dgeqpf.c

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/* dgeqpf.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;

/* Subroutine */ int dgeqpf_(integer *m, integer *n, doublereal *a, integer *
        lda, integer *jpvt, doublereal *tau, doublereal *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    doublereal d__1, d__2;

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

    /* Local variables */
    integer i__, j, ma, mn;
    doublereal aii;
    integer pvt;
    doublereal temp;
    extern doublereal dnrm2_(integer *, doublereal *, integer *);
    doublereal temp2, tol3z;
    extern /* Subroutine */ int dlarf_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *);
    integer itemp;
    extern /* Subroutine */ int dswap_(integer *, doublereal *, integer *, 
            doublereal *, integer *), dgeqr2_(integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *), 
            dorm2r_(char *, char *, integer *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *, integer *);
    extern doublereal dlamch_(char *);
    extern integer idamax_(integer *, doublereal *, integer *);
    extern /* Subroutine */ int dlarfp_(integer *, doublereal *, doublereal *, 
             integer *, doublereal *), xerbla_(char *, integer *);


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

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

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

/*  This routine is deprecated and has been replaced by routine DGEQP3. */

/*  DGEQPF computes a QR factorization with column pivoting of a */
/*  real M-by-N matrix A: A*P = Q*R. */

/*  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) DOUBLE PRECISION 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 triangular 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(i) .ne. 0, the i-th column of A is permuted */
/*          to the front of A*P (a leading column); if JPVT(i) = 0, */
/*          the i-th column of A is a free column. */
/*          On exit, if JPVT(i) = k, then the i-th column of A*P */
/*          was the k-th column of A. */

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

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (3*N) */

/*  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(n) */

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

/*     H = I - tau * v * v' */

/*  where tau is a real scalar, and v is a real 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). */

/*  The matrix P is represented in jpvt as follows: If */
/*     jpvt(j) = i */
/*  then the jth column of P is the ith canonical unit vector. */

/*  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 .. */

/*     Test the input arguments */

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

    /* Function Body */
    *info = 0;
    if (*m < 0) {
        *info = -1;
    } else if (*n < 0) {
        *info = -2;
    } else if (*lda < max(1,*m)) {
        *info = -4;
    }
    if (*info != 0) {
        i__1 = -(*info);
        xerbla_("DGEQPF", &i__1);
        return 0;
    }

    mn = min(*m,*n);
    tol3z = sqrt(dlamch_("Epsilon"));

/*     Move initial columns up front */

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

/*     Compute the QR factorization and update remaining columns */

    if (itemp > 0) {
        ma = min(itemp,*m);
        dgeqr2_(m, &ma, &a[a_offset], lda, &tau[1], &work[1], info);
        if (ma < *n) {
            i__1 = *n - ma;
            dorm2r_("Left", "Transpose", m, &i__1, &ma, &a[a_offset], lda, &
                    tau[1], &a[(ma + 1) * a_dim1 + 1], lda, &work[1], info);
        }
    }

    if (itemp < mn) {

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

        i__1 = *n;
        for (i__ = itemp + 1; i__ <= i__1; ++i__) {
            i__2 = *m - itemp;
            work[i__] = dnrm2_(&i__2, &a[itemp + 1 + i__ * a_dim1], &c__1);
            work[*n + i__] = work[i__];
/* L20: */
        }

/*        Compute factorization */

        i__1 = mn;
        for (i__ = itemp + 1; i__ <= i__1; ++i__) {

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

            i__2 = *n - i__ + 1;
            pvt = i__ - 1 + idamax_(&i__2, &work[i__], &c__1);

            if (pvt != i__) {
                dswap_(m, &a[pvt * a_dim1 + 1], &c__1, &a[i__ * a_dim1 + 1], &
                        c__1);
                itemp = jpvt[pvt];
                jpvt[pvt] = jpvt[i__];
                jpvt[i__] = itemp;
                work[pvt] = work[i__];
                work[*n + pvt] = work[*n + i__];
            }

/*           Generate elementary reflector H(i) */

            if (i__ < *m) {
                i__2 = *m - i__ + 1;
                dlarfp_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + 1 + i__ * 
                        a_dim1], &c__1, &tau[i__]);
            } else {
                dlarfp_(&c__1, &a[*m + *m * a_dim1], &a[*m + *m * a_dim1], &
                        c__1, &tau[*m]);
            }

            if (i__ < *n) {

/*              Apply H(i) to A(i:m,i+1:n) from the left */

                aii = a[i__ + i__ * a_dim1];
                a[i__ + i__ * a_dim1] = 1.;
                i__2 = *m - i__ + 1;
                i__3 = *n - i__;
                dlarf_("LEFT", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &
                        tau[i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[(*
                        n << 1) + 1]);
                a[i__ + i__ * a_dim1] = aii;
            }

/*           Update partial column norms */

            i__2 = *n;
            for (j = i__ + 1; j <= i__2; ++j) {
                if (work[j] != 0.) {

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

                    temp = (d__1 = a[i__ + j * a_dim1], abs(d__1)) / work[j];
/* Computing MAX */
                    d__1 = 0., d__2 = (temp + 1.) * (1. - temp);
                    temp = max(d__1,d__2);
/* Computing 2nd power */
                    d__1 = work[j] / work[*n + j];
                    temp2 = temp * (d__1 * d__1);
                    if (temp2 <= tol3z) {
                        if (*m - i__ > 0) {
                            i__3 = *m - i__;
                            work[j] = dnrm2_(&i__3, &a[i__ + 1 + j * a_dim1], 
                                    &c__1);
                            work[*n + j] = work[j];
                        } else {
                            work[j] = 0.;
                            work[*n + j] = 0.;
                        }
                    } else {
                        work[j] *= sqrt(temp);
                    }
                }
/* L30: */
            }

/* L40: */
        }
    }
    return 0;

/*     End of DGEQPF */

} /* dgeqpf_ */