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64fcfd314f
This slightly complexifies the type of the expressions and implies that we now have to distinguish between scalar*expr and expr*scalar to catch scalar-multiple expression (e.g., see BlasUtil.h), but this brings several advantages: - it makes it clear on each side the scalar is applied, - it clearly reflects that we are dealing with a binary-expression, - the complexity of the type is hidden through macros defined at the end of Macros.h, - distinguishing between "scalar op expr" and "expr op scalar" is important to support non commutative fields (like quaternions) - "scalar op expr" is now fully equivalent to "ConstantExpr(scalar) op expr" - scalar_multiple_op, scalar_quotient1_op and scalar_quotient2_op are not used anymore in officially supported modules (still used in Tensor)
818 lines
34 KiB
C++
818 lines
34 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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template<typename ArrayType> void array(const ArrayType& m)
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{
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
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typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols);
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ArrayType m4 = m1; // copy constructor
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VERIFY_IS_APPROX(m1, m4);
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ColVectorType cv1 = ColVectorType::Random(rows);
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RowVectorType rv1 = RowVectorType::Random(cols);
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Scalar s1 = internal::random<Scalar>(),
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s2 = internal::random<Scalar>();
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// scalar addition
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VERIFY_IS_APPROX(m1 + s1, s1 + m1);
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VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
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VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
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VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
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VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
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VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
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m3 = m1;
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m3 += s2;
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VERIFY_IS_APPROX(m3, m1 + s2);
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m3 = m1;
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m3 -= s1;
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VERIFY_IS_APPROX(m3, m1 - s1);
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// scalar operators via Maps
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 - m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 + m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 * m2);
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m3 = m1;
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m2 = ArrayType::Random(rows,cols);
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m2 = (m2==0).select(1,m2);
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 / m2);
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// reductions
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VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
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VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
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using std::abs;
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
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if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
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VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
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VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar,Scalar>()));
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// vector-wise ops
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
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// Conversion from scalar
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VERIFY_IS_APPROX((m3 = s1), ArrayType::Constant(rows,cols,s1));
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VERIFY_IS_APPROX((m3 = 1), ArrayType::Constant(rows,cols,1));
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VERIFY_IS_APPROX((m3.topLeftCorner(rows,cols) = 1), ArrayType::Constant(rows,cols,1));
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typedef Array<Scalar,
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ArrayType::RowsAtCompileTime==Dynamic?2:ArrayType::RowsAtCompileTime,
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ArrayType::ColsAtCompileTime==Dynamic?2:ArrayType::ColsAtCompileTime,
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ArrayType::Options> FixedArrayType;
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FixedArrayType f1(s1);
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VERIFY_IS_APPROX(f1, FixedArrayType::Constant(s1));
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FixedArrayType f2(numext::real(s1));
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VERIFY_IS_APPROX(f2, FixedArrayType::Constant(numext::real(s1)));
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FixedArrayType f3((int)100*numext::real(s1));
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VERIFY_IS_APPROX(f3, FixedArrayType::Constant((int)100*numext::real(s1)));
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f1.setRandom();
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FixedArrayType f4(f1.data());
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VERIFY_IS_APPROX(f4, f1);
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// Check possible conflicts with 1D ctor
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typedef Array<Scalar, Dynamic, 1> OneDArrayType;
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OneDArrayType o1(rows);
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VERIFY(o1.size()==rows);
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OneDArrayType o4((int)rows);
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VERIFY(o4.size()==rows);
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}
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template<typename ArrayType> void comparisons(const ArrayType& m)
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{
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using std::abs;
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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Index r = internal::random<Index>(0, rows-1),
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c = internal::random<Index>(0, cols-1);
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols),
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m4 = m1;
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m4 = (m4.abs()==Scalar(0)).select(1,m4);
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VERIFY(((m1 + Scalar(1)) > m1).all());
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VERIFY(((m1 - Scalar(1)) < m1).all());
