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Gael Guennebaud8cef5412008-06-21 17:28:07 +00001// This file is part of Eigen, a lightweight C++ template library
Benoit Jacob6347b1d2009-05-22 20:25:33 +02002// for linear algebra.
Gael Guennebaud8cef5412008-06-21 17:28:07 +00003//
Gael Guennebaud28e64b02010-06-24 23:21:58 +02004// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
Gael Guennebaud8cef5412008-06-21 17:28:07 +00005//
Benoit Jacob69124cf2012-07-13 14:42:47 -04006// 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/.
Gael Guennebaud19bc4182013-02-25 01:17:44 +01009
Gael Guennebaud8cef5412008-06-21 17:28:07 +000010#include "main.h"
Gael Guennebaud8cef5412008-06-21 17:28:07 +000011
Benoit Jacobe2775862010-04-28 18:51:38 -040012template<typename ArrayType> void array(const ArrayType& m)
Gael Guennebaud8cef5412008-06-21 17:28:07 +000013{
Hauke Heibelf1679c72010-06-20 17:37:56 +020014 typedef typename ArrayType::Index Index;
Benoit Jacobe2775862010-04-28 18:51:38 -040015 typedef typename ArrayType::Scalar Scalar;
Gael Guennebaudd476cad2016-06-25 10:12:06 +020016 typedef typename ArrayType::RealScalar RealScalar;
Benoit Jacobe2775862010-04-28 18:51:38 -040017 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
18 typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
Gael Guennebaud8cef5412008-06-21 17:28:07 +000019
Hauke Heibelf1679c72010-06-20 17:37:56 +020020 Index rows = m.rows();
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080021 Index cols = m.cols();
Gael Guennebaud8cef5412008-06-21 17:28:07 +000022
Benoit Jacobe2775862010-04-28 18:51:38 -040023 ArrayType m1 = ArrayType::Random(rows, cols),
24 m2 = ArrayType::Random(rows, cols),
Gael Guennebaud8cef5412008-06-21 17:28:07 +000025 m3(rows, cols);
Christoph Hertzberg3be9f5c2015-04-16 13:25:20 +020026 ArrayType m4 = m1; // copy constructor
27 VERIFY_IS_APPROX(m1, m4);
Gael Guennebaud8cef5412008-06-21 17:28:07 +000028
Gael Guennebaud627595a2009-06-10 11:20:30 +020029 ColVectorType cv1 = ColVectorType::Random(rows);
30 RowVectorType rv1 = RowVectorType::Random(cols);
31
Benoit Jacob47160402010-10-25 10:15:22 -040032 Scalar s1 = internal::random<Scalar>(),
Hauke Heibel8cb3e362012-03-02 16:27:27 +010033 s2 = internal::random<Scalar>();
34
Gael Guennebaud59dc1da2008-09-03 17:16:28 +000035 // scalar addition
Gael Guennebaudc70d5422010-01-18 22:54:20 +010036 VERIFY_IS_APPROX(m1 + s1, s1 + m1);
Benoit Jacobe2775862010-04-28 18:51:38 -040037 VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
Gael Guennebaudc70d5422010-01-18 22:54:20 +010038 VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
Benoit Jacobe2775862010-04-28 18:51:38 -040039 VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
40 VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
41 VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
Gael Guennebaud8cef5412008-06-21 17:28:07 +000042 m3 = m1;
Gael Guennebaudc70d5422010-01-18 22:54:20 +010043 m3 += s2;
44 VERIFY_IS_APPROX(m3, m1 + s2);
Gael Guennebaud8cef5412008-06-21 17:28:07 +000045 m3 = m1;
Gael Guennebaudc70d5422010-01-18 22:54:20 +010046 m3 -= s1;
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080047 VERIFY_IS_APPROX(m3, m1 - s1);
48
Hauke Heibelf578dc72010-12-16 17:34:13 +010049 // scalar operators via Maps
50 m3 = m1;
51 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
52 VERIFY_IS_APPROX(m1, m3 - m2);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080053
Hauke Heibelf578dc72010-12-16 17:34:13 +010054 m3 = m1;
55 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
56 VERIFY_IS_APPROX(m1, m3 + m2);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080057
Hauke Heibelf578dc72010-12-16 17:34:13 +010058 m3 = m1;
59 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
60 VERIFY_IS_APPROX(m1, m3 * m2);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080061
Hauke Heibelf578dc72010-12-16 17:34:13 +010062 m3 = m1;
63 m2 = ArrayType::Random(rows,cols);
64 m2 = (m2==0).select(1,m2);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080065 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
Hauke Heibelf578dc72010-12-16 17:34:13 +010066 VERIFY_IS_APPROX(m1, m3 / m2);
Gael Guennebaud05ad0832008-07-19 13:03:23 +000067
Gael Guennebaud59dc1da2008-09-03 17:16:28 +000068 // reductions
