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>
59 #include <blaze/util/NumericCast.h>
60 
61 
62 namespace blaze {
63 
64 //=================================================================================================
65 //
66 // LU DECOMPOSITION FUNCTIONS
67 //
68 //=================================================================================================
69 
70 //*************************************************************************************************
73 template< typename MT1, bool SO1, typename MT2, typename MT3, typename MT4, bool SO2 >
74 void lu( const DenseMatrix<MT1,SO1>& A, DenseMatrix<MT2,SO1>& L,
75  DenseMatrix<MT3,SO1>& U, Matrix<MT4,SO2>& P );
77 //*************************************************************************************************
78 
79 
80 //*************************************************************************************************
93 template< typename MT1 // Type of matrix A
94  , bool SO1 // Storage order of dense matrix A
95  , typename MT2 // Type of matrix P
96  , bool SO2 > // Storage order of matrix P
97 void lu( DenseMatrix<MT1,SO1>& A, Matrix<MT2,SO2>& P )
98 {
99  using std::swap;
100 
102  BLAZE_CONSTRAINT_MUST_BE_BLAS_COMPATIBLE_TYPE( ElementType_t<MT1> );
104 
105  using ET = ElementType_t<MT2>;
106 
107  const int m( numeric_cast<int>( (~A).rows() ) );
108  const int n( numeric_cast<int>( (~A).columns() ) );
109  const int mindim( min( m, n ) );
110  const int size( SO1 ? m : n );
111 
112  const std::unique_ptr<int[]> helper( new int[mindim + size] );
113  int* ipiv ( helper.get() );
114  int* permut( ipiv + mindim );
115 
116  getrf( ~A, ipiv );
117 
118  for( int i=0; i<size; ++i ) {
119  permut[i] = i;
120  }
121 
122  for( int i=0; i<mindim; ++i ) {
123  --ipiv[i];
124  if( ipiv[i] != i ) {
125  swap( permut[ipiv[i]], permut[i] );
126  }
127  }
128 
129  resize( ~P, size, size, false );
130  reset( ~P );
131  for( int i=0; i<size; ++i ) {
132  (~P)( ( SO1 ? permut[i] : i ), ( SO1 ? i : permut[i] ) ) = ET(1);
133  }
134 }
136 //*************************************************************************************************
137 
138 
139 //*************************************************************************************************
215 template< typename MT1 // Type of matrix A
216  , bool SO1 // Storage order of matrix A, L and U
217  , typename MT2 // Type of matrix L
218  , typename MT3 // Type of matrix U
219  , typename MT4 // Type of matrix P
220  , bool SO2 > // Storage order of matrix P
223 {
226 
231 
236 
237  using ET2 = ElementType_t<MT2>;
238  using ET3 = ElementType_t<MT3>;
239 
240  const size_t m( (~A).rows() );
241  const size_t n( (~A).columns() );
242  const size_t mindim( min( m, n ) );
243  const size_t size( SO1 ? m : n );
244 
245  if( ( !IsResizable_v<MT2> && ( (~L).rows() != m || (~L).columns() != mindim ) ) ||
246  ( !IsResizable_v<MT3> && ( (~U).rows() != mindim || (~U).columns() != n ) ) ||
247  ( !IsResizable_v<MT4> && ( (~P).rows() != size || (~P).columns() != size ) ) ) {
248  BLAZE_THROW_INVALID_ARGUMENT( "Dimensions of fixed size matrix do not match" );
249  }
250 
251  if( ( IsSquare_v<MT2> && n < m ) || ( IsSquare_v<MT3> && m < n ) ) {
252  BLAZE_THROW_INVALID_ARGUMENT( "Square matrix cannot be resized to m-by-n" );
253  }
254 
255  decltype(auto) l( derestrict( ~L ) );
256  decltype(auto) u( derestrict( ~U ) );
257 
258  if( m < n )
259  {
260  u = (~A);
261  lu( u, ~P );
262 
263  resize( ~L, m, m, false );
264  reset( l );
265 
266  if( SO1 == rowMajor )
267  {
268  for( size_t i=0UL; i<m; ++i )
269  {
270  for( size_t j=0UL; j<i; ++j ) {
271  l(i,j) = u(i,j);
272  reset( u(i,j) );
273  }
274 
275  l(i,i) = u(i,i);
276  u(i,i) = ET3(1);
277  }
278  }
279  else
280  {
281  for( size_t j=0UL; j<m; ++j )
282  {
283  l(j,j) = ET2(1);
284 
285  for( size_t i=j+1UL; i<m; ++i ) {
286  l(i,j) = u(i,j);
287  reset( u(i,j) );
288  }
289  }
290  }
291  }
292  else
293  {
294  l = (~A);
295  lu( l, ~P );
296 
297  resize( ~U, n, n, false );
298  reset( u );
299 
300  if( SO1 == rowMajor )
301  {
302  for( size_t i=0UL; i<n; ++i )
303  {
304  u(i,i) = ET3(1);
305 
306  for( size_t j=i+1UL; j<n; ++j ) {
307  u(i,j) = l(i,j);
308  reset( l(i,j) );
309  }
310  }
311  }
312  else
313  {
314  for( size_t j=0UL; j<n; ++j )
315  {
316  for( size_t i=0UL; i<j; ++i ) {
317  u(i,j) = l(i,j);
318  reset( l(i,j) );
319  }
320 
321  u(j,j) = l(j,j);
322  l(j,j) = ET2(1);
323  }
324  }
325  }
326 }
327 //*************************************************************************************************
328 
329 } // namespace blaze
330 
331 #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:591
#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:80
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.
Constraint on the data type.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
void swap(CompressedMatrix< Type, SO > &a, CompressedMatrix< Type, SO > &b) noexcept
Swapping the contents of two compressed matrices.
Definition: CompressedMatrix.h:5907
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:1147
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:221
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, a compilation error is created.
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:281
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:109
#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, a compilation error is created.
Definition: Hermitian.h:79
Header file for the IsResizable type trait.
Header file for the LAPACK LU decomposition functions (getrf)