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
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
|
/*
* Copyright (c) 2012, Michael Lehn
*
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1) Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2) Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* 3) Neither the name of the FLENS development group nor the names of
* its contributors may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
* A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
* OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
* LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/* Based on
*
SUBROUTINE DLAQP2( M, N, OFFSET, A, LDA, JPVT, TAU, VN1, VN2,
$ WORK )
*
* -- LAPACK auxiliary routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*/
#ifndef FLENS_LAPACK_LA_LAQP2_TCC
#define FLENS_LAPACK_LA_LAQP2_TCC 1
#include <flens/blas/blas.h>
#include <flens/lapack/lapack.h>
namespace flens { namespace lapack {
//== generic lapack implementation =============================================
namespace generic {
//
// Real variant
//
template <typename MA, typename JPIV, typename VTAU,
typename VN1, typename VN2, typename VWORK>
typename RestrictTo<IsReal<typename MA::ElementType>::value,
void>::Type
laqp2_impl(typename GeMatrix<MA>::IndexType offset,
GeMatrix<MA> &A,
DenseVector<JPIV> &jPiv,
DenseVector<VTAU> &tau,
DenseVector<VN1> &vn1,
DenseVector<VN2> &vn2,
DenseVector<VWORK> &work)
{
using std::abs;
using std::max;
using std::min;
using std::sqrt;
using std::swap;
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType mn = min(m-offset, n);
const ElementType Zero(0), One(1);
const ElementType tol3z = sqrt(lamch<ElementType>(Eps));
//
// Compute factorization.
//
for (IndexType i=1; i<=mn; ++i) {
IndexType offpi = offset + i;
//
// Determine ith pivot column and swap if necessary.
//
IndexType pvt = (i-1) + blas::iamax(vn1(_(i,n)));
if (pvt!=i) {
blas::swap(A(_,pvt), A(_,i));
swap(jPiv(pvt), jPiv(i));
vn1(pvt) = vn1(i);
vn2(pvt) = vn2(i);
}
//
// Generate elementary reflector H(i).
//
if (offpi<m) {
larfg(m-offpi+1, A(offpi,i), A(_(offpi+1,m),i), tau(i));
} else {
larfg(1, A(m,i), A(_(m+1,m),i), tau(i));
}
if (i<=n) {
//
// Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
//
const ElementType Aii = A(offpi,i);
A(offpi,i) = One;
larf(Left, A(_(offpi,m),i), conjugate(tau(i)),
A(_(offpi,m),_(i+1,n)), work(_(1,n)));
A(offpi,i) = Aii;
}
//
// Update partial column norms.
//
for (IndexType j=i+1; j<=n; ++j) {
if (vn1(j)!=Zero) {
//
// NOTE: The following 4 lines follow from the analysis in
// Lapack Working Note 176.
//
ElementType tmp = One - pow(abs(A(offpi,j))/vn1(j), 2);
tmp = max(tmp, Zero);
ElementType tmp2 = tmp*pow(vn1(j)/vn2(j), 2);
if (tmp2<=tol3z) {
if (offpi<m) {
vn1(j) = blas::nrm2(A(_(offpi+1,m),j));
vn2(j) = vn1(j);
} else {
vn1(j) = Zero;
vn2(j) = Zero;
}
} else {
vn1(j) *= sqrt(tmp);
}
}
}
}
}
//
// Complex variant
//
template <typename MA, typename JPIV, typename VTAU,
typename VN1, typename VN2, typename VWORK>
typename RestrictTo<IsComplex<typename MA::ElementType>::value,
void>::Type
laqp2_impl(typename GeMatrix<MA>::IndexType offset,
GeMatrix<MA> &A,
DenseVector<JPIV> &jPiv,
DenseVector<VTAU> &tau,
DenseVector<VN1> &vn1,
DenseVector<VN2> &vn2,
DenseVector<VWORK> &work)
{
using std::abs;
using std::conj;
using std::max;
using std::min;
using std::sqrt;
using std::swap;
typedef typename GeMatrix<MA>::ElementType ElementType;
typedef typename ComplexTrait<ElementType>::PrimitiveType PrimitiveType;
typedef typename GeMatrix<MA>::IndexType IndexType;
const Underscore<IndexType> _;
const IndexType m = A.numRows();
const IndexType n = A.numCols();
const IndexType mn = min(m-offset, n);
const PrimitiveType Zero(0), One(1);
const ElementType CZero(0), COne(1);
const PrimitiveType tol3z = sqrt(lamch<PrimitiveType>(Eps));
//
// Compute factorization.
