Reference documentation for deal.II version 9.3.3
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tensor.cc
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2//
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15
16#include <deal.II/base/tensor.h>
17
20
22
23namespace
24{
25 template <int dim, typename Number>
26 void calculate_svd_in_place(Tensor<2, dim, Number> &A_in_VT_out,
28 {
29 // inputs: A
30 // outputs: V^T, U
31 // SVD: A = U S V^T
32 // Since Tensor stores data in row major order and lapack expects column
33 // major ordering, we take the SVD of A^T by running the gesvd command.
34 // The results (V^T)^T and U^T are provided in column major that we use
35 // as row major results V^T and U.
36 // It essentially computs A^T = (V^T)^T S U^T and gives us V^T and U.
37 // This trick gives what we originally wanted (A = U S V^T) but the order
38 // of U and V^T is reversed.
39 std::array<Number, dim> S;
40 const types::blas_int N = dim;
41 // lwork must be >= max(1, 3*min(m,n)+max(m,n), 5*min(m,n))
42 const types::blas_int lwork = 5 * dim;
43 std::array<Number, lwork> work;
44 types::blas_int info;
45 gesvd(&LAPACKSupport::O, // replace VT in place
47 &N,
48 &N,
49 A_in_VT_out.begin_raw(),
50 &N,
51 S.data(),
52 A_in_VT_out.begin_raw(),
53 &N,
54 U.begin_raw(),
55 &N,
56 work.data(),
57 &lwork,
58 &info);
59 Assert(info == 0, LAPACKSupport::ExcErrorCode("gesvd", info));
60 Assert(S.back() / S.front() > 1.e-10, LACExceptions::ExcSingular());
61 }
62} // namespace
63
64
65
66template <int dim, typename Number>
69{
71 calculate_svd_in_place(VT, U);
72 return U * VT;
73}
74
75
76
89
Definition: tensor.h:472
Number * begin_raw()
Tensor< 2, dim, Number > project_onto_orthogonal_tensors(const Tensor< 2, dim, Number > &A)
#define DEAL_II_NAMESPACE_OPEN
Definition: config.h:402
#define DEAL_II_NAMESPACE_CLOSE
Definition: config.h:403
static ::ExceptionBase & ExcErrorCode(std::string arg1, types::blas_int arg2)
#define Assert(cond, exc)
Definition: exceptions.h:1465
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