slaqp2.c

Go to the documentation of this file.

/* slaqp2.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 slaqp2_(integer *m, integer *n, integer *offset, real *a, 
         integer *lda, integer *jpvt, real *tau, real *vn1, real *vn2, real *
        work)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3;
    real r__1, r__2;

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

    /* Local variables */
    integer i__, j, mn;
    real aii;
    integer pvt;
    real temp, temp2;
    extern doublereal snrm2_(integer *, real *, integer *);
    real tol3z;
    integer offpi;
    extern /* Subroutine */ int slarf_(char *, integer *, integer *, real *, 
            integer *, real *, real *, integer *, real *);
    integer itemp;
    extern /* Subroutine */ int sswap_(integer *, real *, integer *, real *, 
            integer *);
    extern doublereal slamch_(char *);
    extern integer isamax_(integer *, real *, integer *);
    extern /* Subroutine */ int slarfp_(integer *, real *, real *, integer *, 
            real *);


/*  -- LAPACK auxiliary routine (version 3.2) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     November 2006 */

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

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

/*  SLAQP2 computes a QR factorization with column pivoting of */
/*  the block A(OFFSET+1:M,1:N). */
/*  The 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 the matrix A that must be pivoted */
/*          but no factorized. OFFSET >= 0. */

/*  A       (input/output) REAL array, dimension (LDA,N) */
/*          On entry, the M-by-N matrix A. */
/*          On exit, the upper triangle of block A(OFFSET+1:M,1:N) is */
/*          the triangular factor obtained; the elements in block */
/*          A(OFFSET+1:M,1:N) below the diagonal, together with the */
/*          array TAU, represent the orthogonal matrix Q as a product of */
/*          elementary reflectors. Block A(1:OFFSET,1:N) has been */
/*          accordingly pivoted, but no factorized. */

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

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

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

/*  WORK    (workspace) REAL array, dimension (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;
    --work;

    /* Function Body */
/* Computing MIN */
    i__1 = *m - *offset;
    mn = min(i__1,*n);
    tol3z = sqrt(slamch_("Epsilon"));

/*     Compute factorization. */

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

        offpi = *offset + i__;

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

        i__2 = *n - i__ + 1;
        pvt = i__ - 1 + isamax_(&i__2, &vn1[i__], &c__1);

        if (pvt != i__) {
            sswap_(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;
            vn1[pvt] = vn1[i__];
            vn2[pvt] = vn2[i__];
        }

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

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

        if (i__ < *n) {

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

            aii = a[offpi + i__ * a_dim1];
            a[offpi + i__ * a_dim1] = 1.f;
            i__2 = *m - offpi + 1;
            i__3 = *n - i__;
            slarf_("Left", &i__2, &i__3, &a[offpi + i__ * a_dim1], &c__1, &
                    tau[i__], &a[offpi + (i__ + 1) * a_dim1], lda, &work[1]);
            a[offpi + i__ * a_dim1] = aii;
        }

/*        Update partial column norms. */

        i__2 = *n;
        for (j = i__ + 1; j <= i__2; ++j) {
            if (vn1[j] != 0.f) {

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

/* Computing 2nd power */
                r__2 = (r__1 = a[offpi + j * a_dim1], dabs(r__1)) / vn1[j];
                temp = 1.f - r__2 * r__2;
                temp = dmax(temp,0.f);
/* Computing 2nd power */
                r__1 = vn1[j] / vn2[j];
                temp2 = temp * (r__1 * r__1);
                if (temp2 <= tol3z) {
                    if (offpi < *m) {
                        i__3 = *m - offpi;
                        vn1[j] = snrm2_(&i__3, &a[offpi + 1 + j * a_dim1], &
                                c__1);
                        vn2[j] = vn1[j];
                    } else {
                        vn1[j] = 0.f;
                        vn2[j] = 0.f;
                    }
                } else {
                    vn1[j] *= sqrt(temp);
                }
            }
/* L10: */
        }

/* L20: */
    }

    return 0;

/*     End of SLAQP2 */

} /* slaqp2_ */