ergo
template_lapack_geqr2.h
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1/* Ergo, version 3.8, a program for linear scaling electronic structure
2 * calculations.
3 * Copyright (C) 2019 Elias Rudberg, Emanuel H. Rubensson, Pawel Salek,
4 * and Anastasia Kruchinina.
5 *
6 * This program is free software: you can redistribute it and/or modify
7 * it under the terms of the GNU General Public License as published by
8 * the Free Software Foundation, either version 3 of the License, or
9 * (at your option) any later version.
10 *
11 * This program is distributed in the hope that it will be useful,
12 * but WITHOUT ANY WARRANTY; without even the implied warranty of
13 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14 * GNU General Public License for more details.
15 *
16 * You should have received a copy of the GNU General Public License
17 * along with this program. If not, see <http://www.gnu.org/licenses/>.
18 *
19 * Primary academic reference:
20 * Ergo: An open-source program for linear-scaling electronic structure
21 * calculations,
22 * Elias Rudberg, Emanuel H. Rubensson, Pawel Salek, and Anastasia
23 * Kruchinina,
24 * SoftwareX 7, 107 (2018),
25 * <http://dx.doi.org/10.1016/j.softx.2018.03.005>
26 *
27 * For further information about Ergo, see <http://www.ergoscf.org>.
28 */
29
30 /* This file belongs to the template_lapack part of the Ergo source
31 * code. The source files in the template_lapack directory are modified
32 * versions of files originally distributed as CLAPACK, see the
33 * Copyright/license notice in the file template_lapack/COPYING.
34 */
35
36
37#ifndef TEMPLATE_LAPACK_GEQR2_HEADER
38#define TEMPLATE_LAPACK_GEQR2_HEADER
39
40
41template<class Treal>
42int template_lapack_geqr2(const integer *m, const integer *n, Treal *a, const integer *
43 lda, Treal *tau, Treal *work, integer *info)
44{
45/* -- LAPACK routine (version 3.0) --
46 Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
47 Courant Institute, Argonne National Lab, and Rice University
48 February 29, 1992
49
50
51 Purpose
52 =======
53
54 DGEQR2 computes a QR factorization of a real m by n matrix A:
55 A = Q * R.
56
57 Arguments
58 =========
59
60 M (input) INTEGER
61 The number of rows of the matrix A. M >= 0.
62
63 N (input) INTEGER
64 The number of columns of the matrix A. N >= 0.
65
66 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
67 On entry, the m by n matrix A.
68 On exit, the elements on and above the diagonal of the array
69 contain the min(m,n) by n upper trapezoidal matrix R (R is
70 upper triangular if m >= n); the elements below the diagonal,
71 with the array TAU, represent the orthogonal matrix Q as a
72 product of elementary reflectors (see Further Details).
73
74 LDA (input) INTEGER
75 The leading dimension of the array A. LDA >= max(1,M).
76
77 TAU (output) DOUBLE PRECISION array, dimension (min(M,N))
78 The scalar factors of the elementary reflectors (see Further
79 Details).
80
81 WORK (workspace) DOUBLE PRECISION array, dimension (N)
82
83 INFO (output) INTEGER
84 = 0: successful exit
85 < 0: if INFO = -i, the i-th argument had an illegal value
86
87 Further Details
88 ===============
89
90 The matrix Q is represented as a product of elementary reflectors
91
92 Q = H(1) H(2) . . . H(k), where k = min(m,n).
93
94 Each H(i) has the form
95
96 H(i) = I - tau * v * v'
97
98 where tau is a real scalar, and v is a real vector with
99 v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),
100 and tau in TAU(i).
101
102 =====================================================================
103
104
105 Test the input arguments
106
107 Parameter adjustments */
108 /* Table of constant values */
109 integer c__1 = 1;
110
111 /* System generated locals */
112 integer a_dim1, a_offset, i__1, i__2, i__3;
113 /* Local variables */
114 integer i__, k;
115 Treal aii;
116#define a_ref(a_1,a_2) a[(a_2)*a_dim1 + a_1]
117
118
119 a_dim1 = *lda;
120 a_offset = 1 + a_dim1 * 1;
121 a -= a_offset;
122 --tau;
123 --work;
124
125 /* Function Body */
126 *info = 0;
127 if (*m < 0) {
128 *info = -1;
129 } else if (*n < 0) {
130 *info = -2;
131 } else if (*lda < maxMACRO(1,*m)) {
132 *info = -4;
133 }
134 if (*info != 0) {
135 i__1 = -(*info);
136 template_blas_erbla("GEQR2 ", &i__1);
137 return 0;
138 }
139
140 k = minMACRO(*m,*n);
141
142 i__1 = k;
143 for (i__ = 1; i__ <= i__1; ++i__) {
144
145/* Generate elementary reflector H(i) to annihilate A(i+1:m,i)
146
147 Computing MIN */
148 i__2 = i__ + 1;
149 i__3 = *m - i__ + 1;
150 template_lapack_larfg(&i__3, &a_ref(i__, i__), &a_ref(minMACRO(i__2,*m), i__), &c__1, &
151 tau[i__]);
152 if (i__ < *n) {
153
154/* Apply H(i) to A(i:m,i+1:n) from the left */
155
156 aii = a_ref(i__, i__);
157 a_ref(i__, i__) = 1.;
158 i__2 = *m - i__ + 1;
159 i__3 = *n - i__;
160 template_lapack_larf("Left", &i__2, &i__3, &a_ref(i__, i__), &c__1, &tau[i__], &
161 a_ref(i__, i__ + 1), lda, &work[1]);
162 a_ref(i__, i__) = aii;
163 }
164/* L10: */
165 }
166 return 0;
167
168/* End of DGEQR2 */
169
170} /* dgeqr2_ */
171
172#undef a_ref
173
174
175#endif
int template_blas_erbla(const char *srname, integer *info)
Definition: template_blas_common.cc:146
int integer
Definition: template_blas_common.h:40
#define minMACRO(a, b)
Definition: template_blas_common.h:46
#define maxMACRO(a, b)
Definition: template_blas_common.h:45
#define a_ref(a_1, a_2)
int template_lapack_geqr2(const integer *m, const integer *n, Treal *a, const integer *lda, Treal *tau, Treal *work, integer *info)
Definition: template_lapack_geqr2.h:42
int template_lapack_larf(const char *side, const integer *m, const integer *n, const Treal *v, const integer *incv, const Treal *tau, Treal *c__, const integer *ldc, Treal *work)
Definition: template_lapack_larf.h:42
int template_lapack_larfg(const integer *n, Treal *alpha, Treal *x, const integer *incx, Treal *tau)
Definition: template_lapack_larfg.h:43