Reference documentation for deal.II version Git 4c0e8c9979 2020-03-28 07:38:34 +0100

#include <deal.II/lac/sparse_direct.h>

Inheritance diagram for SparseDirectUMFPACK:
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## Public Types

using size_type = types::global_dof_index

## Public Member Functions

SparseDirectUMFPACK ()

~SparseDirectUMFPACK () override

Setting up a sparse factorization
void initialize (const SparsityPattern &sparsity_pattern)

template<class Matrix >
void factorize (const Matrix &matrix)

template<class Matrix >

Functions that represent the inverse of a matrix
void vmult (Vector< double > &dst, const Vector< double > &src) const

void vmult (BlockVector< double > &dst, const BlockVector< double > &src) const

void Tvmult (Vector< double > &dst, const Vector< double > &src) const

void Tvmult (BlockVector< double > &dst, const BlockVector< double > &src) const

size_type m () const

size_type n () const

Functions that solve linear systems
void solve (Vector< double > &rhs_and_solution, const bool transpose=false) const

void solve (Vector< std::complex< double >> &rhs_and_solution, const bool transpose=false) const

void solve (BlockVector< double > &rhs_and_solution, const bool transpose=false) const

void solve (BlockVector< std::complex< double >> &rhs_and_solution, const bool transpose=false) const

template<class Matrix >
void solve (const Matrix &matrix, Vector< double > &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void solve (const Matrix &matrix, Vector< std::complex< double >> &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void solve (const Matrix &matrix, BlockVector< double > &rhs_and_solution, const bool transpose=false)

template<class Matrix >
void solve (const Matrix &matrix, BlockVector< std::complex< double >> &rhs_and_solution, const bool transpose=false)

Public Member Functions inherited from Subscriptor
Subscriptor ()

Subscriptor (const Subscriptor &)

Subscriptor (Subscriptor &&) noexcept

virtual ~Subscriptor ()

Subscriptoroperator= (const Subscriptor &)

Subscriptoroperator= (Subscriptor &&) noexcept

void subscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

void unsubscribe (std::atomic< bool > *const validity, const std::string &identifier="") const

unsigned int n_subscriptions () const

template<typename StreamType >
void list_subscribers (StreamType &stream) const

void list_subscribers () const

template<class Archive >
void serialize (Archive &ar, const unsigned int version)

## Static Public Member Functions

static ::ExceptionBaseExcUMFPACKError (std::string arg1, int arg2)

Static Public Member Functions inherited from Subscriptor
static ::ExceptionBaseExcInUse (int arg1, std::string arg2, std::string arg3)

static ::ExceptionBaseExcNoSubscriber (std::string arg1, std::string arg2)

## Private Member Functions

void clear ()

template<typename number >
void sort_arrays (const SparseMatrixEZ< number > &)

## Private Attributes

size_type n_rows

size_type n_cols

void * symbolic_decomposition

std::vector< types::suitesparse_indexAp

std::vector< double > control

## Detailed Description

This class provides an interface to the sparse direct solver UMFPACK, which is part of the SuiteSparse library (see this link). UMFPACK is a set of routines for solving non-symmetric sparse linear systems, Ax=b, using the Unsymmetric-pattern MultiFrontal method and direct sparse LU factorization. Matrices may have symmetric or unsymmetric sparsity patterns, and may have unsymmetric entries. The use of this class is explained in the step-22 and step-29 tutorial programs.

This matrix class implements the usual interface of preconditioners, that is a function initialize(const SparseMatrix<double>&matrix,const AdditionalData) for initializing and the whole set of vmult() functions common to all matrices. Implemented here are only vmult() and vmult_add(), which perform multiplication with the inverse matrix. Furthermore, this class provides an older interface, consisting of the functions factorize() and solve(). Both interfaces are interchangeable.

Note
This class exists if the UMFPACK interface was not explicitly disabled during configuration.
UMFPACK has its own license, independent of that of deal.II. If you want to use the UMFPACK you have to accept that license. It is linked to from the deal.II ReadMe file. UMFPACK is included courtesy of its author, Timothy A. Davis.

#### Instantiations

There are instantiations of this class for SparseMatrix<double>, SparseMatrix<float>, SparseMatrixEZ<float>, SparseMatrixEZ<double>, BlockSparseMatrix<double>, and BlockSparseMatrix<float>.

Definition at line 90 of file sparse_direct.h.

## ◆ size_type

Declare type for container size.

Definition at line 96 of file sparse_direct.h.