Gael Guennebaud42af5872013-02-23 22:58:14 +010069 VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
70 VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
71 using std::abs;
72 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
73 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
Gael Guennebaud28e139a2013-02-23 23:06:45 +010074 if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
Hauke Heibel83e3c452010-12-16 18:53:02 +010075 VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
Gael Guennebaud66e99ab2016-06-06 15:11:41 +020076 VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
Gael Guennebaud627595a2009-06-10 11:20:30 +020077
78 // vector-wise ops
79 m3 = m1;
80 VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
81 m3 = m1;
82 VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
83 m3 = m1;
84 VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
85 m3 = m1;
86 VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -080087
Gael Guennebaud0a18eec2014-09-19 13:25:28 +020088 // Conversion from scalar
89 VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
90 VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
91 VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
92 typedef Array<Scalar,
93 ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
94 ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
95 ArrayType::Options> FixedArrayType;
96 FixedArrayType f1(s1);
97 VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
98 FixedArrayType f2(numext::real(s1));
99 VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
100 FixedArrayType f3((int)100*numext::real(s1));
101 VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
102 f1.setRandom();
103 FixedArrayType f4(f1.data());
104 VERIFY_IS_APPROX(f4, f1);
Srinivas Vasudevan218764e2016-12-02 14:13:01 -0800105
Gael Guennebaudd476cad2016-06-25 10:12:06 +0200106 // pow
107 VERIFY_IS_APPROX(m1.pow(2), m1.square());
108 VERIFY_IS_APPROX(pow(m1,2), m1.square());
109 VERIFY_IS_APPROX(m1.pow(3), m1.cube());
110 VERIFY_IS_APPROX(pow(m1,3), m1.cube());
111 VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
112 VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
113 ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
114 VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
115 VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
116 VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
117 VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
118 VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
119 VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
Gael Guennebaude61cee72016-07-04 11:49:03 +0200120 VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
Gael Guennebaudd476cad2016-06-25 10:12:06 +0200121
Gael Guennebaud0a18eec2014-09-19 13:25:28 +0200122 // Check possible conflicts with 1D ctor
123 typedef Array<Scalar, Dynamic, 1> OneDArrayType;
124 OneDArrayType o1(rows);
125 VERIFY(o1.size()==rows);
126 OneDArrayType o4((int)rows);
127 VERIFY(o4.size()==rows);
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000128}
129
Benoit Jacobe2775862010-04-28 18:51:38 -0400130template<typename ArrayType> void comparisons(const ArrayType& m)
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000131{
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100132 using std::abs;
Hauke Heibelf1679c72010-06-20 17:37:56 +0200133 typedef typename ArrayType::Index Index;
Benoit Jacobe2775862010-04-28 18:51:38 -0400134 typedef typename ArrayType::Scalar Scalar;
Benoit Jacob874ff5a2009-01-26 17:56:04 +0000135 typedef typename NumTraits<Scalar>::Real RealScalar;
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000136
Hauke Heibelf1679c72010-06-20 17:37:56 +0200137 Index rows = m.rows();
138 Index cols = m.cols();
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000139
Benoit Jacob47160402010-10-25 10:15:22 -0400140 Index r = internal::random<Index>(0, rows-1),
141 c = internal::random<Index>(0, cols-1);
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000142
Benoit Jacobe2775862010-04-28 18:51:38 -0400143 ArrayType m1 = ArrayType::Random(rows, cols),
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200144 m2 = ArrayType::Random(rows, cols),
145 m3(rows, cols),
146 m4 = m1;
Srinivas Vasudevan218764e2016-12-02 14:13:01 -0800147
