GitHub-Proxy/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2025-07-30 16:52:01 +08:00
Code Issues Packages Projects Releases Wiki Activity

Fix perm*sparse return type and nesting, and add several sanity checks for perm*sparse

Browse Source
This commit is contained in:
Gael Guennebaud 2015-10-14 10:16:48 +02:00
parent 527fc4bc86
commit c0adf6e38d
3 changed files with 109 additions and 44 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

3
Eigen/src/SparseCore/SparseMatrix.h
View File

@ -1045,6 +1045,9 @@ EIGEN_DONT_INLINE SparseMatrix<Scalar,_Options,_Index>& SparseMatrix<Scalar,_Opt
const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit); const bool needToTranspose = (Flags & RowMajorBit) != (internal::evaluator<OtherDerived>::Flags & RowMajorBit);
if (needToTranspose) if (needToTranspose)
{ {
#ifdef EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN
EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN
#endif
// two passes algorithm: // two passes algorithm:
// 1 - compute the number of coeffs per dest inner vector // 1 - compute the number of coeffs per dest inner vector
// 2 - do the actual copy/eval // 2 - do the actual copy/eval

63
Eigen/src/SparseCore/SparsePermutation.h
View File

@ -16,15 +16,17 @@ namespace Eigen {
namespace internal { namespace internal {
template<typename MatrixType, int Side, bool Transposed> template<typename ExpressionType, int Side, bool Transposed>
struct permutation_matrix_product<MatrixType, Side, Transposed, SparseShape> struct permutation_matrix_product<ExpressionType, Side, Transposed, SparseShape>
{ {
typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned; typedef typename nested_eval<ExpressionType, 1>::type MatrixType;
typedef typename MatrixTypeNestedCleaned::Scalar Scalar; typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
typedef typename MatrixTypeNestedCleaned::StorageIndex StorageIndex;
typedef typename MatrixTypeCleaned::Scalar Scalar;
typedef typename MatrixTypeCleaned::StorageIndex StorageIndex;
enum { enum {
SrcStorageOrder = MatrixTypeNestedCleaned::Flags&RowMajorBit ? RowMajor : ColMajor, SrcStorageOrder = MatrixTypeCleaned::Flags&RowMajorBit ? RowMajor : ColMajor,
MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight MoveOuter = SrcStorageOrder==RowMajor ? Side==OnTheLeft : Side==OnTheRight
}; };
@ -33,8 +35,9 @@ struct permutation_matrix_product<MatrixType, Side, Transposed, SparseShape>
SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> >::type ReturnType; SparseMatrix<Scalar,int(SrcStorageOrder)==RowMajor?ColMajor:RowMajor,StorageIndex> >::type ReturnType;
template<typename Dest,typename PermutationType> template<typename Dest,typename PermutationType>
static inline void run(Dest& dst, const PermutationType& perm, const MatrixType& mat) static inline void run(Dest& dst, const PermutationType& perm, const ExpressionType& xpr)
{ {
MatrixType mat(xpr);
if(MoveOuter) if(MoveOuter)
{ {
SparseMatrix<Scalar,SrcStorageOrder,StorageIndex> tmp(mat.rows(), mat.cols()); SparseMatrix<Scalar,SrcStorageOrder,StorageIndex> tmp(mat.rows(), mat.cols());
@ -50,7 +53,7 @@ struct permutation_matrix_product<MatrixType, Side, Transposed, SparseShape>
Index jp = perm.indices().coeff(j); Index jp = perm.indices().coeff(j);
Index jsrc = ((Side==OnTheRight) ^ Transposed) ? jp : j; Index jsrc = ((Side==OnTheRight) ^ Transposed) ? jp : j;
Index jdst = ((Side==OnTheLeft) ^ Transposed) ? jp : j; Index jdst = ((Side==OnTheLeft) ^ Transposed) ? jp : j;
for(typename MatrixTypeNestedCleaned::InnerIterator it(mat,jsrc); it; ++it) for(typename MatrixTypeCleaned::InnerIterator it(mat,jsrc); it; ++it)
tmp.insertByOuterInner(jdst,it.index()) = it.value(); tmp.insertByOuterInner(jdst,it.index()) = it.value();
} }
dst = tmp; dst = tmp;
@ -67,11 +70,11 @@ struct permutation_matrix_product<MatrixType, Side, Transposed, SparseShape>
