dlaqps.c

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/* dlaqps.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 doublereal c_b8 = -1.;
static doublereal c_b9 = 1.;
static doublereal c_b16 = 0.;

/* Subroutine */ int dlaqps_(integer *m, integer *n, integer *offset, integer 
        *nb, integer *kb, doublereal *a, integer *lda, integer *jpvt, 
        doublereal *tau, doublereal *vn1, doublereal *vn2, doublereal *auxv, 
        doublereal *f, integer *ldf)
{
    /* System generated locals */
    integer a_dim1, a_offset, f_dim1, f_offset, i__1, i__2;
    doublereal d__1, d__2;

    /* Builtin functions */
    double sqrt(doublereal);
    integer i_dnnt(doublereal *);

    /* Local variables */
    integer j, k, rk;
    doublereal akk;
    integer pvt;
    doublereal temp;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal temp2, tol3z;
    extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, 
            integer *, doublereal *, doublereal *, integer *, doublereal *, 
            integer *, doublereal *, doublereal *, integer *),
             dgemv_(char *, integer *, integer *, doublereal *, doublereal *, 
            integer *, doublereal *, integer *, doublereal *, doublereal *, 
            integer *);
    integer itemp;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlarfp_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *);
    integer lsticc, lastrk;


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

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

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

/*  DLAQPS computes a step of QR factorization with column pivoting */
/*  of a real M-by-N matrix A by using Blas-3.  It tries to factorize */
/*  NB columns from A starting from the row OFFSET+1, and updates all */
/*  of the matrix with Blas-3 xGEMM. */

/*  In some cases, due to catastrophic cancellations, it cannot */
/*  factorize NB columns.  Hence, the actual number of factorized */
/*  columns is returned in KB. */

/*  Block A(1:OFFSET,1:N) is accordingly pivoted, but not factorized. */

/*  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 */

/*  OFFSET  (input) INTEGER */
/*          The number of rows of A that have been factorized in */
/*          previous steps. */

/*  NB      (input) INTEGER */
/*          The number of columns to factorize. */

/*  KB      (output) INTEGER */
/*          The number of columns actually factorized. */

/*  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, block A(OFFSET+1:M,1:KB) is the triangular */
/*          factor obtained and block A(1:OFFSET,1:N) has been */
/*          accordingly pivoted, but no factorized. */
/*          The rest of the matrix, block A(OFFSET+1:M,KB+1:N) has */
/*          been updated. */

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

/*  JPVT    (input/output) INTEGER array, dimension (N) */
/*          JPVT(I) = K <==> Column K of the full matrix A has been */
/*          permuted into position I in AP. */

/*  TAU     (output) DOUBLE PRECISION array, dimension (KB) */
/*          The scalar factors of the elementary reflectors. */

/*  VN1     (input/output) DOUBLE PRECISION array, dimension (N) */
/*          The vector with the partial column norms. */

/*  VN2     (input/output) DOUBLE PRECISION array, dimension (N) */
/*          The vector with the exact column norms. */

/*  AUXV    (input/output) DOUBLE PRECISION array, dimension (NB) */
/*          Auxiliar vector. */

/*  F       (input/output) DOUBLE PRECISION array, dimension (LDF,NB) */
/*          Matrix F' = L*Y'*A. */

/*  LDF     (input) INTEGER */
/*          The leading dimension of the array F. LDF >= max(1,N). */

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

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

/*  Partial column norm updating strategy modified by */
/*    Z. Drmac and Z. Bujanovic, Dept. of Mathematics, */
/*    University of Zagreb, Croatia. */
/*    June 2006. */
/*  For more details see LAPACK Working Note 176. */
/*  ===================================================================== */

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

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --jpvt;
    --tau;
    --vn1;
    --vn2;
    --auxv;
    f_dim1 = *ldf;
    f_offset = 1 + f_dim1;
    f -= f_offset;

    /* Function Body */
/* Computing MIN */
    i__1 = *m, i__2 = *n + *offset;
    lastrk = min(i__1,i__2);
    lsticc = 0;
    k = 0;
    tol3z = sqrt(dlamch_("Epsilon"));

/*     Beginning of while loop. */

L10:
    if (k < *nb && lsticc == 0) {
        ++k;
        rk = *offset + k;

/*        Determine ith pivot column and swap if necessary */

        i__1 = *n - k + 1;
        pvt = k - 1 + idamax_(&i__1, &vn1[k], &c__1);
        if (pvt != k) {
            dswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1);
            i__1 = k - 1;
            dswap_(&i__1, &f[pvt + f_dim1], ldf, &f[k + f_dim1], ldf);
            itemp = jpvt[pvt];
            jpvt[pvt] = jpvt[k];
            jpvt[k] = itemp;
            vn1[pvt] = vn1[k];
            vn2[pvt] = vn2[k];
        }

/*        Apply previous Householder reflectors to column K: */
/*        A(RK:M,K) := A(RK:M,K) - A(RK:M,1:K-1)*F(K,1:K-1)'. */

        if (k > 1) {
            i__1 = *m - rk + 1;
            i__2 = k - 1;
            dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[rk + a_dim1], lda, 
                    &f[k + f_dim1], ldf, &c_b9, &a[rk + k * a_dim1], &c__1);
        }

