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See the GNU + Lesser General Public License for more details. + + You should have received a copy of the GNU Lesser General Public + License along with this library; if not, write to the Free Software + Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA + +Also add information on how to contact you by electronic and paper mail. + +You should also get your employer (if you work as a programmer) or your +school, if any, to sign a "copyright disclaimer" for the library, if +necessary. Here is a sample; alter the names: + + Yoyodyne, Inc., hereby disclaims all copyright interest in the + library `Frob' (a library for tweaking knobs) written by James Random Hacker. + + , 1 April 1990 + Ty Coon, President of Vice + +That's all there is to it! diff --git a/COPYING.README b/COPYING.README index 1d706784d..de5b63215 100644 --- a/COPYING.README +++ b/COPYING.README @@ -5,6 +5,9 @@ Eigen is primarily MPL2 licensed. See COPYING.MPL2 and these links: Some files contain third-party code under BSD or LGPL licenses, whence the other COPYING.* files here. +All the LGPL code is either LGPL 2.1-only, or LGPL 2.1-or-later. +For this reason, the COPYING.LGPL file contains the LGPL 2.1 text. + If you want to guarantee that the Eigen code that you are #including is licensed under the MPL2 and possibly more permissive licenses (like BSD), #define this preprocessor symbol: diff --git a/Eigen/Core b/Eigen/Core index 88337e47e..502a4fc55 100644 --- a/Eigen/Core +++ b/Eigen/Core @@ -87,19 +87,25 @@ // so, to avoid compile errors when windows.h is included after Eigen/Core, ensure intrinsics are extern "C" here too. // notice that since these are C headers, the extern "C" is theoretically needed anyways. extern "C" { - #include - #include - #ifdef EIGEN_VECTORIZE_SSE3 - #include - #endif - #ifdef EIGEN_VECTORIZE_SSSE3 - #include - #endif - #ifdef EIGEN_VECTORIZE_SSE4_1 - #include - #endif - #ifdef EIGEN_VECTORIZE_SSE4_2 - #include + // In theory we should only include immintrin.h and not the other *mmintrin.h header files directly. + // Doing so triggers some issues with ICC. However old gcc versions seems to not have this file, thus: + #ifdef __INTEL_COMPILER + #include + #else + #include + #include + #ifdef EIGEN_VECTORIZE_SSE3 + #include + #endif + #ifdef EIGEN_VECTORIZE_SSSE3 + #include + #endif + #ifdef EIGEN_VECTORIZE_SSE4_1 + #include + #endif + #ifdef EIGEN_VECTORIZE_SSE4_2 + #include + #endif #endif } // end extern "C" #elif defined __ALTIVEC__ diff --git a/Eigen/MetisSupport b/Eigen/MetisSupport new file mode 100644 index 000000000..a44086ad9 --- /dev/null +++ b/Eigen/MetisSupport @@ -0,0 +1,26 @@ +#ifndef EIGEN_METISSUPPORT_MODULE_H +#define EIGEN_METISSUPPORT_MODULE_H + +#include "SparseCore" + +#include "src/Core/util/DisableStupidWarnings.h" + +extern "C" { +#include +} + + +/** \ingroup Support_modules + * \defgroup MetisSupport_Module MetisSupport module + * + * \code + * #include + * \endcode + */ + + +#include "src/MetisSupport/MetisSupport.h" + +#include "src/Core/util/ReenableStupidWarnings.h" + +#endif // EIGEN_METISSUPPORT_MODULE_H diff --git a/Eigen/OrderingMethods b/Eigen/OrderingMethods index 1e2d87452..bb43220e8 100644 --- a/Eigen/OrderingMethods +++ b/Eigen/OrderingMethods @@ -17,7 +17,7 @@ */ #include "src/OrderingMethods/Amd.h" - +#include "src/OrderingMethods/Ordering.h" #include "src/Core/util/ReenableStupidWarnings.h" #endif // EIGEN_ORDERINGMETHODS_MODULE_H diff --git a/Eigen/SparseLU b/Eigen/SparseLU new file mode 100644 index 000000000..452bc9f83 --- /dev/null +++ b/Eigen/SparseLU @@ -0,0 +1,17 @@ +#ifndef EIGEN_SPARSELU_MODULE_H +#define EIGEN_SPARSELU_MODULE_H + +#include "SparseCore" + + +/** \ingroup Sparse_modules + * \defgroup SparseLU_Module SparseLU module + * + */ + +// Ordering interface +#include "OrderingMethods" + +#include "src/SparseLU/SparseLU.h" + +#endif // EIGEN_SPARSELU_MODULE_H diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h index f27ab798a..da0264b0e 100644 --- a/Eigen/src/Core/DiagonalMatrix.h +++ b/Eigen/src/Core/DiagonalMatrix.h @@ -20,6 +20,7 @@ class DiagonalBase : public EigenBase public: typedef typename internal::traits::DiagonalVectorType DiagonalVectorType; typedef typename DiagonalVectorType::Scalar Scalar; + typedef typename DiagonalVectorType::RealScalar RealScalar; typedef typename internal::traits::StorageKind StorageKind; typedef typename internal::traits::Index Index; @@ -65,6 +66,17 @@ class DiagonalBase : public EigenBase return diagonal().cwiseInverse(); } + inline const DiagonalWrapper, const DiagonalVectorType> > + operator*(const Scalar& scalar) const + { + return diagonal() * scalar; + } + friend inline const DiagonalWrapper, const DiagonalVectorType> > + operator*(const Scalar& scalar, const DiagonalBase& other) + { + return other.diagonal() * scalar; + } + #ifdef EIGEN2_SUPPORT template bool isApprox(const DiagonalBase& other, typename NumTraits::Real precision = NumTraits::dummy_precision()) const diff --git a/Eigen/src/Core/Functors.h b/Eigen/src/Core/Functors.h index c9e8ab150..09388972a 100644 --- a/Eigen/src/Core/Functors.h +++ b/Eigen/src/Core/Functors.h @@ -454,7 +454,7 @@ struct functor_traits > * indeed it seems better to declare m_other as a Packet and do the pset1() once * in the constructor. However, in practice: * - GCC does not like m_other as a Packet and generate a load every time it needs it - * - on the other hand GCC is able to moves the pset1() away the loop :) + * - on the other hand GCC is able to moves the pset1() outside the loop :) * - simpler code ;) * (ICC and gcc 4.4 seems to perform well in both cases, the issue is visible with y = a*x + b*y) */ @@ -485,33 +485,6 @@ template struct functor_traits > { enum { Cost = NumTraits::MulCost, PacketAccess = false }; }; -template -struct scalar_quotient1_impl { - typedef typename packet_traits::type Packet; - // FIXME default copy constructors seems bugged with std::complex<> - EIGEN_STRONG_INLINE scalar_quotient1_impl(const scalar_quotient1_impl& other) : m_other(other.m_other) { } - EIGEN_STRONG_INLINE scalar_quotient1_impl(const Scalar& other) : m_other(static_cast(1) / other) {} - EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a * m_other; } - EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const - { return internal::pmul(a, pset1(m_other)); } - const Scalar m_other; -}; -template -struct functor_traits > -{ enum { Cost = NumTraits::MulCost, PacketAccess = packet_traits::HasMul }; }; - -template -struct scalar_quotient1_impl { - // FIXME default copy constructors seems bugged with std::complex<> - EIGEN_STRONG_INLINE scalar_quotient1_impl(const scalar_quotient1_impl& other) : m_other(other.m_other) { } - EIGEN_STRONG_INLINE scalar_quotient1_impl(const Scalar& other) : m_other(other) {} - EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; } - typename add_const_on_value_type::Nested>::type m_other; -}; -template -struct functor_traits > -{ enum { Cost = 2 * NumTraits::MulCost, PacketAccess = false }; }; - /** \internal * \brief Template functor to divide a scalar by a fixed other one * @@ -521,14 +494,19 @@ struct functor_traits > * \sa class CwiseUnaryOp, MatrixBase::operator/ */ template -struct scalar_quotient1_op : scalar_quotient1_impl::IsInteger > { - EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) - : scalar_quotient1_impl::IsInteger >(other) {} +struct scalar_quotient1_op { + typedef typename packet_traits::type Packet; + // FIXME default copy constructors seems bugged with std::complex<> + EIGEN_STRONG_INLINE scalar_quotient1_op(const scalar_quotient1_op& other) : m_other(other.m_other) { } + EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other) : m_other(other) {} + EIGEN_STRONG_INLINE Scalar operator() (const Scalar& a) const { return a / m_other; } + EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const + { return internal::pdiv(a, pset1(m_other)); } + typename add_const_on_value_type::Nested>::type m_other; }; template struct functor_traits > -: functor_traits::IsInteger> > -{}; +{ enum { Cost = 2 * NumTraits::MulCost, PacketAccess = packet_traits::HasDiv }; }; // nullary functors diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h index f138b12d2..521bba18a 100644 --- a/Eigen/src/Core/MatrixBase.h +++ b/Eigen/src/Core/MatrixBase.h @@ -240,7 +240,7 @@ template class MatrixBase // huuuge hack. make Eigen2's matrix.part() work in eigen3. Problem: Diagonal is now a class template instead // of an integer constant. Solution: overload the part() method template wrt template parameters list. - template class U> + template class U> const DiagonalWrapper part() const { return diagonal().asDiagonal(); } #endif // EIGEN2_SUPPORT diff --git a/Eigen/src/Core/Ref.h b/Eigen/src/Core/Ref.h index 38a838cf1..9c409eecf 100644 --- a/Eigen/src/Core/Ref.h +++ b/Eigen/src/Core/Ref.h @@ -195,12 +195,12 @@ template class Ref Base::construct(expr); } template - inline Ref(const MatrixBase& expr, + inline Ref(const DenseBase& expr, typename internal::enable_if::value&&bool(Traits::template match::MatchAtCompileTime)),Derived>::type* = 0, int = Derived::ThisConstantIsPrivateInPlainObjectBase) #else template - inline Ref(MatrixBase& expr) + inline Ref(DenseBase& expr) #endif { Base::construct(expr.const_cast_derived()); @@ -221,7 +221,7 @@ template class Ref - inline Ref(const MatrixBase& expr) + inline Ref(const DenseBase& expr) { // std::cout << match_helper::HasDirectAccess << "," << match_helper::OuterStrideMatch << "," << match_helper::InnerStrideMatch << "\n"; // std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n"; diff --git a/Eigen/src/Core/StableNorm.h b/Eigen/src/Core/StableNorm.h index d8bf7db70..7499b195e 100644 --- a/Eigen/src/Core/StableNorm.h +++ b/Eigen/src/Core/StableNorm.h @@ -131,7 +131,6 @@ MatrixBase::blueNorm() const abig = internal::sqrt(abig); if(abig > overfl) { - eigen_assert(false && "overflow"); return rbig; } if(amed > RealScalar(0)) diff --git a/Eigen/src/Core/TriangularMatrix.h b/Eigen/src/Core/TriangularMatrix.h index 3bf2a257d..fcd40e32f 100644 --- a/Eigen/src/Core/TriangularMatrix.h +++ b/Eigen/src/Core/TriangularMatrix.h @@ -511,6 +511,7 @@ template struct triangular_assignment_selector { typedef typename Derived1::Index Index; + typedef typename Derived1::Scalar Scalar; static inline void run(Derived1 &dst, const Derived2 &src) { for(Index j = 0; j < dst.cols(); ++j) @@ -520,7 +521,7 @@ struct triangular_assignment_selector::type> str // it's important that this value can still be squared without integer overflowing. DynamicAsInteger = 10000, ScalarReadCost = NumTraits::Scalar>::ReadCost, - ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? DynamicAsInteger : ScalarReadCost, + ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost), CoeffReadCost = traits::CoeffReadCost, - CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? DynamicAsInteger : CoeffReadCost, + CoeffReadCostAsInteger = CoeffReadCost == Dynamic ? int(DynamicAsInteger) : int(CoeffReadCost), NAsInteger = n == Dynamic ? int(DynamicAsInteger) : n, CostEvalAsInteger = (NAsInteger+1) * ScalarReadCostAsInteger + CoeffReadCostAsInteger, CostNoEvalAsInteger = NAsInteger * CoeffReadCostAsInteger diff --git a/Eigen/src/Geometry/Umeyama.h b/Eigen/src/Geometry/Umeyama.h index ac0939cde..345b47e0c 100644 --- a/Eigen/src/Geometry/Umeyama.h +++ b/Eigen/src/Geometry/Umeyama.h @@ -153,16 +153,21 @@ umeyama(const MatrixBase& src, const MatrixBase& dst, boo Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose(); } - // Eq. (42) - const Scalar c = 1/src_var * svd.singularValues().dot(S); + if (with_scaling) + { + // Eq. (42) + const Scalar c = 1/src_var * svd.singularValues().dot(S); - // Eq. (41) - // Note that we first assign dst_mean to the destination so that there no need - // for a temporary. - Rt.col(m).head(m) = dst_mean; - Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean; - - if (with_scaling) Rt.block(0,0,m,m) *= c; + // Eq. (41) + Rt.col(m).head(m) = dst_mean; + Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean; + Rt.block(0,0,m,m) *= c; + } + else + { + Rt.col(m).head(m) = dst_mean; + Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean; + } return Rt; } diff --git a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h index 126341be8..5a822e0ea 100644 --- a/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h +++ b/Eigen/src/IterativeLinearSolvers/BiCGSTAB.h @@ -39,10 +39,11 @@ bool bicgstab(const MatrixType& mat, const Rhs& rhs, Dest& x, int maxIters = iters; int n = mat.cols(); + x = precond.solve(x); VectorType r = rhs - mat * x; VectorType r0 = r; - RealScalar r0_sqnorm = r0.squaredNorm(); + RealScalar r0_sqnorm = rhs.squaredNorm(); Scalar rho = 1; Scalar alpha = 1; Scalar w = 1; @@ -223,7 +224,8 @@ public: template void _solve(const Rhs& b, Dest& x) const { - x.setZero(); +// x.setZero(); + x = b; _solveWithGuess(b,x); } diff --git a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h index 224304f0e..5a71531cd 100644 --- a/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h +++ b/Eigen/src/IterativeLinearSolvers/IncompleteLUT.h @@ -10,8 +10,56 @@ #ifndef EIGEN_INCOMPLETE_LUT_H #define EIGEN_INCOMPLETE_LUT_H + namespace Eigen { +namespace internal { + +/** + * Compute a quick-sort split of a vector + * On output, the vector row is permuted such that its elements satisfy + * abs(row(i)) >= abs(row(ncut)) if incut + * \param row The vector of values + * \param ind The array of index for the elements in @p row + * \param ncut The number of largest elements to keep + **/ +template +int QuickSplit(VectorV &row, VectorI &ind, int ncut) +{ + typedef typename VectorV::RealScalar RealScalar; + using std::swap; + int mid; + int n = row.size(); /* length of the vector */ + int first, last ; + + ncut--; /* to fit the zero-based indices */ + first = 0; + last = n-1; + if (ncut < first || ncut > last ) return 0; + + do { + mid = first; + RealScalar abskey = std::abs(row(mid)); + for (int j = first + 1; j <= last; j++) { + if ( std::abs(row(j)) > abskey) { + ++mid; + swap(row(mid), row(j)); + swap(ind(mid), ind(j)); + } + } + /* Interchange for the pivot element */ + swap(row(mid), row(first)); + swap(ind(mid), ind(first)); + + if (mid > ncut) last = mid - 1; + else if (mid < ncut ) first = mid + 1; + } while (mid != ncut ); + + return 0; /* mid is equal to ncut */ +} + +}// end namespace internal /** * \brief Incomplete LU factorization with dual-threshold strategy * During the numerical factorization, two dropping rules are used : @@ -126,10 +174,6 @@ class IncompleteLUT : internal::noncopyable protected: - template - int QuickSplit(VectorV &row, VectorI &ind, int ncut); - - /** keeps off-diagonal entries; drops diagonal entries */ struct keep_diag { inline bool operator() (const Index& row, const Index& col, const Scalar&) const @@ -171,51 +215,6 @@ void IncompleteLUT::setFillfactor(int fillfactor) this->m_fillfactor = fillfactor; } - -/** - * Compute a quick-sort split of a vector - * On output, the vector row is permuted such that its elements satisfy - * abs(row(i)) >= abs(row(ncut)) if incut - * \param row The vector of values - * \param ind The array of index for the elements in @p row - * \param ncut The number of largest elements to keep - **/ -template -template -int IncompleteLUT::QuickSplit(VectorV &row, VectorI &ind, int ncut) -{ - using std::swap; - int mid; - int n = row.size(); /* length of the vector */ - int first, last ; - - ncut--; /* to fit the zero-based indices */ - first = 0; - last = n-1; - if (ncut < first || ncut > last ) return 0; - - do { - mid = first; - RealScalar abskey = std::abs(row(mid)); - for (int j = first + 1; j <= last; j++) { - if ( std::abs(row(j)) > abskey) { - ++mid; - swap(row(mid), row(j)); - swap(ind(mid), ind(j)); - } - } - /* Interchange for the pivot element */ - swap(row(mid), row(first)); - swap(ind(mid), ind(first)); - - if (mid > ncut) last = mid - 1; - else if (mid < ncut ) first = mid + 1; - } while (mid != ncut ); - - return 0; /* mid is equal to ncut */ -} - template template void IncompleteLUT::analyzePattern(const _MatrixType& amat) @@ -400,7 +399,7 @@ void IncompleteLUT::factorize(const _MatrixType& amat) len = (std::min)(sizel, nnzL); typename Vector::SegmentReturnType ul(u.segment(0, sizel)); typename VectorXi::SegmentReturnType jul(ju.segment(0, sizel)); - QuickSplit(ul, jul, len); + internal::QuickSplit(ul, jul, len); // store the largest m_fill elements of the L part m_lu.startVec(ii); @@ -429,7 +428,7 @@ void IncompleteLUT::factorize(const _MatrixType& amat) len = (std::min)(sizeu, nnzU); typename Vector::SegmentReturnType uu(u.segment(ii+1, sizeu-1)); typename VectorXi::SegmentReturnType juu(ju.segment(ii+1, sizeu-1)); - QuickSplit(uu, juu, len); + internal::QuickSplit(uu, juu, len); // store the largest elements of the U part for(int k = ii + 1; k < ii + len; k++) diff --git a/Eigen/src/MetisSupport/CMakeLists.txt b/Eigen/src/MetisSupport/CMakeLists.txt new file mode 100644 index 000000000..2bad31416 --- /dev/null +++ b/Eigen/src/MetisSupport/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_MetisSupport_SRCS "*.h") + +INSTALL(FILES + ${Eigen_MetisSupport_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/MetisSupport COMPONENT Devel + ) diff --git a/Eigen/src/MetisSupport/MetisSupport.h b/Eigen/src/MetisSupport/MetisSupport.h new file mode 100644 index 000000000..a762d96f6 --- /dev/null +++ b/Eigen/src/MetisSupport/MetisSupport.h @@ -0,0 +1,138 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +#ifndef METIS_SUPPORT_H +#define METIS_SUPPORT_H + +namespace Eigen { +/** + * Get the fill-reducing ordering from the METIS package + * + * If A is the original matrix and Ap is the permuted matrix, + * the fill-reducing permutation is defined as follows : + * Row (column) i of A is the matperm(i) row (column) of Ap. + * WARNING: As computed by METIS, this corresponds to the vector iperm (instead of perm) + */ +template +class MetisOrdering +{ +public: + typedef PermutationMatrix PermutationType; + typedef Matrix IndexVector; + + template + void get_symmetrized_graph(const MatrixType& A) + { + Index m = A.cols(); + + // Get the transpose of the input matrix + MatrixType At = A.transpose(); + // Get the number of nonzeros elements in each row/col of At+A + Index TotNz = 0; + IndexVector visited(m); + visited.setConstant(-1); + for (int j = 0; j < m; j++) + { + // Compute the union structure of of A(j,:) and At(j,:) + visited(j) = j; // Do not include the diagonal element + // Get the nonzeros in row/column j of A + for (typename MatrixType::InnerIterator it(A, j); it; ++it) + { + Index idx = it.index(); // Get the row index (for column major) or column index (for row major) + if (visited(idx) != j ) + { + visited(idx) = j; + ++TotNz; + } + } + //Get the nonzeros in row/column j of At + for (typename MatrixType::InnerIterator it(At, j); it; ++it) + { + Index idx = it.index(); + if(visited(idx) != j) + { + visited(idx) = j; + ++TotNz; + } + } + } + // Reserve place for A + At + m_indexPtr.resize(m+1); + m_innerIndices.resize(TotNz); + + // Now compute the real adjacency list of each column/row + visited.setConstant(-1); + Index CurNz = 0; + for (int j = 0; j < m; j++) + { + m_indexPtr(j) = CurNz; + + visited(j) = j; // Do not include the diagonal element + // Add the pattern of row/column j of A to A+At + for (typename MatrixType::InnerIterator it(A,j); it; ++it) + { + Index idx = it.index(); // Get the row index (for column major) or column index (for row major) + if (visited(idx) != j ) + { + visited(idx) = j; + m_innerIndices(CurNz) = idx; + CurNz++; + } + } + //Add the pattern of row/column j of At to A+At + for (typename MatrixType::InnerIterator it(At, j); it; ++it) + { + Index idx = it.index(); + if(visited(idx) != j) + { + visited(idx) = j; + m_innerIndices(CurNz) = idx; + ++CurNz; + } + } + } + m_indexPtr(m) = CurNz; + } + + template + void operator() (const MatrixType& A, PermutationType& matperm) + { + Index m = A.cols(); + IndexVector perm(m),iperm(m); + // First, symmetrize the matrix graph. + get_symmetrized_graph(A); + int output_error; + + // Call the fill-reducing routine from METIS + output_error = METIS_NodeND(&m, m_indexPtr.data(), m_innerIndices.data(), NULL, NULL, perm.data(), iperm.data()); + + if(output_error != METIS_OK) + { + //FIXME The ordering interface should define a class of possible errors + std::cerr << "ERROR WHILE CALLING THE METIS PACKAGE \n"; + return; + } + + // Get the fill-reducing permutation + //NOTE: If Ap is the permuted matrix then perm and iperm vectors are defined as follows + // Row (column) i of Ap is the perm(i) row(column) of A, and row (column) i of A is the iperm(i) row(column) of Ap + + // To be consistent with the use of the permutation in SparseLU module, we thus keep the iperm vector + matperm.resize(m); + for (int j = 0; j < m; j++) + matperm.indices()(j) = iperm(j); + + } + + protected: + IndexVector m_indexPtr; // Pointer to the adjacenccy list of each row/column + IndexVector m_innerIndices; // Adjacency list +}; + +}// end namespace eigen +#endif \ No newline at end of file diff --git a/Eigen/src/OrderingMethods/Eigen_Colamd.h b/Eigen/src/OrderingMethods/Eigen_Colamd.h new file mode 100644 index 000000000..6dc1f280d --- /dev/null +++ b/Eigen/src/OrderingMethods/Eigen_Colamd.h @@ -0,0 +1,1849 @@ +// // This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Desire Nuentsa Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +// This file is modified from the colamd/symamd library. The copyright is below + +// The authors of the code itself are Stefan I. Larimore and Timothy A. +// Davis (davis@cise.ufl.edu), University of Florida. The algorithm was +// developed in collaboration with John Gilbert, Xerox PARC, and Esmond +// Ng, Oak Ridge National Laboratory. +// +// Date: +// +// September 8, 2003. Version 2.3. +// +// Acknowledgements: +// +// This work was supported by the National Science Foundation, under +// grants DMS-9504974 and DMS-9803599. +// +// Notice: +// +// Copyright (c) 1998-2003 by the University of Florida. +// All Rights Reserved. +// +// THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY +// EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. +// +// Permission is hereby granted to use, copy, modify, and/or distribute +// this program, provided that the Copyright, this License, and the +// Availability of the original version is retained on all copies and made +// accessible to the end-user of any code or package that includes COLAMD +// or any modified version of COLAMD. +// +// Availability: +// +// The colamd/symamd library is available at +// +// http://www.cise.ufl.edu/research/sparse/colamd/ + +// This is the http://www.cise.ufl.edu/research/sparse/colamd/colamd.h +// file. It is required by the colamd.c, colamdmex.c, and symamdmex.c +// files, and by any C code that calls the routines whose prototypes are +// listed below, or that uses the colamd/symamd definitions listed below. + +#ifndef EIGEN_COLAMD_H +#define EIGEN_COLAMD_H +namespace internal { +/* Ensure that debugging is turned off: */ +#ifndef COLAMD_NDEBUG +#define COLAMD_NDEBUG +#endif /* NDEBUG */ +/* ========================================================================== */ +/* === Knob and statistics definitions ====================================== */ +/* ========================================================================== */ + +/* size of the knobs [ ] array. Only knobs [0..1] are currently used. */ +#define COLAMD_KNOBS 20 + +/* number of output statistics. Only stats [0..6] are currently used. */ +#define COLAMD_STATS 20 + +/* knobs [0] and stats [0]: dense row knob and output statistic. */ +#define COLAMD_DENSE_ROW 0 + +/* knobs [1] and stats [1]: dense column knob and output statistic. */ +#define COLAMD_DENSE_COL 1 + +/* stats [2]: memory defragmentation count output statistic */ +#define COLAMD_DEFRAG_COUNT 2 + +/* stats [3]: colamd status: zero OK, > 0 warning or notice, < 0 error */ +#define COLAMD_STATUS 3 + +/* stats [4..6]: error info, or info on jumbled columns */ +#define COLAMD_INFO1 4 +#define COLAMD_INFO2 5 +#define COLAMD_INFO3 6 + +/* error codes returned in stats [3]: */ +#define COLAMD_OK (0) +#define COLAMD_OK_BUT_JUMBLED (1) +#define COLAMD_ERROR_A_not_present (-1) +#define COLAMD_ERROR_p_not_present (-2) +#define COLAMD_ERROR_nrow_negative (-3) +#define COLAMD_ERROR_ncol_negative (-4) +#define COLAMD_ERROR_nnz_negative (-5) +#define COLAMD_ERROR_p0_nonzero (-6) +#define COLAMD_ERROR_A_too_small (-7) +#define COLAMD_ERROR_col_length_negative (-8) +#define COLAMD_ERROR_row_index_out_of_bounds (-9) +#define COLAMD_ERROR_out_of_memory (-10) +#define COLAMD_ERROR_internal_error (-999) + +/* ========================================================================== */ +/* === Definitions ========================================================== */ +/* ========================================================================== */ + +#define COLAMD_MAX(a,b) (((a) > (b)) ? (a) : (b)) +#define COLAMD_MIN(a,b) (((a) < (b)) ? (a) : (b)) + +#define ONES_COMPLEMENT(r) (-(r)-1) + +/* -------------------------------------------------------------------------- */ + +#define COLAMD_EMPTY (-1) + +/* Row and column status */ +#define ALIVE (0) +#define DEAD (-1) + +/* Column status */ +#define DEAD_PRINCIPAL (-1) +#define DEAD_NON_PRINCIPAL (-2) + +/* Macros for row and column status update and checking. */ +#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) +#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) +#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) +#define COL_IS_DEAD(c) (Col [c].start < ALIVE) +#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) +#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) +#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } +#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } +#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } + +/* ========================================================================== */ +/* === Colamd reporting mechanism =========================================== */ +/* ========================================================================== */ + + // == Row and Column structures == +typedef struct colamd_col_struct +{ + int start ; /* index for A of first row in this column, or DEAD */ + /* if column is dead */ + int length ; /* number of rows in this column */ + union + { + int thickness ; /* number of original columns represented by this */ + /* col, if the column is alive */ + int parent ; /* parent in parent tree super-column structure, if */ + /* the column is dead */ + } shared1 ; + union + { + int score ; /* the score used to maintain heap, if col is alive */ + int order ; /* pivot ordering of this column, if col is dead */ + } shared2 ; + union + { + int headhash ; /* head of a hash bucket, if col is at the head of */ + /* a degree list */ + int hash ; /* hash value, if col is not in a degree list */ + int prev ; /* previous column in degree list, if col is in a */ + /* degree list (but not at the head of a degree list) */ + } shared3 ; + union + { + int degree_next ; /* next column, if col is in a degree list */ + int hash_next ; /* next column, if col is in a hash list */ + } shared4 ; + +} colamd_col ; + +typedef struct Colamd_Row_struct +{ + int start ; /* index for A of first col in this row */ + int length ; /* number of principal columns in this row */ + union + { + int degree ; /* number of principal & non-principal columns in row */ + int p ; /* used as a row pointer in init_rows_cols () */ + } shared1 ; + union + { + int mark ; /* for computing set differences and marking dead rows*/ + int first_column ;/* first column in row (used in garbage collection) */ + } shared2 ; + +} Colamd_Row ; + +/* ========================================================================== */ +/* === Colamd recommended memory size ======================================= */ +/* ========================================================================== */ + +/* + The recommended length Alen of the array A passed to colamd is given by + the COLAMD_RECOMMENDED (nnz, n_row, n_col) macro. It returns -1 if any + argument is negative. 