Blaze  3.6
heevx.h
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1 //=================================================================================================
33 //=================================================================================================
34 
35 #ifndef _BLAZE_MATH_LAPACK_HEEVX_H_
36 #define _BLAZE_MATH_LAPACK_HEEVX_H_
37 
38 
39 //*************************************************************************************************
40 // Includes
41 //*************************************************************************************************
42 
43 #include <memory>
44 #include <blaze/math/Aliases.h>
50 #include <blaze/math/Exception.h>
55 #include <blaze/util/Assert.h>
58 #include <blaze/util/NumericCast.h>
59 #include <blaze/util/Types.h>
61 
62 
63 namespace blaze {
64 
65 //=================================================================================================
66 //
67 // LAPACK HERMITIAN MATRIX EIGENVALUE FUNCTIONS (HEEVX)
68 //
69 //=================================================================================================
70 
71 //*************************************************************************************************
74 template< typename MT, bool SO, typename VT, bool TF >
75 size_t heevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo );
76 
77 template< typename MT, bool SO, typename VT, bool TF, typename ST >
78 size_t heevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo, ST low, ST upp );
79 
80 template< typename MT1, bool SO1, typename VT, bool TF, typename MT2, bool SO2 >
81 size_t heevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
82  DenseMatrix<MT2,SO2>& Z, char uplo );
83 
84 template< typename MT1, bool SO1, typename VT, bool TF, typename MT2, bool SO2, typename ST >
85 size_t heevx( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
86  DenseMatrix<MT2,SO2>& Z, char uplo, ST low, ST upp );
88 //*************************************************************************************************
89 
90 
91 //*************************************************************************************************
114 template< typename MT // Type of the matrix A
115  , bool SO // Storage order of the matrix A
116  , typename VT // Type of the vector w
117  , bool TF // Transpose flag of the vector w
118  , typename ST > // Type of the scalar boundary values
119 inline size_t heevx_backend( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w,
120  char uplo, char range, ST vl, ST vu, int il, int iu )
121 {
122  BLAZE_INTERNAL_ASSERT( isSquare( ~A ), "Invalid non-square matrix detected" );
123  BLAZE_INTERNAL_ASSERT( range != 'A' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
124  BLAZE_INTERNAL_ASSERT( range != 'V' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
125  BLAZE_INTERNAL_ASSERT( range != 'I' || (~w).size() == size_t( iu-il+1 ), "Invalid vector dimension detected" );
126 
127  using CT = ElementType_t<MT>;
128  using BT = UnderlyingElement_t<CT>;
129 
132 
133  int n ( numeric_cast<int>( (~A).rows() ) );
134  int lda ( numeric_cast<int>( (~A).spacing() ) );
135  int m ( 0 );
136  int info( 0 );
137 
138  int lwork( 12*n + 2 );
139  const std::unique_ptr<CT[]> work ( new CT[lwork] );
140  const std::unique_ptr<BT[]> rwork( new BT[7*n] );
141  const std::unique_ptr<int[]> iwork( new int[5*n] );
142  const std::unique_ptr<int[]> ifail( new int[n] );
143 
144  heevx( 'N', range, uplo, n, (~A).data(), lda, vl, vu, il, iu, BT(0), &m, (~w).data(),
145  nullptr, 1, work.get(), lwork, rwork.get(), iwork.get(), ifail.get(), &info );
146 
147  const size_t num( numeric_cast<size_t>( m ) );
148 
149  BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for eigenvalue computation" );
150  BLAZE_INTERNAL_ASSERT( num <= (~w).size(), "Invalid number of eigenvalues detected" );
151 
152  if( info > 0 ) {
153  BLAZE_THROW_LAPACK_ERROR( "Eigenvalue computation failed" );
154  }
155 
156  return num;
157 }
159 //*************************************************************************************************
160 
161 
162 //*************************************************************************************************
218 template< typename MT // Type of the matrix A
