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
array(const ArrayType & m)12 template<typename ArrayType> void array(const ArrayType& m)
13 {
14 typedef typename ArrayType::Index Index;
15 typedef typename ArrayType::Scalar Scalar;
16 typedef typename NumTraits<Scalar>::Real RealScalar;
17 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
18 typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
19
20 Index rows = m.rows();
21 Index cols = m.cols();
22
23 ArrayType m1 = ArrayType::Random(rows, cols),
24 m2 = ArrayType::Random(rows, cols),
25 m3(rows, cols);
26
27 ColVectorType cv1 = ColVectorType::Random(rows);
28 RowVectorType rv1 = RowVectorType::Random(cols);
29
30 Scalar s1 = internal::random<Scalar>(),
31 s2 = internal::random<Scalar>();
32
33 // scalar addition
34 VERIFY_IS_APPROX(m1 + s1, s1 + m1);
35 VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
36 VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
37 VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
38 VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
39 VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
40 m3 = m1;
41 m3 += s2;
42 VERIFY_IS_APPROX(m3, m1 + s2);
43 m3 = m1;
44 m3 -= s1;
45 VERIFY_IS_APPROX(m3, m1 - s1);
46
47 // scalar operators via Maps
48 m3 = m1;
49 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
50 VERIFY_IS_APPROX(m1, m3 - m2);
51
52 m3 = m1;
53 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
54 VERIFY_IS_APPROX(m1, m3 + m2);
55
56 m3 = m1;
57 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
58 VERIFY_IS_APPROX(m1, m3 * m2);
59
60 m3 = m1;
61 m2 = ArrayType::Random(rows,cols);
62 m2 = (m2==0).select(1,m2);
63 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
64 VERIFY_IS_APPROX(m1, m3 / m2);
65
66 // reductions
67 VERIFY_IS_APPROX(m1.colwise().sum().sum(), m1.sum());
68 VERIFY_IS_APPROX(m1.rowwise().sum().sum(), m1.sum());
69 if (!internal::isApprox(m1.sum(), (m1+m2).sum(), test_precision<Scalar>()))
70 VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
71 VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
72
73 // vector-wise ops
74 m3 = m1;
75 VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
76 m3 = m1;
77 VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
78 m3 = m1;
79 VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
80 m3 = m1;
81 VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
82 }
83
comparisons(const ArrayType & m)84 template<typename ArrayType> void comparisons(const ArrayType& m)
85 {
86 typedef typename ArrayType::Index Index;
87 typedef typename ArrayType::Scalar Scalar;
88 typedef typename NumTraits<Scalar>::Real RealScalar;
89 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> VectorType;
90
91 Index rows = m.rows();
92 Index cols = m.cols();
93
94 Index r = internal::random<Index>(0, rows-1),
95 c = internal::random<Index>(0, cols-1);
96
97 ArrayType m1 = ArrayType::Random(rows, cols),
98 m2 = ArrayType::Random(rows, cols),
99 m3(rows, cols);
100
101 VERIFY(((m1 + Scalar(1)) > m1).all());
102 VERIFY(((m1 - Scalar(1)) < m1).all());
103 if (rows*cols>1)
104 {
105 m3 = m1;
106 m3(r,c) += 1;
107 VERIFY(! (m1 < m3).all() );
108 VERIFY(! (m1 > m3).all() );
109 }
110
111 // comparisons to scalar
112 VERIFY( (m1 != (m1(r,c)+1) ).any() );
113 VERIFY( (m1 > (m1(r,c)-1) ).any() );
114 VERIFY( (m1 < (m1(r,c)+1) ).any() );
115 VERIFY( (m1 == m1(r,c) ).any() );
116
117 // test Select
118 VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
119 VERIFY_IS_APPROX( (m1>m2).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) = internal::abs(m1(i,j))<mid ? 0 : m1(i,j);
124 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
125 .select(ArrayType::Zero(rows,cols),m1), m3);
126 // shorter versions:
127 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
128 .select(0,m1), m3);
129 VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
130 .select(m1,0), m3);
131 // even shorter version:
132 VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
133
134 // count
135 VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
136
137 // and/or
138 VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
139 VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
140 RealScalar a = m1.abs().mean();
141 VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
142
143 typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
144
145 // TODO allows colwise/rowwise for array
146 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
147 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
148 }
149
array_real(const ArrayType & m)150 template<typename ArrayType> void array_real(const ArrayType& m)
151 {
152 typedef typename ArrayType::Index Index;
153 typedef typename ArrayType::Scalar Scalar;
154 typedef typename NumTraits<Scalar>::Real RealScalar;
155
156 Index rows = m.rows();
157 Index cols = m.cols();
158
159 ArrayType m1 = ArrayType::Random(rows, cols),
160 m2 = ArrayType::Random(rows, cols),
161 m3(rows, cols);
162
163 Scalar s1 = internal::random<Scalar>();
164
165 // these tests are mostly to check possible compilation issues.
