Reference documentation for deal.II version Git 427db34 20160430 09:04:09 +0200

#include <deal.II/lac/sparse_direct.h>
Classes  
class  AdditionalData 
Public Types  
typedef types::global_dof_index  size_type 
Public Member Functions  
SparseDirectUMFPACK ()  
~SparseDirectUMFPACK ()  
DeclException2 (ExcUMFPACKError, char *, int,<< "UMFPACK routine "<< arg1<< " returned error status "<< arg2<< "."<< "\n\n"<< ("A complete list of error codes can be found in the file ""<bundled/umfpack/UMFPACK/Include/umfpack.h>.""\n\n""That said, the two most common errors that can happen are ""that your matrix cannot be factorized because it is ""rank deficient, and that UMFPACK runs out of memory ""because your problem is too large.""\n\n""The first of these cases most often happens if you ""forget terms in your bilinear form necessary to ensure ""that the matrix has full rank, or if your equation has a ""spatially variable coefficient (or nonlinearity) that is ""supposed to be strictly positive but, for whatever ""reasons, is negative or zero. In either case, you probably ""want to check your assembly procedure. Similarly, a ""matrix can be rank deficient if you forgot to apply the ""appropriate boundary conditions. For example, the ""Laplace equation without boundary conditions has a ""single zero eigenvalue and its rank is therefore ""deficient by one.""\n\n""The other common situation is that you run out of memory.""On a typical laptop or desktop, it should easily be possible ""to solve problems with 100,000 unknowns in 2d. If you are ""solving problems with many more unknowns than that, in ""particular if you are in 3d, then you may be running out ""of memory and you will need to consider iterative ""solvers instead of the direct solver employed by ""UMFPACK."))  
Setting up a sparse factorization  
void  initialize (const SparsityPattern &sparsity_pattern) 
template<class Matrix >  
void  factorize (const Matrix &matrix) 
template<class Matrix >  
void  initialize (const Matrix &matrix, const AdditionalData additional_data=AdditionalData()) 
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, bool transpose=false) const 
void  solve (BlockVector< double > &rhs_and_solution, bool transpose=false) const 
template<class Matrix >  
void  solve (const Matrix &matrix, Vector< double > &rhs_and_solution, bool transpose=false) 
template<class Matrix >  
void  solve (const Matrix &matrix, BlockVector< double > &rhs_and_solution, bool transpose=false) 
Public Member Functions inherited from Subscriptor  
Subscriptor ()  
Subscriptor (const Subscriptor &)  
Subscriptor (Subscriptor &&)  
virtual  ~Subscriptor () 
Subscriptor &  operator= (const Subscriptor &) 
Subscriptor &  operator= (Subscriptor &&) 
void  subscribe (const char *identifier=0) const 
void  unsubscribe (const char *identifier=0) const 
unsigned int  n_subscriptions () const 
void  list_subscribers () const 
DeclException3 (ExcInUse, int, char *, std::string &,<< "Object of class "<< arg2<< " is still used by "<< arg1<< " other objects."<< "\n\n"<< "(Additional information: "<< arg3<< ")\n\n"<< "See the entry in the Frequently Asked Questions of "<< "deal.II (linked to from http://www.dealii.org/) for "<< "a lot more information on what this error means and "<< "how to fix programs in which it happens.")  
DeclException2 (ExcNoSubscriber, char *, char *,<< "No subscriber with identifier <"<< arg2<< "> subscribes to this object of class "<< arg1<< ". Consequently, it cannot be unsubscribed.")  
template<class Archive >  
void  serialize (Archive &ar, const unsigned int version) 
Private Member Functions  
void  clear () 
template<typename number >  
void  sort_arrays (const SparseMatrixEZ< number > &) 
Private Attributes  
size_type  _m 
size_type  _n 
void *  symbolic_decomposition 
std::vector< SuiteSparse_long >  Ap 
std::vector< double >  control 
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 nonsymmetric sparse linear systems, Ax=b, using the Unsymmetricpattern 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 step22 and step29 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.
There are instantiations of this class for SparseMatrix<double>, SparseMatrix<float>, SparseMatrixEZ<float>, SparseMatrixEZ<double>, BlockSparseMatrix<double>, and BlockSparseMatrix<float>.
Definition at line 82 of file sparse_direct.h.
Declare type for container size.
Definition at line 88 of file sparse_direct.h.
SparseDirectUMFPACK::SparseDirectUMFPACK  (  ) 
Constructor. See the documentation of this class for the meaning of the parameters to this function.
Definition at line 54 of file sparse_direct.cc.
SparseDirectUMFPACK::~SparseDirectUMFPACK  (  ) 
Destructor.
Definition at line 40 of file sparse_direct.cc.
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 48 of file sparse_direct.cc.
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 initialisation method does nothing. Therefore initialise 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 205 of file sparse_direct.cc.
void SparseDirectUMFPACK::initialize  (  const Matrix &  matrix, 
const AdditionalData  additional_data = AdditionalData() 