2*nnz space is required for the row and column + indices of the matrix. colamd_c (n_col) + colamd_r (n_row) space is + required for the Col and Row arrays, respectively, which are internal to + colamd. An additional n_col space is the minimal amount of "elbow room", + and nnz/5 more space is recommended for run time efficiency. + + This macro is not needed when using symamd. + + Explicit typecast to int added Sept. 23, 2002, COLAMD version 2.2, to avoid + gcc -pedantic warning messages. +*/ + +inline int colamd_c(int n_col) +{ return int( ((n_col) + 1) * sizeof (colamd_col) / sizeof (int) ) ; } + +inline int colamd_r(int n_row) +{ return int(((n_row) + 1) * sizeof (Colamd_Row) / sizeof (int)); } + + // Various routines +inline int colamd_recommended (int nnz, int n_row, int n_col) ; + +static inline void colamd_set_defaults (double knobs [COLAMD_KNOBS]) ; + +static bool colamd (int n_row, int n_col, int Alen, int A [], int p [], double knobs[COLAMD_KNOBS], int stats [COLAMD_STATS]) ; + +static int init_rows_cols (int n_row, int n_col, Colamd_Row Row [], colamd_col col [], int A [], int p [], int stats[COLAMD_STATS] ); + +static void init_scoring (int n_row, int n_col, Colamd_Row Row [], colamd_col Col [], int A [], int head [], double knobs[COLAMD_KNOBS], int *p_n_row2, int *p_n_col2, int *p_max_deg); + +static int find_ordering (int n_row, int n_col, int Alen, Colamd_Row Row [], colamd_col Col [], int A [], int head [], int n_col2, int max_deg, int pfree); + +static void order_children (int n_col, colamd_col Col [], int p []); + +static void detect_super_cols ( + colamd_col Col [], + int A [], + int head [], + int row_start, + int row_length ) ; + +static int garbage_collection (int n_row, int n_col, Colamd_Row Row [], colamd_col Col [], int A [], int *pfree) ; + +static inline int clear_mark (int n_row, Colamd_Row Row [] ) ; + +/* === No debugging ========================================================= */ + +#define COLAMD_DEBUG0(params) ; +#define COLAMD_DEBUG1(params) ; +#define COLAMD_DEBUG2(params) ; +#define COLAMD_DEBUG3(params) ; +#define COLAMD_DEBUG4(params) ; + +#define COLAMD_ASSERT(expression) ((void) 0) + + +/** + * \brief Returns the recommended value of Alen + * + * Returns recommended value of Alen for use by colamd. + * Returns -1 if any input argument is negative. + * The use of this routine or macro is optional. + * Note that the macro uses its arguments more than once, + * so be careful for side effects, if you pass expressions as arguments to COLAMD_RECOMMENDED. + * + * \param nnz nonzeros in A + * \param n_row number of rows in A + * \param n_col number of columns in A + * \return recommended value of Alen for use by colamd + */ +inline int colamd_recommended ( int nnz, int n_row, int n_col) +{ + if ((nnz) < 0 || (n_row) < 0 || (n_col) < 0) + return (-1); + else + return (2 * (nnz) + colamd_c (n_col) + colamd_r (n_row) + (n_col) + ((nnz) / 5)); +} + +/** + * \brief set default parameters The use of this routine is optional. + * + * Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col) + * entries are removed prior to ordering. Columns with more than + * (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to + * ordering, and placed last in the output column ordering. + * + * COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1, + * respectively, in colamd.h. Default values of these two knobs + * are both 0.5. Currently, only knobs [0] and knobs [1] are + * used, but future versions may use more knobs. If so, they will + * be properly set to their defaults by the future version of + * colamd_set_defaults, so that the code that calls colamd will + * not need to change, assuming that you either use + * colamd_set_defaults, or pass a (double *) NULL pointer as the + * knobs array to colamd or symamd. + * + * \param knobs parameter settings for colamd + */ +static inline void colamd_set_defaults(double knobs[COLAMD_KNOBS]) +{ + /* === Local variables ================================================== */ + + int i ; + + if (!knobs) + { + return ; /* no knobs to initialize */ + } + for (i = 0 ; i < COLAMD_KNOBS ; i++) + { + knobs [i] = 0 ; + } + knobs [COLAMD_DENSE_ROW] = 0.5 ; /* ignore rows over 50% dense */ + knobs [COLAMD_DENSE_COL] = 0.5 ; /* ignore columns over 50% dense */ +} + +/** + * \brief Computes a column ordering using the column approximate minimum degree ordering + * + * Computes a column ordering (Q) of A such that P(AQ)=LU or + * (AQ)'AQ=LL' have less fill-in and require fewer floating point + * operations than factorizing the unpermuted matrix A or A'A, + * respectively. + * + * + * \param n_row number of rows in A + * \param n_col number of columns in A + * \param Alen, size of the array A + * \param A row indices of the matrix, of size ALen + * \param p column pointers of A, of size n_col+1 + * \param knobs parameter settings for colamd + * \param stats colamd output statistics and error codes + */ +static bool colamd(int n_row, int n_col, int Alen, int *A, int *p, double knobs[COLAMD_KNOBS], int stats[COLAMD_STATS]) +{ + /* === Local variables ================================================== */ + + int i ; /* loop index */ + int nnz ; /* nonzeros in A */ + int Row_size ; /* size of Row [], in integers */ + int Col_size ; /* size of Col [], in integers */ + int need ; /* minimum required length of A */ + Colamd_Row *Row ; /* pointer into A of Row [0..n_row] array */ + colamd_col *Col ; /* pointer into A of Col [0..n_col] array */ + int n_col2 ; /* number of non-dense, non-empty columns */ + int n_row2 ; /* number of non-dense, non-empty rows */ + int ngarbage ; /* number of garbage collections performed */ + int max_deg ; /* maximum row degree */ + double default_knobs [COLAMD_KNOBS] ; /* default knobs array */ + + + /* === Check the input arguments ======================================== */ + + if (!stats) + { + COLAMD_DEBUG0 (("colamd: stats not present\n")) ; + return (false) ; + } + for (i = 0 ; i < COLAMD_STATS ; i++) + { + stats [i] = 0 ; + } + stats [COLAMD_STATUS] = COLAMD_OK ; + stats [COLAMD_INFO1] = -1 ; + stats [COLAMD_INFO2] = -1 ; + + if (!A) /* A is not present */ + { + stats [COLAMD_STATUS] = COLAMD_ERROR_A_not_present ; + COLAMD_DEBUG0 (("colamd: A not present\n")) ; + return (false) ; + } + + if (!p) /* p is not present */ + { + stats [COLAMD_STATUS] = COLAMD_ERROR_p_not_present ; + COLAMD_DEBUG0 (("colamd: p not present\n")) ; + return (false) ; + } + + if (n_row < 0) /* n_row must be >= 0 */ + { + stats [COLAMD_STATUS] = COLAMD_ERROR_nrow_negative ; + stats [COLAMD_INFO1] = n_row ; + COLAMD_DEBUG0 (("colamd: nrow negative %d\n", n_row)) ; + return (false) ; + } + + if (n_col < 0) /* n_col must be >= 0 */ + { + stats [COLAMD_STATUS] = COLAMD_ERROR_ncol_negative ; + stats [COLAMD_INFO1] = n_col ; + COLAMD_DEBUG0 (("colamd: ncol negative %d\n", n_col)) ; + return (false) ; + } + + nnz = p [n_col] ; + if (nnz < 0) /* nnz must be >= 0 */ + { + stats [COLAMD_STATUS] = COLAMD_ERROR_nnz_negative ; + stats [COLAMD_INFO1] = nnz ; + COLAMD_DEBUG0 (("colamd: number of entries negative %d\n", nnz)) ; + return (false) ; + } + + if (p [0] != 0) + { + stats [COLAMD_STATUS] = COLAMD_ERROR_p0_nonzero ; + stats [COLAMD_INFO1] = p [0] ; + COLAMD_DEBUG0 (("colamd: p[0] not zero %d\n", p [0])) ; + return (false) ; + } + + /* === If no knobs, set default knobs =================================== */ + + if (!knobs) + { + colamd_set_defaults (default_knobs) ; + knobs = default_knobs ; + } + + /* === Allocate the Row and Col arrays from array A ===================== */ + + Col_size = colamd_c (n_col) ; + Row_size = colamd_r (n_row) ; + need = 2*nnz + n_col + Col_size + Row_size ; + + if (need > Alen) + { + /* not enough space in array A to perform the ordering */ + stats [COLAMD_STATUS] = COLAMD_ERROR_A_too_small ; + stats [COLAMD_INFO1] = need ; + stats [COLAMD_INFO2] = Alen ; + COLAMD_DEBUG0 (("colamd: Need Alen >= %d, given only Alen = %d\n", need,Alen)); + return (false) ; + } + + Alen -= Col_size + Row_size ; + Col = (colamd_col *) &A [Alen] ; + Row = (Colamd_Row *) &A [Alen + Col_size] ; + + /* === Construct the row and column data structures ===================== */ + + if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats)) + { + /* input matrix is invalid */ + COLAMD_DEBUG0 (("colamd: Matrix invalid\n")) ; + return (false) ; + } + + /* === Initialize scores, kill dense rows/columns ======================= */ + + init_scoring (n_row, n_col, Row, Col, A, p, knobs, + &n_row2, &n_col2, &max_deg) ; + + /* === Order the supercolumns =========================================== */ + + ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, + n_col2, max_deg, 2*nnz) ; + + /* === Order the non-principal columns ================================== */ + + order_children (n_col, Col, p) ; + + /* === Return statistics in stats ======================================= */ + + stats [COLAMD_DENSE_ROW] = n_row - n_row2 ; + stats [COLAMD_DENSE_COL] = n_col - n_col2 ; + stats [COLAMD_DEFRAG_COUNT] = ngarbage ; + COLAMD_DEBUG0 (("colamd: done.\n")) ; + return (true) ; +} + +/* ========================================================================== */ +/* === NON-USER-CALLABLE ROUTINES: ========================================== */ +/* ========================================================================== */ + +/* There are no user-callable routines beyond this point in the file */ + + +/* ========================================================================== */ +/* === init_rows_cols ======================================================= */ +/* ========================================================================== */ + +/* + Takes the column form of the matrix in A and creates the row form of the + matrix. Also, row and column attributes are stored in the Col and Row + structs. If the columns are un-sorted or contain duplicate row indices, + this routine will also sort and remove duplicate row indices from the + column form of the matrix. Returns false if the matrix is invalid, + true otherwise. Not user-callable. +*/ + + static int init_rows_cols /* returns true if OK, or false otherwise */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + Colamd_Row Row [], /* of size n_row+1 */ + colamd_col Col [], /* of size n_col+1 */ + int A [], /* row indices of A, of size Alen */ + int p [], /* pointers to columns in A, of size n_col+1 */ + int stats [COLAMD_STATS] /* colamd statistics */ +) +{ + /* === Local variables ================================================== */ + + int col ; /* a column index */ + int row ; /* a row index */ + int *cp ; /* a column pointer */ + int *cp_end ; /* a pointer to the end of a column */ + int *rp ; /* a row pointer */ + int *rp_end ; /* a pointer to the end of a row */ + int last_row ; /* previous row */ + + /* === Initialize columns, and check column pointers ==================== */ + + for (col = 0 ; col < n_col ; col++) + { + Col [col].start = p [col] ; + Col [col].length = p [col+1] - p [col] ; + + if (Col [col].length < 0) + { + /* column pointers must be non-decreasing */ + stats [COLAMD_STATUS] = COLAMD_ERROR_col_length_negative ; + stats [COLAMD_INFO1] = col ; + stats [COLAMD_INFO2] = Col [col].length ; + COLAMD_DEBUG0 (("colamd: col %d length %d < 0\n", col, Col [col].length)) ; + return (false) ; + } + + Col [col].shared1.thickness = 1 ; + Col [col].shared2.score = 0 ; + Col [col].shared3.prev = COLAMD_EMPTY ; + Col [col].shared4.degree_next = COLAMD_EMPTY ; + } + + /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ + + /* === Scan columns, compute row degrees, and check row indices ========= */ + + stats [COLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/ + + for (row = 0 ; row < n_row ; row++) + { + Row [row].length = 0 ; + Row [row].shared2.mark = -1 ; + } + + for (col = 0 ; col < n_col ; col++) + { + last_row = -1 ; + + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + + while (cp < cp_end) + { + row = *cp++ ; + + /* make sure row indices within range */ + if (row < 0 || row >= n_row) + { + stats [COLAMD_STATUS] = COLAMD_ERROR_row_index_out_of_bounds ; + stats [COLAMD_INFO1] = col ; + stats [COLAMD_INFO2] = row ; + stats [COLAMD_INFO3] = n_row ; + COLAMD_DEBUG0 (("colamd: row %d col %d out of bounds\n", row, col)) ; + return (false) ; + } + + if (row <= last_row || Row [row].shared2.mark == col) + { + /* row index are unsorted or repeated (or both), thus col */ + /* is jumbled. This is a notice, not an error condition. */ + stats [COLAMD_STATUS] = COLAMD_OK_BUT_JUMBLED ; + stats [COLAMD_INFO1] = col ; + stats [COLAMD_INFO2] = row ; + (stats [COLAMD_INFO3]) ++ ; + COLAMD_DEBUG1 (("colamd: row %d col %d unsorted/duplicate\n",row,col)); + } + + if (Row [row].shared2.mark != col) + { + Row [row].length++ ; + } + else + { + /* this is a repeated entry in the column, */ + /* it will be removed */ + Col [col].length-- ; + } + + /* mark the row as having been seen in this column */ + Row [row].shared2.mark = col ; + + last_row = row ; + } + } + + /* === Compute row pointers ============================================= */ + + /* row form of the matrix starts directly after the column */ + /* form of matrix in A */ + Row [0].start = p [n_col] ; + Row [0].shared1.p = Row [0].start ; + Row [0].shared2.mark = -1 ; + for (row = 1 ; row < n_row ; row++) + { + Row [row].start = Row [row-1].start + Row [row-1].length ; + Row [row].shared1.p = Row [row].start ; + Row [row].shared2.mark = -1 ; + } + + /* === Create row form ================================================== */ + + if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) + { + /* if cols jumbled, watch for repeated row indices */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + row = *cp++ ; + if (Row [row].shared2.mark != col) + { + A [(Row [row].shared1.p)++] = col ; + Row [row].shared2.mark = col ; + } + } + } + } + else + { + /* if cols not jumbled, we don't need the mark (this is faster) */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + A [(Row [*cp++].shared1.p)++] = col ; + } + } + } + + /* === Clear the row marks and set row degrees ========================== */ + + for (row = 0 ; row < n_row ; row++) + { + Row [row].shared2.mark = 0 ; + Row [row].shared1.degree = Row [row].length ; + } + + /* === See if we need to re-create columns ============================== */ + + if (stats [COLAMD_STATUS] == COLAMD_OK_BUT_JUMBLED) + { + COLAMD_DEBUG0 (("colamd: reconstructing column form, matrix jumbled\n")) ; + + + /* === Compute col pointers ========================================= */ + + /* col form of the matrix starts at A [0]. */ + /* Note, we may have a gap between the col form and the row */ + /* form if there were duplicate entries, if so, it will be */ + /* removed upon the first garbage collection */ + Col [0].start = 0 ; + p [0] = Col [0].start ; + for (col = 1 ; col < n_col ; col++) + { + /* note that the lengths here are for pruned columns, i.e. */ + /* no duplicate row indices will exist for these columns */ + Col [col].start = Col [col-1].start + Col [col-1].length ; + p [col] = Col [col].start ; + } + + /* === Re-create col form =========================================== */ + + for (row = 0 ; row < n_row ; row++) + { + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + A [(p [*rp++])++] = row ; + } + } + } + + /* === Done. Matrix is not (or no longer) jumbled ====================== */ + + return (true) ; +} + + +/* ========================================================================== */ +/* === init_scoring ========================================================= */ +/* ========================================================================== */ + +/* + Kills dense or empty columns and rows, calculates an initial score for + each column, and places all columns in the degree lists. Not user-callable. +*/ + +static void init_scoring +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + Colamd_Row Row [], /* of size n_row+1 */ + colamd_col Col [], /* of size n_col+1 */ + int A [], /* column form and row form of A */ + int head [], /* of size n_col+1 */ + double knobs [COLAMD_KNOBS],/* parameters */ + int *p_n_row2, /* number of non-dense, non-empty rows */ + int *p_n_col2, /* number of non-dense, non-empty columns */ + int *p_max_deg /* maximum row degree */ +) +{ + /* === Local variables ================================================== */ + + int c ; /* a column index */ + int r, row ; /* a row index */ + int *cp ; /* a column pointer */ + int deg ; /* degree of a row or column */ + int *cp_end ; /* a pointer to the end of a column */ + int *new_cp ; /* new column pointer */ + int col_length ; /* length of pruned column */ + int score ; /* current column score */ + int n_col2 ; /* number of non-dense, non-empty columns */ + int n_row2 ; /* number of non-dense, non-empty rows */ + int dense_row_count ; /* remove rows with more entries than this */ + int dense_col_count ; /* remove cols with more entries than this */ + int min_score ; /* smallest column score */ + int max_deg ; /* maximum row degree */ + int next_col ; /* Used to add to degree list.*/ + + + /* === Extract knobs ==================================================== */ + + dense_row_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ; + dense_col_count = COLAMD_MAX (0, COLAMD_MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ; + COLAMD_DEBUG1 (("colamd: densecount: %d %d\n", dense_row_count, dense_col_count)) ; + max_deg = 0 ; + n_col2 = n_col ; + n_row2 = n_row ; + + /* === Kill empty columns =============================================== */ + + /* Put the empty columns at the end in their natural order, so that LU */ + /* factorization can proceed as far as possible. */ + for (c = n_col-1 ; c >= 0 ; c--) + { + deg = Col [c].length ; + if (deg == 0) + { + /* this is a empty column, kill and order it last */ + Col [c].shared2.order = --n_col2 ; + KILL_PRINCIPAL_COL (c) ; + } + } + COLAMD_DEBUG1 (("colamd: null columns killed: %d\n", n_col - n_col2)) ; + + /* === Kill dense columns =============================================== */ + + /* Put the dense columns at the end, in their natural order */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip any dead columns */ + if (COL_IS_DEAD (c)) + { + continue ; + } + deg = Col [c].length ; + if (deg > dense_col_count) + { + /* this is a dense column, kill and order it last */ + Col [c].shared2.order = --n_col2 ; + /* decrement the row degrees */ + cp = &A [Col [c].start] ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + Row [*cp++].shared1.degree-- ; + } + KILL_PRINCIPAL_COL (c) ; + } + } + COLAMD_DEBUG1 (("colamd: Dense and null columns killed: %d\n", n_col - n_col2)) ; + + /* === Kill dense and empty rows ======================================== */ + + for (r = 0 ; r < n_row ; r++) + { + deg = Row [r].shared1.degree ; + COLAMD_ASSERT (deg >= 0 && deg <= n_col) ; + if (deg > dense_row_count || deg == 0) + { + /* kill a dense or empty row */ + KILL_ROW (r) ; + --n_row2 ; + } + else + { + /* keep track of max degree of remaining rows */ + max_deg = COLAMD_MAX (max_deg, deg) ; + } + } + COLAMD_DEBUG1 (("colamd: Dense and null rows killed: %d\n", n_row - n_row2)) ; + + /* === Compute initial column scores ==================================== */ + + /* At this point the row degrees are accurate. They reflect the number */ + /* of "live" (non-dense) columns in each row. No empty rows exist. */ + /* Some "live" columns may contain only dead rows, however. These are */ + /* pruned in the code below. */ + + /* now find the initial matlab score for each column */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip dead column */ + if (COL_IS_DEAD (c)) + { + continue ; + } + score = 0 ; + cp = &A [Col [c].start] ; + new_cp = cp ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + /* skip if dead */ + if (ROW_IS_DEAD (row)) + { + continue ; + } + /* compact the column */ + *new_cp++ = row ; + /* add row's external degree */ + score += Row [row].shared1.degree - 1 ; + /* guard against integer overflow */ + score = COLAMD_MIN (score, n_col) ; + } + /* determine pruned column length */ + col_length = (int) (new_cp - &A [Col [c].start]) ; + if (col_length == 0) + { + /* a newly-made null column (all rows in this col are "dense" */ + /* and have already been killed) */ + COLAMD_DEBUG2 (("Newly null killed: %d\n", c)) ; + Col [c].shared2.order = --n_col2 ; + KILL_PRINCIPAL_COL (c) ; + } + else + { + /* set column length and set score */ + COLAMD_ASSERT (score >= 0) ; + COLAMD_ASSERT (score <= n_col) ; + Col [c].length = col_length ; + Col [c].shared2.score = score ; + } + } + COLAMD_DEBUG1 (("colamd: Dense, null, and newly-null columns killed: %d\n", + n_col-n_col2)) ; + + /* At this point, all empty rows and columns are dead. All live columns */ + /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ + /* yet). Rows may contain dead columns, but all live rows contain at */ + /* least one live column. */ + + /* === Initialize degree lists ========================================== */ + + + /* clear the hash buckets */ + for (c = 0 ; c <= n_col ; c++) + { + head [c] = COLAMD_EMPTY ; + } + min_score = n_col ; + /* place in reverse order, so low column indices are at the front */ + /* of the lists. This is to encourage natural tie-breaking */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* only add principal columns to degree lists */ + if (COL_IS_ALIVE (c)) + { + COLAMD_DEBUG4 (("place %d score %d minscore %d ncol %d\n", + c, Col [c].shared2.score, min_score, n_col)) ; + + /* === Add columns score to DList =============================== */ + + score = Col [c].shared2.score ; + + COLAMD_ASSERT (min_score >= 0) ; + COLAMD_ASSERT (min_score <= n_col) ; + COLAMD_ASSERT (score >= 0) ; + COLAMD_ASSERT (score <= n_col) ; + COLAMD_ASSERT (head [score] >= COLAMD_EMPTY) ; + + /* now add this column to dList at proper score location */ + next_col = head [score] ; + Col [c].shared3.prev = COLAMD_EMPTY ; + Col [c].shared4.degree_next = next_col ; + + /* if there already was a column with the same score, set its */ + /* previous pointer to this new column */ + if (next_col != COLAMD_EMPTY) + { + Col [next_col].shared3.prev = c ; + } + head [score] = c ; + + /* see if this score is less than current min */ + min_score = COLAMD_MIN (min_score, score) ; + + + } + } + + + /* === Return number of remaining columns, and max row degree =========== */ + + *p_n_col2 = n_col2 ; + *p_n_row2 = n_row2 ; + *p_max_deg = max_deg ; +} + + +/* ========================================================================== */ +/* === find_ordering ======================================================== */ +/* ========================================================================== */ + +/* + Order the principal columns of the supercolumn form of the matrix + (no supercolumns on input). Uses a minimum approximate column minimum + degree ordering method. Not user-callable. +*/ + +static int find_ordering /* return the number of garbage collections */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + int Alen, /* size of A, 2*nnz + n_col or larger */ + Colamd_Row Row [], /* of size n_row+1 */ + colamd_col Col [], /* of size n_col+1 */ + int A [], /* column form and row form of A */ + int head [], /* of size n_col+1 */ + int n_col2, /* Remaining columns to order */ + int max_deg, /* Maximum row degree */ + int pfree /* index of first free slot (2*nnz on entry) */ +) +{ + /* === Local variables ================================================== */ + + int k ; /* current pivot ordering step */ + int pivot_col ; /* current pivot column */ + int *cp ; /* a column pointer */ + int *rp ; /* a row pointer */ + int pivot_row ; /* current pivot row */ + int *new_cp ; /* modified column pointer */ + int *new_rp ; /* modified row pointer */ + int pivot_row_start ; /* pointer to start of pivot row */ + int pivot_row_degree ; /* number of columns in pivot row */ + int pivot_row_length ; /* number of supercolumns in pivot row */ + int pivot_col_score ; /* score of pivot column */ + int needed_memory ; /* free space needed for pivot row */ + int *cp_end ; /* pointer to the end of a column */ + int *rp_end ; /* pointer to the end of a row */ + int row ; /* a row index */ + int col ; /* a column index */ + int max_score ; /* maximum possible score */ + int cur_score ; /* score of current column */ + unsigned int hash ; /* hash value for supernode detection */ + int head_column ; /* head of hash bucket */ + int first_col ; /* first column in hash bucket */ + int tag_mark ; /* marker value for mark array */ + int row_mark ; /* Row [row].shared2.mark */ + int set_difference ; /* set difference size of row with pivot row */ + int min_score ; /* smallest column score */ + int col_thickness ; /* "thickness" (no. of columns in a supercol) */ + int max_mark ; /* maximum value of tag_mark */ + int pivot_col_thickness ; /* number of columns represented by pivot col */ + int prev_col ; /* Used by Dlist operations. */ + int next_col ; /* Used by Dlist operations. */ + int ngarbage ; /* number of garbage collections performed */ + + + /* === Initialization and clear mark ==================================== */ + + max_mark = INT_MAX - n_col ; /* INT_MAX defined in */ + tag_mark = clear_mark (n_row, Row) ; + min_score = 0 ; + ngarbage = 0 ; + COLAMD_DEBUG1 (("colamd: Ordering, n_col2=%d\n", n_col2)) ; + + /* === Order the columns ================================================ */ + + for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) + { + + /* === Select pivot column, and order it ============================ */ + + /* make sure degree list isn't empty */ + COLAMD_ASSERT (min_score >= 0) ; + COLAMD_ASSERT (min_score <= n_col) ; + COLAMD_ASSERT (head [min_score] >= COLAMD_EMPTY) ; + + /* get pivot column from head of minimum degree list */ + while (head [min_score] == COLAMD_EMPTY && min_score < n_col) + { + min_score++ ; + } + pivot_col = head [min_score] ; + COLAMD_ASSERT (pivot_col >= 0 && pivot_col <= n_col) ; + next_col = Col [pivot_col].shared4.degree_next ; + head [min_score] = next_col ; + if (next_col != COLAMD_EMPTY) + { + Col [next_col].shared3.prev = COLAMD_EMPTY ; + } + + COLAMD_ASSERT (COL_IS_ALIVE (pivot_col)) ; + COLAMD_DEBUG3 (("Pivot col: %d\n", pivot_col)) ; + + /* remember score for defrag check */ + pivot_col_score = Col [pivot_col].shared2.score ; + + /* the pivot column is the kth column in the pivot order */ + Col [pivot_col].shared2.order = k ; + + /* increment order count by column thickness */ + pivot_col_thickness = Col [pivot_col].shared1.thickness ; + k += pivot_col_thickness ; + COLAMD_ASSERT (pivot_col_thickness > 0) ; + + /* === Garbage_collection, if necessary ============================= */ + + needed_memory = COLAMD_MIN (pivot_col_score, n_col - k) ; + if (pfree + needed_memory >= Alen) + { + pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; + ngarbage++ ; + /* after garbage collection we will have enough */ + COLAMD_ASSERT (pfree + needed_memory < Alen) ; + /* garbage collection has wiped out the Row[].shared2.mark array */ + tag_mark = clear_mark (n_row, Row) ; + + } + + /* === Compute pivot row pattern ==================================== */ + + /* get starting location for this new merged row */ + pivot_row_start = pfree ; + + /* initialize new row counts to zero */ + pivot_row_degree = 0 ; + + /* tag pivot column as having been visited so it isn't included */ + /* in merged pivot row */ + Col [pivot_col].shared1.thickness = -pivot_col_thickness ; + + /* pivot row is the union of all rows in the pivot column pattern */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + COLAMD_DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ; + /* skip if row is dead */ + if (ROW_IS_DEAD (row)) + { + continue ; + } + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + /* add the column, if alive and untagged */ + col_thickness = Col [col].shared1.thickness ; + if (col_thickness > 0 && COL_IS_ALIVE (col)) + { + /* tag column in pivot row */ + Col [col].shared1.thickness = -col_thickness ; + COLAMD_ASSERT (pfree < Alen) ; + /* place column in pivot row */ + A [pfree++] = col ; + pivot_row_degree += col_thickness ; + } + } + } + + /* clear tag on pivot column */ + Col [pivot_col].shared1.thickness = pivot_col_thickness ; + max_deg = COLAMD_MAX (max_deg, pivot_row_degree) ; + + + /* === Kill all rows used to construct pivot row ==================== */ + + /* also kill pivot row, temporarily */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* may be killing an already dead row */ + row = *cp++ ; + COLAMD_DEBUG3 (("Kill row in pivot col: %d\n", row)) ; + KILL_ROW (row) ; + } + + /* === Select a row index to use as the new pivot row =============== */ + + pivot_row_length = pfree - pivot_row_start ; + if (pivot_row_length > 0) + { + /* pick the "pivot" row arbitrarily (first row in col) */ + pivot_row = A [Col [pivot_col].start] ; + COLAMD_DEBUG3 (("Pivotal row is %d\n", pivot_row)) ; + } + else + { + /* there is no pivot row, since it is of zero length */ + pivot_row = COLAMD_EMPTY ; + COLAMD_ASSERT (pivot_row_length == 0) ; + } + COLAMD_ASSERT (Col [pivot_col].length > 0 || pivot_row_length == 0) ; + + /* === Approximate degree computation =============================== */ + + /* Here begins the computation of the approximate degree. The column */ + /* score is the sum of the pivot row "length", plus the size of the */ + /* set differences of each row in the column minus the pattern of the */ + /* pivot row itself. The column ("thickness") itself is also */ + /* excluded from the column score (we thus use an approximate */ + /* external degree). */ + + /* The time taken by the following code (compute set differences, and */ + /* add them up) is proportional to the size of the data structure */ + /* being scanned - that is, the sum of the sizes of each column in */ + /* the pivot row. Thus, the amortized time to compute a column score */ + /* is proportional to the size of that column (where size, in this */ + /* context, is the column "length", or the number of row indices */ + /* in that column). The number of row indices in a column is */ + /* monotonically non-decreasing, from the length of the original */ + /* column on input to colamd. */ + + /* === Compute set differences ====================================== */ + + COLAMD_DEBUG3 (("** Computing set differences phase. **\n")) ; + + /* pivot row is currently dead - it will be revived later. */ + + COLAMD_DEBUG3 (("Pivot row: ")) ; + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; + COLAMD_DEBUG3 (("Col: %d\n", col)) ; + + /* clear tags used to construct pivot row pattern */ + col_thickness = -Col [col].shared1.thickness ; + COLAMD_ASSERT (col_thickness > 0) ; + Col [col].shared1.thickness = col_thickness ; + + /* === Remove column from degree list =========================== */ + + cur_score = Col [col].shared2.score ; + prev_col = Col [col].shared3.prev ; + next_col = Col [col].shared4.degree_next ; + COLAMD_ASSERT (cur_score >= 0) ; + COLAMD_ASSERT (cur_score <= n_col) ; + COLAMD_ASSERT (cur_score >= COLAMD_EMPTY) ; + if (prev_col == COLAMD_EMPTY) + { + head [cur_score] = next_col ; + } + else + { + Col [prev_col].shared4.degree_next = next_col ; + } + if (next_col != COLAMD_EMPTY) + { + Col [next_col].shared3.prev = prev_col ; + } + + /* === Scan the column ========================================== */ + + cp = &A [Col [col].start] ; + cp_end = cp + Col [col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + continue ; + } + COLAMD_ASSERT (row != pivot_row) ; + set_difference = row_mark - tag_mark ; + /* check if the row has been seen yet */ + if (set_difference < 0) + { + COLAMD_ASSERT (Row [row].shared1.degree <= max_deg) ; + set_difference = Row [row].shared1.degree ; + } + /* subtract column thickness from this row's set difference */ + set_difference -= col_thickness ; + COLAMD_ASSERT (set_difference >= 0) ; + /* absorb this row if the set difference becomes zero */ + if (set_difference == 0) + { + COLAMD_DEBUG3 (("aggressive absorption. Row: %d\n", row)) ; + KILL_ROW (row) ; + } + else + { + /* save the new mark */ + Row [row].shared2.mark = set_difference + tag_mark ; + } + } + } + + + /* === Add up set differences for each column ======================= */ + + COLAMD_DEBUG3 (("** Adding set differences phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + COLAMD_ASSERT (COL_IS_ALIVE (col) && col != pivot_col) ; + hash = 0 ; + cur_score = 0 ; + cp = &A [Col [col].start] ; + /* compact the column */ + new_cp = cp ; + cp_end = cp + Col [col].length ; + + COLAMD_DEBUG4 (("Adding set diffs for Col: %d.\n", col)) ; + + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + COLAMD_ASSERT(row >= 0 && row < n_row) ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + continue ; + } + COLAMD_ASSERT (row_mark > tag_mark) ; + /* compact the column */ + *new_cp++ = row ; + /* compute hash function */ + hash += row ; + /* add set difference */ + cur_score += row_mark - tag_mark ; + /* integer overflow... */ + cur_score = COLAMD_MIN (cur_score, n_col) ; + } + + /* recompute the column's length */ + Col [col].length = (int) (new_cp - &A [Col [col].start]) ; + + /* === Further mass elimination ================================= */ + + if (Col [col].length == 0) + { + COLAMD_DEBUG4 (("further mass elimination. Col: %d\n", col)) ; + /* nothing left but the pivot row in this column */ + KILL_PRINCIPAL_COL (col) ; + pivot_row_degree -= Col [col].shared1.thickness ; + COLAMD_ASSERT (pivot_row_degree >= 0) ; + /* order it */ + Col [col].shared2.order = k ; + /* increment order count by column thickness */ + k += Col [col].shared1.thickness ; + } + else + { + /* === Prepare for supercolumn detection ==================== */ + + COLAMD_DEBUG4 (("Preparing supercol detection for Col: %d.\n", col)) ; + + /* save score so far */ + Col [col].shared2.score = cur_score ; + + /* add column to hash table, for supercolumn detection */ + hash %= n_col + 1 ; + + COLAMD_DEBUG4 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ; + COLAMD_ASSERT (hash <= n_col) ; + + head_column = head [hash] ; + if (head_column > COLAMD_EMPTY) + { + /* degree list "hash" is non-empty, use prev (shared3) of */ + /* first column in degree list as head of hash bucket */ + first_col = Col [head_column].shared3.headhash ; + Col [head_column].shared3.headhash = col ; + } + else + { + /* degree list "hash" is empty, use head as hash bucket */ + first_col = - (head_column + 2) ; + head [hash] = - (col + 2) ; + } + Col [col].shared4.hash_next = first_col ; + + /* save hash function in Col [col].shared3.hash */ + Col [col].shared3.hash = (int) hash ; + COLAMD_ASSERT (COL_IS_ALIVE (col)) ; + } + } + + /* The approximate external column degree is now computed. */ + + /* === Supercolumn detection ======================================== */ + + COLAMD_DEBUG3 (("** Supercolumn detection phase. **\n")) ; + + detect_super_cols ( + + Col, A, head, pivot_row_start, pivot_row_length) ; + + /* === Kill the pivotal column ====================================== */ + + KILL_PRINCIPAL_COL (pivot_col) ; + + /* === Clear mark =================================================== */ + + tag_mark += (max_deg + 1) ; + if (tag_mark >= max_mark) + { + COLAMD_DEBUG2 (("clearing tag_mark\n")) ; + tag_mark = clear_mark (n_row, Row) ; + } + + /* === Finalize the new pivot row, and column scores ================ */ + + COLAMD_DEBUG3 (("** Finalize scores phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + /* compact the pivot row */ + new_rp = rp ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + /* skip dead columns */ + if (COL_IS_DEAD (col)) + { + continue ; + } + *new_rp++ = col ; + /* add new pivot row to column */ + A [Col [col].start + (Col [col].length++)] = pivot_row ; + + /* retrieve score so far and add on pivot row's degree. */ + /* (we wait until here for this in case the pivot */ + /* row's degree was reduced due to mass elimination). */ + cur_score = Col [col].shared2.score + pivot_row_degree ; + + /* calculate the max possible score as the number of */ + /* external columns minus the 'k' value minus the */ + /* columns thickness */ + max_score = n_col - k - Col [col].shared1.thickness ; + + /* make the score the external degree of the union-of-rows */ + cur_score -= Col [col].shared1.thickness ; + + /* make sure score is less or equal than the max score */ + cur_score = COLAMD_MIN (cur_score, max_score) ; + COLAMD_ASSERT (cur_score >= 0) ; + + /* store updated score */ + Col [col].shared2.score = cur_score ; + + /* === Place column back in degree list ========================= */ + + COLAMD_ASSERT (min_score >= 0) ; + COLAMD_ASSERT (min_score <= n_col) ; + COLAMD_ASSERT (cur_score >= 0) ; + COLAMD_ASSERT (cur_score <= n_col) ; + COLAMD_ASSERT (head [cur_score] >= COLAMD_EMPTY) ; + next_col = head [cur_score] ; + Col [col].shared4.degree_next = next_col ; + Col [col].shared3.prev = COLAMD_EMPTY ; + if (next_col != COLAMD_EMPTY) + { + Col [next_col].shared3.prev = col ; + } + head [cur_score] = col ; + + /* see if this score is less than current min */ + min_score = COLAMD_MIN (min_score, cur_score) ; + + } + + /* === Resurrect the new pivot row ================================== */ + + if (pivot_row_degree > 0) + { + /* update pivot row length to reflect any cols that were killed */ + /* during super-col detection and mass elimination */ + Row [pivot_row].start = pivot_row_start ; + Row [pivot_row].length = (int) (new_rp - &A[pivot_row_start]) ; + Row [pivot_row].shared1.degree = pivot_row_degree ; + Row [pivot_row].shared2.mark = 0 ; + /* pivot row is no longer dead */ + } + } + + /* === All principal columns have now been ordered ====================== */ + + return (ngarbage) ; +} + + +/* ========================================================================== */ +/* === order_children ======================================================= */ +/* ========================================================================== */ + +/* + The find_ordering routine has ordered all of the principal columns (the + representatives of the supercolumns). The non-principal columns have not + yet been ordered. This routine orders those columns by walking up the + parent tree (a column is a child of the column which absorbed it). The + final permutation vector is then placed in p [0 ... n_col-1], with p [0] + being the first column, and p [n_col-1] being the last. It doesn't look + like it at first glance, but be assured that this routine takes time linear + in the number of columns. Although not immediately obvious, the time + taken by this routine is O (n_col), that is, linear in the number of + columns. Not user-callable. +*/ + +static inline void order_children +( + /* === Parameters ======================================================= */ + + int n_col, /* number of columns of A */ + colamd_col Col [], /* of size n_col+1 */ + int p [] /* p [0 ... n_col-1] is the column permutation*/ +) +{ + /* === Local variables ================================================== */ + + int i ; /* loop counter for all columns */ + int c ; /* column index */ + int parent ; /* index of column's parent */ + int order ; /* column's order */ + + /* === Order each non-principal column ================================== */ + + for (i = 0 ; i < n_col ; i++) + { + /* find an un-ordered non-principal column */ + COLAMD_ASSERT (COL_IS_DEAD (i)) ; + if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == COLAMD_EMPTY) + { + parent = i ; + /* once found, find its principal parent */ + do + { + parent = Col [parent].shared1.parent ; + } while (!COL_IS_DEAD_PRINCIPAL (parent)) ; + + /* now, order all un-ordered non-principal columns along path */ + /* to this parent. collapse tree at the same time */ + c = i ; + /* get order of parent */ + order = Col [parent].shared2.order ; + + do + { + COLAMD_ASSERT (Col [c].shared2.order == COLAMD_EMPTY) ; + + /* order this column */ + Col [c].shared2.order = order++ ; + /* collaps tree */ + Col [c].shared1.parent = parent ; + + /* get immediate parent of this column */ + c = Col [c].shared1.parent ; + + /* continue until we hit an ordered column. There are */ + /* guarranteed not to be anymore unordered columns */ + /* above an ordered column */ + } while (Col [c].shared2.order == COLAMD_EMPTY) ; + + /* re-order the super_col parent to largest order for this group */ + Col [parent].shared2.order = order ; + } + } + + /* === Generate the permutation ========================================= */ + + for (c = 0 ; c < n_col ; c++) + { + p [Col [c].shared2.order] = c ; + } +} + + +/* ========================================================================== */ +/* === detect_super_cols ==================================================== */ +/* ========================================================================== */ + +/* + Detects supercolumns by finding matches between columns in the hash buckets. + Check amongst columns in the set A [row_start ... row_start + row_length-1]. + The columns under consideration are currently *not* in the degree lists, + and have already been placed in the hash buckets. + + The hash bucket for columns whose hash function is equal to h is stored + as follows: + + if head [h] is >= 0, then head [h] contains a degree list, so: + + head [h] is the first column in degree bucket h. + Col [head [h]].headhash gives the first column in hash bucket h. + + otherwise, the degree list is empty, and: + + -(head [h] + 2) is the first column in hash bucket h. + + For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous + column" pointer. Col [c].shared3.hash is used instead as the hash number + for that column. The value of Col [c].shared4.hash_next is the next column + in the same hash bucket. + + Assuming no, or "few" hash collisions, the time taken by this routine is + linear in the sum of the sizes (lengths) of each column whose score has + just been computed in the approximate degree computation. + Not user-callable. +*/ + +static void detect_super_cols +( + /* === Parameters ======================================================= */ + + colamd_col Col [], /* of size n_col+1 */ + int A [], /* row indices of A */ + int head [], /* head of degree lists and hash buckets */ + int row_start, /* pointer to set of columns to check */ + int row_length /* number of columns to check */ +) +{ + /* === Local variables ================================================== */ + + int hash ; /* hash value for a column */ + int *rp ; /* pointer to a row */ + int c ; /* a column index */ + int super_c ; /* column index of the column to absorb into */ + int *cp1 ; /* column pointer for column super_c */ + int *cp2 ; /* column pointer for column c */ + int length ; /* length of column super_c */ + int prev_c ; /* column preceding c in hash bucket */ + int i ; /* loop counter */ + int *rp_end ; /* pointer to the end of the row */ + int col ; /* a column index in the row to check */ + int head_column ; /* first column in hash bucket or degree list */ + int first_col ; /* first column in hash bucket */ + + /* === Consider each column in the row ================================== */ + + rp = &A [row_start] ; + rp_end = rp + row_length ; + while (rp < rp_end) + { + col = *rp++ ; + if (COL_IS_DEAD (col)) + { + continue ; + } + + /* get hash number for this column */ + hash = Col [col].shared3.hash ; + COLAMD_ASSERT (hash <= n_col) ; + + /* === Get the first column in this hash bucket ===================== */ + + head_column = head [hash] ; + if (head_column > COLAMD_EMPTY) + { + first_col = Col [head_column].shared3.headhash ; + } + else + { + first_col = - (head_column + 2) ; + } + + /* === Consider each column in the hash bucket ====================== */ + + for (super_c = first_col ; super_c != COLAMD_EMPTY ; + super_c = Col [super_c].shared4.hash_next) + { + COLAMD_ASSERT (COL_IS_ALIVE (super_c)) ; + COLAMD_ASSERT (Col [super_c].shared3.hash == hash) ; + length = Col [super_c].length ; + + /* prev_c is the column preceding column c in the hash bucket */ + prev_c = super_c ; + + /* === Compare super_c with all columns after it ================ */ + + for (c = Col [super_c].shared4.hash_next ; + c != COLAMD_EMPTY ; c = Col [c].shared4.hash_next) + { + COLAMD_ASSERT (c != super_c) ; + COLAMD_ASSERT (COL_IS_ALIVE (c)) ; + COLAMD_ASSERT (Col [c].shared3.hash == hash) ; + + /* not identical if lengths or scores are different */ + if (Col [c].length != length || + Col [c].shared2.score != Col [super_c].shared2.score) + { + prev_c = c ; + continue ; + } + + /* compare the two columns */ + cp1 = &A [Col [super_c].start] ; + cp2 = &A [Col [c].start] ; + + for (i = 0 ; i < length ; i++) + { + /* the columns are "clean" (no dead rows) */ + COLAMD_ASSERT (ROW_IS_ALIVE (*cp1)) ; + COLAMD_ASSERT (ROW_IS_ALIVE (*cp2)) ; + /* row indices will same order for both supercols, */ + /* no gather scatter nessasary */ + if (*cp1++ != *cp2++) + { + break ; + } + } + + /* the two columns are different if the for-loop "broke" */ + if (i != length) + { + prev_c = c ; + continue ; + } + + /* === Got it! two columns are identical =================== */ + + COLAMD_ASSERT (Col [c].shared2.score == Col [super_c].shared2.score) ; + + Col [super_c].shared1.thickness += Col [c].shared1.thickness ; + Col [c].shared1.parent = super_c ; + KILL_NON_PRINCIPAL_COL (c) ; + /* order c later, in order_children() */ + Col [c].shared2.order = COLAMD_EMPTY ; + /* remove c from hash bucket */ + Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; + } + } + + /* === Empty this hash bucket ======================================= */ + + if (head_column > COLAMD_EMPTY) + { + /* corresponding degree list "hash" is not empty */ + Col [head_column].shared3.headhash = COLAMD_EMPTY ; + } + else + { + /* corresponding degree list "hash" is empty */ + head [hash] = COLAMD_EMPTY ; + } + } +} + + +/* ========================================================================== */ +/* === garbage_collection =================================================== */ +/* ========================================================================== */ + +/* + Defragments and compacts columns and rows in the workspace A. Used when + all avaliable memory has been used while performing row merging. Returns + the index of the first free position in A, after garbage collection. The + time taken by this routine is linear is the size of the array A, which is + itself linear in the number of nonzeros in the input matrix. + Not user-callable. +*/ + +static int garbage_collection /* returns the new value of pfree */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows */ + int n_col, /* number of columns */ + Colamd_Row Row [], /* row info */ + colamd_col Col [], /* column info */ + int A [], /* A [0 ... Alen-1] holds the matrix */ + int *pfree /* &A [0] ... pfree is in use */ +) +{ + /* === Local variables ================================================== */ + + int *psrc ; /* source pointer */ + int *pdest ; /* destination pointer */ + int j ; /* counter */ + int r ; /* a row index */ + int c ; /* a column index */ + int length ; /* length of a row or column */ + + /* === Defragment the columns =========================================== */ + + pdest = &A[0] ; + for (c = 0 ; c < n_col ; c++) + { + if (COL_IS_ALIVE (c)) + { + psrc = &A [Col [c].start] ; + + /* move and compact the column */ + COLAMD_ASSERT (pdest <= psrc) ; + Col [c].start = (int) (pdest - &A [0]) ; + length = Col [c].length ; + for (j = 0 ; j < length ; j++) + { + r = *psrc++ ; + if (ROW_IS_ALIVE (r)) + { + *pdest++ = r ; + } + } + Col [c].length = (int) (pdest - &A [Col [c].start]) ; + } + } + + /* === Prepare to defragment the rows =================================== */ + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + if (Row [r].length == 0) + { + /* this row is of zero length. cannot compact it, so kill it */ + COLAMD_DEBUG3 (("Defrag row kill\n")) ; + KILL_ROW (r) ; + } + else + { + /* save first column index in Row [r].shared2.first_column */ + psrc = &A [Row [r].start] ; + Row [r].shared2.first_column = *psrc ; + COLAMD_ASSERT (ROW_IS_ALIVE (r)) ; + /* flag the start of the row with the one's complement of row */ + *psrc = ONES_COMPLEMENT (r) ; + + } + } + } + + /* === Defragment the rows ============================================== */ + + psrc = pdest ; + while (psrc < pfree) + { + /* find a negative number ... the start of a row */ + if (*psrc++ < 0) + { + psrc-- ; + /* get the row index */ + r = ONES_COMPLEMENT (*psrc) ; + COLAMD_ASSERT (r >= 0 && r < n_row) ; + /* restore first column index */ + *psrc = Row [r].shared2.first_column ; + COLAMD_ASSERT (ROW_IS_ALIVE (r)) ; + + /* move and compact the row */ + COLAMD_ASSERT (pdest <= psrc) ; + Row [r].start = (int) (pdest - &A [0]) ; + length = Row [r].length ; + for (j = 0 ; j < length ; j++) + { + c = *psrc++ ; + if (COL_IS_ALIVE (c)) + { + *pdest++ = c ; + } + } + Row [r].length = (int) (pdest - &A [Row [r].start]) ; + + } + } + /* ensure we found all the rows */ + COLAMD_ASSERT (debug_rows == 0) ; + + /* === Return the new value of pfree ==================================== */ + + return ((int) (pdest - &A [0])) ; +} + + +/* ========================================================================== */ +/* === clear_mark =========================================================== */ +/* ========================================================================== */ + +/* + Clears the Row [].shared2.mark array, and returns the new tag_mark. + Return value is the new tag_mark. Not user-callable. +*/ + +static inline int clear_mark /* return the new value for tag_mark */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows in A */ + Colamd_Row Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */ +) +{ + /* === Local variables ================================================== */ + + int r ; + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + Row [r].shared2.mark = 0 ; + } + } + return (1) ; +} + + +} // namespace internal +#endif diff --git a/Eigen/src/OrderingMethods/Ordering.h b/Eigen/src/OrderingMethods/Ordering.h new file mode 100644 index 000000000..f5757b319 --- /dev/null +++ b/Eigen/src/OrderingMethods/Ordering.h @@ -0,0 +1,158 @@ + +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// 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 . + +#ifndef EIGEN_ORDERING_H +#define EIGEN_ORDERING_H + +#include "Amd.h" +namespace Eigen { + +#include "Eigen_Colamd.h" + +namespace internal { + + /** + * Get the symmetric pattern A^T+A from the input matrix A. + * FIXME: The values should not be considered here + */ + template + void ordering_helper_at_plus_a(const MatrixType& mat, MatrixType& symmat) + { + MatrixType C; + C = mat.transpose(); // NOTE: Could be costly + for (int i = 0; i < C.rows(); i++) + { + for (typename MatrixType::InnerIterator it(C, i); it; ++it) + it.valueRef() = 0.0; + } + symmat = C + mat; + } + +} + +/** + * Get the approximate minimum degree ordering + * If the matrix is not structurally symmetric, an ordering of A^T+A is computed + * \tparam Index The type of indices of the matrix + */ +template +class AMDOrdering +{ + public: + typedef PermutationMatrix PermutationType; + + /** Compute the permutation vector from a sparse matrix + * This routine is much faster if the input matrix is column-major + */ + template + void operator()(const MatrixType& mat, PermutationType& perm) + { + // Compute the symmetric pattern + SparseMatrix symm; + internal::ordering_helper_at_plus_a(mat,symm); + + // Call the AMD routine + //m_mat.prune(keep_diag()); + internal::minimum_degree_ordering(symm, perm); + } + + /** Compute the permutation with a selfadjoint matrix */ + template + void operator()(const SparseSelfAdjointView& mat, PermutationType& perm) + { + SparseMatrix C = mat; + + // Call the AMD routine + // m_mat.prune(keep_diag()); //Remove the diagonal elements + internal::minimum_degree_ordering(C, perm); + } +}; + +/** + * Get the natural ordering + * + *NOTE Returns an empty permutation matrix + * \tparam Index The type of indices of the matrix + */ +template +class NaturalOrdering +{ + public: + typedef PermutationMatrix PermutationType; + + /** Compute the permutation vector from a