Blaze  3.6
LU.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_DENSE_LU_H_
36 #define _BLAZE_MATH_DENSE_LU_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <memory>
44 #include <utility>
45 #include <blaze/math/Aliases.h>
54 #include <blaze/math/Exception.h>
60 #include <blaze/util/NumericCast.h>
61 
62 
63 namespace blaze {
64 
65 //=================================================================================================
66 //
67 // LU DECOMPOSITION FUNCTIONS
68 //
69 //=================================================================================================
70 
71 //*************************************************************************************************
74 template< typename MT1, bool SO1, typename MT2, typename MT3, typename MT4, bool SO2 >
75 void lu( const DenseMatrix<MT1,SO1>& A, DenseMatrix<MT2,SO1>& L,
76  DenseMatrix<MT3,SO1>& U, Matrix<MT4,SO2>& P );
78 //*************************************************************************************************
79 
80 
81 //*************************************************************************************************
94 template< typename MT1 // Type of matrix A
95  , bool SO1 // Storage order of dense matrix A
96  , typename MT2 // Type of matrix P
97  , bool SO2 > // Storage order of matrix P
98 void lu( DenseMatrix<MT1,SO1>& A, Matrix<MT2,SO2>& P )
99 {
100  using std::swap;
101 
103  BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT1> );
105 
106  using ET = ElementType_t<MT2>;
107 
108  const int m( numeric_cast<int>( (~A).rows() ) );
109  const int n( numeric_cast<int>( (~A).columns() ) );
110  const int mindim( min( m, n ) );
111  const int size( SO1 ? m : n );
112 
113  const std::unique_ptr<int[]> helper( new int[mindim + size] );
114  int* ipiv ( helper.get() );
115  int* permut( ipiv + mindim );
116 
117  getrf( ~A, ipiv );
118 
119  for( int i=0; i<size; ++i ) {
120  permut[i] = i;
121  }
122 
123  for( int i=0; i<mindim; ++i ) {
124  --ipiv[i];
125  if( ipiv[i] != i ) {
126  swap( permut[ipiv[i]], permut[i] );
127  }
128  }
129 
130  resize( ~P, size, size, false );
131  reset( ~P );
132  for( int i=0; i<size; ++i ) {
133  (~P)( ( SO1 ? permut[i] : i ), ( SO1 ? i : permut[i] ) ) = ET(1);
134  }
135 }
137 //*************************************************************************************************
138 
139 
140 //*************************************************************************************************
216 template< typename MT1 // Type of matrix A
217  , bool SO1 // Storage order of matrix A, L and U
218  , typename MT2 // Type of matrix L
219  , typename MT3 // Type of matrix U
220  , typename MT4 // Type of matrix P
221  , bool SO2 > // Storage order of matrix P
224 {
227 
232 
237 
238  using ET2 = ElementType_t<MT2>;
239  using ET3 = ElementType_t<MT3>;
240 
241  const size_t m( (~A).rows() );
242  const size_t n( (~A).columns() );
243  const size_t mindim( min( m, n ) );
244  const size_t size( SO1 ? m : n );
245 
246  if( ( !IsResizable_v<MT2> && ( (~L).rows() != m || (~L).columns() != mindim ) ) ||
247  ( !IsResizable_v<MT3> && ( (~U).rows() != mindim || (~U).columns() != n ) ) ||
248  ( !IsResizable_v<MT4> && ( (~P).rows() != size || (~P).columns() != size ) ) ) {
249  BLAZE_THROW_INVALID_ARGUMENT( "Dimensions of fixed size matrix do not match" );
250  }
251 
252  if( ( IsSquare_v<MT2> && n < m ) || ( IsSquare_v<MT3> && m < n ) ) {
253  BLAZE_THROW_INVALID_ARGUMENT( "Square matrix cannot be resized to m-by-n" );
254  }
255 
256  decltype(auto) l( derestrict( ~L ) );
257  decltype(auto) u( derestrict( ~U ) );
258 
259  if( m < n )
260  {
261  u = (~A);
262  lu( u, ~P );
263 
264  resize( ~L, m, m, false );
265  reset( l );
266 
267  if( SO1 == rowMajor )
268  {
269  for( size_t i=0UL; i<m; ++i )
270  {
271  for( size_t j=0UL; j<i; ++j ) {
272  l(i,j) = u(i,j);