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if (rows*cols>1)
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{
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m3 = m1;
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m3(r,c) += 1;
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VERIFY(! (m1 < m3).all() );
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VERIFY(! (m1 > m3).all() );
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}
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VERIFY(!(m1 > m2 && m1 < m2).any());
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VERIFY((m1 <= m2 || m1 >= m2).all());
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// comparisons array to scalar
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VERIFY( (m1 != (m1(r,c)+1) ).any() );
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VERIFY( (m1 > (m1(r,c)-1) ).any() );
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VERIFY( (m1 < (m1(r,c)+1) ).any() );
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VERIFY( (m1 == m1(r,c) ).any() );
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// comparisons scalar to array
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VERIFY( ( (m1(r,c)+1) != m1).any() );
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VERIFY( ( (m1(r,c)-1) < m1).any() );
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VERIFY( ( (m1(r,c)+1) > m1).any() );
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VERIFY( ( m1(r,c) == m1).any() );
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// test Select
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VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
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VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
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Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
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for (int j=0; j<cols; ++j)
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for (int i=0; i<rows; ++i)
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m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
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VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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.select(ArrayType::Zero(rows,cols),m1), m3);
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// shorter versions:
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VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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.select(0,m1), m3);
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VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
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.select(m1,0), m3);
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// even shorter version:
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VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
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// count
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VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
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// and/or
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VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
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VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
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RealScalar a = m1.abs().mean();
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VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
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typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
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// TODO allows colwise/rowwise for array
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VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
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VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
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}
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template<typename ArrayType> void array_real(const ArrayType& m)
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{
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using std::abs;
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using std::sqrt;
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols),
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m4 = m1;
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m4 = (m4.abs()==Scalar(0)).select(1,m4);
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Scalar s1 = internal::random<Scalar>();
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// these tests are mostly to check possible compilation issues with free-functions.
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VERIFY_IS_APPROX(m1.sin(), sin(m1));
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VERIFY_IS_APPROX(m1.cos(), cos(m1));
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VERIFY_IS_APPROX(m1.tan(), tan(m1));
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VERIFY_IS_APPROX(m1.asin(), asin(m1));
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VERIFY_IS_APPROX(m1.acos(), acos(m1));
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VERIFY_IS_APPROX(m1.atan(), atan(m1));
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VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
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VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
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VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
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#if EIGEN_HAS_C99_MATH
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VERIFY_IS_APPROX(m1.lgamma(), lgamma(m1));
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VERIFY_IS_APPROX(m1.digamma(), digamma(m1));
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VERIFY_IS_APPROX(m1.erf(), erf(m1));
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VERIFY_IS_APPROX(m1.erfc(), erfc(m1));
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#endif // EIGEN_HAS_C99_MATH
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VERIFY_IS_APPROX(m1.arg(), arg(m1));
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VERIFY_IS_APPROX(m1.round(), round(m1));
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VERIFY_IS_APPROX(m1.floor(), floor(m1));
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VERIFY_IS_APPROX(m1.ceil(), ceil(m1));
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VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
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VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
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VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
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VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
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VERIFY_IS_APPROX(m1.abs(), abs(m1));
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VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
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VERIFY_IS_APPROX(m1.square(), square(m1));
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VERIFY_IS_APPROX(m1.cube(), cube(m1));