166 VERIFY_IS_APPROX(m1.sin(), std::sin(m1));
167 VERIFY_IS_APPROX(m1.sin(), internal::sin(m1));
168 VERIFY_IS_APPROX(m1.cos(), std::cos(m1));
169 VERIFY_IS_APPROX(m1.cos(), internal::cos(m1));
170 VERIFY_IS_APPROX(m1.asin(), std::asin(m1));
171 VERIFY_IS_APPROX(m1.asin(), internal::asin(m1));
172 VERIFY_IS_APPROX(m1.acos(), std::acos(m1));
173 VERIFY_IS_APPROX(m1.acos(), internal::acos(m1));
174 VERIFY_IS_APPROX(m1.tan(), std::tan(m1));
175 VERIFY_IS_APPROX(m1.tan(), internal::tan(m1));
176
177 VERIFY_IS_APPROX(internal::cos(m1+RealScalar(3)*m2), internal::cos((m1+RealScalar(3)*m2).eval()));
178 VERIFY_IS_APPROX(std::cos(m1+RealScalar(3)*m2), std::cos((m1+RealScalar(3)*m2).eval()));
179
180 VERIFY_IS_APPROX(m1.abs().sqrt(), std::sqrt(std::abs(m1)));
181 VERIFY_IS_APPROX(m1.abs().sqrt(), internal::sqrt(internal::abs(m1)));
182 VERIFY_IS_APPROX(m1.abs(), internal::sqrt(internal::abs2(m1)));
183
184 VERIFY_IS_APPROX(internal::abs2(internal::real(m1)) + internal::abs2(internal::imag(m1)), internal::abs2(m1));
185 VERIFY_IS_APPROX(internal::abs2(std::real(m1)) + internal::abs2(std::imag(m1)), internal::abs2(m1));
186 if(!NumTraits<Scalar>::IsComplex)
187 VERIFY_IS_APPROX(internal::real(m1), m1);
188
189 VERIFY_IS_APPROX(m1.abs().log(), std::log(std::abs(m1)));
190 VERIFY_IS_APPROX(m1.abs().log(), internal::log(internal::abs(m1)));
191
192 VERIFY_IS_APPROX(m1.exp(), std::exp(m1));
193 VERIFY_IS_APPROX(m1.exp() * m2.exp(), std::exp(m1+m2));
194 VERIFY_IS_APPROX(m1.exp(), internal::exp(m1));
195 VERIFY_IS_APPROX(m1.exp() / m2.exp(), std::exp(m1-m2));
196
197 VERIFY_IS_APPROX(m1.pow(2), m1.square());
198 VERIFY_IS_APPROX(std::pow(m1,2), m1.square());
199
200 ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
201 VERIFY_IS_APPROX(std::pow(m1,exponents), m1.square());
202
203 m3 = m1.abs();
204 VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
205 VERIFY_IS_APPROX(std::pow(m3,RealScalar(0.5)), m3.sqrt());
206
207 // scalar by array division
208 const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
209 s1 += Scalar(tiny);
210 m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
211 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
212 }
213
array_complex(const ArrayType & m)214 template<typename ArrayType> void array_complex(const ArrayType& m)
215 {
216 typedef typename ArrayType::Index Index;
217
218 Index rows = m.rows();
219 Index cols = m.cols();
220
221 ArrayType m1 = ArrayType::Random(rows, cols),
222 m2(rows, cols);
223
224 for (Index i = 0; i < m.rows(); ++i)
225 for (Index j = 0; j < m.cols(); ++j)
226 m2(i,j) = std::sqrt(m1(i,j));
227
228 VERIFY_IS_APPROX(m1.sqrt(), m2);
229 VERIFY_IS_APPROX(m1.sqrt(), std::sqrt(m1));
230 VERIFY_IS_APPROX(m1.sqrt(), internal::sqrt(m1));
231 }
232
min_max(const ArrayType & m)233 template<typename ArrayType> void min_max(const ArrayType& m)
234 {
235 typedef typename ArrayType::Index Index;
236 typedef typename ArrayType::Scalar Scalar;
237
238 Index rows = m.rows();
239 Index cols = m.cols();
240
241 ArrayType m1 = ArrayType::Random(rows, cols);
242
243 // min/max with array
244 Scalar maxM1 = m1.maxCoeff();
245 Scalar minM1 = m1.minCoeff();
246
247 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
248 VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
249
250 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
251 VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
252
253 // min/max with scalar input
254 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
255 VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
256
257 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
258 VERIFY_IS_APPROX(m1, (m1.max)( minM1));
259
260 }
261
test_array()262 void test_array()
263 {
264 for(int i = 0; i < g_repeat; i++) {
265 CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
266 CALL_SUBTEST_2( array(Array22f()) );
267 CALL_SUBTEST_3( array(Array44d()) );
268 CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
269 CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
270 CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
271 }
272 for(int i = 0; i < g_repeat; i++) {
273 CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
274 CALL_SUBTEST_2( comparisons(Array22f()) );
275 CALL_SUBTEST_3( comparisons(Array44d()) );
276 CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
277 CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
278 }
279 for(int i = 0; i < g_repeat; i++) {
280 CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
281 CALL_SUBTEST_2( min_max(Array22f()) );
282 CALL_SUBTEST_3( min_max(Array44d()) );
283 CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
284 CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
285 }
286 for(int i = 0; i < g_repeat; i++) {
287 CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
288 CALL_SUBTEST_2( array_real(Array22f()) );
289 CALL_SUBTEST_3( array_real(Array44d()) );
290 CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
291 }
292 for(int i = 0; i < g_repeat; i++) {
293 CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
294 }
295
296 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
297 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
298 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
299 typedef CwiseUnaryOp<internal::scalar_sum_op<double>, ArrayXd > Xpr;
300 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
301 ArrayBase<Xpr>
302 >::value));
303 }
304