219  , bool SO // Storage order of the matrix A
220  , typename VT // Type of the vector w
221  , bool TF > // Transpose flag of the vector w
222 inline size_t heevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo )
223 {
230 
236 
237  using CT = ElementType_t<MT>;
238  using BT = UnderlyingElement_t<CT>;
239 
240  const size_t N( (~A).rows() );
241 
242  if( !isSquare( ~A ) ) {
243  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
244  }
245 
246  if( uplo != 'L' && uplo != 'U' ) {
247  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
248  }
249 
250  resize( ~w, N, false );
251 
252  if( N == 0UL ) {
253  return 0;
254  }
255 
256  return heevx_backend( ~A, ~w, uplo, 'A', BT(), BT(), 0, 0 );
257 }
258 //*************************************************************************************************
259 
260 
261 //*************************************************************************************************
347 template< typename MT // Type of the matrix A
348  , bool SO // Storage order of the matrix A
349  , typename VT // Type of the vector w
350  , bool TF // Transpose flag of the vector w
351  , typename ST > // Type of the scalar boundary values
352 inline size_t heevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo, ST low, ST upp )
353 {
360 
366 
367  if( !isSquare( ~A ) ) {
368  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
369  }
370 
371  if( IsFloatingPoint_v<ST> && low >= upp ) {
372  BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
373  }
374 
375  if( !IsFloatingPoint_v<ST> && low > upp ) {
376  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
377  }
378 
379  const size_t N( (~A).rows() );
380  const size_t num( IsFloatingPoint_v<ST> ? N : size_t( upp - low ) + 1UL );
381 
382  if( !IsFloatingPoint_v<ST> && num > N ) {
383  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
384  }
385 
386  if( uplo != 'L' && uplo != 'U' ) {
387  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
388  }
389 
390  resize( ~w, num, false );
391 
392  if( N == 0UL ) {
393  return 0;
394  }
395 
396  const char range( IsFloatingPoint_v<ST> ? 'V' : 'I' );
397  const ST vl ( IsFloatingPoint_v<ST> ? low : ST() );
398  const ST vu ( IsFloatingPoint_v<ST> ? upp : ST() );
399  const int il ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<int>( low ) );
400  const int iu ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<int>( upp ) );
401 
402  return heevx_backend( ~A, ~w, uplo, range, vl, vu, il, iu );
403 }
404 //*************************************************************************************************
405 
406 
407 //*************************************************************************************************
431 template< typename MT1 // Type of the matrix A
432  , bool SO1 // Storage order of the matrix A
433  , typename VT // Type of the vector w
434  , bool TF // Transpose flag of the vector w
435  , typename MT2 // Type of the matrix Z
436  , bool SO2 // Storage order of the matrix Z
437  , typename ST > // Type of the scalar boundary values
438 inline size_t heevx_backend( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
439  DenseMatrix<MT2,SO2>& Z, char uplo, char range,
440  ST vl, ST vu, int il, int iu )
441 {
442  BLAZE_INTERNAL_ASSERT( isSquare( ~A ), "Invalid non-square matrix detected" );
443  BLAZE_INTERNAL_ASSERT( range != 'A' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
444  BLAZE_INTERNAL_ASSERT( range != 'V' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
445  BLAZE_INTERNAL_ASSERT( range != 'I' || (~w).size() == size_t( iu-il+1 ), "Invalid vector dimension detected" );
446  BLAZE_INTERNAL_ASSERT( SO2 || (~Z).rows() == (~w).size(), "Invalid matrix dimension detected" );
447  BLAZE_INTERNAL_ASSERT( SO2 || (~Z).columns() == (~A).rows(), "Invalid matrix dimension detected" );
448  BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).rows() == (~A).rows(), "Invalid matrix dimension detected" );
449  BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).columns() == (~w).size(), "Invalid matrix dimension detected" );
450 
451  using CT = ElementType_t<MT1>;
452  using BT = UnderlyingElement_t<CT>;
453 
456 
457  int n ( numeric_cast<int>( (~A).rows() ) );
