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That's all there is to it!

3
COPYING.README
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@ -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.
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32
Eigen/Core
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@ -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 <emmintrin.h>
#include <xmmintrin.h>
#ifdef EIGEN_VECTORIZE_SSE3
#include <pmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSSE3
#include <tmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_1
#include <smmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_2
#include <nmmintrin.h>
// 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 <immintrin.h>
#else
#include <emmintrin.h>
#include <xmmintrin.h>
#ifdef EIGEN_VECTORIZE_SSE3
#include <pmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSSE3
#include <tmmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_1
#include <smmintrin.h>
#endif
#ifdef EIGEN_VECTORIZE_SSE4_2
#include <nmmintrin.h>
#endif
#endif
} // end extern "C"
#elif defined __ALTIVEC__

26
Eigen/MetisSupport Normal file
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@ -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 <metis.h>
}
/** \ingroup Support_modules
* \defgroup MetisSupport_Module MetisSupport module
*
* \code
* #include <Eigen/MetisSupport>
* \endcode
*/
#include "src/MetisSupport/MetisSupport.h"
#include "src/Core/util/ReenableStupidWarnings.h"
#endif // EIGEN_METISSUPPORT_MODULE_H

2
Eigen/OrderingMethods
View File

@ -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

17
Eigen/SparseLU Normal file
View File

@ -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

12
Eigen/src/Core/DiagonalMatrix.h
View File

@ -20,6 +20,7 @@ class DiagonalBase : public EigenBase<Derived>
public:
typedef typename internal::traits<Derived>::DiagonalVectorType DiagonalVectorType;
typedef typename DiagonalVectorType::Scalar Scalar;
typedef typename DiagonalVectorType::RealScalar RealScalar;
typedef typename internal::traits<Derived>::StorageKind StorageKind;
typedef typename internal::traits<Derived>::Index Index;
@ -65,6 +66,17 @@ class DiagonalBase : public EigenBase<Derived>
return diagonal().cwiseInverse();
}
inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
operator*(const Scalar& scalar) const
{
return diagonal() * scalar;
}
friend inline const DiagonalWrapper<const CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DiagonalVectorType> >
operator*(const Scalar& scalar, const DiagonalBase& other)
{
return other.diagonal() * scalar;
}
#ifdef EIGEN2_SUPPORT
template<typename OtherDerived>
bool isApprox(const DiagonalBase<OtherDerived>& other, typename NumTraits<Scalar>::Real precision = NumTraits<Scalar>::dummy_precision()) const

44
Eigen/src/Core/Functors.h
View File

@ -454,7 +454,7 @@ struct functor_traits<scalar_log_op<Scalar> >
* 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<typename Scalar1,typename Scalar2>
struct functor_traits<scalar_multiple2_op<Scalar1,Scalar2> >
{ enum { Cost = NumTraits<Scalar1>::MulCost, PacketAccess = false }; };
template<typename Scalar, bool IsInteger>
struct scalar_quotient1_impl {
typedef typename packet_traits<Scalar>::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<Scalar>(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<Packet>(m_other)); }
const Scalar m_other;
};
template<typename Scalar>
struct functor_traits<scalar_quotient1_impl<Scalar,false> >
{ enum { Cost = NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasMul }; };
template<typename Scalar>
struct scalar_quotient1_impl<Scalar,true> {
// 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<typename NumTraits<Scalar>::Nested>::type m_other;
};
template<typename Scalar>
struct functor_traits<scalar_quotient1_impl<Scalar,true> >
{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = false }; };
/** \internal
* \brief Template functor to divide a scalar by a fixed other one
*
@ -521,14 +494,19 @@ struct functor_traits<scalar_quotient1_impl<Scalar,true> >
* \sa class CwiseUnaryOp, MatrixBase::operator/
*/
template<typename Scalar>
struct scalar_quotient1_op : scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger > {
EIGEN_STRONG_INLINE scalar_quotient1_op(const Scalar& other)
: scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger >(other) {}
struct scalar_quotient1_op {
typedef typename packet_traits<Scalar>::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<Packet>(m_other)); }
typename add_const_on_value_type<typename NumTraits<Scalar>::Nested>::type m_other;
};
template<typename Scalar>
struct functor_traits<scalar_quotient1_op<Scalar> >
: functor_traits<scalar_quotient1_impl<Scalar, NumTraits<Scalar>::IsInteger> >
{};
{ enum { Cost = 2 * NumTraits<Scalar>::MulCost, PacketAccess = packet_traits<Scalar>::HasDiv }; };
// nullary functors

2
Eigen/src/Core/MatrixBase.h
View File

@ -240,7 +240,7 @@ template<typename Derived> class MatrixBase
// huuuge hack. make Eigen2's matrix.part<Diagonal>() 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<template<typename T, int n> class U>
template<template<typename T, int N> class U>
const DiagonalWrapper<ConstDiagonalReturnType> part() const
{ return diagonal().asDiagonal(); }
#endif // EIGEN2_SUPPORT

6
Eigen/src/Core/Ref.h
View File

@ -195,12 +195,12 @@ template<typename PlainObjectType, int Options, typename StrideType> class Ref
Base::construct(expr);
}
template<typename Derived>
inline Ref(const MatrixBase<Derived>& expr,
inline Ref(const DenseBase<Derived>& expr,
typename internal::enable_if<bool(internal::is_lvalue<Derived>::value&&bool(Traits::template match<Derived>::MatchAtCompileTime)),Derived>::type* = 0,
int = Derived::ThisConstantIsPrivateInPlainObjectBase)
#else
template<typename Derived>
inline Ref(MatrixBase<Derived>& expr)
inline Ref(DenseBase<Derived>& expr)
#endif
{
Base::construct(expr.const_cast_derived());
@ -221,7 +221,7 @@ template<typename PlainObjectType, int Options, typename StrideType> class Ref<c
EIGEN_DENSE_PUBLIC_INTERFACE(Ref)
template<typename Derived>
inline Ref(const MatrixBase<Derived>& expr)
inline Ref(const DenseBase<Derived>& expr)
{
// std::cout << match_helper<Derived>::HasDirectAccess << "," << match_helper<Derived>::OuterStrideMatch << "," << match_helper<Derived>::InnerStrideMatch << "\n";
// std::cout << int(StrideType::OuterStrideAtCompileTime) << " - " << int(Derived::OuterStrideAtCompileTime) << "\n";

1
Eigen/src/Core/StableNorm.h
View File

@ -131,7 +131,6 @@ MatrixBase<Derived>::blueNorm() const
abig = internal::sqrt(abig);
if(abig > overfl)
{
eigen_assert(false && "overflow");
return rbig;
}
if(amed > RealScalar(0))

3
Eigen/src/Core/TriangularMatrix.h
View File

@ -511,6 +511,7 @@ template<typename Derived1, typename Derived2, bool ClearOpposite>
struct triangular_assignment_selector<Derived1, Derived2, StrictlyUpper, Dynamic, ClearOpposite>
{
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<Derived1, Derived2, StrictlyUpper, Dynamic
dst.copyCoeff(i, j, src);
if (ClearOpposite)
for(Index i = maxi; i < dst.rows(); ++i)
dst.coeffRef(i, j) = 0;
dst.coeffRef(i, j) = Scalar(0);
}
}
};

4
Eigen/src/Core/products/GeneralMatrixVector.h
View File

@ -81,7 +81,7 @@ EIGEN_DONT_INLINE static void run(
const Index peels = 2;
const Index LhsPacketAlignedMask = LhsPacketSize-1;
const Index ResPacketAlignedMask = ResPacketSize-1;
const Index PeelAlignedMask = ResPacketSize*peels-1;
// const Index PeelAlignedMask = ResPacketSize*peels-1;
const Index size = rows;
// How many coeffs of the result do we have to skip to be aligned.
@ -335,7 +335,7 @@ EIGEN_DONT_INLINE static void run(
const Index peels = 2;
const Index RhsPacketAlignedMask = RhsPacketSize-1;
const Index LhsPacketAlignedMask = LhsPacketSize-1;
const Index PeelAlignedMask = RhsPacketSize*peels-1;
// const Index PeelAlignedMask = RhsPacketSize*peels-1;
const Index depth = cols;
// How many coeffs of the result do we have to skip to be aligned.