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VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
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VERIFY_IS_APPROX(m1.sign(), sign(m1));
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// avoid NaNs with abs() so verification doesn't fail
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m3 = m1.abs();
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VERIFY_IS_APPROX(m3.sqrt(), sqrt(abs(m1)));
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VERIFY_IS_APPROX(m3.rsqrt(), Scalar(1)/sqrt(abs(m1)));
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VERIFY_IS_APPROX(m3.log(), log(m3));
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VERIFY_IS_APPROX(m3.log1p(), log1p(m3));
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VERIFY_IS_APPROX(m3.log10(), log10(m3));
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VERIFY((!(m1>m2) == (m1<=m2)).all());
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VERIFY_IS_APPROX(sin(m1.asin()), m1);
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VERIFY_IS_APPROX(cos(m1.acos()), m1);
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VERIFY_IS_APPROX(tan(m1.atan()), m1);
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VERIFY_IS_APPROX(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
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VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
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VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
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VERIFY_IS_APPROX(arg(m1), ((m1<0).template cast<Scalar>())*std::acos(-1.0));
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VERIFY((round(m1) <= ceil(m1) && round(m1) >= floor(m1)).all());
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VERIFY((Eigen::isnan)((m1*0.0)/0.0).all());
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VERIFY((Eigen::isinf)(m4/0.0).all());
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VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*0.0/0.0)) && (!(Eigen::isfinite)(m4/0.0))).all());
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VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
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VERIFY((abs(m1) == m1 || abs(m1) == -m1).all());
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VERIFY_IS_APPROX(m3, sqrt(abs2(m1)));
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VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
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VERIFY_IS_APPROX( m1*m1.sign(),m1.abs());
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VERIFY_IS_APPROX(m1.sign() * m1.abs(), m1);
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VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
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VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
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if(!NumTraits<Scalar>::IsComplex)
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VERIFY_IS_APPROX(numext::real(m1), m1);
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// shift argument of logarithm so that it is not zero
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Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
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VERIFY_IS_APPROX((m3 + smallNumber).log() , log(abs(m1) + smallNumber));
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VERIFY_IS_APPROX((m3 + smallNumber + 1).log() , log1p(abs(m1) + smallNumber));
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VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
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VERIFY_IS_APPROX(m1.exp(), exp(m1));
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VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
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VERIFY_IS_APPROX(m1.pow(2), m1.square());
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VERIFY_IS_APPROX(pow(m1,2), m1.square());
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VERIFY_IS_APPROX(m1.pow(3), m1.cube());
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VERIFY_IS_APPROX(pow(m1,3), m1.cube());
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VERIFY_IS_APPROX((-m1).pow(3), -m1.cube());
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VERIFY_IS_APPROX(pow(2*m1,3), 8*m1.cube());
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ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
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VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
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VERIFY_IS_APPROX(m1.pow(exponents), m1.square());
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VERIFY_IS_APPROX(Eigen::pow(2*m1,exponents), 4*m1.square());
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VERIFY_IS_APPROX((2*m1).pow(exponents), 4*m1.square());
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VERIFY_IS_APPROX(Eigen::pow(m1,2*exponents), m1.square().square());
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VERIFY_IS_APPROX(m1.pow(2*exponents), m1.square().square());
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VERIFY_IS_APPROX(pow(m1(0,0), exponents), ArrayType::Constant(rows,cols,m1(0,0)*m1(0,0)));
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VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
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VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
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VERIFY_IS_APPROX(m3.pow(RealScalar(-0.5)), m3.rsqrt());
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VERIFY_IS_APPROX(pow(m3,RealScalar(-0.5)), m3.rsqrt());
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VERIFY_IS_APPROX(log10(m3), log(m3)/log(10));
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// scalar by array division
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const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
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s1 += Scalar(tiny);
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m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
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VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
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#if EIGEN_HAS_C99_MATH
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// check special functions (comparing against numpy implementation)
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if (!NumTraits<Scalar>::IsComplex)
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{
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{
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// Test various propreties of igamma & igammac. These are normalized
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// gamma integrals where
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// igammac(a, x) = Gamma(a, x) / Gamma(a)
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// igamma(a, x) = gamma(a, x) / Gamma(a)
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// where Gamma and gamma are considered the standard unnormalized
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// upper and lower incomplete gamma functions, respectively.
