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/* Ergo, version 3.8.2, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2023 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
* and Anastasia Kruchinina.
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*
* Primary academic reference:
* Ergo: An open-source program for linear-scaling electronic structure
* calculations,
* Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
* Kruchinina,
* SoftwareX 7, 107 (2018),
* <http://dx.doi.org/10.1016/j.softx.2018.03.005>
*
* For further information about Ergo, see <http://www.ergoscf.org>.
*/
/* This file belongs to the template_lapack part of the Ergo source
* code. The source files in the template_lapack directory are modified
* versions of files originally distributed as CLAPACK, see the
* Copyright/license notice in the file template_lapack/COPYING.
*/
#ifndef TEMPLATE_LAPACK_PPTRF_HEADER
#define TEMPLATE_LAPACK_PPTRF_HEADER
#include "template_lapack_common.h"
template<class Treal>
int template_lapack_pptrf(const char *uplo, const integer *n, Treal *ap, integer *
info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
March 31, 1993
Purpose
=======
DPPTRF computes the Cholesky factorization of a real symmetric
positive definite matrix A stored in packed format.
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.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) INTEGER
The order of the matrix A. N >= 0.
AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the symmetric matrix
A, packed columnwise in a linear array. The j-th column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, if INFO = 0, the triangular factor U or L from the
Cholesky factorization A = U**T*U or A = L*L**T, in the same
storage format as A.
INFO (output) 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.
Further Details
======= =======
The packed storage scheme is illustrated by the following example
when N = 4, UPLO = 'U':
Two-dimensional storage of the symmetric matrix A:
a11 a12 a13 a14
a22 a23 a24
a33 a34 (aij = aji)
a44
Packed storage of the upper triangle of A:
AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
Treal c_b16 = -1.;
/* System generated locals */
integer i__1, i__2;
Treal d__1;
/* Local variables */
integer j;
logical upper;
integer jc, jj;
Treal ajj;
--ap;
/* Function Body */
*info = 0;
upper = template_blas_lsame(uplo, "U");
if (! upper && ! template_blas_lsame(uplo, "L")) {
*info = -1;
} else if (*n < 0) {
*info = -2;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("DPPTRF", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
jc = jj + 1;
jj += j;
/* Compute elements 1:J-1 of column J. */
if (j > 1) {
i__2 = j - 1;
template_blas_tpsv("Upper", "Transpose", "Non-unit", &i__2, &ap[1], &ap[
jc], &c__1);
}
/* Compute U(J,J) and test for non-positive-definiteness. */
i__2 = j - 1;
ajj = ap[jj] - template_blas_dot(&i__2, &ap[jc], &c__1, &ap[jc], &c__1);
if (ajj <= 0.) {
ap[jj] = ajj;
goto L30;
}
ap[jj] = template_blas_sqrt(ajj);
/* L10: */
}
} else {
/* Compute the Cholesky factorization A = L*L'. */
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Compute L(J,J) and test for non-positive-definiteness. */
ajj = ap[jj];
if (ajj <= 0.) {
ap[jj] = ajj;
goto L30;
}
ajj = template_blas_sqrt(ajj);
ap[jj] = ajj;
/* Compute elements J+1:N of column J and update the trailing
submatrix. */
if (j < *n) {
i__2 = *n - j;
d__1 = 1. / ajj;
template_blas_scal(&i__2, &d__1, &ap[jj + 1], &c__1);
i__2 = *n - j;
template_blas_spr("Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n
- j + 1]);
jj = jj + *n - j + 1;
}
/* L20: */
}
}
goto L40;
L30:
*info = j;
L40:
return 0;
/* End of DPPTRF */
} /* dpptrf_ */
#endif
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