Reference documentation for deal.II version 9.0.0
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#include <deal.II/lac/petsc_parallel_sparse_matrix.h>
Classes | |
struct | Traits |
Public Types | |
typedef types::global_dof_index | size_type |
Public Types inherited from PETScWrappers::MatrixBase | |
typedef MatrixIterators::const_iterator | const_iterator |
typedef types::global_dof_index | size_type |
typedef PetscScalar | value_type |
Public Member Functions | |
SparseMatrix () | |
~SparseMatrix () | |
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, const size_type n_offdiag_nonzero_per_row=0) | |
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, const std::vector< size_type > &offdiag_row_lengths=std::vector< size_type >()) | |
template<typename SparsityPatternType > | |
SparseMatrix (const MPI_Comm &communicator, const SparsityPatternType &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) | |
SparseMatrix & | operator= (const value_type d) |
void | copy_from (const SparseMatrix &other) |
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, const size_type n_offdiag_nonzero_per_row=0) |
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, const std::vector< size_type > &offdiag_row_lengths=std::vector< size_type >()) |
template<typename SparsityPatternType > | |
void | reinit (const MPI_Comm &communicator, const SparsityPatternType &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) |
template<typename SparsityPatternType > | |
void | reinit (const IndexSet &local_rows, const IndexSet &local_columns, const SparsityPatternType &sparsity_pattern, const MPI_Comm &communicator) |
void | reinit (const SparseMatrix &other) |
virtual const MPI_Comm & | get_mpi_communicator () const |
PetscScalar | matrix_norm_square (const Vector &v) const |
PetscScalar | matrix_scalar_product (const Vector &u, const Vector &v) const |
IndexSet | locally_owned_domain_indices () const |
IndexSet | locally_owned_range_indices () const |
void | mmult (SparseMatrix &C, const SparseMatrix &B, const MPI::Vector &V=MPI::Vector()) const |
void | Tmmult (SparseMatrix &C, const SparseMatrix &B, const MPI::Vector &V=MPI::Vector()) const |
Public Member Functions inherited from PETScWrappers::MatrixBase | |
MatrixBase () | |
MatrixBase (const MatrixBase &)=delete | |
MatrixBase & | operator= (const MatrixBase &)=delete |
virtual | ~MatrixBase () |
MatrixBase & | operator= (const value_type d) |
void | clear () |
void | set (const size_type i, const size_type j, const PetscScalar value) |
void | set (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false) |
void | set (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=false) |
void | set (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=false) |
void | set (const size_type row, const size_type n_cols, const size_type *col_indices, const PetscScalar *values, const bool elide_zero_values=false) |
void | add (const size_type i, const size_type j, const PetscScalar value) |
void | add (const std::vector< size_type > &indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true) |
void | add (const std::vector< size_type > &row_indices, const std::vector< size_type > &col_indices, const FullMatrix< PetscScalar > &full_matrix, const bool elide_zero_values=true) |
void | add (const size_type row, const std::vector< size_type > &col_indices, const std::vector< PetscScalar > &values, const bool elide_zero_values=true) |
void | add (const size_type row, const size_type n_cols, const size_type *col_indices, const PetscScalar *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) |
void | clear_row (const size_type row, const PetscScalar new_diag_value=0) |
void | clear_rows (const std::vector< size_type > &rows, const PetscScalar new_diag_value=0) |
void | compress (const VectorOperation::values operation) |
PetscScalar | operator() (const size_type i, const size_type j) const |
PetscScalar | el (const size_type i, const size_type j) const |
PetscScalar | diag_element (const size_type i) const |
size_type | m () const |
size_type | n () const |
size_type | local_size () const |
std::pair< size_type, size_type > | local_range () const |
bool | in_local_range (const size_type index) const |
size_type | n_nonzero_elements () const |
size_type | row_length (const size_type row) const |
PetscReal | l1_norm () const |
PetscReal | linfty_norm () const |
PetscReal | frobenius_norm () const |
PetscScalar | matrix_norm_square (const VectorBase &v) const |
PetscScalar | matrix_scalar_product (const VectorBase &u, const VectorBase &v) const |
PetscScalar | trace () const |
MatrixBase & | operator*= (const PetscScalar factor) |
MatrixBase & | operator/= (const PetscScalar factor) |
MatrixBase & | add (const PetscScalar factor, const MatrixBase &other) |
MatrixBase & | add (const MatrixBase &other, const PetscScalar factor) |
void | vmult (VectorBase &dst, const VectorBase &src) const |
void | Tvmult (VectorBase &dst, const VectorBase &src) const |
void | vmult_add (VectorBase &dst, const VectorBase &src) const |
void | Tvmult_add (VectorBase &dst, const VectorBase &src) const |
PetscScalar | residual (VectorBase &dst, const VectorBase &x, const VectorBase &b) const |
const_iterator | begin () const |
const_iterator | end () const |
const_iterator | begin (const size_type r) const |
const_iterator | end (const size_type r) const |
operator Mat () const | |
Mat & | petsc_matrix () |
void | transpose () |
PetscBool | is_symmetric (const double tolerance=1.e-12) |
PetscBool | is_hermitian (const double tolerance=1.e-12) |
void | write_ascii (const PetscViewerFormat format=PETSC_VIEWER_DEFAULT) |
void | print (std::ostream &out, const bool alternative_output=false) const |
std::size_t | memory_consumption () const |
