (*info == 0) {
        if (*m == 0 || *n == 0) {
            lwkopt = 1;
        } else {

/*           Determine the block size.  NB may be at most NBMAX, where */
/*           NBMAX is used to define the local array T. */

/* Computing MIN */
/* 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 = 64, i__2 = ilaenv_(&c__1, "DORMRQ", ch__1, m, n, k, &c_n1);
            nb = min(i__1,i__2);
            lwkopt = nw * nb;
        }
        work[1] = (doublereal) lwkopt;

        if (*lwork < nw && ! lquery) {
            *info = -12;
        }
    }

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

/*     Quick return if possible */

    if (*m == 0 || *n == 0) {
        return 0;
    }

    nbmin = 2;
    ldwork = nw;
    if (nb > 1 && nb < *k) {
        iws = nw * nb;
        if (*lwork < iws) {
            nb = *lwork / ldwork;
/* Computing MAX */
/* 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 = 2, i__2 = ilaenv_(&c__2, "DORMRQ", ch__1, m, n, k, &c_n1);
            nbmin = max(i__1,i__2);
        }
    } else {
        iws = nw;
    }

    if (nb < nbmin || nb >= *k) {

/*        Use unblocked code */

        dormr2_(side, trans, m, n, k, &a[a_offset], lda, &tau[1], &c__[
                c_offset], ldc, &work[1], &iinfo);
    } else {

/*        Use blocked code */

        if (left && ! notran || ! left && notran) {
            i1 = 1;
            i2 = *k;
            i3 = nb;
        } else {
            i1 = (*k - 1) / nb * nb + 1;
            i2 = 1;
            i3 = -nb;
        }

        if (left) {
            ni = *n;
        } else {
            mi = *m;
        }

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

        i__1 = i2;
        i__2 = i3;
        for (i__ = i1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ += i__2) {
/* Computing MIN */
            i__4 = nb, i__5 = *k - i__ + 1;
            ib = min(i__4,i__5);

/*           Form the triangular factor of the block reflector */
/*           H = H(i+ib-1) . . . H(i+1) H(i) */

            i__4 = nq - *k + i__ + ib - 1;
            dlarft_("Backward", "Rowwise", &i__4, &ib, &a[i__ + a_dim1], lda, 
                    &tau[i__], t, &c__65);
            if (left) {

/*              H or H' is applied to C(1:m-k+i+ib-1,1:n) */

                mi = *m - *k + i__ + ib - 1;
            } else {

/*              H or H' is applied to C(1:m,1:n-k+i+ib-1) */

                ni = *n - *k + i__ + ib - 1;
            }

/*           Apply H or H' */

            dlarfb_(side, transt, "Backward", "Rowwise", &mi, &ni, &ib, &a[
                    i__ + a_dim1], lda, t, &c__65, &c__[c_offset], ldc, &work[
                    1], &ldwork);
/* L10: */
        }
    }
    work[1] = (doublereal) lwkopt;
    return 0;

/*     End of DORMRQ */

} /* dormrq_ */