286 lines
8.4 KiB
C++
286 lines
8.4 KiB
C++
/* static/dpotrf2.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 doublereal c_b9 = 1.;
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static doublereal c_b11 = -1.;
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/* > \brief \b DPOTRF2 */
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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 DPOTRF2( UPLO, N, A, LDA, INFO ) */
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/* .. Scalar Arguments .. */
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/* CHARACTER UPLO */
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/* INTEGER INFO, LDA, N */
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/* .. */
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/* .. Array Arguments .. */
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/* REAL 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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/* > DPOTRF2 computes the Cholesky factorization of a real symmetric */
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/* > positive definite matrix A using the recursive algorithm. */
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/* > */
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/* > The factorization has the form */
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/* > A = U**T * U, if UPLO = 'U', or */
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/* > A = L * L**T, if UPLO = 'L', */
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/* > where U is an upper triangular matrix and L is lower triangular. */
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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 = n/2 */
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/* > [ A21 | A22 ] n2 = n-n1 */
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/* > */
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/* > The subroutine calls itself to factor A11. Update and scale A21 */
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/* > or A12, update A22 then calls itself to factor A22. */
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/* > */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] UPLO */
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/* > \verbatim */
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/* > UPLO is CHARACTER*1 */
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/* > = 'U': Upper triangle of A is stored; */
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/* > = 'L': Lower triangle of A is stored. */
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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 order 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 symmetric matrix A. If UPLO = 'U', the leading */
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/* > N-by-N upper triangular part of A contains the upper */
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/* > triangular part of the matrix A, and the strictly lower */
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/* > triangular part of A is not referenced. If UPLO = 'L', the */
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/* > leading N-by-N lower triangular part of A contains the lower */
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/* > triangular part of the matrix A, and the strictly upper */
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/* > triangular part of A is not referenced. */
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/* > */
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/* > On exit, if INFO = 0, the factor U or L from the Cholesky */
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/* > factorization A = U**T*U or A = L*L**T. */
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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,N). */
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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, the leading minor of order i is not */
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/* > positive definite, and the factorization could not be */
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/* > completed. */
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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 doublePOcomputational */
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/* ===================================================================== */
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/* Subroutine */ int dpotrf2_(char *uplo, integer *n, doublereal *a, integer *
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lda, integer *info, ftnlen uplo_len)
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{
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/* System generated locals */
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integer a_dim1, a_offset, i__1;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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integer n1, n2;
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extern logical lsame_(char *, char *, ftnlen, ftnlen);
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integer iinfo;
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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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logical upper;
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extern /* Subroutine */ int dsyrk_(char *, char *, integer *, integer *,
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doublereal *, doublereal *, integer *, doublereal *, doublereal *,
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integer *, ftnlen, ftnlen);
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extern logical disnan_(doublereal *);
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extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
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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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/* Function Body */
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*info = 0;
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upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1);
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if (! upper && ! lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) {
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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,*n)) {
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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 *)"DPOTRF2", &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 (*n == 0) {
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return 0;
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}
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/* N=1 case */
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if (*n == 1) {
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/* Test for non-positive-definiteness */
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if (a[a_dim1 + 1] <= 0. || disnan_(&a[a_dim1 + 1])) {
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*info = 1;
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return 0;
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}
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/* Factor */
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a[a_dim1 + 1] = sqrt(a[a_dim1 + 1]);
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/* Use recursive code */
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} else {
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n1 = *n / 2;
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n2 = *n - n1;
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/* Factor A11 */
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dpotrf2_(uplo, &n1, &a[a_dim1 + 1], lda, &iinfo, (ftnlen)1);
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if (iinfo != 0) {
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*info = iinfo;
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return 0;
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}
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/* Compute the Cholesky factorization A = U**T*U */
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if (upper) {
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/* Update and scale A12 */
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dtrsm_((char *)"L", (char *)"U", (char *)"T", (char *)"N", &n1, &n2, &c_b9, &a[a_dim1 + 1], lda, &
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a[(n1 + 1) * a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (
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ftnlen)1, (ftnlen)1);
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/* Update and factor A22 */
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dsyrk_(uplo, (char *)"T", &n2, &n1, &c_b11, &a[(n1 + 1) * a_dim1 + 1],
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lda, &c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)
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1, (ftnlen)1);
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dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (
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ftnlen)1);
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if (iinfo != 0) {
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*info = iinfo + n1;
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return 0;
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}
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/* Compute the Cholesky factorization A = L*L**T */
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} else {
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/* Update and scale A21 */
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dtrsm_((char *)"R", (char *)"L", (char *)"T", (char *)"N", &n2, &n1, &c_b9, &a[a_dim1 + 1], lda, &
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a[n1 + 1 + a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1,
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(ftnlen)1);
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/* Update and factor A22 */
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dsyrk_(uplo, (char *)"N", &n2, &n1, &c_b11, &a[n1 + 1 + a_dim1], lda, &
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c_b9, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, (ftnlen)1, (
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ftnlen)1);
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dpotrf2_(uplo, &n2, &a[n1 + 1 + (n1 + 1) * a_dim1], lda, &iinfo, (
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ftnlen)1);
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if (iinfo != 0) {
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*info = iinfo + n1;
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return 0;
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}
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}
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}
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return 0;
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/* End of DPOTRF2 */
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} /* dpotrf2_ */
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#ifdef __cplusplus
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}
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#endif
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