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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_SPGST_HEADER
#define TEMPLATE_LAPACK_SPGST_HEADER
#include "template_lapack_common.h"
template<class Treal>
int template_lapack_spgst(const integer *itype, const char *uplo, const integer *n,
Treal *ap, const Treal *bp, 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
=======
DSPGST reduces a real symmetric-definite generalized eigenproblem
to standard form, using packed storage.
If ITYPE = 1, the problem is A*x = lambda*B*x,
and A is overwritten by inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T)
If ITYPE = 2 or 3, the problem is A*B*x = lambda*x or
B*A*x = lambda*x, and A is overwritten by U*A*U**T or L**T*A*L.
B must have been previously factorized as U**T*U or L*L**T by DPPTRF.
Arguments
=========
ITYPE (input) INTEGER
= 1: compute inv(U**T)*A*inv(U) or inv(L)*A*inv(L**T);
= 2 or 3: compute U*A*U**T or L**T*A*L.
UPLO (input) CHARACTER
= 'U': Upper triangle of A is stored and B is factored as
U**T*U;
= 'L': Lower triangle of A is stored and B is factored as
L*L**T.
N (input) INTEGER
The order of the matrices A and B. 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.
On exit, if INFO = 0, the transformed matrix, stored in the
same format as A.
BP (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The triangular factor from the Cholesky factorization of B,
stored in the same format as A, as returned by DPPTRF.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
=====================================================================
Test the input parameters.
Parameter adjustments */
/* Table of constant values */
integer c__1 = 1;
Treal c_b9 = -1.;
Treal c_b11 = 1.;
/* System generated locals */
integer i__1, i__2;
Treal d__1;
/* Local variables */
integer j, k;
logical upper;
integer j1, k1;
integer jj, kk;
Treal ct;
Treal ajj;
integer j1j1;
Treal akk;
integer k1k1;
Treal bjj, bkk;
--bp;
--ap;
/* Function Body */
*info = 0;
upper = template_blas_lsame(uplo, "U");
if (*itype < 1 || *itype > 3) {
*info = -1;
} else if (! upper && ! template_blas_lsame(uplo, "L")) {
*info = -2;
} else if (*n < 0) {
*info = -3;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("SPGST ", &i__1);
return 0;
}
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U)
J1 and JJ are the indices of A(1,j) and A(j,j) */
jj = 0;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
j1 = jj + 1;
jj += j;
/* Compute the j-th column of the upper triangle of A */
bjj = bp[jj];
template_blas_tpsv(uplo, "Transpose", "Nonunit", &j, &bp[1], &ap[j1], &
c__1);
i__2 = j - 1;
template_blas_spmv(uplo, &i__2, &c_b9, &ap[1], &bp[j1], &c__1, &c_b11, &
ap[j1], &c__1);
i__2 = j - 1;
d__1 = 1. / bjj;
template_blas_scal(&i__2, &d__1, &ap[j1], &c__1);
i__2 = j - 1;
ap[jj] = (ap[jj] - template_blas_dot(&i__2, &ap[j1], &c__1, &bp[j1], &
c__1)) / bjj;
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L')
KK and K1K1 are the indices of A(k,k) and A(k+1,k+1) */
kk = 1;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
k1k1 = kk + *n - k + 1;
/* Update the lower triangle of A(k:n,k:n) */
akk = ap[kk];
bkk = bp[kk];
/* Computing 2nd power */
d__1 = bkk;
akk /= d__1 * d__1;
ap[kk] = akk;
if (k < *n) {
i__2 = *n - k;
d__1 = 1. / bkk;
template_blas_scal(&i__2, &d__1, &ap[kk + 1], &c__1);
ct = akk * -.5;
i__2 = *n - k;
template_blas_axpy(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
template_blas_spr2(uplo, &i__2, &c_b9, &ap[kk + 1], &c__1, &bp[kk + 1]
, &c__1, &ap[k1k1]);
i__2 = *n - k;
template_blas_axpy(&i__2, &ct, &bp[kk + 1], &c__1, &ap[kk + 1], &c__1)
;
i__2 = *n - k;
template_blas_tpsv(uplo, "No transpose", "Non-unit", &i__2, &bp[k1k1],
&ap[kk + 1], &c__1);
}
kk = k1k1;
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U'
K1 and KK are the indices of A(1,k) and A(k,k) */
kk = 0;
i__1 = *n;
for (k = 1; k <= i__1; ++k) {
k1 = kk + 1;
kk += k;
/* Update the upper triangle of A(1:k,1:k) */
akk = ap[kk];
bkk = bp[kk];
i__2 = k - 1;
template_blas_tpmv(uplo, "No transpose", "Non-unit", &i__2, &bp[1], &ap[
k1], &c__1);
ct = akk * .5;
i__2 = k - 1;
template_blas_axpy(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
template_blas_spr2(uplo, &i__2, &c_b11, &ap[k1], &c__1, &bp[k1], &c__1, &
ap[1]);
i__2 = k - 1;
template_blas_axpy(&i__2, &ct, &bp[k1], &c__1, &ap[k1], &c__1);
i__2 = k - 1;
template_blas_scal(&i__2, &bkk, &ap[k1], &c__1);
/* Computing 2nd power */
d__1 = bkk;
ap[kk] = akk * (d__1 * d__1);
/* L30: */
}
} else {
/* Compute L'*A*L
JJ and J1J1 are the indices of A(j,j) and A(j+1,j+1) */
jj = 1;
i__1 = *n;
for (j = 1; j <= i__1; ++j) {
j1j1 = jj + *n - j + 1;
/* Compute the j-th column of the lower triangle of A */
ajj = ap[jj];
bjj = bp[jj];
i__2 = *n - j;
ap[jj] = ajj * bjj + template_blas_dot(&i__2, &ap[jj + 1], &c__1, &bp[jj
+ 1], &c__1);
i__2 = *n - j;
template_blas_scal(&i__2, &bjj, &ap[jj + 1], &c__1);
i__2 = *n - j;
template_blas_spmv(uplo, &i__2, &c_b11, &ap[j1j1], &bp[jj + 1], &c__1, &
c_b11, &ap[jj + 1], &c__1);
i__2 = *n - j + 1;
template_blas_tpmv(uplo, "Transpose", "Non-unit", &i__2, &bp[jj], &ap[jj],
&c__1);
jj = j1j1;
/* L40: */
}
}
}
return 0;
/* End of DSPGST */
} /* dspgst_ */
#endif
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