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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_TPTRI_HEADER
#define TEMPLATE_LAPACK_TPTRI_HEADER
#include "template_lapack_common.h"
template<class Treal>
int template_lapack_tptri(const char *uplo, const char *diag, 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
September 30, 1994
Purpose
=======
DTPTRI computes the inverse of a real upper or lower triangular
matrix A stored in packed format.
Arguments
=========
UPLO (input) CHARACTER*1
= 'U': A is upper triangular;
= 'L': A is lower triangular.
DIAG (input) CHARACTER*1
= 'N': A is non-unit triangular;
= 'U': A is unit triangular.
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 triangular matrix A, stored
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)*((2*n-j)/2) = A(i,j) for j<=i<=n.
See below for further details.
On exit, the (triangular) inverse of the original matrix, in
the same packed storage format.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: if INFO = i, A(i,i) is exactly zero. The triangular
matrix is singular and its inverse can not be computed.
Further Details
===============
A triangular matrix A can be transferred to packed storage using one
of the following program segments:
UPLO = 'U': UPLO = 'L':
JC = 1 JC = 1
DO 2 J = 1, N DO 2 J = 1, N
DO 1 I = 1, J DO 1 I = J, N
AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J)
1 CONTINUE 1 CONTINUE
JC = JC + J JC = JC + N - J + 1
2 CONTINUE 2 CONTINUE
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
/* System generated locals */
integer i__1, i__2;
/* Local variables */
integer j;
logical upper;
integer jc, jj;
integer jclast;
logical nounit;
Treal ajj;
--ap;
/* Initialization added by Elias to get rid of compiler warnings. */
jclast = 0;
/* Function Body */
*info = 0;
upper = template_blas_lsame(uplo, "U");
nounit = template_blas_lsame(diag, "N");
if (! upper && ! template_blas_lsame(uplo, "L")) {
*info = -1;
} else if (! nounit && ! template_blas_lsame(diag, "U")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("TPTRI ", &i__1);
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
if (upper) {
jj = 0;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
jj += *info;
if (ap[jj] == 0.) {
return 0;
}
/* L10: */
}
} else {
jj = 1;
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
if (ap[jj] == 0.) {
return 0;
}
jj = jj + *n - *info + 1;
/* L20: */
}
}
*info = 0;
}
if (upper) {
/* Compute inverse of upper triangular matrix. */
jc = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
if (nounit) {
ap[jc + j - 1] = 1. / ap[jc + j - 1];
ajj = -ap[jc + j - 1];
} else {
ajj = -1.;
}
/* Compute elements 1:j-1 of j-th column. */
i__2 = j - 1;
template_blas_tpmv("Upper", "No transpose", diag, &i__2, &ap[1], &ap[jc], &
c__1);
i__2 = j - 1;
template_blas_scal(&i__2, &ajj, &ap[jc], &c__1);
jc += j;
/* L30: */
}
} else {
/* Compute inverse of lower triangular matrix. */
jc = *n * (*n + 1) / 2;
for (j = *n; j >= 1; --j) {
if (nounit) {
ap[jc] = 1. / ap[jc];
ajj = -ap[jc];
} else {
ajj = -1.;
}
if (j < *n) {
/* Compute elements j+1:n of j-th column. */
i__1 = *n - j;
template_blas_tpmv("Lower", "No transpose", diag, &i__1, &ap[jclast], &ap[
jc + 1], &c__1);
i__1 = *n - j;
template_blas_scal(&i__1, &ajj, &ap[jc + 1], &c__1);
}
jclast = jc;
jc = jc - *n + j - 2;
/* L40: */
}
}
return 0;
/* End of DTPTRI */
} /* dtptri_ */
#endif
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