4
Eigen/src/Core/util/XprHelper.h
View File

@ -322,9 +322,9 @@ template<typename T, int n=1, typename PlainObject = typename eval<T>::type> str
// it's important that this value can still be squared without integer overflowing.
DynamicAsInteger = 10000,
ScalarReadCost = NumTraits<typename traits<T>::Scalar>::ReadCost,
ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? DynamicAsInteger : ScalarReadCost,
ScalarReadCostAsInteger = ScalarReadCost == Dynamic ? int(DynamicAsInteger) : int(ScalarReadCost),
CoeffReadCost = traits<T>::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

23
Eigen/src/Geometry/Umeyama.h
View File

@ -153,16 +153,21 @@ umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& 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;
}

6
Eigen/src/IterativeLinearSolvers/BiCGSTAB.h
View File

@ -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<typename Rhs,typename Dest>
void _solve(const Rhs& b, Dest& x) const
{
x.setZero();
// x.setZero();
x = b;
_solveWithGuess(b,x);
}

101
Eigen/src/IterativeLinearSolvers/IncompleteLUT.h
View File

@ -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 i<ncut
* abs(row(i)) <= abs(row(ncut)) if i>ncut
* \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 <typename VectorV, typename VectorI>
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 <typename VectorV, typename VectorI>
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<Scalar>::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 i<ncut
* abs(row(i)) <= abs(row(ncut)) if i>ncut
* \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 <typename Scalar>
template <typename VectorV, typename VectorI>
int IncompleteLUT<Scalar>::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 <typename Scalar>
template<typename _MatrixType>
void IncompleteLUT<Scalar>::analyzePattern(const _MatrixType& amat)
@ -400,7 +399,7 @@ void IncompleteLUT<Scalar>::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<Scalar>::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++)

6
Eigen/src/MetisSupport/CMakeLists.txt Normal file
View File

@ -0,0 +1,6 @@
FILE(GLOB Eigen_MetisSupport_SRCS "*.h")
INSTALL(FILES
${Eigen_MetisSupport_SRCS}
DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/MetisSupport COMPONENT Devel
)

138
Eigen/src/MetisSupport/MetisSupport.h Normal file
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@ -0,0 +1,138 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Index>
class MetisOrdering
{
public:
typedef PermutationMatrix<Dynamic,Dynamic,Index> PermutationType;
typedef Matrix<Index,Dynamic,1> IndexVector;
template <typename MatrixType>
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 <typename MatrixType>
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

1849
Eigen/src/OrderingMethods/Eigen_Colamd.h Normal file
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File diff suppressed because it is too large Load Diff

158
Eigen/src/OrderingMethods/Ordering.h Normal file
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@ -0,0 +1,158 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#ifndef 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<typename MatrixType>
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 <typename Index>
class AMDOrdering
{
public:
typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
/** Compute the permutation vector from a sparse matrix
* This routine is much faster if the input matrix is column-major
*/
template <typename MatrixType>
void operator()(const MatrixType& mat, PermutationType& perm)
{
// Compute the symmetric pattern
SparseMatrix<typename MatrixType::Scalar, ColMajor, Index> 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 <typename SrcType, unsigned int SrcUpLo>
void operator()(const SparseSelfAdjointView<SrcType, SrcUpLo>& mat, PermutationType& perm)
{
SparseMatrix<typename SrcType::Scalar, ColMajor, Index> 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 <typename Index>
class NaturalOrdering
{
public:
typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
/** Compute the permutation vector from a column-major sparse matrix */
template <typename MatrixType>
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<typename Index>
class COLAMDOrdering;
#include "Eigen_Colamd.h"
template<typename Index>
class COLAMDOrdering
{
public:
typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
typedef Matrix<Index, Dynamic, 1> IndexVector;
/** Compute the permutation vector form a sparse matrix */
template <typename MatrixType>
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

12
Eigen/src/SparseCore/SparseMatrix.h
View File

@ -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<RealScalar>::dummy_precision())
{

5
Eigen/src/SparseCore/SparseUtil.h
View File

@ -113,9 +113,10 @@ template<typename T,int Rows> struct sparse_eval<T,Rows,1> {
template<typename T,int Rows,int Cols> struct sparse_eval {
typedef typename traits<T>::Scalar _Scalar;
enum { _Flags = traits<T>::Flags };
typedef typename traits<T>::Index _Index;
enum { _Options = ((traits<T>::Flags&RowMajorBit)==RowMajorBit) ? RowMajor : ColMajor };
public:
typedef SparseMatrix<_Scalar, _Flags> type;
typedef SparseMatrix<_Scalar, _Options, _Index> type;
};
template<typename T> struct sparse_eval<T,1,1> {

6
Eigen/src/SparseLU/CMakeLists.txt Normal file
View File

@ -0,0 +1,6 @@
FILE(GLOB Eigen_SparseLU_SRCS "*.h")
INSTALL(FILES
${Eigen_SparseLU_SRCS}
DESTINATION ${INCLUDE_INSTALL_DIR}/Eigen/src/SparseLU COMPONENT Devel
)

