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

   1 // This file is part of Eigen, a lightweight C++ template library
   2 // for linear algebra.
   3 //
   4 // Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
   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 #include "main.h"
  11
  12 template<typename MatrixType> void array_for_matrix(const MatrixType& m)
  13 {
  14   typedef typename MatrixType::Index Index;
  15   typedef typename MatrixType::Scalar Scalar;
  16   typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType;
  17   typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
  18
  19   Index rows = m.rows();
  20   Index cols = m.cols();
  21
  22   MatrixType m1 = MatrixType::Random(rows, cols),
  23              m2 = MatrixType::Random(rows, cols),
  24              m3(rows, cols);
  25
  26   ColVectorType cv1 = ColVectorType::Random(rows);
  27   RowVectorType rv1 = RowVectorType::Random(cols);
  28
  29   Scalar  s1 = internal::random<Scalar>(),
  30           s2 = internal::random<Scalar>();
  31
  32   // scalar addition
  33   VERIFY_IS_APPROX(m1.array() + s1, s1 + m1.array());
  34   VERIFY_IS_APPROX((m1.array() + s1).matrix(), MatrixType::Constant(rows,cols,s1) + m1);
  35   VERIFY_IS_APPROX(((m1*Scalar(2)).array() - s2).matrix(), (m1+m1) - MatrixType::Constant(rows,cols,s2) );
  36   m3 = m1;
  37   m3.array() += s2;
  38   VERIFY_IS_APPROX(m3, (m1.array() + s2).matrix());
  39   m3 = m1;
  40   m3.array() -= s1;
  41   VERIFY_IS_APPROX(m3, (m1.array() - s1).matrix());
  42
  43   // reductions
  44   VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum().sum() - m1.sum(), m1.squaredNorm());
  45   VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum().sum() - m1.sum(), m1.squaredNorm());
  46   VERIFY_IS_MUCH_SMALLER_THAN(m1.colwise().sum() + m2.colwise().sum() - (m1+m2).colwise().sum(), (m1+m2).squaredNorm());
  47   VERIFY_IS_MUCH_SMALLER_THAN(m1.rowwise().sum() - m2.rowwise().sum() - (m1-m2).rowwise().sum(), (m1-m2).squaredNorm());
  48   VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
  49
  50   // vector-wise ops
  51   m3 = m1;
  52   VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
  53   m3 = m1;
  54   VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
  55   m3 = m1;
  56   VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
  57   m3 = m1;
  58   VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
  59
  60   // empty objects
  61   VERIFY_IS_APPROX(m1.block(0,0,0,cols).colwise().sum(),  RowVectorType::Zero(cols));
  62   VERIFY_IS_APPROX(m1.block(0,0,rows,0).rowwise().prod(), ColVectorType::Ones(rows));
  63
  64   // verify the const accessors exist
  65   const Scalar& ref_m1 = m.matrix().array().coeffRef(0);
  66   const Scalar& ref_m2 = m.matrix().array().coeffRef(0,0);
  67   const Scalar& ref_a1 = m.array().matrix().coeffRef(0);
  68   const Scalar& ref_a2 = m.array().matrix().coeffRef(0,0);
  69   VERIFY(&ref_a1 == &ref_m1);
  70   VERIFY(&ref_a2 == &ref_m2);
  71
  72   // Check write accessors:
  73   m1.array().coeffRef(0,0) = 1;
  74   VERIFY_IS_APPROX(m1(0,0),Scalar(1));
  75   m1.array()(0,0) = 2;
  76   VERIFY_IS_APPROX(m1(0,0),Scalar(2));
  77   m1.array().matrix().coeffRef(0,0) = 3;
  78   VERIFY_IS_APPROX(m1(0,0),Scalar(3));
  79   m1.array().matrix()(0,0) = 4;
  80   VERIFY_IS_APPROX(m1(0,0),Scalar(4));
  81 }
  82
  83 template<typename MatrixType> void comparisons(const MatrixType& m)
  84 {
  85   using std::abs;
  86   typedef typename MatrixType::Index Index;
  87   typedef typename MatrixType::Scalar Scalar;
  88   typedef typename NumTraits<Scalar>::Real RealScalar;
  89
  90   Index rows = m.rows();
  91   Index cols = m.cols();
  92
  93   Index r = internal::random<Index>(0, rows-1),
  94         c = internal::random<Index>(0, cols-1);
  95
  96   MatrixType m1 = MatrixType::Random(rows, cols),
  97              m2 = MatrixType::Random(rows, cols),
  98              m3(rows, cols);
  99
 100   VERIFY(((m1.array() + Scalar(1)) > m1.array()).all());
 101   VERIFY(((m1.array() - Scalar(1)) < m1.array()).all());
