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add a KroneckerProduct module (unsupported) from Kolja Brix and Andreas Platen materials.

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This commit is contained in:
Gael Guennebaud 2011-06-22 14:39:11 +02:00
parent 7aabce7c76
commit 3ecf7e8f6e
7 changed files with 397 additions and 1 deletions
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2
unsupported/Eigen/CMakeLists.txt
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@ -1,6 +1,6 @@
set(Eigen_HEADERS AdolcForward BVH IterativeSolvers MatrixFunctions MoreVectorization AutoDiff AlignedVector3 Polynomials
CholmodSupport FFT NonLinearOptimization SparseExtra SuperLUSupport UmfPackSupport IterativeSolvers
NumericalDiff Skyline MPRealSupport OpenGLSupport
NumericalDiff Skyline MPRealSupport OpenGLSupport KroneckerProduct
)
install(FILES

26
unsupported/Eigen/KroneckerProduct Normal file
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@ -0,0 +1,26 @@
#ifndef EIGEN_KRONECKER_PRODUCT_MODULE_H
#define EIGEN_KRONECKER_PRODUCT_MODULE_H
#include "../../Eigen/Core"
#include "../../Eigen/src/Core/util/DisableStupidWarnings.h"
namespace Eigen {
/** \ingroup Unsupported_modules
* \defgroup KroneckerProduct_Module KroneckerProduct module
*
* This module contains an experimental Kronecker product implementation.
*
* \code
* #include <Eigen/KroneckerProduct>
* \endcode
*/
#include "src/KroneckerProduct/KroneckerTensorProduct.h"
} // namespace Eigen
#include "../../Eigen/src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_KRONECKER_PRODUCT_MODULE_H

1
unsupported/Eigen/src/CMakeLists.txt
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@ -9,3 +9,4 @@ ADD_SUBDIRECTORY(NumericalDiff)
ADD_SUBDIRECTORY(Polynomials)
ADD_SUBDIRECTORY(Skyline)
ADD_SUBDIRECTORY(SparseExtra)
ADD_SUBDIRECTORY(KroneckerProduct)

6
unsupported/Eigen/src/KroneckerProduct/CMakeLists.txt Normal file
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@ -0,0 +1,6 @@
FILE(GLOB Eigen_KroneckerProduct_SRCS "*.h")
INSTALL(FILES
${Eigen_KroneckerProduct_SRCS}
DESTINATION ${INCLUDE_INSTALL_DIR}/unsupported/Eigen/src/KroneckerProduct COMPONENT Devel
)