630
Eigen/src/SparseLU/SparseLU.h Normal file
View File

@ -0,0 +1,630 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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<double, ColMajor> A;
* SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<int> > 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 <typename _MatrixType, typename _OrderingType>
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<Scalar,ColMajor,Index> NCMatrix;
typedef SuperNodalMatrix<Scalar, Index> SCMatrix;
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
typedef Matrix<Index,Dynamic,1> IndexVector;
typedef PermutationMatrix<Dynamic, Dynamic, Index> 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<typename Rhs>
inline const internal::solve_retval<SparseLU, Rhs> solve(const MatrixBase<Rhs>& 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<SparseLU, Rhs>(*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<typename Rhs, typename Dest>
bool _solve(const MatrixBase<Rhs> &B, MatrixBase<Dest> &_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<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(m_Lstore.valuePtr()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) );
Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
U = A.template triangularView<Upper>().solve(U);
}
for (int j = 0; j < nrhs; ++j)
{
for (int jcol = fsupc; jcol < fsupc + nsupc; jcol++)
{
typename MappedSparseMatrix<Scalar>::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<Scalar> 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<IndexVector, ScalarVector> 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 <typename MatrixType, typename OrderingType>
void SparseLU<MatrixType, OrderingType>::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<Scalar,Index>::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<Scalar,Index>::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 <typename MatrixType, typename OrderingType>
void SparseLU<MatrixType, OrderingType>::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<Scalar,Index>::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<Scalar,Index>::LU_heap_relax_snode(n, m_etree, m_perfv.relax, marker, relax_end);
else
SparseLUBase<Scalar,Index>::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, <panel_size> 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<Scalar,Index>::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<Scalar,Index>::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<Scalar,Index>::LU_snode_bmod(icol, fsupc, dense, m_glu);
// Eliminate the current column
info = SparseLUBase<Scalar,Index>::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 <<std::endl;
m_factorizationIsOk = false;
return;
}
}
jcol = icol; // The last column te be eliminated
}
else
{ // Work on one panel of panel_size columns
// Adjust panel size so that a panel won't overlap with the next relaxed snode.
int panel_size = m_perfv.panel_size; // upper bound on panel width
for (k = jcol + 1; k < (std::min)(jcol+panel_size, n); k++)
{
if (relax_end(k) != IND_EMPTY)
{
panel_size = k - jcol;
break;
}
}
if (k == n)
panel_size = n - jcol;
// Symbolic outer factorization on a panel of columns
SparseLUBase<Scalar,Index>::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<Scalar,Index>::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<IndexVector> panel_lsubk(panel_lsub, k, m);
VectorBlock<IndexVector> repfnz_k(repfnz, k, m);
info = SparseLUBase<Scalar,Index>::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<ScalarVector> dense_k(dense, k, m);
VectorBlock<IndexVector> segrep_k(segrep, nseg1, m-nseg1);
info = SparseLUBase<Scalar,Index>::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<Scalar,Index>::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<Scalar,Index>::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 <<std::endl;
m_info = NumericalIssue;
m_factorizationIsOk = false;
return;
}
// Prune columns (0:jj-1) using column jj
SparseLUBase<Scalar,Index>::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<Scalar,Index>::LU_countnz(n, m_nnzL, m_nnzU, m_glu);
// Apply permutation to the L subscripts
SparseLUBase<Scalar,Index>::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<Scalar> ( 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<typename _MatrixType, typename Derived, typename Rhs>
struct solve_retval<SparseLU<_MatrixType,Derived>, Rhs>
: solve_retval_base<SparseLU<_MatrixType,Derived>, Rhs>
{
typedef SparseLU<_MatrixType,Derived> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
} // end namespace internal
} // End namespace Eigen
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
struct SparseLUBase
{
typedef Matrix<Scalar,Dynamic,1> ScalarVector;
typedef Matrix<Index,Dynamic,1> IndexVector;
typedef typename ScalarVector::RealScalar RealScalar;
typedef VectorBlock<Matrix<Scalar,Dynamic,1> > BlockScalarVector;
typedef VectorBlock<Matrix<Index,Dynamic,1> > BlockIndexVector;
// typedef Ref<Matrix<Scalar,Dynamic,1> > BlockScalarVector;
// typedef Ref<Matrix<Index,Dynamic,1> > BlockIndexVector;
typedef LU_GlobalLU_t<IndexVector, ScalarVector> GlobalLU_t;
typedef SparseMatrix<Scalar,ColMajor,Index> 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 <typename VectorType>
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 <typename VectorType>
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<IndexVector, ScalarVector>& 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 <typename Traits>
static void LU_dfs_kernel(const int jj, IndexVector& perm_r,
int& nseg, IndexVector& panel_lsub, IndexVector& segrep,
Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> 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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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<Scalar,Index>::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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <typename _Scalar, typename _Index>
class SuperNodalMatrix
{
public:
typedef _Scalar Scalar;
typedef _Index Index;
typedef Matrix<Index,Dynamic,1> IndexVector;
typedef Matrix<Scalar,Dynamic,1> 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<typename Dest>
void solveInPlace( MatrixBase<Dest>&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<typename Scalar, typename Index>
class SuperNodalMatrix<Scalar,Index>::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<Scalar&>(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<typename Scalar, typename Index>
template<typename Dest>
void SuperNodalMatrix<Scalar,Index>::solveInPlace( MatrixBase<Dest>&X) const
{
Index n = X.rows();
int nrhs = X.cols();
const Scalar * Lval = valuePtr(); // Nonzero values
Matrix<Scalar,Dynamic,Dynamic> 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<const Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(Lval[luptr]), nsupc, nsupc, OuterStride<>(nsupr) );
Map< Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > U (&(X(fsupc,0)), nsupc, nrhs, OuterStride<>(n) );
U = A.template triangularView<UnitLower>().solve(U);
// Matrix-vector product
new (&A) Map<const Matrix<Scalar,Dynamic,Dynamic>, 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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
template <typename VectorType>
int SparseLUBase<Scalar,Index>::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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<ScalarVector>(glu.lusup, glu.nzlumax, 0, 0, num_expansions);
expand<ScalarVector>(glu.ucol,glu.nzumax, 0, 0, num_expansions);
expand<IndexVector>(glu.lsub,glu.nzlmax, 0, 0, num_expansions);
expand<IndexVector>(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 <typename Scalar, typename Index>
template <typename VectorType>
int SparseLUBase<Scalar,Index>::LUMemXpand(VectorType& vec, int& maxlen, int nbElts, LU_MemType memtype, int& num_expansions)
{
int failed_size;
if (memtype == USUB)
failed_size = expand<VectorType>(vec, maxlen, nbElts, 1, num_expansions);
else
failed_size = expand<VectorType>(vec, maxlen, nbElts, 0, num_expansions);
if (failed_size)
return failed_size;
return 0 ;
}
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename IndexVector, typename ScalarVector>
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 <panel_size> 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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<Dynamic>::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<ScalarVector>(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<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) );
VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
u = A.template triangularView<UnitLower>().solve(u);
new (&A) Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) );
VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
l.noalias() -= A * u;
} // End if fst_col
return 0;
}
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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<typename IndexVector, typename ScalarVector>
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<IndexVector, ScalarVector>& 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<Scalar,Index>::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<IndexVector, ScalarVector>& m_glu;
};
template <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<IndexVector> marker2(marker, 2*m, m);
LU_column_dfs_traits<IndexVector, ScalarVector> 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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<ScalarVector>(glu.ucol, glu.nzumax, nextu, UCOL, glu.num_expansions);
if (mem) return mem;
mem = LUMemXpand<IndexVector>(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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <int SegSizeAtCompileTime> struct LU_kernel_bmod
{
template <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
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<Matrix<Scalar,SegSizeAtCompileTime,SegSizeAtCompileTime>, 0, OuterStride<> > A( &(lusup.data()[luptr]), segsize, segsize, OuterStride<>(nsupr) );
Map<Matrix<Scalar,SegSizeAtCompileTime,1> > u(tempv.data(), segsize);
u = A.template triangularView<UnitLower>().solve(u);
// Dense matrix-vector product y <-- B*x
luptr += segsize;
Map<Matrix<Scalar,Dynamic,SegSizeAtCompileTime>, 0, OuterStride<> > B( &(lusup.data()[luptr]), nrow, segsize, OuterStride<>(nsupr) );
Map<Matrix<Scalar,Dynamic,1> > 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 <typename BlockScalarVector, typename ScalarVector, typename IndexVector>
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<nrow)
dense.coeffRef(*(irow++)) -= f * *(a++);
}
};
#endif

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
// Copyright (C) 2012 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// 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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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<IndexVector> 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<Matrix<Scalar,Dynamic,Dynamic> > 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<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
VectorBlock<ScalarVector> 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<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > A(glu.lusup.data()+luptr, u_rows, u_rows, OuterStride<>(nsupr) );
U = A.template triangularView<UnitLower>().solve(U);
// update
luptr += u_rows;
Map<Matrix<Scalar,Dynamic,Dynamic>, 0, OuterStride<> > B(glu.lusup.data()+luptr, nrow, u_rows, OuterStride<>(nsupr) );
assert(tempv.size()>w*u_rows + nrow*w);
Map<Matrix<Scalar,Dynamic,Dynamic> > 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<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
VectorBlock<ScalarVector> 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<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero column index for each row
VectorBlock<ScalarVector> 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<Dynamic>::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

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
template <typename Traits>
void SparseLUBase<Scalar,Index>::LU_dfs_kernel(const int jj, IndexVector& perm_r,
int& nseg, IndexVector& panel_lsub, IndexVector& segrep,
Ref<IndexVector> repfnz_col, IndexVector& xprune, Ref<IndexVector> 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<typename IndexVector>
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]<m_jcol)
{
m_marker[krep] = jj;
return true;
}
return false;
}
void mem_expand(IndexVector& /*glu.lsub*/, int /*nextl*/, int /*chmark*/) {}
enum { ExpandMem = false };
Index m_jcol;
Index* m_marker;
};
template <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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<IndexVector> marker1(marker, m, m);
nseg = 0;
LU_panel_dfs_traits<IndexVector> traits(jcol, marker1.data());
// For each column in the panel
for (int jj = jcol; jj < jcol + w; jj++)
{
nextl_col = (jj - jcol) * m;
VectorBlock<IndexVector> repfnz_col(repfnz, nextl_col, m); // First nonzero location in each row
VectorBlock<ScalarVector> 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

