332 lines
8.8 KiB
C++
332 lines
8.8 KiB
C++
/* static/dgetrf2.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* Table of constant values */
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static integer c__1 = 1;
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static doublereal c_b13 = 1.;
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static doublereal c_b16 = -1.;
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/* > \brief \b DGETRF2 */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* Definition: */
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/* =========== */
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/* RECURSIVE SUBROUTINE DGETRF2( M, N, A, LDA, IPIV, INFO ) */
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/* .. Scalar Arguments .. */
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/* INTEGER INFO, LDA, M, N */
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/* .. */
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/* .. Array Arguments .. */
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/* INTEGER IPIV( * ) */
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/* DOUBLE PRECISION A( LDA, * ) */
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/* .. */
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/* > \par Purpose: */
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/* ============= */
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/* > */
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/* > \verbatim */
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/* > */
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/* > DGETRF2 computes an LU factorization of a general M-by-N matrix A */
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/* > using partial pivoting with row interchanges. */
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/* > */
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/* > The factorization has the form */
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/* > A = P * L * U */
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/* > where P is a permutation matrix, L is lower triangular with unit */
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/* > diagonal elements (lower trapezoidal if m > n), and U is upper */
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/* > triangular (upper trapezoidal if m < n). */
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/* > */
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/* > This is the recursive version of the algorithm. It divides */
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/* > the matrix into four submatrices: */
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/* > */
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/* > [ A11 | A12 ] where A11 is n1 by n1 and A22 is n2 by n2 */
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/* > A = [ -----|----- ] with n1 = min(m,n)/2 */
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/* > [ A21 | A22 ] n2 = n-n1 */
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/* > */
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/* > [ A11 ] */
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/* > The subroutine calls itself to factor [ --- ], */
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/* > [ A12 ] */
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/* > [ A12 ] */
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/* > do the swaps on [ --- ], solve A12, update A22, */
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/* > [ A22 ] */
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/* > */
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/* > then calls itself to factor A22 and do the swaps on A21. */
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/* > */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] M */
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/* > \verbatim */
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/* > M is INTEGER */
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/* > The number of rows of the matrix A. M >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] N */
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/* > \verbatim */
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/* > N is INTEGER */
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/* > The number of columns of the matrix A. N >= 0. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] A */
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/* > \verbatim */
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/* > A is DOUBLE PRECISION array, dimension (LDA,N) */
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/* > On entry, the M-by-N matrix to be factored. */
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/* > On exit, the factors L and U from the factorization */
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/* > A = P*L*U; the unit diagonal elements of L are not stored. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] LDA */
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/* > \verbatim */
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/* > LDA is INTEGER */
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/* > The leading dimension of the array A. LDA >= max(1,M). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] IPIV */
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/* > \verbatim */
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/* > IPIV is INTEGER array, dimension (min(M,N)) */
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/* > The pivot indices; for 1 <= i <= min(M,N), row i of the */
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/* > matrix was interchanged with row IPIV(i). */
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/* > \endverbatim */
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/* > */
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/* > \param[out] INFO */
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/* > \verbatim */
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/* > INFO is INTEGER */
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/* > = 0: successful exit */
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/* > < 0: if INFO = -i, the i-th argument had an illegal value */
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/* > > 0: if INFO = i, U(i,i) is exactly zero. The factorization */
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/* > has been completed, but the factor U is exactly */
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/* > singular, and division by zero will occur if it is used */
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/* > to solve a system of equations. */
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/* > \endverbatim */
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/* Authors: */
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/* ======== */
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/* > \author Univ. of Tennessee */
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/* > \author Univ. of California Berkeley */
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/* > \author Univ. of Colorado Denver */
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/* > \author NAG Ltd. */
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/* > \ingroup doubleGEcomputational */
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/* ===================================================================== */
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/* Subroutine */ int dgetrf2_(integer *m, integer *n, doublereal *a, integer *
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lda, integer *ipiv, integer *info)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1, i__2;
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doublereal d__1;
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/* Local variables */
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integer i__, n1, n2;
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doublereal temp;
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extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *,
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integer *), dgemm_(char *, char *, integer *, integer *, integer *
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, doublereal *, doublereal *, integer *, doublereal *, integer *,
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doublereal *, doublereal *, integer *, ftnlen, ftnlen);
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integer iinfo;
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doublereal sfmin;
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extern /* Subroutine */ int dtrsm_(char *, char *, char *, char *,
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integer *, integer *, doublereal *, doublereal *, integer *,