perm_cpy = perm.transpose(); perm_cpy = perm.transpose();
for(Index j=0; j<mat.outerSize(); ++j) for(Index j=0; j<mat.outerSize(); ++j)
for(typename MatrixTypeNestedCleaned::InnerIterator it(mat,j); it; ++it) for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)
sizes[perm_cpy.indices().coeff(it.index())]++; sizes[perm_cpy.indices().coeff(it.index())]++;
tmp.reserve(sizes); tmp.reserve(sizes);
for(Index j=0; j<mat.outerSize(); ++j) for(Index j=0; j<mat.outerSize(); ++j)
for(typename MatrixTypeNestedCleaned::InnerIterator it(mat,j); it; ++it) for(typename MatrixTypeCleaned::InnerIterator it(mat,j); it; ++it)
tmp.insertByOuterInner(perm_cpy.indices().coeff(it.index()),j) = it.value(); tmp.insertByOuterInner(perm_cpy.indices().coeff(it.index()),j) = it.value();
dst = tmp; dst = tmp;
} }
@ -90,40 +93,48 @@ template <int ProductTag> struct product_promote_storage_type<PermutationStorage
// whereas it should be correctly handled by traits<Product<> >::PlainObject // whereas it should be correctly handled by traits<Product<> >::PlainObject
template<typename Lhs, typename Rhs, int ProductTag> template<typename Lhs, typename Rhs, int ProductTag>
struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, PermutationShape, SparseShape, typename traits<Lhs>::Scalar, typename traits<Rhs>::Scalar> struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, PermutationShape, SparseShape>
: public evaluator<typename permutation_matrix_product<Rhs,OnTheRight,false,SparseShape>::ReturnType> : public evaluator<typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType>
{ {
typedef Product<Lhs, Rhs, AliasFreeProduct> XprType; typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;
typedef typename permutation_matrix_product<Rhs,OnTheRight,false,SparseShape>::ReturnType PlainObject; typedef typename permutation_matrix_product<Rhs,OnTheLeft,false,SparseShape>::ReturnType PlainObject;
typedef evaluator<PlainObject> Base; typedef evaluator<PlainObject> Base;
enum {
Flags = Base::Flags | EvalBeforeNestingBit
};
explicit product_evaluator(const XprType& xpr) explicit product_evaluator(const XprType& xpr)
: m_result(xpr.rows(), xpr.cols()) : m_result(xpr.rows(), xpr.cols())
{ {
::new (static_cast<Base*>(this)) Base(m_result); ::new (static_cast<Base*>(this)) Base(m_result);
generic_product_impl<Lhs, Rhs, PermutationShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs()); generic_product_impl<Lhs, Rhs, PermutationShape, SparseShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
} }
protected: protected:
PlainObject m_result; PlainObject m_result;
}; };
template<typename Lhs, typename Rhs, int ProductTag> template<typename Lhs, typename Rhs, int ProductTag>
struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, SparseShape, PermutationShape, typename traits<Lhs>::Scalar, typename traits<Rhs>::Scalar> struct product_evaluator<Product<Lhs, Rhs, AliasFreeProduct>, ProductTag, SparseShape, PermutationShape >
: public evaluator<typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType> : public evaluator<typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType>
{ {
typedef Product<Lhs, Rhs, AliasFreeProduct> XprType; typedef Product<Lhs, Rhs, AliasFreeProduct> XprType;
typedef typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType PlainObject; typedef typename permutation_matrix_product<Lhs,OnTheRight,false,SparseShape>::ReturnType PlainObject;
typedef evaluator<PlainObject> Base; typedef evaluator<PlainObject> Base;
enum {
Flags = Base::Flags | EvalBeforeNestingBit
};
explicit product_evaluator(const XprType& xpr) explicit product_evaluator(const XprType& xpr)
: m_result(xpr.rows(), xpr.cols()) : m_result(xpr.rows(), xpr.cols())
{ {
::new (static_cast<Base*>(this)) Base(m_result); ::new (static_cast<Base*>(this)) Base(m_result);