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Eigen/src/SparseLU/SparseLU_pivotL.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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

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Eigen/src/SparseLU/SparseLU_pruneL.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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

73
Eigen/src/SparseLU/SparseLU_relax_snode.h Normal file
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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
void SparseLUBase<Scalar,Index>::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

72
Eigen/src/SparseLU/SparseLU_snode_bmod.h Normal file
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@ -0,0 +1,72 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<Matrix<Scalar,Dynamic,Dynamic>,0,OuterStride<> > A( &(glu.lusup.data()[luptr]), nsupc, nsupc, OuterStride<>(nsupr) );
VectorBlock<ScalarVector> u(glu.lusup, ufirst, nsupc);
u = A.template triangularView<UnitLower>().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<Matrix<Scalar,Dynamic,Dynamic>,0,OuterStride<> > ( &(glu.lusup.data()[luptr+nsupc]), nrow, nsupc, OuterStride<>(nsupr) );
VectorBlock<ScalarVector> l(glu.lusup, ufirst+nsupc, nrow);
l.noalias() -= A * u;
}
return 0;
}
#endif

95
Eigen/src/SparseLU/SparseLU_snode_dfs.h Normal file
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@ -0,0 +1,95 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <typename Scalar, typename Index>
int SparseLUBase<Scalar,Index>::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<IndexVector>(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<IndexVector>(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

1
Eigen/src/SuperLUSupport/SuperLUSupport.h
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@ -612,6 +612,7 @@ void SuperLU<MatrixType>::factorize(const MatrixType& a)
this->initFactorization(a);
m_sluOptions.ColPerm = COLAMD;
int info = 0;
RealScalar recip_pivot_growth, rcond;
RealScalar ferr, berr;

6
Eigen/src/plugins/ArrayCwiseBinaryOps.h
View File

@ -33,7 +33,8 @@ EIGEN_MAKE_CWISE_BINARY_OP(min,internal::scalar_min_op)
*
* \sa max()
*/
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived, const ConstantReturnType>
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_min_op<Scalar>, const Derived,
const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, 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<internal::scalar_max_op<Scalar>, const Derived, const ConstantReturnType>
EIGEN_STRONG_INLINE const CwiseBinaryOp<internal::scalar_max_op<Scalar>, const Derived,
const CwiseNullaryOp<internal::scalar_constant_op<Scalar>, PlainObject> >
(max)(const Scalar &other) const
{
return (max)(Derived::PlainObject::Constant(rows(), cols(), other));

1
Eigen/src/plugins/ArrayCwiseUnaryOps.h
View File

@ -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)

13
bench/spbench/CMakeLists.txt
View File

@ -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})

125
bench/spbench/sp_solver.cpp Normal file
View File

@ -0,0 +1,125 @@
// Small bench routine for Eigen available in Eigen
// (C) Desire NUENTSA WAKAM, INRIA
#include <iostream>
#include <fstream>
#include <iomanip>
#include <Eigen/Jacobi>
#include <Eigen/Householder>
#include <Eigen/IterativeLinearSolvers>
#include <Eigen/LU>
#include <unsupported/Eigen/SparseExtra>
//#include <Eigen/SparseLU>
#include <Eigen/SuperLUSupport>
// #include <unsupported/Eigen/src/IterativeSolvers/Scaling.h>
#include <bench/BenchTimer.h>
#include <unsupported/Eigen/IterativeSolvers>
using namespace std;
using namespace Eigen;
int main(int argc, char **args)
{
SparseMatrix<double, ColMajor> A;
typedef SparseMatrix<double, ColMajor>::Index Index;
typedef Matrix<double, Dynamic, Dynamic> DenseMatrix;
typedef Matrix<double, Dynamic, 1> DenseRhs;
VectorXd b, x, tmp;
BenchTimer timer,totaltime;
//SparseLU<SparseMatrix<double, ColMajor> > solver;
// SuperLU<SparseMatrix<double, ColMajor> > solver;
ConjugateGradient<SparseMatrix<double, ColMajor>, Lower,IncompleteCholesky<double,Lower> > 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<double, ColMajor> temp;
temp = A;
A = temp.selfadjointView<Lower>();
}
timer.stop();
n = A.cols();
// ====== TESTS FOR SPARSE TUTORIAL ======
// cout<< "OuterSize " << A.outerSize() << " inner " << A.innerSize() << endl;
// SparseMatrix<double, RowMajor> mat1(A);
// SparseMatrix<double, RowMajor> mat2;
// cout << " norm of A " << mat1.norm() << endl; ;
// PermutationMatrix<Dynamic, Dynamic, int> 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() <<endl;
/* Fill the right hand side */
// solver.set_restart(374);
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 ;
}
// Scaling<SparseMatrix<double> > 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() <<" " <<A.cols() <<"\n";
solver.compute(A);
// solver.analyzePattern(A);
// solver.factorize(A);
if (solver.info() != Success) {
std::cout<< "The solver failed \n";
return -1;
}
timer.stop();
float time_comp = timer.value();
cout <<" Compute Time " << time_comp<< endl;
timer.reset();
timer.start();
x = solver.solve(b);
// x = scal.RightScaling().cwiseProduct(x);
timer.stop();
float time_solve = timer.value();
cout<< " Time to solve " << time_solve << endl;
/* Check the accuracy */
VectorXd tmp2 = b - A*x;
double tempNorm = tmp2.norm()/b.norm();
cout << "Relative norm of the computed solution : " << tempNorm <<"\n";
// cout << "Iterations : " << solver.iterations() << "\n";
totaltime.stop();
cout << "Total time " << totaltime.value() << "\n";
// std::cout<<x.transpose()<<"\n";
return 0;
}

83
bench/spbench/spbench.xsl
View File

@ -1,83 +0,0 @@
<?xml version="1.0" encoding="UTF-8"?>
<xsl:stylesheet version="1.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform" >
<!-- Desire Nuentsa, Inria -->
<xsl:output method="html" indent="no"/>
<xsl:template match="/"> <!-- Root of the document -->
<html>
<head>
<style type="text/css">
td { white-space: nowrap;}
</style>
</head>
<body>
<table border="1" width="100%" height="100%">
<TR> <!-- Write the table header -->
<TH>Matrix</TH> <TH>N</TH> <TH> NNZ</TH> <TH> Sym</TH> <TH> SPD</TH> <TH> </TH>
<xsl:for-each select="BENCH/AVAILSOLVER/SOLVER">
<xsl:sort select="@ID" data-type="number"/>
<TH>
<xsl:value-of select="TYPE" />
<xsl:text></xsl:text>
<xsl:value-of select="PACKAGE" />
<xsl:text></xsl:text>
</TH>
</xsl:for-each>
</TR>
<xsl:for-each select="BENCH/LINEARSYSTEM">
<TR> <!-- print statistics for one linear system-->
<TH rowspan="4"> <xsl:value-of select="MATRIX/NAME" /> </TH>
<TD rowspan="4"> <xsl:value-of select="MATRIX/SIZE" /> </TD>
<TD rowspan="4"> <xsl:value-of select="MATRIX/ENTRIES" /> </TD>
<TD rowspan="4"> <xsl:value-of select="MATRIX/SYMMETRY" /> </TD>
<TD rowspan="4"> <xsl:value-of select="MATRIX/POSDEF" /> </TD>
<TH> Compute Time </TH>
<xsl:for-each select="SOLVER_STAT">
<xsl:sort select="@ID" data-type="number"/>
<TD> <xsl:value-of select="TIME/COMPUTE" /> </TD>
</xsl:for-each>
</TR>
<TR>
<TH> Solve Time </TH>
<xsl:for-each select="SOLVER_STAT">
<xsl:sort select="@ID" data-type="number"/>
<TD> <xsl:value-of select="TIME/SOLVE" /> </TD>
</xsl:for-each>
</TR>
<TR>
<TH> Total Time </TH>
<xsl:for-each select="SOLVER_STAT">
<xsl:sort select="@ID" data-type="number"/>
<xsl:choose>
<xsl:when test="@ID=../BEST_SOLVER/@ID">
<TD style="background-color:red"> <xsl:value-of select="TIME/TOTAL" /> </TD>
</xsl:when>
<xsl:otherwise>
<TD> <xsl:value-of select="TIME/TOTAL" /></TD>
</xsl:otherwise>
</xsl:choose>
</xsl:for-each>
</TR>
<TR>
<TH> Error </TH>
<xsl:for-each select="SOLVER_STAT">
<xsl:sort select="@ID" data-type="number"/>
<TD> <xsl:value-of select="ERROR" />
<xsl:if test="ITER">
<xsl:text>(</xsl:text>
<xsl:value-of select="ITER" />
<xsl:text>)</xsl:text>
</xsl:if> </TD>
</xsl:for-each>
</TR>
</xsl:for-each>
</table>
</body>
</html>
</xsl:template>
</xsl:stylesheet>