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ArrayType a = m1.abs() + 2;
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ArrayType x = m2.abs() + 2;
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ArrayType zero = ArrayType::Zero(rows, cols);
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ArrayType one = ArrayType::Constant(rows, cols, Scalar(1.0));
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ArrayType a_m1 = a - one;
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ArrayType Gamma_a_x = Eigen::igammac(a, x) * a.lgamma().exp();
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ArrayType Gamma_a_m1_x = Eigen::igammac(a_m1, x) * a_m1.lgamma().exp();
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ArrayType gamma_a_x = Eigen::igamma(a, x) * a.lgamma().exp();
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ArrayType gamma_a_m1_x = Eigen::igamma(a_m1, x) * a_m1.lgamma().exp();
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// Gamma(a, 0) == Gamma(a)
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VERIFY_IS_APPROX(Eigen::igammac(a, zero), one);
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// Gamma(a, x) + gamma(a, x) == Gamma(a)
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VERIFY_IS_APPROX(Gamma_a_x + gamma_a_x, a.lgamma().exp());
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// Gamma(a, x) == (a - 1) * Gamma(a-1, x) + x^(a-1) * exp(-x)
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VERIFY_IS_APPROX(Gamma_a_x, (a - 1) * Gamma_a_m1_x + x.pow(a-1) * (-x).exp());
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// gamma(a, x) == (a - 1) * gamma(a-1, x) - x^(a-1) * exp(-x)
|
|
VERIFY_IS_APPROX(gamma_a_x, (a - 1) * gamma_a_m1_x - x.pow(a-1) * (-x).exp());
|
|
}
|
|
|
|
// Check exact values of igamma and igammac against a third party calculation.
|
|
Scalar a_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
|
|
Scalar x_s[] = {Scalar(0), Scalar(1), Scalar(1.5), Scalar(4), Scalar(0.0001), Scalar(1000.5)};
|
|
|
|
// location i*6+j corresponds to a_s[i], x_s[j].
|
|
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
|
|
Scalar igamma_s[][6] = {{0.0, nan, nan, nan, nan, nan},
|
|
{0.0, 0.6321205588285578, 0.7768698398515702,
|
|
0.9816843611112658, 9.999500016666262e-05, 1.0},
|
|
{0.0, 0.4275932955291202, 0.608374823728911,
|
|
0.9539882943107686, 7.522076445089201e-07, 1.0},
|
|
{0.0, 0.01898815687615381, 0.06564245437845008,
|
|
0.5665298796332909, 4.166333347221828e-18, 1.0},
|
|
{0.0, 0.9999780593618628, 0.9999899967080838,
|
|
0.9999996219837988, 0.9991370418689945, 1.0},
|
|
{0.0, 0.0, 0.0, 0.0, 0.0, 0.5042041932513908}};
|
|
Scalar igammac_s[][6] = {{nan, nan, nan, nan, nan, nan},
|
|
{1.0, 0.36787944117144233, 0.22313016014842982,
|
|
0.018315638888734182, 0.9999000049998333, 0.0},
|
|
{1.0, 0.5724067044708798, 0.3916251762710878,
|
|
0.04601170568923136, 0.9999992477923555, 0.0},
|
|
{1.0, 0.9810118431238462, 0.9343575456215499,
|
|
0.4334701203667089, 1.0, 0.0},
|
|
{1.0, 2.1940638138146658e-05, 1.0003291916285e-05,
|
|
3.7801620118431334e-07, 0.0008629581310054535,
|
|
0.0},
|
|
{1.0, 1.0, 1.0, 1.0, 1.0, 0.49579580674813944}};
|
|
for (int i = 0; i < 6; ++i) {
|
|
for (int j = 0; j < 6; ++j) {
|
|
if ((std::isnan)(igamma_s[i][j])) {
|
|
VERIFY((std::isnan)(numext::igamma(a_s[i], x_s[j])));
|
|
} else {
|
|
VERIFY_IS_APPROX(numext::igamma(a_s[i], x_s[j]), igamma_s[i][j]);
|
|
}
|
|
|
|
if ((std::isnan)(igammac_s[i][j])) {
|
|
VERIFY((std::isnan)(numext::igammac(a_s[i], x_s[j])));
|
|
} else {
|
|
VERIFY_IS_APPROX(numext::igammac(a_s[i], x_s[j]), igammac_s[i][j]);
|
|
}
|
|
}
|
|
}
|
|
}
|
|
#endif // EIGEN_HAS_C99_MATH
|
|
|
|
// 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;
|
|
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(rows, cols),
|
|
m4 = m1;
|
|
|
|
m4.real() = (m4.real().abs()==RealScalar(0)).select(RealScalar(1),m4.real());
|
|
m4.imag() = (m4.imag().abs()==RealScalar(0)).select(RealScalar(1),m4.imag());
|
|
|
|
Array<RealScalar, -1, -1> m3(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));
|
|
|
|
// these tests are mostly to check possible compilation issues with free-functions.
