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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_POTF2_HEADER
#define TEMPLATE_LAPACK_POTF2_HEADER
template<class Treal>
int template_lapack_potf2(const char *uplo, const integer *n, Treal *a, const integer *
lda, integer *info)
{
/* -- LAPACK routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
February 29, 1992
Purpose
=======
DPOTF2 computes the Cholesky factorization of a real symmetric
positive definite matrix A.
The factorization has the form
A = U' * U , if UPLO = 'U', or
A = L * L', if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular.
This is the unblocked version of the algorithm, calling Level 2 BLAS.
Arguments
=========
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A. N >= 0.
A (input/output) 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'*U or A = L*L'.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -k, the k-th argument had an illegal value
> 0: if INFO = k, the leading minor of order k is not
positive definite, and the factorization could not be
completed.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
Treal c_b10 = -1.;
Treal c_b12 = 1.;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2, i__3;
Treal d__1;
/* Local variables */
integer j;
logical upper;
Treal ajj;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
/* 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;
} else if (*lda < maxMACRO(1,*n)) {
*info = -4;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("POTF2 ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
if (upper) {
/* Compute the Cholesky factorization A = U'*U. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Compute U(J,J) and test for non-positive-definiteness. */
i__2 = j - 1;
ajj = a_ref(j, j) - template_blas_dot(&i__2, &a_ref(1, j), &c__1, &a_ref(1, j)
, &c__1);
if (ajj <= 0.) {
a_ref(j, j) = ajj;
goto L30;
}
ajj = template_blas_sqrt(ajj);
a_ref(j, j) = ajj;
/* Compute elements J+1:N of row J. */
if (j < *n) {
i__2 = j - 1;
i__3 = *n - j;
template_blas_gemv("Transpose", &i__2, &i__3, &c_b10, &a_ref(1, j + 1),
lda, &a_ref(1, j), &c__1, &c_b12, &a_ref(j, j + 1),
lda);
i__2 = *n - j;
d__1 = 1. / ajj;
template_blas_scal(&i__2, &d__1, &a_ref(j, j + 1), lda);
}
/* L10: */
}
} else {
/* Compute the Cholesky factorization A = L*L'. */
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
/* Compute L(J,J) and test for non-positive-definiteness. */
i__2 = j - 1;
ajj = a_ref(j, j) - template_blas_dot(&i__2, &a_ref(j, 1), lda, &a_ref(j, 1),
lda);
if (ajj <= 0.) {
a_ref(j, j) = ajj;
goto L30;
}
ajj = template_blas_sqrt(ajj);
a_ref(j, j) = ajj;
/* Compute elements J+1:N of column J. */
if (j < *n) {
i__2 = *n - j;
i__3 = j - 1;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b10, &a_ref(j + 1, 1),
lda, &a_ref(j, 1), lda, &c_b12, &a_ref(j + 1, j), &
c__1);
i__2 = *n - j;
d__1 = 1. / ajj;
template_blas_scal(&i__2, &d__1, &a_ref(j + 1, j), &c__1);
}
/* L20: */
}
}
goto L40;
L30:
*info = j;
L40:
return 0;
/* End of DPOTF2 */
} /* dpotf2_ */
#undef a_ref
#endif
|
