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>
49 #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 inline 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 inline 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 inline 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 inline 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_<MT>;
128  using BT = UnderlyingElement_<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 {
229 
234 
235  using CT = ElementType_<MT>;
236  using BT = UnderlyingElement_<CT>;
237 
238  const size_t N( (~A).rows() );
239 
240  if( !isSquare( ~A ) ) {
241  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
242  }
243 
244  if( uplo != 'L' && uplo != 'U' ) {
245  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
246  }
247 
248  resize( ~w, N, false );
249 
250  if( N == 0UL ) {
251  return 0;
252  }
253 
254  return heevx_backend( ~A, ~w, uplo, 'A', BT(), BT(), 0, 0 );
255 }
256 //*************************************************************************************************
257 
258 
259 //*************************************************************************************************
345 template< typename MT // Type of the matrix A
346  , bool SO // Storage order of the matrix A
347  , typename VT // Type of the vector w
348  , bool TF // Transpose flag of the vector w
349  , typename ST > // Type of the scalar boundary values
350 inline size_t heevx( DenseMatrix<MT,SO>& A, DenseVector<VT,TF>& w, char uplo, ST low, ST upp )
351 {
357 
362 
363  if( !isSquare( ~A ) ) {
364  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
365  }
366 
367  if( IsFloatingPoint<ST>::value && low >= upp ) {
368  BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
369  }
370 
371  if( !IsFloatingPoint<ST>::value && low > upp ) {
372  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
373  }
374 
375  const size_t N( (~A).rows() );
376  const size_t num( IsFloatingPoint<ST>::value ? N : size_t( upp - low ) + 1UL );
377 
378  if( !IsFloatingPoint<ST>::value && num > N ) {
379  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
380  }
381 
382  if( uplo != 'L' && uplo != 'U' ) {
383  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
384  }
385 
386  resize( ~w, num, false );
387 
388  if( N == 0UL ) {
389  return 0;
390  }
391 
392  const char range( IsFloatingPoint<ST>::value ? 'V' : 'I' );
393  const ST vl ( IsFloatingPoint<ST>::value ? low : ST() );
394  const ST vu ( IsFloatingPoint<ST>::value ? upp : ST() );
395  const int il ( IsFloatingPoint<ST>::value ? 0 : numeric_cast<int>( low ) );
396  const int iu ( IsFloatingPoint<ST>::value ? 0 : numeric_cast<int>( upp ) );
397 
398  return heevx_backend( ~A, ~w, uplo, range, vl, vu, il, iu );
399 }
400 //*************************************************************************************************
401 
402 
403 //*************************************************************************************************
427 template< typename MT1 // Type of the matrix A
428  , bool SO1 // Storage order of the matrix A
429  , typename VT // Type of the vector w
430  , bool TF // Transpose flag of the vector w
431  , typename MT2 // Type of the matrix Z
432  , bool SO2 // Storage order of the matrix Z
433  , typename ST > // Type of the scalar boundary values
434 inline size_t heevx_backend( DenseMatrix<MT1,SO1>& A, DenseVector<VT,TF>& w,
435  DenseMatrix<MT2,SO2>& Z, char uplo, char range,
436  ST vl, ST vu, int il, int iu )
437 {
438  BLAZE_INTERNAL_ASSERT( isSquare( ~A ), "Invalid non-square matrix detected" );
439  BLAZE_INTERNAL_ASSERT( range != 'A' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
440  BLAZE_INTERNAL_ASSERT( range != 'V' || (~w).size() == (~A).rows(), "Invalid vector dimension detected" );
441  BLAZE_INTERNAL_ASSERT( range != 'I' || (~w).size() == size_t( iu-il+1 ), "Invalid vector dimension detected" );