|
|
VERIFY_IS_APPROX(m1.sin(), sin(m1));
|
|
VERIFY_IS_APPROX(m1.cos(), cos(m1));
|
|
VERIFY_IS_APPROX(m1.tan(), tan(m1));
|
|
VERIFY_IS_APPROX(m1.sinh(), sinh(m1));
|
|
VERIFY_IS_APPROX(m1.cosh(), cosh(m1));
|
|
VERIFY_IS_APPROX(m1.tanh(), tanh(m1));
|
|
VERIFY_IS_APPROX(m1.arg(), arg(m1));
|
|
VERIFY((m1.isNaN() == (Eigen::isnan)(m1)).all());
|
|
VERIFY((m1.isInf() == (Eigen::isinf)(m1)).all());
|
|
VERIFY((m1.isFinite() == (Eigen::isfinite)(m1)).all());
|
|
VERIFY_IS_APPROX(m1.inverse(), inverse(m1));
|
|
VERIFY_IS_APPROX(m1.log(), log(m1));
|
|
VERIFY_IS_APPROX(m1.log10(), log10(m1));
|
|
VERIFY_IS_APPROX(m1.abs(), abs(m1));
|
|
VERIFY_IS_APPROX(m1.abs2(), abs2(m1));
|
|
VERIFY_IS_APPROX(m1.sqrt(), sqrt(m1));
|
|
VERIFY_IS_APPROX(m1.square(), square(m1));
|
|
VERIFY_IS_APPROX(m1.cube(), cube(m1));
|
|
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
|
|
VERIFY_IS_APPROX(m1.sign(), sign(m1));
|
|
|
|
|
|
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(sinh(m1), 0.5*(exp(m1)-exp(-m1)));
|
|
VERIFY_IS_APPROX(cosh(m1), 0.5*(exp(m1)+exp(-m1)));
|
|
VERIFY_IS_APPROX(tanh(m1), (0.5*(exp(m1)-exp(-m1)))/(0.5*(exp(m1)+exp(-m1))));
|
|
|
|
for (Index i = 0; i < m.rows(); ++i)
|
|
for (Index j = 0; j < m.cols(); ++j)
|
|
m3(i,j) = std::atan2(imag(m1(i,j)), real(m1(i,j)));
|
|
VERIFY_IS_APPROX(arg(m1), m3);
|
|
|
|
std::complex<RealScalar> zero(0.0,0.0);
|
|
VERIFY((Eigen::isnan)(m1*zero/zero).all());
|
|
#if EIGEN_COMP_MSVC
|
|
// msvc complex division is not robust
|
|
VERIFY((Eigen::isinf)(m4/RealScalar(0)).all());
|
|
#else
|
|
#if EIGEN_COMP_CLANG
|
|
// clang's complex division is notoriously broken too
|
|
if((numext::isinf)(m4(0,0)/RealScalar(0))) {
|
|
#endif
|
|
VERIFY((Eigen::isinf)(m4/zero).all());
|
|
#if EIGEN_COMP_CLANG
|
|
}
|
|
else
|
|
{
|
|
VERIFY((Eigen::isinf)(m4.real()/zero.real()).all());
|
|
}
|
|
#endif
|
|
#endif // MSVC
|
|
|
|
VERIFY(((Eigen::isfinite)(m1) && (!(Eigen::isfinite)(m1*zero/zero)) && (!(Eigen::isfinite)(m1/zero))).all());
|
|
|
|
VERIFY_IS_APPROX(inverse(inverse(m1)),m1);
|
|
VERIFY_IS_APPROX(conj(m1.conjugate()), m1);
|
|
VERIFY_IS_APPROX(abs(m1), sqrt(square(real(m1))+square(imag(m1))));
|
|
VERIFY_IS_APPROX(abs(m1), sqrt(abs2(m1)));
|
|
VERIFY_IS_APPROX(log10(m1), log(m1)/log(10));
|
|
|
|
VERIFY_IS_APPROX( m1.sign(), -(-m1).sign() );
|
|
VERIFY_IS_APPROX( m1.sign() * m1.abs(), m1);
|
|
|
|
// scalar by array division
|
|
Scalar s1 = internal::random<Scalar>();
|
|
const RealScalar tiny = std::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
|
|
m2 = m1;
|
|
m2.transposeInPlace();
|
|
VERIFY_IS_APPROX(m2, m1.transpose());
|
|
m2.transposeInPlace();
|
|
VERIFY_IS_APPROX(m2, 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));
|
|
|
|
}
|
|
|
|
template<typename X, typename Y>
|
|
void verify_component_wise(const X& x, const Y& y)
|
|
{
|
|
for(Index i=0; i<x.size(); ++i)
|
|
{
|
|
if((numext::isfinite)(y(i)))
|
|
