sgerqf.c

Go to the documentation of this file.

/* sgerqf.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__3 = 3;
static integer c__2 = 2;

/* Subroutine */ int sgerqf_(integer *m, integer *n, real *a, integer *lda, 
        real *tau, real *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;

    /* Local variables */
    integer i__, k, ib, nb, ki, kk, mu, nu, nx, iws, nbmin, iinfo;
    extern /* Subroutine */ int sgerq2_(integer *, integer *, real *, integer 
            *, real *, real *, integer *), slarfb_(char *, char *, char *, 
            char *, integer *, integer *, integer *, real *, integer *, real *
, integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int slarft_(char *, char *, integer *, integer *, 
            real *, integer *, real *, real *, integer *);
    integer ldwork, 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 */
/*  ======= */

/*  SGERQF computes an RQ factorization of a real M-by-N matrix A: */
/*  A = R * Q. */

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

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

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

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, */
/*          if m <= n, the upper triangle of the subarray */
/*          A(1:m,n-m+1:n) contains the M-by-M upper triangular matrix R; */
/*          if m >= n, the elements on and above the (m-n)-th subdiagonal */
/*          contain the M-by-N upper trapezoidal matrix R; */
/*          the remaining elements, with the array TAU, represent the */
/*          orthogonal matrix Q as a product of min(m,n) elementary */
/*          reflectors (see Further Details). */

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

/*  TAU     (output) REAL array, dimension (min(M,N)) */
/*          The scalar factors of the elementary reflectors (see Further */
/*          Details). */

/*  WORK    (workspace/output) REAL 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,M). */
/*          For optimum performance LWORK >= M*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 */

/*  Further Details */
/*  =============== */

/*  The matrix Q is represented as a product of elementary reflectors */

/*     Q = H(1) H(2) . . . H(k), where k = min(m,n). */

/*  Each H(i) has the form */

/*     H(i) = I - tau * v * v' */

/*  where tau is a real scalar, and v is a real vector with */
/*  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in */
/*  A(m-k+i,1:n-k+i-1), and tau in TAU(i). */

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

/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. External 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;
    lquery = *lwork == -1;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*m)) {
        *info = -4;
    } else if (*lwork < max(1,*m) && ! lquery) {
        *info = -7;
    }

    if (*info == 0) {
        k = min(*m,*n);
        if (k == 0) {
            lwkopt = 1;
        } else {
            nb = ilaenv_(&c__1, "SGERQF", " ", m, n, &c_n1, &c_n1);
            lwkopt = *m * nb;
            work[1] = (real) lwkopt;
        }
        work[1] = (real) lwkopt;

        if (*lwork < max(1,*m) && ! lquery) {
            *info = -7;
        }
    }

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

/*     Quick return if possible */

    if (k == 0) {
        return 0;
    }

    nbmin = 2;
    nx = 1;
    iws = *m;
    if (nb > 1 && nb < k) {

/*        Determine when to cross over from blocked to unblocked code. */

/* Computing MAX */
        i__1 = 0, i__2 = ilaenv_(&c__3, "SGERQF", " ", m, n, &c_n1, &c_n1);
        nx = max(i__1,i__2);
        if (nx < k) {

/*           Determine if workspace is large enough for blocked code. */

            ldwork = *m;
            iws = ldwork * nb;
            if (*lwork < iws) {

/*              Not enough workspace to use optimal NB:  reduce NB and */
/*              determine the minimum value of NB. */

                nb = *lwork / ldwork;
/* Computing MAX */
                i__1 = 2, i__2 = ilaenv_(&c__2, "SGERQF", " ", m, n, &c_n1, &
                        c_n1);
                nbmin = max(i__1,i__2);
            }
        }
    }

    if (nb >= nbmin && nb < k && nx < k) {

/*        Use blocked code initially. */
/*        The last kk rows are handled by the block method. */

        ki = (k - nx - 1) / nb * nb;
/* Computing MIN */
        i__1 = k, i__2 = ki + nb;
        kk = min(i__1,i__2);

        i__1 = k - kk + 1;
        i__2 = -nb;
        for (i__ = k - kk + ki + 1; i__2 < 0 ? i__ >= i__1 : i__ <= i__1; i__ 
                += i__2) {
/* Computing MIN */
            i__3 = k - i__ + 1;
            ib = min(i__3,nb);

/*           Compute the RQ factorization of the current block */
/*           A(m-k+i:m-k+i+ib-1,1:n-k+i+ib-1) */

            i__3 = *n - k + i__ + ib - 1;
            sgerq2_(&ib, &i__3, &a[*m - k + i__ + a_dim1], lda, &tau[i__], &
                    work[1], &iinfo);
            if (*m - k + i__ > 1) {

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

                i__3 = *n - k + i__ + ib - 1;
                slarft_("Backward", "Rowwise", &i__3, &ib, &a[*m - k + i__ + 
                        a_dim1], lda, &tau[i__], &work[1], &ldwork);

/*              Apply H to A(1:m-k+i-1,1:n-k+i+ib-1) from the right */

                i__3 = *m - k + i__ - 1;
                i__4 = *n - k + i__ + ib - 1;
                slarfb_("Right", "No transpose", "Backward", "Rowwise", &i__3, 
                         &i__4, &ib, &a[*m - k + i__ + a_dim1], lda, &work[1], 
                         &ldwork, &a[a_offset], lda, &work[ib + 1], &ldwork);
            }
/* L10: */
        }
        mu = *m - k + i__ + nb - 1;
        nu = *n - k + i__ + nb - 1;
    } else {
        mu = *m;
        nu = *n;
    }

/*     Use unblocked code to factor the last or only block */

    if (mu > 0 && nu > 0) {
        sgerq2_(&mu, &nu, &a[a_offset], lda, &tau[1], &work[1], &iinfo);
    }

    work[1] = (real) iws;
    return 0;

/*     End of SGERQF */

} /* sgerqf_ */