column-major sparse matrix */ + template + void operator()(const MatrixType& mat, PermutationType& perm) + { + perm.resize(0); + } + +}; + +/** + * Get the column approximate minimum degree ordering + * The matrix should be in column-major format + */ +template +class COLAMDOrdering; +#include "Eigen_Colamd.h" + +template +class COLAMDOrdering +{ + public: + typedef PermutationMatrix PermutationType; + typedef Matrix IndexVector; + /** Compute the permutation vector form a sparse matrix */ + template + void operator() (const MatrixType& mat, PermutationType& perm) + { + int m = mat.rows(); + int n = mat.cols(); + int nnz = mat.nonZeros(); + // Get the recommended value of Alen to be used by colamd + int Alen = internal::colamd_recommended(nnz, m, n); + // Set the default parameters + double knobs [COLAMD_KNOBS]; + int stats [COLAMD_STATS]; + internal::colamd_set_defaults(knobs); + + int info; + IndexVector p(n+1), A(Alen); + for(int i=0; i <= n; i++) p(i) = mat.outerIndexPtr()[i]; + for(int i=0; i < nnz; i++) A(i) = mat.innerIndexPtr()[i]; + // Call Colamd routine to compute the ordering + info = internal::colamd(m, n, Alen, A.data(), p.data(), knobs, stats); + eigen_assert( info && "COLAMD failed " ); + + perm.resize(n); + for (int i = 0; i < n; i++) perm.indices()(p(i)) = i; + + } + +}; + +} // end namespace Eigen +#endif \ No newline at end of file diff --git a/Eigen/src/SparseCore/SparseMatrix.h b/Eigen/src/SparseCore/SparseMatrix.h index 743fa3afc..573804837 100644 --- a/Eigen/src/SparseCore/SparseMatrix.h +++ b/Eigen/src/SparseCore/SparseMatrix.h @@ -469,6 +469,18 @@ class SparseMatrix m_data.squeeze(); } + /** Turns the matrix into the uncompressed mode */ + void uncompress() + { + if(m_innerNonZeros != 0) + return; + m_innerNonZeros = new Index[m_outerSize]; + for (int i = 0; i < m_outerSize; i++) + { + m_innerNonZeros[i] = m_outerIndex[i+1] - m_outerIndex[i]; + } + } + /** Suppresses all nonzeros which are \b much \b smaller \b than \a reference under the tolerence \a epsilon */ void prune(const Scalar& reference, const RealScalar& epsilon = NumTraits::dummy_precision()) { diff --git a/Eigen/src/SparseCore/SparseUtil.h b/Eigen/src/SparseCore/SparseUtil.h index 6062a086f..a686e08da 100644 --- a/Eigen/src/SparseCore/SparseUtil.h +++ b/Eigen/src/SparseCore/SparseUtil.h @@ -113,9 +113,10 @@ template struct sparse_eval { template struct sparse_eval { typedef typename traits::Scalar _Scalar; - enum { _Flags = traits::Flags }; + typedef typename traits::Index _Index; + enum { _Options = ((traits::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor }; public: - typedef SparseMatrix<_Scalar, _Flags> type; + typedef SparseMatrix<_Scalar, _Options, _Index> type; }; template struct sparse_eval { diff --git a/Eigen/src/SparseLU/CMakeLists.txt b/Eigen/src/SparseLU/CMakeLists.txt new file mode 100644 index 000000000..69729ee89 --- /dev/null +++ b/Eigen/src/SparseLU/CMakeLists.txt @@ -0,0 +1,6 @@ +FILE(GLOB Eigen_SparseLU_SRCS "*.h") + +INSTALL(FILES + ${Eigen_SparseLU_SRCS} + DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseLU COMPONENT Devel + ) diff --git a/Eigen/src/SparseLU/SparseLU.h b/Eigen/src/SparseLU/SparseLU.h new file mode 100644 index 000000000..9ea121ce5 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU.h @@ -0,0 +1,630 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_SPARSE_LU_H +#define EIGEN_SPARSE_LU_H + +namespace Eigen { + + +// Data structure needed by all routines +#include "SparseLU_Structs.h" +#include "SparseLU_Matrix.h" + +// Base structure containing all the factorization routines +#include "SparseLUBase.h" +/** + * \ingroup SparseLU_Module + * \brief Sparse supernodal LU factorization for general matrices + * + * This class implements the supernodal LU factorization for general matrices. + * It uses the main techniques from the sequential SuperLU package + * (http://crd-legacy.lbl.gov/~xiaoye/SuperLU/). It handles transparently real + * and complex arithmetics with single and double precision, depending on the + * scalar type of your input matrix. + * The code has been optimized to provide BLAS-3 operations during supernode-panel updates. + * It benefits directly from the built-in high-performant Eigen BLAS routines. + * Moreover, when the size of a supernode is very small, the BLAS calls are avoided to + * enable a better optimization from the compiler. For best performance, + * you should compile it with NDEBUG flag to avoid the numerous bounds checking on vectors. + * + * An important parameter of this class is the ordering method. It is used to reorder the columns + * (and eventually the rows) of the matrix to reduce the number of new elements that are created during + * numerical factorization. The cheapest method available is COLAMD. + * See \link Ordering_Modules the Ordering module \endlink for the list of + * built-in and external ordering methods. + * + * Simple example with key steps + * \code + * VectorXd x(n), b(n); + * SparseMatrix A; + * SparseLU, COLAMDOrdering > solver; + * // fill A and b; + * // Compute the ordering permutation vector from the structural pattern of A + * solver.analyzePattern(A); + * // Compute the numerical factorization + * solver.factorize(A); + * //Use the factors to solve the linear system + * x = solver.solve(b); + * \endcode + * + * \WARNING The input matrix A should be in a \b compressed and \b column-major form. + * Otherwise an expensive copy will be made. You can call the inexpensive makeCompressed() to get a compressed matrix. + * + * \NOTE Unlike the initial SuperLU implementation, there is no step to equilibrate the matrix. + * For badly scaled matrices, this step can be useful to reduce the pivoting during factorization. + * If this is the case for your matrices, you can try the basic scaling method at + * "unsupported/Eigen/src/IterativeSolvers/Scaling.h" + * + * \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<> + * \tparam _OrderingType The ordering method to use, either AMD, COLAMD or METIS + * + * + * \sa \ref TutorialSparseDirectSolvers + * \sa \ref Ordering_Modules + */ +template +class SparseLU +{ + public: + typedef _MatrixType MatrixType; + typedef _OrderingType OrderingType; + typedef typename MatrixType::Scalar Scalar; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename MatrixType::Index Index; + typedef SparseMatrix NCMatrix; + typedef SuperNodalMatrix SCMatrix; + typedef Matrix ScalarVector; + typedef Matrix IndexVector; + typedef PermutationMatrix PermutationType; + + public: + SparseLU():m_isInitialized(true),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0) + { + initperfvalues(); + } + SparseLU(const MatrixType& matrix):m_isInitialized(true),m_Ustore(0,0,0,0,0,0),m_symmetricmode(false),m_diagpivotthresh(1.0) + { + initperfvalues(); + compute(matrix); + } + + ~SparseLU() + { + // Free all explicit dynamic pointers + } + + void analyzePattern (const MatrixType& matrix); + void factorize (const MatrixType& matrix); + void simplicialfactorize(const MatrixType& matrix); + + /** + * Compute the symbolic and numeric factorization of the input sparse matrix. + * The input matrix should be in column-major storage. + */ + void compute (const MatrixType& matrix) + { + // Analyze + analyzePattern(matrix); + //Factorize + factorize(matrix); + } + + inline Index rows() const { return m_mat.rows(); } + inline Index cols() const { return m_mat.cols(); } + /** Indicate that the pattern of the input matrix is symmetric */ + void isSymmetric(bool sym) + { + m_symmetricmode = sym; + } + + /** Set the threshold used for a diagonal entry to be an acceptable pivot. */ + void diagPivotThresh(RealScalar thresh) + { + m_diagpivotthresh = thresh; + } + + /** Return the number of nonzero elements in the L factor */ + int nnzL() + { + if (m_factorizationIsOk) + return m_nnzL; + else + { + std::cerr<<"Numerical factorization should be done before\n"; + return 0; + } + } + /** Return the number of nonzero elements in the U factor */ + int nnzU() + { + if (m_factorizationIsOk) + return m_nnzU; + else + { + std::cerr<<"Numerical factorization should be done before\n"; + return 0; + } + } + /** \returns the solution X of \f$ A X = B \f$ using the current decomposition of A. + * + * \sa compute() + */ + template + inline const internal::solve_retval solve(const MatrixBase& B) const + { + eigen_assert(m_factorizationIsOk && "SparseLU is not initialized."); + eigen_assert(rows()==B.rows() + && "SparseLU::solve(): invalid number of rows of the right hand side matrix B"); + return internal::solve_retval(*this, B.derived()); + } + + + /** \brief Reports whether previous computation was successful. + * + * \returns \c Success if computation was succesful, + * \c NumericalIssue if the PaStiX reports a problem + * \c InvalidInput if the input matrix is invalid + * + * \sa iparm() + */ + ComputationInfo info() const + { + eigen_assert(m_isInitialized && "Decomposition is not initialized."); + return m_info; + } + + template + bool _solve(const MatrixBase &B, MatrixBase &_X) const + { + Dest& X(_X.derived()); + eigen_assert(m_factorizationIsOk && "The matrix should be factorized first"); + EIGEN_STATIC_ASSERT((Dest::Flags&RowMajorBit)==0, + THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES); + + + int nrhs = B.cols(); + Index n = B.rows(); + + // Permute the right hand side to form X = Pr*B + // on return, X is overwritten by the computed solution + X.resize(n,nrhs); + for(int j = 0; j < nrhs; ++j) + X.col(j) = m_perm_r * B.col(j); + + //Forward substitution with L + m_Lstore.solveInPlace(X); + + // Backward solve with U + for (int k = m_Lstore.nsuper(); k >= 0; k--) + { + Index fsupc = m_Lstore.supToCol()[k]; + Index istart = m_Lstore.rowIndexPtr()[fsupc]; + Index nsupr = m_Lstore.rowIndexPtr()[fsupc+1] - istart; + Index nsupc = m_Lstore.supToCol()[k+1] - fsupc; + Index luptr = m_Lstore.colIndexPtr()[fsupc]; + + if (nsupc == 1) + { + for (int j = 0; j < nrhs; j++) + { + X(fsupc, j) /= m_Lstore.valuePtr()[luptr]; + } + } + else + { + Map, 0, OuterStride<> > A( &(m_Lstore.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) ); + Map< Matrix, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) ); + U = A.template triangularView().solve(U); + } + + for (int j = 0; j < nrhs; ++j) + { + for (int jcol = fsupc; jcol < fsupc + nsupc; jcol++) + { + typename MappedSparseMatrix::InnerIterator it(m_Ustore, jcol); + for ( ; it; ++it) + { + Index irow = it.index(); + X(irow, j) -= X(jcol, j) * it.value(); + } + } + } + } // End For U-solve + + // Permute back the solution + for (int j = 0; j < nrhs; ++j) + X.col(j) = m_perm_c.inverse() * X.col(j); + + return true; + } + + protected: + // Functions + void initperfvalues() + { + m_perfv.panel_size = 12; + m_perfv.relax = 1; + m_perfv.maxsuper = 100; + m_perfv.rowblk = 200; + m_perfv.colblk = 60; + m_perfv.fillfactor = 20; + } + + // Variables + mutable ComputationInfo m_info; + bool m_isInitialized; + bool m_factorizationIsOk; + bool m_analysisIsOk; + NCMatrix m_mat; // The input (permuted ) matrix + SCMatrix m_Lstore; // The lower triangular matrix (supernodal) + MappedSparseMatrix m_Ustore; // The upper triangular matrix + PermutationType m_perm_c; // Column permutation + PermutationType m_perm_r ; // Row permutation + IndexVector m_etree; // Column elimination tree + + LU_GlobalLU_t m_glu; + + // SuperLU/SparseLU options + bool m_symmetricmode; + + // values for performance + LU_perfvalues m_perfv; + RealScalar m_diagpivotthresh; // Specifies the threshold used for a diagonal entry to be an acceptable pivot + int m_nnzL, m_nnzU; // Nonzeros in L and U factors + + private: + // Copy constructor + SparseLU (SparseLU& ) {} + +}; // End class SparseLU + + +// Functions needed by the anaysis phase +/** + * Compute the column permutation to minimize the fill-in + * + * - Apply this permutation to the input matrix - + * + * - Compute the column elimination tree on the permuted matrix + * + * - Postorder the elimination tree and the column permutation + * + */ +template +void SparseLU::analyzePattern(const MatrixType& mat) +{ + + //TODO It is possible as in SuperLU to compute row and columns scaling vectors to equilibrate the matrix mat. + + OrderingType ord; + ord(mat,m_perm_c); + + // Apply the permutation to the column of the input matrix +// m_mat = mat * m_perm_c.inverse(); //FIXME It should be less expensive here to permute only the structural pattern of the matrix + + //First copy the whole input matrix. + m_mat = mat; + m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. FIXME : This vector is filled but not subsequently used. + //Then, permute only the column pointers + for (int i = 0; i < mat.cols(); i++) + { + m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = mat.outerIndexPtr()[i]; + m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = mat.outerIndexPtr()[i+1] - mat.outerIndexPtr()[i]; + } + + // Compute the column elimination tree of the permuted matrix + /*if (m_etree.size() == 0) */m_etree.resize(m_mat.cols()); + + SparseLUBase::LU_sp_coletree(m_mat, m_etree); + + // In symmetric mode, do not do postorder here + if (!m_symmetricmode) { + IndexVector post, iwork; + // Post order etree + SparseLUBase::LU_TreePostorder(m_mat.cols(), m_etree, post); + + + // Renumber etree in postorder + int m = m_mat.cols(); + iwork.resize(m+1); + for (int i = 0; i < m; ++i) iwork(post(i)) = post(m_etree(i)); + m_etree = iwork; + + // Postmultiply A*Pc by post, i.e reorder the matrix according to the postorder of the etree + PermutationType post_perm(m); //FIXME Use directly a constructor with post + for (int i = 0; i < m; i++) + post_perm.indices()(i) = post(i); + + // Combine the two permutations : postorder the permutation for future use + m_perm_c = post_perm * m_perm_c; + + } // end postordering + + m_analysisIsOk = true; +} + +// Functions needed by the numerical factorization phase + + +/** + * - Numerical factorization + * - Interleaved with the symbolic factorization + * On exit, info is + * + * = 0: successful factorization + * + * > 0: if info = i, and i is + * + * <= A->ncol: U(i,i) is exactly zero. The factorization has + * been completed, but the factor U is exactly singular, + * and division by zero will occur if it is used to solve a + * system of equations. + * + * > A->ncol: number of bytes allocated when memory allocation + * failure occurred, plus A->ncol. If lwork = -1, it is + * the estimated amount of space needed, plus A->ncol. + */ +template +void SparseLU::factorize(const MatrixType& matrix) +{ + + eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); + eigen_assert((matrix.rows() == matrix.cols()) && "Only for squared matrices"); + + typedef typename IndexVector::Scalar Index; + + + // Apply the column permutation computed in analyzepattern() + // m_mat = matrix * m_perm_c.inverse(); + m_mat = matrix; + m_mat.uncompress(); //NOTE: The effect of this command is only to create the InnerNonzeros pointers. + //Then, permute only the column pointers + for (int i = 0; i < matrix.cols(); i++) + { + m_mat.outerIndexPtr()[m_perm_c.indices()(i)] = matrix.outerIndexPtr()[i]; + m_mat.innerNonZeroPtr()[m_perm_c.indices()(i)] = matrix.outerIndexPtr()[i+1] - matrix.outerIndexPtr()[i]; + } + + int m = m_mat.rows(); + int n = m_mat.cols(); + int nnz = m_mat.nonZeros(); + int maxpanel = m_perfv.panel_size * m; + // Allocate working storage common to the factor routines + int lwork = 0; + int info = SparseLUBase::LUMemInit(m, n, nnz, lwork, m_perfv.fillfactor, m_perfv.panel_size, m_glu); + if (info) + { + std::cerr << "UNABLE TO ALLOCATE WORKING MEMORY\n\n" ; + m_factorizationIsOk = false; + return ; + } + + // Set up pointers for integer working arrays + IndexVector segrep(m); segrep.setZero(); + IndexVector parent(m); parent.setZero(); + IndexVector xplore(m); xplore.setZero(); + IndexVector repfnz(maxpanel); + IndexVector panel_lsub(maxpanel); + IndexVector xprune(n); xprune.setZero(); + IndexVector marker(m*LU_NO_MARKER); marker.setZero(); + + repfnz.setConstant(-1); + panel_lsub.setConstant(-1); + + // Set up pointers for scalar working arrays + ScalarVector dense; + dense.setZero(maxpanel); + ScalarVector tempv; + tempv.setZero(LU_NUM_TEMPV(m, m_perfv.panel_size, m_perfv.maxsuper, m_perfv.rowblk) ); + + // Compute the inverse of perm_c + PermutationType iperm_c(m_perm_c.inverse()); + + // Identify initial relaxed snodes + IndexVector relax_end(n); + if ( m_symmetricmode == true ) + SparseLUBase::LU_heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end); + else + SparseLUBase::LU_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end); + + + m_perm_r.resize(m); + m_perm_r.indices().setConstant(-1); + marker.setConstant(-1); + + m_glu.supno(0) = IND_EMPTY; m_glu.xsup.setConstant(0); + m_glu.xsup(0) = m_glu.xlsub(0) = m_glu.xusub(0) = m_glu.xlusup(0) = Index(0); + + // Work on one 'panel' at a time. A panel is one of the following : + // (a) a relaxed supernode at the bottom of the etree, or + // (b) panel_size contiguous columns, defined by the user + int jcol,kcol; + IndexVector panel_histo(n); + Index nextu, nextlu, jsupno, fsupc, new_next; + Index pivrow; // Pivotal row number in the original row matrix + int nseg1; // Number of segments in U-column above panel row jcol + int nseg; // Number of segments in each U-column + int irep, icol; + int i, k, jj; + for (jcol = 0; jcol < n; ) + { + if (relax_end(jcol) != IND_EMPTY) + { // Starting a relaxed node from jcol + kcol = relax_end(jcol); // End index of the relaxed snode + + // Factorize the relaxed supernode(jcol:kcol) + // First, determine the union of the row structure of the snode + info = SparseLUBase::LU_snode_dfs(jcol, kcol, m_mat, xprune, marker, m_glu); + if ( info ) + { + std::cerr << "MEMORY ALLOCATION FAILED IN SNODE_DFS() \n"; + m_info = NumericalIssue; + m_factorizationIsOk = false; + return; + } + nextu = m_glu.xusub(jcol); //starting location of column jcol in ucol + nextlu = m_glu.xlusup(jcol); //Starting location of column jcol in lusup (rectangular supernodes) + jsupno = m_glu.supno(jcol); // Supernode number which column jcol belongs to + fsupc = m_glu.xsup(jsupno); //First column number of the current supernode + new_next = nextlu + (m_glu.xlsub(fsupc+1)-m_glu.xlsub(fsupc)) * (kcol - jcol + 1); + int mem; + while (new_next > m_glu.nzlumax ) + { + mem = SparseLUBase::LUMemXpand(m_glu.lusup, m_glu.nzlumax, nextlu, LUSUP, m_glu.num_expansions); + if (mem) + { + std::cerr << "MEMORY ALLOCATION FAILED FOR L FACTOR \n"; + m_factorizationIsOk = false; + return; + } + } + + // Now, left-looking factorize each column within the snode + for (icol = jcol; icol<=kcol; icol++){ + m_glu.xusub(icol+1) = nextu; + // Scatter into SPA dense(*) + for (typename MatrixType::InnerIterator it(m_mat, icol); it; ++it) + dense(it.row()) = it.value(); + + // Numeric update within the snode + SparseLUBase::LU_snode_bmod(icol, fsupc, dense, m_glu); + + // Eliminate the current column + info = SparseLUBase::LU_pivotL(icol, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu); + if ( info ) + { + m_info = NumericalIssue; + std::cerr<< "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT " << info <::LU_panel_dfs(m, panel_size, jcol, m_mat, m_perm_r.indices(), nseg1, dense, panel_lsub, segrep, repfnz, xprune, marker, parent, xplore, m_glu); + + // Numeric sup-panel updates in topological order + SparseLUBase::LU_panel_bmod(m, panel_size, jcol, nseg1, dense, tempv, segrep, repfnz, m_perfv, m_glu); + + // Sparse LU within the panel, and below the panel diagonal + for ( jj = jcol; jj< jcol + panel_size; jj++) + { + k = (jj - jcol) * m; // Column index for w-wide arrays + + nseg = nseg1; // begin after all the panel segments + //Depth-first-search for the current column + VectorBlock panel_lsubk(panel_lsub, k, m); + VectorBlock repfnz_k(repfnz, k, m); + info = SparseLUBase::LU_column_dfs(m, jj, m_perm_r.indices(), m_perfv.maxsuper, nseg, panel_lsubk, segrep, repfnz_k, xprune, marker, parent, xplore, m_glu); + if ( info ) + { + std::cerr << "UNABLE TO EXPAND MEMORY IN COLUMN_DFS() \n"; + m_info = NumericalIssue; + m_factorizationIsOk = false; + return; + } + // Numeric updates to this column + VectorBlock dense_k(dense, k, m); + VectorBlock segrep_k(segrep, nseg1, m-nseg1); + info = SparseLUBase::LU_column_bmod(jj, (nseg - nseg1), dense_k, tempv, segrep_k, repfnz_k, jcol, m_glu); + if ( info ) + { + std::cerr << "UNABLE TO EXPAND MEMORY IN COLUMN_BMOD() \n"; + m_info = NumericalIssue; + m_factorizationIsOk = false; + return; + } + + // Copy the U-segments to ucol(*) + info = SparseLUBase::LU_copy_to_ucol(jj, nseg, segrep, repfnz_k ,m_perm_r.indices(), dense_k, m_glu); + if ( info ) + { + std::cerr << "UNABLE TO EXPAND MEMORY IN COPY_TO_UCOL() \n"; + m_info = NumericalIssue; + m_factorizationIsOk = false; + return; + } + + // Form the L-segment + info = SparseLUBase::LU_pivotL(jj, m_diagpivotthresh, m_perm_r.indices(), iperm_c.indices(), pivrow, m_glu); + if ( info ) + { + std::cerr<< "THE MATRIX IS STRUCTURALLY SINGULAR ... ZERO COLUMN AT " << info <::LU_pruneL(jj, m_perm_r.indices(), pivrow, nseg, segrep, repfnz_k, xprune, m_glu); + + // Reset repfnz for this column + for (i = 0; i < nseg; i++) + { + irep = segrep(i); + repfnz_k(irep) = IND_EMPTY; + } + } // end SparseLU within the panel + jcol += panel_size; // Move to the next panel + } // end else + } // end for -- end elimination + + // Count the number of nonzeros in factors + SparseLUBase::LU_countnz(n, m_nnzL, m_nnzU, m_glu); + // Apply permutation to the L subscripts + SparseLUBase::LU_fixupL(n, m_perm_r.indices(), m_glu); + + // Create supernode matrix L + m_Lstore.setInfos(m, n, m_glu.lusup, m_glu.xlusup, m_glu.lsub, m_glu.xlsub, m_glu.supno, m_glu.xsup); + // Create the column major upper sparse matrix U; + new (&m_Ustore) MappedSparseMatrix ( m, n, m_nnzU, m_glu.xusub.data(), m_glu.usub.data(), m_glu.ucol.data() ); + + m_info = Success; + m_factorizationIsOk = true; +} + +// #include "SparseLU_simplicialfactorize.h" +namespace internal { + +template +struct solve_retval, Rhs> + : solve_retval_base, Rhs> +{ + typedef SparseLU<_MatrixType,Derived> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } +}; + +} // end namespace internal + +} // End namespace Eigen +#endif diff --git a/Eigen/src/SparseLU/SparseLUBase.h b/Eigen/src/SparseLU/SparseLUBase.h new file mode 100644 index 000000000..c00bc0532 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLUBase.h @@ -0,0 +1,74 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +#ifndef SPARSELUBASE_H +#define SPARSELUBASE_H +/** + * Base class for sparseLU + */ +template +struct SparseLUBase +{ + typedef Matrix ScalarVector; + typedef Matrix IndexVector; + typedef typename ScalarVector::RealScalar RealScalar; + typedef VectorBlock > BlockScalarVector; + typedef VectorBlock > BlockIndexVector; +// typedef Ref > BlockScalarVector; +// typedef Ref > BlockIndexVector; + typedef LU_GlobalLU_t GlobalLU_t; + typedef SparseMatrix MatrixType; + + static int etree_find (int i, IndexVector& pp); + static int LU_sp_coletree(const MatrixType& mat, IndexVector& parent); + static void LU_nr_etdfs (int n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, int postnum); + static void LU_TreePostorder(int n, IndexVector& parent, IndexVector& post); + template + static int expand(VectorType& vec, int& length, int nbElts, int keep_prev, int& num_expansions); + static int LUMemInit(int m, int n, int annz, int lwork, int fillratio, int panel_size, GlobalLU_t& glu); + template + static int LUMemXpand(VectorType& vec, int& maxlen, int nbElts, LU_MemType memtype, int& num_expansions); + static void LU_heap_relax_snode (const int n, IndexVector& et, const int relax_columns, IndexVector& descendants, IndexVector& relax_end); + static void LU_relax_snode (const int n, IndexVector& et, const int relax_columns, IndexVector& descendants, IndexVector& relax_end); + static int LU_snode_dfs(const int jcol, const int kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, LU_GlobalLU_t& glu); + static int LU_snode_bmod (const int jcol, const int fsupc, ScalarVector& dense, GlobalLU_t& glu); + static int LU_pivotL(const int jcol, const RealScalar diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, int& pivrow, GlobalLU_t& glu); + template + static void LU_dfs_kernel(const int jj, IndexVector& perm_r, + int& nseg, IndexVector& panel_lsub, IndexVector& segrep, + Ref repfnz_col, IndexVector& xprune, Ref marker, IndexVector& parent, + IndexVector& xplore, GlobalLU_t& glu, int& nextl_col, int krow, Traits& traits); + static void LU_panel_dfs(const int m, const int w, const int jcol, MatrixType& A, IndexVector& perm_r, int& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu); + + static void LU_panel_bmod(const int m, const int w, const int jcol, const int nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, LU_perfvalues& perfv, GlobalLU_t& glu); + static int LU_column_dfs(const int m, const int jcol, IndexVector& perm_r, int maxsuper, int& nseg, BlockIndexVector& lsub_col, IndexVector& segrep, BlockIndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu); + static int LU_column_bmod(const int jcol, const int nseg, BlockScalarVector& dense, ScalarVector& tempv, BlockIndexVector& segrep, BlockIndexVector& repfnz, int fpanelc, GlobalLU_t& glu); + static int LU_copy_to_ucol(const int jcol, const int nseg, IndexVector& segrep, BlockIndexVector& repfnz ,IndexVector& perm_r, BlockScalarVector& dense, GlobalLU_t& glu); + static void LU_pruneL(const int jcol, const IndexVector& perm_r, const int pivrow, const int nseg, const IndexVector& segrep, BlockIndexVector& repfnz, IndexVector& xprune, GlobalLU_t& glu); + static void LU_countnz(const int n, int& nnzL, int& nnzU, GlobalLU_t& glu); + static void LU_fixupL(const int n, const IndexVector& perm_r, GlobalLU_t& glu); + +}; + +#include "SparseLU_Coletree.h" +#include "SparseLU_Memory.h" +#include "SparseLU_heap_relax_snode.h" +#include "SparseLU_relax_snode.h" +#include "SparseLU_snode_dfs.h" +#include "SparseLU_snode_bmod.h" +#include "SparseLU_pivotL.h" +#include "SparseLU_panel_dfs.h" +#include "SparseLU_kernel_bmod.h" +#include "SparseLU_panel_bmod.h" +#include "SparseLU_column_dfs.h" +#include "SparseLU_column_bmod.h" +#include "SparseLU_copy_to_ucol.h" +#include "SparseLU_pruneL.h" +#include "SparseLU_Utils.h" + +#endif diff --git a/Eigen/src/SparseLU/SparseLU_Coletree.h b/Eigen/src/SparseLU/SparseLU_Coletree.h new file mode 100644 index 000000000..d3bc36ea4 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_Coletree.h @@ -0,0 +1,180 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +/* + + * NOTE: This file is the modified version of sp_coletree.c file in SuperLU + + * -- SuperLU routine (version 3.1) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * August 1, 