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
|
//=================================================================================================
/*!
// \file blaze/math/lapack/ormlq.h
// \brief Header file for the LAPACK functions to multiply Q from a LQ decomposition with a matrix (ormlq)
//
// Copyright (C) 2013 Klaus Iglberger - All Rights Reserved
//
// This file is part of the Blaze library. You can redistribute it and/or modify it under
// the terms of the New (Revised) BSD License. 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 names of the Blaze 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 HOLDER 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.
*/
//=================================================================================================
#ifndef _BLAZE_MATH_LAPACK_ORMLQ_H_
#define _BLAZE_MATH_LAPACK_ORMLQ_H_
//*************************************************************************************************
// Includes
//*************************************************************************************************
#include <memory>
#include <boost/cast.hpp>
#include <blaze/math/Aliases.h>
#include <blaze/math/constraints/Adaptor.h>
#include <blaze/math/constraints/BLASCompatible.h>
#include <blaze/math/constraints/Computation.h>
#include <blaze/math/constraints/MutableDataAccess.h>
#include <blaze/math/Exception.h>
#include <blaze/math/expressions/DenseMatrix.h>
#include <blaze/math/lapack/clapack/ormlq.h>
#include <blaze/math/lapack/clapack/ormqr.h>
#include <blaze/math/typetraits/IsRowMajorMatrix.h>
#include <blaze/util/Assert.h>
#include <blaze/util/constraints/FloatingPoint.h>
#include <blaze/util/mpl/Xor.h>
namespace blaze {
//=================================================================================================
//
// LAPACK FUNCTIONS TO MULTIPLY Q FROM A LQ DECOMPOSITION WITH A MATRIX (ORMLQ)
//
//=================================================================================================
//*************************************************************************************************
/*!\name LAPACK functions to multiply Q from a LQ decomposition with a matrix (ormlq) */
//@{
template< typename MT1, bool SO1, typename MT2, bool SO2 >
inline void ormlq( DenseMatrix<MT1,SO1>& C, const DenseMatrix<MT2,SO2>& A,
char side, char trans, const ElementType_<MT2>* tau );
//@}
//*************************************************************************************************
//*************************************************************************************************
/*!\brief LAPACK kernel for the multiplication of the double precision Q from a LQ decomposition
// with another matrix.
// \ingroup lapack_decomposition
//
// \param C The matrix multiplier.
// \param A The decomposed matrix.
// \param side \c 'L' to apply \f$ Q \f$ or \f$ Q^T \f$ from the left, \c 'R' to apply from the right.
// \param trans \c 'N' for \f$ Q \f$, \c 'T' for \f$ Q^T \f$.
// \param tau Array for the scalar factors of the elementary reflectors.
// \return void
// \exception std::invalid_argument Invalid size of Q matrix.
// \exception std::invalid_argument Invalid side argument provided.
// \exception std::invalid_argument Invalid trans argument provided.
//
// This function multiplies a square \a Q matrix resulting from the LQ decomposition of the
// gelqf() functions with the given general \a m-by-\a n matrix \a C. Depending on the settings
// of \a side and \a trans it overwrites \a C with
\code
| side = 'L' | side = 'R'
-------------|--------------|--------------
trans = 'N': | Q * C | C * Q
trans = 'T': | trans(Q) * C | C * trans(Q)
\endcode
// Note that the size of matrix \c C is preserved, which means that the function does not work for
// non-square Q matrices. Therefore in case the number of rows of \a A is larger than the number
// of columns, a \a std::invalid_argument exception is thrown. Also Note that this function can
// only be used for general, non-adapted matrices with \c float or \c double element type. The
// attempt to call the function with any adapted matrix or matrices of any other element type
// results in a compile time error!
//
// The following code example demonstrates the use of the ormlq() function:
\code
using blaze::DynamicMatrix;
using blaze::columnMajor;
DynamicMatrix<double,columnMajor> A;
DynamicMatrix<double,columnMajor> C;
DynamicVector<double> tau;
// ... Resizing and initialization
gelqf( A, tau.data() ); // Performing the LQ decomposition
ormlq( C, A, 'R', 'N', tau.data() ); // Computing C = C * Q
\endcode
// For more information on the ormlq() functions (i.e. sormlq() and dormlq()) see the LAPACK
// online documentation browser:
//
// http://www.netlib.org/lapack/explore-html/
//
// \note This function can only be used if the fitting LAPACK library is available and linked to
// the executable. Otherwise a call to this function will result in a linker error.
*/
template< typename MT1, bool SO1, typename MT2, bool SO2 >
inline void ormlq( DenseMatrix<MT1,SO1>& C, const DenseMatrix<MT2,SO2>& A,
char side, char trans, const ElementType_<MT2>* tau )
{
using boost::numeric_cast;
BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT1 );
BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT1 );
BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS( MT1 );
BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_<MT1> );
BLAZE_CONSTRAINT_MUST_BE_FLOATING_POINT_TYPE( ElementType_<MT1> );
BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE( MT2 );
BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE( MT2 );
BLAZE_CONSTRAINT_MUST_HAVE_CONST_DATA_ACCESS( MT2 );
BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_<MT2> );
BLAZE_CONSTRAINT_MUST_BE_FLOATING_POINT_TYPE( ElementType_<MT2> );
typedef ElementType_<MT1> ET;
if( (~A).rows() > (~A).columns() ) {
BLAZE_THROW_INVALID_ARGUMENT( "Invalid size of Q matrix" );
}
if( side != 'L' && side != 'R' ) {
BLAZE_THROW_INVALID_ARGUMENT( "Invalid side argument provided" );
}
if( trans != 'N' && trans != 'T' ) {
BLAZE_THROW_INVALID_ARGUMENT( "Invalid trans argument provided" );
}
int m ( numeric_cast<int>( SO1 ? (~C).rows() : (~C).columns() ) );
int n ( numeric_cast<int>( SO1 ? (~C).columns() : (~C).rows() ) );
int k ( numeric_cast<int>( min( (~A).rows(), (~A).columns() ) ) );
int lda ( numeric_cast<int>( (~A).spacing() ) );
int ldc ( numeric_cast<int>( (~C).spacing() ) );
int info( 0 );
if( m == 0 || n == 0 || k == 0 ) {
return;
}
if( IsRowMajorMatrix<MT1>::value ) {
( side == 'L' )?( side = 'R' ):( side = 'L' );
}
if( Xor< IsRowMajorMatrix<MT1>, IsRowMajorMatrix<MT2> >::value ) {
( trans == 'N' )?( trans = 'T' ):( trans = 'N' );
}
int lwork( k*ldc );
const std::unique_ptr<ET[]> work( new ET[lwork] );
if( SO2 ) {
ormlq( side, trans, m, n, k, (~A).data(), lda, tau, (~C).data(), ldc, work.get(), lwork, &info );
}
else {
ormqr( side, trans, m, n, k, (~A).data(), lda, tau, (~C).data(), ldc, work.get(), lwork, &info );
}
BLAZE_INTERNAL_ASSERT( info == 0, "Invalid argument for Q multiplication" );
}
//*************************************************************************************************
} // namespace blaze
#endif
|