458  int lda ( numeric_cast<int>( (~A).spacing() ) );
459  int m ( 0 );
460  int ldz ( numeric_cast<int>( (~Z).spacing() ) );
461  int info( 0 );
462 
463  int lwork( 12*n + 2 );
464  const std::unique_ptr<CT[]> work ( new CT[lwork] );
465  const std::unique_ptr<BT[]> rwork( new BT[7*n] );
466  const std::unique_ptr<int[]> iwork( new int[5*n] );
467  const std::unique_ptr<int[]> ifail( new int[n] );
468 
469  heevx( 'N', range, uplo, n, (~A).data(), lda, vl, vu, il, iu, BT(0), &m, (~w).data(),
470  (~Z).data(), ldz, work.get(), lwork, rwork.get(), iwork.get(), ifail.get(), &info );
471 
472  const size_t num( numeric_cast<size_t>( m ) );
473 
474  BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for eigenvalue computation" );
475  BLAZE_INTERNAL_ASSERT( num <= (~w).size(), "Invalid number of eigenvalues detected" );
476 
477  if( info > 0 ) {
478  BLAZE_THROW_LAPACK_ERROR( "Eigenvalue computation failed" );
479  }
480 
481  return num;
482 }
484 //*************************************************************************************************
485 
486 
487 //*************************************************************************************************
550 template< typename MT1 // Type of the matrix A
551  , bool SO1 // Storage order of the matrix A
552  , typename VT // Type of the vector w
553  , bool TF // Transpose flag of the vector w
554  , typename MT2 // Type of the matrix Z
555  , bool SO2 > // Storage order of the matrix Z
557  DenseMatrix<MT2,SO2>& Z, char uplo )
558 {
565 
571 
578 
579  using CT = ElementType_t<MT1>;
580  using BT = UnderlyingElement_t<CT>;
581 
582  const size_t N( (~A).rows() );
583 
584  if( !isSquare( ~A ) ) {
585  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
586  }
587 
588  if( uplo != 'L' && uplo != 'U' ) {
589  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
590  }
591 
592  resize( ~w, N, false );
593  resize( ~Z, N, N, false );
594 
595  if( N == 0UL ) {
596  return 0;
597  }
598 
599  return heevx_backend( ~A, ~w, ~Z, uplo, 'A', BT(), BT(), 0, 0 );
600 }
601 //*************************************************************************************************
602 
603 
604 //*************************************************************************************************
700 template< typename MT1 // Type of the matrix A
701  , bool SO1 // Storage order of the matrix A
702  , typename VT // Type of the vector w
703  , bool TF // Transpose flag of the vector w
704  , typename MT2 // Type of the matrix Z
705  , bool SO2 // Storage order of the matrix Z
706  , typename ST > // Type of the scalar boundary values
708  DenseMatrix<MT2,SO2>& Z, char uplo, ST low, ST upp )
709 {
716 
722 
729 
730  if( !isSquare( ~A ) ) {
731  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
732  }
733 
734  if( IsFloatingPoint_v<ST> && low >= upp ) {
735  BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
736  }
737 
738  if( !IsFloatingPoint_v<ST> && low > upp ) {
739  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
740  }
741 
742  const size_t N( (~A).rows() );
743  const size_t num( IsFloatingPoint_v<ST> ? N : size_t( upp - low ) + 1UL );
744 
745  if( !IsFloatingPoint_v<ST> && num > N ) {
746  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
747  }
748 
749  if( uplo != 'L' && uplo != 'U' ) {
750  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
751  }
752 
753  resize( ~w, num, false );
754  resize( ~Z, ( IsRowMajorMatrix_v<MT2> ? num : N ),
755  ( IsRowMajorMatrix_v<MT2> ? N : num ), false );
756 
757  if( N == 0UL ) {
758  return 0;
759  }
760 
761  const char range( IsFloatingPoint_v<ST> ? 'V' : 'I' );
762  const ST vl ( IsFloatingPoint_v<ST> ? low : ST() );
763  const ST vu ( IsFloatingPoint_v<ST> ? upp : ST() );
764  const int il ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<int>( low ) );
765  const int iu ( IsFloatingPoint_v<ST> ? 0 : numeric_cast<int>( upp ) );
766 
767  return heevx_backend( ~A, ~w, ~Z, uplo, range, vl, vu, il, iu );
768 }
769 //*************************************************************************************************
770 
771 } // namespace blaze
772 
773 #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
Constraint on the data type.
