Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/array.cpp b/test/array.cpp
new file mode 100644
index 0000000..68f6b3d
--- /dev/null
+++ b/test/array.cpp
@@ -0,0 +1,308 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+
+template<typename ArrayType> void array(const ArrayType& m)
+{
+ typedef typename ArrayType::Index Index;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
+ typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols);
+
+ ColVectorType cv1 = ColVectorType::Random(rows);
+ RowVectorType rv1 = RowVectorType::Random(cols);
+
+ Scalar s1 = internal::random<Scalar>(),
+ s2 = internal::random<Scalar>();
+
+ // scalar addition
+ VERIFY_IS_APPROX(m1 + s1, s1 + m1);
+ VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
+ VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
+ VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
+ VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
+ VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
+ m3 = m1;
+ m3 += s2;
+ VERIFY_IS_APPROX(m3, m1 + s2);
+ m3 = m1;
+ m3 -= s1;
+ VERIFY_IS_APPROX(m3, m1 - s1);
+
+ // scalar operators via Maps
+ m3 = m1;
+ ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m1, m3 - m2);
+
+ m3 = m1;
+ ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m1, m3 + m2);
+
+ m3 = m1;
+ ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m1, m3 * m2);
+
+ m3 = m1;
+ m2 = ArrayType::Random(rows,cols);
+ m2 = (m2==0).select(1,m2);
+ ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
+ VERIFY_IS_APPROX(m1, m3 / m2);
+
+ // reductions
+ VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
+ VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
+ using std::abs;
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
+ VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
+ if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
+ VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
+ VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
+
+ // vector-wise ops
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
+ m3 = m1;
+ VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
+}
+
+template<typename ArrayType> void comparisons(const ArrayType& m)
+{
+ using std::abs;
+ typedef typename ArrayType::Index Index;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ Index r = internal::random<Index>(0, rows-1),
+ c = internal::random<Index>(0, cols-1);
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols);
+
+ VERIFY(((m1 + Scalar(1)) > m1).all());
+ VERIFY(((m1 - Scalar(1)) < m1).all());
+ if (rows*cols>1)
+ {
+ m3 = m1;
+ m3(r,c) += 1;
+ VERIFY(! (m1 < m3).all() );
+ VERIFY(! (m1 > m3).all() );
+ }
+ VERIFY(!(m1 > m2 && m1 < m2).any());
+ VERIFY((m1 <= m2 || m1 >= m2).all());
+
+ // comparisons to scalar
+ VERIFY( (m1 != (m1(r,c)+1) ).any() );
+ VERIFY( (m1 > (m1(r,c)-1) ).any() );
+ VERIFY( (m1 < (m1(r,c)+1) ).any() );
+ VERIFY( (m1 == m1(r,c) ).any() );
+
+ // test Select
+ VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
+ VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
+ Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
+ for (int j=0; j<cols; ++j)
+ for (int i=0; i<rows; ++i)
+ m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
+ VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
+ .select(ArrayType::Zero(rows,cols),m1), m3);
+ // shorter versions:
+ VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
+ .select(0,m1), m3);
+ VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
+ .select(m1,0), m3);
+ // even shorter version:
+ VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
+
+ // count
+ VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
+
+ // and/or
+ VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
+ VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
+ RealScalar a = m1.abs().mean();
+ VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
+
+ typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
+
+ // TODO allows colwise/rowwise for array
+ VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
+ VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
+}
+
+template<typename ArrayType> void array_real(const ArrayType& m)
+{
+ using std::abs;
+ using std::sqrt;
+ typedef typename ArrayType::Index Index;
+ typedef typename ArrayType::Scalar Scalar;
+ typedef typename NumTraits<Scalar>::Real RealScalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2 = ArrayType::Random(rows, cols),
+ m3(rows, cols);
+
+ Scalar s1 = internal::random<Scalar>();
+
+ // these tests are mostly to check possible compilation issues.
+ VERIFY_IS_APPROX(m1.sin(), sin(m1));
+ VERIFY_IS_APPROX(m1.cos(), cos(m1));
+ VERIFY_IS_APPROX(m1.asin(), asin(m1));
+ VERIFY_IS_APPROX(m1.acos(), acos(m1));
+ VERIFY_IS_APPROX(m1.tan(), tan(m1));
+
+ VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
+
+ VERIFY_IS_APPROX(m1.abs().sqrt(), sqrt(abs(m1)));
+ VERIFY_IS_APPROX(m1.abs(), sqrt(numext::abs2(m1)));
+
+ VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
+ VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
+ if(!NumTraits<Scalar>::IsComplex)
+ VERIFY_IS_APPROX(numext::real(m1), m1);
+
+ // shift argument of logarithm so that it is not zero
+ Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
+ VERIFY_IS_APPROX((m1.abs() + smallNumber).log() , log(abs(m1) + smallNumber));
+
+ VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
+ VERIFY_IS_APPROX(m1.exp(), exp(m1));
+ VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
+
+ VERIFY_IS_APPROX(m1.pow(2), m1.square());
+ VERIFY_IS_APPROX(pow(m1,2), m1.square());
+
+ ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
+ VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
+
+ m3 = m1.abs();
+ VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
+ VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
+
+ // scalar by array division
+ const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
+ s1 += Scalar(tiny);
+ m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
+ VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
+
+ // check inplace transpose
+ m3 = m1;
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1.transpose());
+ m3.transposeInPlace();
+ VERIFY_IS_APPROX(m3,m1);
+}
+
+template<typename ArrayType> void array_complex(const ArrayType& m)
+{
+ typedef typename ArrayType::Index Index;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols),
+ m2(rows, cols);
+
+ for (Index i = 0; i < m.rows(); ++i)
+ for (Index j = 0; j < m.cols(); ++j)
+ m2(i,j) = sqrt(m1(i,j));
+
+ VERIFY_IS_APPROX(m1.sqrt(), m2);
+ VERIFY_IS_APPROX(m1.sqrt(), Eigen::sqrt(m1));
+}
+
+template<typename ArrayType> void min_max(const ArrayType& m)
+{
+ typedef typename ArrayType::Index Index;
+ typedef typename ArrayType::Scalar Scalar;
+
+ Index rows = m.rows();
+ Index cols = m.cols();
+
+ ArrayType m1 = ArrayType::Random(rows, cols);
+
+ // min/max with array
+ Scalar maxM1 = m1.maxCoeff();
+ Scalar minM1 = m1.minCoeff();
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
+ VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
+ VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
+
+ // min/max with scalar input
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
+ VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
+
+ VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
+ VERIFY_IS_APPROX(m1, (m1.max)( minM1));
+
+}
+
+void test_array()
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( array(Array22f()) );
+ CALL_SUBTEST_3( array(Array44d()) );
+ CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( comparisons(Array22f()) );
+ CALL_SUBTEST_3( comparisons(Array44d()) );
+ CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( min_max(Array22f()) );
+ CALL_SUBTEST_3( min_max(Array44d()) );
+ CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
+ CALL_SUBTEST_2( array_real(Array22f()) );
+ CALL_SUBTEST_3( array_real(Array44d()) );
+ CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
+ }
+
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
+ typedef CwiseUnaryOp<internal::scalar_sum_op<double>, ArrayXd > Xpr;
+ VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
+ ArrayBase<Xpr>
+ >::value));
+}