2
bench/spbench/spbenchsolver.cpp
View File

@ -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 <RelErr> Sets the relative tolerance for iterative solvers (default 1e-08) \n\n";
cout<< " --maxits <MaxIts> Sets the maximum number of iterations (default 1000) \n\n";

134
bench/spbench/spbenchsolver.h
View File

@ -10,7 +10,7 @@
#include <iostream>
#include <fstream>
#include "Eigen/SparseCore"
#include <Eigen/SparseCore>
#include <bench/BenchTimer.h>
#include <cstdlib>
#include <string>
@ -21,6 +21,13 @@
#include <unsupported/Eigen/IterativeSolvers>
#include <Eigen/LU>
#include <unsupported/Eigen/SparseExtra>
#include <Eigen/SparseLU>
#include "spbenchstyle.h"
#ifdef EIGEN_METIS_SUPPORT
#include <Eigen/MetisSupport>
#endif
#ifdef EIGEN_CHOLMOD_SUPPORT
#include <Eigen/CholmodSupport>
@ -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 << "<?xml version=\"1.0\" encoding=\"UTF-8\"?> \n";
out << "<?xml-stylesheet type=\"text/xsl\" href=\"spbench.xsl\" ?> \n";
out << "<!DOCTYPE BENCH SYSTEM \"spbench.dtd\"> \n";
out << "\n<!-- Generated by the Eigen library -->\n";
out << "<?xml version='1.0' encoding='UTF-8'?> \n";
out << "<?xml-stylesheet type='text/xsl' href='#stylesheet' ?> \n";
out << "<!DOCTYPE BENCH [\n<!ATTLIST xsl:stylesheet\n id\t ID #REQUIRED>\n]>";
out << "\n\n<!-- Generated by the Eigen library -->\n";
// Write the root XML element
out << "\n<BENCH> \n" ;
out << "\n<BENCH> \n" ; //root XML element
// Print the xsl style section
printBenchStyle(out);
// List all available solvers
out << " <AVAILSOLVER> \n";
#ifdef EIGEN_UMFPACK_SUPPORT
out <<" <SOLVER ID=\"" << EIGEN_UMFPACK << "\">\n";
out <<" <SOLVER ID='" << EIGEN_UMFPACK << "'>\n";
out << " <TYPE> LU </TYPE> \n";
out << " <PACKAGE> UMFPACK </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
#ifdef EIGEN_SUPERLU_SUPPORT
out <<" <SOLVER ID=\"" << EIGEN_SUPERLU << "\">\n";
out <<" <SOLVER ID='" << EIGEN_SUPERLU << "'>\n";
out << " <TYPE> LU </TYPE> \n";
out << " <PACKAGE> SUPERLU </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
#ifdef EIGEN_CHOLMOD_SUPPORT
out <<" <SOLVER ID=\"" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SIMPLICIAL_LLT << "'>\n";
out << " <TYPE> LLT SP</TYPE> \n";
out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_CHOLMOD_SUPERNODAL_LLT << "'>\n";
out << " <TYPE> LLT</TYPE> \n";
out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_CHOLMOD_LDLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_CHOLMOD_LDLT << "'>\n";
out << " <TYPE> LDLT </TYPE> \n";
out << " <PACKAGE> CHOLMOD </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
#ifdef EIGEN_PARDISO_SUPPORT
out <<" <SOLVER ID=\"" << EIGEN_PARDISO << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PARDISO << "'>\n";
out << " <TYPE> LU </TYPE> \n";
out << " <PACKAGE> PARDISO </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_PARDISO_LLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PARDISO_LLT << "'>\n";
out << " <TYPE> LLT </TYPE> \n";
out << " <PACKAGE> PARDISO </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_PARDISO_LDLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PARDISO_LDLT << "'>\n";
out << " <TYPE> LDLT </TYPE> \n";
out << " <PACKAGE> PARDISO </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
#ifdef EIGEN_PASTIX_SUPPORT
out <<" <SOLVER ID=\"" << EIGEN_PASTIX << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PASTIX << "'>\n";
out << " <TYPE> LU </TYPE> \n";
out << " <PACKAGE> PASTIX </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_PASTIX_LLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PASTIX_LLT << "'>\n";
out << " <TYPE> LLT </TYPE> \n";
out << " <PACKAGE> PASTIX </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_PASTIX_LDLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_PASTIX_LDLT << "'>\n";
out << " <TYPE> LDLT </TYPE> \n";
out << " <PACKAGE> PASTIX </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
out <<" <SOLVER ID=\"" << EIGEN_BICGSTAB << "\">\n";
out <<" <SOLVER ID='" << EIGEN_BICGSTAB << "'>\n";
out << " <TYPE> BICGSTAB </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_BICGSTAB_ILUT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_BICGSTAB_ILUT << "'>\n";
out << " <TYPE> BICGSTAB_ILUT </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_GMRES_ILUT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_GMRES_ILUT << "'>\n";
out << " <TYPE> GMRES_ILUT </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_SIMPLICIAL_LDLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LDLT << "'>\n";
out << " <TYPE> LDLT </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_SIMPLICIAL_LLT << "\">\n";
out <<" <SOLVER ID='" << EIGEN_SIMPLICIAL_LLT << "'>\n";
out << " <TYPE> LLT </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID=\"" << EIGEN_CG << "\">\n";
out <<" <SOLVER ID='" << EIGEN_CG << "'>\n";
out << " <TYPE> CG </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
out <<" <SOLVER ID='" << EIGEN_SPARSELU_COLAMD << "'>\n";
out << " <TYPE> LU_COLAMD </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
#ifdef EIGEN_METIS_SUPPORT
out <<" <SOLVER ID='" << EIGEN_SPARSELU_METIS << "'>\n";
out << " <TYPE> LU_METIS </TYPE> \n";
out << " <PACKAGE> EIGEN </PACKAGE> \n";
out << " </SOLVER> \n";
#endif
out << " </AVAILSOLVER> \n";
}
@ -260,7 +279,7 @@ template<typename Solver, typename Scalar>
void call_directsolver(Solver& solver, const int solver_id, const typename Solver::MatrixType& A, const Matrix<Scalar, Dynamic, 1>& b, const Matrix<Scalar, Dynamic, 1>& refX, std::string& statFile)
{
std::ofstream statbuf(statFile.c_str(), std::ios::app);
statbuf << " <SOLVER_STAT ID=\"" << solver_id <<"\">\n";
statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
call_solver(solver, solver_id, A, b, refX,statbuf);
statbuf << " </SOLVER_STAT>\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 << " <SOLVER_STAT ID=\"" << solver_id <<"\">\n";
statbuf << " <SOLVER_STAT ID='" << solver_id <<"'>\n";
call_solver(solver, solver_id, A, b, refX,statbuf);
statbuf << " <ITER> "<< solver.iterations() << "</ITER>\n";
statbuf << " </SOLVER_STAT>\n";
@ -303,7 +322,6 @@ void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar
cout << "\nSolving with SUPERLU ... \n";
SuperLU<SpMat> 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<Scalar>&A, unsigned int sym, Matrix<Scalar
call_directsolver(solver, EIGEN_PARDISO, A, b, refX,statFile);
}
#endif
// Eigen SparseLU METIS
cout << "\n Solving with Sparse LU AND COLAMD ... \n";
SparseLU<SpMat, COLAMDOrdering<int> > 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<SpMat, MetisOrdering<int> > solver;
call_directsolver(solver, EIGEN_SPARSELU_METIS, A, b, refX, statFile);
}
#endif
//BiCGSTAB
{
@ -448,7 +477,6 @@ void SelectSolvers(const SparseMatrix<Scalar>&A, unsigned int sym, Matrix<Scalar
// cout << "\nSolving with CG and IdentityPreconditioner ... \n";
// ConjugateGradient<SpMat, Lower, IdentityPreconditioner> 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 << " <BEST_SOLVER ID=\""<< best_time_id
<< "\"></BEST_SOLVER>\n";
statbuf << " <BEST_SOLVER ID='"<< best_time_id
<< "'></BEST_SOLVER>\n";
statbuf << " </LINEARSYSTEM> \n";
statbuf.close();
}