//
for (IndexType i=1; i<=mn; ++i) {
IndexType offpi = offset + i;
//
// Determine ith pivot column and swap if necessary.
//
IndexType pvt = (i-1) + blas::iamax(vn1(_(i,n)));
if (pvt!=i) {
blas::swap(A(_,pvt), A(_,i));
swap(jPiv(pvt), jPiv(i));
vn1(pvt) = vn1(i);
vn2(pvt) = vn2(i);
}
//
// Generate elementary reflector H(i).
//
if (offpi<m) {
larfg(m-offpi+1, A(offpi,i), A(_(offpi+1,m),i), tau(i));
} else {
larfg(1, A(m,i), A(_(m+1,m),i), tau(i));
}
if (i<=n) {
//
// Apply H(i)**T to A(offset+i:m,i+1:n) from the left.
//
const ElementType Aii = A(offpi,i);
A(offpi,i) = One;
larf(Left, A(_(offpi,m),i), conj(tau(i)), A(_(offpi,m),_(i+1,n)),
work(_(1,n)));
A(offpi,i) = Aii;
}
//
// Update partial column norms.
//
for (IndexType j=i+1; j<=n; ++j) {
if (vn1(j)!=Zero) {
//
// NOTE: The following 4 lines follow from the analysis in
// Lapack Working Note 176.
//
PrimitiveType tmp = One - pow(abs(A(offpi,j))/vn1(j), 2);
tmp = max(tmp, Zero);
PrimitiveType tmp2 = tmp*pow(vn1(j)/vn2(j), 2);
if (tmp2<=tol3z) {
if (offpi<m) {
vn1(j) = blas::nrm2(A(_(offpi+1,m),j));
vn2(j) = vn1(j);
} else {
vn1(j) = Zero;
vn2(j) = Zero;
}
} else {
vn1(j) *= sqrt(tmp);
}
}
}
}
}
} // namespace generic
//== interface for native lapack ===============================================
#ifdef USE_CXXLAPACK
namespace external {
template <typename MA, typename JPIV, typename VTAU,
typename VN1, typename VN2, typename VWORK>
void
laqp2_impl(typename GeMatrix<MA>::IndexType offset,
GeMatrix<MA> &A,
DenseVector<JPIV> &jPiv,
DenseVector<VTAU> &tau,
DenseVector<VN1> &vn1,
DenseVector<VN2> &vn2,
DenseVector<VWORK> &work)
{
typedef typename GeMatrix<MA>::IndexType IndexType;
cxxlapack::laqp2<IndexType>(A.numRows(),
A.numCols(),
offset,
A.data(),
A.leadingDimension(),
jPiv.data(),
tau.data(),
vn1.data(),
vn2.data(),
work.data());
}
} // namespace external
#endif // USE_CXXLAPACK
//== public interface ==========================================================
//
// Real and complex variant
//
template <typename IndexType, typename MA, typename JPIV, typename VTAU,
typename VN1, typename VN2, typename VWORK>
typename RestrictTo<((IsRealGeMatrix<MA>::value &&
IsRealDenseVector<VTAU>::value &&
IsRealDenseVector<VWORK>::value)
|| (IsComplexGeMatrix<MA>::value &&
IsComplexDenseVector<VTAU>::value &&
IsComplexDenseVector<VWORK>::value))
&& IsIntegerDenseVector<JPIV>::value
&& IsRealDenseVector<VN1>::value
&& IsRealDenseVector<VN2>::value,
void>::Type
laqp2(IndexType offset,
MA &&A,
JPIV &&jPiv,
VTAU &&tau,
VN1 &&vn1,
VN2 &&vn2,
VWORK &&work)
{
using std::min;
//
// Remove references from rvalue types
//
# ifdef CHECK_CXXLAPACK
typedef typename RemoveRef<MA>::Type MatrixA;
typedef typename RemoveRef<JPIV>::Type VectorJPiv;
typedef typename RemoveRef<VTAU>::Type VectorTau;
typedef typename RemoveRef<VN1>::Type VectorVN1;
typedef typename RemoveRef<VN2>::Type VectorVN2;
typedef typename RemoveRef<VWORK>::Type VectorWork;
# endif
# ifndef NDEBUG
//
// Test the input parameters
//
ASSERT(A.firstRow()==1);
ASSERT(A.firstCol()==1);
ASSERT(jPiv.firstIndex()==1);
ASSERT(tau.firstIndex()==1);
ASSERT(vn1.firstIndex()==1);
ASSERT(vn2.firstIndex()==1);
ASSERT(work.firstIndex()==1);
const IndexType m = A.numRows();
const IndexType n = A.numCols();
// Lehn: I think there is a bug in the DLAQP2 documentation. This should
// be the length of tau.
