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// $Id: petsc_parallel_sparse_matrix.h 30233 2013-08-05 22:41:29Z heister $
//
// Copyright (C) 2004 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, 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 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__petsc_parallel_sparse_matrix_h
#define __deal2__petsc_parallel_sparse_matrix_h
#include <deal.II/base/config.h>
#ifdef DEAL_II_WITH_PETSC
# include <deal.II/lac/exceptions.h>
# include <deal.II/lac/petsc_matrix_base.h>
# include <deal.II/lac/petsc_parallel_vector.h>
# include <vector>
DEAL_II_NAMESPACE_OPEN
// forward declaration
template <typename Matrix> class BlockMatrixBase;
namespace PETScWrappers
{
namespace MPI
{
/**
* Implementation of a parallel sparse matrix class based on PETSC, with rows
* of the matrix distributed across an MPI network. All the functionality is
* actually in the base class, except for the calls to generate a parallel
* sparse matrix. This is possible since PETSc only works on an abstract
* matrix type and internally distributes to functions that do the actual work
* depending on the actual matrix type (much like using virtual
* functions). Only the functions creating a matrix of specific type differ,
* and are implemented in this particular class.
*
* There are a number of comments on the communication model as well as access
* to individual elements in the documentation to the parallel vector
* class. These comments apply here as well.
*
*
* <h3>Partitioning of matrices</h3>
*
* PETSc partitions parallel matrices so that each MPI process "owns" a
* certain number of rows (i.e. only this process stores the respective
* entries in these rows). The number of rows each process owns has to be
* passed to the constructors and reinit() functions via the argument @p
* local_rows. The individual values passed as @p local_rows on all the MPI
* processes of course have to add up to the global number of rows of the
* matrix.
*
* In addition to this, PETSc also partitions the rectangular chunk of the
* matrix it owns (i.e. the @p local_rows times n() elements in the matrix),
* so that matrix vector multiplications can be performed efficiently. This
* column-partitioning therefore has to match the partitioning of the vectors
* with which the matrix is multiplied, just as the row-partitioning has to
* match the partitioning of destination vectors. This partitioning is passed
* to the constructors and reinit() functions through the @p local_columns
* variable, which again has to add up to the global number of columns in the
* matrix. The name @p local_columns may be named inappropriately since it
* does not reflect that only these columns are stored locally, but it
* reflects the fact that these are the columns for which the elements of
* incoming vectors are stored locally.
*
* To make things even more complicated, PETSc needs a very good estimate of
* the number of elements to be stored in each row to be efficient. Otherwise
* it spends most of the time with allocating small chunks of memory, a
* process that can slow down programs to a crawl if it happens to often. As
* if a good estimate of the number of entries per row isn't even, it even
* needs to split this as follows: for each row it owns, it needs an estimate
* for the number of elements in this row that fall into the columns that are
* set apart for this process (see above), and the number of elements that are
* in the rest of the columns.
*
* Since in general this information is not readily available, most of the
* initializing functions of this class assume that all of the number of
* elements you give as an argument to @p n_nonzero_per_row or by @p
* row_lengths fall into the columns "owned" by this process, and none into
* the other ones. This is a fair guess for most of the rows, since in a good
* domain partitioning, nodes only interact with nodes that are within the
* same subdomain. It does not hold for nodes on the interfaces of subdomain,
* however, and for the rows corresponding to these nodes, PETSc will have to
* allocate additional memory, a costly process.
*
* The only way to avoid this is to tell PETSc where the actual entries of the
* matrix will be. For this, there are constructors and reinit() functions of
* this class that take a CompressedSparsityPattern object containing all this
* information. While in the general case it is sufficient if the constructors
* and reinit() functions know the number of local rows and columns, the
* functions getting a sparsity pattern also need to know the number of local
* rows (@p local_rows_per_process) and columns (@p local_columns_per_process)
* for all other processes, in order to compute which parts of the matrix are
* which. Thus, it is not sufficient to just count the number of degrees of
* freedom that belong to a particular process, but you have to have the
* numbers for all processes available at all processes.
*
* @ingroup PETScWrappers
* @ingroup Matrix1
* @author Wolfgang Bangerth, 2004
*/
class SparseMatrix : public MatrixBase
{
public:
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* A structure that describes some of
* the traits of this class in terms
* of its run-time behavior. Some
* other classes (such as the block
* matrix classes) that take one or
* other of the matrix classes as its
* template parameters can tune their
* behavior based on the variables in
* this class.
*/
struct Traits
{
/**
* It is not safe to elide
* additions of zeros to
* individual elements of this
* matrix. The reason is that
* additions to the matrix may
* trigger collective operations
* synchronising buffers on
* multiple processes. If an
* addition is elided on one
* process, this may lead to
* other processes hanging in an
* infinite waiting loop.