94
bench/spbench/spbenchstyle.h Normal file
View File

@ -0,0 +1,94 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 << "<xsl:stylesheet id='stylesheet' version='1.0' \
xmlns:xsl='http://www.w3.org/1999/XSL/Transform' >\n \
<xsl:template match='xsl:stylesheet' />\n \
<xsl:template match='/'> <!-- Root of the document -->\n \
<html>\n \
<head> \n \
<style type='text/css'> \n \
td { white-space: nowrap;}\n \
</style>\n \
</head>\n \
<body>";
out<<"<table border='1' width='100%' height='100%'>\n \
<TR> <!-- Write the table header -->\n \
<TH>Matrix</TH> <TH>N</TH> <TH> NNZ</TH> <TH> Sym</TH> <TH> SPD</TH> <TH> </TH>\n \
<xsl:for-each select='BENCH/AVAILSOLVER/SOLVER'>\n \
<xsl:sort select='@ID' data-type='number'/>\n \
<TH>\n \
<xsl:value-of select='TYPE' />\n \
<xsl:text></xsl:text>\n \
<xsl:value-of select='PACKAGE' />\n \
<xsl:text></xsl:text>\n \
</TH>\n \
</xsl:for-each>\n \
</TR>";
out<<" <xsl:for-each select='BENCH/LINEARSYSTEM'>\n \
<TR> <!-- print statistics for one linear system-->\n \
<TH rowspan='4'> <xsl:value-of select='MATRIX/NAME' /> </TH>\n \
<TD rowspan='4'> <xsl:value-of select='MATRIX/SIZE' /> </TD>\n \
<TD rowspan='4'> <xsl:value-of select='MATRIX/ENTRIES' /> </TD>\n \
<TD rowspan='4'> <xsl:value-of select='MATRIX/SYMMETRY' /> </TD>\n \
<TD rowspan='4'> <xsl:value-of select='MATRIX/POSDEF' /> </TD>\n \
<TH> Compute Time </TH>\n \
<xsl:for-each select='SOLVER_STAT'>\n \
<xsl:sort select='@ID' data-type='number'/>\n \
<TD> <xsl:value-of select='TIME/COMPUTE' /> </TD>\n \
</xsl:for-each>\n \
</TR>";
out<<" <TR>\n \
<TH> Solve Time </TH>\n \
<xsl:for-each select='SOLVER_STAT'>\n \
<xsl:sort select='@ID' data-type='number'/>\n \
<TD> <xsl:value-of select='TIME/SOLVE' /> </TD>\n \
</xsl:for-each>\n \
</TR>\n \
<TR>\n \
<TH> Total Time </TH>\n \
<xsl:for-each select='SOLVER_STAT'>\n \
<xsl:sort select='@ID' data-type='number'/>\n \
<xsl:choose>\n \
<xsl:when test='@ID=../BEST_SOLVER/@ID'>\n \
<TD style='background-color:red'> <xsl:value-of select='TIME/TOTAL' /> </TD>\n \
</xsl:when>\n \
<xsl:otherwise>\n \
<TD> <xsl:value-of select='TIME/TOTAL' /></TD>\n \
</xsl:otherwise>\n \
</xsl:choose>\n \
</xsl:for-each>\n \
</TR>";
out<<" <TR>\n \
<TH> Error </TH>\n \
<xsl:for-each select='SOLVER_STAT'>\n \
<xsl:sort select='@ID' data-type='number'/>\n \
<TD> <xsl:value-of select='ERROR' />\n \
<xsl:if test='ITER'>\n \
<xsl:text>(</xsl:text>\n \
<xsl:value-of select='ITER' />\n \
<xsl:text>)</xsl:text>\n \
</xsl:if> </TD>\n \
</xsl:for-each>\n \
</TR>\n \
</xsl:for-each>\n \
</table>\n \
</body>\n \
</html>\n \
</xsl:template>\n \
</xsl:stylesheet>\n\n";
}
#endif

93
bench/spbench/test_sparseLU.cpp Normal file
View File

@ -0,0 +1,93 @@
// Small bench routine for Eigen available in Eigen
// (C) Desire NUENTSA WAKAM, INRIA
#include <iostream>
#include <fstream>
#include <iomanip>
#include <unsupported/Eigen/SparseExtra>
#include <Eigen/SparseLU>
#include <bench/BenchTimer.h>
#ifdef EIGEN_METIS_SUPPORT
#include <Eigen/MetisSupport>
#endif
using namespace std;
using namespace Eigen;
int main(int argc, char **args)
{
// typedef complex<double> scalar;
typedef double scalar;
SparseMatrix<scalar, ColMajor> A;
typedef SparseMatrix<scalar, ColMajor>::Index Index;
typedef Matrix<scalar, Dynamic, Dynamic> DenseMatrix;
typedef Matrix<scalar, Dynamic, 1> DenseRhs;
Matrix<scalar, Dynamic, 1> b, x, tmp;
// SparseLU<SparseMatrix<scalar, ColMajor>, AMDOrdering<int> > solver;
// #ifdef EIGEN_METIS_SUPPORT
// SparseLU<SparseMatrix<scalar, ColMajor>, MetisOrdering<int> > solver;
// std::cout<< "ORDERING : METIS\n";
// #else
SparseLU<SparseMatrix<scalar, ColMajor>, COLAMDOrdering<int> > 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<scalar, ColMajor> temp;
temp = A;
A = temp.selfadjointView<Lower>();
}
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<scalar, Dynamic, 1> 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;
}

6
blas/common.h
View File

@ -10,6 +10,9 @@
#ifndef EIGEN_BLAS_COMMON_H
#define EIGEN_BLAS_COMMON_H
#include <Eigen/Core>
#include <Eigen/Jacobi>
#include <iostream>
#include <complex>
@ -68,9 +71,6 @@ inline bool check_uplo(const char* uplo)
return UPLO(*uplo)!=0xff;
}
#include <Eigen/Core>
#include <Eigen/Jacobi>
namespace Eigen {
#include "BandTriangularSolver.h"

3
cmake/FindMetis.cmake
View File

@ -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

4
debug/gdb/printers.py
View File

@ -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])

2
doc/C09_TutorialSparse.dox
View File

@ -211,7 +211,7 @@ Here is a typical usage example:
\code
typedef Eigen::Triplet<double> T;
std::vector<T> tripletList;
triplets.reserve(estimation_of_entries);
tripletList.reserve(estimation_of_entries);
for(...)
{
// ...