generic_product_impl<Lhs, Rhs, SparseShape, PermutationShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs()); generic_product_impl<Lhs, Rhs, SparseShape, PermutationShape, ProductTag>::evalTo(m_result, xpr.lhs(), xpr.rhs());
} }
protected: protected:
PlainObject m_result; PlainObject m_result;
}; };
@ -132,34 +143,34 @@ protected:
/** \returns the matrix with the permutation applied to the columns /** \returns the matrix with the permutation applied to the columns
*/ */
template<typename SparseDerived, typename PermDerived> template<typename SparseDerived, typename PermDerived>
inline const Product<SparseDerived, PermDerived> inline const Product<SparseDerived, PermDerived, AliasFreeProduct>
operator*(const SparseMatrixBase<SparseDerived>& matrix, const PermutationBase<PermDerived>& perm) operator*(const SparseMatrixBase<SparseDerived>& matrix, const PermutationBase<PermDerived>& perm)
{ return Product<SparseDerived, PermDerived>(matrix.derived(), perm.derived()); } { return Product<SparseDerived, PermDerived, AliasFreeProduct>(matrix.derived(), perm.derived()); }
/** \returns the matrix with the permutation applied to the rows /** \returns the matrix with the permutation applied to the rows
*/ */
template<typename SparseDerived, typename PermDerived> template<typename SparseDerived, typename PermDerived>
inline const Product<PermDerived, SparseDerived> inline const Product<PermDerived, SparseDerived, AliasFreeProduct>
operator*( const PermutationBase<PermDerived>& perm, const SparseMatrixBase<SparseDerived>& matrix) operator*( const PermutationBase<PermDerived>& perm, const SparseMatrixBase<SparseDerived>& matrix)
{ return Product<PermDerived, SparseDerived>(perm.derived(), matrix.derived()); } { return Product<PermDerived, SparseDerived, AliasFreeProduct>(perm.derived(), matrix.derived()); }
/** \returns the matrix with the inverse permutation applied to the columns. /** \returns the matrix with the inverse permutation applied to the columns.
*/ */
template<typename SparseDerived, typename PermutationType> template<typename SparseDerived, typename PermutationType>
inline const Product<SparseDerived, Inverse<PermutationType > > inline const Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>
operator*(const SparseMatrixBase<SparseDerived>& matrix, const InverseImpl<PermutationType, PermutationStorage>& tperm) operator*(const SparseMatrixBase<SparseDerived>& matrix, const InverseImpl<PermutationType, PermutationStorage>& tperm)
{ {
return Product<SparseDerived, Inverse<PermutationType> >(matrix.derived(), tperm.derived()); return Product<SparseDerived, Inverse<PermutationType>, AliasFreeProduct>(matrix.derived(), tperm.derived());
} }
/** \returns the matrix with the inverse permutation applied to the rows. /** \returns the matrix with the inverse permutation applied to the rows.
*/ */
template<typename SparseDerived, typename PermutationType> template<typename SparseDerived, typename PermutationType>
inline const Product<Inverse<PermutationType>, SparseDerived> inline const Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>
operator*(const InverseImpl<PermutationType,PermutationStorage>& tperm, const SparseMatrixBase<SparseDerived>& matrix) operator*(const InverseImpl<PermutationType,PermutationStorage>& tperm, const SparseMatrixBase<SparseDerived>& matrix)
{ {
return Product<Inverse<PermutationType>, SparseDerived>(tperm.derived(), matrix.derived()); return Product<Inverse<PermutationType>, SparseDerived, AliasFreeProduct>(tperm.derived(), matrix.derived());
} }
} // end namespace Eigen } // end namespace Eigen

87
test/sparse_permutations.cpp
View File

@ -1,14 +1,46 @@
// This file is part of Eigen, a lightweight C++ template library // This file is part of Eigen, a lightweight C++ template library
// for linear algebra. // for linear algebra.