VERIFY_IS_APPROX( x(i), y(i) );
|
|
else if((numext::isnan)(y(i)))
|
|
VERIFY((numext::isnan)(x(i)));
|
|
else
|
|
VERIFY_IS_EQUAL( x(i), y(i) );
|
|
}
|
|
}
|
|
|
|
// check special functions (comparing against numpy implementation)
|
|
template<typename ArrayType> void array_special_functions()
|
|
{
|
|
using std::abs;
|
|
using std::sqrt;
|
|
typedef typename ArrayType::Scalar Scalar;
|
|
typedef typename NumTraits<Scalar>::Real RealScalar;
|
|
|
|
Scalar plusinf = std::numeric_limits<Scalar>::infinity();
|
|
Scalar nan = std::numeric_limits<Scalar>::quiet_NaN();
|
|
|
|
// Check the zeta function against scipy.special.zeta
|
|
{
|
|
ArrayType x(7), q(7), res(7), ref(7);
|
|
x << 1.5, 4, 10.5, 10000.5, 3, 1, 0.9;
|
|
q << 2, 1.5, 3, 1.0001, -2.5, 1.2345, 1.2345;
|
|
ref << 1.61237534869, 0.234848505667, 1.03086757337e-5, 0.367879440865, 0.054102025820864097, plusinf, nan;
|
|
CALL_SUBTEST( verify_component_wise(ref, ref); );
|
|
CALL_SUBTEST( res = x.zeta(q); verify_component_wise(res, ref); );
|
|
CALL_SUBTEST( res = zeta(x,q); verify_component_wise(res, ref); );
|
|
}
|
|
|
|
// digamma
|
|
{
|
|
ArrayType x(7), res(7), ref(7);
|
|
x << 1, 1.5, 4, -10.5, 10000.5, 0, -1;
|
|
ref << -0.5772156649015329, 0.03648997397857645, 1.2561176684318, 2.398239129535781, 9.210340372392849, plusinf, plusinf;
|
|
CALL_SUBTEST( verify_component_wise(ref, ref); );
|
|
|
|
CALL_SUBTEST( res = x.digamma(); verify_component_wise(res, ref); );
|
|
CALL_SUBTEST( res = digamma(x); verify_component_wise(res, ref); );
|
|
}
|
|
|
|
|
|
#if EIGEN_HAS_C99_MATH
|
|
{
|
|
ArrayType n(11), x(11), res(11), ref(11);
|
|
n << 1, 1, 1, 1.5, 17, 31, 28, 8, 42, 147, 170;
|
|
x << 2, 3, 25.5, 1.5, 4.7, 11.8, 17.7, 30.2, 15.8, 54.1, 64;
|
|
ref << 0.644934066848, 0.394934066848, 0.0399946696496, nan, 293.334565435, 0.445487887616, -2.47810300902e-07, -8.29668781082e-09, -0.434562276666, 0.567742190178, -0.0108615497927;
|
|
CALL_SUBTEST( verify_component_wise(ref, ref); );
|
|
|
|
if(sizeof(RealScalar)>=8) { // double
|
|
// Reason for commented line: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
|
|
// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res, ref); );
|
|
CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res, ref); );
|
|
}
|
|
else {
|
|
// CALL_SUBTEST( res = x.polygamma(n); verify_component_wise(res.head(8), ref.head(8)); );
|
|
CALL_SUBTEST( res = polygamma(n,x); verify_component_wise(res.head(8), ref.head(8)); );
|
|
}
|
|
}
|
|
#endif
|
|
|
|
#if EIGEN_HAS_C99_MATH
|
|
{
|
|
// Inputs and ground truth generated with scipy via:
|
|
// a = np.logspace(-3, 3, 5) - 1e-3
|
|
// b = np.logspace(-3, 3, 5) - 1e-3
|
|
// x = np.linspace(-0.1, 1.1, 5)
|
|
// (full_a, full_b, full_x) = np.vectorize(lambda a, b, x: (a, b, x))(*np.ix_(a, b, x))
|
|
// full_a = full_a.flatten().tolist() # same for full_b, full_x
|
|
// v = scipy.special.betainc(full_a, full_b, full_x).flatten().tolist()