*/
static const bool zero_addition_can_be_elided = false;
};
/**
* Default constructor. Create an
* empty matrix.
*/
SparseMatrix ();
/**
* Destructor to free the PETSc object.
*/
~SparseMatrix ();
/**
* Create a sparse matrix of
* dimensions @p m times @p n, with
* an initial guess of @p
* n_nonzero_per_row nonzero elements
* per row. PETSc is able to cope
* with the situation that more than
* this number of elements are later
* allocated for a row, but this
* involves copying data, and is thus
* expensive.
*
* For the meaning of the @p
* local_row and @p local_columns
* parameters, see the class
* documentation.
*
* The @p is_symmetric flag determines
* whether we should tell PETSc that
* the matrix is going to be symmetric
* (as indicated by the call
* <tt>MatSetOption(mat,
* MAT_SYMMETRIC)</tt>. Note that the
* PETSc documentation states that one
* cannot form an ILU decomposition of
* a matrix for which this flag has
* been set to @p true, only an
* ICC. The default value of this flag
* is @p false.
*/
SparseMatrix (const MPI_Comm &communicator,
const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const size_type n_nonzero_per_row,
const bool is_symmetric = false);
/**
* Initialize a rectangular matrix
* with @p m rows and @p n columns.
* The maximal number of nonzero
* entries for each row separately is
* given by the @p row_lengths array.
*
* For the meaning of the @p
* local_row and @p local_columns
* parameters, see the class
* documentation.
*
* Just as for the other
* constructors: PETSc is able to
* cope with the situation that more
* than this number of elements are
* later allocated for a row, but
* this involves copying data, and is
* thus expensive.
*
* The @p is_symmetric flag
* determines whether we should tell
* PETSc that the matrix is going to
* be symmetric (as indicated by the
* call <tt>MatSetOption(mat,
* MAT_SYMMETRIC)</tt>. Note that the
* PETSc documentation states that
* one cannot form an ILU
* decomposition of a matrix for
* which this flag has been set to @p
* true, only an ICC. The default
* value of this flag is @p false.
*/
SparseMatrix (const MPI_Comm &communicator,
const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const std::vector<size_type> &row_lengths,
const bool is_symmetric = false);
/**
* Initialize using the given
* sparsity pattern with
* communication happening over the
* provided @p communicator.
*
* For the meaning of the @p
* local_rows_per_process and @p
* local_columns_per_process
* parameters, see the class
* documentation.
*
* Note that PETSc can be very slow
* if you do not provide it with a
* good estimate of the lengths of
* rows. Using the present function
* is a very efficient way to do
* this, as it uses the exact number
* of nonzero entries for each row of
* the matrix by using the given
* sparsity pattern argument. If the
* @p preset_nonzero_locations flag
* is @p true, this function in
* addition not only sets the correct
* row sizes up front, but also
* pre-allocated the correct nonzero
* entries in the matrix.
*
* PETsc allows to later add
* additional nonzero entries to a
* matrix, by simply writing to these
* elements. However, this will then
* lead to additional memory
* allocations which are very
* inefficient and will greatly slow
* down your program. It is therefore
* significantly more efficient to
* get memory allocation right from
* the start.
*/
template <typename SparsityType>
SparseMatrix (const MPI_Comm &communicator,
const SparsityType &sparsity_pattern,
const std::vector<size_type> &local_rows_per_process,
const std::vector<size_type> &local_columns_per_process,
const unsigned int this_process,
const bool preset_nonzero_locations = true);
/**
* This operator assigns a scalar to
* a matrix. Since this does usually
* not make much sense (should we set
* all matrix entries to this value?
* Only the nonzero entries of the
* sparsity pattern?), this operation
* is only allowed if the actual
* value to be assigned is zero. This
* operator only exists to allow for
* the obvious notation
* <tt>matrix=0</tt>, which sets all
* elements of the matrix to zero,
* but keep the sparsity pattern
* previously used.
*/
SparseMatrix &operator = (const value_type d);
/**
* Make a copy of the PETSc matrix @p other. It is assumed that both matrices have
* the same SparsityPattern.
*/
void copy_from(const SparseMatrix &other);
/**
* Throw away the present matrix and
* generate one that has the same
* properties as if it were created by
* the constructor of this class with
* the same argument list as the
* present function.
*/
void reinit (const MPI_Comm &communicator,
const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const size_type n_nonzero_per_row,
const bool is_symmetric = false);
/**
* Throw away the present matrix and
* generate one that has the same
* properties as if it were created by
* the constructor of this class with
* the same argument list as the
* present function.
*/
void reinit (const MPI_Comm &communicator,
const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const std::vector<size_type> &row_lengths,
const bool is_symmetric = false);
/**
* Initialize using the given
* sparsity pattern with
* communication happening over the
* provided @p communicator.