// //
// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2011-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
// //
// This Source Code Form is subject to the terms of the Mozilla // 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 // 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/. // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
static long int nb_transposed_copies;
#define EIGEN_SPARSE_TRANSPOSED_COPY_PLUGIN {nb_transposed_copies++;}
#define VERIFY_TRANSPOSITION_COUNT(XPR,N) {\
nb_transposed_copies = 0; \
XPR; \
if(nb_transposed_copies!=N) std::cerr << "nb_transposed_copies == " << nb_transposed_copies << "\n"; \
VERIFY( (#XPR) && nb_transposed_copies==N ); \
}
#include "sparse.h" #include "sparse.h"
template<typename T>
bool is_sorted(const T& mat) {
for(Index k = 0; k<mat.outerSize(); ++k)
{
Index prev = -1;
for(typename T::InnerIterator it(mat,k); it; ++it)
{
if(prev>=it.index())
return false;
prev = it.index();
}
}
return true;
}
template<typename T>
typename internal::nested_eval<T,1>::type eval(const T &xpr)
{
VERIFY( int(internal::nested_eval<T,1>::type::Flags&RowMajorBit) == int(internal::evaluator<T>::Flags&RowMajorBit) );
return xpr;
}
template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(const SparseMatrixType& ref) template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(const SparseMatrixType& ref)
{ {
const Index rows = ref.rows(); const Index rows = ref.rows();
@ -18,6 +50,8 @@ template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(c
typedef SparseMatrix<Scalar, OtherStorage, StorageIndex> OtherSparseMatrixType; typedef SparseMatrix<Scalar, OtherStorage, StorageIndex> OtherSparseMatrixType;
typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix;
typedef Matrix<StorageIndex,Dynamic,1> VectorI; typedef Matrix<StorageIndex,Dynamic,1> VectorI;
// bool IsRowMajor1 = SparseMatrixType::IsRowMajor;
// bool IsRowMajor2 = OtherSparseMatrixType::IsRowMajor;
double density = (std::max)(8./(rows*cols), 0.01); double density = (std::max)(8./(rows*cols), 0.01);
@ -42,58 +76,69 @@ template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(c
randomPermutationVector(pi, cols); randomPermutationVector(pi, cols);
p.indices() = pi; p.indices() = pi;
res = mat*p; VERIFY( is_sorted( eval(mat*p) ));
VERIFY( is_sorted( res = mat*p ));
VERIFY_TRANSPOSITION_COUNT( eval(mat*p), 0);
//VERIFY_TRANSPOSITION_COUNT( res = mat*p, IsRowMajor ? 1 : 0 );
res_d = mat_d*p; res_d = mat_d*p;
VERIFY(res.isApprox(res_d) && "mat*p"); VERIFY(res.isApprox(res_d) && "mat*p");
res = p*mat; VERIFY( is_sorted( eval(p*mat) ));
VERIFY( is_sorted( res = p*mat ));
VERIFY_TRANSPOSITION_COUNT( eval(p*mat), 0);
res_d = p*mat_d; res_d = p*mat_d;
VERIFY(res.isApprox(res_d) && "p*mat"); VERIFY(res.isApprox(res_d) && "p*mat");
res = mat*p.inverse(); VERIFY( is_sorted( (mat*p).eval() ));
VERIFY( is_sorted( res = mat*p.inverse() ));
VERIFY_TRANSPOSITION_COUNT( eval(mat*p.inverse()), 0);
res_d = mat*p.inverse(); res_d = mat*p.inverse();
VERIFY(res.isApprox(res_d) && "mat*inv(p)"); VERIFY(res.isApprox(res_d) && "mat*inv(p)");
res = p.inverse()*mat; VERIFY( is_sorted( (p*mat+p*mat).eval() ));
VERIFY( is_sorted( res = p.inverse()*mat ));
VERIFY_TRANSPOSITION_COUNT( eval(p.inverse()*mat), 0);
res_d = p.inverse()*mat_d; res_d = p.inverse()*mat_d;
VERIFY(res.isApprox(res_d) && "inv(p)*mat"); VERIFY(res.isApprox(res_d) && "inv(p)*mat");
res = mat.twistedBy(p); VERIFY( is_sorted( (p * mat * p.inverse()).eval() ));
VERIFY( is_sorted( res = mat.twistedBy(p) ));
VERIFY_TRANSPOSITION_COUNT( eval(p * mat * p.inverse()), 0);
res_d = (p * mat_d) * p.inverse(); res_d = (p * mat_d) * p.inverse();
VERIFY(res.isApprox(res_d) && "p*mat*inv(p)"); VERIFY(res.isApprox(res_d) && "p*mat*inv(p)");
res = mat.template selfadjointView<Upper>().twistedBy(p_null); VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p_null) ));
res_d = up_sym_d; res_d = up_sym_d;
VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
res = mat.template selfadjointView<Lower>().twistedBy(p_null); VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p_null) ));
