```/* <![CDATA[ */
2// for linear algebra.
3//
4// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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_NO_STATIC_ASSERT
11
12#include "main.h"
13
15
17  template<typename Vec, typename Mat, typename Scalar>
18  static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
19    VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3),     numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), 0));
20    VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2),       s1*v3.dot(v1)+s2*v3.dot(v2), 0));
21
22    // check compatibility of dot and adjoint
23    VERIFY(test_isApproxWithRef(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), 0));
24  }
25};
26
28  template<typename Vec, typename Mat, typename Scalar>
29  static void run(const Vec& v1, const Vec& v2, Vec& v3, const Mat& square, Scalar s1, Scalar s2) {
30    typedef typename NumTraits<Scalar>::Real RealScalar;
31    using std::abs;
32
33    RealScalar ref = NumTraits<Scalar>::IsInteger ? RealScalar(0) : (std::max)((s1 * v1 + s2 * v2).norm(),v3.norm());
34    VERIFY(test_isApproxWithRef((s1 * v1 + s2 * v2).dot(v3),     numext::conj(s1) * v1.dot(v3) + numext::conj(s2) * v2.dot(v3), ref));
35    VERIFY(test_isApproxWithRef(v3.dot(s1 * v1 + s2 * v2),       s1*v3.dot(v1)+s2*v3.dot(v2), ref));
36
37    VERIFY_IS_APPROX(v1.squaredNorm(),                v1.norm() * v1.norm());
38    // check normalized() and normalize()
39    VERIFY_IS_APPROX(v1, v1.norm() * v1.normalized());
40    v3 = v1;
41    v3.normalize();
42    VERIFY_IS_APPROX(v1, v1.norm() * v3);
43    VERIFY_IS_APPROX(v3, v1.normalized());
44    VERIFY_IS_APPROX(v3.norm(), RealScalar(1));
45
46    // check compatibility of dot and adjoint
47    ref = NumTraits<Scalar>::IsInteger ? 0 : (std::max)((std::max)(v1.norm(),v2.norm()),(std::max)((square * v2).norm(),(square.adjoint() * v1).norm()));
48    VERIFY(internal::isMuchSmallerThan(abs(v1.dot(square * v2) - (square.adjoint() * v1).dot(v2)), ref, test_precision<Scalar>()));
49
50    // check that Random().normalized() works: tricky as the random xpr must be evaluated by
51    // normalized() in order to produce a consistent result.
52    VERIFY_IS_APPROX(Vec::Random(v1.size()).normalized().norm(), RealScalar(1));
53  }
54};
55
56template<typename MatrixType> void adjoint(const MatrixType& m)
57{
58  /* this test covers the following files:
59     Transpose.h Conjugate.h Dot.h
60  */
61  using std::abs;
62  typedef typename MatrixType::Index Index;
63  typedef typename MatrixType::Scalar Scalar;
64  typedef typename NumTraits<Scalar>::Real RealScalar;
65  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
66  typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType;
67
68  Index rows = m.rows();
69  Index cols = m.cols();
70
71  MatrixType m1 = MatrixType::Random(rows, cols),
72             m2 = MatrixType::Random(rows, cols),
73             m3(rows, cols),
74             square = SquareMatrixType::Random(rows, rows);
75  VectorType v1 = VectorType::Random(rows),
76             v2 = VectorType::Random(rows),
77             v3 = VectorType::Random(rows),
78             vzero = VectorType::Zero(rows);
79
80  Scalar s1 = internal::random<Scalar>(),
81         s2 = internal::random<Scalar>();
82
83  // check basic compatibility of adjoint, transpose, conjugate
86
87  // check multiplicative behavior
90
91  // check basic properties of dot, squaredNorm
92  VERIFY_IS_APPROX(numext::conj(v1.dot(v2)),               v2.dot(v1));
93  VERIFY_IS_APPROX(numext::real(v1.dot(v1)),               v1.squaredNorm());
94
95  adjoint_specific<NumTraits<Scalar>::IsInteger>::run(v1, v2, v3, square, s1, s2);
96
97  VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)),  static_cast<RealScalar>(1));
98
99  // like in testBasicStuff, test operator() to check const-qualification
100  Index r = internal::random<Index>(0, rows-1),
101      c = internal::random<Index>(0, cols-1);
102  VERIFY_IS_APPROX(m1.conjugate()(r,c), numext::conj(m1(r,c)));
104
105  // check inplace transpose
106  m3 = m1;
107  m3.transposeInPlace();
108  VERIFY_IS_APPROX(m3,m1.transpose());
109  m3.transposeInPlace();
110  VERIFY_IS_APPROX(m3,m1);
111
113  m3 = m1;
116  m3.transposeInPlace();
117  VERIFY_IS_APPROX(m3,m1.conjugate());
118
119  // check mixed dot product
120  typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
121  RealVectorType rv1 = RealVectorType::Random(rows);
122  VERIFY_IS_APPROX(v1.dot(rv1.template cast<Scalar>()), v1.dot(rv1));
123  VERIFY_IS_APPROX(rv1.template cast<Scalar>().dot(v1), rv1.dot(v1));
124}
125
127{
128  for(int i = 0; i < g_repeat; i++) {
129    CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) );
135  }
136  // test a large static matrix only once
137  CALL_SUBTEST_7( adjoint(Matrix<float, 100, 100>()) );
138
139#ifdef EIGEN_TEST_PART_4
140  {
141    MatrixXcf a(10,10), b(10,10);
142    VERIFY_RAISES_ASSERT(a = a.transpose());
143    VERIFY_RAISES_ASSERT(a = a.transpose() + b);
144    VERIFY_RAISES_ASSERT(a = b + a.transpose());
145    VERIFY_RAISES_ASSERT(a = a.conjugate().transpose());
147    VERIFY_RAISES_ASSERT(a = a.adjoint() + b);
148    VERIFY_RAISES_ASSERT(a = b + a.adjoint());
149
150    // no assertion should be triggered for these cases:
151    a.transpose() = a.transpose();
152    a.transpose() += a.transpose();
153    a.transpose() += a.transpose() + b;