1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342
|
/* 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_SYGST_HEADER
#define TEMPLATE_LAPACK_SYGST_HEADER
#include "template_lapack_sygs2.h"
template<class Treal>
int template_lapack_sygst(const integer *itype, const char *uplo, const integer *n,
Treal *a, const integer *lda, Treal *b, const integer *ldb, 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
=======
DSYGST reduces a real symmetric-definite generalized eigenproblem
to standard form.
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 DPOTRF.
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.
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 transformed matrix, stored in the
same format as A.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= max(1,N).
B (input) DOUBLE PRECISION array, dimension (LDB,N)
The triangular factor from the Cholesky factorization of B,
as returned by DPOTRF.
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
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;
integer c_n1 = -1;
Treal c_b14 = 1.;
Treal c_b16 = -.5;
Treal c_b19 = -1.;
Treal c_b52 = .5;
/* System generated locals */
integer a_dim1, a_offset, b_dim1, b_offset, i__1, i__2, i__3;
/* Local variables */
integer k;
logical upper;
integer kb;
integer nb;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define b_ref(a_1,a_2) b[(a_2)*b_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
b_dim1 = *ldb;
b_offset = 1 + b_dim1 * 1;
b -= b_offset;
/* 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;
} else if (*lda < maxMACRO(1,*n)) {
*info = -5;
} else if (*ldb < maxMACRO(1,*n)) {
*info = -7;
}
if (*info != 0) {
i__1 = -(*info);
template_blas_erbla("SYGST ", &i__1);
return 0;
}
/* Quick return if possible */
if (*n == 0) {
return 0;
}
/* Determine the block size for this environment. */
nb = template_lapack_ilaenv(&c__1, "DSYGST", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (
ftnlen)1);
if (nb <= 1 || nb >= *n) {
/* Use unblocked code */
template_lapack_sygs2(itype, uplo, n, &a[a_offset], lda, &b[b_offset], ldb, info);
} else {
/* Use blocked code */
if (*itype == 1) {
if (upper) {
/* Compute inv(U')*A*inv(U) */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = minMACRO(i__3,nb);
/* Update the upper triangle of A(k:n,k:n) */
template_lapack_sygs2(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
template_blas_trsm("Left", uplo, "Transpose", "Non-unit", &kb, &
i__3, &c_b14, &b_ref(k, k), ldb, &a_ref(k, k
+ kb), lda);
i__3 = *n - k - kb + 1;
template_blas_symm("Left", uplo, &kb, &i__3, &c_b16, &a_ref(k, k),
lda, &b_ref(k, k + kb), ldb, &c_b14, &a_ref(
k, k + kb), lda);
i__3 = *n - k - kb + 1;
template_blas_syr2k(uplo, "Transpose", &i__3, &kb, &c_b19, &a_ref(
k, k + kb), lda, &b_ref(k, k + kb), ldb, &
c_b14, &a_ref(k + kb, k + kb), lda);
i__3 = *n - k - kb + 1;
template_blas_symm("Left", uplo, &kb, &i__3, &c_b16, &a_ref(k, k),
lda, &b_ref(k, k + kb), ldb, &c_b14, &a_ref(
k, k + kb), lda);
i__3 = *n - k - kb + 1;
template_blas_trsm("Right", uplo, "No transpose", "Non-unit", &kb,
&i__3, &c_b14, &b_ref(k + kb, k + kb), ldb, &
a_ref(k, k + kb), lda);
}
/* L10: */
}
} else {
