1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008-2009 Gael Guennebaud <[email protected]>
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
13 // Test the corner cases of pow(x, y) for real types.
14 template<typename Scalar>
pow_test()15 void pow_test() {
16 const Scalar zero = Scalar(0);
17 const Scalar eps = Eigen::NumTraits<Scalar>::epsilon();
18 const Scalar one = Scalar(1);
19 const Scalar two = Scalar(2);
20 const Scalar three = Scalar(3);
21 const Scalar sqrt_half = Scalar(std::sqrt(0.5));
22 const Scalar sqrt2 = Scalar(std::sqrt(2));
23 const Scalar inf = Eigen::NumTraits<Scalar>::infinity();
24 const Scalar nan = Eigen::NumTraits<Scalar>::quiet_NaN();
25 const Scalar denorm_min = std::numeric_limits<Scalar>::denorm_min();
26 const Scalar min = (std::numeric_limits<Scalar>::min)();
27 const Scalar max = (std::numeric_limits<Scalar>::max)();
28 const Scalar max_exp = (static_cast<Scalar>(int(Eigen::NumTraits<Scalar>::max_exponent())) * Scalar(EIGEN_LN2)) / eps;
29
30 const static Scalar abs_vals[] = {zero,
31 denorm_min,
32 min,
33 eps,
34 sqrt_half,
35 one,
36 sqrt2,
37 two,
38 three,
39 max_exp,
40 max,
41 inf,
42 nan};
43 const int abs_cases = 13;
44 const int num_cases = 2*abs_cases * 2*abs_cases;
45 // Repeat the same value to make sure we hit the vectorized path.
46 const int num_repeats = 32;
47 Array<Scalar, Dynamic, Dynamic> x(num_repeats, num_cases);
48 Array<Scalar, Dynamic, Dynamic> y(num_repeats, num_cases);
49 int count = 0;
50 for (int i = 0; i < abs_cases; ++i) {
51 const Scalar abs_x = abs_vals[i];
52 for (int sign_x = 0; sign_x < 2; ++sign_x) {
53 Scalar x_case = sign_x == 0 ? -abs_x : abs_x;
54 for (int j = 0; j < abs_cases; ++j) {
55 const Scalar abs_y = abs_vals[j];
56 for (int sign_y = 0; sign_y < 2; ++sign_y) {
57 Scalar y_case = sign_y == 0 ? -abs_y : abs_y;
58 for (int repeat = 0; repeat < num_repeats; ++repeat) {
59 x(repeat, count) = x_case;
60 y(repeat, count) = y_case;
61 }
62 ++count;
63 }
64 }
65 }
66 }
67
68 Array<Scalar, Dynamic, Dynamic> actual = x.pow(y);
69 const Scalar tol = test_precision<Scalar>();
70 bool all_pass = true;
71 for (int i = 0; i < 1; ++i) {
72 for (int j = 0; j < num_cases; ++j) {
73 Scalar e = static_cast<Scalar>(std::pow(x(i,j), y(i,j)));
74 Scalar a = actual(i, j);
75 bool fail = !(a==e) && !internal::isApprox(a, e, tol) && !((numext::isnan)(a) && (numext::isnan)(e));
76 all_pass &= !fail;
77 if (fail) {
78 std::cout << "pow(" << x(i,j) << "," << y(i,j) << ") = " << a << " != " << e << std::endl;
79 }
80 }
81 }
82 VERIFY(all_pass);
83 }
84
array(const ArrayType & m)85 template<typename ArrayType> void array(const ArrayType& m)
86 {
87 typedef typename ArrayType::Scalar Scalar;
88 typedef typename ArrayType::RealScalar RealScalar;
89 typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
90 typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
91
92 Index rows = m.rows();
93 Index cols = m.cols();
94
95 ArrayType m1 = ArrayType::Random(rows, cols),
96 m2 = ArrayType::Random(rows, cols),
97 m3(rows, cols);
98 ArrayType m4 = m1; // copy constructor
99 VERIFY_IS_APPROX(m1, m4);
100
101 ColVectorType cv1 = ColVectorType::Random(rows);
102 RowVectorType rv1 = RowVectorType::Random(cols);
103
104 Scalar s1 = internal::random<Scalar>(),
105 s2 = internal::random<Scalar>();
106
107 // scalar addition
108 VERIFY_IS_APPROX(m1 + s1, s1 + m1);
109 VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
110 VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
111 VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
112 VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
113 VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
114 m3 = m1;
115 m3 += s2;
116 VERIFY_IS_APPROX(m3, m1 + s2);
117 m3 = m1;
118 m3 -= s1;
119 VERIFY_IS_APPROX(m3, m1 - s1);
120
121 // scalar operators via Maps
122 m3 = m1;
123 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
