array_cwise.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) 2008-2009 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 
13 // Test the corner cases of pow(x, y) for real types.
14 template<typename Scalar>
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 
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 
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 
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 
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 
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>
632  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>
640  Scalar operator()(const Scalar& v) const {
641  return v >> N;
642  }
643 };
644 
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 
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 }
gtsam.examples.DogLegOptimizerExample.int
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autogenerated on Sat Nov 16 2024 04:01:49