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Merge in jdh8's branch.

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* Enable singular matrix power and complex exponents.
* Eliminate unnecessary copying for sparse Kronecker product.
This commit is contained in:
Jitse Niesen
2013-07-21 20:50:15 +01:00
parent 660b905e12 01190b3544
commit 5879937f58
15 changed files with 669 additions and 282 deletions
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21
unsupported/test/kronecker_product.cpp
View File

@@ -107,31 +107,34 @@ void test_kronecker_product()
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test kroneckerProduct(DM_block,DM,DM_fixedSize)
// test DM_fixedSize = kroneckerProduct(DM_block,DM)
Matrix<double, 6, 6> DM_fix_ab = kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a.topLeftCorner<2,3>(),DM_b)));
for(int i=0;i<DM_fix_ab.rows();++i)
for(int j=0;j<DM_fix_ab.cols();++j)
VERIFY_IS_APPROX(kroneckerProduct(DM_a,DM_b).coeff(i,j), DM_fix_ab(i,j));
// test kroneckerProduct(DM,DM,DM_block)
// test DM_block = kroneckerProduct(DM,DM)
MatrixXd DM_block_ab(10,15);
DM_block_ab.block<6,6>(2,5) = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block<6,6>(2,5)));
// test kroneckerProduct(DM,DM,DM)
// test DM = kroneckerProduct(DM,DM)
MatrixXd DM_ab = kroneckerProduct(DM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(DM_ab));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,DM_b)));
// test kroneckerProduct(SM,DM,SM)
// test SM = kroneckerProduct(SM,DM)
SparseMatrix<double> SM_ab = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2 = kroneckerProduct(SM_a,DM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,DM_b)));
// test kroneckerProduct(DM,SM,SM)
// test SM = kroneckerProduct(DM,SM)
SM_ab.setZero();
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(DM_a,SM_b);
@@ -140,8 +143,9 @@ void test_kronecker_product()
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(DM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(DM_a,SM_b)));
// test kroneckerProduct(SM,SM,SM)
// test SM = kroneckerProduct(SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
SM_ab = kroneckerProduct(SM_a,SM_b);
@@ -150,8 +154,9 @@ void test_kronecker_product()
SM_ab2.insert(0,0)=37.0;
SM_ab2 = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
CALL_SUBTEST(check_kronecker_product(kroneckerProduct(SM_a,SM_b)));
// test kroneckerProduct(SM,SM,SM) with sparse pattern
// test SM = kroneckerProduct(SM,SM) with sparse pattern
SM_a.resize(4,5);
SM_b.resize(3,2);
SM_a.resizeNonZeros(0);
@@ -169,7 +174,7 @@ void test_kronecker_product()
SM_ab = kroneckerProduct(SM_a,SM_b);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of kroneckerProduct(DM,DM,DM)
// test dimension of result of DM = kroneckerProduct(DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2 = kroneckerProduct(DM_a2,DM_b2);

41
unsupported/test/matrix_functions.h
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@@ -10,27 +10,48 @@
#include "main.h"
#include <unsupported/Eigen/MatrixFunctions>
// For complex matrices, any matrix is fine.
template<typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct processTriangularMatrix
{
static void run(MatrixType&, MatrixType&, const MatrixType&)
{ }
};
// For real matrices, make sure none of the eigenvalues are negative.
template<typename MatrixType>
struct processTriangularMatrix<MatrixType,0>
{
static void run(MatrixType& m, MatrixType& T, const MatrixType& U)
{
typedef typename MatrixType::Index Index;
const Index size = m.cols();
for (Index i=0; i < size; ++i) {
if (i == size - 1 || T.coeff(i+1,i) == 0)
T.coeffRef(i,i) = std::abs(T.coeff(i,i));
else
++i;
}
m = U * T * U.transpose();
}
};
template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
struct generateTestMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTestMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
MatrixType mat = MatrixType::Random(size, size);
EigenSolver<MatrixType> es(mat);
typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues();
for (typename MatrixType::Index i = 0; i < size; ++i) {
if (eivals(i).imag() == 0 && eivals(i).real() < 0)
eivals(i) = -eivals(i);
}
result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real();
result = MatrixType::Random(size, size);
RealSchur<MatrixType> schur(result);
MatrixType T = schur.matrixT();
processTriangularMatrix<MatrixType>::run(result, T, schur.matrixU());
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTestMatrix<MatrixType,1>
{