124 VERIFY_IS_APPROX(m1, m3 - m2);
125
126 m3 = m1;
127 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
128 VERIFY_IS_APPROX(m1, m3 + m2);
129
130 m3 = m1;
131 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
132 VERIFY_IS_APPROX(m1, m3 * m2);
133
134 m3 = m1;
135 m2 = ArrayType::Random(rows,cols);
136 m2 = (m2==0).select(1,m2);
137 ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
138 VERIFY_IS_APPROX(m1, m3 / m2);
139
140 // reductions
141 VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
142 VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
143 using std::abs;
144 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
145 VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
146 if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
147 VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
148 VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
149
150 // vector-wise ops
151 m3 = m1;
152 VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
153 m3 = m1;
154 VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
155 m3 = m1;
156 VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
157 m3 = m1;
158 VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
159
160 // Conversion from scalar
161 VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
162 VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
163 VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
164 typedef Array<Scalar,
165 ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
166 ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
167 ArrayType::Options> FixedArrayType;
168 {
169 FixedArrayType f1(s1);
170 VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
171 FixedArrayType f2(numext::real(s1));
172 VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
173 FixedArrayType f3((int)100*numext::real(s1));
174 VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
175 f1.setRandom();
176 FixedArrayType f4(f1.data());
177 VERIFY_IS_APPROX(f4, f1);
178 }
179 #if EIGEN_HAS_CXX11
180 {
181 FixedArrayType f1{s1};
182 VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
183 FixedArrayType f2{numext::real(s1)};
184 VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
185 FixedArrayType f3{(int)100*numext::real(s1)};
186 VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
187 f1.setRandom();
188 FixedArrayType f4{f1.data()};
189 VERIFY_IS_APPROX(f4, f1);
190 }
191 #endif
192
193 // pow
194 VERIFY_IS_APPROX(m1.pow(2), m1.square());
195 VERIFY_IS_APPROX(pow(m1,2), m1.square());
196 VERIFY_IS_APPROX(m1.pow(3), m1.cube());
197 VERIFY_IS_APPROX(pow(m1,3), m1.cube());
198 VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
199 VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
200 ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
201 VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
202 VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
203 VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
204 VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
205 VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
206 VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
207 VERIFY_IS_APPROX(Eigen::pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
208
209 // Check possible conflicts with 1D ctor
210 typedef Array<Scalar, Dynamic, 1> OneDArrayType;
211 {
212 OneDArrayType o1(rows);
213 VERIFY(o1.size()==rows);
214 OneDArrayType o2(static_cast<int>(rows));
215 VERIFY(o2.size()==rows);
216 }
217 #if EIGEN_HAS_CXX11
218 {
219 OneDArrayType o1{rows};
220 VERIFY(o1.size()==rows);
221 OneDArrayType o4{int(rows)};
222 VERIFY(o4.size()==rows);
223 }
224 #endif
225 // Check possible conflicts with 2D ctor
226 typedef Array<Scalar, Dynamic, Dynamic> TwoDArrayType;
227 typedef Array<Scalar, 2, 1> ArrayType2;
228 {
229 TwoDArrayType o1(rows,cols);
230 VERIFY(o1.rows()==rows);
231 VERIFY(o1.cols()==cols);
