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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_LATRD_HEADER
#define TEMPLATE_LAPACK_LATRD_HEADER
template<class Treal>
int template_lapack_latrd(const char *uplo, const integer *n, const integer *nb, Treal *
a, const integer *lda, Treal *e, Treal *tau, Treal *w,
const integer *ldw)
{
/* -- 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
=======
DLATRD reduces NB rows and columns of a real symmetric matrix A to
symmetric tridiagonal form by an orthogonal similarity
transformation Q' * A * Q, and returns the matrices V and W which are
needed to apply the transformation to the unreduced part of A.
If UPLO = 'U', DLATRD reduces the last NB rows and columns of a
matrix, of which the upper triangle is supplied;
if UPLO = 'L', DLATRD reduces the first NB rows and columns of a
matrix, of which the lower triangle is supplied.
This is an auxiliary routine called by DSYTRD.
Arguments
=========
UPLO (input) CHARACTER
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored:
= 'U': Upper triangular
= 'L': Lower triangular
N (input) INTEGER
The order of the matrix A.
NB (input) INTEGER
The number of rows and columns to be reduced.
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 UPLO = 'U', the last NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements above the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors;
if UPLO = 'L', the first NB columns have been reduced to
tridiagonal form, with the diagonal elements overwriting
the diagonal elements of A; the elements below the diagonal
with the array TAU, represent the orthogonal matrix Q as a
product of elementary reflectors.
See Further Details.
LDA (input) INTEGER
The leading dimension of the array A. LDA >= (1,N).
E (output) DOUBLE PRECISION array, dimension (N-1)
If UPLO = 'U', E(n-nb:n-1) contains the superdiagonal
elements of the last NB columns of the reduced matrix;
if UPLO = 'L', E(1:nb) contains the subdiagonal elements of
the first NB columns of the reduced matrix.
TAU (output) DOUBLE PRECISION array, dimension (N-1)
The scalar factors of the elementary reflectors, stored in
TAU(n-nb:n-1) if UPLO = 'U', and in TAU(1:nb) if UPLO = 'L'.
See Further Details.
W (output) DOUBLE PRECISION array, dimension (LDW,NB)
The n-by-nb matrix W required to update the unreduced part
of A.
LDW (input) INTEGER
The leading dimension of the array W. LDW >= max(1,N).
Further Details
===============
If UPLO = 'U', the matrix Q is represented as a product of elementary
reflectors
Q = H(n) H(n-1) . . . H(n-nb+1).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(i:n) = 0 and v(i-1) = 1; v(1:i-1) is stored on exit in A(1:i-1,i),
and tau in TAU(i-1).
If UPLO = 'L', the matrix Q is represented as a product of elementary
reflectors
Q = H(1) H(2) . . . H(nb).
Each H(i) has the form
H(i) = I - tau * v * v'
where tau is a real scalar, and v is a real vector with
v(1:i) = 0 and v(i+1) = 1; v(i+1:n) is stored on exit in A(i+1:n,i),
and tau in TAU(i).
The elements of the vectors v together form the n-by-nb matrix V
which is needed, with W, to apply the transformation to the unreduced
part of the matrix, using a symmetric rank-2k update of the form:
A := A - V*W' - W*V'.
The contents of A on exit are illustrated by the following examples
with n = 5 and nb = 2:
if UPLO = 'U': if UPLO = 'L':
( a a a v4 v5 ) ( d )
( a a v4 v5 ) ( 1 d )
( a 1 v5 ) ( v1 1 a )
( d 1 ) ( v1 v2 a a )
( d ) ( v1 v2 a a a )
where d denotes a diagonal element of the reduced matrix, a denotes
an element of the original matrix that is unchanged, and vi denotes
an element of the vector defining H(i).
