dgeql2.c

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/* dgeql2.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 dgeql2_(integer *m, integer *n, doublereal *a, integer *
        lda, doublereal *tau, doublereal *work, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2;

    /* Local variables */
    integer i__, k;
    doublereal aii;
    extern /* Subroutine */ int dlarf_(char *, integer *, integer *, 
            doublereal *, integer *, doublereal *, doublereal *, integer *, 
            doublereal *), dlarfp_(integer *, doublereal *, 
            doublereal *, integer *, doublereal *), xerbla_(char *, integer *);


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

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

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

/*  DGEQL2 computes a QL factorization of a real m by n matrix A: */
/*  A = Q * L. */

/*  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, if m >= n, the lower triangle of the subarray */
/*          A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; */
/*          if m <= n, the elements on and below the (n-m)-th */
/*          superdiagonal contain the m by n lower trapezoidal matrix L; */
/*          the remaining elements, with the array TAU, represent the */
/*          orthogonal matrix Q as a product of elementary reflectors */
/*          (see Further Details). */

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

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

/*  WORK    (workspace) DOUBLE PRECISION array, dimension (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in */
/*  A(1:m-k+i-1,n-k+i), and tau in TAU(i). */

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

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic 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;
    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_("DGEQL2", &i__1);
        return 0;
    }

    k = min(*m,*n);

    for (i__ = k; i__ >= 1; --i__) {

/*        Generate elementary reflector H(i) to annihilate */
/*        A(1:m-k+i-1,n-k+i) */

        i__1 = *m - k + i__;
        dlarfp_(&i__1, &a[*m - k + i__ + (*n - k + i__) * a_dim1], &a[(*n - k 
                + i__) * a_dim1 + 1], &c__1, &tau[i__]);

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

        aii = a[*m - k + i__ + (*n - k + i__) * a_dim1];
        a[*m - k + i__ + (*n - k + i__) * a_dim1] = 1.;
        i__1 = *m - k + i__;
        i__2 = *n - k + i__ - 1;
        dlarf_("Left", &i__1, &i__2, &a[(*n - k + i__) * a_dim1 + 1], &c__1, &
                tau[i__], &a[a_offset], lda, &work[1]);
        a[*m - k + i__ + (*n - k + i__) * a_dim1] = aii;
/* L10: */
    }
    return 0;

/*     End of DGEQL2 */

} /* dgeql2_ */