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doublereal *, integer *, ftnlen, ftnlen, ftnlen, ftnlen);
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extern doublereal dlamch_(char *, ftnlen);
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extern integer idamax_(integer *, doublereal *, integer *);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen), dlaswp_(
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integer *, doublereal *, integer *, integer *, integer *, integer
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*, integer *);
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/* -- LAPACK computational routine -- */
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Functions .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Test the input parameters */
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/* Parameter adjustments */
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a_dim1 = *lda;
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a_offset = 1 + a_dim1;
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a -= a_offset;
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--ipiv;
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/* Function Body */
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*info = 0;
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if (*m < 0) {
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*info = -1;
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} else if (*n < 0) {
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*info = -2;
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} else if (*lda < max(1,*m)) {
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*info = -4;
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}
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if (*info != 0) {
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i__1 = -(*info);
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xerbla_((char *)"DGETRF2", &i__1, (ftnlen)7);
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return 0;
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}
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/* Quick return if possible */
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if (*m == 0 || *n == 0) {
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return 0;
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}
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if (*m == 1) {
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/* Use unblocked code for one row case */
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/* Just need to handle IPIV and INFO */
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ipiv[1] = 1;
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if (a[a_dim1 + 1] == 0.) {
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*info = 1;
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}
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} else if (*n == 1) {
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/* Use unblocked code for one column case */
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/* Compute machine safe minimum */
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sfmin = dlamch_((char *)"S", (ftnlen)1);
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/* Find pivot and test for singularity */
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i__ = idamax_(m, &a[a_dim1 + 1], &c__1);
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ipiv[1] = i__;
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if (a[i__ + a_dim1] != 0.) {
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/* Apply the interchange */
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if (i__ != 1) {
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temp = a[a_dim1 + 1];
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a[a_dim1 + 1] = a[i__ + a_dim1];
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a[i__ + a_dim1] = temp;
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}
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/* Compute elements 2:M of the column */
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if ((d__1 = a[a_dim1 + 1], abs(d__1)) >= sfmin) {
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i__1 = *m - 1;
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d__1 = 1. / a[a_dim1 + 1];
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dscal_(&i__1, &d__1, &a[a_dim1 + 2], &c__1);
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} else {
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i__1 = *m - 1;
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for (i__ = 1; i__ <= i__1; ++i__) {
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a[i__ + 1 + a_dim1] /= a[a_dim1 + 1];
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/* L10: */
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}
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}
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} else {
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*info = 1;
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}
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} else {
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/* Use recursive code */
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n1 = min(*m,*n) / 2;
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n2 = *n - n1;
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/* [ A11 ] */
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/* Factor [ --- ] */
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/* [ A21 ] */
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dgetrf2_(m, &n1, &a[a_offset], lda, &ipiv[1], &iinfo);
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if (*info == 0 && iinfo > 0) {
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*info = iinfo;
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}
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/* [ A12 ] */
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/* Apply interchanges to [ --- ] */
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/* [ A22 ] */
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dlaswp_(&n2, &a[(n1 + 1) * a_dim1 + 1], lda, &c__1, &n1, &ipiv[1], &
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c__1);
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/* Solve A12 */
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dtrsm_((char *)"L", (char *)"L", (char *)"N", (char *)"U", &n1, &n2, &c_b13, &a[a_offset], lda, &a[(
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n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1, (
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ftnlen)1);
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/* Update A22 */
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i__1 = *m - n1;
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dgemm_((char *)"N", (char *)"N", &i__1, &n2, &n1, &c_b16, &a[n1 + 1 + a_dim1], lda, &
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a[(n1 + 1) * a_dim1 + 1], lda, &c_b13, &a[n1 + 1 + (n1 + 1) *
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a_dim1], lda, (ftnlen)1, (ftnlen)1);
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/* Factor A22 */
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i__1 = *m - n1;
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dgetrf2_(&i__1, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &ipiv[n1 +
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1], &iinfo);
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/* Adjust INFO and the pivot indices */
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if (*info == 0 && iinfo > 0) {
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*info = iinfo + n1;
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}
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i__1 = min(*m,*n);
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for (i__ = n1 + 1; i__ <= i__1; ++i__) {
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ipiv[i__] += n1;
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/* L20: */
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}
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/* Apply interchanges to A21 */
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i__1 = n1 + 1;
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i__2 = min(*m,*n);
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dlaswp_(&n1, &a[a_dim1 + 1], lda, &i__1, &i__2, &ipiv[1], &c__1);
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}
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return 0;
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/* End of DGETRF2 */
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} /* dgetrf2_ */
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#ifdef __cplusplus
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}
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#endif
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