168
unsupported/Eigen/src/KroneckerProduct/KroneckerTensorProduct.h Normal file
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@ -0,0 +1,168 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef KRONECKER_TENSOR_PRODUCT_H
#define KRONECKER_TENSOR_PRODUCT_H
namespace internal {
/*!
* Kronecker tensor product helper function for dense matrices
*
* \param A Dense matrix A
* \param B Dense matrix B
* \param AB_ Kronecker tensor product of A and B
*/
template<typename Derived_A, typename Derived_B, typename Derived_AB>
void kroneckerProduct_full(const Derived_A& A, const Derived_B& B, Derived_AB & AB)
{
const unsigned int Ar = A.rows(),
Ac = A.cols(),
Br = B.rows(),
Bc = B.cols();
for (unsigned int i=0; i<Ar; ++i)
for (unsigned int j=0; j<Ac; ++j)
AB.block(i*Br,j*Bc,Br,Bc) = A(i,j)*B;
}
/*!
* Kronecker tensor product helper function for matrices, where at least one is sparse
*
* \param A Matrix A
* \param B Matrix B
* \param AB_ Kronecker tensor product of A and B
*/
template<typename Derived_A, typename Derived_B, typename Derived_AB>
void kroneckerProduct_sparse(const Derived_A &A, const Derived_B &B, Derived_AB &AB)
{
const unsigned int Ar = A.rows(),
Ac = A.cols(),
Br = B.rows(),
Bc = B.cols();
AB.resize(Ar*Br,Ac*Bc);
AB.resizeNonZeros(0);
AB.reserve(A.nonZeros()*B.nonZeros());
for (int kA=0; kA<A.outerSize(); ++kA)
{
for (int kB=0; kB<B.outerSize(); ++kB)
{
for (typename Derived_A::InnerIterator itA(A,kA); itA; ++itA)
{
for (typename Derived_B::InnerIterator itB(B,kB); itB; ++itB)
{
const unsigned int iA = itA.row(),
jA = itA.col(),
iB = itB.row(),
jB = itB.col(),
i = iA*Br + iB,
j = jA*Bc + jB;
AB.insert(i,j) = itA.value() * itB.value();
}
}
}
}
}
} // end namespace internal
/*!
* Computes Kronecker tensor product of two dense matrices
*
* \param a Dense matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename CScalar,int CRows,int CCols, int COptions, int CMaxRows, int CMaxCols>
void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, Matrix<CScalar,CRows,CCols,COptions,CMaxRows,CMaxCols>& c)
{
c.resize(a.rows()*b.rows(),a.cols()*b.cols());
internal::kroneckerProduct_full(a.derived(), b.derived(), c);
}
/*!
* Computes Kronecker tensor product of two dense matrices
*
* Remark: this function uses the const cast hack and has been
* implemented to make the function call possible, where the
* output matrix is a submatrix, e.g.
* kroneckerProduct(A,B,AB.block(2,5,6,6));
*
* \param a Dense matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const MatrixBase<A>& a, const MatrixBase<B>& b, MatrixBase<C> const & c_)
{
MatrixBase<C>& c = const_cast<MatrixBase<C>& >(c_);
internal::kroneckerProduct_full(a.derived(), b.derived(), c.derived());
}
/*!
* Computes Kronecker tensor product of a dense and a sparse matrix
*
* \param a Dense matrix a
* \param b Sparse matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const MatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
}
/*!
* Computes Kronecker tensor product of a sparse and a dense matrix
*
* \param a Sparse matrix a
* \param b Dense matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const SparseMatrixBase<A>& a, const MatrixBase<B>& b, SparseMatrixBase<C>& c)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
}
/*!
* Computes Kronecker tensor product of two sparse matrices
*
* \param a Sparse matrix a
* \param b Sparse matrix b
* \param c Kronecker tensor product of a and b
*/
template<typename A,typename B,typename C>
void kroneckerProduct(const SparseMatrixBase<A>& a, const SparseMatrixBase<B>& b, SparseMatrixBase<C>& c)
{
internal::kroneckerProduct_sparse(a.derived(), b.derived(), c.derived());
}
#endif // KRONECKER_TENSOR_PRODUCT_H

1
unsupported/test/CMakeLists.txt
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@ -138,3 +138,4 @@ endif(GSL_FOUND)
ei_add_test(polynomialsolver " " "${GSL_LIBRARIES}" )
ei_add_test(polynomialutils)
ei_add_test(kronecker_product)