|
|
//
|
|
// Note in Eigen, we call betainc with arguments in the order (x, a, b).
|
|
ArrayType a(125);
|
|
ArrayType b(125);
|
|
ArrayType x(125);
|
|
ArrayType v(125);
|
|
ArrayType res(125);
|
|
|
|
a << 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
|
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 999.999;
|
|
|
|
b << 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379, 0.999,
|
|
0.999, 0.999, 0.999, 0.999, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379, 999.999,
|
|
999.999, 999.999, 999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.999, 0.999, 0.999, 0.999,
|
|
0.999, 31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
|
|
999.999, 999.999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.03062277660168379,
|
|
0.03062277660168379, 0.03062277660168379, 0.03062277660168379,
|
|
0.03062277660168379, 0.999, 0.999, 0.999, 0.999, 0.999,
|
|
31.62177660168379, 31.62177660168379, 31.62177660168379,
|
|
31.62177660168379, 31.62177660168379, 999.999, 999.999, 999.999,
|
|
999.999, 999.999;
|
|
|
|
x << -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
|
|
0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
|
|
0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
|
|
0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1,
|
|
-0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8,
|
|
1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
|
|
0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2,
|
|
0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1,
|
|
0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5, 0.8, 1.1, -0.1, 0.2, 0.5,
|
|
0.8, 1.1;
|
|
|
|
v << nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
|
|
nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan, nan,
|
|
nan, nan, nan, 0.47972119876364683, 0.5, 0.5202788012363533, nan, nan,
|
|
0.9518683957740043, 0.9789663010413743, 0.9931729188073435, nan, nan,
|
|
0.999995949033062, 0.9999999999993698, 0.9999999999999999, nan, nan,
|
|
0.9999999999999999, 0.9999999999999999, 0.9999999999999999, nan, nan,
|
|
nan, nan, nan, nan, nan, 0.006827081192655869, 0.0210336989586256,
|
|
0.04813160422599567, nan, nan, 0.20014344256217678, 0.5000000000000001,
|
|
0.7998565574378232, nan, nan, 0.9991401428435834, 0.999999999698403,
|
|
0.9999999999999999, nan, nan, 0.9999999999999999, 0.9999999999999999,
|
|
0.9999999999999999, nan, nan, nan, nan, nan, nan, nan,
|
|
1.0646600232370887e-25, 6.301722877826246e-13, 4.050966937974938e-06,
|
|
nan, nan, 7.864342668429763e-23, 3.015969667594166e-10,
|
|
0.0008598571564165444, nan, nan, 6.031987710123844e-08,
|
|
0.5000000000000007, 0.9999999396801229, nan, nan, 0.9999999999999999,
|
|
0.9999999999999999, 0.9999999999999999, nan, nan, nan, nan, nan, nan,
|
|
nan, 0.0, 7.029920380986636e-306, 2.2450728208591345e-101, nan, nan,
|
|
0.0, 9.275871147869727e-302, 1.2232913026152827e-97, nan, nan, 0.0,
|
|