232 TwoDArrayType o2(static_cast<int>(rows),static_cast<int>(cols));
233 VERIFY(o2.rows()==rows);
234 VERIFY(o2.cols()==cols);
235
236 ArrayType2 o3(rows,cols);
237 VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
238 ArrayType2 o4(static_cast<int>(rows),static_cast<int>(cols));
239 VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
240 }
241 #if EIGEN_HAS_CXX11
242 {
243 TwoDArrayType o1{rows,cols};
244 VERIFY(o1.rows()==rows);
245 VERIFY(o1.cols()==cols);
246 TwoDArrayType o2{int(rows),int(cols)};
247 VERIFY(o2.rows()==rows);
248 VERIFY(o2.cols()==cols);
249
250 ArrayType2 o3{rows,cols};
251 VERIFY(o3(0)==Scalar(rows) && o3(1)==Scalar(cols));
252 ArrayType2 o4{int(rows),int(cols)};
253 VERIFY(o4(0)==Scalar(rows) && o4(1)==Scalar(cols));
254 }
255 #endif
256 }
257
comparisons(const ArrayType & m)258 template<typename ArrayType> void comparisons(const ArrayType& m)
259 {
260 using std::abs;
261 typedef typename ArrayType::Scalar Scalar;
262 typedef typename NumTraits<Scalar>::Real RealScalar;
263
264 Index rows = m.rows();
265 Index cols = m.cols();
266
267 Index r = internal::random<Index>(0, rows-1),
268 c = internal::random<Index>(0, cols-1);
269
270 ArrayType m1 = ArrayType::Random(rows, cols),
271 m2 = ArrayType::Random(rows, cols),
272 m3(rows, cols),
273 m4 = m1;
274
275 m4 = (m4.abs()==Scalar(0)).select(1,m4);
276
277 VERIFY(((m1 + Scalar(1)) > m1).all());
278 VERIFY(((m1 - Scalar(1)) < m1).all());
279 if (rows*cols>1)
280 {
281 m3 = m1;
282 m3(r,c) += 1;
283 VERIFY(! (m1 < m3).all() );
284 VERIFY(! (m1 > m3).all() );
285 }
286 VERIFY(!(m1 > m2 && m1 < m2).any());
287 VERIFY((m1 <= m2 || m1 >= m2).all());
288
289 // comparisons array to scalar
290 VERIFY( (m1 != (m1(r,c)+1) ).any() );
291 VERIFY( (m1 > (m1(r,c)-1) ).any() );
292 VERIFY( (m1 < (m1(r,c)+1) ).any() );
293 VERIFY( (m1 == m1(r,c) ).any() );
294
295 // comparisons scalar to array
296 VERIFY( ( (m1(r,c)+1) != m1).any() );
297 VERIFY( ( (m1(r,c)-1) < m1).any() );
298 VERIFY( ( (m1(r,c)+1) > m1).any() );
299 VERIFY( ( m1(r,c) == m1).any() );
300
301 // test Select
302 VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
303 VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
304 Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
305 for (int j=0; j<cols; ++j)
306 for (int i=0; i<rows; ++i)
307 m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
308 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
309 .select(ArrayType::Zero(rows,cols),m1), m3);
310 // shorter versions:
311 VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
312 .select(0,m1), m3);
313 VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
314 .select(m1,0), m3);
315 // even shorter version:
316 VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
317
318 // count
319 VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
320
321 // and/or
322 VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
323 VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
324 RealScalar a = m1.abs().mean();
325 VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
326
327 typedef Array<Index, Dynamic, 1> ArrayOfIndices;
328
329 // TODO allows colwise/rowwise for array
330 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
331 VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
332 }
333
array_real(const ArrayType & m)334 template<typename ArrayType> void array_real(const ArrayType& m)
335 {
336 using std::abs;
337 using std::sqrt;
338 typedef typename ArrayType::Scalar Scalar;
339 typedef typename NumTraits<Scalar>::Real RealScalar;
340
341 Index rows = m.rows();
342 Index cols = m.cols();
343
344 ArrayType m1 = ArrayType::Random(rows, cols),
345 m2 = ArrayType::Random(rows, cols),
346 m3(rows, cols),
347 m4 = m1;
348
349 m4 = (m4.abs()==Scalar(0)).select(Scalar(1),m4);
350
351 Scalar s1 = internal::random<Scalar>();
352
353 // these tests are mostly to check possible compilation issues with free-functions.
