redux.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) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
5 // Copyright (C) 2015 Gael Guennebaud <gael.guennebaud@inria.fr>
6 //
7 // This Source Code Form is subject to the terms of the Mozilla
8 // Public License v. 2.0. If a copy of the MPL was not distributed
9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10 
11 #define TEST_ENABLE_TEMPORARY_TRACKING
12 #define EIGEN_CACHEFRIENDLY_PRODUCT_THRESHOLD 8
13 // ^^ see bug 1449
14 
15 #include "main.h"
16 
17 template<typename MatrixType> void matrixRedux(const MatrixType& m)
18 {
19  typedef typename MatrixType::Scalar Scalar;
20  typedef typename MatrixType::RealScalar RealScalar;
21 
22  Index rows = m.rows();
23  Index cols = m.cols();
24 
25  MatrixType m1 = MatrixType::Random(rows, cols);
26 
27  // The entries of m1 are uniformly distributed in [0,1], so m1.prod() is very small. This may lead to test
28  // failures if we underflow into denormals. Thus, we scale so that entries are close to 1.
29  MatrixType m1_for_prod = MatrixType::Ones(rows, cols) + RealScalar(0.2) * m1;
30 
31  Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> m2(rows,rows);
32  m2.setRandom();
33 
34  VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows, cols).sum(), Scalar(1));
35  VERIFY_IS_APPROX(MatrixType::Ones(rows, cols).sum(), Scalar(float(rows*cols))); // the float() here to shut up excessive MSVC warning about int->complex conversion being lossy
36  Scalar s(0), p(1), minc(numext::real(m1.coeff(0))), maxc(numext::real(m1.coeff(0)));
37  for(int j = 0; j < cols; j++)
38  for(int i = 0; i < rows; i++)
39  {
40  s += m1(i,j);
41  p *= m1_for_prod(i,j);
42  minc = (std::min)(numext::real(minc), numext::real(m1(i,j)));
43  maxc = (std::max)(numext::real(maxc), numext::real(m1(i,j)));
44  }
45  const Scalar mean = s/Scalar(RealScalar(rows*cols));
46 
47  VERIFY_IS_APPROX(m1.sum(), s);
48  VERIFY_IS_APPROX(m1.mean(), mean);
49  VERIFY_IS_APPROX(m1_for_prod.prod(), p);
50  VERIFY_IS_APPROX(m1.real().minCoeff(), numext::real(minc));
51  VERIFY_IS_APPROX(m1.real().maxCoeff(), numext::real(maxc));
52 
53  // test that partial reduction works if nested expressions is forced to evaluate early
54  VERIFY_IS_APPROX((m1.matrix() * m1.matrix().transpose()) .cwiseProduct(m2.matrix()).rowwise().sum().sum(),
55  (m1.matrix() * m1.matrix().transpose()).eval().cwiseProduct(m2.matrix()).rowwise().sum().sum());
56 
57  // test slice vectorization assuming assign is ok
58  Index r0 = internal::random<Index>(0,rows-1);
59  Index c0 = internal::random<Index>(0,cols-1);
60  Index r1 = internal::random<Index>(r0+1,rows)-r0;
61  Index c1 = internal::random<Index>(c0+1,cols)-c0;
62  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).sum(), m1.block(r0,c0,r1,c1).eval().sum());
63  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).mean(), m1.block(r0,c0,r1,c1).eval().mean());
64  VERIFY_IS_APPROX(m1_for_prod.block(r0,c0,r1,c1).prod(), m1_for_prod.block(r0,c0,r1,c1).eval().prod());
65  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().minCoeff(), m1.block(r0,c0,r1,c1).real().eval().minCoeff());
66  VERIFY_IS_APPROX(m1.block(r0,c0,r1,c1).real().maxCoeff(), m1.block(r0,c0,r1,c1).real().eval().maxCoeff());
67 
68  // regression for bug 1090
69  const int R1 = MatrixType::RowsAtCompileTime>=2 ? MatrixType::RowsAtCompileTime/2 : 6;
70  const int C1 = MatrixType::ColsAtCompileTime>=2 ? MatrixType::ColsAtCompileTime/2 : 6;
71  if(R1<=rows-r0 && C1<=cols-c0)
72  {
73  VERIFY_IS_APPROX( (m1.template block<R1,C1>(r0,c0).sum()), m1.block(r0,c0,R1,C1).sum() );
74  }
75 
76  // test empty objects
77  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).sum(), Scalar(0));
78  VERIFY_IS_APPROX(m1.block(r0,c0,0,0).prod(), Scalar(1));
79 
80  // test nesting complex expression
81  VERIFY_EVALUATION_COUNT( (m1.matrix()*m1.matrix().transpose()).sum(), (MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1) );
82  VERIFY_EVALUATION_COUNT( ((m1.matrix()*m1.matrix().transpose())+m2).sum(),(MatrixType::IsVectorAtCompileTime && MatrixType::SizeAtCompileTime!=1 ? 0 : 1));
83 }
84 
85 template<typename VectorType> void vectorRedux(const VectorType& w)