3.0891393081932924e-252, 2.9303043666183996e-60, nan, nan,
|
|
2.248913486879199e-196, 0.5000000000004947, 0.9999999999999999, nan;
|
|
|
|
CALL_SUBTEST(res = betainc(a, b, x);
|
|
verify_component_wise(res, v););
|
|
}
|
|
|
|
// Test various properties of betainc
|
|
{
|
|
ArrayType m1 = ArrayType::Random(32);
|
|
ArrayType m2 = ArrayType::Random(32);
|
|
ArrayType m3 = ArrayType::Random(32);
|
|
ArrayType one = ArrayType::Constant(32, Scalar(1.0));
|
|
const Scalar eps = std::numeric_limits<Scalar>::epsilon();
|
|
ArrayType a = (m1 * 4.0).exp();
|
|
ArrayType b = (m2 * 4.0).exp();
|
|
ArrayType x = m3.abs();
|
|
|
|
// betainc(a, 1, x) == x**a
|
|
CALL_SUBTEST(
|
|
ArrayType test = betainc(a, one, x);
|
|
ArrayType expected = x.pow(a);
|
|
verify_component_wise(test, expected););
|
|
|
|
// betainc(1, b, x) == 1 - (1 - x)**b
|
|
CALL_SUBTEST(
|
|
ArrayType test = betainc(one, b, x);
|
|
ArrayType expected = one - (one - x).pow(b);
|
|
verify_component_wise(test, expected););
|
|
|
|
// betainc(a, b, x) == 1 - betainc(b, a, 1-x)
|
|
CALL_SUBTEST(
|
|
ArrayType test = betainc(a, b, x) + betainc(b, a, one - x);
|
|
ArrayType expected = one;
|
|
verify_component_wise(test, expected););
|
|
|
|
// betainc(a+1, b, x) = betainc(a, b, x) - x**a * (1 - x)**b / (a * beta(a, b))
|
|
CALL_SUBTEST(
|
|
ArrayType num = x.pow(a) * (one - x).pow(b);
|
|
ArrayType denom = a * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
|
|
// Add eps to rhs and lhs so that component-wise test doesn't result in
|
|
// nans when both outputs are zeros.
|
|
ArrayType expected = betainc(a, b, x) - num / denom + eps;
|
|
ArrayType test = betainc(a + one, b, x) + eps;
|
|
if (sizeof(Scalar) >= 8) { // double
|
|
verify_component_wise(test, expected);
|
|
} else {
|
|
// Reason for limited test: http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1232
|
|
verify_component_wise(test.head(8), expected.head(8));
|
|
});
|
|
|
|
// betainc(a, b+1, x) = betainc(a, b, x) + x**a * (1 - x)**b / (b * beta(a, b))
|
|
CALL_SUBTEST(
|
|
// Add eps to rhs and lhs so that component-wise test doesn't result in
|
|
// nans when both outputs are zeros.
|
|
ArrayType num = x.pow(a) * (one - x).pow(b);
|
|
ArrayType denom = b * (a.lgamma() + b.lgamma() - (a + b).lgamma()).exp();
|
|
ArrayType expected = betainc(a, b, x) + num / denom + eps;
|
|
ArrayType test = betainc(a, b + one, x) + eps;
|
|
verify_component_wise(test, expected););
|
|
}
|
|
#endif
|
|
}
|
|
|
|
void test_array()
|
|
{
|
|
#ifndef EIGEN_HAS_C99_MATH
|
|
std::cerr << "WARNING: testing of special math functions disabled" << std::endl;
|
|
#endif
|
|
|
|
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_abs_op<double>, ArrayXd > Xpr;
|
|
VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
|
|
ArrayBase<Xpr>
|
|
>::value));
|
|
|
|
CALL_SUBTEST_7(array_special_functions<ArrayXf>());
|
|
CALL_SUBTEST_7(array_special_functions<ArrayXd>());
|
|
}
|