354 VERIFY_IS_APPROX(m1.sin(), sin(m1));
355 VERIFY_IS_APPROX(m1.cos(), cos(m1));
356 VERIFY_IS_APPROX(m1.tan(), tan(m1));
357 VERIFY_IS_APPROX(m1.asin(), asin(m1));
358 VERIFY_IS_APPROX(m1.acos(), acos(m1));
359 VERIFY_IS_APPROX(m1.atan(), atan(m1));
360 VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
361 VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
362 VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
363 #if EIGEN_HAS_CXX11_MATH
364 VERIFY_IS_APPROX(m1.tanh().atanh(), atanh(tanh(m1)));
365 VERIFY_IS_APPROX(m1.sinh().asinh(), asinh(sinh(m1)));
366 VERIFY_IS_APPROX(m1.cosh().acosh(), acosh(cosh(m1)));
367 #endif
368 VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
369
370 VERIFY_IS_APPROX(m1.arg(), arg(m1));
371 VERIFY_IS_APPROX(m1.round(), round(m1));
372 VERIFY_IS_APPROX(m1.rint(), rint(m1));
373 VERIFY_IS_APPROX(m1.floor(), floor(m1));
374 VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
375 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
376 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
377 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
378 VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
379 VERIFY_IS_APPROX(m1.abs(), abs(m1));
380 VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
381 VERIFY_IS_APPROX(m1.square(), square(m1));
382 VERIFY_IS_APPROX(m1.cube(), cube(m1));
383 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
384 VERIFY_IS_APPROX(m1.sign(), sign(m1));
385 VERIFY((m1.sqrt().sign().isNaN() == (Eigen::isnan)(sign(sqrt(m1)))).all());
386
387 // avoid inf and NaNs so verification doesn't fail
388 m3 = m4.abs();
389 VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m3)));
390 VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m3)));
391 VERIFY_IS_APPROX(rsqrt(m3), Scalar(1)/sqrt(abs(m3)));
392 VERIFY_IS_APPROX(m3.log(), log(m3));
393 VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
394 VERIFY_IS_APPROX(m3.log10(), log10(m3));
395 VERIFY_IS_APPROX(m3.log2(), log2(m3));
396
397
398 VERIFY((!(m1>m2) == (m1<=m2)).all());
399
400 VERIFY_IS_APPROX(sin(m1.asin()), m1);
401 VERIFY_IS_APPROX(cos(m1.acos()), m1);
402 VERIFY_IS_APPROX(tan(m1.atan()), m1);
403 VERIFY_IS_APPROX(sinh(m1), Scalar(0.5)*(exp(m1)-exp(-m1)));
404 VERIFY_IS_APPROX(cosh(m1), Scalar(0.5)*(exp(m1)+exp(-m1)));
405 VERIFY_IS_APPROX(tanh(m1), (Scalar(0.5)*(exp(m1)-exp(-m1)))/(Scalar(0.5)*(exp(m1)+exp(-m1))));
406 VERIFY_IS_APPROX(logistic(m1), (Scalar(1)/(Scalar(1)+exp(-m1))));
407 VERIFY_IS_APPROX(arg(m1), ((m1<Scalar(0)).template cast<Scalar>())*Scalar(std::acos(Scalar(-1))));
408 VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
409 VERIFY((rint(m1) <= ceil(m1) && rint(m1) >= floor(m1)).all());
410 VERIFY(((ceil(m1) - round(m1)) <= Scalar(0.5) || (round(m1) - floor(m1)) <= Scalar(0.5)).all());
411 VERIFY(((ceil(m1) - round(m1)) <= Scalar(1.0) && (round(m1) - floor(m1)) <= Scalar(1.0)).all());
412 VERIFY(((ceil(m1) - rint(m1)) <= Scalar(0.5) || (rint(m1) - floor(m1)) <= Scalar(0.5)).all());
413 VERIFY(((ceil(m1) - rint(m1)) <= Scalar(1.0) && (rint(m1) - floor(m1)) <= Scalar(1.0)).all());
414 VERIFY((Eigen::isnan)((m1*Scalar(0))/Scalar(0)).all());