2008 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_COLETREE_H +#define SPARSELU_COLETREE_H +/** Find the root of the tree/set containing the vertex i : Use Path halving */ +template< typename Scalar,typename Index> +int SparseLUBase::etree_find (int i, IndexVector& pp) +{ + int p = pp(i); // Parent + int gp = pp(p); // Grand parent + while (gp != p) + { + pp(i) = gp; // Parent pointer on find path is changed to former grand parent + i = gp; + p = pp(i); + gp = pp(p); + } + return p; +} + +/** Compute the column elimination tree of a sparse matrix + * NOTE : The matrix is supposed to be in column-major format. + * + */ +template +int SparseLUBase::LU_sp_coletree(const MatrixType& mat, IndexVector& parent) +{ + int nc = mat.cols(); // Number of columns + int nr = mat.rows(); // Number of rows + + IndexVector root(nc); // root of subtree of etree + root.setZero(); + IndexVector pp(nc); // disjoint sets + pp.setZero(); // Initialize disjoint sets + IndexVector firstcol(nr); // First nonzero column in each row + + //Compute first nonzero column in each row + int row,col; + firstcol.setConstant(nc); //for (row = 0; row < nr; firstcol(row++) = nc); + for (col = 0; col < nc; col++) + { + for (typename MatrixType::InnerIterator it(mat, col); it; ++it) + { // Is it necessary to browse the whole matrix, the lower part should do the job ?? + row = it.row(); + firstcol(row) = (std::min)(firstcol(row), col); + } + } + /* Compute etree by Liu's algorithm for symmetric matrices, + except use (firstcol[r],c) in place of an edge (r,c) of A. + Thus each row clique in A'*A is replaced by a star + centered at its first vertex, which has the same fill. */ + int rset, cset, rroot; + for (col = 0; col < nc; col++) + { + pp(col) = col; + cset = col; + root(cset) = col; + parent(col) = nc; + for (typename MatrixType::InnerIterator it(mat, col); it; ++it) + { // A sequence of interleaved find and union is performed + row = firstcol(it.row()); + if (row >= col) continue; + rset = etree_find(row, pp); // Find the name of the set containing row + rroot = root(rset); + if (rroot != col) + { + parent(rroot) = col; + pp(cset) = rset; + cset = rset; + root(cset) = col; + } + } + } + return 0; +} + +/** + * Depth-first search from vertex n. No recursion. + * This routine was contributed by Cédric Doucet, CEDRAT Group, Meylan, France. +*/ +template +void SparseLUBase::LU_nr_etdfs (int n, IndexVector& parent, IndexVector& first_kid, IndexVector& next_kid, IndexVector& post, int postnum) +{ + int current = n, first, next; + while (postnum != n) + { + // No kid for the current node + first = first_kid(current); + + // no kid for the current node + if (first == -1) + { + // Numbering this node because it has no kid + post(current) = postnum++; + + // looking for the next kid + next = next_kid(current); + while (next == -1) + { + // No more kids : back to the parent node + current = parent(current); + // numbering the parent node + post(current) = postnum++; + + // Get the next kid + next = next_kid(current); + } + // stopping criterion + if (postnum == n+1) return; + + // Updating current node + current = next; + } + else + { + current = first; + } + } +} + + +/** + * Post order a tree + * \param parent Input tree + * \param post postordered tree + */ +template +void SparseLUBase::LU_TreePostorder(int n, IndexVector& parent, IndexVector& post) +{ + IndexVector first_kid, next_kid; // Linked list of children + int postnum; + // Allocate storage for working arrays and results + first_kid.resize(n+1); + next_kid.setZero(n+1); + post.setZero(n+1); + + // Set up structure describing children + int v, dad; + first_kid.setConstant(-1); + for (v = n-1; v >= 0; v--) + { + dad = parent(v); + next_kid(v) = first_kid(dad); + first_kid(dad) = v; + } + + // Depth-first search from dummy root vertex #n + postnum = 0; + LU_nr_etdfs(n, parent, first_kid, next_kid, post, postnum); +} + +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_Matrix.h b/Eigen/src/SparseLU/SparseLU_Matrix.h new file mode 100644 index 000000000..31aeee64d --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_Matrix.h @@ -0,0 +1,313 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_SPARSELU_MATRIX_H +#define EIGEN_SPARSELU_MATRIX_H + +/** \ingroup SparseLU_Module + * \brief a class to manipulate the L supernodal factor from the SparseLU factorization + * + * This class contain the data to easily store + * and manipulate the supernodes during the factorization and solution phase of Sparse LU. + * Only the lower triangular matrix has supernodes. + * + * NOTE : This class corresponds to the SCformat structure in SuperLU + * + */ +/* TO DO + * InnerIterator as for sparsematrix + * SuperInnerIterator to iterate through all supernodes + * Function for triangular solve + */ +template +class SuperNodalMatrix +{ + public: + typedef _Scalar Scalar; + typedef _Index Index; + typedef Matrix IndexVector; + typedef Matrix ScalarVector; + public: + SuperNodalMatrix() + { + + } + SuperNodalMatrix(int m, int n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind, + IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col ) + { + setInfos(m, n, nzval, nzval_colptr, rowind, rowind_colptr, col_to_sup, sup_to_col); + } + + ~SuperNodalMatrix() + { + + } + /** + * Set appropriate pointers for the lower triangular supernodal matrix + * These infos are available at the end of the numerical factorization + * FIXME This class will be modified such that it can be use in the course + * of the factorization. + */ + void setInfos(int m, int n, ScalarVector& nzval, IndexVector& nzval_colptr, IndexVector& rowind, + IndexVector& rowind_colptr, IndexVector& col_to_sup, IndexVector& sup_to_col ) + { + m_row = m; + m_col = n; + m_nzval = nzval.data(); + m_nzval_colptr = nzval_colptr.data(); + m_rowind = rowind.data(); + m_rowind_colptr = rowind_colptr.data(); + m_nsuper = col_to_sup(n); + m_col_to_sup = col_to_sup.data(); + m_sup_to_col = sup_to_col.data(); + + } + + /** + * Number of rows + */ + int rows() + { + return m_row; + } + + /** + * Number of columns + */ + int cols() + { + return m_col; + } + + /** + * Return the array of nonzero values packed by column + * + * The size is nnz + */ + Scalar* valuePtr() + { + return m_nzval; + } + + const Scalar* valuePtr() const + { + return m_nzval; + } + /** + * Return the pointers to the beginning of each column in \ref valuePtr() + */ + Index* colIndexPtr() + { + return m_nzval_colptr; + } + + const Index* colIndexPtr() const + { + return m_nzval_colptr; + } + + /** + * Return the array of compressed row indices of all supernodes + */ + Index* rowIndex() + { + return m_rowind; + } + + const Index* rowIndex() const + { + return m_rowind; + } + + /** + * Return the location in \em rowvaluePtr() which starts each column + */ + Index* rowIndexPtr() + { + return m_rowind_colptr; + } + + const Index* rowIndexPtr() const + { + return m_rowind_colptr; + } + + /** + * Return the array of column-to-supernode mapping + */ + Index* colToSup() + { + return m_col_to_sup; + } + + const Index* colToSup() const + { + return m_col_to_sup; + } + /** + * Return the array of supernode-to-column mapping + */ + Index* supToCol() + { + return m_sup_to_col; + } + + const Index* supToCol() const + { + return m_sup_to_col; + } + + /** + * Return the number of supernodes + */ + int nsuper() const + { + return m_nsuper; + } + + class InnerIterator; + template + void solveInPlace( MatrixBase&X) const; + + + + + protected: + Index m_row; // Number of rows + Index m_col; // Number of columns + Index m_nsuper; // Number of supernodes + Scalar* m_nzval; //array of nonzero values packed by column + Index* m_nzval_colptr; //nzval_colptr[j] Stores the location in nzval[] which starts column j + Index* m_rowind; // Array of compressed row indices of rectangular supernodes + Index* m_rowind_colptr; //rowind_colptr[j] stores the location in rowind[] which starts column j + Index* m_col_to_sup; // col_to_sup[j] is the supernode number to which column j belongs + Index* m_sup_to_col; //sup_to_col[s] points to the starting column of the s-th supernode + + private : +}; + +/** + * \brief InnerIterator class to iterate over nonzero values of the current column in the supernode + * + */ +template +class SuperNodalMatrix::InnerIterator +{ + public: + InnerIterator(const SuperNodalMatrix& mat, Index outer) + : m_matrix(mat), + m_outer(outer), + m_idval(mat.colIndexPtr()[outer]), + m_startval(m_idval), + m_endval(mat.colIndexPtr()[outer+1]), + m_idrow(mat.rowIndexPtr()[outer]), + m_startidrow(m_idrow), + m_endidrow(mat.rowIndexPtr()[outer+1]) + {} + inline InnerIterator& operator++() + { + m_idval++; + m_idrow++; + return *this; + } + inline Scalar value() const { return m_matrix.valuePtr()[m_idval]; } + + inline Scalar& valueRef() { return const_cast(m_matrix.valuePtr()[m_idval]); } + + inline Index index() const { return m_matrix.rowIndex()[m_idrow]; } + inline Index row() const { return index(); } + inline Index col() const { return m_outer; } + + inline Index supIndex() const { return m_matrix.colToSup()[m_outer]; } + + inline operator bool() const + { + return ( (m_idval < m_endval) && (m_idval > m_startval) && + (m_idrow < m_endidrow) && (m_idrow > m_startidrow) ); + } + + protected: + const SuperNodalMatrix& m_matrix; // Supernodal lower triangular matrix + const Index m_outer; // Current column + Index m_idval; //Index to browse the values in the current column + const Index m_startval; // Start of the column value + const Index m_endval; // End of the column value + Index m_idrow; //Index to browse the row indices + const Index m_startidrow; // Start of the row indices of the current column value + const Index m_endidrow; // End of the row indices of the current column value +}; + +/** + * \brief Solve with the supernode triangular matrix + * + */ +template +template +void SuperNodalMatrix::solveInPlace( MatrixBase&X) const +{ + Index n = X.rows(); + int nrhs = X.cols(); + const Scalar * Lval = valuePtr(); // Nonzero values + Matrix work(n, nrhs); // working vector + work.setZero(); + for (int k = 0; k <= nsuper(); k ++) + { + Index fsupc = supToCol()[k]; // First column of the current supernode + Index istart = rowIndexPtr()[fsupc]; // Pointer index to the subscript of the current column + Index nsupr = rowIndexPtr()[fsupc+1] - istart; // Number of rows in the current supernode + Index nsupc = supToCol()[k+1] - fsupc; // Number of columns in the current supernode + Index nrow = nsupr - nsupc; // Number of rows in the non-diagonal part of the supernode + Index irow; //Current index row + + if (nsupc == 1 ) + { + for (int j = 0; j < nrhs; j++) + { + InnerIterator it(*this, fsupc); + ++it; // Skip the diagonal element + for (; it; ++it) + { + irow = it.row(); + X(irow, j) -= X(fsupc, j) * it.value(); + } + } + } + else + { + // The supernode has more than one column + Index luptr = colIndexPtr()[fsupc]; + + // Triangular solve + Map, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(nsupr) ); + Map< Matrix, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) ); + U = A.template triangularView().solve(U); + + // Matrix-vector product + new (&A) Map, 0, OuterStride<> > ( &(Lval[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) ); + work.block(0, 0, nrow, nrhs) = A * U; + + //Begin Scatter + for (int j = 0; j < nrhs; j++) + { + Index iptr = istart + nsupc; + for (int i = 0; i < nrow; i++) + { + irow = rowIndex()[iptr]; + X(irow, j) -= work(i, j); // Scatter operation + work(i, j) = Scalar(0); + iptr++; + } + } + } + } +} + + +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_Memory.h b/Eigen/src/SparseLU/SparseLU_Memory.h new file mode 100644 index 000000000..7b9f01355 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_Memory.h @@ -0,0 +1,204 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]memory.c files in SuperLU + + * -- SuperLU routine (version 3.1) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * August 1, 2008 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ + +#ifndef EIGEN_SPARSELU_MEMORY +#define EIGEN_SPARSELU_MEMORY + +#define LU_NO_MARKER 3 +#define LU_NUM_TEMPV(m,w,t,b) ((std::max)(m, (t+b)*w) ) +#define IND_EMPTY (-1) + +#define LU_Reduce(alpha) ((alpha + 1) / 2) // i.e (alpha-1)/2 + 1 +#define LU_GluIntArray(n) (5* (n) + 5) +#define LU_TempSpace(m, w) ( (2*w + 4 + LU_NO_MARKER) * m * sizeof(Index) \ + + (w + 1) * m * sizeof(Scalar) ) + + +/** + * Expand the existing storage to accomodate more fill-ins + * \param vec Valid pointer to the vector to allocate or expand + * \param [in,out]length At input, contain the current length of the vector that is to be increased. At output, length of the newly allocated vector + * \param [in]nbElts Current number of elements in the factors + * \param keep_prev 1: use length and do not expand the vector; 0: compute new_len and expand + * \param [in,out]num_expansions Number of times the memory has been expanded + */ +template +template +int SparseLUBase::expand(VectorType& vec, int& length, int nbElts, int keep_prev, int& num_expansions) +{ + + float alpha = 1.5; // Ratio of the memory increase + int new_len; // New size of the allocated memory + + if(num_expansions == 0 || keep_prev) + new_len = length ; // First time allocate requested + else + new_len = alpha * length ; + + VectorType old_vec; // Temporary vector to hold the previous values + if (nbElts > 0 ) + old_vec = vec.segment(0,nbElts); + + //Allocate or expand the current vector + try + { + vec.resize(new_len); + } + catch(std::bad_alloc& ) + { + if ( !num_expansions ) + { + // First time to allocate from LUMemInit() + throw; // Pass the exception to LUMemInit() which has a try... catch block + } + if (keep_prev) + { + // In this case, the memory length should not not be reduced + return new_len; + } + else + { + // Reduce the size and increase again + int tries = 0; // Number of attempts + do + { + alpha = LU_Reduce(alpha); + new_len = alpha * length ; + try + { + vec.resize(new_len); + } + catch(std::bad_alloc& ) + { + tries += 1; + if ( tries > 10) return new_len; + } + } while (!vec.size()); + } + } + //Copy the previous values to the newly allocated space + if (nbElts > 0) + vec.segment(0, nbElts) = old_vec; + + + length = new_len; + if(num_expansions) ++num_expansions; + return 0; +} + +/** + * \brief Allocate various working space for the numerical factorization phase. + * \param m number of rows of the input matrix + * \param n number of columns + * \param annz number of initial nonzeros in the matrix + * \param lwork if lwork=-1, this routine returns an estimated size of the required memory + * \param glu persistent data to facilitate multiple factors : will be deleted later ?? + * \return an estimated size of the required memory if lwork = -1; otherwise, return the size of actually allocated memory when allocation failed, and 0 on success + * NOTE Unlike SuperLU, this routine does not support successive factorization with the same pattern and the same row permutation + */ +template +int SparseLUBase::LUMemInit(int m, int n, int annz, int lwork, int fillratio, int panel_size, GlobalLU_t& glu) +{ + int& num_expansions = glu.num_expansions; //No memory expansions so far + num_expansions = 0; + glu.nzumax = glu.nzlumax = (std::max)(fillratio * annz, m*n); // estimated number of nonzeros in U + glu.nzlmax = (std::max)(1., fillratio/4.) * annz; // estimated nnz in L factor + + // Return the estimated size to the user if necessary + if (lwork == IND_EMPTY) + { + int estimated_size; + estimated_size = LU_GluIntArray(n) * sizeof(Index) + LU_TempSpace(m, panel_size) + + (glu.nzlmax + glu.nzumax) * sizeof(Index) + (glu.nzlumax+glu.nzumax) * sizeof(Scalar) + n; + return estimated_size; + } + + // Setup the required space + + // First allocate Integer pointers for L\U factors + glu.xsup.resize(n+1); + glu.supno.resize(n+1); + glu.xlsub.resize(n+1); + glu.xlusup.resize(n+1); + glu.xusub.resize(n+1); + + // Reserve memory for L/U factors + do + { + try + { + expand(glu.lusup, glu.nzlumax, 0, 0, num_expansions); + expand(glu.ucol,glu.nzumax, 0, 0, num_expansions); + expand(glu.lsub,glu.nzlmax, 0, 0, num_expansions); + expand(glu.usub,glu.nzumax, 0, 1, num_expansions); + } + catch(std::bad_alloc& ) + { + //Reduce the estimated size and retry + glu.nzlumax /= 2; + glu.nzumax /= 2; + glu.nzlmax /= 2; + if (glu.nzlumax < annz ) return glu.nzlumax; + } + + } while (!glu.lusup.size() || !glu.ucol.size() || !glu.lsub.size() || !glu.usub.size()); + + + + ++num_expansions; + return 0; + +} // end LuMemInit + +/** + * \brief Expand the existing storage + * \param vec vector to expand + * \param [in,out]maxlen On input, previous size of vec (Number of elements to copy ). on output, new size + * \param nbElts current number of elements in the vector. + * \param glu Global data structure + * \return 0 on success, > 0 size of the memory allocated so far + */ +template +template +int SparseLUBase::LUMemXpand(VectorType& vec, int& maxlen, int nbElts, LU_MemType memtype, int& num_expansions) +{ + int failed_size; + if (memtype == USUB) + failed_size = expand(vec, maxlen, nbElts, 1, num_expansions); + else + failed_size = expand(vec, maxlen, nbElts, 0, num_expansions); + + if (failed_size) + return failed_size; + + return 0 ; + +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_Structs.h b/Eigen/src/SparseLU/SparseLU_Structs.h new file mode 100644 index 000000000..7b3aa250c --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_Structs.h @@ -0,0 +1,103 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + * NOTE: This file comes from a partly modified version of files slu_[s,d,c,z]defs.h + * -- SuperLU routine (version 4.1) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November, 2010 + * + * Global data structures used in LU factorization - + * + * nsuper: #supernodes = nsuper + 1, numbered [0, nsuper]. + * (xsup,supno): supno[i] is the supernode no to which i belongs; + * xsup(s) points to the beginning of the s-th supernode. + * e.g. supno 0 1 2 2 3 3 3 4 4 4 4 4 (n=12) + * xsup 0 1 2 4 7 12 + * Note: dfs will be performed on supernode rep. relative to the new + * row pivoting ordering + * + * (xlsub,lsub): lsub[*] contains the compressed subscript of + * rectangular supernodes; xlsub[j] points to the starting + * location of the j-th column in lsub[*]. Note that xlsub + * is indexed by column. + * Storage: original row subscripts + * + * During the course of sparse LU factorization, we also use + * (xlsub,lsub) for the purpose of symmetric pruning. For each + * supernode {s,s+1,...,t=s+r} with first column s and last + * column t, the subscript set + * lsub[j], j=xlsub[s], .., xlsub[s+1]-1 + * is the structure of column s (i.e. structure of this supernode). + * It is used for the storage of numerical values. + * Furthermore, + * lsub[j], j=xlsub[t], .., xlsub[t+1]-1 + * is the structure of the last column t of this supernode. + * It is for the purpose of symmetric pruning. Therefore, the + * structural subscripts can be rearranged without making physical + * interchanges among the numerical values. + * + * However, if the supernode has only one column, then we + * only keep one set of subscripts. For any subscript interchange + * performed, similar interchange must be done on the numerical + * values. + * + * The last column structures (for pruning) will be removed + * after the numercial LU factorization phase. + * + * (xlusup,lusup): lusup[*] contains the numerical values of the + * rectangular supernodes; xlusup[j] points to the starting + * location of the j-th column in storage vector lusup[*] + * Note: xlusup is indexed by column. + * Each rectangular supernode is stored by column-major + * scheme, consistent with Fortran 2-dim array storage. + * + * (xusub,ucol,usub): ucol[*] stores the numerical values of + * U-columns outside the rectangular supernodes. The row + * subscript of nonzero ucol[k] is stored in usub[k]. + * xusub[i] points to the starting location of column i in ucol. + * Storage: new row subscripts; that is subscripts of PA. + */ +#ifndef EIGEN_LU_STRUCTS +#define EIGEN_LU_STRUCTS +typedef enum {LUSUP, UCOL, LSUB, USUB, LLVL, ULVL} LU_MemType; + + +template +struct LU_GlobalLU_t { + typedef typename IndexVector::Scalar Index; + IndexVector xsup; //First supernode column ... xsup(s) points to the beginning of the s-th supernode + IndexVector supno; // Supernode number corresponding to this column (column to supernode mapping) + ScalarVector lusup; // nonzero values of L ordered by columns + IndexVector lsub; // Compressed row indices of L rectangular supernodes. + IndexVector xlusup; // pointers to the beginning of each column in lusup + IndexVector xlsub; // pointers to the beginning of each column in lsub + Index nzlmax; // Current max size of lsub + Index nzlumax; // Current max size of lusup + ScalarVector ucol; // nonzero values of U ordered by columns + IndexVector usub; // row indices of U columns in ucol + IndexVector xusub; // Pointers to the beginning of each column of U in ucol + Index nzumax; // Current max size of ucol + Index n; // Number of columns in the matrix + int num_expansions; +}; + +// Values to set for performance +struct LU_perfvalues { + int panel_size; // a panel consists of at most consecutive columns + int relax; // To control degree of relaxing supernodes. If the number of nodes (columns) + // in a subtree of the elimination tree is less than relax, this subtree is considered + // as one supernode regardless of the row structures of those columns + int maxsuper; // The maximum size for a supernode in complete LU + int rowblk; // The minimum row dimension for 2-D blocking to be used; + int colblk; // The minimum column dimension for 2-D blocking to be used; + int fillfactor; // The estimated fills factors for L and U, compared with A +}; +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_Utils.h b/Eigen/src/SparseLU/SparseLU_Utils.h new file mode 100644 index 000000000..b13930dbb --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_Utils.h @@ -0,0 +1,75 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + + +#ifndef EIGEN_SPARSELU_UTILS_H +#define EIGEN_SPARSELU_UTILS_H + + +/** + * \brief Count Nonzero elements in the factors + */ +template +void SparseLUBase::LU_countnz(const int n, int& nnzL, int& nnzU, GlobalLU_t& glu) +{ + nnzL = 0; + nnzU = (glu.xusub)(n); + int nsuper = (glu.supno)(n); + int jlen; + int i, j, fsupc; + if (n <= 0 ) return; + // For each supernode + for (i = 0; i <= nsuper; i++) + { + fsupc = glu.xsup(i); + jlen = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); + + for (j = fsupc; j < glu.xsup(i+1); j++) + { + nnzL += jlen; + nnzU += j - fsupc + 1; + jlen--; + } + } + +} +/** + * \brief Fix up the data storage lsub for L-subscripts. + * + * It removes the subscripts sets for structural pruning, + * and applies permutation to the remaining subscripts + * + */ +template +void SparseLUBase::LU_fixupL(const int n, const IndexVector& perm_r, GlobalLU_t& glu) +{ + int fsupc, i, j, k, jstart; + + int nextl = 0; + int nsuper = (glu.supno)(n); + + // For each supernode + for (i = 0; i <= nsuper; i++) + { + fsupc = glu.xsup(i); + jstart = glu.xlsub(fsupc); + glu.xlsub(fsupc) = nextl; + for (j = jstart; j < glu.xlsub(fsupc + 1); j++) + { + glu.lsub(nextl) = perm_r(glu.lsub(j)); // Now indexed into P*A + nextl++; + } + for (k = fsupc+1; k < glu.xsup(i+1); k++) + glu.xlsub(k) = nextl; // other columns in supernode i + } + + glu.xlsub(n) = nextl; +} + +#endif diff --git a/Eigen/src/SparseLU/SparseLU_column_bmod.h b/Eigen/src/SparseLU/SparseLU_column_bmod.h new file mode 100644 index 000000000..94f18fb73 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_column_bmod.h @@ -0,0 +1,162 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of xcolumn_bmod.c file in SuperLU + + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_COLUMN_BMOD_H +#define SPARSELU_COLUMN_BMOD_H + +/** + * \brief Performs numeric block updates (sup-col) in topological order + * + * \param jcol current column to update + * \param nseg Number of segments in the U part + * \param dense Store the full representation of the column + * \param tempv working array + * \param segrep segment representative ... + * \param repfnz ??? First nonzero column in each row ??? ... + * \param fpanelc First column in the current panel + * \param glu Global LU data. + * \return 0 - successful return + * > 0 - number of bytes allocated when run out of space + * + */ +template +int SparseLUBase::LU_column_bmod(const int jcol, const int nseg, BlockScalarVector& dense, ScalarVector& tempv, BlockIndexVector& segrep, BlockIndexVector& repfnz, int fpanelc, GlobalLU_t& glu) +{ + int jsupno, k, ksub, krep, ksupno; + int lptr, nrow, isub, irow, nextlu, new_next, ufirst; + int fsupc, nsupc, nsupr, luptr, kfnz, no_zeros; + /* krep = representative of current k-th supernode + * fsupc = first supernodal column + * nsupc = number of columns in a supernode + * nsupr = number of rows in a supernode + * luptr = location of supernodal LU-block in storage + * kfnz = first nonz in the k-th supernodal segment + * no_zeros = no lf leading zeros in a supernodal U-segment + */ + + jsupno = glu.supno(jcol); + // For each nonzero supernode segment of U[*,j] in topological order + k = nseg - 1; + int d_fsupc; // distance between the first column of the current panel and the + // first column of the current snode + int fst_col; // First column within small LU update + int segsize; + for (ksub = 0; ksub < nseg; ksub++) + { + krep = segrep(k); k--; + ksupno = glu.supno(krep); + if (jsupno != ksupno ) + { + // outside the rectangular supernode + fsupc = glu.xsup(ksupno); + fst_col = (std::max)(fsupc, fpanelc); + + // Distance from the current supernode to the current panel; + // d_fsupc = 0 if fsupc > fpanelc + d_fsupc = fst_col - fsupc; + + luptr = glu.xlusup(fst_col) + d_fsupc; + lptr = glu.xlsub(fsupc) + d_fsupc; + + kfnz = repfnz(krep); + kfnz = (std::max)(kfnz, fpanelc); + + segsize = krep - kfnz + 1; + nsupc = krep - fst_col + 1; + nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); + nrow = nsupr - d_fsupc - nsupc; + + // Perform a triangular solver and block update, + // then scatter the result of sup-col update to dense + no_zeros = kfnz - fst_col; + if(segsize==1) + LU_kernel_bmod<1>::run(segsize, dense, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + else + LU_kernel_bmod::run(segsize, dense, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + } // end if jsupno + } // end for each segment + + // Process the supernodal portion of L\U[*,j] + nextlu = glu.xlusup(jcol); + fsupc = glu.xsup(jsupno); + + // copy the SPA dense into L\U[*,j] + int mem; + new_next = nextlu + glu.xlsub(fsupc + 1) - glu.xlsub(fsupc); + while (new_next > glu.nzlumax ) + { + mem = LUMemXpand(glu.lusup, glu.nzlumax, nextlu, LUSUP, glu.num_expansions); + if (mem) return mem; + } + + for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++) + { + irow = glu.lsub(isub); + glu.lusup(nextlu) = dense(irow); + dense(irow) = Scalar(0.0); + ++nextlu; + } + + glu.xlusup(jcol + 1) = nextlu; // close L\U(*,jcol); + + /* For more updates within the panel (also within the current supernode), + * should start from the first column of the panel, or the first column + * of the supernode, whichever is bigger. There are two cases: + * 1) fsupc < fpanelc, then fst_col <-- fpanelc + * 2) fsupc >= fpanelc, then fst_col <-- fsupc + */ + fst_col = (std::max)(fsupc, fpanelc); + + if (fst_col < jcol) + { + // Distance between the current supernode and the current panel + // d_fsupc = 0 if fsupc >= fpanelc + d_fsupc = fst_col - fsupc; + + lptr = glu.xlsub(fsupc) + d_fsupc; + luptr = glu.xlusup(fst_col) + d_fsupc; + nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); // leading dimension + nsupc = jcol - fst_col; // excluding jcol + nrow = nsupr - d_fsupc - nsupc; + + // points to the beginning of jcol in snode L\U(jsupno) + ufirst = glu.xlusup(jcol) + d_fsupc; + Map, 0, OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) ); + VectorBlock u(glu.lusup, ufirst, nsupc); + u = A.template triangularView().solve(u); + + new (&A) Map, 0, OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) ); + VectorBlock l(glu.lusup, ufirst+nsupc, nrow); + l.noalias() -= A * u; + + } // End if fst_col + return 0; +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_column_dfs.h b/Eigen/src/SparseLU/SparseLU_column_dfs.h new file mode 100644 index 000000000..fa8dcf18d --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_column_dfs.h @@ -0,0 +1,164 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]column_dfs.c file in SuperLU + + * -- SuperLU routine (version 2.