=====================================================================
Quick return if possible
Parameter adjustments */
/* Table of constant values */
Treal c_b5 = -1.;
Treal c_b6 = 1.;
integer c__1 = 1;
Treal c_b16 = 0.;
/* System generated locals */
integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3;
/* Local variables */
integer i__;
Treal alpha;
integer iw;
#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
#define w_ref(a_1,a_2) w[(a_2)*w_dim1 + a_1]
a_dim1 = *lda;
a_offset = 1 + a_dim1 * 1;
a -= a_offset;
--e;
--tau;
w_dim1 = *ldw;
w_offset = 1 + w_dim1 * 1;
w -= w_offset;
/* Function Body */
if (*n <= 0) {
return 0;
}
if (template_blas_lsame(uplo, "U")) {
/* Reduce last NB columns of upper triangle */
i__1 = *n - *nb + 1;
for (i__ = *n; i__ >= i__1; --i__) {
iw = i__ - *n + *nb;
if (i__ < *n) {
/* Update A(1:i,i) */
i__2 = *n - i__;
template_blas_gemv("No transpose", &i__, &i__2, &c_b5, &a_ref(1, i__ + 1),
lda, &w_ref(i__, iw + 1), ldw, &c_b6, &a_ref(1, i__),
&c__1);
i__2 = *n - i__;
template_blas_gemv("No transpose", &i__, &i__2, &c_b5, &w_ref(1, iw + 1),
ldw, &a_ref(i__, i__ + 1), lda, &c_b6, &a_ref(1, i__),
&c__1);
}
if (i__ > 1) {
/* Generate elementary reflector H(i) to annihilate
A(1:i-2,i) */
i__2 = i__ - 1;
template_lapack_larfg(&i__2, &a_ref(i__ - 1, i__), &a_ref(1, i__), &c__1, &
tau[i__ - 1]);
e[i__ - 1] = a_ref(i__ - 1, i__);
a_ref(i__ - 1, i__) = 1.;
/* Compute W(1:i-1,i) */
i__2 = i__ - 1;
template_blas_symv("Upper", &i__2, &c_b6, &a[a_offset], lda, &a_ref(1,
i__), &c__1, &c_b16, &w_ref(1, iw), &c__1);
if (i__ < *n) {
i__2 = i__ - 1;
i__3 = *n - i__;
template_blas_gemv("Transpose", &i__2, &i__3, &c_b6, &w_ref(1, iw + 1)
, ldw, &a_ref(1, i__), &c__1, &c_b16, &w_ref(i__
+ 1, iw), &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &a_ref(1, i__
+ 1), lda, &w_ref(i__ + 1, iw), &c__1, &c_b6, &
w_ref(1, iw), &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
template_blas_gemv("Transpose", &i__2, &i__3, &c_b6, &a_ref(1, i__ +
1), lda, &a_ref(1, i__), &c__1, &c_b16, &w_ref(
i__ + 1, iw), &c__1);
i__2 = i__ - 1;
i__3 = *n - i__;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &w_ref(1, iw
+ 1), ldw, &w_ref(i__ + 1, iw), &c__1, &c_b6, &
w_ref(1, iw), &c__1);
}
i__2 = i__ - 1;
template_blas_scal(&i__2, &tau[i__ - 1], &w_ref(1, iw), &c__1);
i__2 = i__ - 1;
alpha = tau[i__ - 1] * -.5 * template_blas_dot(&i__2, &w_ref(1, iw), &
c__1, &a_ref(1, i__), &c__1);
i__2 = i__ - 1;
template_blas_axpy(&i__2, &alpha, &a_ref(1, i__), &c__1, &w_ref(1, iw), &
c__1);
}
/* L10: */
}
} else {
/* Reduce first NB columns of lower triangle */
i__1 = *nb;
for (i__ = 1; i__ <= i__1; ++i__) {
/* Update A(i:n,i) */
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &a_ref(i__, 1), lda, &
w_ref(i__, 1), ldw, &c_b6, &a_ref(i__, i__), &c__1);
i__2 = *n - i__ + 1;
i__3 = i__ - 1;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &w_ref(i__, 1), ldw, &
a_ref(i__, 1), lda, &c_b6, &a_ref(i__, i__), &c__1);
if (i__ < *n) {
/* Generate elementary reflector H(i) to annihilate
A(i+2:n,i)
Computing MIN */
i__2 = i__ + 2;
i__3 = *n - i__;
template_lapack_larfg(&i__3, &a_ref(i__ + 1, i__), &a_ref(minMACRO(i__2,*n), i__)
, &c__1, &tau[i__]);
e[i__] = a_ref(i__ + 1, i__);
a_ref(i__ + 1, i__) = 1.;
/* Compute W(i+1:n,i) */
i__2 = *n - i__;
template_blas_symv("Lower", &i__2, &c_b6, &a_ref(i__ + 1, i__ + 1), lda, &
a_ref(i__ + 1, i__), &c__1, &c_b16, &w_ref(i__ + 1,
i__), &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
template_blas_gemv("Transpose", &i__2, &i__3, &c_b6, &w_ref(i__ + 1, 1),
ldw, &a_ref(i__ + 1, i__), &c__1, &c_b16, &w_ref(1,
i__), &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &a_ref(i__ + 1, 1)
, lda, &w_ref(1, i__), &c__1, &c_b6, &w_ref(i__ + 1,
i__), &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
template_blas_gemv("Transpose", &i__2, &i__3, &c_b6, &a_ref(i__ + 1, 1),
lda, &a_ref(i__ + 1, i__), &c__1, &c_b16, &w_ref(1,
i__), &c__1);
i__2 = *n - i__;
i__3 = i__ - 1;
template_blas_gemv("No transpose", &i__2, &i__3, &c_b5, &w_ref(i__ + 1, 1)
, ldw, &w_ref(1, i__), &c__1, &c_b6, &w_ref(i__ + 1,
i__), &c__1);
i__2 = *n - i__;
template_blas_scal(&i__2, &tau[i__], &w_ref(i__ + 1, i__), &c__1);
i__2 = *n - i__;
alpha = tau[i__] * -.5 * template_blas_dot(&i__2, &w_ref(i__ + 1, i__), &
c__1, &a_ref(i__ + 1, i__), &c__1);
i__2 = *n - i__;
template_blas_axpy(&i__2, &alpha, &a_ref(i__ + 1, i__), &c__1, &w_ref(i__
+ 1, i__), &c__1);
}
/* L20: */
}
}
return 0;
/* End of DLATRD */
} /* dlatrd_ */
#undef w_ref
#undef a_ref
#endif
|
