/* -- translated by f2c (version 20100827).
You must link the resulting object file with libf2c:
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*/
#include "f2c.h"
/* Table of constant values */
static integer c__1 = 1;
static integer c_n1 = -1;
static doublereal c_b13 = -1.;
static doublereal c_b14 = 1.;
/* > \brief \b DPOTRF
=========== DOCUMENTATION ===========
Online html documentation available at
http://www.netlib.org/lapack/explore-html/
> \htmlonly
> Download DPOTRF + dependencies
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpotrf.
f">
> [TGZ]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpotrf.
f">
> [ZIP]</a>
> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpotrf.
f">
> [TXT]</a>
> \endhtmlonly
Definition:
===========
SUBROUTINE DPOTRF( UPLO, N, A, LDA, INFO )
CHARACTER UPLO
INTEGER INFO, LDA, N
DOUBLE PRECISION A( LDA, * )
> \par Purpose:
=============
>
> \verbatim
>
> DPOTRF computes the Cholesky factorization of a real symmetric
> positive definite matrix A.
>
> The factorization has the form
> A = U**T * U, if UPLO = 'U', or
> A = L * L**T, if UPLO = 'L',
> where U is an upper triangular matrix and L is lower triangular.
>
> This is the block version of the algorithm, calling Level 3 BLAS.
> \endverbatim
Arguments:
==========
> \param[in] UPLO
> \verbatim
> UPLO is CHARACTER*1
> = 'U': Upper triangle of A is stored;
> = 'L': Lower triangle of A is stored.
> \endverbatim
>
> \param[in] N
> \verbatim
> N is INTEGER
> The order of the matrix A. N >= 0.
> \endverbatim
>
> \param[in,out] A
> \verbatim
> A is DOUBLE PRECISION array, dimension (LDA,N)
> On entry, the symmetric matrix A. If UPLO = 'U', the leading
> N-by-N upper triangular part of A contains the upper
> triangular part of the matrix A, and the strictly lower
> triangular part of A is not referenced. If UPLO = 'L', the
> leading N-by-N lower triangular part of A contains the lower
> triangular part of the matrix A, and the strictly upper
> triangular part of A is not referenced.
>
> On exit, if INFO = 0, the factor U or L from the Cholesky
> factorization A = U**T*U or A = L*L**T.
> \endverbatim
>
> \param[in] LDA
> \verbatim
> LDA is INTEGER
> The leading dimension of the array A. LDA >= max(1,N).
> \endverbatim
>
> \param[out] INFO
> \verbatim
> INFO is INTEGER
> = 0: successful exit
> < 0: if INFO = -i, the i-th argument had an illegal value
> > 0: if INFO = i, the leading minor of order i is not
> positive definite, and the factorization could not be
> completed.
> \endverbatim
Authors:
========
> \author Univ. of Tennessee
> \author Univ. of California Berkeley
> \author Univ. of Colorado Denver
> \author NAG Ltd.
> \date November 2011
> \ingroup doublePOcomputational
=====================================================================
Subroutine */ int igraphdpotrf_(char *uplo, integer *n, doublereal *a, integer *
lda, integer *info)
{
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
/* Local variables */
integer j, jb, nb;
extern /* Subroutine */ int igraphdgemm_(char *, char *, integer *, integer *,
integer *, doublereal *, doublereal *, integer *, doublereal *,
integer *, doublereal *, doublereal *, integer *);
extern logical igraphlsame_(char *, char *);
extern /* Subroutine */ int igraphdtrsm_(char *, char *, char *, char *,
integer *, integer *, doublereal *, doublereal *, integer *,
doublereal *, integer *);
logical upper;
extern /* Subroutine */ int igraphdsyrk_(char *, char *, integer *, integer *,
doublereal *, doublereal *, integer *, doublereal *, doublereal *,
integer *), igraphdpotf2_(char *, integer *,
doublereal *, integer *, integer *), igraphxerbla_(char *,
integer *, ftnlen);
extern integer igraphilaenv_(integer *, char *, char *, integer *, integer *,
integer *, integer *, ftnlen, ftnlen);
/* -- LAPACK computational routine (version 3.4.0) --
-- LAPACK is a software package provided by Univ. of Tennessee, --
-- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
November 2011
=====================================================================
Test the input parameters.
Parameter adjustments */
a_dim1 = *lda;
a_offset = 1 + a_dim1;
a -= a_offset;
/* Function Body */
*info = 0;
upper = igraphlsame_(uplo, "U");
if (! upper && ! igraphlsame_(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
} else if (*lda < max(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
igraphxerbla_("DPOTRF", &i__1, (ftnlen)6);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = igraphilaenv_(&c__1, "DPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code. */
igraphdpotf2_(uplo, n, &a[a_offset], lda, info);
} else {
/* Use blocked code. */
if (upper) {
/* Compute the Cholesky factorization A = U**T*U. */
i__1 = *n;
i__2 = nb;
for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) {
/* Update and factorize the current diagonal block and test
for non-positive-definiteness.
Computing MIN */
i__3 = nb, i__4 = *n - j + 1;
jb = min(i__3,i__4);
i__3 = j - 1;
igraphdsyrk_("Upper", "Transpose", &jb, &i__3, &c_b13, &a[j *
a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda);
igraphdpotf2_("Upper", &jb, &a[j + j * a_dim1], lda, info);
if (*info != 0) {
goto L30;
}
if (j + jb <= *n) {
/* Compute the current block row. */
i__3 = *n - j - jb + 1;
i__4 = j - 1;
igraphdgemm_("Transpose", "No transpose", &jb, &i__3, &i__4, &
c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) *
a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) *
a_dim1], lda);
i__3 = *n - j - jb + 1;
igraphdtrsm_("Left", "Upper", "Transpose", "Non-unit", &jb, &
i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j
+ jb) * a_dim1], lda);
}
/* L10: */
}
} else {
/* Compute the Cholesky factorization A = L*L**T. */
i__2 = *n;
i__1 = nb;
for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) {
/* Update and factorize the current diagonal block and test
for non-positive-definiteness.
Computing MIN */
i__3 = nb, i__4 = *n - j + 1;
jb = min(i__3,i__4);
i__3 = j - 1;
igraphdsyrk_("Lower", "No transpose", &jb, &i__3, &c_b13, &a[j +
a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda);
igraphdpotf2_("Lower", &jb, &a[j + j * a_dim1], lda, info);
if (*info != 0) {
goto L30;
}
if (j + jb <= *n) {
/* Compute the current block column. */
i__3 = *n - j - jb + 1;
i__4 = j - 1;
igraphdgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, &
c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1],
lda, &c_b14, &a[j + jb + j * a_dim1], lda);
i__3 = *n - j - jb + 1;
igraphdtrsm_("Right", "Lower", "Transpose", "Non-unit", &i__3, &
jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb +
j * a_dim1], lda);
}
/* L20: */
}
}
}
goto L40;
L30:
*info = *info + j - 1;
L40:
return 0;
/* End of DPOTRF */
} /* igraphdpotrf_ */