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merge Sparse LU branch
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Desire NUENTSA
commit
fdd0f0c5fc
Eigen
MetisSupportOrderingMethodsSparseLU
src
MetisSupport
OrderingMethods
SparseCore
SparseLU
CMakeLists.txtSparseLU.hSparseLU_Coletree.hSparseLU_Matrix.hSparseLU_Memory.hSparseLU_Structs.hSparseLU_Utils.hSparseLU_column_bmod.hSparseLU_column_dfs.hSparseLU_copy_to_ucol.hSparseLU_heap_relax_snode.hSparseLU_kernel_bmod.hSparseLU_panel_bmod.hSparseLU_panel_dfs.hSparseLU_pivotL.hSparseLU_pruneL.hSparseLU_relax_snode.hSparseLU_snode_bmod.hSparseLU_snode_dfs.h
SuperLUSupport
bench/spbench
cmake
doc
test
26
Eigen/MetisSupport
Normal file
26
Eigen/MetisSupport
Normal file
@ -0,0 +1,26 @@
|
||||
#ifndef EIGEN_METISSUPPORT_MODULE_H
|
||||
#define EIGEN_METISSUPPORT_MODULE_H
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|
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#include "SparseCore"
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|
||||
#include "src/Core/util/DisableStupidWarnings.h"
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||||
|
||||
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"
|
||||
|
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#endif // EIGEN_METISSUPPORT_MODULE_H
|
||||
@ -17,7 +17,7 @@
|
||||
*/
|
||||
|
||||
#include "src/OrderingMethods/Amd.h"
|
||||
|
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#include "src/OrderingMethods/Ordering.h"
|
||||
#include "src/Core/util/ReenableStupidWarnings.h"
|
||||
|
||||
#endif // EIGEN_ORDERINGMETHODS_MODULE_H
|
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|
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17
Eigen/SparseLU
Normal file
17
Eigen/SparseLU
Normal file
@ -0,0 +1,17 @@
|
||||
#ifndef EIGEN_SPARSELU_MODULE_H
|
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#define EIGEN_SPARSELU_MODULE_H
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|
||||
#include "SparseCore"
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|
||||
|
||||
/** \ingroup Sparse_modules
|
||||
* \defgroup SparseLU_Module SparseLU module
|
||||
*
|
||||
*/
|
||||
|
||||
// Ordering interface
|
||||
#include "OrderingMethods"
|
||||
|
||||
#include "src/SparseLU/SparseLU.h"
|
||||
|
||||
#endif // EIGEN_SPARSELU_MODULE_H
|
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6
Eigen/src/MetisSupport/CMakeLists.txt
Normal file
6
Eigen/src/MetisSupport/CMakeLists.txt
Normal 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
138
Eigen/src/MetisSupport/MetisSupport.h
Normal file
@ -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
|
||||
2514
Eigen/src/OrderingMethods/Eigen_Colamd.h
Normal file
2514
Eigen/src/OrderingMethods/Eigen_Colamd.h
Normal file
File diff suppressed because it is too large
Load Diff
156
Eigen/src/OrderingMethods/Ordering.h
Normal file
156
Eigen/src/OrderingMethods/Ordering.h
Normal file
@ -0,0 +1,156 @@
|
||||
|
||||
// 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"
|
||||
#include "Eigen_Colamd.h"
|
||||
namespace Eigen {
|
||||
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 = eigen_colamd_recommended(nnz, m, n);
|
||||
// Set the default parameters
|
||||
double knobs [EIGEN_COLAMD_KNOBS];
|
||||
int stats [EIGEN_COLAMD_STATS];
|
||||
eigen_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 = eigen_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
|
||||
@ -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())
|
||||
{
|
||||
|
||||
6
Eigen/src/SparseLU/CMakeLists.txt
Normal file
6
Eigen/src/SparseLU/CMakeLists.txt
Normal 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
|
||||
)
|
||||
613
Eigen/src/SparseLU/SparseLU.h
Normal file
613
Eigen/src/SparseLU/SparseLU.h
Normal file
@ -0,0 +1,613 @@
|
||||
// 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"
|
||||
|
||||
/**
|
||||
* \ingroup SparseLU_Module
|
||||
* \brief Sparse supernodal LU factorization for general matrices
|
||||
*
|
||||
* This class implements the supernodal LU factorization for general matrices.