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200148 m4 = (m4.abs()==Scalar(0)).select(1,m4);
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000149
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100150 VERIFY(((m1 + Scalar(1)) > m1).all());
151 VERIFY(((m1 - Scalar(1)) < m1).all());
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000152 if (rows*cols>1)
153 {
154 m3 = m1;
155 m3(r,c) += 1;
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100156 VERIFY(! (m1 < m3).all() );
157 VERIFY(! (m1 > m3).all() );
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000158 }
Christoph Hertzberg494fa992015-05-07 17:28:40 +0200159 VERIFY(!(m1 > m2 && m1 < m2).any());
160 VERIFY((m1 <= m2 || m1 >= m2).all());
Gael Guennebaud627595a2009-06-10 11:20:30 +0200161
Christoph Hertzberg36052c42013-10-17 15:37:29 +0200162 // comparisons array to scalar
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100163 VERIFY( (m1 != (m1(r,c)+1) ).any() );
Christoph Hertzberg36052c42013-10-17 15:37:29 +0200164 VERIFY( (m1 > (m1(r,c)-1) ).any() );
165 VERIFY( (m1 < (m1(r,c)+1) ).any() );
166 VERIFY( (m1 == m1(r,c) ).any() );
167
168 // comparisons scalar to array
169 VERIFY( ( (m1(r,c)+1) != m1).any() );
170 VERIFY( ( (m1(r,c)-1) < m1).any() );
171 VERIFY( ( (m1(r,c)+1) > m1).any() );
172 VERIFY( ( m1(r,c) == m1).any() );
Gael Guennebaud627595a2009-06-10 11:20:30 +0200173
Gael Guennebaud59dc1da2008-09-03 17:16:28 +0000174 // test Select
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100175 VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
176 VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
Gael Guennebaud9f795582009-12-16 19:18:40 +0100177 Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
Gael Guennebaud59dc1da2008-09-03 17:16:28 +0000178 for (int j=0; j<cols; ++j)
179 for (int i=0; i<rows; ++i)
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100180 m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
Benoit Jacobe2775862010-04-28 18:51:38 -0400181 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
182 .select(ArrayType::Zero(rows,cols),m1), m3);
Gael Guennebaude14aa8c2008-09-03 17:56:06 +0000183 // shorter versions:
Benoit Jacobe2775862010-04-28 18:51:38 -0400184 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
Gael Guennebaud59dc1da2008-09-03 17:16:28 +0000185 .select(0,m1), m3);
Benoit Jacobe2775862010-04-28 18:51:38 -0400186 VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
Gael Guennebaud59dc1da2008-09-03 17:16:28 +0000187 .select(m1,0), m3);
Gael Guennebaude14aa8c2008-09-03 17:56:06 +0000188 // even shorter version:
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100189 VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
Gael Guennebaud627595a2009-06-10 11:20:30 +0200190
Gael Guennebaud56c7e162009-01-24 15:22:44 +0000191 // count
Gael Guennebaudc70d5422010-01-18 22:54:20 +0100192 VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
Benoit Jacobaaaade42010-05-30 16:00:58 -0400193
Gael Guennebaud35c11582011-05-31 22:17:34 +0200194 // and/or
195 VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
196 VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
197 RealScalar a = m1.abs().mean();
198 VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
199
Benoit Jacobaaaade42010-05-30 16:00:58 -0400200 typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
Gael Guennebaud4ebb8042010-06-02 09:45:57 +0200201
Gael Guennebaud9f795582009-12-16 19:18:40 +0100202 // TODO allows colwise/rowwise for array
Benoit Jacobaaaade42010-05-30 16:00:58 -0400203 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
204 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
Benoit Jacobe8009992008-11-03 22:47:00 +0000205}
206
Benoit Jacobe2775862010-04-28 18:51:38 -0400207template<typename ArrayType> void array_real(const ArrayType& m)
Gael Guennebaud0ce5bc02010-01-27 23:23:59 +0100208{
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100209 using std::abs;
Gael Guennebaud9b9177f2013-07-05 13:35:34 +0200210 using std::sqrt;
Hauke Heibelf1679c72010-06-20 17:37:56 +0200211 typedef typename ArrayType::Index Index;
Benoit Jacobe2775862010-04-28 18:51:38 -0400212 typedef typename ArrayType::Scalar Scalar;
Gael Guennebaud0ce5bc02010-01-27 23:23:59 +0100213 typedef typename NumTraits<Scalar>::Real RealScalar;