 102   if (rows*cols>1)
 103   {
 104     m3 = m1;
 105     m3(r,c) += 1;
 106     VERIFY(! (m1.array() < m3.array()).all() );
 107     VERIFY(! (m1.array() > m3.array()).all() );
 108   }
 109
 110   // comparisons to scalar
 111   VERIFY( (m1.array() != (m1(r,c)+1) ).any() );
 112   VERIFY( (m1.array() > (m1(r,c)-1) ).any() );
 113   VERIFY( (m1.array() < (m1(r,c)+1) ).any() );
 114   VERIFY( (m1.array() == m1(r,c) ).any() );
 115   VERIFY( m1.cwiseEqual(m1(r,c)).any() );
 116
 117   // test Select
 118   VERIFY_IS_APPROX( (m1.array()<m2.array()).select(m1,m2), m1.cwiseMin(m2) );
 119   VERIFY_IS_APPROX( (m1.array()>m2.array()).select(m1,m2), m1.cwiseMax(m2) );
 120   Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
 121   for (int j=0; j<cols; ++j)
 122   for (int i=0; i<rows; ++i)
 123     m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
 124   VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())
 125                         .select(MatrixType::Zero(rows,cols),m1), m3);
 126   // shorter versions:
 127   VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())
 128                         .select(0,m1), m3);
 129   VERIFY_IS_APPROX( (m1.array().abs()>=MatrixType::Constant(rows,cols,mid).array())
 130                         .select(m1,0), m3);
 131   // even shorter version:
 132   VERIFY_IS_APPROX( (m1.array().abs()<mid).select(0,m1), m3);
 133
 134   // count
 135   VERIFY(((m1.array().abs()+1)>RealScalar(0.1)).count() == rows*cols);
 136
 137   // and/or
 138   VERIFY( ((m1.array()<RealScalar(0)).matrix() && (m1.array()>RealScalar(0)).matrix()).count() == 0);
 139   VERIFY( ((m1.array()<RealScalar(0)).matrix() || (m1.array()>=RealScalar(0)).matrix()).count() == rows*cols);
 140   RealScalar a = m1.cwiseAbs().mean();
 141   VERIFY( ((m1.array()<-a).matrix() || (m1.array()>a).matrix()).count() == (m1.cwiseAbs().array()>a).count());
 142
 143   typedef Matrix<typename MatrixType::Index, Dynamic, 1> VectorOfIndices;
 144
 145   // TODO allows colwise/rowwise for array
 146   VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().colwise().count(), VectorOfIndices::Constant(cols,rows).transpose());
 147   VERIFY_IS_APPROX(((m1.array().abs()+1)>RealScalar(0.1)).matrix().rowwise().count(), VectorOfIndices::Constant(rows, cols));
 148 }
 149
 150 template<typename VectorType> void lpNorm(const VectorType& v)
 151 {
 152   using std::sqrt;
 153   typedef typename VectorType::RealScalar RealScalar;
 154   VectorType u = VectorType::Random(v.size());
 155
 156   if(v.size()==0)
 157   {
 158     VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), RealScalar(0));
 159     VERIFY_IS_APPROX(u.template lpNorm<1>(), RealScalar(0));
 160     VERIFY_IS_APPROX(u.template lpNorm<2>(), RealScalar(0));
 161     VERIFY_IS_APPROX(u.template lpNorm<5>(), RealScalar(0));
 162   }
 163   else
 164   {
 165     VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
 166   }
 167
 168   VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());
 169   VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum()));
 170   VERIFY_IS_APPROX(numext::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());
 171 }
 172
 173 template<typename MatrixType> void cwise_min_max(const MatrixType& m)
 174 {
 175   typedef typename MatrixType::Index Index;
 176   typedef typename MatrixType::Scalar Scalar;
 177
 178   Index rows = m.rows();
 179   Index cols = m.cols();
 180
 181   MatrixType m1 = MatrixType::Random(rows, cols);
 182
 183   // min/max with array
 184   Scalar maxM1 = m1.maxCoeff();
 185   Scalar minM1 = m1.minCoeff();
 186
 187   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin(MatrixType::Constant(rows,cols, minM1)));
 188   VERIFY_IS_APPROX(m1, m1.cwiseMin(MatrixType::Constant(rows,cols, maxM1)));
 189
 190   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax(MatrixType::Constant(rows,cols, maxM1)));
 191   VERIFY_IS_APPROX(m1, m1.cwiseMax(MatrixType::Constant(rows,cols, minM1)));
 192
 193   // min/max with scalar input
 194   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1), m1.cwiseMin( minM1));