|
||||
*
|
||||
* \tparam _MatrixType The type of the sparse matrix. It must be a column-major SparseMatrix<>
|
||||
*/
|
||||
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);
|
||||
|
||||
/**
|
||||
* 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 = 6;
|
||||
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; // persistent data to facilitate multiple factors
|
||||
// FIXME All fields of this struct can be defined separately as class members
|
||||
|
||||
// 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
|
||||
#include "SparseLU_Coletree.h"
|
||||
/**
|
||||
* Compute the column permutation to minimize the fill-in (file amd.c )
|
||||
*
|
||||
* - Apply this permutation to the input matrix -
|
||||
*
|
||||
* - Compute the column elimination tree on the permuted matrix (file Eigen_Coletree.h)
|
||||
*
|
||||
* - Postorder the elimination tree and the column permutation (file Eigen_Coletree.h)
|
||||
*
|
||||
*/
|
||||
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);
|
||||
//FIXME Check the right semantic behind m_perm_c
|
||||
// that is, column j of mat goes to column m_perm_c(j) of 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());
|
||||
|
||||
LU_sp_coletree(m_mat, m_etree);
|
||||
|
||||
// In symmetric mode, do not do postorder here
|
||||
if (!m_symmetricmode) {
|
||||
IndexVector post, iwork;
|
||||
// Post order etree
|
||||
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
|
||||
#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"
|
||||
|
||||
|
||||
/**
|
||||
* - Numerical factorization
|
||||
* - Interleaved with the symbolic factorization
|
||||
* \tparam MatrixType The type of the matrix, it should be a column-major sparse matrix
|
||||
* \return info where
|
||||
* : successful exit
|
||||
* = 0: successful exit
|
||||
* > 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 = 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 )
|
||||
LU_heap_relax_snode<IndexVector>(n, m_etree, m_perfv.relax, marker, relax_end);
|
||||
else
|
||||
LU_relax_snode<IndexVector>(n, m_etree, m_perfv.relax, marker, relax_end);
|
||||
|
||||
|
||||
m_perm_r.resize(m);
|
||||
m_perm_r.indices().setConstant(-1);
|
||||
marker.setConstant(-1);
|
||||
|
||||
IndexVector& xsup = m_glu.xsup;
|
||||
IndexVector& supno = m_glu.supno;
|
||||
IndexVector& xlsub = m_glu.xlsub;
|
||||
IndexVector& xlusup = m_glu.xlusup;
|
||||
IndexVector& xusub = m_glu.xusub;
|
||||
ScalarVector& lusup = m_glu.lusup;
|
||||
Index& nzlumax = m_glu.nzlumax;
|
||||
|
||||
supno(0) = IND_EMPTY; xsup.setConstant(0);
|
||||
xsup(0) = xlsub(0) = xusub(0) = 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 = 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 = xusub(jcol); //starting location of column jcol in ucol
|
||||
nextlu = xlusup(jcol); //Starting location of column jcol in lusup (rectangular supernodes)
|
||||
jsupno = supno(jcol); // Supernode number which column jcol belongs to
|
||||
fsupc = xsup(jsupno); //First column number of the current supernode
|
||||
new_next = nextlu + (xlsub(fsupc+1)-xlsub(fsupc)) * (kcol - jcol + 1);
|
||||
int mem;
|
||||
while (new_next > nzlumax )
|
||||
{
|
||||
mem = LUMemXpand(lusup, 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++){
|
||||
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
|
||||
LU_snode_bmod(icol, fsupc, dense, m_glu);
|
||||
|
||||
// Eliminate the current column
|
||||
info = 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
|
||||
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
|
||||
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 = 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 = 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 = 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 = 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
|
||||
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
|
||||
LU_countnz(n, m_nnzL, m_nnzU, m_glu);
|
||||
// Apply permutation to the L subscripts
|
||||
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;
|
||||
}
|
||||
|
||||
|
||||
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
|
||||
180
Eigen/src/SparseLU/SparseLU_Coletree.h
Normal file
180
Eigen/src/SparseLU/SparseLU_Coletree.h
Normal file
@ -0,0 +1,180 @@
|
||||
// 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 IndexVector>
|
||||
int 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 MatrixType, typename IndexVector>
|
||||
int 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 IndexVector>
|
||||
void 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 IndexVector>
|
||||
void 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
|
||||
313
Eigen/src/SparseLU/SparseLU_Matrix.h
Normal file
313
Eigen/src/SparseLU/SparseLU_Matrix.h
Normal file
@ -0,0 +1,313 @@
|
||||
// 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
|
||||
205