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November 15, 1997 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_COLUMN_DFS_H +#define SPARSELU_COLUMN_DFS_H +/** + * \brief Performs a symbolic factorization on column jcol and decide the supernode boundary + * + * A supernode representative is the last column of a supernode. + * The nonzeros in U[*,j] are segments that end at supernodes representatives. + * The routine returns a list of the supernodal representatives + * in topological order of the dfs that generates them. + * The location of the first nonzero in each supernodal segment + * (supernodal entry location) is also returned. + * + * \param m number of rows in the matrix + * \param jcol Current column + * \param perm_r Row permutation + * \param maxsuper Maximum number of column allowed in a supernode + * \param [in,out] nseg Number of segments in current U[*,j] - new segments appended + * \param lsub_col defines the rhs vector to start the dfs + * \param [in,out] segrep Segment representatives - new segments appended + * \param repfnz First nonzero location in each row + * \param xprune + * \param marker marker[i] == jj, if i was visited during dfs of current column jj; + * \param parent + * \param xplore working array + * \param glu global LU data + * \return 0 success + * > 0 number of bytes allocated when run out of space + * + */ +template +struct LU_column_dfs_traits +{ + typedef typename IndexVector::Scalar Index; + typedef typename ScalarVector::Scalar Scalar; + LU_column_dfs_traits(Index jcol, Index& jsuper, LU_GlobalLU_t& glu) + : m_jcol(jcol), m_jsuper_ref(jsuper), m_glu(glu) + {} + bool update_segrep(Index /*krep*/, Index /*jj*/) + { + return true; + } + void mem_expand(IndexVector& lsub, int& nextl, int chmark) + { + if (nextl >= m_glu.nzlmax) + SparseLUBase::LUMemXpand(lsub, m_glu.nzlmax, nextl, LSUB, m_glu.num_expansions); + if (chmark != (m_jcol-1)) m_jsuper_ref = IND_EMPTY; + } + enum { ExpandMem = true }; + + int m_jcol; + int& m_jsuper_ref; + LU_GlobalLU_t& m_glu; +}; + +template +int SparseLUBase::LU_column_dfs(const int m, const int jcol, IndexVector& perm_r, int maxsuper, int& nseg, BlockIndexVector& lsub_col, IndexVector& segrep, BlockIndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu) +{ + + int jsuper = glu.supno(jcol); + int nextl = glu.xlsub(jcol); + VectorBlock marker2(marker, 2*m, m); + + + LU_column_dfs_traits traits(jcol, jsuper, glu); + + // For each nonzero in A(*,jcol) do dfs + for (int k = 0; lsub_col[k] != IND_EMPTY; k++) + { + int krow = lsub_col(k); + lsub_col(k) = IND_EMPTY; + int kmark = marker2(krow); + + // krow was visited before, go to the next nonz; + if (kmark == jcol) continue; + + LU_dfs_kernel(jcol, perm_r, nseg, glu.lsub, segrep, repfnz, xprune, marker2, parent, + xplore, glu, nextl, krow, traits); + } // for each nonzero ... + + int fsupc, jptr, jm1ptr, ito, ifrom, istop; + int nsuper = glu.supno(jcol); + int jcolp1 = jcol + 1; + int jcolm1 = jcol - 1; + + // check to see if j belongs in the same supernode as j-1 + if ( jcol == 0 ) + { // Do nothing for column 0 + nsuper = glu.supno(0) = 0 ; + } + else + { + fsupc = glu.xsup(nsuper); + jptr = glu.xlsub(jcol); // Not yet compressed + jm1ptr = glu.xlsub(jcolm1); + + // Use supernodes of type T2 : see SuperLU paper + if ( (nextl-jptr != jptr-jm1ptr-1) ) jsuper = IND_EMPTY; + + // Make sure the number of columns in a supernode doesn't + // exceed threshold + if ( (jcol - fsupc) >= maxsuper) jsuper = IND_EMPTY; + + /* If jcol starts a new supernode, reclaim storage space in + * glu.lsub from previous supernode. Note we only store + * the subscript set of the first and last columns of + * a supernode. (first for num values, last for pruning) + */ + if (jsuper == IND_EMPTY) + { // starts a new supernode + if ( (fsupc < jcolm1-1) ) + { // >= 3 columns in nsuper + ito = glu.xlsub(fsupc+1); + glu.xlsub(jcolm1) = ito; + istop = ito + jptr - jm1ptr; + xprune(jcolm1) = istop; // intialize xprune(jcol-1) + glu.xlsub(jcol) = istop; + + for (ifrom = jm1ptr; ifrom < nextl; ++ifrom, ++ito) + glu.lsub(ito) = glu.lsub(ifrom); + nextl = ito; // = istop + length(jcol) + } + nsuper++; + glu.supno(jcol) = nsuper; + } // if a new supernode + } // end else: jcol > 0 + + // Tidy up the pointers before exit + glu.xsup(nsuper+1) = jcolp1; + glu.supno(jcolp1) = nsuper; + xprune(jcol) = nextl; // Intialize upper bound for pruning + glu.xlsub(jcolp1) = nextl; + + return 0; +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h new file mode 100644 index 000000000..d3227469d --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_copy_to_ucol.h @@ -0,0 +1,100 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. +/* + + * NOTE: This file is the modified version of [s,d,c,z]copy_to_ucol.c file in SuperLU + + * -- SuperLU routine (version 2.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November 15, 1997 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_COPY_TO_UCOL_H +#define SPARSELU_COPY_TO_UCOL_H + +/** + * \brief Performs numeric block updates (sup-col) in topological order + * + * \param jcol current column to update + * \param nseg Number of segments in the U part + * \param segrep segment representative ... + * \param repfnz First nonzero column in each row ... + * \param perm_r Row permutation + * \param dense Store the full representation of the column + * \param glu Global LU data. + * \return 0 - successful return + * > 0 - number of bytes allocated when run out of space + * + */ +template +int SparseLUBase::LU_copy_to_ucol(const int jcol, const int nseg, IndexVector& segrep, BlockIndexVector& repfnz ,IndexVector& perm_r, BlockScalarVector& dense, GlobalLU_t& glu) +{ + Index ksub, krep, ksupno; + + Index jsupno = glu.supno(jcol); + + // For each nonzero supernode segment of U[*,j] in topological order + int k = nseg - 1, i; + Index nextu = glu.xusub(jcol); + Index kfnz, isub, segsize; + Index new_next,irow; + Index fsupc, mem; + for (ksub = 0; ksub < nseg; ksub++) + { + krep = segrep(k); k--; + ksupno = glu.supno(krep); + if (jsupno != ksupno ) // should go into ucol(); + { + kfnz = repfnz(krep); + if (kfnz != IND_EMPTY) + { // Nonzero U-segment + fsupc = glu.xsup(ksupno); + isub = glu.xlsub(fsupc) + kfnz - fsupc; + segsize = krep - kfnz + 1; + new_next = nextu + segsize; + while (new_next > glu.nzumax) + { + mem = LUMemXpand(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions); + if (mem) return mem; + mem = LUMemXpand(glu.usub, glu.nzumax, nextu, USUB, glu.num_expansions); + if (mem) return mem; + + } + + for (i = 0; i < segsize; i++) + { + irow = glu.lsub(isub); + glu.usub(nextu) = perm_r(irow); // Unlike the L part, the U part is stored in its final order + glu.ucol(nextu) = dense(irow); + dense(irow) = Scalar(0.0); + nextu++; + isub++; + } + + } // end nonzero U-segment + + } // end if jsupno + + } // end for each segment + glu.xusub(jcol + 1) = nextu; // close U(*,jcol) + return 0; +} + +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h new file mode 100644 index 000000000..69e1d4da9 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_heap_relax_snode.h @@ -0,0 +1,119 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* This file is a modified version of heap_relax_snode.c file in SuperLU + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ + +#ifndef SPARSELU_HEAP_RELAX_SNODE_H +#define SPARSELU_HEAP_RELAX_SNODE_H +#include "SparseLU_Coletree.h" +/** + * \brief Identify the initial relaxed supernodes + * + * This routine applied to a symmetric elimination tree. + * It assumes that the matrix has been reordered according to the postorder of the etree + * \param et elimination tree + * \param relax_columns Maximum number of columns allowed in a relaxed snode + * \param descendants Number of descendants of each node in the etree + * \param relax_end last column in a supernode + */ +template +void SparseLUBase::LU_heap_relax_snode (const int n, IndexVector& et, const int relax_columns, IndexVector& descendants, IndexVector& relax_end) +{ + + // The etree may not be postordered, but its heap ordered + IndexVector post; + LU_TreePostorder(n, et, post); // Post order etree + IndexVector inv_post(n+1); + int i; + for (i = 0; i < n+1; ++i) inv_post(post(i)) = i; // inv_post = post.inverse()??? + + // Renumber etree in postorder + IndexVector iwork(n); + IndexVector et_save(n+1); + for (i = 0; i < n; ++i) + { + iwork(post(i)) = post(et(i)); + } + et_save = et; // Save the original etree + et = iwork; + + // compute the number of descendants of each node in the etree + relax_end.setConstant(IND_EMPTY); + int j, parent; + descendants.setZero(); + for (j = 0; j < n; j++) + { + parent = et(j); + if (parent != n) // not the dummy root + descendants(parent) += descendants(j) + 1; + } + // Identify the relaxed supernodes by postorder traversal of the etree + int snode_start; // beginning of a snode + int k; + int nsuper_et_post = 0; // Number of relaxed snodes in postordered etree + int nsuper_et = 0; // Number of relaxed snodes in the original etree + int l; + for (j = 0; j < n; ) + { + parent = et(j); + snode_start = j; + while ( parent != n && descendants(parent) < relax_columns ) + { + j = parent; + parent = et(j); + } + // Found a supernode in postordered etree, j is the last column + ++nsuper_et_post; + k = n; + for (i = snode_start; i <= j; ++i) + k = (std::min)(k, inv_post(i)); + l = inv_post(j); + if ( (l - k) == (j - snode_start) ) // Same number of columns in the snode + { + // This is also a supernode in the original etree + relax_end(k) = l; // Record last column + ++nsuper_et; + } + else + { + for (i = snode_start; i <= j; ++i) + { + l = inv_post(i); + if (descendants(i) == 0) + { + relax_end(l) = l; + ++nsuper_et; + } + } + } + j++; + // Search for a new leaf + while (descendants(j) != 0 && j < n) j++; + } // End postorder traversal of the etree + + // Recover the original etree + et = et_save; +} +#endif diff --git a/Eigen/src/SparseLU/SparseLU_kernel_bmod.h b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h new file mode 100644 index 000000000..b15ff9c50 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_kernel_bmod.h @@ -0,0 +1,109 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef SPARSELU_KERNEL_BMOD_H +#define SPARSELU_KERNEL_BMOD_H + +/** + * \brief Performs numeric block updates from a given supernode to a single column + * + * \param segsize Size of the segment (and blocks ) to use for updates + * \param [in,out]dense Packed values of the original matrix + * \param tempv temporary vector to use for updates + * \param lusup array containing the supernodes + * \param nsupr Number of rows in the supernode + * \param nrow Number of rows in the rectangular part of the supernode + * \param lsub compressed row subscripts of supernodes + * \param lptr pointer to the first column of the current supernode in lsub + * \param no_zeros Number of nonzeros elements before the diagonal part of the supernode + * \return 0 on success + */ +template struct LU_kernel_bmod +{ + template + EIGEN_DONT_INLINE static void run(const int segsize, BlockScalarVector& dense, ScalarVector& tempv, ScalarVector& lusup, int& luptr, const int nsupr, const int nrow, IndexVector& lsub, const int lptr, const int no_zeros) + { + typedef typename ScalarVector::Scalar Scalar; + // First, copy U[*,j] segment from dense(*) to tempv(*) + // The result of triangular solve is in tempv[*]; + // The result of matric-vector update is in dense[*] + int isub = lptr + no_zeros; + int i, irow; + for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++) + { + irow = lsub(isub); + tempv(i) = dense(irow); + ++isub; + } + // Dense triangular solve -- start effective triangle + luptr += nsupr * no_zeros + no_zeros; + // Form Eigen matrix and vector + Map, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(nsupr) ); + Map > u(tempv.data(), segsize); + + u = A.template triangularView().solve(u); + + // Dense matrix-vector product y <-- B*x + luptr += segsize; + Map, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(nsupr) ); + Map > l(tempv.data()+segsize, nrow); + if(SegSizeAtCompileTime==2) + l = u(0) * B.col(0) + u(1) * B.col(1); + else if(SegSizeAtCompileTime==3) + l = u(0) * B.col(0) + u(1) * B.col(1) + u(2) * B.col(2); + else + l.noalias() = B * u; + + // Scatter tempv[] into SPA dense[] as a temporary storage + isub = lptr + no_zeros; + for (i = 0; i < ((SegSizeAtCompileTime==Dynamic)?segsize:SegSizeAtCompileTime); i++) + { + irow = lsub(isub++); + dense(irow) = tempv(i); + } + + // Scatter l into SPA dense[] + for (i = 0; i < nrow; i++) + { + irow = lsub(isub++); + dense(irow) -= l(i); + } + } +}; + +template <> struct LU_kernel_bmod<1> +{ + template + EIGEN_DONT_INLINE static void run(const int /*segsize*/, BlockScalarVector& dense, ScalarVector& /*tempv*/, ScalarVector& lusup, int& luptr, const int nsupr, const int nrow, IndexVector& lsub, const int lptr, const int no_zeros) + { + typedef typename ScalarVector::Scalar Scalar; + Scalar f = dense(lsub(lptr + no_zeros)); + luptr += nsupr * no_zeros + no_zeros + 1; + const Scalar* a(lusup.data() + luptr); + const typename IndexVector::Scalar* irow(lsub.data()+lptr + no_zeros + 1); + int i = 0; + for (; i+1 < nrow; i+=2) + { + int i0 = *(irow++); + int i1 = *(irow++); + Scalar a0 = *(a++); + Scalar a1 = *(a++); + Scalar d0 = dense.coeff(i0); + Scalar d1 = dense.coeff(i1); + d0 -= f*a0; + d1 -= f*a1; + dense.coeffRef(i0) = d0; + dense.coeffRef(i1) = d1; + } + if(i +// Copyright (C) 2012 Gael Guennebaud +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]panel_bmod.c file in SuperLU + + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_PANEL_BMOD_H +#define SPARSELU_PANEL_BMOD_H +/** + * \brief Performs numeric block updates (sup-panel) in topological order. + * + * Before entering this routine, the original nonzeros in the panel + * were already copied i nto the spa[m,w] + * + * \param m number of rows in the matrix + * \param w Panel size + * \param jcol Starting column of the panel + * \param nseg Number of segments in the U part + * \param dense Store the full representation of the panel + * \param tempv working array + * \param segrep segment representative... first row in the segment + * \param repfnz First nonzero rows + * \param glu Global LU data. + * + * + */ +template +void SparseLUBase::LU_panel_bmod(const int m, const int w, const int jcol, const int nseg, ScalarVector& dense, ScalarVector& tempv, IndexVector& segrep, IndexVector& repfnz, LU_perfvalues& perfv, GlobalLU_t& glu) +{ + + int ksub,jj,nextl_col; + int fsupc, nsupc, nsupr, nrow; + int krep, kfnz; + int lptr; // points to the row subscripts of a supernode + int luptr; // ... + int segsize,no_zeros ; + // For each nonz supernode segment of U[*,j] in topological order + int k = nseg - 1; + for (ksub = 0; ksub < nseg; ksub++) + { // For each updating supernode + + /* krep = representative of current k-th supernode + * fsupc = first supernodal column + * nsupc = number of columns in a supernode + * nsupr = number of rows in a supernode + */ + krep = segrep(k); k--; + fsupc = glu.xsup(glu.supno(krep)); + nsupc = krep - fsupc + 1; + nsupr = glu.xlsub(fsupc+1) - glu.xlsub(fsupc); + nrow = nsupr - nsupc; + lptr = glu.xlsub(fsupc); + + // loop over the panel columns to detect the actual number of columns and rows + int u_rows = 0; + int u_cols = 0; + for (jj = jcol; jj < jcol + w; jj++) + { + nextl_col = (jj-jcol) * m; + VectorBlock repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row + + kfnz = repfnz_col(krep); + if ( kfnz == IND_EMPTY ) + continue; // skip any zero segment + + segsize = krep - kfnz + 1; + u_cols++; + u_rows = (std::max)(segsize,u_rows); + } + + // if the blocks are large enough, use level 3 + // TODO find better heuristics! + if( nsupc >= perfv.colblk && nrow > perfv.rowblk && u_cols>perfv.relax) + { + Map > U(tempv.data(), u_rows, u_cols); + + // gather U + int u_col = 0; + for (jj = jcol; jj < jcol + w; jj++) + { + nextl_col = (jj-jcol) * m; + VectorBlock repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row + VectorBlock dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here + + kfnz = repfnz_col(krep); + if ( kfnz == IND_EMPTY ) + continue; // skip any zero segment + + segsize = krep - kfnz + 1; + luptr = glu.xlusup(fsupc); + no_zeros = kfnz - fsupc; + + int isub = lptr + no_zeros; + int off = u_rows-segsize; + for (int i = 0; i < off; i++) U(i,u_col) = 0; + for (int i = 0; i < segsize; i++) + { + int irow = glu.lsub(isub); + U(i+off,u_col) = dense_col(irow); + ++isub; + } + u_col++; + } + // solve U = A^-1 U + luptr = glu.xlusup(fsupc); + no_zeros = (krep - u_rows + 1) - fsupc; + luptr += nsupr * no_zeros + no_zeros; + Map, 0, OuterStride<> > A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(nsupr) ); + U = A.template triangularView().solve(U); + + // update + luptr += u_rows; + Map, 0, OuterStride<> > B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(nsupr) ); + assert(tempv.size()>w*u_rows + nrow*w); + Map > L(tempv.data()+w*u_rows, nrow, u_cols); + L.noalias() = B * U; + + // scatter U and L + u_col = 0; + for (jj = jcol; jj < jcol + w; jj++) + { + nextl_col = (jj-jcol) * m; + VectorBlock repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row + VectorBlock dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here + + kfnz = repfnz_col(krep); + if ( kfnz == IND_EMPTY ) + continue; // skip any zero segment + + segsize = krep - kfnz + 1; + no_zeros = kfnz - fsupc; + int isub = lptr + no_zeros; + + int off = u_rows-segsize; + for (int i = 0; i < segsize; i++) + { + int irow = glu.lsub(isub++); + dense_col(irow) = U.coeff(i+off,u_col); + U.coeffRef(i+off,u_col) = 0; + } + + // Scatter l into SPA dense[] + for (int i = 0; i < nrow; i++) + { + int irow = glu.lsub(isub++); + dense_col(irow) -= L.coeff(i,u_col); + L.coeffRef(i,u_col) = 0; + } + u_col++; + } + } + else // level 2 only + { + // Sequence through each column in the panel + for (jj = jcol; jj < jcol + w; jj++) + { + nextl_col = (jj-jcol) * m; + VectorBlock repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row + VectorBlock dense_col(dense, nextl_col, m); // Scatter/gather entire matrix column from/to here + + kfnz = repfnz_col(krep); + if ( kfnz == IND_EMPTY ) + continue; // skip any zero segment + + segsize = krep - kfnz + 1; + luptr = glu.xlusup(fsupc); + + // Perform a trianglar solve and block update, + // then scatter the result of sup-col update to dense[] + no_zeros = kfnz - fsupc; + if(segsize==1) LU_kernel_bmod<1>::run(segsize, dense_col, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + else if(segsize==2) LU_kernel_bmod<2>::run(segsize, dense_col, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + else if(segsize==3) LU_kernel_bmod<3>::run(segsize, dense_col, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + else LU_kernel_bmod::run(segsize, dense_col, tempv, glu.lusup, luptr, nsupr, nrow, glu.lsub, lptr, no_zeros); + } // End for each column in the panel + } + + } // End for each updating supernode +} +#endif diff --git a/Eigen/src/SparseLU/SparseLU_panel_dfs.h b/Eigen/src/SparseLU/SparseLU_panel_dfs.h new file mode 100644 index 000000000..5d3025388 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_panel_dfs.h @@ -0,0 +1,247 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]panel_dfs.c file in SuperLU + + * -- SuperLU routine (version 2.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November 15, 1997 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_PANEL_DFS_H +#define SPARSELU_PANEL_DFS_H +template +template +void SparseLUBase::LU_dfs_kernel(const int jj, IndexVector& perm_r, + int& nseg, IndexVector& panel_lsub, IndexVector& segrep, + Ref repfnz_col, IndexVector& xprune, Ref marker, IndexVector& parent, + IndexVector& xplore, GlobalLU_t& glu, + int& nextl_col, int krow, Traits& traits + ) +{ + + int kmark = marker(krow); + + // For each unmarked krow of jj + marker(krow) = jj; + int kperm = perm_r(krow); + if (kperm == IND_EMPTY ) { + // krow is in L : place it in structure of L(*, jj) + panel_lsub(nextl_col++) = krow; // krow is indexed into A + + traits.mem_expand(panel_lsub, nextl_col, kmark); + } + else + { + // krow is in U : if its supernode-representative krep + // has been explored, update repfnz(*) + // krep = supernode representative of the current row + int krep = glu.xsup(glu.supno(kperm)+1) - 1; + // First nonzero element in the current column: + int myfnz = repfnz_col(krep); + + if (myfnz != IND_EMPTY ) + { + // Representative visited before + if (myfnz > kperm ) repfnz_col(krep) = kperm; + + } + else + { + // Otherwise, perform dfs starting at krep + int oldrep = IND_EMPTY; + parent(krep) = oldrep; + repfnz_col(krep) = kperm; + int xdfs = glu.xlsub(krep); + int maxdfs = xprune(krep); + + int kpar; + do + { + // For each unmarked kchild of krep + while (xdfs < maxdfs) + { + int kchild = glu.lsub(xdfs); + xdfs++; + int chmark = marker(kchild); + + if (chmark != jj ) + { + marker(kchild) = jj; + int chperm = perm_r(kchild); + + if (chperm == IND_EMPTY) + { + // case kchild is in L: place it in L(*, j) + panel_lsub(nextl_col++) = kchild; + traits.mem_expand(panel_lsub, nextl_col, chmark); + } + else + { + // case kchild is in U : + // chrep = its supernode-rep. If its rep has been explored, + // update its repfnz(*) + int chrep = glu.xsup(glu.supno(chperm)+1) - 1; + myfnz = repfnz_col(chrep); + + if (myfnz != IND_EMPTY) + { // Visited before + if (myfnz > chperm) + repfnz_col(chrep) = chperm; + } + else + { // Cont. dfs at snode-rep of kchild + xplore(krep) = xdfs; + oldrep = krep; + krep = chrep; // Go deeper down G(L) + parent(krep) = oldrep; + repfnz_col(krep) = chperm; + xdfs = glu.xlsub(krep); + maxdfs = xprune(krep); + + } // end if myfnz != -1 + } // end if chperm == -1 + + } // end if chmark !