/* Compute inv(L)*A*inv(L') */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = minMACRO(i__3,nb);
/* Update the lower triangle of A(k:n,k:n) */
template_lapack_sygs2(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
if (k + kb <= *n) {
i__3 = *n - k - kb + 1;
template_blas_trsm("Right", uplo, "Transpose", "Non-unit", &i__3,
&kb, &c_b14, &b_ref(k, k), ldb, &a_ref(k + kb,
k), lda);
i__3 = *n - k - kb + 1;
template_blas_symm("Right", uplo, &i__3, &kb, &c_b16, &a_ref(k, k)
, lda, &b_ref(k + kb, k), ldb, &c_b14, &a_ref(
k + kb, k), lda);
i__3 = *n - k - kb + 1;
template_blas_syr2k(uplo, "No transpose", &i__3, &kb, &c_b19, &
a_ref(k + kb, k), lda, &b_ref(k + kb, k), ldb,
&c_b14, &a_ref(k + kb, k + kb), lda);
i__3 = *n - k - kb + 1;
template_blas_symm("Right", uplo, &i__3, &kb, &c_b16, &a_ref(k, k)
, lda, &b_ref(k + kb, k), ldb, &c_b14, &a_ref(
k + kb, k), lda);
i__3 = *n - k - kb + 1;
template_blas_trsm("Left", uplo, "No transpose", "Non-unit", &
i__3, &kb, &c_b14, &b_ref(k + kb, k + kb),
ldb, &a_ref(k + kb, k), lda);
}
/* L20: */
}
}
} else {
if (upper) {
/* Compute U*A*U' */
i__1 = *n;
i__2 = nb;
for (k = 1; i__2 < 0 ? k >= i__1 : k <= i__1; k += i__2) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = minMACRO(i__3,nb);
/* Update the upper triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
template_blas_trmm("Left", uplo, "No transpose", "Non-unit", &i__3, &
kb, &c_b14, &b[b_offset], ldb, &a_ref(1, k), lda);
i__3 = k - 1;
template_blas_symm("Right", uplo, &i__3, &kb, &c_b52, &a_ref(k, k),
lda, &b_ref(1, k), ldb, &c_b14, &a_ref(1, k), lda);
i__3 = k - 1;
template_blas_syr2k(uplo, "No transpose", &i__3, &kb, &c_b14, &a_ref(
1, k), lda, &b_ref(1, k), ldb, &c_b14, &a[
a_offset], lda);
i__3 = k - 1;
template_blas_symm("Right", uplo, &i__3, &kb, &c_b52, &a_ref(k, k),
lda, &b_ref(1, k), ldb, &c_b14, &a_ref(1, k), lda);
i__3 = k - 1;
template_blas_trmm("Right", uplo, "Transpose", "Non-unit", &i__3, &kb,
&c_b14, &b_ref(k, k), ldb, &a_ref(1, k), lda);
template_lapack_sygs2(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
/* L30: */
}
} else {
/* Compute L'*A*L */
i__2 = *n;
i__1 = nb;
for (k = 1; i__1 < 0 ? k >= i__2 : k <= i__2; k += i__1) {
/* Computing MIN */
i__3 = *n - k + 1;
kb = minMACRO(i__3,nb);
/* Update the lower triangle of A(1:k+kb-1,1:k+kb-1) */
i__3 = k - 1;
template_blas_trmm("Right", uplo, "No transpose", "Non-unit", &kb, &
i__3, &c_b14, &b[b_offset], ldb, &a_ref(k, 1),
lda);
i__3 = k - 1;
template_blas_symm("Left", uplo, &kb, &i__3, &c_b52, &a_ref(k, k),
lda, &b_ref(k, 1), ldb, &c_b14, &a_ref(k, 1), lda);
i__3 = k - 1;
template_blas_syr2k(uplo, "Transpose", &i__3, &kb, &c_b14, &a_ref(k,
1), lda, &b_ref(k, 1), ldb, &c_b14, &a[a_offset],
lda);
i__3 = k - 1;
template_blas_symm("Left", uplo, &kb, &i__3, &c_b52, &a_ref(k, k),
lda, &b_ref(k, 1), ldb, &c_b14, &a_ref(k, 1), lda);
i__3 = k - 1;
template_blas_trmm("Left", uplo, "Transpose", "Non-unit", &kb, &i__3,
&c_b14, &b_ref(k, k), ldb, &a_ref(k, 1), lda);
template_lapack_sygs2(itype, uplo, &kb, &a_ref(k, k), lda, &b_ref(k, k),
ldb, info);
/* L40: */
}
}
}
}
return 0;
/* End of DSYGST */
} /* dsygst_ */
#undef b_ref
#undef a_ref
#endif
|