QR.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_DENSE_QR_H_
36 #define _BLAZE_MATH_DENSE_QR_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <memory>
44 #include <blaze/math/Aliases.h>
52 #include <blaze/math/Exception.h>
54 #include <blaze/math/Functions.h>
62 #include <blaze/util/EnableIf.h>
63 
64 
65 namespace blaze {
66 
67 //=================================================================================================
68 //
69 // QR DECOMPOSITION FUNCTIONS
70 //
71 //=================================================================================================
72 
73 //*************************************************************************************************
76 template< typename MT1, bool SO1, typename MT2, bool SO2, typename MT3, bool SO3 >
77 void qr( const DenseMatrix<MT1,SO1>& A, DenseMatrix<MT2,SO2>& Q, DenseMatrix<MT3,SO3>& R );
79 //*************************************************************************************************
80 
81 
82 //*************************************************************************************************
94 template< typename MT1 > // Type of matrix A
95 inline EnableIf_<IsBuiltin< ElementType_<MT1> > >
96  qr_backend( MT1& A, const ElementType_<MT1>* tau )
97 {
98  orgqr( A, tau );
99 }
101 //*************************************************************************************************
102 
103 
104 //*************************************************************************************************
116 template< typename MT1 > // Type of matrix A
117 inline EnableIf_<IsComplex< ElementType_<MT1> > >
118  qr_backend( MT1& A, const ElementType_<MT1>* tau )
119 {
120  ungqr( A, tau );
121 }
123 //*************************************************************************************************
124 
125 
126 //*************************************************************************************************
174 template< typename MT1 // Type of matrix A
175  , bool SO1 // Storage order of matrix A
176  , typename MT2 // Type of matrix Q
177  , bool SO2 // Storage order of matrix Q
178  , typename MT3 // Type of matrix R
179  , bool SO3 > // Storage order of matrix R
181 {
184 
187 
193 
194  typedef ElementType_<MT1> ET1;
195 
196  const size_t m( (~A).rows() );
197  const size_t n( (~A).columns() );
198  const size_t mindim( min( m, n ) );
199 
200  if( ( !IsResizable<MT2>::value && ( (~Q).rows() != m || (~Q).columns() != mindim ) ) ||
201  ( !IsResizable<MT3>::value && ( (~R).rows() != mindim || (~R).columns() != n ) ) ) {
202  BLAZE_THROW_INVALID_ARGUMENT( "Dimensions of fixed size matrix do not match" );
203  }
204 
205  if( IsSquare<MT3>::value && mindim != n ) {
206  BLAZE_THROW_INVALID_ARGUMENT( "Square matrix cannot be resized to min(m,n)-by-n" );
207  }
208 
209  const std::unique_ptr<ET1[]> tau( new ET1[mindim] );
210  DerestrictTrait_<MT3> r( derestrict( ~R ) );
211 
212  if( m < n )
213  {
214  r = A;
215  geqrf( r, tau.get() );
216  (~Q) = submatrix( r, 0UL, 0UL, m, m );
217  qr_backend( ~Q, tau.get() );
218 
219  for( size_t i=1UL; i<m; ++i ) {
220  for( size_t j=0UL; j<i; ++j ) {
221  reset( r(i,j) );
222  }
223  }
224  }
225  else
226  {
227  (~Q) = A;
228  geqrf( ~Q, tau.get() );
229 
230  resize( ~R, n, n );
231  reset( r );
232 
233  for( size_t i=0UL; i<n; ++i ) {
234  for( size_t j=i; j<n; ++j ) {
235  r(i,j) = (~Q)(i,j);
236  }
237  }
238 
239  qr_backend( ~Q, tau.get() );
240  }
241 }
242 //*************************************************************************************************
243 
244 } // namespace blaze
245 
246 #endif
Header file for the implementation of the Submatrix view.
#define BLAZE_THROW_INVALID_ARGUMENT(MESSAGE)
Macro for the emission of a std::invalid_argument exception.This macro encapsulates the default way o...
Definition: Exception.h:235
Header file for auxiliary alias declarations.