110
doc/I17_SparseLinearSystems.dox Normal file
View File

@ -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 <Eigen/RequiredModuleName>
// ...
SparseMatrix<double> A;
// fill A
VectorXd b, x;
// fill b
// solve Ax = b
SolverClassName<SparseMatrix<double> > 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<SparseMatrix<double>, OrderingMethod<IndexType> > 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<SparseMatrix<double>, PreconditionerName<SparseMatrix<double> > 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.
<TABLE border="1">
<TR><TH>Matrix <TH> N <TH> NNZ <TH> <TH > UMFPACK <TH > SUPERLU <TH > PASTIX LU <TH >BiCGSTAB <TH > BiCGSTAB+ILUT <TH >GMRES+ILUT<TH > LDLT <TH> CHOLMOD LDLT <TH > PASTIX LDLT <TH > LLT <TH > CHOLMOD SP LLT <TH > CHOLMOD LLT <TH > PASTIX LLT <TH> CG</TR>
<TR><TH rowspan="4">vector_graphics <TD rowspan="4"> 12855 <TD rowspan="4"> 72069 <TH>Compute Time <TD>0.0254549<TD>0.0215677<TD>0.0701827<TD>0.000153388<TD>0.0140107<TD>0.0153709<TD>0.0101601<TD style="background-color:red">0.00930502<TD>0.0649689
<TR><TH>Solve Time <TD>0.00337835<TD>0.000951826<TD>0.00484373<TD>0.0374886<TD>0.0046445<TD>0.00847754<TD>0.000541813<TD style="background-color:red">0.000293696<TD>0.00485376
<TR><TH>Total Time <TD>0.0288333<TD>0.0225195<TD>0.0750265<TD>0.037642<TD>0.0186552<TD>0.0238484<TD>0.0107019<TD style="background-color:red">0.00959871<TD>0.0698227
<TR><TH>Error(Iter) <TD> 1.299e-16 <TD> 2.04207e-16 <TD> 4.83393e-15 <TD> 3.94856e-11 (80) <TD> 1.03861e-12 (3) <TD> 5.81088e-14 (6) <TD> 1.97578e-16 <TD> 1.83927e-16 <TD> 4.24115e-15
<TR><TH rowspan="4">poisson_SPD <TD rowspan="4"> 19788 <TD rowspan="4"> 308232 <TH>Compute Time <TD>0.425026<TD>1.82378<TD>0.617367<TD>0.000478921<TD>1.34001<TD>1.33471<TD>0.796419<TD>0.857573<TD>0.473007<TD>0.814826<TD style="background-color:red">0.184719<TD>0.861555<TD>0.470559<TD>0.000458188
<TR><TH>Solve Time <TD>0.0280053<TD>0.0194402<TD>0.0268747<TD>0.249437<TD>0.0548444<TD>0.0926991<TD>0.00850204<TD>0.0053171<TD>0.0258932<TD>0.00874603<TD style="background-color:red">0.00578155<TD>0.00530361<TD>0.0248942<TD>0.239093
<TR><TH>Total Time <TD>0.453031<TD>1.84322<TD>0.644241<TD>0.249916<TD>1.39486<TD>1.42741<TD>0.804921<TD>0.862891<TD>0.4989<TD>0.823572<TD style="background-color:red">0.190501<TD>0.866859<TD>0.495453<TD>0.239551
<TR><TH>Error(Iter) <TD> 4.67146e-16 <TD> 1.068e-15 <TD> 1.3397e-15 <TD> 6.29233e-11 (201) <TD> 3.68527e-11 (6) <TD> 3.3168e-15 (16) <TD> 1.86376e-15 <TD> 1.31518e-16 <TD> 1.42593e-15 <TD> 3.45361e-15 <TD> 3.14575e-16 <TD> 2.21723e-15 <TD> 7.21058e-16 <TD> 9.06435e-12 (261)
<TR><TH rowspan="4">sherman2 <TD rowspan="4"> 1080 <TD rowspan="4"> 23094 <TH>Compute Time <TD style="background-color:red">0.00631754<TD>0.015052<TD>0.0247514 <TD> -<TD>0.0214425<TD>0.0217988
<TR><TH>Solve Time <TD style="background-color:red">0.000478424<TD>0.000337998<TD>0.0010291 <TD> -<TD>0.00243152<TD>0.00246152
<TR><TH>Total Time <TD style="background-color:red">0.00679597<TD>0.01539<TD>0.0257805 <TD> -<TD>0.023874<TD>0.0242603
<TR><TH>Error(Iter) <TD> 1.83099e-15 <TD> 8.19351e-15 <TD> 2.625e-14 <TD> 1.3678e+69 (1080) <TD> 4.1911e-12 (7) <TD> 5.0299e-13 (12)
<TR><TH rowspan="4">bcsstk01_SPD <TD rowspan="4"> 48 <TD rowspan="4"> 400 <TH>Compute Time <TD>0.000169079<TD>0.00010789<TD>0.000572538<TD>1.425e-06<TD>9.1612e-05<TD>8.3985e-05<TD style="background-color:red">5.6489e-05<TD>7.0913e-05<TD>0.000468251<TD>5.7389e-05<TD>8.0212e-05<TD>5.8394e-05<TD>0.000463017<TD>1.333e-06
<TR><TH>Solve Time <TD>1.2288e-05<TD>1.1124e-05<TD>0.000286387<TD>8.5896e-05<TD>1.6381e-05<TD>1.6984e-05<TD style="background-color:red">3.095e-06<TD>4.115e-06<TD>0.000325438<TD>3.504e-06<TD>7.369e-06<TD>3.454e-06<TD>0.000294095<TD>6.0516e-05
<TR><TH>Total Time <TD>0.000181367<TD>0.000119014<TD>0.000858925<TD>8.7321e-05<TD>0.000107993<TD>0.000100969<TD style="background-color:red">5.9584e-05<TD>7.5028e-05<TD>0.000793689<TD>6.0893e-05<TD>8.7581e-05<TD>6.1848e-05<TD>0.000757112<TD>6.1849e-05
<TR><TH>Error(Iter) <TD> 1.03474e-16 <TD> 2.23046e-16 <TD> 2.01273e-16 <TD> 4.87455e-07 (48) <TD> 1.03553e-16 (2) <TD> 3.55965e-16 (2) <TD> 2.48189e-16 <TD> 1.88808e-16 <TD> 1.97976e-16 <TD> 2.37248e-16 <TD> 1.82701e-16 <TD> 2.71474e-16 <TD> 2.11322e-16 <TD> 3.547e-09 (48)
<TR><TH rowspan="4">sherman1 <TD rowspan="4"> 1000 <TD rowspan="4"> 3750 <TH>Compute Time <TD>0.00228805<TD>0.00209231<TD>0.00528268<TD>9.846e-06<TD>0.00163522<TD>0.00162155<TD>0.000789259<TD style="background-color:red">0.000804495<TD>0.00438269
<TR><TH>Solve Time <TD>0.000213788<TD>9.7983e-05<TD>0.000938831<TD>0.00629835<TD>0.000361764<TD>0.00078794<TD>4.3989e-05<TD style="background-color:red">2.5331e-05<TD>0.000917166
<TR><TH>Total Time <TD>0.00250184<TD>0.00219029<TD>0.00622151<TD>0.0063082<TD>0.00199698<TD>0.00240949<TD>0.000833248<TD style="background-color:red">0.000829826<TD>0.00529986
<TR><TH>Error(Iter) <TD> 1.16839e-16 <TD> 2.25968e-16 <TD> 2.59116e-16 <TD> 3.76779e-11 (248) <TD> 4.13343e-11 (4) <TD> 2.22347e-14 (10) <TD> 2.05861e-16 <TD> 1.83555e-16 <TD> 1.02917e-15
<TR><TH rowspan="4">young1c <TD rowspan="4"> 841 <TD rowspan="4"> 4089 <TH>Compute Time <TD>0.00235843<TD style="background-color:red">0.00217228<TD>0.00568075<TD>1.2735e-05<TD>0.00264866<TD>0.00258236
<TR><TH>Solve Time <TD>0.000329599<TD style="background-color:red">0.000168634<TD>0.00080118<TD>0.0534738<TD>0.00187193<TD>0.00450211
<TR><TH>Total Time <TD>0.00268803<TD style="background-color:red">0.00234091<TD>0.00648193<TD>0.0534865<TD>0.00452059<TD>0.00708447
<TR><TH>Error(Iter) <TD> 1.27029e-16 <TD> 2.81321e-16 <TD> 5.0492e-15 <TD> 8.0507e-11 (706) <TD> 3.00447e-12 (8) <TD> 1.46532e-12 (16)
<TR><TH rowspan="4">mhd1280b <TD rowspan="4"> 1280 <TD rowspan="4"> 22778 <TH>Compute Time <TD>0.00234898<TD>0.00207079<TD>0.00570918<TD>2.5976e-05<TD>0.00302563<TD>0.00298036<TD>0.00144525<TD style="background-color:red">0.000919922<TD>0.00426444
<TR><TH>Solve Time <TD>0.00103392<TD>0.000211911<TD>0.00105<TD>0.0110432<TD>0.000628287<TD>0.00392089<TD>0.000138303<TD style="background-color:red">6.2446e-05<TD>0.00097564
<TR><TH>Total Time <TD>0.0033829<TD>0.0022827<TD>0.00675918<TD>0.0110692<TD>0.00365392<TD>0.00690124<TD>0.00158355<TD style="background-color:red">0.000982368<TD>0.00524008
<TR><TH>Error(Iter) <TD> 1.32953e-16 <TD> 3.08646e-16 <TD> 6.734e-16 <TD> 8.83132e-11 (40) <TD> 1.51153e-16 (1) <TD> 6.08556e-16 (8) <TD> 1.89264e-16 <TD> 1.97477e-16 <TD> 6.68126e-09
<TR><TH rowspan="4">crashbasis <TD rowspan="4"> 160000 <TD rowspan="4"> 1750416 <TH>Compute Time <TD>3.2019<TD>5.7892<TD>15.7573<TD style="background-color:red">0.00383515<TD>3.1006<TD>3.09921
<TR><TH>Solve Time <TD>0.261915<TD>0.106225<TD>0.402141<TD style="background-color:red">1.49089<TD>0.24888<TD>0.443673
<TR><TH>Total Time <TD>3.46381<TD>5.89542<TD>16.1594<TD style="background-color:red">1.49473<TD>3.34948<TD>3.54288
<TR><TH>Error(Iter) <TD> 1.76348e-16 <TD> 4.58395e-16 <TD> 1.67982e-14 <TD> 8.64144e-11 (61) <TD> 8.5996e-12 (2) <TD> 6.04042e-14 (5)
</TABLE>
*/
}