res_d = lo_sym_d; res_d = lo_sym_d;
VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
res = up.template selfadjointView<Upper>().twistedBy(p_null); VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p_null) ));
res_d = up_sym_d; res_d = up_sym_d;
VERIFY(res.isApprox(res_d) && "upper selfadjoint to full"); VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
res = lo.template selfadjointView<Lower>().twistedBy(p_null); VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p_null) ));
res_d = lo_sym_d; res_d = lo_sym_d;
VERIFY(res.isApprox(res_d) && "lower selfadjoint full"); VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
res = mat.template selfadjointView<Upper>(); VERIFY( is_sorted( res = mat.template selfadjointView<Upper>() ));
res_d = up_sym_d; res_d = up_sym_d;
VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint upper to full");
res = mat.template selfadjointView<Lower>(); VERIFY( is_sorted( res = mat.template selfadjointView<Lower>() ));
res_d = lo_sym_d; res_d = lo_sym_d;
VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint lower to full");
res = up.template selfadjointView<Upper>(); VERIFY( is_sorted( res = up.template selfadjointView<Upper>() ));
res_d = up_sym_d; res_d = up_sym_d;
VERIFY(res.isApprox(res_d) && "upper selfadjoint to full"); VERIFY(res.isApprox(res_d) && "upper selfadjoint to full");
res = lo.template selfadjointView<Lower>(); VERIFY( is_sorted( res = lo.template selfadjointView<Lower>() ));
res_d = lo_sym_d; res_d = lo_sym_d;
VERIFY(res.isApprox(res_d) && "lower selfadjoint full"); VERIFY(res.isApprox(res_d) && "lower selfadjoint full");
@ -150,19 +195,19 @@ template<int OtherStorage, typename SparseMatrixType> void sparse_permutations(c
VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to lower"); VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to lower");
res = mat.template selfadjointView<Upper>().twistedBy(p); VERIFY( is_sorted( res = mat.template selfadjointView<Upper>().twistedBy(p) ));
res_d = (p * up_sym_d) * p.inverse(); res_d = (p * up_sym_d) * p.inverse();
VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint upper twisted to full");
res = mat.template selfadjointView<Lower>().twistedBy(p); VERIFY( is_sorted( res = mat.template selfadjointView<Lower>().twistedBy(p) ));
res_d = (p * lo_sym_d) * p.inverse(); res_d = (p * lo_sym_d) * p.inverse();
VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to full"); VERIFY(res.isApprox(res_d) && "full selfadjoint lower twisted to full");
res = up.template selfadjointView<Upper>().twistedBy(p); VERIFY( is_sorted( res = up.template selfadjointView<Upper>().twistedBy(p) ));
res_d = (p * up_sym_d) * p.inverse(); res_d = (p * up_sym_d) * p.inverse();
VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to full"); VERIFY(res.isApprox(res_d) && "upper selfadjoint twisted to full");
res = lo.template selfadjointView<Lower>().twistedBy(p); VERIFY( is_sorted( res = lo.template selfadjointView<Lower>().twistedBy(p) ));
res_d = (p * lo_sym_d) * p.inverse(); res_d = (p * lo_sym_d) * p.inverse();
VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to full"); VERIFY(res.isApprox(res_d) && "lower selfadjoint twisted to full");
} }
@ -182,4 +227,10 @@ void test_sparse_permutations()
CALL_SUBTEST_1(( sparse_permutations_all<double>(s) )); CALL_SUBTEST_1(( sparse_permutations_all<double>(s) ));
CALL_SUBTEST_2(( sparse_permutations_all<std::complex<double> >(s) )); CALL_SUBTEST_2(( sparse_permutations_all<std::complex<double> >(s) ));
} }
VERIFY((internal::is_same<typename internal::permutation_matrix_product<SparseMatrix<double>,OnTheRight,false,SparseShape>::ReturnType,
typename internal::nested_eval<Product<SparseMatrix<double>,PermutationMatrix<Dynamic,Dynamic>,AliasFreeProduct>,1>::type>::value));
VERIFY((internal::is_same<typename internal::permutation_matrix_product<SparseMatrix<double>,OnTheLeft,false,SparseShape>::ReturnType,
typename internal::nested_eval<Product<PermutationMatrix<Dynamic,Dynamic>,SparseMatrix<double>,AliasFreeProduct>,1>::type>::value));
} }