86 {
87  using std::abs;
88  typedef typename VectorType::Scalar Scalar;
89  typedef typename NumTraits<Scalar>::Real RealScalar;
90  Index size = w.size();
91 
92  VectorType v = VectorType::Random(size);
93  VectorType v_for_prod = VectorType::Ones(size) + Scalar(0.2) * v; // see comment above declaration of m1_for_prod
94 
95  for(int i = 1; i < size; i++)
96  {
97  Scalar s(0), p(1);
98  RealScalar minc(numext::real(v.coeff(0))), maxc(numext::real(v.coeff(0)));
99  for(int j = 0; j < i; j++)
100  {
101  s += v[j];
102  p *= v_for_prod[j];
103  minc = (std::min)(minc, numext::real(v[j]));
104  maxc = (std::max)(maxc, numext::real(v[j]));
105  }
106  VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
107  VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
108  VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
109  VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
110  }
111 
112  for(int i = 0; i < size-1; i++)
113  {
114  Scalar s(0), p(1);
115  RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
116  for(int j = i; j < size; j++)
117  {
118  s += v[j];
119  p *= v_for_prod[j];
120  minc = (std::min)(minc, numext::real(v[j]));
121  maxc = (std::max)(maxc, numext::real(v[j]));
122  }
123  VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));
124  VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());
125  VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());
126  VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());
127  }
128 
129  for(int i = 0; i < size/2; i++)
130  {
131  Scalar s(0), p(1);
132  RealScalar minc(numext::real(v.coeff(i))), maxc(numext::real(v.coeff(i)));
133  for(int j = i; j < size-i; j++)
134  {
135  s += v[j];
136  p *= v_for_prod[j];
137  minc = (std::min)(minc, numext::real(v[j]));
138  maxc = (std::max)(maxc, numext::real(v[j]));
139  }
140  VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
141  VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());
142  VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());
143  VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());
144  }
145 
146  // test empty objects
147  VERIFY_IS_APPROX(v.head(0).sum(), Scalar(0));
148  VERIFY_IS_APPROX(v.tail(0).prod(), Scalar(1));
149  VERIFY_RAISES_ASSERT(v.head(0).mean());
150  VERIFY_RAISES_ASSERT(v.head(0).minCoeff());
151  VERIFY_RAISES_ASSERT(v.head(0).maxCoeff());
152 }
153 
154 EIGEN_DECLARE_TEST(redux)
155 {
156  // the max size cannot be too large, otherwise reduxion operations obviously generate large errors.
157  int maxsize = (std::min)(100,EIGEN_TEST_MAX_SIZE);
158  TEST_SET_BUT_UNUSED_VARIABLE(maxsize);
159  for(int i = 0; i < g_repeat; i++) {
160  CALL_SUBTEST_1( matrixRedux(Matrix<float, 1, 1>()) );
161  CALL_SUBTEST_1( matrixRedux(Array<float, 1, 1>()) );
162  CALL_SUBTEST_2( matrixRedux(Matrix2f()) );
163  CALL_SUBTEST_2( matrixRedux(Array2f()) );
164  CALL_SUBTEST_2( matrixRedux(Array22f()) );
165  CALL_SUBTEST_3( matrixRedux(Matrix4d()) );
166  CALL_SUBTEST_3( matrixRedux(Array4d()) );
167  CALL_SUBTEST_3( matrixRedux(Array44d()) );
168  CALL_SUBTEST_4( matrixRedux(MatrixXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
169  CALL_SUBTEST_4( matrixRedux(ArrayXXcf(internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
170  CALL_SUBTEST_5( matrixRedux(MatrixXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
171  CALL_SUBTEST_5( matrixRedux(ArrayXXd (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
172  CALL_SUBTEST_6( matrixRedux(MatrixXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
173  CALL_SUBTEST_6( matrixRedux(ArrayXXi (internal::random<int>(1,maxsize), internal::random<int>(1,maxsize))) );
174  }
175  for(int i = 0; i < g_repeat; i++) {
176  CALL_SUBTEST_7( vectorRedux(Vector4f()) );
177  CALL_SUBTEST_7( vectorRedux(Array4f()) );
178  CALL_SUBTEST_5( vectorRedux(VectorXd(internal::random<int>(1,maxsize))) );
179  CALL_SUBTEST_5( vectorRedux(ArrayXd(internal::random<int>(1,maxsize))) );
180  CALL_SUBTEST_8( vectorRedux(VectorXf(internal::random<int>(1,maxsize))) );
181  CALL_SUBTEST_8( vectorRedux(ArrayXf(internal::random<int>(1,maxsize))) );
182  }
183 }
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