=jj + } // end while xdfs < maxdfs + + // krow has no more unexplored nbrs : + // Place snode-rep krep in postorder DFS, if this + // segment is seen for the first time. (Note that + // "repfnz(krep)" may change later.) + // Baktrack dfs to its parent + if(traits.update_segrep(krep,jj)) + //if (marker1(krep) < jcol ) + { + segrep(nseg) = krep; + ++nseg; + //marker1(krep) = jj; + } + + kpar = parent(krep); // Pop recursion, mimic recursion + if (kpar == IND_EMPTY) + break; // dfs done + krep = kpar; + xdfs = xplore(krep); + maxdfs = xprune(krep); + + } while (kpar != IND_EMPTY); // Do until empty stack + + } // end if (myfnz = -1) + + } // end if (kperm == -1) +} + +/** + * \brief Performs a symbolic factorization on a panel of columns [jcol, jcol+w) + * + * A supernode representative is the last column of a supernode. + * The nonzeros in U[*,j] are segments that end at supernodes representatives + * + * The routine returns a list of the supernodal representatives + * in topological order of the dfs that generates them. This list is + * a superset of the topological order of each individual column within + * the panel. + * The location of the first nonzero in each supernodal segment + * (supernodal entry location) is also returned. Each column has + * a separate list for this purpose. + * + * Two markers arrays are used for dfs : + * marker[i] == jj, if i was visited during dfs of current column jj; + * marker1[i] >= jcol, if i was visited by earlier columns in this panel; + * + * \param [in]m number of rows in the matrix + * \param [in]w Panel size + * \param [in]jcol Starting column of the panel + * \param [in]A Input matrix in column-major storage + * \param [in]perm_r Row permutation + * \param [out]nseg Number of U segments + * \param [out]dense Accumulate the column vectors of the panel + * \param [out]panel_lsub Subscripts of the row in the panel + * \param [out]segrep Segment representative i.e first nonzero row of each segment + * \param [out]repfnz First nonzero location in each row + * \param [out]xprune + * \param [out]marker + * + * + */ + +template +struct LU_panel_dfs_traits +{ + typedef typename IndexVector::Scalar Index; + LU_panel_dfs_traits(Index jcol, Index* marker) + : m_jcol(jcol), m_marker(marker) + {} + bool update_segrep(Index krep, Index jj) + { + if(m_marker[krep] +void SparseLUBase::LU_panel_dfs(const int m, const int w, const int jcol, MatrixType& A, IndexVector& perm_r, int& nseg, ScalarVector& dense, IndexVector& panel_lsub, IndexVector& segrep, IndexVector& repfnz, IndexVector& xprune, IndexVector& marker, IndexVector& parent, IndexVector& xplore, GlobalLU_t& glu) +{ + int nextl_col; // Next available position in panel_lsub[*,jj] + + // Initialize pointers + VectorBlock marker1(marker, m, m); + nseg = 0; + + LU_panel_dfs_traits traits(jcol, marker1.data()); + + // For each column in the panel + for (int jj = jcol; jj < jcol + w; jj++) + { + nextl_col = (jj - jcol) * m; + + VectorBlock repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row + VectorBlock dense_col(dense,nextl_col, m); // Accumulate a column vector here + + + // For each nnz in A[*, jj] do depth first search + for (typename MatrixType::InnerIterator it(A, jj); it; ++it) + { + int krow = it.row(); + dense_col(krow) = it.value(); + + int kmark = marker(krow); + if (kmark == jj) + continue; // krow visited before, go to the next nonzero + + LU_dfs_kernel(jj, perm_r, nseg, panel_lsub, segrep, repfnz_col, xprune, marker, parent, + xplore, glu, nextl_col, krow, traits); + }// end for nonzeros in column jj + + } // end for column jj + +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_pivotL.h b/Eigen/src/SparseLU/SparseLU_pivotL.h new file mode 100644 index 000000000..c4a9f1c74 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_pivotL.h @@ -0,0 +1,125 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of xpivotL.c file in SuperLU + + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_PIVOTL_H +#define SPARSELU_PIVOTL_H +/** + * \brief Performs the numerical pivotin on the current column of L, and the CDIV operation. + * + * Pivot policy : + * (1) Compute thresh = u * max_(i>=j) abs(A_ij); + * (2) IF user specifies pivot row k and abs(A_kj) >= thresh THEN + * pivot row = k; + * ELSE IF abs(A_jj) >= thresh THEN + * pivot row = j; + * ELSE + * pivot row = m; + * + * Note: If you absolutely want to use a given pivot order, then set u=0.0. + * + * \param jcol The current column of L + * \param u diagonal pivoting threshold + * \param [in,out]perm_r Row permutation (threshold pivoting) + * \param [in] iperm_c column permutation - used to finf diagonal of Pc*A*Pc' + * \param [out]pivrow The pivot row + * \param glu Global LU data + * \return 0 if success, i > 0 if U(i,i) is exactly zero + * + */ +template +int SparseLUBase::LU_pivotL(const int jcol, const RealScalar diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, int& pivrow, GlobalLU_t& glu) +{ + + Index fsupc = (glu.xsup)((glu.supno)(jcol)); // First column in the supernode containing the column jcol + Index nsupc = jcol - fsupc; // Number of columns in the supernode portion, excluding jcol; nsupc >=0 + Index lptr = glu.xlsub(fsupc); // pointer to the starting location of the row subscripts for this supernode portion + Index nsupr = glu.xlsub(fsupc+1) - lptr; // Number of rows in the supernode + Scalar* lu_sup_ptr = &(glu.lusup.data()[glu.xlusup(fsupc)]); // Start of the current supernode + Scalar* lu_col_ptr = &(glu.lusup.data()[glu.xlusup(jcol)]); // Start of jcol in the supernode + Index* lsub_ptr = &(glu.lsub.data()[lptr]); // Start of row indices of the supernode + + // Determine the largest abs numerical value for partial pivoting + Index diagind = iperm_c(jcol); // diagonal index + RealScalar pivmax = 0.0; + Index pivptr = nsupc; + Index diag = IND_EMPTY; + RealScalar rtemp; + Index isub, icol, itemp, k; + for (isub = nsupc; isub < nsupr; ++isub) { + rtemp = std::abs(lu_col_ptr[isub]); + if (rtemp > pivmax) { + pivmax = rtemp; + pivptr = isub; + } + if (lsub_ptr[isub] == diagind) diag = isub; + } + + // Test for singularity + if ( pivmax == 0.0 ) { + pivrow = lsub_ptr[pivptr]; + perm_r(pivrow) = jcol; + return (jcol+1); + } + + RealScalar thresh = diagpivotthresh * pivmax; + + // Choose appropriate pivotal element + + { + // Test if the diagonal element can be used as a pivot (given the threshold value) + if (diag >= 0 ) + { + // Diagonal element exists + rtemp = std::abs(lu_col_ptr[diag]); + if (rtemp != 0.0 && rtemp >= thresh) pivptr = diag; + } + pivrow = lsub_ptr[pivptr]; + } + + // Record pivot row + perm_r(pivrow) = jcol; + // Interchange row subscripts + if (pivptr != nsupc ) + { + std::swap( lsub_ptr[pivptr], lsub_ptr[nsupc] ); + // Interchange numerical values as well, for the two rows in the whole snode + // such that L is indexed the same way as A + for (icol = 0; icol <= nsupc; icol++) + { + itemp = pivptr + icol * nsupr; + std::swap(lu_sup_ptr[itemp], lu_sup_ptr[nsupc + icol * nsupr]); + } + } + // cdiv operations + Scalar temp = Scalar(1.0) / lu_col_ptr[nsupc]; + for (k = nsupc+1; k < nsupr; k++) + lu_col_ptr[k] *= temp; + return 0; +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_pruneL.h b/Eigen/src/SparseLU/SparseLU_pruneL.h new file mode 100644 index 000000000..d8c58e039 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_pruneL.h @@ -0,0 +1,129 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]pruneL.c file in SuperLU + + * -- SuperLU routine (version 2.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November 15, 1997 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_PRUNEL_H +#define SPARSELU_PRUNEL_H + +/** + * \brief Prunes the L-structure. + * + * It prunes the L-structure of supernodes whose L-structure contains the current pivot row "pivrow" + * + * + * \param jcol The current column of L + * \param [in]perm_r Row permutation + * \param [out]pivrow The pivot row + * \param nseg Number of segments + * \param segrep + * \param repfnz + * \param [out]xprune + * \param glu Global LU data + * + */ +template +void SparseLUBase::LU_pruneL(const int jcol, const IndexVector& perm_r, const int pivrow, const int nseg, const IndexVector& segrep, BlockIndexVector& repfnz, IndexVector& xprune, GlobalLU_t& glu) +{ + // For each supernode-rep irep in U(*,j] + int jsupno = glu.supno(jcol); + int i,irep,irep1; + bool movnum, do_prune = false; + Index kmin, kmax, minloc, maxloc,krow; + for (i = 0; i < nseg; i++) + { + irep = segrep(i); + irep1 = irep + 1; + do_prune = false; + + // Don't prune with a zero U-segment + if (repfnz(irep) == IND_EMPTY) continue; + + // If a snode overlaps with the next panel, then the U-segment + // is fragmented into two parts -- irep and irep1. We should let + // pruning occur at the rep-column in irep1s snode. + if (glu.supno(irep) == glu.supno(irep1) ) continue; // don't prune + + // If it has not been pruned & it has a nonz in row L(pivrow,i) + if (glu.supno(irep) != jsupno ) + { + if ( xprune (irep) >= glu.xlsub(irep1) ) + { + kmin = glu.xlsub(irep); + kmax = glu.xlsub(irep1) - 1; + for (krow = kmin; krow <= kmax; krow++) + { + if (glu.lsub(krow) == pivrow) + { + do_prune = true; + break; + } + } + } + + if (do_prune) + { + // do a quicksort-type partition + // movnum=true means that the num values have to be exchanged + movnum = false; + if (irep == glu.xsup(glu.supno(irep)) ) // Snode of size 1 + movnum = true; + + while (kmin <= kmax) + { + if (perm_r(glu.lsub(kmax)) == IND_EMPTY) + kmax--; + else if ( perm_r(glu.lsub(kmin)) != IND_EMPTY) + kmin++; + else + { + // kmin below pivrow (not yet pivoted), and kmax + // above pivrow: interchange the two suscripts + std::swap(glu.lsub(kmin), glu.lsub(kmax)); + + // If the supernode has only one column, then we + // only keep one set of subscripts. For any subscript + // intercnahge performed, similar interchange must be + // done on the numerical values. + if (movnum) + { + minloc = glu.xlusup(irep) + ( kmin - glu.xlsub(irep) ); + maxloc = glu.xlusup(irep) + ( kmax - glu.xlsub(irep) ); + std::swap(glu.lusup(minloc), glu.lusup(maxloc)); + } + kmin++; + kmax--; + } + } // end while + + xprune(irep) = kmin; //Pruning + } // end if do_prune + } // end pruning + } // End for each U-segment +} + +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_relax_snode.h b/Eigen/src/SparseLU/SparseLU_relax_snode.h new file mode 100644 index 000000000..8db8619c1 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_relax_snode.h @@ -0,0 +1,73 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* This file is a modified version of heap_relax_snode.c file in SuperLU + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ + +#ifndef SPARSELU_RELAX_SNODE_H +#define SPARSELU_RELAX_SNODE_H +/** + * \brief Identify the initial relaxed supernodes + * + * This routine is applied to a column elimination tree. + * It assumes that the matrix has been reordered according to the postorder of the etree + * \param et elimination tree + * \param relax_columns Maximum number of columns allowed in a relaxed snode + * \param descendants Number of descendants of each node in the etree + * \param relax_end last column in a supernode + */ +template +void SparseLUBase::LU_relax_snode (const int n, IndexVector& et, const int relax_columns, IndexVector& descendants, IndexVector& relax_end) +{ + + // compute the number of descendants of each node in the etree + int j, parent; + relax_end.setConstant(IND_EMPTY); + descendants.setZero(); + for (j = 0; j < n; j++) + { + parent = et(j); + if (parent != n) // not the dummy root + descendants(parent) += descendants(j) + 1; + } + // Identify the relaxed supernodes by postorder traversal of the etree + int snode_start; // beginning of a snode + for (j = 0; j < n; ) + { + parent = et(j); + snode_start = j; + while ( parent != n && descendants(parent) < relax_columns ) + { + j = parent; + parent = et(j); + } + // Found a supernode in postordered etree, j is the last column + relax_end(snode_start) = j; // Record last column + j++; + // Search for a new leaf + while (descendants(j) != 0 && j < n) j++; + } // End postorder traversal of the etree + +} +#endif diff --git a/Eigen/src/SparseLU/SparseLU_snode_bmod.h b/Eigen/src/SparseLU/SparseLU_snode_bmod.h new file mode 100644 index 000000000..beea71e31 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_snode_bmod.h @@ -0,0 +1,72 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]snode_bmod.c file in SuperLU + + * -- SuperLU routine (version 3.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * October 15, 2003 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_SNODE_BMOD_H +#define SPARSELU_SNODE_BMOD_H +template +int SparseLUBase::LU_snode_bmod (const int jcol, const int fsupc, ScalarVector& dense, GlobalLU_t& glu) +{ + /* lsub : Compressed row subscripts of ( rectangular supernodes ) + * xlsub : xlsub[j] is the starting location of the j-th column in lsub(*) + * lusup : Numerical values of the rectangular supernodes + * xlusup[j] is the starting location of the j-th column in lusup(*) + */ + int nextlu = glu.xlusup(jcol); // Starting location of the next column to add + int irow, isub; + // Process the supernodal portion of L\U[*,jcol] + for (isub = glu.xlsub(fsupc); isub < glu.xlsub(fsupc+1); isub++) + { + irow = glu.lsub(isub); + glu.lusup(nextlu) = dense(irow); + dense(irow) = 0; + ++nextlu; + } + glu.xlusup(jcol + 1) = nextlu; // Initialize xlusup for next column ( jcol+1 ) + + if (fsupc < jcol ){ + int luptr = glu.xlusup(fsupc); // points to the first column of the supernode + int nsupr = glu.xlsub(fsupc + 1) -glu.xlsub(fsupc); //Number of rows in the supernode + int nsupc = jcol - fsupc; // Number of columns in the supernodal portion of L\U[*,jcol] + int ufirst = glu.xlusup(jcol); // points to the beginning of column jcol in supernode L\U(jsupno) + + int nrow = nsupr - nsupc; // Number of rows in the off-diagonal blocks + + // Solve the triangular system for U(fsupc:jcol, jcol) with L(fspuc:jcol, fsupc:jcol) + Map,0,OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) ); + VectorBlock u(glu.lusup, ufirst, nsupc); + u = A.template triangularView().solve(u); // Call the Eigen dense triangular solve interface + + // Update the trailing part of the column jcol U(jcol:jcol+nrow, jcol) using L(jcol:jcol+nrow, fsupc:jcol) and U(fsupc:jcol) + new (&A) Map,0,OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) ); + VectorBlock l(glu.lusup, ufirst+nsupc, nrow); + l.noalias() -= A * u; + } + return 0; +} +#endif \ No newline at end of file diff --git a/Eigen/src/SparseLU/SparseLU_snode_dfs.h b/Eigen/src/SparseLU/SparseLU_snode_dfs.h new file mode 100644 index 000000000..199436cd7 --- /dev/null +++ b/Eigen/src/SparseLU/SparseLU_snode_dfs.h @@ -0,0 +1,95 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +/* + + * NOTE: This file is the modified version of [s,d,c,z]snode_dfs.c file in SuperLU + + * -- SuperLU routine (version 2.0) -- + * Univ. of California Berkeley, Xerox Palo Alto Research Center, + * and Lawrence Berkeley National Lab. + * November 15, 1997 + * + * Copyright (c) 1994 by Xerox Corporation. All rights reserved. + * + * THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + * EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + * + * Permission is hereby granted to use or copy this program for any + * purpose, provided the above notices are retained on all copies. + * Permission to modify the code and to distribute modified code is + * granted, provided the above notices are retained, and a notice that + * the code was modified is included with the above copyright notice. + */ +#ifndef SPARSELU_SNODE_DFS_H +#define SPARSELU_SNODE_DFS_H + /** + * \brief Determine the union of the row structures of those columns within the relaxed snode. + * NOTE: The relaxed snodes are leaves of the supernodal etree, therefore, + * the portion outside the rectangular supernode must be zero. + * + * \param jcol start of the supernode + * \param kcol end of the supernode + * \param asub Row indices + * \param colptr Pointer to the beginning of each column + * \param xprune (out) The pruned tree ?? + * \param marker (in/out) working vector + * \return 0 on success, > 0 size of the memory when memory allocation failed + */ +template +int SparseLUBase::LU_snode_dfs(const int jcol, const int kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, GlobalLU_t& glu) +{ + int mem; + Index nsuper = ++glu.supno(jcol); // Next available supernode number + int nextl = glu.xlsub(jcol); //Index of the starting location of the jcol-th column in lsub + int krow,kmark; + for (int i = jcol; i <=kcol; i++) + { + // For each nonzero in A(*,i) + for (typename MatrixType::InnerIterator it(mat, i); it; ++it) + { + krow = it.row(); + kmark = marker(krow); + if ( kmark != kcol ) + { + // First time to visit krow + marker(krow) = kcol; + glu.lsub(nextl++) = krow; + if( nextl >= glu.nzlmax ) + { + mem = LUMemXpand(glu.lsub, glu.nzlmax, nextl, LSUB, glu.num_expansions); + if (mem) return mem; // Memory expansion failed... Return the memory allocated so far + } + } + } + glu.supno(i) = nsuper; + } + + // If supernode > 1, then make a copy of the subscripts for pruning + if (jcol < kcol) + { + Index new_next = nextl + (nextl - glu.xlsub(jcol)); + while (new_next > glu.nzlmax) + { + mem = LUMemXpand(glu.lsub, glu.nzlmax, nextl, LSUB, glu.num_expansions); + if (mem) return mem; // Memory expansion failed... Return the memory allocated so far + } + Index ifrom, ito = nextl; + for (ifrom = glu.xlsub(jcol); ifrom < nextl;) + glu.lsub(ito++) = glu.lsub(ifrom++); + for (int i = jcol+1; i <=kcol; i++) glu.xlsub(i) = nextl; + nextl = ito; + } + glu.xsup(nsuper+1) = kcol + 1; // Start of next available supernode + glu.supno(kcol+1) = nsuper; + xprune(kcol) = nextl; + glu.xlsub(kcol+1) = nextl; + return 0; +} +#endif \ No newline at end of file diff --git a/Eigen/src/SuperLUSupport/SuperLUSupport.h b/Eigen/src/SuperLUSupport/SuperLUSupport.h index d8a54e18c..cd6c4b91f 100644 --- a/Eigen/src/SuperLUSupport/SuperLUSupport.h +++ b/Eigen/src/SuperLUSupport/SuperLUSupport.h @@ -612,6 +612,7 @@ void SuperLU::factorize(const MatrixType& a) this->initFactorization(a); + m_sluOptions.ColPerm = COLAMD; int info = 0; RealScalar recip_pivot_growth, rcond; RealScalar ferr, berr; diff --git a/Eigen/src/plugins/ArrayCwiseBinaryOps.h b/Eigen/src/plugins/ArrayCwiseBinaryOps.h index 5b979ebf8..1e751ad62 100644 --- a/Eigen/src/plugins/ArrayCwiseBinaryOps.h +++ b/Eigen/src/plugins/ArrayCwiseBinaryOps.h @@ -33,7 +33,8 @@ EIGEN_MAKE_CWISE_BINARY_OP(min,internal::scalar_min_op) * * \sa max() */ -EIGEN_STRONG_INLINE const CwiseBinaryOp, const Derived, const ConstantReturnType> +EIGEN_STRONG_INLINE const CwiseBinaryOp, const Derived, + const CwiseNullaryOp, PlainObject> > (min)(const Scalar &other) const { return (min)(Derived::PlainObject::Constant(rows(), cols(), other)); @@ -52,7 +53,8 @@ EIGEN_MAKE_CWISE_BINARY_OP(max,internal::scalar_max_op) * * \sa min() */ -EIGEN_STRONG_INLINE const CwiseBinaryOp, const Derived, const ConstantReturnType> +EIGEN_STRONG_INLINE const CwiseBinaryOp, const Derived, + const CwiseNullaryOp, PlainObject> > (max)(const Scalar &other) const { return (max)(Derived::PlainObject::Constant(rows(), cols(), other)); diff --git a/Eigen/src/plugins/ArrayCwiseUnaryOps.h b/Eigen/src/plugins/ArrayCwiseUnaryOps.h index 0dffaf413..a59636790 100644 --- a/Eigen/src/plugins/ArrayCwiseUnaryOps.h +++ b/Eigen/src/plugins/ArrayCwiseUnaryOps.h @@ -200,3 +200,4 @@ EIGEN_MAKE_SCALAR_CWISE_UNARY_OP(operator<=, std::less_equal) EIGEN_MAKE_SCALAR_CWISE_UNARY_OP(operator>, std::greater) EIGEN_MAKE_SCALAR_CWISE_UNARY_OP(operator>=, std::greater_equal) + diff --git a/bench/spbench/CMakeLists.txt b/bench/spbench/CMakeLists.txt index 079912266..6e0e1b103 100644 --- a/bench/spbench/CMakeLists.txt +++ b/bench/spbench/CMakeLists.txt @@ -55,6 +55,12 @@ if(PASTIX_FOUND AND BLAS_FOUND) set(PASTIX_ALL_LIBS ${PASTIX_LIBRARIES} ${BLAS_LIBRARIES}) endif(PASTIX_FOUND AND BLAS_FOUND) +if(METIS_FOUND) + include_directories(${METIS_INCLUDES}) + set (SPARSE_LIBS ${SPARSE_LIBS} ${METIS_LIBRARIES}) + add_definitions("-DEIGEN_METIS_SUPPORT") +endif(METIS_FOUND) + find_library(RT_LIBRARY rt) if(RT_LIBRARY) set(SPARSE_LIBS ${SPARSE_LIBS} ${RT_LIBRARY}) @@ -63,3 +69,10 @@ endif(RT_LIBRARY) add_executable(spbenchsolver spbenchsolver.cpp) target_link_libraries (spbenchsolver ${SPARSE_LIBS}) +add_executable(spsolver sp_solver.cpp) +target_link_libraries (spsolver ${SPARSE_LIBS}) + + +add_executable(test_sparseLU test_sparseLU.cpp) +target_link_libraries (test_sparseLU ${SPARSE_LIBS}) + diff --git a/bench/spbench/sp_solver.cpp b/bench/spbench/sp_solver.cpp new file mode 100644 index 000000000..a1f4bac8a --- /dev/null +++ b/bench/spbench/sp_solver.cpp @@ -0,0 +1,125 @@ +// Small bench routine for Eigen available in Eigen +// (C) Desire NUENTSA WAKAM, INRIA + +#include +#include +#include +#include +#include +#include +#include +#include +//#include +#include +// #include +#include +#include +using namespace std; +using namespace Eigen; + +int main(int argc, char **args) +{ + SparseMatrix A; + typedef SparseMatrix::Index Index; + typedef Matrix DenseMatrix; + typedef Matrix DenseRhs; + VectorXd b, x, tmp; + BenchTimer timer,totaltime; + //SparseLU > solver; +// SuperLU > solver; + ConjugateGradient, Lower,IncompleteCholesky > solver; + ifstream matrix_file; + string line; + int n; + // Set parameters +// solver.iparm(IPARM_THREAD_NBR) = 4; + /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */ + if (argc < 2) assert(false && "please, give the matrix market file "); + + timer.start(); + totaltime.start(); + loadMarket(A, args[1]); + cout << "End charging matrix " << endl; + bool iscomplex=false, isvector=false; + int sym; + getMarketHeader(args[1], sym, iscomplex, isvector); + if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; } + if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;} + if (sym != 0) { // symmetric matrices, only the lower part is stored + SparseMatrix temp; + temp = A; + A = temp.selfadjointView(); + } + timer.stop(); + + n = A.cols(); + // ====== TESTS FOR SPARSE TUTORIAL ====== +// cout<< "OuterSize " << A.outerSize() << " inner " << A.innerSize() << endl; +// SparseMatrix mat1(A); +// SparseMatrix mat2; +// cout << " norm of A " << mat1.norm() << endl; ; +// PermutationMatrix perm(n); +// perm.resize(n,1); +// perm.indices().setLinSpaced(n, 0, n-1); +// mat2 = perm * mat1; +// mat.subrows(); +// mat2.resize(n,n); +// mat2.reserve(10); +// mat2.setConstant(); +// std::cout<< "NORM " << mat1.squaredNorm()<< endl; + + cout<< "Time to load the matrix " << timer.value() < 2) + loadMarketVector(b, args[2]); + else + { + b.resize(n); + tmp.resize(n); +// tmp.setRandom(); + for (int i = 0; i < n; i++) tmp(i) = i; + b = A * tmp ; + } +// Scaling > scal; +// scal.computeRef(A); +// b = scal.LeftScaling().cwiseProduct(b); + + /* Compute the factorization */ + cout<< "Starting the factorization "<< endl; + timer.reset(); + timer.start(); + cout<< "Size of Input Matrix "<< b.size()<<"\n\n"; + cout<< "Rows and columns "<< A.rows() <<" " < - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Matrix N NNZ Sym SPD - - - - -
Compute Time
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Total Time
Error - - ( - - ) -
- - - - - \ No newline at end of file diff --git a/bench/spbench/spbenchsolver.cpp b/bench/spbench/spbenchsolver.cpp index ff0ce4c7d..4acd0039c 100644 --- a/bench/spbench/spbenchsolver.cpp +++ b/bench/spbench/spbenchsolver.cpp @@ -14,7 +14,7 @@ void bench_printhelp() cout<< " OPTIONS : \n"; cout<< " -h or --help \n print this help and return\n\n"; cout<< " -d matrixdir \n Use matrixdir as the matrix folder instead of the one specified in the environment variable EIGEN_MATRIXDIR\n\n"; - cout<< " -o outputfile.html \n Output the statistics to a html file \n\n"; + cout<< " -o outputfile.xml \n Output the statistics to a xml file \n\n"; cout<< " --eps Sets the relative tolerance for iterative solvers (default 1e-08) \n\n"; cout<< " --maxits Sets the maximum number of iterations (default 1000) \n\n"; diff --git a/bench/spbench/spbenchsolver.h b/bench/spbench/spbenchsolver.h index 99f05aabc..19c719c04 100644 --- a/bench/spbench/spbenchsolver.h +++ b/bench/spbench/spbenchsolver.h @@ -10,7 +10,7 @@ #include #include -#include "Eigen/SparseCore" +#include #include #include #include @@ -21,6 +21,13 @@ #include #include #include +#include + +#include "spbenchstyle.h" + +#ifdef EIGEN_METIS_SUPPORT +#include +#endif #ifdef EIGEN_CHOLMOD_SUPPORT #include @@ -43,26 +50,27 @@ #endif // CONSTANTS -#define EIGEN_UMFPACK 0 -#define EIGEN_SUPERLU 1 -#define EIGEN_PASTIX 2 -#define EIGEN_PARDISO 3 -#define EIGEN_BICGSTAB 4 -#define EIGEN_BICGSTAB_ILUT 5 -#define EIGEN_GMRES 6 -#define EIGEN_GMRES_ILUT 7 -#define EIGEN_SIMPLICIAL_LDLT 8 -#define EIGEN_CHOLMOD_LDLT 9 -#define EIGEN_PASTIX_LDLT 10 -#define EIGEN_PARDISO_LDLT 11 -#define EIGEN_SIMPLICIAL_LLT 12 -#define EIGEN_CHOLMOD_SUPERNODAL_LLT 13 -#define EIGEN_CHOLMOD_SIMPLICIAL_LLT 14 -#define EIGEN_PASTIX_LLT 15 -#define EIGEN_PARDISO_LLT 16 -#define EIGEN_CG 17 -#define EIGEN_CG_PRECOND 18 -#define EIGEN_ALL_SOLVERS 19 +#define EIGEN_UMFPACK 10 +#define EIGEN_SUPERLU 20 +#define EIGEN_PASTIX 30 +#define EIGEN_PARDISO 40 +#define EIGEN_SPARSELU_COLAMD 50 +#define EIGEN_SPARSELU_METIS 51 +#define EIGEN_BICGSTAB 60 +#define EIGEN_BICGSTAB_ILUT 61 +#define EIGEN_GMRES 70 +#define EIGEN_GMRES_ILUT 71 +#define EIGEN_SIMPLICIAL_LDLT 80 +#define EIGEN_CHOLMOD_LDLT 90 +#define EIGEN_PASTIX_LDLT 100 +#define EIGEN_PARDISO_LDLT 110 +#define EIGEN_SIMPLICIAL_LLT 120 +#define EIGEN_CHOLMOD_SUPERNODAL_LLT 130 +#define EIGEN_CHOLMOD_SIMPLICIAL_LLT 140 +#define EIGEN_PASTIX_LLT 150 +#define EIGEN_PARDISO_LLT 160 +#define EIGEN_CG 170 +#define EIGEN_CG_PRECOND 180 using namespace Eigen; using namespace std; @@ -85,107 +93,118 @@ void printStatheader(std::ofstream& out) // Print XML header // NOTE It would have been much easier to write these XML documents using external libraries like tinyXML or Xerces-C++. - out << " \n"; - out << " \n"; - out << " \n"; - out << "\n\n"; + out << " \n"; + out << " \n"; + out << "\n]>"; + out << "\n\n\n"; - - // Write the root XML element - out << "\n \n" ; + out << "\n \n" ; //root XML element + // Print the xsl style section + printBenchStyle(out); // List all available solvers out << " \n"; #ifdef EIGEN_UMFPACK_SUPPORT - out <<" \n"; + out <<" \n"; out << " LU \n"; out << " UMFPACK \n"; out << " \n"; #endif #ifdef EIGEN_SUPERLU_SUPPORT - out <<" \n"; + out <<" \n"; out << " LU \n"; out << " SUPERLU \n"; out << " \n"; #endif #ifdef EIGEN_CHOLMOD_SUPPORT - out <<" \n"; + out <<" \n"; out << " LLT SP \n"; out << " CHOLMOD \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LLT \n"; out << " CHOLMOD \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LDLT \n"; out << " CHOLMOD \n"; out << " \n"; #endif #ifdef EIGEN_PARDISO_SUPPORT - out <<" \n"; + out <<" \n"; out << " LU \n"; out << " PARDISO \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LLT \n"; out << " PARDISO \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LDLT \n"; out << " PARDISO \n"; out << " \n"; #endif #ifdef EIGEN_PASTIX_SUPPORT - out <<" \n"; + out <<" \n"; out << " LU \n"; out << " PASTIX \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LLT \n"; out << " PASTIX \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LDLT \n"; out << " PASTIX \n"; out << " \n"; #endif - out <<" \n"; + out <<" \n"; out << " BICGSTAB \n"; out << " EIGEN \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " BICGSTAB_ILUT \n"; out << " EIGEN \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " GMRES_ILUT \n"; out << " EIGEN \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LDLT \n"; out << " EIGEN \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " LLT \n"; out << " EIGEN \n"; out << " \n"; - out <<" \n"; + out <<" \n"; out << " CG \n"; out << " EIGEN \n"; out << " \n"; + out <<" \n"; + out << " LU_COLAMD \n"; + out << " EIGEN \n"; + out << " \n"; + +#ifdef EIGEN_METIS_SUPPORT + out <<" \n"; + out << " LU_METIS \n"; + out << " EIGEN \n"; + out << " \n"; +#endif out << " \n"; } @@ -260,7 +279,7 @@ template void call_directsolver(Solver& solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix& b, const Matrix& refX, std::string& statFile) { std::ofstream statbuf(statFile.c_str(), std::ios::app); - statbuf << " \n"; + statbuf << " \n"; call_solver(solver, solver_id, A, b, refX,statbuf); statbuf << " \n"; statbuf.close(); @@ -273,7 +292,7 @@ void call_itersolver(Solver &solver, const int solver_id, const typename Solver: solver.setMaxIterations(MaximumIters); std::ofstream statbuf(statFile.c_str(), std::ios::app); - statbuf << " \n"; + statbuf << " \n"; call_solver(solver, solver_id, A, b, refX,statbuf); statbuf << " "<< solver.iterations() << "\n"; statbuf << " \n"; @@ -303,7 +322,6 @@ void SelectSolvers(const SparseMatrix&A, unsigned int sym, Matrix solver; call_directsolver(solver, EIGEN_SUPERLU, A, b, refX,statFile); - printStatItem(stat, best_time_id, best_time_val); } #endif @@ -324,8 +342,19 @@ void SelectSolvers(const SparseMatrix&A, unsigned int sym, Matrix > solver; + call_directsolver(solver, EIGEN_SPARSELU_COLAMD, A, b, refX, statFile); + // Eigen SparseLU METIS + #ifdef EIGEN_METIS_SUPPORT + { + cout << "\n Solving with Sparse LU AND METIS ... \n"; + SparseLU > solver; + call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile); + } + #endif //BiCGSTAB { @@ -448,7 +477,6 @@ void SelectSolvers(const SparseMatrix&A, unsigned int sym, Matrix solver; // call_itersolver(solver,EIGEN_CG_PRECOND, A, b, refX,statFile); -// printStatItem(stat, best_time_id, best_time_val); // } } // End SPD matrices } @@ -504,8 +532,8 @@ void Browse_Matrices(const string folder, bool statFileExists, std::string& stat if(statFileExists) { std::ofstream statbuf(statFile.c_str(), std::ios::app); - statbuf << " \n"; + statbuf << " \n"; statbuf << " \n"; statbuf.close(); } diff --git a/bench/spbench/spbenchstyle.h b/bench/spbench/spbenchstyle.h new file mode 100644 index 000000000..17a05ce71 --- /dev/null +++ b/bench/spbench/spbenchstyle.h @@ -0,0 +1,94 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef SPBENCHSTYLE_H +#define SPBENCHSTYLE_H + +void printBenchStyle(std::ofstream& out) +{ + out << "\n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + "; + out<<"\n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + "; + + out<<" \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + "; + out<<" \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + "; + out<<" \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ + \n \ +