const IndexType k = min(m-offset, n);
ASSERT(jPiv.length()==n);
ASSERT(tau.length()==k);
ASSERT(vn1.length()==n);
ASSERT(vn1.length()==n);
ASSERT(work.length()==n);
# endif
# ifdef CHECK_CXXLAPACK
//
// Make copies of output arguments
//
typename MatrixA::NoView A_org = A;
typename VectorJPiv::NoView jPiv_org = jPiv;
typename VectorTau::NoView tau_org = tau;
typename VectorVN1::NoView vn1_org = vn1;
typename VectorVN2::NoView vn2_org = vn2;
typename VectorWork::NoView work_org = work;
# endif
//
// Call implementation
//
LAPACK_SELECT::laqp2_impl(offset, A, jPiv, tau, vn1, vn2, work);
# ifdef CHECK_CXXLAPACK
//
// Restore output arguments
//
typename MatrixA::NoView A_generic = A;
typename VectorJPiv::NoView jPiv_generic = jPiv;
typename VectorTau::NoView tau_generic = tau;
typename VectorVN1::NoView vn1_generic = vn1;
typename VectorVN2::NoView vn2_generic = vn2;
typename VectorWork::NoView work_generic = work;
A = A_org;
jPiv = jPiv_org;
tau = tau_org;
vn1 = vn1_org;
vn2 = vn2_org;
work = work_org;
//
// Compare results
//
external::laqp2_impl(offset, A, jPiv, tau, vn1, vn2, work);
bool failed = false;
if (! isIdentical(A_generic, A, "A_generic", "A")) {
std::cerr << "CXXLAPACK: A_generic = " << A_generic << std::endl;
std::cerr << "F77LAPACK: A = " << A << std::endl;
failed = true;
}
if (! isIdentical(jPiv_generic, jPiv, "jPiv_generic", "jPiv")) {
std::cerr << "CXXLAPACK: jPiv_generic = " << jPiv_generic << std::endl;
std::cerr << "F77LAPACK: jPiv = " << jPiv << std::endl;
failed = true;
}
if (! isIdentical(tau_generic, tau, "tau_generic", "tau")) {
std::cerr << "CXXLAPACK: tau_generic = " << tau_generic << std::endl;
std::cerr << "F77LAPACK: tau = " << tau << std::endl;
failed = true;
}
if (! isIdentical(vn1_generic, vn1, "vn1_generic", "vn1")) {
std::cerr << "CXXLAPACK: vn1_generic = " << vn1_generic << std::endl;
std::cerr << "F77LAPACK: vn1 = " << vn1 << std::endl;
failed = true;
}
if (! isIdentical(vn2_generic, vn2, "vn2_generic", "vn2")) {
std::cerr << "CXXLAPACK: vn2_generic = " << vn2_generic << std::endl;
std::cerr << "F77LAPACK: vn2 = " << vn2 << std::endl;
failed = true;
}
if (! isIdentical(work_generic, work, "work_generic", "work")) {
std::cerr << "CXXLAPACK: work_generic = " << work_generic << std::endl;
std::cerr << "F77LAPACK: work = " << work << std::endl;
failed = true;
}
if (failed) {
std::cerr << "offset = " << offset << std::endl;
std::cerr << "A = " << A << std::endl;
std::cerr << "jPiv = " << jPiv << std::endl;
std::cerr << "tau = " << tau << std::endl;
std::cerr << "vn1 = " << vn1 << std::endl;
std::cerr << "vn2 = " << vn2 << std::endl;
std::cerr << "work = " << work << std::endl;
ASSERT(0);
}
# endif
}
} } // namespace lapack, flens
#endif // FLENS_LAPACK_LA_LAQP2_TCC
|