415 VERIFY((Eigen::isinf)(m4/Scalar(0)).all());
416 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*Scalar(0)/Scalar(0))) && (!(Eigen::isfinite)(m4/Scalar(0)))).all());
417 VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
418 VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
419 VERIFY_IS_APPROX(m3, sqrt(abs2(m3)));
420 VERIFY_IS_APPROX(m1.absolute_difference(m2), (m1 > m2).select(m1 - m2, m2 - m1));
421 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
422 VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
423 VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
424
425 VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
426 VERIFY_IS_APPROX(numext::abs2(Eigen::real(m1)) + numext::abs2(Eigen::imag(m1)), numext::abs2(m1));
427 if(!NumTraits<Scalar>::IsComplex)
428 VERIFY_IS_APPROX(numext::real(m1), m1);
429
430 // shift argument of logarithm so that it is not zero
431 Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
432 VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m3) + smallNumber));
433 VERIFY_IS_APPROX((m3 + smallNumber + Scalar(1)).log() , log1p(abs(m3) + smallNumber));
434
435 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
436 VERIFY_IS_APPROX(m1.exp(), exp(m1));
437 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
438
439 VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
440 VERIFY_IS_APPROX((m3 + smallNumber).exp() - Scalar(1), expm1(abs(m3) + smallNumber));
441
442 VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
443 VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
444
445 VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
446 VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
447
448 // Avoid inf and NaN.
449 m3 = (m1.square()<NumTraits<Scalar>::epsilon()).select(Scalar(1),m3);
450 VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
451 pow_test<Scalar>();
452
453 VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10)));
454 VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2)));
455
456 // scalar by array division
457 const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
458 s1 += Scalar(tiny);
459 m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
460 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
461
462 // check inplace transpose
463 m3 = m1;
464 m3.transposeInPlace();
465 VERIFY_IS_APPROX(m3, m1.transpose());
466 m3.transposeInPlace();
467 VERIFY_IS_APPROX(m3, m1);
468 }
469
array_complex(const ArrayType & m)470 template<typename ArrayType> void array_complex(const ArrayType& m)
471 {
472 typedef typename ArrayType::Scalar Scalar;
473 typedef typename NumTraits<Scalar>::Real RealScalar;
474
475 Index rows = m.rows();
476 Index cols = m.cols();
477
478 ArrayType m1 = ArrayType::Random(rows, cols),
479 m2(rows, cols),
480 m4 = m1;
481
482 m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
483 m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
484
485 Array<RealScalar, -1, -1> m3(rows, cols);
486
487 for (Index i = 0; i < m.rows(); ++i)
488 for (Index j = 0; j < m.cols(); ++j)
489 m2(i,j) = sqrt(m1(i,j));
490
491 // these tests are mostly to check possible compilation issues with free-functions.