214
Hauke Heibelf1679c72010-06-20 17:37:56 +0200215 Index rows = m.rows();
216 Index cols = m.cols();
Gael Guennebaud0ce5bc02010-01-27 23:23:59 +0100217
Benoit Jacobe2775862010-04-28 18:51:38 -0400218 ArrayType m1 = ArrayType::Random(rows, cols),
Gael Guennebaudc695cbf2013-06-24 13:33:44 +0200219 m2 = ArrayType::Random(rows, cols),
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200220 m3(rows, cols),
221 m4 = m1;
Benoit Steiner83149622015-12-10 13:13:45 -0800222
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200223 m4 = (m4.abs()==Scalar(0)).select(1,m4);
Gael Guennebaud0ce5bc02010-01-27 23:23:59 +0100224
Gael Guennebaud9b1ad5e2012-03-09 12:08:06 +0100225 Scalar s1 = internal::random<Scalar>();
226
Deanna Hood41b717d2015-03-18 03:11:03 +1000227 // these tests are mostly to check possible compilation issues with free-functions.
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100228 VERIFY_IS_APPROX(m1.sin(), sin(m1));
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100229 VERIFY_IS_APPROX(m1.cos(), cos(m1));
Deanna Hoodf89fcef2015-03-11 13:13:30 +1000230 VERIFY_IS_APPROX(m1.tan(), tan(m1));
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100231 VERIFY_IS_APPROX(m1.asin(), asin(m1));
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100232 VERIFY_IS_APPROX(m1.acos(), acos(m1));
Jitse Niesende150b12014-06-19 15:12:33 +0100233 VERIFY_IS_APPROX(m1.atan(), atan(m1));
Deanna Hoodf89fcef2015-03-11 13:13:30 +1000234 VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
235 VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
236 VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
Gael Guennebaud2f7e2612016-07-08 11:13:55 +0200237
Deanna Hooda5e49972015-03-11 08:56:42 +1000238 VERIFY_IS_APPROX(m1.arg(), arg(m1));
Deanna Hood31fdd672015-03-11 06:39:23 +1000239 VERIFY_IS_APPROX(m1.round(), round(m1));
240 VERIFY_IS_APPROX(m1.floor(), floor(m1));
241 VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200242 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
243 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
244 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
Deanna Hood41b717d2015-03-18 03:11:03 +1000245 VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
246 VERIFY_IS_APPROX(m1.abs(), abs(m1));
247 VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
248 VERIFY_IS_APPROX(m1.square(), square(m1));
249 VERIFY_IS_APPROX(m1.cube(), cube(m1));
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100250 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
Gael Guennebaud3f32f5e2015-11-27 16:27:53 +0100251 VERIFY_IS_APPROX(m1.sign(), sign(m1));
Gael Guennebaud4ebb8042010-06-02 09:45:57 +0200252
Deanna Hood41b717d2015-03-18 03:11:03 +1000253
254 // avoid NaNs with abs() so verification doesn't fail
255 m3 = m1.abs();
256 VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m1)));
Benoit Steinere25e3a02015-12-03 18:16:35 -0800257 VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m1)));
Gael Guennebaud9e8476e2016-07-20 11:59:49 +0200258 VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m1)));
Deanna Hood41b717d2015-03-18 03:11:03 +1000259 VERIFY_IS_APPROX(m3.log(), log(m3));
Gael Guennebaud89099b02016-06-01 17:00:08 +0200260 VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
Deanna Hood41b717d2015-03-18 03:11:03 +1000261 VERIFY_IS_APPROX(m3.log10(), log10(m3));
262
263
264 VERIFY((!(m1>m2) == (m1<=m2)).all());
265
266 VERIFY_IS_APPROX(sin(m1.asin()), m1);
267 VERIFY_IS_APPROX(cos(m1.acos()), m1);
268 VERIFY_IS_APPROX(tan(m1.atan()), m1);
269 VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
270 VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
271 VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
Gael Guennebaud2e0ece72015-10-06 17:22:12 +0200272 VERIFY_IS_APPROX(arg(m1), ((m1<0).template cast<Scalar>())*std::acos(-1.0));
Deanna Hood41b717d2015-03-18 03:11:03 +1000273 VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200274 VERIFY((Eigen::isnan)((m1*0.0)/0.0).all());
275 VERIFY((Eigen::isinf)(m4/0.0).all());
276 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*0.0/0.0)) && (!(Eigen::isfinite)(m4/0.0))).all());
Deanna Hood41b717d2015-03-18 03:11:03 +1000277 VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