Eigen/src/SparseLU/SparseLU_Memory.h
Normal file
205
Eigen/src/SparseLU/SparseLU_Memory.h
Normal file
@ -0,0 +1,205 @@
|
||||
// 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 VectorType >
|
||||
int 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 IndexVector,typename ScalarVector>
|
||||
int LUMemInit(int m, int n, int annz, int lwork, int fillratio, int panel_size, LU_GlobalLU_t<IndexVector,ScalarVector>& glu)
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
|
||||
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 VectorType>
|
||||
int 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
|
||||
103
Eigen/src/SparseLU/SparseLU_Structs.h
Normal file
103
Eigen/src/SparseLU/SparseLU_Structs.h
Normal file
@ -0,0 +1,103 @@
|
||||
// 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
|
||||
75
Eigen/src/SparseLU/SparseLU_Utils.h
Normal file
75
Eigen/src/SparseLU/SparseLU_Utils.h
Normal file
@ -0,0 +1,75 @@
|
||||
// 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 IndexVector, typename ScalarVector>
|
||||
void LU_countnz(const int n, int& nnzL, int& nnzU, LU_GlobalLU_t<IndexVector, ScalarVector>& 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 IndexVector, typename ScalarVector>
|
||||
void LU_fixupL(const int n, const IndexVector& perm_r, LU_GlobalLU_t<IndexVector, ScalarVector>& 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
|
||||
167
Eigen/src/SparseLU/SparseLU_column_bmod.h
Normal file
167
Eigen/src/SparseLU/SparseLU_column_bmod.h
Normal file
@ -0,0 +1,167 @@
|
||||
// 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 IndexVector, typename ScalarVector, typename BlockIndexVector, typename BlockScalarVector>
|
||||
int LU_column_bmod(const int jcol, const int nseg, BlockScalarVector& dense, ScalarVector& tempv, BlockIndexVector& segrep, BlockIndexVector& repfnz, int fpanelc, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
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;
|
||||
|
||||
// NOTE Unlike the original implementation in SuperLU, the only feature
|
||||
// available here is a sup-col update.
|
||||
|
||||
// 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
|
||||
165
Eigen/src/SparseLU/SparseLU_column_dfs.h
Normal file
165
Eigen/src/SparseLU/SparseLU_column_dfs.h
Normal file
@ -0,0 +1,165 @@
|
||||
// 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
|
||||
* \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
|
||||
* \param xprune
|
||||
* \param marker
|
||||
* \param parent
|
||||
* \param xplore
|
||||
* \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;
|
||||
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)
|
||||
LUMemXpand<IndexVector>(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 IndexVector, typename ScalarVector, typename BlockIndexVector>
|
||||
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, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
|
||||
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
|
||||
102
Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
Normal file
102
Eigen/src/SparseLU/SparseLU_copy_to_ucol.h
Normal file
@ -0,0 +1,102 @@
|
||||
// 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 IndexVector, typename ScalarVector, typename SegRepType, typename RepfnzType, typename DenseType>
|
||||
int LU_copy_to_ucol(const int jcol, const int nseg, SegRepType& segrep, RepfnzType& repfnz ,IndexVector& perm_r, DenseType& dense, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
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
|
||||
119
Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
Normal file
119
Eigen/src/SparseLU/SparseLU_heap_relax_snode.h
Normal file
@ -0,0 +1,119 @@
|
||||
// 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 IndexVector>
|
||||
void 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
|
||||
109
Eigen/src/SparseLU/SparseLU_kernel_bmod.h
Normal file
109
Eigen/src/SparseLU/SparseLU_kernel_bmod.h
Normal file
@ -0,0 +1,109 @@
|
||||
// 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
|
||||
208
Eigen/src/SparseLU/SparseLU_panel_bmod.h
Normal file
208
Eigen/src/SparseLU/SparseLU_panel_bmod.h
Normal file
@ -0,0 +1,208 @@
|
||||
// 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] ... FIXME to be checked
|
||||
*
|
||||
* \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 DenseIndexBlock, typename IndexVector, typename ScalarVector>
|
||||
void LU_panel_bmod(const int m, const int w, const int jcol, const int nseg, ScalarVector& dense, ScalarVector& tempv, DenseIndexBlock& segrep, DenseIndexBlock& repfnz, LU_perfvalues& perfv, LU_GlobalLU_t<IndexVector,ScalarVector>& glu)
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
|
||||
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);
|
||||
|
||||
// NOTE : Unlike the original implementation in SuperLU,
|
||||
// there is no update feature for col-col, 2col-col ...