## ◆ SparseDirectUMFPACK()

 SparseDirectUMFPACK::SparseDirectUMFPACK ( )

Constructor. See the documentation of this class for the meaning of the parameters to this function.

Definition at line 55 of file sparse_direct.cc.

## ◆ ~SparseDirectUMFPACK()

 SparseDirectUMFPACK::~SparseDirectUMFPACK ( )
override

Destructor.

Definition at line 42 of file sparse_direct.cc.

## ◆ initialize() [1/2]

 void SparseDirectUMFPACK::initialize ( const SparsityPattern & sparsity_pattern )

This function does nothing. It is only here to provide a interface consistent with other sparse direct solvers.

Definition at line 49 of file sparse_direct.cc.

## ◆ factorize()

template<class Matrix >
 void SparseDirectUMFPACK::factorize ( const Matrix & matrix )

Factorize the matrix. This function may be called multiple times for different matrices, after the object of this class has been initialized for a certain sparsity pattern. You may therefore save some computing time if you want to invert several matrices with the same sparsity pattern. However, note that the bulk of the computing time is actually spent in the factorization, so this functionality may not always be of large benefit.

In contrast to the other direct solver classes, the initialization method does nothing. Therefore initialize is not automatically called by this method, when the initialization step has not been performed yet.

This function copies the contents of the matrix into its own storage; the matrix can therefore be deleted after this operation, even if subsequent solves are required.

Definition at line 214 of file sparse_direct.cc.

## ◆ initialize() [2/2]

template<class Matrix >
 void SparseDirectUMFPACK::initialize ( const Matrix & matrix, const AdditionalData additional_data = AdditionalData() )

Initialize memory and call SparseDirectUMFPACK::factorize.

Definition at line 755 of file sparse_direct.cc.

## ◆ vmult() [1/2]

 void SparseDirectUMFPACK::vmult ( Vector< double > & dst, const Vector< double > & src ) const

Preconditioner interface function. Usually, given the source vector, this method returns an approximate solution of Ax = b. As this class provides a wrapper to a direct solver, here it is actually the exact solution (exact within the range of numerical accuracy of course).

In other words, this function actually multiplies with the exact inverse of the matrix, $$A^{-1}$$.

Definition at line 762 of file sparse_direct.cc.

## ◆ vmult() [2/2]

 void SparseDirectUMFPACK::vmult ( BlockVector< double > & dst, const BlockVector< double > & src ) const

Same as before, but for block vectors.

Definition at line 771 of file sparse_direct.cc.

## ◆ Tvmult() [1/2]

 void SparseDirectUMFPACK::Tvmult ( Vector< double > & dst, const Vector< double > & src ) const

Same as before, but uses the transpose of the matrix, i.e. this function multiplies with $$A^{-T}$$.

Definition at line 780 of file sparse_direct.cc.

## ◆ Tvmult() [2/2]

 void SparseDirectUMFPACK::Tvmult ( BlockVector< double > & dst, const BlockVector< double > & src ) const

Same as before, but for block vectors

Definition at line 790 of file sparse_direct.cc.

## ◆ m()

 SparseDirectUMFPACK::size_type SparseDirectUMFPACK::m ( ) const

Return the dimension of the codomain (or range) space. Note that the matrix is of dimension $$m \times n$$.

Definition at line 798 of file sparse_direct.cc.

## ◆ n()

 SparseDirectUMFPACK::size_type SparseDirectUMFPACK::n ( ) const

Return the dimension of the domain space. Note that the matrix is of dimension $$m \times n$$.

Definition at line 805 of file sparse_direct.cc.

## ◆ solve() [1/8]

 void SparseDirectUMFPACK::solve ( Vector< double > & rhs_and_solution, const bool transpose = false ) const

Solve for a certain right hand side vector. This function may be called multiple times for different right hand side vectors after the matrix has been factorized. This yields substantial savings in computing time, since the actual solution is fast, compared to the factorization of the matrix.

The solution will be returned in place of the right hand side vector.

Parameters
 [in,out] rhs_and_solution A vector that contains the right hand side $$b$$ of a linear system $$Ax=b$$ upon calling this function, and that contains the solution $$x$$ of the linear system after calling this function. [in] transpose If set to true, this function solves the linear $$A^T x = b$$ instead of $$Ax=b$$.
Precondition
You need to call factorize() before this function can be called.

Definition at line 344 of file sparse_direct.cc.

