Reference documentation for deal.II version GIT ca9e7e8105 2023-03-24 14:15:03+00:00
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tensor.cc
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2 //
3 // Copyright (C) 2005 - 2022 by the deal.II authors
4 //
5 // This file is part of the deal.II library.
6 //
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8 // it, and/or modify it under the terms of the GNU Lesser General
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10 // version 2.1 of the License, or (at your option) any later version.
11 // The full text of the license can be found in the file LICENSE.md at
12 // the top level directory of deal.II.
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15 
17 #include <deal.II/base/tensor.h>
18 
19 #include <deal.II/lac/exceptions.h>
21 
22 #include <array>
23 
25 
26 namespace
27 {
28  template <int dim, typename Number>
29  void
30  calculate_svd_in_place(Tensor<2, dim, Number> &A_in_VT_out,
32  {
33  // inputs: A
34  // outputs: V^T, U
35  // SVD: A = U S V^T
36  // Since Tensor stores data in row major order and lapack expects column
37  // major ordering, we take the SVD of A^T by running the gesvd command.
38  // The results (V^T)^T and U^T are provided in column major that we use
39  // as row major results V^T and U.
40  // It essentially computs A^T = (V^T)^T S U^T and gives us V^T and U.
41  // This trick gives what we originally wanted (A = U S V^T) but the order
42  // of U and V^T is reversed.
43  std::array<Number, dim> S;
44  const types::blas_int N = dim;
45  // lwork must be >= max(1, 3*min(m,n)+max(m,n), 5*min(m,n))
46  const types::blas_int lwork = 5 * dim;
47  std::array<Number, lwork> work;
48  types::blas_int info;
49  constexpr std::size_t size =
51  std::array<Number, size> A_array;
52  A_in_VT_out.unroll(A_array.begin(), A_array.end());
53  std::array<Number, size> U_array;
54  U.unroll(U_array.begin(), U_array.end());
55  gesvd(&LAPACKSupport::O, // replace VT in place
57  &N,
58  &N,
59  A_array.data(),
60  &N,
61  S.data(),
62  A_array.data(),
63  &N,
64  U_array.data(),
65  &N,
66  work.data(),
67  &lwork,
68  &info);
69  Assert(info == 0, LAPACKSupport::ExcErrorCode("gesvd", info));
70  Assert(S.back() / S.front() > 1.e-10, LACExceptions::ExcSingular());
71 
72  A_in_VT_out =
73  Tensor<2, dim, Number>(make_array_view(A_array.begin(), A_array.end()));
74  U = Tensor<2, dim, Number>(make_array_view(U_array.begin(), U_array.end()));
75  }
76 } // namespace
77 
78 
79 
80 template <int dim, typename Number>
83 {
85  calculate_svd_in_place(VT, U);
86  return U * VT;
87 }
88 
89 
90 
91 template Tensor<2, 1, float>
93 template Tensor<2, 2, float>
95 template Tensor<2, 3, float>
97 template Tensor<2, 1, double>
99 template Tensor<2, 2, double>
101 template Tensor<2, 3, double>
103 
ArrayView< typename std::remove_reference< typename std::iterator_traits< Iterator >::reference >::type, MemorySpaceType > make_array_view(const Iterator begin, const Iterator end)
Definition: array_view.h:704
void unroll(Vector< OtherNumber > &result) const
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:474
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:475
static ::ExceptionBase & ExcErrorCode(std::string arg1, types::blas_int arg2)
#define Assert(cond, exc)
Definition: exceptions.h:1586
static ::ExceptionBase & ExcSingular()
void gesvd(const char *, const char *, const ::types::blas_int *, const ::types::blas_int *, number1 *, const ::types::blas_int *, number2 *, number3 *, const ::types::blas_int *, number4 *, const ::types::blas_int *, number5 *, const ::types::blas_int *, ::types::blas_int *)
static const char U
static const char A
static const char N
static const char O
int blas_int
Tensor< 2, dim, Number > project_onto_orthogonal_tensors(const Tensor< 2, dim, Number > &A)
Definition: tensor.cc:82