sgeqp3.c

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/* sgeqp3.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 sgeqp3_(integer *m, integer *n, real *a, integer *lda, 
        integer *jpvt, real *tau, real *work, integer *lwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;

    /* Local variables */
    integer j, jb, na, nb, sm, sn, nx, fjb, iws, nfxd;
    extern doublereal snrm2_(integer *, real *, integer *);
    integer nbmin, minmn, minws;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
            integer *), slaqp2_(integer *, integer *, integer *, real *, 
            integer *, integer *, real *, real *, real *, real *), xerbla_(
            char *, integer *);
    extern integer ilaenv_(integer *, char *, char *, integer *, integer *, 
            integer *, integer *);
    extern /* Subroutine */ int sgeqrf_(integer *, integer *, real *, integer 
            *, real *, real *, integer *, integer *);
    integer topbmn, sminmn;
    extern /* Subroutine */ int slaqps_(integer *, integer *, integer *, 
            integer *, integer *, real *, integer *, integer *, real *, real *
, real *, real *, real *, integer *);
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ int sormqr_(char *, char *, integer *, integer *, 
            integer *, real *, integer *, real *, real *, integer *, real *, 
            integer *, integer *);


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

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

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

/*  SGEQP3 computes a QR factorization with column pivoting of a */
/*  matrix A:  A*P = Q*R  using Level 3 BLAS. */

/*  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, the upper triangle of the array contains the */
/*          min(M,N)-by-N upper trapezoidal matrix R; the elements below */
/*          the diagonal, together with the array TAU, represent the */
/*          orthogonal matrix Q as a product of min(M,N) elementary */
/*          reflectors. */

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

/*  JPVT    (input/output) INTEGER array, dimension (N) */
/*          On entry, if JPVT(J).ne.0, the J-th column of A is permuted */
/*          to the front of A*P (a leading column); if JPVT(J)=0, */
/*          the J-th column of A is a free column. */
/*          On exit, if JPVT(J)=K, then the J-th column of A*P was the */
/*          the K-th column of A. */

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

/*  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 >= 3*N+1. */
/*          For optimal performance LWORK >= 2*N+( N+1 )*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/complex scalar, and v is a real/complex vector */
/*  with v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in */
/*  A(i+1:m,i), and tau in TAU(i). */

/*  Based on contributions by */
/*    G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain */
/*    X. Sun, Computer Science Dept., Duke University, USA */

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

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

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --jpvt;
    --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;
    }

    if (*info == 0) {
        minmn = min(*m,*n);
        if (minmn == 0) {
            iws = 1;
            lwkopt = 1;
        } else {
            iws = *n * 3 + 1;
            nb = ilaenv_(&c__1, "SGEQRF", " ", m, n, &c_n1, &c_n1);
            lwkopt = (*n << 1) + (*n + 1) * nb;
        }
        work[1] = (real) lwkopt;

        if (*lwork < iws && ! lquery) {
            *info = -8;
        }
    }

    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("SGEQP3", &i__1);
        return 0;
    } else if (lquery) {
        return 0;
    }

/*     Quick return if possible. */

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

/*     Move initial columns up front. */

    nfxd = 1;
    i__1 = *n;
    for (j = 1; j <= i__1; ++j) {
        if (jpvt[j] != 0) {
            if (j != nfxd) {
                sswap_(m, &a[j * a_dim1 + 1], &c__1, &a[nfxd * a_dim1 + 1], &
                        c__1);
                jpvt[j] = jpvt[nfxd];
                jpvt[nfxd] = j;
            } else {
                jpvt[j] = j;
            }
            ++nfxd;
        } else {
            jpvt[j] = j;
        }
/* L10: */
    }
    --nfxd;

/*     Factorize fixed columns */
/*     ======================= */

/*     Compute the QR factorization of fixed columns and update */
/*     remaining columns. */

    if (nfxd > 0) {
        na = min(*m,nfxd);
/* CC      CALL SGEQR2( M, NA, A, LDA, TAU, WORK, INFO ) */
        sgeqrf_(m, &na, &a[a_offset], lda, &tau[1], &work[1], lwork, info);
/* Computing MAX */
        i__1 = iws, i__2 = (integer) work[1];
        iws = max(i__1,i__2);
        if (na < *n) {
/* CC         CALL SORM2R( 'Left', 'Transpose', M, N-NA, NA, A, LDA, */
/* CC  $                   TAU, A( 1, NA+1 ), LDA, WORK, INFO ) */
            i__1 = *n - na;
            sormqr_("Left", "Transpose", m, &i__1, &na, &a[a_offset], lda, &
                    tau[1], &a[(na + 1) * a_dim1 + 1], lda, &work[1], lwork, 
                    info);
/* Computing MAX */
            i__1 = iws, i__2 = (integer) work[1];
            iws = max(i__1,i__2);
        }
    }

/*     Factorize free columns */
/*     ====================== */

    if (nfxd < minmn) {

        sm = *m - nfxd;
        sn = *n - nfxd;
        sminmn = minmn - nfxd;

/*        Determine the block size. */

        nb = ilaenv_(&c__1, "SGEQRF", " ", &sm, &sn, &c_n1, &c_n1);
        nbmin = 2;
        nx = 0;

        if (nb > 1 && nb < sminmn) {

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

/* Computing MAX */
            i__1 = 0, i__2 = ilaenv_(&c__3, "SGEQRF", " ", &sm, &sn, &c_n1, &
                    c_n1);
            nx = max(i__1,i__2);


            if (nx < sminmn) {

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

                minws = (sn << 1) + (sn + 1) * nb;
                iws = max(iws,minws);
                if (*lwork < minws) {

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

                    nb = (*lwork - (sn << 1)) / (sn + 1);
/* Computing MAX */
                    i__1 = 2, i__2 = ilaenv_(&c__2, "SGEQRF", " ", &sm, &sn, &
                            c_n1, &c_n1);
                    nbmin = max(i__1,i__2);


                }
            }
        }

/*        Initialize partial column norms. The first N elements of work */
/*        store the exact column norms. */

        i__1 = *n;
        for (j = nfxd + 1; j <= i__1; ++j) {
            work[j] = snrm2_(&sm, &a[nfxd + 1 + j * a_dim1], &c__1);
            work[*n + j] = work[j];
/* L20: */
        }

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

/*           Use blocked code initially. */

            j = nfxd + 1;

/*           Compute factorization: while loop. */


            topbmn = minmn - nx;
L30:
            if (j <= topbmn) {
/* Computing MIN */
                i__1 = nb, i__2 = topbmn - j + 1;
                jb = min(i__1,i__2);

/*              Factorize JB columns among columns J:N. */

                i__1 = *n - j + 1;
                i__2 = j - 1;
                i__3 = *n - j + 1;
                slaqps_(m, &i__1, &i__2, &jb, &fjb, &a[j * a_dim1 + 1], lda, &
                        jpvt[j], &tau[j], &work[j], &work[*n + j], &work[(*n 
                        << 1) + 1], &work[(*n << 1) + jb + 1], &i__3);

                j += fjb;
                goto L30;
            }
        } else {
            j = nfxd + 1;
        }

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


        if (j <= minmn) {
            i__1 = *n - j + 1;
            i__2 = j - 1;
            slaqp2_(m, &i__1, &i__2, &a[j * a_dim1 + 1], lda, &jpvt[j], &tau[
                    j], &work[j], &work[*n + j], &work[(*n << 1) + 1]);
        }

    }

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

/*     End of SGEQP3 */

} /* sgeqp3_ */