lammps/lib/linalg/dgeqr2.cpp

/* fortran/dgeqr2.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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*/

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

/* Table of constant values */

static integer c__1 = 1;

/* > \brief \b DGEQR2 computes the QR 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 DGEQR2 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

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

/*       SUBROUTINE DGEQR2( 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 */
/* > */
/* > DGEQR2 computes a QR factorization of a real m-by-n matrix A: */
/* > */
/* >    A = Q * ( R ), */
/* >            ( 0 ) */
/* > */
/* > where: */
/* > */
/* >    Q is a m-by-m orthogonal matrix; */
/* >    R is an upper-triangular n-by-n matrix; */
/* >    0 is a (m-n)-by-n 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 above the diagonal of the array */
/* >          contain the min(m,n) by n upper trapezoidal matrix R (R is */
/* >          upper triangular if m >= n); the elements below 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 (N) */
/* > \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(1) H(2) . . . H(k), 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:m) is stored on exit in A(i+1:m,i), */
/* >  and tau in TAU(i). */
/* > \endverbatim */
/* > */
/*  ===================================================================== */
/* Subroutine */ int dgeqr2_(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 *)"DGEQR2", &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+1:m,i) */

        i__2 = *m - i__ + 1;
/* Computing MIN */
        i__3 = i__ + 1;
        dlarfg_(&i__2, &a[i__ + i__ * a_dim1], &a[min(i__3,*m) + i__ * a_dim1]
                , &c__1, &tau[i__]);
        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_((char *)"Left", &i__2, &i__3, &a[i__ + i__ * a_dim1], &c__1, &tau[
                    i__], &a[i__ + (i__ + 1) * a_dim1], lda, &work[1], (
                    ftnlen)4);
            a[i__ + i__ * a_dim1] = aii;
        }
/* L10: */
    }
    return 0;

/*     End of DGEQR2 */

} /* dgeqr2_ */

#ifdef __cplusplus
        }
#endif