/* fortran/dgelq2.f -- translated by f2c (version 20200916).
   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
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        Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,

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*/

#ifdef __cplusplus
extern "C" {
#endif
#include "lmp_f2c.h"

/* > \brief \b DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorit
hm. */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download DGELQ2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgelq2.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgelq2.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgelq2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE DGELQ2( M, N, A, LDA, TAU, WORK, INFO ) */

/*       .. Scalar Arguments .. */
/*       INTEGER            INFO, LDA, M, N */
/*       .. */
/*       .. Array Arguments .. */
/*       DOUBLE PRECISION   A( LDA, * ), TAU( * ), WORK( * ) */
/*       .. */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > DGELQ2 computes an LQ factorization of a real m-by-n matrix A: */
/* > */
/* >    A = ( L 0 ) *  Q */
/* > */
/* > where: */
/* > */
/* >    Q is a n-by-n orthogonal matrix; */
/* >    L is a lower-triangular m-by-m matrix; */
/* >    0 is a m-by-(n-m) zero matrix, if m < n. */
/* > */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] M */
/* > \verbatim */
/* >          M is INTEGER */
/* >          The number of rows of the matrix A.  M >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The number of columns of the matrix A.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is DOUBLE PRECISION array, dimension (LDA,N) */
/* >          On entry, the m by n matrix A. */
/* >          On exit, the elements on and below the diagonal of the array */
/* >          contain the m by min(m,n) lower trapezoidal matrix L (L is */
/* >          lower triangular if m <= n); the elements above the diagonal, */
/* >          with the array TAU, represent the orthogonal matrix Q as a */
/* >          product of elementary reflectors (see Further Details). */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of the array A.  LDA >= max(1,M). */
/* > \endverbatim */
/* > */
/* > \param[out] TAU */
/* > \verbatim */
/* >          TAU is DOUBLE PRECISION array, dimension (min(M,N)) */
/* >          The scalar factors of the elementary reflectors (see Further */
/* >          Details). */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is DOUBLE PRECISION array, dimension (M) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0: successful exit */
/* >          < 0: if INFO = -i, the i-th argument had an illegal value */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \ingroup doubleGEcomputational */

/* > \par Further Details: */
/*  ===================== */
/* > */
/* > \verbatim */
/* > */
/* >  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**T */
/* > */
/* >  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:n) is stored on exit in A(i,i+1:n), */
/* >  and tau in TAU(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ int dgelq2_(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, i__3;

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


/*  -- LAPACK computational routine -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

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

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

/*     .. 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_((char *)"DGELQ2", &i__1, (ftnlen)6);
        return 0;
    }

    k = min(*m,*n);

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

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

        i__2 = *n - i__ + 1;
/* Computing MIN */
        i__3 = i__ + 1;
        dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[i__ + min(i__3,*n) * a_dim1]
                , lda, &tau[i__]);
        if (i__ < *m) {

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

            aii = a[i__ + i__ * a_dim1];
            a[i__ + i__ * a_dim1] = 1.;
            i__2 = *m - i__;
            i__3 = *n - i__ + 1;
            dlarf_((char *)"Right", &i__2, &i__3, &a[i__ + i__ * a_dim1], lda, &tau[
                    i__], &a[i__ + 1 + i__ * a_dim1], lda, &work[1], (ftnlen)
                    5);
            a[i__ + i__ * a_dim1] = aii;
        }
/* L10: */
    }
    return 0;

/*     End of DGELQ2 */

} /* dgelq2_ */

#ifdef __cplusplus
        }
#endif