492 VERIFY_IS_APPROX(m1.sin(), sin(m1));
493 VERIFY_IS_APPROX(m1.cos(), cos(m1));
494 VERIFY_IS_APPROX(m1.tan(), tan(m1));
495 VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
496 VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
497 VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
498 VERIFY_IS_APPROX(m1.logistic(), logistic(m1));
499 VERIFY_IS_APPROX(m1.arg(), arg(m1));
500 VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
501 VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
502 VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
503 VERIFY_IS_APPROX(m4.inverse(), inverse(m4));
504 VERIFY_IS_APPROX(m1.log(), log(m1));
505 VERIFY_IS_APPROX(m1.log10(), log10(m1));
506 VERIFY_IS_APPROX(m1.log2(), log2(m1));
507 VERIFY_IS_APPROX(m1.abs(), abs(m1));
508 VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
509 VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
510 VERIFY_IS_APPROX(m1.square(), square(m1));
511 VERIFY_IS_APPROX(m1.cube(), cube(m1));
512 VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
513 VERIFY_IS_APPROX(m1.sign(), sign(m1));
514
515
516 VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
517 VERIFY_IS_APPROX(m1.exp(), exp(m1));
518 VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
519
520 VERIFY_IS_APPROX(m1.expm1(), expm1(m1));
521 VERIFY_IS_APPROX(expm1(m1), exp(m1) - 1.);
522 // Check for larger magnitude complex numbers that expm1 matches exp - 1.
523 VERIFY_IS_APPROX(expm1(10. * m1), exp(10. * m1) - 1.);
524
525 VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
526 VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
527 VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
528 VERIFY_IS_APPROX(logistic(m1), (1.0/(1.0 + exp(-m1))));
529
530 for (Index i = 0; i < m.rows(); ++i)
531 for (Index j = 0; j < m.cols(); ++j)
532 m3(i,j) = std::atan2(m1(i,j).imag(), m1(i,j).real());
533 VERIFY_IS_APPROX(arg(m1), m3);
534
535 std::complex<RealScalar> zero(0.0,0.0);
536 VERIFY((Eigen::isnan)(m1*zero/zero).all());
537 #if EIGEN_COMP_MSVC
538 // msvc complex division is not robust
539 VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
540 #else
541 #if EIGEN_COMP_CLANG
542 // clang's complex division is notoriously broken too
543 if((numext::isinf)(m4(0,0)/RealScalar(0))) {
544 #endif
545 VERIFY((Eigen::isinf)(m4/zero).all());
546 #if EIGEN_COMP_CLANG
547 }
548 else
549 {
550 VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
551 }
552 #endif
553 #endif // MSVC
554
555 VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
556
557 VERIFY_IS_APPROX(inverse(inverse(m4)),m4);
558 VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
559 VERIFY_IS_APPROX(abs(m1), sqrt(square(m1.real())+square(m1.imag())));
560 VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
561 VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
562 VERIFY_IS_APPROX(log2(m1), log(m1)/log(2));
563
564 VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
565 VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
566
567 // scalar by array division
568 Scalar s1 = internal::random<Scalar>();
569 const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
570 s1 += Scalar(tiny);
571 m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
572 VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
573
574 // check inplace transpose
575 m2 = m1;
576 m2.transposeInPlace();
577 VERIFY_IS_APPROX(m2, m1.transpose());
578 m2.transposeInPlace();
579 VERIFY_IS_APPROX(m2, m1);
580 // Check vectorized inplace transpose.
581 ArrayType m5 = ArrayType::Random(131, 131);
582 ArrayType m6 = m5;
583 m6.transposeInPlace();
584 VERIFY_IS_APPROX(m6, m5.transpose());
585 }
586
min_max(const ArrayType & m)587 template<typename ArrayType> void min_max(const ArrayType& m)
588 {
589 typedef typename ArrayType::Scalar Scalar;
590
591 Index rows = m.rows();
592 Index cols = m.cols();
593
594 ArrayType m1 = ArrayType::Random(rows, cols);
595
596 // min/max with array
597 Scalar maxM1 = m1.maxCoeff();
598 Scalar minM1 = m1.minCoeff();
599
600 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
601 VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
602
603 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
604 VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
605
606 // min/max with scalar input
607 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
608 VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
609
610 VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
611 VERIFY_IS_APPROX(m1, (m1.max)( minM1));
612
613
614 // min/max with various NaN propagation options.
