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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_LANSY_HEADER
#define TEMPLATE_LAPACK_LANSY_HEADER
template<class Treal>
Treal template_lapack_lansy(const char *norm, const char *uplo, const integer *n, const Treal *a, const integer
*lda, Treal *work)
{
/* -- LAPACK auxiliary routine (version 3.0) --
Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
Courant Institute, Argonne National Lab, and Rice University
October 31, 1992
Purpose
=======
DLANSY returns the value of the one norm, or the Frobenius norm, or
the infinity norm, or the element of largest absolute value of a
real symmetric matrix A.
Description
===========
DLANSY returns the value
DLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
(
( norm1(A), NORM = '1', 'O' or 'o'
(
( normI(A), NORM = 'I' or 'i'
(
( normF(A), NORM = 'F', 'f', 'E' or 'e'
where norm1 denotes the one norm of a matrix (maximum column sum),
normI denotes the infinity norm of a matrix (maximum row sum) and
normF denotes the Frobenius norm of a matrix (square root of sum of
squares). Note that max(abs(A(i,j))) is not a matrix norm.
Arguments
=========
NORM (input) CHARACTER*1
Specifies the value to be returned in DLANSY as described
above.
UPLO (input) CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is to be referenced.
= 'U': Upper triangular part of A is referenced
= 'L': Lower triangular part of A is referenced
N (input) INTEGER
The order of the matrix A. N >= 0. When N = 0, DLANSY is
set to zero.
A (input) DOUBLE PRECISION array, dimension (LDA,N)
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.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(N,1).
WORK (workspace) DOUBLE PRECISION array, dimension (LWORK),
where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
WORK is not referenced.
=====================================================================
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
/* System generated locals */
integer a_dim1, a_offset, i__1, i__2;
Treal ret_val, d__1, d__2, d__3;
/* Local variables */
Treal absa;
integer i__, j;
Treal scale;
Treal value;
Treal sum;
#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;
--work;
/* Initialization added by Elias to get rid of compiler warnings. */
value = 0;
/* Function Body */
if (*n == 0) {
value = 0.;
} else if (template_blas_lsame(norm, "M")) {
/* Find max(abs(A(i,j))). */
value = 0.;
if (template_blas_lsame(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = j;
for (i__ = 1; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
value = maxMACRO(d__2,d__3);
/* L10: */
}
/* L20: */
}
} else {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
i__2 = *n;
for (i__ = j; i__ <= i__2; ++i__) {
/* Computing MAX */
d__2 = value, d__3 = (d__1 = a_ref(i__, j), absMACRO(d__1));
value = maxMACRO(d__2,d__3);
/* L30: */
}
/* L40: */
}
}
} else if (template_blas_lsame(norm, "I") || template_blas_lsame(norm, "O") || *(unsigned char *)norm == '1') {
/* Find normI(A) ( = norm1(A), since A is symmetric). */
value = 0.;
if (template_blas_lsame(uplo, "U")) {
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = 0.;
i__2 = j - 1;
for (i__ = 1; i__ <= i__2; ++i__) {
absa = (d__1 = a_ref(i__, j), absMACRO(d__1));
sum += absa;
work[i__] += absa;
/* L50: */
}
work[j] = sum + (d__1 = a_ref(j, j), absMACRO(d__1));
/* L60: */
}
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Computing MAX */
d__1 = value, d__2 = work[i__];
value = maxMACRO(d__1,d__2);
/* L70: */
}
} else {
i__1 = *n;
for (i__ = 1; i__ <= i__1; ++i__) {
work[i__] = 0.;
/* L80: */
}
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
sum = work[j] + (d__1 = a_ref(j, j), absMACRO(d__1));
i__2 = *n;
for (i__ = j + 1; i__ <= i__2; ++i__) {
absa = (d__1 = a_ref(i__, j), absMACRO(d__1));
sum += absa;
work[i__] += absa;
/* L90: */
}
value = maxMACRO(value,sum);
/* L100: */
}
}
} else if (template_blas_lsame(norm, "F") || template_blas_lsame(norm, "E")) {
/* Find normF(A). */
scale = 0.;
sum = 1.;
if (template_blas_lsame(uplo, "U")) {
i__1 = *n;
for (j = 2; j <= i__1; ++j) {
i__2 = j - 1;
template_lapack_lassq(&i__2, &a_ref(1, j), &c__1, &scale, &sum);
/* L110: */
}
} else {
i__1 = *n - 1;
for (j = 1; j <= i__1; ++j) {
i__2 = *n - j;
template_lapack_lassq(&i__2, &a_ref(j + 1, j), &c__1, &scale, &sum);
/* L120: */
}
}
sum *= 2;
i__1 = *lda + 1;
template_lapack_lassq(n, &a[a_offset], &i__1, &scale, &sum);
value = scale * template_blas_sqrt(sum);
}
ret_val = value;
return ret_val;
/* End of DLANSY */
} /* dlansy_ */
#undef a_ref
#endif
|