Matrix N NNZ Sym SPD \n \ + \n \ + \n \ + \n \ + \n \ +
Compute Time
Solve Time
Total Time
Error \n \ + \n \ + (\n \ + \n \ + )\n \ +
\n \ + \n \ + \n \ + \n \ + \n\n"; + +} +#endif \ No newline at end of file diff --git a/bench/spbench/test_sparseLU.cpp b/bench/spbench/test_sparseLU.cpp new file mode 100644 index 000000000..f8ecbe69b --- /dev/null +++ b/bench/spbench/test_sparseLU.cpp @@ -0,0 +1,93 @@ +// Small bench routine for Eigen available in Eigen +// (C) Desire NUENTSA WAKAM, INRIA + +#include +#include +#include +#include +#include +#include +#ifdef EIGEN_METIS_SUPPORT +#include +#endif + +using namespace std; +using namespace Eigen; + +int main(int argc, char **args) +{ +// typedef complex scalar; + typedef double scalar; + SparseMatrix A; + typedef SparseMatrix::Index Index; + typedef Matrix DenseMatrix; + typedef Matrix DenseRhs; + Matrix b, x, tmp; +// SparseLU, AMDOrdering > solver; +// #ifdef EIGEN_METIS_SUPPORT +// SparseLU, MetisOrdering > solver; +// std::cout<< "ORDERING : METIS\n"; +// #else + SparseLU, COLAMDOrdering > solver; + std::cout<< "ORDERING : COLAMD\n"; +// #endif + + ifstream matrix_file; + string line; + int n; + BenchTimer timer; + + // Set parameters + /* Fill the matrix with sparse matrix stored in Matrix-Market coordinate column-oriented format */ + if (argc < 2) assert(false && "please, give the matrix market file "); + loadMarket(A, args[1]); + cout << "End charging matrix " << endl; + bool iscomplex=false, isvector=false; + int sym; + getMarketHeader(args[1], sym, iscomplex, isvector); +// if (iscomplex) { cout<< " Not for complex matrices \n"; return -1; } + if (isvector) { cout << "The provided file is not a matrix file\n"; return -1;} + if (sym != 0) { // symmetric matrices, only the lower part is stored + SparseMatrix temp; + temp = A; + A = temp.selfadjointView(); + } + n = A.cols(); + /* Fill the right hand side */ + + if (argc > 2) + loadMarketVector(b, args[2]); + else + { + b.resize(n); + tmp.resize(n); +// tmp.setRandom(); + for (int i = 0; i < n; i++) tmp(i) = i; + b = A * tmp ; + } + + /* Compute the factorization */ +// solver.isSymmetric(true); + timer.start(); +// solver.compute(A); + solver.analyzePattern(A); + timer.stop(); + cout << "Time to analyze " << timer.value() << std::endl; + timer.reset(); + timer.start(); + solver.factorize(A); + timer.stop(); + cout << "Factorize Time " << timer.value() << std::endl; + timer.reset(); + timer.start(); + x = solver.solve(b); + timer.stop(); + cout << "solve time " << timer.value() << std::endl; + /* Check the accuracy */ + Matrix tmp2 = b - A*x; + scalar tempNorm = tmp2.norm()/b.norm(); + cout << "Relative norm of the computed solution : " << tempNorm <<"\n"; + cout << "Number of nonzeros in the factor : " << solver.nnzL() + solver.nnzU() << std::endl; + + return 0; +} \ No newline at end of file diff --git a/blas/common.h b/blas/common.h index ee38b31d1..2bf642c6b 100644 --- a/blas/common.h +++ b/blas/common.h @@ -10,6 +10,9 @@ #ifndef EIGEN_BLAS_COMMON_H #define EIGEN_BLAS_COMMON_H +#include +#include + #include #include @@ -68,9 +71,6 @@ inline bool check_uplo(const char* uplo) return UPLO(*uplo)!=0xff; } -#include -#include - namespace Eigen { #include "BandTriangularSolver.h" diff --git a/cmake/FindMetis.cmake b/cmake/FindMetis.cmake index e4d6ef258..627c3e9ae 100644 --- a/cmake/FindMetis.cmake +++ b/cmake/FindMetis.cmake @@ -12,10 +12,11 @@ find_path(METIS_INCLUDES ${INCLUDE_INSTALL_DIR} PATH_SUFFIXES metis + include ) -find_library(METIS_LIBRARIES metis PATHS $ENV{METISDIR} ${LIB_INSTALL_DIR}) +find_library(METIS_LIBRARIES metis PATHS $ENV{METISDIR} ${LIB_INSTALL_DIR} PATH_SUFFIXES lib) include(FindPackageHandleStandardArgs) find_package_handle_standard_args(METIS DEFAULT_MSG diff --git a/debug/gdb/printers.py b/debug/gdb/printers.py index 9187acb33..86996a4f9 100644 --- a/debug/gdb/printers.py +++ b/debug/gdb/printers.py @@ -51,12 +51,12 @@ class EigenMatrixPrinter: template_params = m.split(',') template_params = map(lambda x:x.replace(" ", ""), template_params) - if template_params[1] == '-0x00000000000000001' or template_params[1] == '-0x000000001': + if template_params[1] == '-0x00000000000000001' or template_params[1] == '-0x000000001' or template_params[1] == '-1': self.rows = val['m_storage']['m_rows'] else: self.rows = int(template_params[1]) - if template_params[2] == '-0x00000000000000001' or template_params[2] == '-0x000000001': + if template_params[2] == '-0x00000000000000001' or template_params[2] == '-0x000000001' or template_params[2] == '-1': self.cols = val['m_storage']['m_cols'] else: self.cols = int(template_params[2]) diff --git a/doc/C09_TutorialSparse.dox b/doc/C09_TutorialSparse.dox index 20671f57b..6a16c3ae2 100644 --- a/doc/C09_TutorialSparse.dox +++ b/doc/C09_TutorialSparse.dox @@ -211,7 +211,7 @@ Here is a typical usage example: \code typedef Eigen::Triplet T; std::vector tripletList; -triplets.reserve(estimation_of_entries); +tripletList.reserve(estimation_of_entries); for(...) { // ... diff --git a/doc/I17_SparseLinearSystems.dox b/doc/I17_SparseLinearSystems.dox new file mode 100644 index 000000000..cc8987d8a --- /dev/null +++ b/doc/I17_SparseLinearSystems.dox @@ -0,0 +1,110 @@ +namespace Eigen { +/** \page TopicSparseSystems Solving Sparse Linear Systems +In Eigen, there are several methods available to solve linear systems when the coefficient matrix is sparse. Because of the special representation of this class of matrices, special care should be taken in order to get a good performance. See \ref TutorialSparse for a detailed introduction about sparse matrices in Eigen. In this page, we briefly present the main steps that are common to all the linear solvers in Eigen together with the main concepts behind them. Depending on the properties of the matrix, the desired accuracy, the end-user is able to tune these steps in order to improve the performance of its code. However, an impatient user does not need to know deeply what's hiding behind these steps: the last section presents a benchmark routine that can be easily used to get an insight on the performance of all the available solvers. + +\b Table \b of \b contents \n + - \ref TheSparseCompute + - \ref TheSparseSolve + - \ref BenchmarkRoutine + + As summarized in \ref TutorialSparseDirectSolvers, there are many built-in solvers in Eigen as well as interface to external solvers libraries. All these solvers follow the same calling sequence. The basic steps are as follows : +\code +#include +// ... +SparseMatrix A; +// fill A +VectorXd b, x; +// fill b +// solve Ax = b +SolverClassName > solver; +solver.compute(A); +if(solver.info()!=Succeeded) { + // decomposition failed + return; +} +x = solver.solve(b); +if(solver.info()!=Succeeded) { + // solving failed + return; +} +\endcode + +\section TheSparseCompute The Compute Step +In the compute() function, the matrix is generally factorized: LLT for self-adjoint matrices, LDLT for general hermitian matrices and LU for non hermitian matrices. These are the results of using direct solvers. For this class of solvers precisely, the compute step is further subdivided into analyzePattern() and factorize(). + +The goal of analyzePattern() is to reorder the nonzero elements of the matrix, such that the factorization step creates less fill-in. This step exploits only the structure of the matrix. Hence, the results of this step can be used for other linear systems where the matrix has the same structure. Note however that sometimes, some external solvers (like SuperLU) require that the values of the matrix are set in this step, for instance to equilibrate the rows and columns of the matrix. In this situation, the results of this step can note be used with other matrices. + +Eigen provides a limited set of methods to reorder the matrix in this step, either built-in (COLAMD, AMD) or external (METIS). These methods are set in template parameter list of the solver : +\code +DirectSolverClassName, OrderingMethod > solver; +\endcode + +See \link Ordering_Modules the Ordering module \endlink for the list of available methods and the associated options. + +In factorize(), the factors of the coefficient matrix are computed. This step should be called each time the values of the matrix change. However, the structural pattern of the matrix should not change between multiple calls. + +For iterative solvers, the compute step is used to eventually setup a preconditioner. Remember that, basically, the goal of the preconditioner is to speedup the convergence of an iterative method by solving a modified linear system where the coefficient matrix has more clustered eigenvalues. For real problems, an iterative solver should always be used with a preconditioner. In Eigen, a preconditioner is selected by simply adding it as a template parameter to the iterative solver object. +\code +IterativeSolverClassName, PreconditionerName > solver; +\endcode +The member function preconditioner() returns a read-write reference to the preconditioner + to directly interact with it. + +For instance, with the ILUT preconditioner, the incomplete factors L and U are computed in this step. +See \link Sparse_modules the Sparse module \endlink for the list of available preconditioners in Eigen. +\section TheSparseSolve The Solve step +The solve() function computes the solution of the linear systems with one or many right hand sides. +\code +X = solver.solve(B); +\endcode +Here, B can be a vector or a matrix where the columns form the different right hand sides. The solve() function can be called several times as well, for instance When all the right hand sides are not available at once. +\code +x1 = solver.solve(b1); +// Get the second right hand side b2 +x2 = solver.solve(b2); +// ... +\endcode +For direct methods, the solution are computed at the machine precision. Sometimes, the solution need not be too accurate. In this case, the iterative methods are more suitable and the desired accuracy can be set before the solve step using setTolerance(). For all the available functions, please, refer to the documentation of the \link IterativeLinearSolvers_module Iterative solvers module \endlink. + +\section BenchmarkRoutine +Most of the time, all you need is to know how much time it will take to qolve your system, and hopefully, what is the most suitable solver. In Eigen, we provide a benchmark routine that can be used for this purpose. It is very easy to use. First, it should be activated at the configuration step with the flag TEST_REAL_CASES. Then, in bench/spbench, you can compile the routine by typing \b make \e spbenchsolver. You can then run it with --help option to get the list of all available options. Basically, the matrices to test should be in \link http://math.nist.gov/MatrixMarket/formats.html MatrixMarket Coordinate format \endlink, and the routine returns the statistics from all available solvers in Eigen. + +The following table gives an example of XHTML statistics from several Eigen built-in and external solvers. + + +
Matrix N NNZ UMFPACK SUPERLU PASTIX LU BiCGSTAB BiCGSTAB+ILUT GMRES+ILUT LDLT CHOLMOD LDLT PASTIX LDLT LLT CHOLMOD SP LLT CHOLMOD LLT PASTIX LLT CG
vector_graphics 12855 72069 Compute Time 0.02545490.02156770.07018270.0001533880.01401070.01537090.01016010.009305020.0649689 +
Solve Time 0.003378350.0009518260.004843730.03748860.00464450.008477540.0005418130.0002936960.00485376 +
Total Time 0.02883330.02251950.07502650.0376420.01865520.02384840.01070190.009598710.0698227 +
Error(Iter) 1.299e-16 2.04207e-16 4.83393e-15 3.94856e-11 (80) 1.03861e-12 (3) 5.81088e-14 (6) 1.97578e-16 1.83927e-16 4.24115e-15 +
poisson_SPD 19788 308232 Compute Time 0.4250261.823780.6173670.0004789211.340011.334710.7964190.8575730.4730070.8148260.1847190.8615550.4705590.000458188 +
Solve Time 0.02800530.01944020.02687470.2494370.05484440.09269910.008502040.00531710.02589320.008746030.005781550.005303610.02489420.239093 +
Total Time 0.4530311.843220.6442410.2499161.394861.427410.8049210.8628910.49890.8235720.1905010.8668590.4954530.239551 +
Error(Iter) 4.67146e-16 1.068e-15 1.3397e-15 6.29233e-11 (201) 3.68527e-11 (6) 3.3168e-15 (16) 1.86376e-15 1.31518e-16 1.42593e-15 3.45361e-15 3.14575e-16 2.21723e-15 7.21058e-16 9.06435e-12 (261) +
sherman2 1080 23094 Compute Time 0.006317540.0150520.0247514 -0.02144250.0217988 +
Solve Time 0.0004784240.0003379980.0010291 -0.002431520.00246152 +
Total Time 0.006795970.015390.0257805 -0.0238740.0242603 +
Error(Iter) 1.83099e-15 8.19351e-15 2.625e-14 1.3678e+69 (1080) 4.1911e-12 (7) 5.0299e-13 (12) +
bcsstk01_SPD 48 400 Compute Time 0.0001690790.000107890.0005725381.425e-069.1612e-058.3985e-055.6489e-057.0913e-050.0004682515.7389e-058.0212e-055.8394e-050.0004630171.333e-06 +
Solve Time 1.2288e-051.1124e-050.0002863878.5896e-051.6381e-051.6984e-053.095e-064.115e-060.0003254383.504e-067.369e-063.454e-060.0002940956.0516e-05 +
Total Time 0.0001813670.0001190140.0008589258.7321e-050.0001079930.0001009695.9584e-057.5028e-050.0007936896.0893e-058.7581e-056.1848e-050.0007571126.1849e-05 +
Error(Iter) 1.03474e-16 2.23046e-16 2.01273e-16 4.87455e-07 (48) 1.03553e-16 (2) 3.55965e-16 (2) 2.48189e-16 1.88808e-16 1.97976e-16 2.37248e-16 1.82701e-16 2.71474e-16 2.11322e-16 3.547e-09 (48) +
sherman1 1000 3750 Compute Time 0.002288050.002092310.005282689.846e-060.001635220.001621550.0007892590.0008044950.00438269 +
Solve Time 0.0002137889.7983e-050.0009388310.006298350.0003617640.000787944.3989e-052.5331e-050.000917166 +
Total Time 0.002501840.002190290.006221510.00630820.001996980.002409490.0008332480.0008298260.00529986 +
Error(Iter) 1.16839e-16 2.25968e-16 2.59116e-16 3.76779e-11 (248) 4.13343e-11 (4) 2.22347e-14 (10) 2.05861e-16 1.83555e-16 1.02917e-15 +
young1c 841 4089 Compute Time 0.002358430.002172280.005680751.2735e-050.002648660.00258236 +
Solve Time 0.0003295990.0001686340.000801180.05347380.001871930.00450211 +
Total Time 0.002688030.002340910.006481930.05348650.004520590.00708447 +
Error(Iter) 1.27029e-16 2.81321e-16 5.0492e-15 8.0507e-11 (706) 3.00447e-12 (8) 1.46532e-12 (16) +
mhd1280b 1280 22778 Compute Time 0.002348980.002070790.005709182.5976e-050.003025630.002980360.001445250.0009199220.00426444 +
Solve Time 0.001033920.0002119110.001050.01104320.0006282870.003920890.0001383036.2446e-050.00097564 +
Total Time 0.00338290.00228270.006759180.01106920.003653920.006901240.001583550.0009823680.00524008 +
Error(Iter) 1.32953e-16 3.08646e-16 6.734e-16 8.83132e-11 (40) 1.51153e-16 (1) 6.08556e-16 (8) 1.89264e-16 1.97477e-16 6.68126e-09 +
crashbasis 160000 1750416 Compute Time 3.20195.789215.75730.003835153.10063.09921 +
Solve Time 0.2619150.1062250.4021411.490890.248880.443673 +
Total Time 3.463815.8954216.15941.494733.349483.54288 +
Error(Iter) 1.76348e-16 4.58395e-16 1.67982e-14 8.64144e-11 (61) 8.5996e-12 (2) 6.04042e-14 (5) + +
+*/ +} \ No newline at end of file diff --git a/test/CMakeLists.txt b/test/CMakeLists.txt index 164f9c275..cbea4dd0a 100644 --- a/test/CMakeLists.txt +++ b/test/CMakeLists.txt @@ -205,7 +205,7 @@ ei_add_test(vectorwiseop) ei_add_test(simplicial_cholesky) ei_add_test(conjugate_gradient) ei_add_test(bicgstab) - +ei_add_test(sparselu) if(UMFPACK_FOUND) ei_add_test(umfpack_support "" "${UMFPACK_ALL_LIBS}") diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp index a9cd54294..5a599c321 100644 --- a/test/array_for_matrix.cpp +++ b/test/array_for_matrix.cpp @@ -168,6 +168,12 @@ template void cwise_min_max(const MatrixType& m) VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1), m1.cwiseMax( maxM1)); VERIFY_IS_APPROX(m1, m1.cwiseMax( minM1)); + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, minM1).array(), (m1.array().min)( minM1)); + VERIFY_IS_APPROX(m1.array(), (m1.array().min)( maxM1)); + + VERIFY_IS_APPROX(MatrixType::Constant(rows,cols, maxM1).array(), (m1.array().max)( maxM1)); + VERIFY_IS_APPROX(m1.array(), (m1.array().max)( minM1)); + } template void resize(const MatrixTraits& t) diff --git a/test/diagonalmatrices.cpp b/test/diagonalmatrices.cpp index 3f5776dfc..7e9c80d7b 100644 --- a/test/diagonalmatrices.cpp +++ b/test/diagonalmatrices.cpp @@ -32,6 +32,8 @@ template void diagonalmatrices(const MatrixType& m) rv2 = RowVectorType::Random(cols); LeftDiagonalMatrix ldm1(v1), ldm2(v2); RightDiagonalMatrix rdm1(rv1), rdm2(rv2); + + Scalar s1 = internal::random(); SquareMatrixType sq_m1 (v1.asDiagonal()); VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix()); @@ -76,6 +78,13 @@ template void diagonalmatrices(const MatrixType& m) big.block(i,j,rows,cols) = big.block(i,j,rows,cols) * rv1.asDiagonal(); VERIFY_IS_APPROX((big.block(i,j,rows,cols)) , m1 * rv1.asDiagonal() ); + + // scalar multiple + VERIFY_IS_APPROX(LeftDiagonalMatrix(ldm1*s1).diagonal(), ldm1.diagonal() * s1); + VERIFY_IS_APPROX(LeftDiagonalMatrix(s1*ldm1).diagonal(), s1 * ldm1.diagonal()); + + VERIFY_IS_APPROX(m1 * (rdm1 * s1), (m1 * rdm1) * s1); + VERIFY_IS_APPROX(m1 * (s1 * rdm1), (m1 * rdm1) * s1); } void test_diagonalmatrices() diff --git a/test/sparse_solver.h b/test/sparse_solver.h index 75fa85082..73d92874c 100644 --- a/test/sparse_solver.h +++ b/test/sparse_solver.h @@ -158,9 +158,9 @@ inline std::string get_matrixfolder() { std::string mat_folder = TEST_REAL_CASES; if( internal::is_same >::value || internal::is_same >::value ) - mat_folder = mat_folder + static_cast("/complex/"); + mat_folder = mat_folder + static_cast("/complex/"); else - mat_folder = mat_folder + static_cast("/real/"); + mat_folder = mat_folder + static_cast("/real/"); return mat_folder; } #endif diff --git a/test/sparselu.cpp b/test/sparselu.cpp new file mode 100644 index 000000000..e960f9c93 --- /dev/null +++ b/test/sparselu.cpp @@ -0,0 +1,43 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// 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 . +#include "sparse_solver.h" +#include +#include + +template void test_sparselu_T() +{ + SparseLU, COLAMDOrdering > sparselu_colamd; + SparseLU, AMDOrdering > sparselu_amd; + + check_sparse_square_solving(sparselu_colamd); + check_sparse_square_solving(sparselu_amd); +} + +void test_sparselu() +{ + CALL_SUBTEST_1(test_sparselu_T()); + CALL_SUBTEST_2(test_sparselu_T()); + CALL_SUBTEST_3(test_sparselu_T >()); + CALL_SUBTEST_4(test_sparselu_T >()); +} \ No newline at end of file diff --git a/unsupported/Eigen/IterativeSolvers b/unsupported/Eigen/IterativeSolvers index 6c6946d91..c3cc97cd2 100644 --- a/unsupported/Eigen/IterativeSolvers +++ b/unsupported/Eigen/IterativeSolvers @@ -33,6 +33,7 @@ #include "../../Eigen/Jacobi" #include "../../Eigen/Householder" #include "src/IterativeSolvers/GMRES.h" +#include "src/IterativeSolvers/IncompleteCholesky.h" //#include "src/IterativeSolvers/SSORPreconditioner.h" //@} diff --git a/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h new file mode 100644 index 000000000..5bc41c0f8 --- /dev/null +++ b/unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h @@ -0,0 +1,221 @@ +// This file is part of Eigen, a lightweight C++ template library +// for linear algebra. +// +// Copyright (C) 2012 Désiré Nuentsa-Wakam +// +// This Source Code Form is subject to the terms of the Mozilla +// Public License v. 2.0. If a copy of the MPL was not distributed +// with this file, You can obtain one at http://mozilla.org/MPL/2.0/. + +#ifndef EIGEN_INCOMPLETE_CHOlESKY_H +#define EIGEN_INCOMPLETE_CHOlESKY_H +#include "Eigen/src/IterativeLinearSolvers/IncompleteLUT.h" +#include +#include + +namespace Eigen { +/** + * \brief Modified Incomplete Cholesky with dual threshold + * + * References : C-J. Lin and J. J. Moré, Incomplete Cholesky Factorizations with + * Limited memory, SIAM J. Sci. Comput. 21(1), pp. 24-45, 1999 + * + * \tparam _MatrixType The type of the sparse matrix. It should be a symmetric + * matrix. It is advised to give a row-oriented sparse matrix + * \tparam _UpLo The triangular part of the matrix to reference. + * \tparam _OrderingType + */ + +template > +class IncompleteCholesky : internal::noncopyable +{ + public: + typedef SparseMatrix MatrixType; + typedef _OrderingType OrderingType; + typedef typename MatrixType::RealScalar RealScalar; + typedef typename MatrixType::Index Index; + typedef PermutationMatrix PermutationType; + typedef Matrix VectorType; + typedef Matrix IndexType; + + public: + IncompleteCholesky() {} + IncompleteCholesky(const MatrixType& matrix) + { + compute(matrix); + } + + Index rows() const { return m_L.rows(); } + + Index cols() const { return m_L.cols(); } + + + /** \brief Reports whether previous computation was successful. + * + * \returns \c Success if computation was succesful, + * \c NumericalIssue if the matrix appears to be negative. + */ + ComputationInfo info() const + { + eigen_assert(m_isInitialized && "IncompleteLLT is not initialized."); + return m_info; + } + /** + * \brief Computes the fill reducing permutation vector. + */ + template + void analyzePattern(const MatrixType& mat) + { + OrderingType ord; + ord(mat, m_perm); + m_analysisIsOk = true; + } + + template + void factorize(const MatrixType& amat); + + template + void compute (const MatrixType& matrix) + { + analyzePattern(matrix); + factorize(matrix); + } + + template + void _solve(const Rhs& b, Dest& x) const + { + eigen_assert(m_factorizationIsOk && "factorize() should be called first"); + if (m_perm.rows() == b.rows()) + x = m_perm.inverse() * b; + else + x = b; + x = m_L.template triangularView().solve(x); + x = m_L.adjoint().template triangularView().solve(x); + if (m_perm.rows() == b.rows()) + x = m_perm * x; + } + template inline const internal::solve_retval + solve(const MatrixBase& b) const + { + eigen_assert(m_isInitialized && "IncompleteLLT is not initialized."); + eigen_assert(cols()==b.rows() + && "IncompleteLLT::solve(): invalid number of rows of the right hand side matrix b"); + return internal::solve_retval(*this, b.derived()); + } + protected: + SparseMatrix m_L; // The lower part stored in CSC + bool m_analysisIsOk; + bool m_factorizationIsOk; + bool m_isInitialized; + ComputationInfo m_info; + PermutationType m_perm; + +}; + +template +template +void IncompleteCholesky::factorize(const _MatrixType& mat) +{ + eigen_assert(m_analysisIsOk && "analyzePattern() should be called first"); + + // FIXME Stability: We should probably compute the scaling factors and the shifts that are needed to ensure a succesful LLT factorization and an efficient preconditioner. + + // Dropping strategies : Keep only the p largest elements per column, where p is the number of elements in the column of the original matrix. Other strategies will be added + + // Apply the fill-reducing permutation computed in analyzePattern() + if (m_perm.rows() == mat.rows() ) + m_L.template selfadjointView() = mat.template selfadjointView<_UpLo>().twistedBy(m_perm); + else + m_L.template selfadjointView() = mat.template selfadjointView<_UpLo>(); + + int n = mat.cols(); + + Scalar *vals = m_L.valuePtr(); //Values + Index *rowIdx = m_L.innerIndexPtr(); //Row indices + Index *colPtr = m_L.outerIndexPtr(); // Pointer to the beginning of each row + VectorType firstElt(n-1); // for each j, points to the next entry in vals that will be used in the factorization + // Initialize firstElt; + for (int j = 0; j < n-1; j++) firstElt(j) = colPtr[j]+1; + std::vector > listCol(n); // listCol(j) is a linked list of columns to update column j + VectorType curCol(n); // Store a nonzero values in each column + VectorType irow(n); // Row indices of nonzero elements in each column + // jki version of the Cholesky factorization + for (int j=0; j < n; j++) + { + //Left-looking factorize the column j + // First, load the jth column into curCol + Scalar diag = vals[colPtr[j]]; // Lower diagonal matrix with + curCol.setZero(); + irow.setLinSpaced(n,0,n-1); + for (int i = colPtr[j] + 1; i < colPtr[j+1]; i++) + { + curCol(rowIdx[i]) = vals[i]; + irow(rowIdx[i]) = rowIdx[i]; + } + + std::list::iterator k; + // Browse all previous columns that will update column j + for(k = listCol[j].begin(); k != listCol[j].end(); k++) + { + int jk = firstElt(*k); // First element to use in the column + Scalar a_jk = vals[jk]; + diag -= a_jk * a_jk; + jk += 1; + for (int i = jk; i < colPtr[*k]; i++) + { + curCol(rowIdx[i]) -= vals[i] * a_jk ; + } + firstElt(*k) = jk; + if (jk < colPtr[*k+1]) + { + // Add this column to the updating columns list for column *k+1 + listCol[rowIdx[jk]].push_back(*k); + } + } + + // Select the largest p elements + // p is the original number of elements in the column (without the diagonal) + int p = colPtr[j+1] - colPtr[j] - 2 ; + internal::QuickSplit(curCol, irow, p); + if(RealScalar(diag) <= 0) + { //FIXME We can use heuristics (Kershaw, 1978 or above reference ) to get a dynamic shift + m_info = NumericalIssue; + return; + } + RealScalar rdiag = internal::sqrt(RealScalar(diag)); + Scalar scal = Scalar(1)/rdiag; + vals[colPtr[j]] = rdiag; + // Insert the largest p elements in the matrix and scale them meanwhile + int cpt = 0; + for (int i = colPtr[j]+1; i < colPtr[j+1]; i++) + { + vals[i] = curCol(cpt) * scal; + rowIdx[i] = irow(cpt); + cpt ++; + } + } + m_factorizationIsOk = true; + m_isInitialized = true; + m_info = Success; +} + +namespace internal { + +template +struct solve_retval, Rhs> + : solve_retval_base, Rhs> +{ + typedef IncompleteCholesky<_MatrixType> Dec; + EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs) + + template void evalTo(Dest& dst) const + { + dec()._solve(rhs(),dst); + } +}; + +} // end namespace internal + +} // end namespace Eigen + +#endif \ No newline at end of file diff --git a/unsupported/test/matrix_power.cpp b/unsupported/test/matrix_power.cpp index db356450a..95c63c574 100644 --- a/unsupported/test/matrix_power.cpp +++ b/unsupported/test/matrix_power.cpp @@ -34,8 +34,8 @@ template void test2dHyperbolicRotation(double tol) { Matrix,2,2> A, B, C; - T angle, ch = std::cosh(1); - std::complex ish(0, std::sinh(1)); + T angle, ch = std::cosh((T)1); + std::complex ish(0, std::sinh((T)1)); A << ch, ish, -ish, ch; MatrixPower,2,2> > Apow(A);