151
unsupported/test/matrix_power.cpp
View File

@@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Chen-Pang He <jdh8@ms63.hinet.net>
// Copyright (C) 2012, 2013 Chen-Pang He <jdh8@ms63.hinet.net>
//
// 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
@@ -9,33 +9,6 @@
#include "matrix_functions.h"
template <typename MatrixType, int IsComplex = NumTraits<typename MatrixType::Scalar>::IsComplex>
struct generateTriangularMatrix;
// for real matrices, make sure none of the eigenvalues are negative
template <typename MatrixType>
struct generateTriangularMatrix<MatrixType,0>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result.resize(size, size);
result.template triangularView<Upper>() = MatrixType::Random(size, size);
for (typename MatrixType::Index i = 0; i < size; ++i)
result.coeffRef(i,i) = std::abs(result.coeff(i,i));
}
};
// for complex matrices, any matrix is fine
template <typename MatrixType>
struct generateTriangularMatrix<MatrixType,1>
{
static void run(MatrixType& result, typename MatrixType::Index size)
{
result.resize(size, size);
result.template triangularView<Upper>() = MatrixType::Random(size, size);
}
};
template<typename T>
void test2dRotation(double tol)
{
@@ -53,7 +26,7 @@ void test2dRotation(double tol)
C = Apow(std::ldexp(angle,1) / M_PI);
std::cout << "test2dRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
VERIFY(C.isApprox(B, tol));
}
}
@@ -75,12 +48,26 @@ void test2dHyperbolicRotation(double tol)
C = Apow(angle);
std::cout << "test2dHyperbolicRotation: i = " << i << " error powerm = " << relerr(C,B) << '\n';
VERIFY(C.isApprox(B, static_cast<T>(tol)));
VERIFY(C.isApprox(B, tol));
}
}
template<typename T>
void test3dRotation(double tol)
{
Matrix<T,3,1> v;
T angle;
for (int i=0; i<=20; ++i) {
v = Matrix<T,3,1>::Random();
v.normalize();
angle = pow(10, (i-10) / 5.);
VERIFY(AngleAxis<T>(angle, v).matrix().isApprox(AngleAxis<T>(1,v).matrix().pow(angle), tol));
}
}
template<typename MatrixType>
void testExponentLaws(const MatrixType& m, double tol)
void testGeneral(const MatrixType& m, double tol)
{
typedef typename MatrixType::RealScalar RealScalar;
MatrixType m1, m2, m3, m4, m5;
@@ -97,19 +84,64 @@ void testExponentLaws(const MatrixType& m, double tol)
m4 = mpow(x+y);
m5.noalias() = m2 * m3;
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
VERIFY(m4.isApprox(m5, tol));
m4 = mpow(x*y);
m5 = m2.pow(y);
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
VERIFY(m4.isApprox(m5, tol));
m4 = (std::abs(x) * m1).pow(y);
m5 = std::pow(std::abs(x), y) * m3;
VERIFY(m4.isApprox(m5, static_cast<RealScalar>(tol)));
VERIFY(m4.isApprox(m5, tol));
}
}
template<typename MatrixType>
void testSingular(MatrixType m, double tol)
{
const int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex;
typedef typename internal::conditional< IsComplex, MatrixSquareRootTriangular<MatrixType>,
MatrixSquareRootQuasiTriangular<MatrixType> >::type SquareRootType;
typedef typename internal::conditional<IsComplex, TriangularView<MatrixType,Upper>, const MatrixType&>::type TriangularType;
typename internal::conditional< IsComplex, ComplexSchur<MatrixType>, RealSchur<MatrixType> >::type schur;
MatrixType T;
for (int i=0; i < g_repeat; ++i) {
m.setRandom();
m.col(0).fill(0);
schur.compute(m);
T = schur.matrixT();
const MatrixType& U = schur.matrixU();
processTriangularMatrix<MatrixType>::run(m, T, U);
MatrixPower<MatrixType> mpow(m);
SquareRootType(T).compute(T);
VERIFY(mpow(0.5).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
SquareRootType(T).compute(T);
VERIFY(mpow(0.25).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
