real_qz.cpp
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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9 
10 #define EIGEN_RUNTIME_NO_MALLOC
11 #include "main.h"
12 #include <limits>
13 #include <Eigen/Eigenvalues>
14 
15 template<typename MatrixType> void real_qz(const MatrixType& m)
16 {
17  /* this test covers the following files:
18  RealQZ.h
19  */
20  using std::abs;
21  typedef typename MatrixType::Scalar Scalar;
22 
23  Index dim = m.cols();
24 
25  MatrixType A = MatrixType::Random(dim,dim),
26  B = MatrixType::Random(dim,dim);
27 
28 
29  // Regression test for bug 985: Randomly set rows or columns to zero
30  Index k=internal::random<Index>(0, dim-1);
31  switch(internal::random<int>(0,10)) {
32  case 0:
33  A.row(k).setZero(); break;
34  case 1:
35  A.col(k).setZero(); break;
36  case 2:
37  B.row(k).setZero(); break;
38  case 3:
39  B.col(k).setZero(); break;
40  default:
41  break;
42  }
43 
45  // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
46  //Eigen::internal::set_is_malloc_allowed(false);
47  qz.compute(A,B);
48  //Eigen::internal::set_is_malloc_allowed(true);
49 
51  // check for zeros
52  bool all_zeros = true;
53  for (Index i=0; i<A.cols(); i++)
54  for (Index j=0; j<i; j++) {
55  if (abs(qz.matrixT()(i,j))!=Scalar(0.0))
56  {
57  std::cerr << "Error: T(" << i << "," << j << ") = " << qz.matrixT()(i,j) << std::endl;
58  all_zeros = false;
59  }
60  if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))
61  {
62  std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << std::endl;
63  all_zeros = false;
64  }
65  if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
66  {
67  std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << " && S(" << i-1 << "," << j-1 << ") = " << qz.matrixS()(i-1,j-1) << std::endl;
68  all_zeros = false;
69  }
70  }
71  VERIFY_IS_EQUAL(all_zeros, true);
72  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
73  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
74  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
75  VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
76 }
77 
79 {
80  int s = 0;
81  for(int i = 0; i < g_repeat; i++) {
82  CALL_SUBTEST_1( real_qz(Matrix4f()) );
83  s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
84  CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
85 
86  // some trivial but implementation-wise tricky cases
87  CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
88  CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
89  CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
90  CALL_SUBTEST_4( real_qz(Matrix2d()) );
91  }
92 
94 }
Matrix3f m
SCALAR Scalar
Definition: bench_gemm.cpp:33
void real_qz(const MatrixType &m)
Definition: real_qz.cpp:15
ComputationInfo info() const
Reports whether previous computation was successful.
Definition: RealQZ.h:166
const MatrixType & matrixT() const
Returns matrix S in the QZ decomposition.
Definition: RealQZ.h:148
MatrixXf MatrixType
Matrix< SCALARA, Dynamic, Dynamic > A
Definition: bench_gemm.cpp:35
Matrix< SCALARB, Dynamic, Dynamic > B
Definition: bench_gemm.cpp:36
#define VERIFY_IS_APPROX(a, b)
void test_real_qz()
Definition: real_qz.cpp:78
#define VERIFY_IS_EQUAL(a, b)
Definition: main.h:331
static int g_repeat
Definition: main.h:144
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
RealQZ< MatrixXf > qz(4)
const MatrixType & matrixS() const
Returns matrix S in the QZ decomposition.
Definition: RealQZ.h:139
RealScalar s
const MatrixType & matrixZ() const
Returns matrix Z in the QZ decomposition.
Definition: RealQZ.h:129
const mpreal dim(const mpreal &a, const mpreal &b, mp_rnd_t r=mpreal::get_default_rnd())
Definition: mpreal.h:2201
#define TEST_SET_BUT_UNUSED_VARIABLE(X)
Definition: main.h:91
#define EIGEN_TEST_MAX_SIZE
RealQZ & compute(const MatrixType &A, const MatrixType &B, bool computeQZ=true)
Computes QZ decomposition of given matrix.
Definition: RealQZ.h:556
const MatrixType & matrixQ() const
Returns matrix Q in the QZ decomposition.
Definition: RealQZ.h:119
The matrix class, also used for vectors and row-vectors.
#define abs(x)
Definition: datatypes.h:17
std::ptrdiff_t j


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autogenerated on Sat May 8 2021 02:43:48