*
* Note that PETSc can be very slow
* if you do not provide it with a
* good estimate of the lengths of
* rows. Using the present function
* is a very efficient way to do
* this, as it uses the exact number
* of nonzero entries for each row of
* the matrix by using the given
* sparsity pattern argument. If the
* @p preset_nonzero_locations flag
* is @p true, this function in
* addition not only sets the correct
* row sizes up front, but also
* pre-allocated the correct nonzero
* entries in the matrix.
*
* PETsc allows to later add
* additional nonzero entries to a
* matrix, by simply writing to these
* elements. However, this will then
* lead to additional memory
* allocations which are very
* inefficient and will greatly slow
* down your program. It is therefore
* significantly more efficient to
* get memory allocation right from
* the start.
*/
template <typename SparsityType>
void reinit (const MPI_Comm &communicator,
const SparsityType &sparsity_pattern,
const std::vector<size_type> &local_rows_per_process,
const std::vector<size_type> &local_columns_per_process,
const unsigned int this_process,
const bool preset_nonzero_locations = true);
/**
* Create a matrix where the size() of the IndexSets determine the global
* number of rows and columns and the entries of the IndexSet give
* the rows and columns for the calling processor.
* Note that only contiguous IndexSets are supported.
*/
template <typename SparsityType>
void reinit (const IndexSet &local_rows,
const IndexSet &local_columns,
const SparsityType &sparsity_pattern,
const MPI_Comm &communicator);
/**
* Return a reference to the MPI
* communicator object in use with
* this matrix.
*/
virtual const MPI_Comm &get_mpi_communicator () const;
/** @addtogroup Exceptions
* @{ */
/**
* Exception
*/
DeclException2 (ExcLocalRowsTooLarge,
int, int,
<< "The number of local rows " << arg1
<< " must be larger than the total number of rows " << arg2);
//@}
/**
* Return the square of the norm
* of the vector $v$ with respect
* to the norm induced by this
* matrix,
* i.e. $\left(v,Mv\right)$. This
* is useful, e.g. in the finite
* element context, where the
* $L_2$ norm of a function
* equals the matrix norm with
* respect to the mass matrix of
* the vector representing the
* nodal values of the finite
* element function.
*
* Obviously, the matrix needs to
* be quadratic for this operation.
*
* The implementation of this function
* is not as efficient as the one in
* the @p MatrixBase class used in
* deal.II (i.e. the original one, not
* the PETSc wrapper class) since PETSc
* doesn't support this operation and
* needs a temporary vector.
*/
PetscScalar matrix_norm_square (const Vector &v) const;
/**
* Compute the matrix scalar
* product $\left(u,Mv\right)$.
*
* The implementation of this function
* is not as efficient as the one in
* the @p MatrixBase class used in
* deal.II (i.e. the original one, not
* the PETSc wrapper class) since PETSc
* doesn't support this operation and
* needs a temporary vector.
*/
PetscScalar matrix_scalar_product (const Vector &u,
const Vector &v) const;
private:
/**
* Copy of the communicator object to
* be used for this parallel vector.
*/
MPI_Comm communicator;
/**
* Do the actual work for the
* respective reinit() function and
* the matching constructor,
* i.e. create a matrix. Getting rid
* of the previous matrix is left to
* the caller.
*/
void do_reinit (const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const size_type n_nonzero_per_row,
const bool is_symmetric = false);
/**
* Same as previous function.
*/
void do_reinit (const size_type m,
const size_type n,
const size_type local_rows,
const size_type local_columns,
const std::vector<size_type> &row_lengths,
const bool is_symmetric = false);
/**
* Same as previous functions.
*/
template <typename SparsityType>
void do_reinit (const SparsityType &sparsity_pattern,
const std::vector<size_type> &local_rows_per_process,
const std::vector<size_type> &local_columns_per_process,
const unsigned int this_process,
const bool preset_nonzero_locations);
/**
* Same as previous functions.
*/
template <typename SparsityType>
void do_reinit (const IndexSet &local_rows,
const IndexSet &local_columns,
const SparsityType &sparsity_pattern);
/**
* To allow calling protected
* prepare_add() and
* prepare_set().
*/
friend class BlockMatrixBase<SparseMatrix>;
};
// -------- template and inline functions ----------
inline
const MPI_Comm &
SparseMatrix::get_mpi_communicator () const
{
return communicator;
}
}
}
DEAL_II_NAMESPACE_CLOSE
#endif // DEAL_II_WITH_PETSC
/*---------------------------- petsc_parallel_sparse_matrix.h ---------------------------*/
#endif
/*---------------------------- petsc_parallel_sparse_matrix.h ---------------------------*/
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