SquareRootType(T).compute(T);
VERIFY(mpow(0.125).isApprox(U * (TriangularType(T) * U.adjoint()), tol));
}
}
template<typename MatrixType>
void testLogThenExp(MatrixType m, double tol)
{
typedef typename MatrixType::Scalar Scalar;
Scalar x;
for (int i=0; i < g_repeat; ++i) {
generateTestMatrix<MatrixType>::run(m, m.rows());
x = internal::random<Scalar>();
VERIFY(m.pow(x).isApprox((x * m.log()).exp(), tol));
}
}
typedef Matrix<double,3,3,RowMajor> Matrix3dRowMajor;
typedef Matrix<long double,3,3> Matrix3e;
typedef Matrix<long double,Dynamic,Dynamic> MatrixXe;
void test_matrix_power()
@@ -121,13 +153,46 @@ void test_matrix_power()
CALL_SUBTEST_1(test2dHyperbolicRotation<float>(1e-5));
CALL_SUBTEST_9(test2dHyperbolicRotation<long double>(1e-14));
CALL_SUBTEST_2(testExponentLaws(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testExponentLaws(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testExponentLaws(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testExponentLaws(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testExponentLaws(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testExponentLaws(Matrix3cf(), 1e-4));
CALL_SUBTEST_8(testExponentLaws(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testExponentLaws(MatrixXf(2,2), 1e-3)); // see bug 614
CALL_SUBTEST_9(testExponentLaws(MatrixXe(7,7), 1e-13));
CALL_SUBTEST_10(test3dRotation<double>(1e-13));
CALL_SUBTEST_11(test3dRotation<float>(1e-5));
CALL_SUBTEST_12(test3dRotation<long double>(1e-13));
CALL_SUBTEST_2(testGeneral(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testGeneral(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testGeneral(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testGeneral(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testGeneral(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testGeneral(Matrix3cf(), 1e-4));
CALL_SUBTEST_8(testGeneral(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testGeneral(MatrixXf(2,2), 1e-3)); // see bug 614
CALL_SUBTEST_9(testGeneral(MatrixXe(7,7), 1e-13));
CALL_SUBTEST_10(testGeneral(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testGeneral(Matrix3f(), 1e-4));
CALL_SUBTEST_12(testGeneral(Matrix3e(), 1e-13));
CALL_SUBTEST_2(testSingular(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testSingular(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testSingular(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testSingular(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testSingular(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testSingular(Matrix3cf(), 1e-4));
CALL_SUBTEST_8(testSingular(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testSingular(MatrixXf(2,2), 1e-3));
CALL_SUBTEST_9(testSingular(MatrixXe(7,7), 1e-13));
CALL_SUBTEST_10(testSingular(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testSingular(Matrix3f(), 1e-4));
CALL_SUBTEST_12(testSingular(Matrix3e(), 1e-13));
CALL_SUBTEST_2(testLogThenExp(Matrix2d(), 1e-13));
CALL_SUBTEST_7(testLogThenExp(Matrix3dRowMajor(), 1e-13));
CALL_SUBTEST_3(testLogThenExp(Matrix4cd(), 1e-13));
CALL_SUBTEST_4(testLogThenExp(MatrixXd(8,8), 2e-12));
CALL_SUBTEST_1(testLogThenExp(Matrix2f(), 1e-4));
CALL_SUBTEST_5(testLogThenExp(Matrix3cf(), 1e-4));
CALL_SUBTEST_8(testLogThenExp(Matrix4f(), 1e-4));
CALL_SUBTEST_6(testLogThenExp(MatrixXf(2,2), 1e-3));
CALL_SUBTEST_9(testLogThenExp(MatrixXe(7,7), 1e-13));
CALL_SUBTEST_10(testLogThenExp(Matrix3d(), 1e-13));
CALL_SUBTEST_11(testLogThenExp(Matrix3f(), 1e-4));
CALL_SUBTEST_12(testLogThenExp(Matrix3e(), 1e-13));
}