|
||||
|
||||
// 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
|
||||
247
Eigen/src/SparseLU/SparseLU_panel_dfs.h
Normal file
247
Eigen/src/SparseLU/SparseLU_panel_dfs.h
Normal file
@ -0,0 +1,247 @@
|
||||
// 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 ScalarVector, typename IndexVector, typename MarkerType, typename Traits>
|
||||
void LU_dfs_kernel(const int jj, IndexVector& perm_r,
|
||||
int& nseg, IndexVector& panel_lsub, IndexVector& segrep,
|
||||
VectorBlock<IndexVector>& repfnz_col, IndexVector& xprune, MarkerType& marker, IndexVector& parent,
|
||||
IndexVector& xplore, LU_GlobalLU_t<IndexVector, ScalarVector>& 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 MatrixType, typename ScalarVector, typename IndexVector>
|
||||
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, LU_GlobalLU_t<IndexVector, ScalarVector>& 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
|
||||
128
Eigen/src/SparseLU/SparseLU_pivotL.h
Normal file
128
Eigen/src/SparseLU/SparseLU_pivotL.h
Normal file
@ -0,0 +1,128 @@
|
||||
// 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 IndexVector, typename ScalarVector>
|
||||
int LU_pivotL(const int jcol, const typename ScalarVector::RealScalar diagpivotthresh, IndexVector& perm_r, IndexVector& iperm_c, int& pivrow, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
typedef typename ScalarVector::RealScalar RealScalar;
|
||||
|
||||
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
|
||||
132
Eigen/src/SparseLU/SparseLU_pruneL.h
Normal file
132
Eigen/src/SparseLU/SparseLU_pruneL.h
Normal file
@ -0,0 +1,132 @@
|
||||
// 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 IndexVector, typename ScalarVector, typename BlockIndexVector>
|
||||
void LU_pruneL(const int jcol, const IndexVector& perm_r, const int pivrow, const int nseg, const IndexVector& segrep, BlockIndexVector& repfnz, IndexVector& xprune, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
|
||||
// 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
73
Eigen/src/SparseLU/SparseLU_relax_snode.h
Normal file
@ -0,0 +1,73 @@
|
||||
// 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 IndexVector>
|
||||
void 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
|
||||
74
Eigen/src/SparseLU/SparseLU_snode_bmod.h
Normal file
74
Eigen/src/SparseLU/SparseLU_snode_bmod.h
Normal file
@ -0,0 +1,74 @@
|
||||
// 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 IndexVector, typename ScalarVector>
|
||||
int LU_snode_bmod (const int jcol, const int fsupc, ScalarVector& dense, LU_GlobalLU_t<IndexVector,ScalarVector>& glu)
|
||||
{
|
||||
typedef typename ScalarVector::Scalar Scalar;
|
||||
|
||||
/* 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
|
||||
96
Eigen/src/SparseLU/SparseLU_snode_dfs.h
Normal file
96
Eigen/src/SparseLU/SparseLU_snode_dfs.h
Normal file
@ -0,0 +1,96 @@
|
||||
// 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 MatrixType, typename IndexVector, typename ScalarVector>
|
||||
int LU_snode_dfs(const int jcol, const int kcol,const MatrixType& mat, IndexVector& xprune, IndexVector& marker, LU_GlobalLU_t<IndexVector, ScalarVector>& glu)
|
||||
{
|
||||
typedef typename IndexVector::Scalar Index;
|
||||
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
|
||||
@ -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;
|
||||
|
||||
@ -63,3 +63,15 @@ endif(RT_LIBRARY)
|
||||
add_executable(spbenchsolver spbenchsolver.cpp)
|
||||
target_link_libraries (spbenchsolver ${SPARSE_LIBS})
|
||||
|
||||
add_executable(spsolver sp_solver.cpp)
|
||||
target_link_libraries (spsolver ${SPARSE_LIBS})
|
||||
|
||||
if(METIS_FOUND)
|
||||
include_directories(${METIS_INCLUDES})
|
||||
set (SPARSE_LIBS ${SPARSE_LIBS} ${METIS_LIBRARIES})
|
||||
add_definitions("-DEIGEN_METIS_SUPPORT")
|
||||
endif(METIS_FOUND)
|
||||
|
||||
add_executable(test_sparseLU test_sparseLU.cpp)
|
||||
target_link_libraries (test_sparseLU ${SPARSE_LIBS})
|
||||
|
||||
|
||||
124
bench/spbench/sp_solver.cpp
Normal file
124
bench/spbench/sp_solver.cpp
Normal file
@ -0,0 +1,124 @@
|
||||
// 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>
|
||||
|
||||
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;
|
||||
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;
|
||||
}
|
||||
93
bench/spbench/test_sparseLU.cpp
Normal file
93
bench/spbench/test_sparseLU.cpp
Normal 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;
|
||||
}
|
||||
@ -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
|
||||
|
||||
110
doc/I17_SparseLinearSystems.dox
Normal file
110
doc/I17_SparseLinearSystems.dox
Normal 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
|
||||
|
||||
FIXME How to get a reference to the preconditioner, in order to set the parameters
|
||||
|
||||
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>
|
||||
*/
|
||||
}
|
||||
@ -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}")
|
||||
|
||||
@ -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
43
test/sparselu.cpp
Normal file
@ -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> >());
|
||||
}
|
||||
Loading…
x
Reference in New Issue
Block a user