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/* Ergo, version 3.8, a program for linear scaling electronic structure
* calculations.
* Copyright (C) 2019 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_TRTRI_HEADER
#define TEMPLATE_LAPACK_TRTRI_HEADER
template<class Treal>
int template_lapack_trtri(const char *uplo, const char *diag,
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
March 31, 1993
Purpose
=======
DTRTRI computes the inverse of a real upper or lower triangular
matrix A.
This is the Level 3 BLAS version of the algorithm.
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.
A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the triangular matrix A. If UPLO = 'U', the
leading N-by-N upper triangular part of the array A contains
the upper triangular matrix, and the strictly lower
triangular part of A is not referenced. If UPLO = 'L', the
leading N-by-N lower triangular part of the array A contains
the lower triangular matrix, and the strictly upper
triangular part of A is not referenced. If DIAG = 'U', the
diagonal elements of A are also not referenced and are
assumed to be 1.
On exit, the (triangular) inverse of the original matrix, in
the same storage format.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
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.
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
integer c_n1 = -1;
integer c__2 = 2;
Treal c_b18 = 1.;
Treal c_b22 = -1.;
/* System generated locals */
address a__1[2];
integer a_dim1, a_offset, i__1, i__2[2], i__3, i__4, i__5;
char ch__1[2];
/* Local variables */
integer j;
logical upper;
integer jb, nb, nn;
logical nounit;
#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");
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;
} else if (*lda < maxMACRO(1,*n)) {
*info = -5;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("TRTRI ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Check for singularity if non-unit. */
if (nounit) {
i__1 = *n;
for (*info = 1; *info <= i__1; ++(*info)) {
if (a_ref(*info, *info) == 0.) {
return 0;
}
/* L10: */
}
*info = 0;
}
/* Determine the block size for this environment.
Writing concatenation */
i__2[0] = 1, a__1[0] = (char*)uplo;
i__2[1] = 1, a__1[1] = (char*)diag;
template_blas_s_cat(ch__1, a__1, i__2, &c__2, (ftnlen)2);
nb = template_lapack_ilaenv(&c__1, "DTRTRI", ch__1, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)2);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
template_lapack_trti2(uplo, diag, n, &a[a_offset], lda, info);
} else {
/* Use blocked code */
if (upper) {
/* Compute inverse of upper triangular matrix */
i__1 = *n;
i__3 = nb;
for (j = 1; i__3 < 0 ? j >= i__1 : j <= i__1; j += i__3) {
/* Computing MIN */
i__4 = nb, i__5 = *n - j + 1;
jb = minMACRO(i__4,i__5);
/* Compute rows 1:j-1 of current block column */
i__4 = j - 1;
template_blas_trmm("Left", "Upper", "No transpose", diag, &i__4, &jb, &
c_b18, &a[a_offset], lda, &a_ref(1, j), lda);
i__4 = j - 1;
template_blas_trsm("Right", "Upper", "No transpose", diag, &i__4, &jb, &
c_b22, &a_ref(j, j), lda, &a_ref(1, j), lda);
/* Compute inverse of current diagonal block */
template_lapack_trti2("Upper", diag, &jb, &a_ref(j, j), lda, info);
/* L20: */
}
} else {
/* Compute inverse of lower triangular matrix */
nn = (*n - 1) / nb * nb + 1;
i__3 = -nb;
for (j = nn; i__3 < 0 ? j >= 1 : j <= 1; j += i__3) {
/* Computing MIN */
i__1 = nb, i__4 = *n - j + 1;
jb = minMACRO(i__1,i__4);
if (j + jb <= *n) {
/* Compute rows j+jb:n of current block column */
i__1 = *n - j - jb + 1;
template_blas_trmm("Left", "Lower", "No transpose", diag, &i__1, &jb,
&c_b18, &a_ref(j + jb, j + jb), lda, &a_ref(j +
jb, j), lda);
i__1 = *n - j - jb + 1;
template_blas_trsm("Right", "Lower", "No transpose", diag, &i__1, &jb,
&c_b22, &a_ref(j, j), lda, &a_ref(j + jb, j),
lda);
}
/* Compute inverse of current diagonal block */
template_lapack_trti2("Lower", diag, &jb, &a_ref(j, j), lda, info);
/* L30: */
}
}
}
return 0;
/* End of DTRTRI */
} /* dtrtri_ */
#undef a_ref
#endif
|