/*        Generate elementary reflector H(k). */

        if (rk < *m) {
            i__1 = *m - rk + 1;
            dlarfp_(&i__1, &a[rk + k * a_dim1], &a[rk + 1 + k * a_dim1], &
                    c__1, &tau[k]);
        } else {
            dlarfp_(&c__1, &a[rk + k * a_dim1], &a[rk + k * a_dim1], &c__1, &
                    tau[k]);
        }

        akk = a[rk + k * a_dim1];
        a[rk + k * a_dim1] = 1.;

/*        Compute Kth column of F: */

/*        Compute  F(K+1:N,K) := tau(K)*A(RK:M,K+1:N)'*A(RK:M,K). */

        if (k < *n) {
            i__1 = *m - rk + 1;
            i__2 = *n - k;
            dgemv_("Transpose", &i__1, &i__2, &tau[k], &a[rk + (k + 1) * 
                    a_dim1], lda, &a[rk + k * a_dim1], &c__1, &c_b16, &f[k + 
                    1 + k * f_dim1], &c__1);
        }

/*        Padding F(1:K,K) with zeros. */

        i__1 = k;
        for (j = 1; j <= i__1; ++j) {
            f[j + k * f_dim1] = 0.;
/* L20: */
        }

/*        Incremental updating of F: */
/*        F(1:N,K) := F(1:N,K) - tau(K)*F(1:N,1:K-1)*A(RK:M,1:K-1)' */
/*                    *A(RK:M,K). */

        if (k > 1) {
            i__1 = *m - rk + 1;
            i__2 = k - 1;
            d__1 = -tau[k];
            dgemv_("Transpose", &i__1, &i__2, &d__1, &a[rk + a_dim1], lda, &a[
                    rk + k * a_dim1], &c__1, &c_b16, &auxv[1], &c__1);

            i__1 = k - 1;
            dgemv_("No transpose", n, &i__1, &c_b9, &f[f_dim1 + 1], ldf, &
                    auxv[1], &c__1, &c_b9, &f[k * f_dim1 + 1], &c__1);
        }

/*        Update the current row of A: */
/*        A(RK,K+1:N) := A(RK,K+1:N) - A(RK,1:K)*F(K+1:N,1:K)'. */

        if (k < *n) {
            i__1 = *n - k;
            dgemv_("No transpose", &i__1, &k, &c_b8, &f[k + 1 + f_dim1], ldf, 
                    &a[rk + a_dim1], lda, &c_b9, &a[rk + (k + 1) * a_dim1], 
                    lda);
        }

/*        Update partial column norms. */

        if (rk < lastrk) {
            i__1 = *n;
            for (j = k + 1; j <= i__1; ++j) {
                if (vn1[j] != 0.) {

/*                 NOTE: The following 4 lines follow from the analysis in */
/*                 Lapack Working Note 176. */

                    temp = (d__1 = a[rk + j * a_dim1], abs(d__1)) / vn1[j];
/* Computing MAX */
                    d__1 = 0., d__2 = (temp + 1.) * (1. - temp);
                    temp = max(d__1,d__2);
/* Computing 2nd power */
                    d__1 = vn1[j] / vn2[j];
                    temp2 = temp * (d__1 * d__1);
                    if (temp2 <= tol3z) {
                        vn2[j] = (doublereal) lsticc;
                        lsticc = j;
                    } else {
                        vn1[j] *= sqrt(temp);
                    }
                }
/* L30: */
            }
        }

        a[rk + k * a_dim1] = akk;

/*        End of while loop. */

        goto L10;
    }
    *kb = k;
    rk = *offset + *kb;

/*     Apply the block reflector to the rest of the matrix: */
/*     A(OFFSET+KB+1:M,KB+1:N) := A(OFFSET+KB+1:M,KB+1:N) - */
/*                         A(OFFSET+KB+1:M,1:KB)*F(KB+1:N,1:KB)'. */

/* Computing MIN */
    i__1 = *n, i__2 = *m - *offset;
    if (*kb < min(i__1,i__2)) {
        i__1 = *m - rk;
        i__2 = *n - *kb;
        dgemm_("No transpose", "Transpose", &i__1, &i__2, kb, &c_b8, &a[rk + 
                1 + a_dim1], lda, &f[*kb + 1 + f_dim1], ldf, &c_b9, &a[rk + 1 
                + (*kb + 1) * a_dim1], lda);
    }

/*     Recomputation of difficult columns. */

L40:
    if (lsticc > 0) {
        itemp = i_dnnt(&vn2[lsticc]);
        i__1 = *m - rk;
        vn1[lsticc] = dnrm2_(&i__1, &a[rk + 1 + lsticc * a_dim1], &c__1);

/*        NOTE: The computation of VN1( LSTICC ) relies on the fact that */
/*        SNRM2 does not fail on vectors with norm below the value of */
/*        SQRT(DLAMCH('S')) */

        vn2[lsticc] = vn1[lsticc];
        lsticc = itemp;
        goto L40;
    }

    return 0;

/*     End of DLAQPS */

} /* dlaqps_ */