615 if (m1.size() > 1 && !NumTraits<Scalar>::IsInteger) {
616 m1(0,0) = NumTraits<Scalar>::quiet_NaN();
617 maxM1 = m1.template maxCoeff<PropagateNaN>();
618 minM1 = m1.template minCoeff<PropagateNaN>();
619 VERIFY((numext::isnan)(maxM1));
620 VERIFY((numext::isnan)(minM1));
621
622 maxM1 = m1.template maxCoeff<PropagateNumbers>();
623 minM1 = m1.template minCoeff<PropagateNumbers>();
624 VERIFY(!(numext::isnan)(maxM1));
625 VERIFY(!(numext::isnan)(minM1));
626 }
627 }
628
629 template<int N>
630 struct shift_left {
631 template<typename Scalar>
operator ()shift_left632 Scalar operator()(const Scalar& v) const {
633 return v << N;
634 }
635 };
636
637 template<int N>
638 struct arithmetic_shift_right {
639 template<typename Scalar>
operator ()arithmetic_shift_right640 Scalar operator()(const Scalar& v) const {
641 return v >> N;
642 }
643 };
644
array_integer(const ArrayType & m)645 template<typename ArrayType> void array_integer(const ArrayType& m)
646 {
647 Index rows = m.rows();
648 Index cols = m.cols();
649
650 ArrayType m1 = ArrayType::Random(rows, cols),
651 m2(rows, cols);
652
653 m2 = m1.template shiftLeft<2>();
654 VERIFY( (m2 == m1.unaryExpr(shift_left<2>())).all() );
655 m2 = m1.template shiftLeft<9>();
656 VERIFY( (m2 == m1.unaryExpr(shift_left<9>())).all() );
657
658 m2 = m1.template shiftRight<2>();
659 VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<2>())).all() );
660 m2 = m1.template shiftRight<9>();
661 VERIFY( (m2 == m1.unaryExpr(arithmetic_shift_right<9>())).all() );
662 }
663
EIGEN_DECLARE_TEST(array_cwise)664 EIGEN_DECLARE_TEST(array_cwise)
665 {
666 for(int i = 0; i < g_repeat; i++) {
667 CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
668 CALL_SUBTEST_2( array(Array22f()) );
669 CALL_SUBTEST_3( array(Array44d()) );
670 CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
671 CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
672 CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
673 CALL_SUBTEST_6( array(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
674 CALL_SUBTEST_6( array_integer(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
675 CALL_SUBTEST_6( array_integer(Array<Index,Dynamic,Dynamic>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
676 }
677 for(int i = 0; i < g_repeat; i++) {
678 CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
679 CALL_SUBTEST_2( comparisons(Array22f()) );
680 CALL_SUBTEST_3( comparisons(Array44d()) );
681 CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
682 CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
683 }
684 for(int i = 0; i < g_repeat; i++) {
685 CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
686 CALL_SUBTEST_2( min_max(Array22f()) );
687 CALL_SUBTEST_3( min_max(Array44d()) );
688 CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
689 CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
690 }
691 for(int i = 0; i < g_repeat; i++) {
692 CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
693 CALL_SUBTEST_2( array_real(Array22f()) );
694 CALL_SUBTEST_3( array_real(Array44d()) );
695 CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
696 CALL_SUBTEST_7( array_real(Array<Eigen::half, 32, 32>()) );
697 CALL_SUBTEST_8( array_real(Array<Eigen::bfloat16, 32, 32>()) );
698 }
699 for(int i = 0; i < g_repeat; i++) {
700 CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
701 }
702
703 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
704 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
705 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
706 typedef CwiseUnaryOp<internal::scalar_abs_op<double>, ArrayXd > Xpr;
707 VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
708 ArrayBase<Xpr>
709 >::value));
710 }
711