Header file for mathematical functions.
typename DerestrictTrait< T >::Type DerestrictTrait_
Auxiliary alias declaration for the DerestrictTrait type trait.The DerestrictTrait_ alias declaration...
Definition: DerestrictTrait.h:110
void ungqr(int m, int n, int k, complex< float > *A, int lda, const complex< float > *tau, complex< float > *work, int lwork, int *info)
LAPACK kernel for the reconstruction of the orthogonal matrix Q from a QR decomposition.
Definition: ungqr.h:117
void orgqr(int m, int n, int k, float *A, int lda, const float *tau, float *work, int lwork, int *info)
LAPACK kernel for the reconstruction of the orthogonal matrix Q from a QR decomposition.
Definition: orgqr.h:117
Header file for the LAPACK functions to reconstruct Q from a QR decomposition (orgqr) ...
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:533
const ElementType_< MT > min(const DenseMatrix< MT, SO > &dm)
Returns the smallest element of the dense matrix.
Definition: DenseMatrix.h:1669
#define BLAZE_CONSTRAINT_MUST_NOT_BE_UNITRIANGULAR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a lower or upper unitriangular matrix ty...
Definition: UniTriangular.h:81
Constraint on the data type.
Constraint on the data type.
#define BLAZE_CONSTRAINT_MUST_NOT_BE_ADAPTOR_TYPE(T)
Constraint on the data type.In case the given data type T is an adaptor type (as for instance LowerMa...
Definition: Adaptor.h:81
Base class for dense matrices.The DenseMatrix class is a base class for all dense matrix classes...
Definition: DenseMatrix.h:70
Constraint on the data type.
Header file for the IsSquare type trait.
Constraint on the data type.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:57
Header file for the LAPACK QR decomposition functions (geqrf)
Header file for the DenseMatrix base class.
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Compile time check for square matrices.This type trait tests whether or not the given template parame...
Definition: IsSquare.h:88
BLAZE_ALWAYS_INLINE size_t columns(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of columns of the matrix.
Definition: Matrix.h:330
Header file for the exception macros of the math module.
BLAZE_ALWAYS_INLINE void resize(Matrix< MT, SO > &matrix, size_t rows, size_t columns, bool preserve=true)
Changing the size of the matrix.
Definition: Matrix.h:538
Header file for the EnableIf class template.
Header file for the DerestrictTrait class template.
Constraint on the data type.
void qr(const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO2 > &Q, DenseMatrix< MT3, SO3 > &R)
QR decomposition of the given dense matrix.
Definition: QR.h:180
Compile time check for resizable data types.This type trait tests whether the given data type is a re...
Definition: IsResizable.h:75
#define BLAZE_CONSTRAINT_MUST_NOT_BE_SYMMETRIC_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a symmetric matrix type, a compilation error is created.
Definition: Symmetric.h:79
void geqrf(int m, int n, float *A, int lda, float *tau, float *work, int lwork, int *info)
LAPACK kernel for the QR decomposition of the given dense single precision column-major matrix...
Definition: geqrf.h:143
#define BLAZE_CONSTRAINT_MUST_NOT_BE_LOWER_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a lower triangular matrix type...
Definition: Lower.h:81
#define BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE(T)
Constraint on the data type.In case the given data type T is not a BLAS compatible data type (i...
Definition: BLASCompatible.h:61
Constraint on the data type.
Constraint on the data type.
#define BLAZE_CONSTRAINT_MUST_NOT_BE_STRICTLY_TRIANGULAR_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a strictly lower or upper triangular mat...
Definition: StrictlyTriangular.h:81
BLAZE_ALWAYS_INLINE size_t rows(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of rows of the matrix.
Definition: Matrix.h:314
#define BLAZE_CONSTRAINT_MUST_NOT_BE_HERMITIAN_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is an Hermitian matrix type, a compilation error is created.
Definition: Hermitian.h:79
Header file for the LAPACK functions to reconstruct Q from a QR decomposition (ungqr) ...
SubmatrixExprTrait_< MT, unaligned > submatrix(Matrix< MT, SO > &matrix, size_t row, size_t column, size_t m, size_t n)
Creating a view on a specific submatrix of the given matrix.
Definition: Submatrix.h:167
Header file for the IsResizable type trait.