278 VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
279 VERIFY_IS_APPROX(m3, sqrt(abs2(m1)));
Gael Guennebaud3f32f5e2015-11-27 16:27:53 +0100280 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
281 VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
282 VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
Benoit Jacob5d63d2c2010-04-28 22:42:34 -0400283
Gael Guennebaud62670c82013-06-10 23:40:56 +0200284 VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
285 VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
Benoit Jacob5d63d2c2010-04-28 22:42:34 -0400286 if(!NumTraits<Scalar>::IsComplex)
Gael Guennebaud62670c82013-06-10 23:40:56 +0200287 VERIFY_IS_APPROX(numext::real(m1), m1);
Gael Guennebaud4ebb8042010-06-02 09:45:57 +0200288
Jitse Niesen6fecb6f2014-02-24 14:10:17 +0000289 // shift argument of logarithm so that it is not zero
290 Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
Deanna Hood41b717d2015-03-18 03:11:03 +1000291 VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m1) + smallNumber));
Gael Guennebaud89099b02016-06-01 17:00:08 +0200292 VERIFY_IS_APPROX((m3 + smallNumber + 1).log() , log1p(abs(m1) + smallNumber));
Gael Guennebaud4ebb8042010-06-02 09:45:57 +0200293
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100294 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
295 VERIFY_IS_APPROX(m1.exp(), exp(m1));
296 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
Gael Guennebaud575ac542010-06-19 23:17:07 +0200297
Srinivas Vasudevan218764e2016-12-02 14:13:01 -0800298 VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
299 VERIFY_IS_APPROX((m3 + smallNumber).exp() - 1, expm1(abs(m3) + smallNumber));
300
Gael Guennebaud575ac542010-06-19 23:17:07 +0200301 VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100302 VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
Benoit Steinere25e3a02015-12-03 18:16:35 -0800303
304 VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
305 VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
306
Deanna Hood41b717d2015-03-18 03:11:03 +1000307 VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));
Hauke Heibel81c13362012-03-07 08:58:42 +0100308
309 // scalar by array division
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100310 const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
Hauke Heibeldd9365e2012-03-09 14:04:13 +0100311 s1 += Scalar(tiny);
312 m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
Hauke Heibel81c13362012-03-07 08:58:42 +0100313 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
Eugene Brevdof7362772015-12-24 21:15:38 -0800314
Gael Guennebaudc695cbf2013-06-24 13:33:44 +0200315 // check inplace transpose
316 m3 = m1;
317 m3.transposeInPlace();
Deanna Hood41b717d2015-03-18 03:11:03 +1000318 VERIFY_IS_APPROX(m3, m1.transpose());
Gael Guennebaudc695cbf2013-06-24 13:33:44 +0200319 m3.transposeInPlace();
Deanna Hood41b717d2015-03-18 03:11:03 +1000320 VERIFY_IS_APPROX(m3, m1);
Gael Guennebaud0ce5bc02010-01-27 23:23:59 +0100321}
322
Jitse Niesen837db082011-05-09 10:17:41 +0100323template<typename ArrayType> void array_complex(const ArrayType& m)
324{
325 typedef typename ArrayType::Index Index;
Deanna Hood41b717d2015-03-18 03:11:03 +1000326 typedef typename ArrayType::Scalar Scalar;
327 typedef typename NumTraits<Scalar>::Real RealScalar;
Jitse Niesen837db082011-05-09 10:17:41 +0100328
329 Index rows = m.rows();
330 Index cols = m.cols();
331
332 ArrayType m1 = ArrayType::Random(rows, cols),
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200333 m2(rows, cols),
334 m4 = m1;
Srinivas Vasudevan218764e2016-12-02 14:13:01 -0800335
Gael Guennebaud9fc1c922015-06-22 16:48:27 +0200336 m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
337 m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
Jitse Niesen837db082011-05-09 10:17:41 +0100338
Deanna Hood41b717d2015-03-18 03:11:03 +1000339 Array<RealScalar, -1, -1> m3(rows, cols);
340
Jitse Niesen837db082011-05-09 10:17:41 +0100341 for (Index i = 0; i < m.rows(); ++i)
342 for (Index j = 0; j < m.cols(); ++j)
Gael Guennebauda76fbbf2012-11-06 15:25:50 +0100343 m2(i,j) = sqrt(m1(i,j));
Jitse Niesen837db082011-05-09 10:17:41 +0100344
Deanna Hood41b717d2015-03-18 03:11:03 +1000345 // these tests are mostly to check possible compilation issues with free-functions.
Deanna Hoodf89fcef2015-03-11 13:13:30 +1000346 VERIFY_IS_APPROX(m1.sin(), sin(m1));
347 VERIFY_IS_APPROX(m1.cos(), cos(m1));
348 VERIFY_IS_APPROX(m1.tan(), tan(m1));
349 VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
350 VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
351 VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
Deanna Hood41b717d2015-03-18 03:11:03 +1000352 VERIFY_IS_APPROX(m1.arg(), arg(m1));
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200353 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
354 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
355 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
Deanna Hood41b717d2015-03-18 03:11:03 +1000356 VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
357 VERIFY_IS_APPROX(m1.log(), log(m1));
358 VERIFY_IS_APPROX(m1.log10(), log10(m1));
359 VERIFY_IS_APPROX(m1.abs(), abs(m1));
360 VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
361 VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
362 VERIFY_IS_APPROX(m1.square(), square(m1));
363 VERIFY_IS_APPROX(m1.cube(), cube(m1));
364 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
Gael Guennebaud3f32f5e2015-11-27 16:27:53 +0100365 VERIFY_IS_APPROX(m1.sign(), sign(m1));
Deanna Hood41b717d2015-03-18 03:11:03 +1000366
367
368 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
369 VERIFY_IS_APPROX(m1.exp(), exp(m1));
370 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
371
372 VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
373 VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
374 VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
375
376 for (Index i = 0; i < m.rows(); ++i)
377 for (Index j = 0; j < m.cols(); ++j)
378 m3(i,j) = std::atan2(imag(m1(i,j)), real(m1(i,j)));
379 VERIFY_IS_APPROX(arg(m1), m3);
380
381 std::complex<RealScalar> zero(0.0,0.0);
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200382 VERIFY((Eigen::isnan)(m1*zero/zero).all());
Gael Guennebaud4a985e72015-11-20 14:52:08 +0100383#if EIGEN_COMP_MSVC
384 // msvc complex division is not robust
385 VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
386#else
Gael Guennebaud40f326e2015-06-17 15:33:09 +0200387#if EIGEN_COMP_CLANG
Gael Guennebaud4a985e72015-11-20 14:52:08 +0100388 // clang's complex division is notoriously broken too
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200389 if((numext::isinf)(m4(0,0)/RealScalar(0))) {
Gael Guennebaud40f326e2015-06-17 15:33:09 +0200390#endif
Gael Guennebaud4a985e72015-11-20 14:52:08 +0100391 VERIFY((Eigen::isinf)(m4/zero).all());
Gael Guennebaud40f326e2015-06-17 15:33:09 +0200392#if EIGEN_COMP_CLANG
393 }
394 else
395 {
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200396 VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
Gael Guennebaud40f326e2015-06-17 15:33:09 +0200397 }
398#endif
Gael Guennebaud4a985e72015-11-20 14:52:08 +0100399#endif // MSVC
400
Christoph Hertzberg61e09772015-08-14 17:32:34 +0200401 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
Deanna Hood41b717d2015-03-18 03:11:03 +1000402
403 VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
404 VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
405 VERIFY_IS_APPROX(abs(m1), sqrt(square(real(m1))+square(imag(m1))));
406 VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
407 VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
408
Gael Guennebaud3f32f5e2015-11-27 16:27:53 +0100409 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
410 VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
411
Deanna Hood41b717d2015-03-18 03:11:03 +1000412 // scalar by array division
Eugene Brevdof7362772015-12-24 21:15:38 -0800413 Scalar s1 = internal::random<Scalar>();
Benoit Steiner2d74ef92016-05-17 07:20:11 -0700414 const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
Deanna Hood41b717d2015-03-18 03:11:03 +1000415 s1 += Scalar(tiny);
416 m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
417 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
418
419 // check inplace transpose
420 m2 = m1;
421 m2.transposeInPlace();
422 VERIFY_IS_APPROX(m2, m1.transpose());
423 m2.transposeInPlace();
424 VERIFY_IS_APPROX(m2, m1);
Deanna Hood31fdd672015-03-11 06:39:23 +1000425
Jitse Niesen837db082011-05-09 10:17:41 +0100426}
427
Abraham Bachrach039408c2012-01-11 11:00:30 -0500428template<typename ArrayType> void min_max(const ArrayType& m)
429{
430 typedef typename ArrayType::Index Index;
431 typedef typename ArrayType::Scalar Scalar;
432
433 Index rows = m.rows();
434 Index cols = m.cols();
435
436 ArrayType m1 = ArrayType::Random(rows, cols);
437
438 // min/max with array
439 Scalar maxM1 = m1.maxCoeff();
440 Scalar minM1 = m1.minCoeff();
441
442 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
443 VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
444
445 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
446 VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
447
448 // min/max with scalar input
449 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
450 VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
451
452 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
453 VERIFY_IS_APPROX(m1, (m1.max)( minM1));
454
455}
456
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000457void test_array()
458{
459 for(int i = 0; i < g_repeat; i++) {
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100460 CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
Hauke Heibelb31e1242010-12-16 19:07:23 +0100461 CALL_SUBTEST_2( array(Array22f()) );
462 CALL_SUBTEST_3( array(Array44d()) );
Gael Guennebauda8f66fe2011-07-12 14:41:00 +0200463 CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
464 CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
465 CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000466 }
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100467 for(int i = 0; i < g_repeat; i++) {
468 CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
Hauke Heibelb31e1242010-12-16 19:07:23 +0100469 CALL_SUBTEST_2( comparisons(Array22f()) );
470 CALL_SUBTEST_3( comparisons(Array44d()) );
Gael Guennebauda8f66fe2011-07-12 14:41:00 +0200471 CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
472 CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100473 }
474 for(int i = 0; i < g_repeat; i++) {
Abraham Bachrach039408c2012-01-11 11:00:30 -0500475 CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
476 CALL_SUBTEST_2( min_max(Array22f()) );
477 CALL_SUBTEST_3( min_max(Array44d()) );
478 CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
479 CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
480 }
481 for(int i = 0; i < g_repeat; i++) {
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100482 CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
Hauke Heibelb31e1242010-12-16 19:07:23 +0100483 CALL_SUBTEST_2( array_real(Array22f()) );
484 CALL_SUBTEST_3( array_real(Array44d()) );
Gael Guennebauda8f66fe2011-07-12 14:41:00 +0200485 CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100486 }
Jitse Niesen837db082011-05-09 10:17:41 +0100487 for(int i = 0; i < g_repeat; i++) {
Gael Guennebauda8f66fe2011-07-12 14:41:00 +0200488 CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
Jitse Niesen837db082011-05-09 10:17:41 +0100489 }
Benoit Jacob5d63d2c2010-04-28 22:42:34 -0400490
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100491 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
492 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
493 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
Gael Guennebaud64fcfd32016-06-14 11:26:57 +0200494 typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
Hauke Heibel2d0dfe52010-12-16 17:36:10 +0100495 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
496 ArrayBase<Xpr>
497 >::value));
Gael Guennebaud8cef5412008-06-21 17:28:07 +0000498}