## ◆ solve() [2/8]

 void SparseDirectUMFPACK::solve ( Vector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) const

Like the previous function, but for a complex-valued right hand side and solution vector.

If the matrix that was previously factorized had complex-valued entries, then the rhs_and_solution vector will, upon return from this function, simply contain the solution of the linear system $$Ax=b$$. If the matrix was real-valued, then this is also true, but the solution will simply be computed by applying the factorized $$A^{-1}$$ to both the real and imaginary parts of the right hand side vector.

Definition at line 384 of file sparse_direct.cc.

## ◆ solve() [3/8]

 void SparseDirectUMFPACK::solve ( BlockVector< double > & rhs_and_solution, const bool transpose = false ) const

Same as before, but for block vectors.

Definition at line 499 of file sparse_direct.cc.

## ◆ solve() [4/8]

 void SparseDirectUMFPACK::solve ( BlockVector< std::complex< double >> & rhs_and_solution, const bool transpose = false ) const

Same as before, but for complex-valued block vectors.

Definition at line 514 of file sparse_direct.cc.

## ◆ solve() [5/8]

template<class Matrix >
 void SparseDirectUMFPACK::solve ( const Matrix & matrix, Vector< double > & rhs_and_solution, const bool transpose = false )

Call the two functions factorize() and solve() in that order, i.e. perform the whole solution process for the given right hand side vector.

The solution will be returned in place of the right hand side vector.

Definition at line 540 of file sparse_direct.cc.

## ◆ solve() [6/8]

template<class Matrix >
 void SparseDirectUMFPACK::solve ( const Matrix & matrix, Vector< std::complex< double >> & rhs_and_solution, const bool transpose = false )

Same as before, but for complex-valued solution vectors.

Definition at line 552 of file sparse_direct.cc.

## ◆ solve() [7/8]

template<class Matrix >
 void SparseDirectUMFPACK::solve ( const Matrix & matrix, BlockVector< double > & rhs_and_solution, const bool transpose = false )

Same as before, but for block vectors.

Definition at line 576 of file sparse_direct.cc.

## ◆ solve() [8/8]

template<class Matrix >
 void SparseDirectUMFPACK::solve ( const Matrix & matrix, BlockVector< std::complex< double >> & rhs_and_solution, const bool transpose = false )

Same as before, but for complex-valued block vectors.

Definition at line 588 of file sparse_direct.cc.

## ◆ clear()

 void SparseDirectUMFPACK::clear ( )
private

Free all memory that hasn't been freed yet.

Definition at line 68 of file sparse_direct.cc.

## ◆ sort_arrays()

template<typename number >
 void SparseDirectUMFPACK::sort_arrays ( const SparseMatrixEZ< number > & matrix )
private

Make sure that the arrays Ai and Ap are sorted in each row. UMFPACK wants it this way. We need to have three versions of this function, one for the usual SparseMatrix, one for the SparseMatrixEZ, and one for the BlockSparseMatrix classes

Definition at line 150 of file sparse_direct.cc.

## ◆ n_rows

 size_type SparseDirectUMFPACK::n_rows
private

The dimension of the range space, i.e., the number of rows of the matrix.

Definition at line 367 of file sparse_direct.h.

## ◆ n_cols

 size_type SparseDirectUMFPACK::n_cols
private

The dimension of the domain space, i.e., the number of columns of the matrix.

Definition at line 373 of file sparse_direct.h.

## ◆ symbolic_decomposition

 void* SparseDirectUMFPACK::symbolic_decomposition
private

The UMFPACK routines allocate objects in which they store information about symbolic and numeric values of the decomposition. The actual data type of these objects is opaque, and only passed around as void pointers.

Definition at line 380 of file sparse_direct.h.

## ◆ Ap

 std::vector SparseDirectUMFPACK::Ap
private

The arrays in which we store the data for the solver. These are documented in the descriptions of the umfpack_*_symbolic() and umfpack_*_numeric() functions, but in short:

• Ap is the array saying which row starts where in Ai
• Ai is the array that stores the column indices of nonzero entries
• Ax is the array that stores the values of nonzero entries; if the matrix is complex-valued, then it stores the real parts
• Az is the array that stores the imaginary parts of nonzero entries, and is used only if the matrix is complex-valued.

Definition at line 418 of file sparse_direct.h.

## ◆ control

 std::vector SparseDirectUMFPACK::control
private

Control and work arrays for the solver routines.

Definition at line 426 of file sparse_direct.h.

The documentation for this class was generated from the following files: