ground/gcs/src/libs/eigen/test/adjoint.cpp

   1 // This file is part of Eigen, a lightweight C++ template library
   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
  14 template<bool IsInteger> struct adjoint_specific;
  15
  16 template<> struct adjoint_specific<true> {
  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
  27 template<> struct adjoint_specific<false> {
  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
  56 template<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
  84   VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(),    m1);
  85   VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(),    m1);
  86
  87   // check multiplicative behavior
  88   VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(),           m2.adjoint() * m1);
  89   VERIFY_IS_APPROX((s1 * m1).adjoint(),                     numext::conj(s1) * m1.adjoint());
  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)));
 103   VERIFY_IS_APPROX(m1.adjoint()(c,r), 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
 112   // check inplace adjoint
 113   m3 = m1;
 114   m3.adjointInPlace();
 115   VERIFY_IS_APPROX(m3,m1.adjoint());
 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
 126 void test_adjoint()
 127 {
 128   for(int i = 0; i < g_repeat; i++) {
 129     CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) );
 130     CALL_SUBTEST_2( adjoint(Matrix3d()) );
 131     CALL_SUBTEST_3( adjoint(Matrix4f()) );
 132     CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2), internal::random<int>(1,EIGEN_TEST_MAX_SIZE/2))) );
 133     CALL_SUBTEST_5( adjoint(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 134     CALL_SUBTEST_6( adjoint(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 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());
 146     VERIFY_RAISES_ASSERT(a = a.adjoint());
 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;
 154     a.transpose() = a.adjoint();
 155     a.transpose() += a.adjoint();
 156     a.transpose() += a.adjoint() + b;
 157   }
 158 #endif
 159 }
 160