) 
Initialize memory and call SparseDirectUMFPACK::factorize.
Definition at line 428 of file sparse_direct.cc.
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 436 of file sparse_direct.cc.
void SparseDirectUMFPACK::vmult  (  BlockVector< double > &  dst, 
const BlockVector< double > &  src  
)  const 
Same as before, but for block vectors.
Definition at line 447 of file sparse_direct.cc.
Same as before, but uses the transpose of the matrix, i.e. this function multiplies with \(A^{T}\).
Definition at line 457 of file sparse_direct.cc.
void SparseDirectUMFPACK::Tvmult  (  BlockVector< double > &  dst, 
const BlockVector< double > &  src  
)  const 
Same as before, but for block vectors
Definition at line 468 of file sparse_direct.cc.
SparseDirectUMFPACK::size_type SparseDirectUMFPACK::m  (  )  const 
Return the dimension of the codomain (or range) space. To remember: the matrix is of dimension \(m \times n\).
Definition at line 477 of file sparse_direct.cc.
SparseDirectUMFPACK::size_type SparseDirectUMFPACK::n  (  )  const 
Return the dimension of the domain space. To remember: the matrix is of dimension \(m \times n\).
Definition at line 484 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  Vector< double > &  rhs_and_solution, 
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 a big saving 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.
If the factorization has not happened before, strange things will happen. Note that we can't actually call the factorize() function from here if it has not yet been called, since we have no access to the actual matrix.
If transpose
is set to true this function solves for the transpose of the matrix, i.e. \(x=A^{T}b\).
Definition at line 301 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  BlockVector< double > &  rhs_and_solution, 
bool  transpose = false 

)  const 
Same as before, but for block vectors.
Definition at line 329 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
Vector< double > &  rhs_and_solution,  
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 345 of file sparse_direct.cc.
void SparseDirectUMFPACK::solve  (  const Matrix &  matrix, 
BlockVector< double > &  rhs_and_solution,  
bool  transpose = false 

) 
Same as before, but for block vectors.
Definition at line 356 of file sparse_direct.cc.
SparseDirectUMFPACK::DeclException2  (  ExcUMFPACKError  , 
char *  ,  
int  ,  
<< "UMFPACK routine "<< arg1<< " returned error status "<< arg2<< "."<< "\n\n"<<  "A complete list of error codes can be found in the file ""<bundled/umfpack/UMFPACK/Include/umfpack.h>.""\n\n""That said, the two most common errors that can happen are ""that your matrix cannot be factorized because it is ""rank deficient, and that UMFPACK runs out of memory ""because your problem is too large.""\n\n""The first of these cases most often happens if you ""forget terms in your bilinear form necessary to ensure ""that the matrix has full rank, or if your equation has a ""spatially variable coefficient (or nonlinearity) that is ""supposed to be strictly positive but, for whatever ""reasons, is negative or zero. In either case, you probably ""want to check your assembly procedure. Similarly, a ""matrix can be rank deficient if you forgot to apply the ""appropriate boundary conditions. For example, the ""Laplace equation without boundary conditions has a ""single zero eigenvalue and its rank is therefore ""deficient by one.""\n\n""The other common situation is that you run out of memory.""On a typical laptop or desktop, it should easily be possible ""to solve problems with 100,000 unknowns in 2d. If you are ""solving problems with many more unknowns than that, in ""particular if you are in 3d, then you may be running out ""of memory and you will need to consider iterative ""solvers instead of the direct solver employed by ""UMFPACK."  
) 
One of the UMFPack routines threw an error. The error code is included in the output and can be looked up in the UMFPack user manual. The name of the routine is included for reference.

private 
Free all memory that hasn't been freed yet.
Definition at line 68 of file sparse_direct.cc.

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 144 of file sparse_direct.cc.

private 
The dimension of the range space.
Definition at line 302 of file sparse_direct.h.

private 
The dimension of the domain space.
Definition at line 307 of file sparse_direct.h.

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 314 of file sparse_direct.h.

private 
The arrays in which we store the data for the solver. SuiteSparse_long has to be used here for Windows 64 build, if we used only long int, compilation would fail.
Definition at line 342 of file sparse_direct.h.

private 
Control and info arrays for the solver routines.
Definition at line 349 of file sparse_direct.h.