194
unsupported/test/kronecker_product.cpp Normal file
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@ -0,0 +1,194 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2011 Kolja Brix <brix@igpm.rwth-aachen.de>
// Copyright (C) 2011 Andreas Platen <andiplaten@gmx.de>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "sparse.h"
#include <Eigen/SparseExtra>
#include <Eigen/KroneckerProduct>
template<typename MatrixType>
void check_dimension(const MatrixType& ab, const unsigned int rows, const unsigned int cols)
{
VERIFY_IS_EQUAL(ab.rows(), rows);
VERIFY_IS_EQUAL(ab.cols(), cols);
}
template<typename MatrixType>
void check_kronecker_product(const MatrixType& ab)
{
VERIFY_IS_EQUAL(ab.rows(), 6);
VERIFY_IS_EQUAL(ab.cols(), 6);
VERIFY_IS_EQUAL(ab.nonZeros(), 36);
VERIFY_IS_APPROX(ab.coeff(0,0), -0.4017367630386106);
VERIFY_IS_APPROX(ab.coeff(0,1), 0.1056863433932735);
VERIFY_IS_APPROX(ab.coeff(0,2), -0.7255206194554212);
VERIFY_IS_APPROX(ab.coeff(0,3), 0.1908653336744706);
VERIFY_IS_APPROX(ab.coeff(0,4), 0.350864567234111);
VERIFY_IS_APPROX(ab.coeff(0,5), -0.0923032108308013);
VERIFY_IS_APPROX(ab.coeff(1,0), 0.415417514804677);
VERIFY_IS_APPROX(ab.coeff(1,1), -0.2369227701722048);
VERIFY_IS_APPROX(ab.coeff(1,2), 0.7502275131458511);
VERIFY_IS_APPROX(ab.coeff(1,3), -0.4278731019742696);
VERIFY_IS_APPROX(ab.coeff(1,4), -0.3628129162264507);
VERIFY_IS_APPROX(ab.coeff(1,5), 0.2069210808481275);
VERIFY_IS_APPROX(ab.coeff(2,0), 0.05465890160863986);
VERIFY_IS_APPROX(ab.coeff(2,1), -0.2634092511419858);
VERIFY_IS_APPROX(ab.coeff(2,2), 0.09871180285793758);
VERIFY_IS_APPROX(ab.coeff(2,3), -0.4757066334017702);
VERIFY_IS_APPROX(ab.coeff(2,4), -0.04773740823058334);
VERIFY_IS_APPROX(ab.coeff(2,5), 0.2300535609645254);
VERIFY_IS_APPROX(ab.coeff(3,0), -0.8172945853260133);
VERIFY_IS_APPROX(ab.coeff(3,1), 0.2150086428359221);
VERIFY_IS_APPROX(ab.coeff(3,2), 0.5825113847292743);
VERIFY_IS_APPROX(ab.coeff(3,3), -0.1532433770097174);
VERIFY_IS_APPROX(ab.coeff(3,4), -0.329383387282399);
VERIFY_IS_APPROX(ab.coeff(3,5), 0.08665207912033064);
VERIFY_IS_APPROX(ab.coeff(4,0), 0.8451267514863225);
VERIFY_IS_APPROX(ab.coeff(4,1), -0.481996458918977);
VERIFY_IS_APPROX(ab.coeff(4,2), -0.6023482390791535);
VERIFY_IS_APPROX(ab.coeff(4,3), 0.3435339347164565);
VERIFY_IS_APPROX(ab.coeff(4,4), 0.3406002157428891);
VERIFY_IS_APPROX(ab.coeff(4,5), -0.1942526344200915);
VERIFY_IS_APPROX(ab.coeff(5,0), 0.1111982482925399);
VERIFY_IS_APPROX(ab.coeff(5,1), -0.5358806424754169);
VERIFY_IS_APPROX(ab.coeff(5,2), -0.07925446559335647);
VERIFY_IS_APPROX(ab.coeff(5,3), 0.3819388757769038);
VERIFY_IS_APPROX(ab.coeff(5,4), 0.04481475387219876);
VERIFY_IS_APPROX(ab.coeff(5,5), -0.2159688616158057);
}
template<typename MatrixType>
void check_sparse_kronecker_product(const MatrixType& ab)
{
VERIFY_IS_EQUAL(ab.rows(), 12);
VERIFY_IS_EQUAL(ab.cols(), 10);
VERIFY_IS_EQUAL(ab.nonZeros(), 3*2);
VERIFY_IS_APPROX(ab.coeff(3,0), -0.04);
VERIFY_IS_APPROX(ab.coeff(5,1), 0.05);
VERIFY_IS_APPROX(ab.coeff(0,6), -0.08);