2
test/CMakeLists.txt
View File

@ -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}")

6
test/array_for_matrix.cpp
View File

@ -168,6 +168,12 @@ template<typename MatrixType> 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<typename MatrixTraits> void resize(const MatrixTraits& t)

9
test/diagonalmatrices.cpp
View File

@ -32,6 +32,8 @@ template<typename MatrixType> void diagonalmatrices(const MatrixType& m)
rv2 = RowVectorType::Random(cols);
LeftDiagonalMatrix ldm1(v1), ldm2(v2);
RightDiagonalMatrix rdm1(rv1), rdm2(rv2);
Scalar s1 = internal::random<Scalar>();
SquareMatrixType sq_m1 (v1.asDiagonal());
VERIFY_IS_APPROX(sq_m1, v1.asDiagonal().toDenseMatrix());
@ -76,6 +78,13 @@ template<typename MatrixType> 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()

4
test/sparse_solver.h
View File

@ -158,9 +158,9 @@ inline std::string get_matrixfolder()
{
std::string mat_folder = TEST_REAL_CASES;
if( internal::is_same<Scalar, std::complex<float> >::value || internal::is_same<Scalar, std::complex<double> >::value )
mat_folder = mat_folder + static_cast<string>("/complex/");
mat_folder = mat_folder + static_cast<std::string>("/complex/");
else
mat_folder = mat_folder + static_cast<string>("/real/");
mat_folder = mat_folder + static_cast<std::string>("/real/");
return mat_folder;
}
#endif

43
test/sparselu.cpp Normal file
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@ -0,0 +1,43 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#include "sparse_solver.h"
#include <Eigen/SparseLU>
#include <unsupported/Eigen/SparseExtra>
template<typename T> void test_sparselu_T()
{
SparseLU<SparseMatrix<T, ColMajor>, COLAMDOrdering<int> > sparselu_colamd;
SparseLU<SparseMatrix<T, ColMajor>, AMDOrdering<int> > sparselu_amd;
check_sparse_square_solving(sparselu_colamd);
check_sparse_square_solving(sparselu_amd);
}
void test_sparselu()
{
CALL_SUBTEST_1(test_sparselu_T<float>());
CALL_SUBTEST_2(test_sparselu_T<double>());
CALL_SUBTEST_3(test_sparselu_T<std::complex<float> >());
CALL_SUBTEST_4(test_sparselu_T<std::complex<double> >());
}

1
unsupported/Eigen/IterativeSolvers
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@ -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"
//@}

221
unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h Normal file
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@ -0,0 +1,221 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr>
//
// 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 <Eigen/OrderingMethods>
#include <list>
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 <typename Scalar, int _UpLo = Lower, typename _OrderingType = NaturalOrdering<int> >
class IncompleteCholesky : internal::noncopyable
{
public:
typedef SparseMatrix<Scalar,ColMajor> MatrixType;
typedef _OrderingType OrderingType;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
typedef PermutationMatrix<Dynamic, Dynamic, Index> PermutationType;
typedef Matrix<Scalar,Dynamic,1> VectorType;
typedef Matrix<Index,Dynamic, 1> 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<typename MatrixType>
void analyzePattern(const MatrixType& mat)
{
OrderingType ord;
ord(mat, m_perm);
m_analysisIsOk = true;
}
template<typename MatrixType>
void factorize(const MatrixType& amat);
template<typename MatrixType>
void compute (const MatrixType& matrix)
{
analyzePattern(matrix);
factorize(matrix);
}
template<typename Rhs, typename Dest>
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<UnitLower>().solve(x);
x = m_L.adjoint().template triangularView<Upper>().solve(x);
if (m_perm.rows() == b.rows())
x = m_perm * x;
}
template<typename Rhs> inline const internal::solve_retval<IncompleteCholesky, Rhs>
solve(const MatrixBase<Rhs>& 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<IncompleteCholesky, Rhs>(*this, b.derived());
}
protected:
SparseMatrix<Scalar,ColMajor> m_L; // The lower part stored in CSC
bool m_analysisIsOk;
bool m_factorizationIsOk;
bool m_isInitialized;
ComputationInfo m_info;
PermutationType m_perm;
};
template<typename Scalar, int _UpLo, typename OrderingType>
template<typename _MatrixType>
void IncompleteCholesky<Scalar,_UpLo, OrderingType>::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<Lower>() = mat.template selfadjointView<_UpLo>().twistedBy(m_perm);
else
m_L.template selfadjointView<Lower>() = 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<std::list<Index> > 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<int>::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<typename _MatrixType, typename Rhs>
struct solve_retval<IncompleteCholesky<_MatrixType>, Rhs>
: solve_retval_base<IncompleteCholesky<_MatrixType>, Rhs>
{
typedef IncompleteCholesky<_MatrixType> Dec;
EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)
template<typename Dest> void evalTo(Dest& dst) const
{
dec()._solve(rhs(),dst);
}
};
} // end namespace internal
} // end namespace Eigen
#endif

4
unsupported/test/matrix_power.cpp
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@ -34,8 +34,8 @@ template<typename T>
void test2dHyperbolicRotation(double tol)
{
Matrix<std::complex<T>,2,2> A, B, C;
T angle, ch = std::cosh(1);
std::complex<T> ish(0, std::sinh(1));
T angle, ch = std::cosh((T)1);
std::complex<T> ish(0, std::sinh((T)1));
A << ch, ish, -ish, ch;
MatrixPower<Matrix<std::complex<T>,2,2> > Apow(A);