273  reset( u(i,j) );
274  }
275 
276  l(i,i) = u(i,i);
277  u(i,i) = ET3(1);
278  }
279  }
280  else
281  {
282  for( size_t j=0UL; j<m; ++j )
283  {
284  l(j,j) = ET2(1);
285 
286  for( size_t i=j+1UL; i<m; ++i ) {
287  l(i,j) = u(i,j);
288  reset( u(i,j) );
289  }
290  }
291  }
292  }
293  else
294  {
295  l = (~A);
296  lu( l, ~P );
297 
298  resize( ~U, n, n, false );
299  reset( u );
300 
301  if( SO1 == rowMajor )
302  {
303  for( size_t i=0UL; i<n; ++i )
304  {
305  u(i,i) = ET3(1);
306 
307  for( size_t j=i+1UL; j<n; ++j ) {
308  u(i,j) = l(i,j);
309  reset( l(i,j) );
310  }
311  }
312  }
313  else
314  {
315  for( size_t j=0UL; j<n; ++j )
316  {
317  for( size_t i=0UL; i<j; ++i ) {
318  u(i,j) = l(i,j);
319  reset( l(i,j) );
320  }
321 
322  u(j,j) = l(j,j);
323  l(j,j) = ET2(1);
324  }
325  }
326  }
327 }
328 //*************************************************************************************************
329 
330 } // namespace blaze
331 
332 #endif
#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.
Headerfile for the generic min algorithm.
void reset(const DiagonalProxy< MT > &proxy)
Resetting the represented element to the default initial values.
Definition: DiagonalProxy.h:595
#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.
Cast operators for numeric types.
constexpr size_t columns(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of columns of the matrix.
Definition: Matrix.h:514
constexpr bool rowMajor
Storage order flag for row-major matrices.
Definition: StorageOrder.h:71
#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:81
typename T::ElementType ElementType_t
Alias declaration for nested ElementType type definitions.The ElementType_t alias declaration provide...
Definition: Aliases.h:170
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:58
decltype(auto) min(const DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
Computes the componentwise minimum of the dense matrices lhs and rhs.
Definition: DMatDMatMapExpr.h:1162
Header file for the DenseMatrix base class.
void lu(const DenseMatrix< MT1, SO1 > &A, DenseMatrix< MT2, SO1 > &L, DenseMatrix< MT3, SO1 > &U, Matrix< MT4, SO2 > &P)
LU decomposition of the given dense matrix.
Definition: LU.h:222
Header file for the exception macros of the math module.
#define BLAZE_CONSTRAINT_MUST_NOT_BE_UPPER_MATRIX_TYPE(T)
Constraint on the data type.In case the given data type T is a upper triangular matrix type,...
Definition: Upper.h:81
void resize(Matrix< MT, SO > &matrix, size_t rows, size_t columns, bool preserve=true)
Changing the size of the matrix.
Definition: Matrix.h:738
Constraint on the data type.
#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,...
Definition: Symmetric.h:79
void getrf(int m, int n, float *A, int lda, int *ipiv, int *info)
LAPACK kernel for the LU decomposition of the given dense general single precision column-major matri...
Definition: getrf.h:131
Constraint on the data type.
#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
void swap(DiagonalMatrix< MT, SO, DF > &a, DiagonalMatrix< MT, SO, DF > &b) noexcept
Swapping the contents of two matrices.
Definition: DiagonalMatrix.h:282
constexpr size_t size(const Matrix< MT, SO > &matrix) noexcept
Returns the total number of elements of the matrix.
Definition: Matrix.h:530
Base class for matrices.The Matrix class is a base class for all dense and sparse matrix classes with...
Definition: Forward.h:114
#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.
constexpr size_t rows(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of rows of the matrix.
Definition: Matrix.h:498
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
#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,...
Definition: Hermitian.h:79
Header file for the IsResizable type trait.
Header file for the LAPACK LU decomposition functions (getrf)