442  BLAZE_INTERNAL_ASSERT( SO2 || (~Z).rows() == (~w).size(), "Invalid matrix dimension detected" );
443  BLAZE_INTERNAL_ASSERT( SO2 || (~Z).columns() == (~A).rows(), "Invalid matrix dimension detected" );
444  BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).rows() == (~A).rows(), "Invalid matrix dimension detected" );
445  BLAZE_INTERNAL_ASSERT( !SO2 || (~Z).columns() == (~w).size(), "Invalid matrix dimension detected" );
446 
447  using CT = ElementType_<MT1>;
448  using BT = UnderlyingElement_<CT>;
449 
452 
453  int n ( numeric_cast<int>( (~A).rows() ) );
454  int lda ( numeric_cast<int>( (~A).spacing() ) );
455  int m ( 0 );
456  int ldz ( numeric_cast<int>( (~Z).spacing() ) );
457  int info( 0 );
458 
459  int lwork( 12*n + 2 );
460  const std::unique_ptr<CT[]> work ( new CT[lwork] );
461  const std::unique_ptr<BT[]> rwork( new BT[7*n] );
462  const std::unique_ptr<int[]> iwork( new int[5*n] );
463  const std::unique_ptr<int[]> ifail( new int[n] );
464 
465  heevx( 'N', range, uplo, n, (~A).data(), lda, vl, vu, il, iu, BT(0), &m, (~w).data(),
466  (~Z).data(), ldz, work.get(), lwork, rwork.get(), iwork.get(), ifail.get(), &info );
467 
468  const size_t num( numeric_cast<size_t>( m ) );
469 
470  BLAZE_INTERNAL_ASSERT( info >= 0, "Invalid argument for eigenvalue computation" );
471  BLAZE_INTERNAL_ASSERT( num <= (~w).size(), "Invalid number of eigenvalues detected" );
472 
473  if( info > 0 ) {
474  BLAZE_THROW_LAPACK_ERROR( "Eigenvalue computation failed" );
475  }
476 
477  return num;
478 }
480 //*************************************************************************************************
481 
482 
483 //*************************************************************************************************
546 template< typename MT1 // Type of the matrix A
547  , bool SO1 // Storage order of the matrix A
548  , typename VT // Type of the vector w
549  , bool TF // Transpose flag of the vector w
550  , typename MT2 // Type of the matrix Z
551  , bool SO2 > // Storage order of the matrix Z
553  DenseMatrix<MT2,SO2>& Z, char uplo )
554 {
560 
565 
571 
572  using CT = ElementType_<MT1>;
573  using BT = UnderlyingElement_<CT>;
574 
575  const size_t N( (~A).rows() );
576 
577  if( !isSquare( ~A ) ) {
578  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
579  }
580 
581  if( uplo != 'L' && uplo != 'U' ) {
582  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
583  }
584 
585  resize( ~w, N, false );
586  resize( ~Z, N, N, false );
587 
588  if( N == 0UL ) {
589  return 0;
590  }
591 
592  return heevx_backend( ~A, ~w, ~Z, uplo, 'A', BT(), BT(), 0, 0 );
593 }
594 //*************************************************************************************************
595 
596 
597 //*************************************************************************************************
693 template< typename MT1 // Type of the matrix A
694  , bool SO1 // Storage order of the matrix A
695  , typename VT // Type of the vector w
696  , bool TF // Transpose flag of the vector w
697  , typename MT2 // Type of the matrix Z
698  , bool SO2 // Storage order of the matrix Z
699  , typename ST > // Type of the scalar boundary values
701  DenseMatrix<MT2,SO2>& Z, char uplo, ST low, ST upp )
702 {
708 
713 
719 
720  if( !isSquare( ~A ) ) {
721  BLAZE_THROW_INVALID_ARGUMENT( "Invalid non-square matrix provided" );
722  }
723 
724  if( IsFloatingPoint<ST>::value && low >= upp ) {
725  BLAZE_THROW_INVALID_ARGUMENT( "Invalid value range provided" );
726  }
727 
728  if( !IsFloatingPoint<ST>::value && low > upp ) {
729  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
730  }
731 
732  const size_t N( (~A).rows() );
733  const size_t num( IsFloatingPoint<ST>::value ? N : size_t( upp - low ) + 1UL );
734 
735  if( !IsFloatingPoint<ST>::value && num > N ) {