VERIFY_IS_APPROX(ab.coeff(2,7), 0.10);
VERIFY_IS_APPROX(ab.coeff(6,8), 0.12);
VERIFY_IS_APPROX(ab.coeff(8,9), -0.15);
}
void test_kronecker_product()
{
// DM = dense matrix; SM = sparse matrix
Matrix<double, 2, 3> DM_a;
MatrixXd DM_b(3,2);
SparseMatrix<double> SM_a(2,3);
SparseMatrix<double> SM_b(3,2);
SM_a.insert(0,0) = DM_a(0,0) = -0.4461540300782201;
SM_a.insert(0,1) = DM_a(0,1) = -0.8057364375283049;
SM_a.insert(0,2) = DM_a(0,2) = 0.3896572459516341;
SM_a.insert(1,0) = DM_a(1,0) = -0.9076572187376921;
SM_a.insert(1,1) = DM_a(1,1) = 0.6469156566545853;
SM_a.insert(1,2) = DM_a(1,2) = -0.3658010398782789;
SM_b.insert(0,0) = DM_b(0,0) = 0.9004440976767099;
SM_b.insert(0,1) = DM_b(0,1) = -0.2368830858139832;
SM_b.insert(1,0) = DM_b(1,0) = -0.9311078389941825;
SM_b.insert(1,1) = DM_b(1,1) = 0.5310335762980047;
SM_b.insert(2,0) = DM_b(2,0) = -0.1225112806872035;
SM_b.insert(2,1) = DM_b(2,1) = 0.5903998022741264;
SparseMatrix<double,RowMajor> SM_row_a(SM_a), SM_row_b(SM_b);
// test kroneckerProduct(DM_block,DM,DM_fixedSize)
Matrix<double, 6, 6> DM_fix_ab;
DM_fix_ab(0,0)=37.0;
kroneckerProduct(DM_a.block(0,0,2,3),DM_b,DM_fix_ab);
CALL_SUBTEST(check_kronecker_product(DM_fix_ab));
// test kroneckerProduct(DM,DM,DM_block)
MatrixXd DM_block_ab(10,15);
DM_block_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_block_ab.block(2,5,6,6));
CALL_SUBTEST(check_kronecker_product(DM_block_ab.block(2,5,6,6)));
// test kroneckerProduct(DM,DM,DM)
MatrixXd DM_ab(1,5);
DM_ab(0,0)=37.0;
kroneckerProduct(DM_a,DM_b,DM_ab);
CALL_SUBTEST(check_kronecker_product(DM_ab));
// test kroneckerProduct(SM,DM,SM)
SparseMatrix<double> SM_ab(1,20);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SparseMatrix<double,RowMajor> SM_ab2(10,3);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,DM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(DM,SM,SM)
SM_ab.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(DM_a,SM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM)
SM_ab.resize(2,33);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
CALL_SUBTEST(check_kronecker_product(SM_ab));
SM_ab2.resize(5,11);
SM_ab2.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab2);
CALL_SUBTEST(check_kronecker_product(SM_ab2));
// test kroneckerProduct(SM,SM,SM) with sparse pattern
SM_a.resize(4,5);
SM_b.resize(3,2);
SM_a.resizeNonZeros(0);
SM_b.resizeNonZeros(0);
SM_a.insert(1,0) = -0.1;
SM_a.insert(0,3) = -0.2;
SM_a.insert(2,4) = 0.3;
SM_a.finalize();
SM_b.insert(0,0) = 0.4;
SM_b.insert(2,1) = -0.5;
SM_b.finalize();
SM_ab.resize(1,1);
SM_ab.insert(0,0)=37.0;
kroneckerProduct(SM_a,SM_b,SM_ab);
CALL_SUBTEST(check_sparse_kronecker_product(SM_ab));
// test dimension of result of kroneckerProduct(DM,DM,DM)
MatrixXd DM_a2(2,1);
MatrixXd DM_b2(5,4);
MatrixXd DM_ab2;
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
CALL_SUBTEST(check_dimension(DM_ab2,2*5,1*4));
DM_a2.resize(10,9);
DM_b2.resize(4,8);
kroneckerProduct(DM_a2,DM_b2,DM_ab2);
CALL_SUBTEST(check_dimension(DM_ab2,10*4,9*8));
}