Header file for auxiliary alias declarations.
#define BLAZE_CONSTRAINT_MUST_HAVE_MUTABLE_DATA_ACCESS(T)
Constraint on the data type.In case the given data type T does not provide low-level data access to m...
Definition: MutableDataAccess.h:61
Header file for basic type definitions.
MT::ElementType * data(DenseMatrix< MT, SO > &dm) noexcept
Low-level data access to the dense matrix elements.
Definition: DenseMatrix.h:170
#define BLAZE_CONSTRAINT_MUST_NOT_BE_COMPUTATION_TYPE(T)
Constraint on the data type.In case the given data type T is a computational expression (i....
Definition: Computation.h:81
Constraint on the data type.
Header file for the DenseVector base class.
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
#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
size_t spacing(const DenseMatrix< MT, SO > &dm) noexcept
Returns the spacing between the beginning of two rows/columns.
Definition: DenseMatrix.h:253
Constraint on the data type.
void heevx(char jobz, char range, char uplo, int n, complex< float > *A, int lda, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex< float > *Z, int ldz, complex< float > *work, int lwork, float *rwork, int *iwork, int *ifail, int *info)
LAPACK kernel for computing the eigenvalues of the given dense Hermitian single precision complex col...
Definition: heevx.h:160
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the IsFloatingPoint type trait.
#define BLAZE_CONSTRAINT_MUST_BE_CONTIGUOUS_TYPE(T)
Constraint on the data type.In case the given data type T is not an array-like data type with contigu...
Definition: Contiguous.h:61
Header file for the DenseMatrix base class.
Base class for N-dimensional dense vectors.The DenseVector class is a base class for all arbitrarily ...
Definition: DenseVector.h:76
Header file for the exception macros of the math module.
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.
Header file for run time assertion macros.
constexpr size_t size(const Matrix< MT, SO > &matrix) noexcept
Returns the total number of elements of the matrix.
Definition: Matrix.h:530
#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
constexpr size_t rows(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of rows of the matrix.
Definition: Matrix.h:498
#define BLAZE_CONSTRAINT_MUST_BE_BUILTIN_TYPE(T)
Constraint on the data type.In case the given data type T is not a built-in data type,...
Definition: Builtin.h:60
Header file for the CLAPACK heevx wrapper functions.
#define BLAZE_CONSTRAINT_MUST_BE_COMPLEX_TYPE(T)
Constraint on the data type.This compile time constraint checks that the given data type T is a compl...
Definition: Complex.h:62
Header file for the IsRowMajorMatrix type trait.
#define BLAZE_THROW_LAPACK_ERROR(MESSAGE)
Macro for the emission of an exception on detection of a LAPACK error.This macro encapsulates the def...
Definition: Exception.h:146
typename UnderlyingElement< T >::Type UnderlyingElement_t
Auxiliary alias declaration for the UnderlyingElement type trait.The UnderlyingElement_t alias declar...
Definition: UnderlyingElement.h:119
bool isSquare(const Matrix< MT, SO > &matrix) noexcept
Checks if the given matrix is a square matrix.
Definition: Matrix.h:951
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression,...
Definition: Assert.h:101
Constraint on the data type.