 195   VERIFY_IS_APPROX(m1, m1.cwiseMin(maxM1));
 196   VERIFY_IS_APPROX(-m1, (-m1).cwiseMin(-minM1));
 197   VERIFY_IS_APPROX(-m1.array(), ((-m1).array().min)( -minM1));
 198
 199   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax( maxM1));
 200   VERIFY_IS_APPROX(m1, m1.cwiseMax(minM1));
 201   VERIFY_IS_APPROX(-m1, (-m1).cwiseMax(-maxM1));
 202   VERIFY_IS_APPROX(-m1.array(), ((-m1).array().max)(-maxM1));
 203
 204   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1).array(), (m1.array().min)( minM1));
 205   VERIFY_IS_APPROX(m1.array(), (m1.array().min)( maxM1));
 206
 207   VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1).array(), (m1.array().max)( maxM1));
 208   VERIFY_IS_APPROX(m1.array(), (m1.array().max)( minM1));
 209
 210 }
 211
 212 template<typename MatrixTraits> void resize(const MatrixTraits& t)
 213 {
 214   typedef typename MatrixTraits::Index Index;
 215   typedef typename MatrixTraits::Scalar Scalar;
 216   typedef Matrix<Scalar,Dynamic,Dynamic> MatrixType;
 217   typedef Array<Scalar,Dynamic,Dynamic> Array2DType;
 218   typedef Matrix<Scalar,Dynamic,1> VectorType;
 219   typedef Array<Scalar,Dynamic,1> Array1DType;
 220
 221   Index rows = t.rows(), cols = t.cols();
 222
 223   MatrixType m(rows,cols);
 224   VectorType v(rows);
 225   Array2DType a2(rows,cols);
 226   Array1DType a1(rows);
 227
 228   m.array().resize(rows+1,cols+1);
 229   VERIFY(m.rows()==rows+1 && m.cols()==cols+1);
 230   a2.matrix().resize(rows+1,cols+1);
 231   VERIFY(a2.rows()==rows+1 && a2.cols()==cols+1);
 232   v.array().resize(cols);
 233   VERIFY(v.size()==cols);
 234   a1.matrix().resize(cols);
 235   VERIFY(a1.size()==cols);
 236 }
 237
 238 void regression_bug_654()
 239 {
 240   ArrayXf a = RowVectorXf(3);
 241   VectorXf v = Array<float,1,Dynamic>(3);
 242 }
 243
 244 void test_array_for_matrix()
 245 {
 246   for(int i = 0; i < g_repeat; i++) {
 247     CALL_SUBTEST_1( array_for_matrix(Matrix<float, 1, 1>()) );
 248     CALL_SUBTEST_2( array_for_matrix(Matrix2f()) );
 249     CALL_SUBTEST_3( array_for_matrix(Matrix4d()) );
 250     CALL_SUBTEST_4( array_for_matrix(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 251     CALL_SUBTEST_5( array_for_matrix(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 252     CALL_SUBTEST_6( array_for_matrix(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 253   }
 254   for(int i = 0; i < g_repeat; i++) {
 255     CALL_SUBTEST_1( comparisons(Matrix<float, 1, 1>()) );
 256     CALL_SUBTEST_2( comparisons(Matrix2f()) );
 257     CALL_SUBTEST_3( comparisons(Matrix4d()) );
 258     CALL_SUBTEST_5( comparisons(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 259     CALL_SUBTEST_6( comparisons(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 260   }
 261   for(int i = 0; i < g_repeat; i++) {
 262     CALL_SUBTEST_1( cwise_min_max(Matrix<float, 1, 1>()) );
 263     CALL_SUBTEST_2( cwise_min_max(Matrix2f()) );
 264     CALL_SUBTEST_3( cwise_min_max(Matrix4d()) );
 265     CALL_SUBTEST_5( cwise_min_max(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 266     CALL_SUBTEST_6( cwise_min_max(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 267   }
 268   for(int i = 0; i < g_repeat; i++) {
 269     CALL_SUBTEST_1( lpNorm(Matrix<float, 1, 1>()) );
 270     CALL_SUBTEST_2( lpNorm(Vector2f()) );
 271     CALL_SUBTEST_7( lpNorm(Vector3d()) );
 272     CALL_SUBTEST_8( lpNorm(Vector4f()) );
 273     CALL_SUBTEST_5( lpNorm(VectorXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 274     CALL_SUBTEST_4( lpNorm(VectorXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 275   }
 276   CALL_SUBTEST_5( lpNorm(VectorXf(0)) );
 277   CALL_SUBTEST_4( lpNorm(VectorXcf(0)) );
 278   for(int i = 0; i < g_repeat; i++) {
 279     CALL_SUBTEST_4( resize(MatrixXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 280     CALL_SUBTEST_5( resize(MatrixXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 281     CALL_SUBTEST_6( resize(MatrixXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
 282   }
 283   CALL_SUBTEST_6( regression_bug_654() );
 284 }