736  BLAZE_THROW_INVALID_ARGUMENT( "Invalid index range provided" );
737  }
738 
739  if( uplo != 'L' && uplo != 'U' ) {
740  BLAZE_THROW_INVALID_ARGUMENT( "Invalid uplo argument provided" );
741  }
742 
743  resize( ~w, num, false );
744  resize( ~Z, ( IsRowMajorMatrix<MT2>::value ? num : N ),
745  ( IsRowMajorMatrix<MT2>::value ? N : num ), false );
746 
747  if( N == 0UL ) {
748  return 0;
749  }
750 
751  const char range( IsFloatingPoint<ST>::value ? 'V' : 'I' );
752  const ST vl ( IsFloatingPoint<ST>::value ? low : ST() );
753  const ST vu ( IsFloatingPoint<ST>::value ? upp : ST() );
754  const int il ( IsFloatingPoint<ST>::value ? 0 : numeric_cast<int>( low ) );
755  const int iu ( IsFloatingPoint<ST>::value ? 0 : numeric_cast<int>( upp ) );
756 
757  return heevx_backend( ~A, ~w, ~Z, uplo, range, vl, vu, il, iu );
758 }
759 //*************************************************************************************************
760 
761 } // namespace blaze
762 
763 #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.
BLAZE_ALWAYS_INLINE size_t size(const Vector< VT, TF > &vector) noexcept
Returns the current size/dimension of the vector.
Definition: Vector.h:265
#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.
Cast operators for numeric types.
#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
BLAZE_ALWAYS_INLINE size_t spacing(const DenseMatrix< MT, SO > &dm) noexcept
Returns the spacing between the beginning of two rows/columns.
Definition: DenseMatrix.h:252
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:151
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Compile time check for row-major matrix types.This type trait tests whether or not the given template...
Definition: IsRowMajorMatrix.h:110
Header file for the IsFloatingPoint type trait.
Header file for the DenseMatrix base class.
typename UnderlyingElement< T >::Type UnderlyingElement_
Auxiliary alias declaration for the UnderlyingElement type trait.The UnderlyingElement_ alias declara...
Definition: UnderlyingElement.h:132
typename T::ElementType ElementType_
Alias declaration for nested ElementType type definitions.The ElementType_ alias declaration provides...
Definition: Aliases.h:163
Base class for N-dimensional dense vectors.The DenseVector class is a base class for all arbitrarily ...
Definition: DenseVector.h:76
BLAZE_ALWAYS_INLINE size_t columns(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of columns of the matrix.
Definition: Matrix.h:506
Header file for the exception macros of the math module.
Compile time check for floating point data types.This type trait tests whether or not the given templ...
Definition: IsFloatingPoint.h:75
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:714
Constraint on the data type.
Header file for run time assertion macros.
#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
#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, a compilation error is created.
Definition: Builtin.h:60
BLAZE_ALWAYS_INLINE size_t rows(const Matrix< MT, SO > &matrix) noexcept
Returns the current number of rows of the matrix.
Definition: Matrix.h:490
Header file for the CLAPACK heevx wrapper functions.
BLAZE_ALWAYS_INLINE MT::ElementType * data(DenseMatrix< MT, SO > &dm) noexcept
Low-level data access to the dense matrix elements.
Definition: DenseMatrix.h:169
#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
BLAZE_ALWAYS_INLINE bool isSquare(const Matrix< MT, SO > &matrix) noexcept
Checks if the given matrix is a square matrix.
Definition: Matrix.h:908
Header file for the IsResizable type trait.
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression, the program execution is terminated. The BLAZE_INTERNAL_ASSERT macro can be disabled by setting the BLAZE_USER_ASSERTION flag to zero or by defining NDEBUG during the compilation.
Definition: Assert.h:101
Constraint on the data type.