Public Member Functions inherited from Subscriptor | |
Subscriptor () | |
Subscriptor (const Subscriptor &) | |
Subscriptor (Subscriptor &&) noexcept | |
virtual | ~Subscriptor () |
Subscriptor & | operator= (const Subscriptor &) |
Subscriptor & | operator= (Subscriptor &&) noexcept |
void | subscribe (const char *identifier=nullptr) const |
void | unsubscribe (const char *identifier=nullptr) const |
unsigned int | n_subscriptions () const |
void | list_subscribers () const |
template<class Archive > | |
void | serialize (Archive &ar, const unsigned int version) |
Static Public Member Functions | |
static ::ExceptionBase & | ExcLocalRowsTooLarge (int arg1, int arg2) |
Static Public Member Functions inherited from PETScWrappers::MatrixBase | |
static ::ExceptionBase & | ExcSourceEqualsDestination () |
static ::ExceptionBase & | ExcWrongMode (int arg1, int arg2) |
Static Public Member Functions inherited from Subscriptor | |
static ::ExceptionBase & | ExcInUse (int arg1, std::string arg2, std::string arg3) |
static ::ExceptionBase & | ExcNoSubscriber (std::string arg1, std::string arg2) |
Private Member Functions | |
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, const size_type n_offdiag_nonzero_per_row=0) |
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, const std::vector< size_type > &offdiag_row_lengths=std::vector< size_type >()) |
template<typename SparsityPatternType > | |
void | do_reinit (const SparsityPatternType &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) |
template<typename SparsityPatternType > | |
void | do_reinit (const IndexSet &local_rows, const IndexSet &local_columns, const SparsityPatternType &sparsity_pattern) |
Private Attributes | |
MPI_Comm | communicator |
Friends | |
class | BlockMatrixBase< SparseMatrix > |
Additional Inherited Members | |
Protected Member Functions inherited from PETScWrappers::MatrixBase | |
void | prepare_action (const VectorOperation::values new_action) |
void | assert_is_compressed () |
void | prepare_add () |
void | prepare_set () |
void | mmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const |
void | Tmmult (MatrixBase &C, const MatrixBase &B, const VectorBase &V) const |
Protected Attributes inherited from PETScWrappers::MatrixBase | |
Mat | matrix |
VectorOperation::values | last_action |
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.
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 local_rows
. The individual values passed as 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 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 local_columns
variable, which again has to add up to the global number of columns in the matrix. The name 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 n_nonzero_per_row
or by 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 DynamicSparsityPattern 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 (local_rows_per_process
) and columns (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.
Definition at line 119 of file petsc_parallel_sparse_matrix.h.
Declare type for container size.
Definition at line 125 of file petsc_parallel_sparse_matrix.h.
SparseMatrix< number >::SparseMatrix | ( | ) |
Default constructor. Create an empty matrix.
Definition at line 33 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix< number >::~SparseMatrix | ( | ) |
Destructor to free the PETSc object.
Definition at line 47 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix< number >::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 , |
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const size_type | n_offdiag_nonzero_per_row = 0 |
||
) |
Create a sparse matrix of dimensions m
times n
, with an initial guess of n_nonzero_per_row
and n_offdiag_nonzero_per_row
nonzero elements per row (see documentation of the MatCreateAIJ PETSc function for more information about these parameters). 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 local_row
and local_columns
parameters, see the class documentation.
The is_symmetric
flag determines whether we should tell PETSc that the matrix is going to be symmetric (as indicated by the call MatSetOption(mat, MAT_SYMMETRIC)
. Note that the PETSc documentation states that one cannot form an ILU decomposition of a matrix for which this flag has been set to true
, only an ICC. The default value of this flag is false
.
Definition at line 52 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix< number >::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 , |
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const std::vector< size_type > & | offdiag_row_lengths = std::vector<size_type>() |
||
) |
Initialize a rectangular matrix with m
rows and n
columns. The maximal number of nonzero entries for diagonal and off- diagonal blocks of each row is given by the row_lengths
and offdiag_row_lengths
arrays.
For the meaning of the local_row
and 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 is_symmetric
flag determines whether we should tell PETSc that the matrix is going to be symmetric (as indicated by the call MatSetOption(mat, MAT_SYMMETRIC)
. Note that the PETSc documentation states that one cannot form an ILU decomposition of a matrix for which this flag has been set to true
, only an ICC. The default value of this flag is false
.
Definition at line 70 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix< SparsityPatternType >::SparseMatrix | ( | const MPI_Comm & | communicator, |
const SparsityPatternType & | 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 |
||
) |
Initialize using the given sparsity pattern with communication happening over the provided communicator
.
For the meaning of the local_rows_per_process
and 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 preset_nonzero_locations
flag is 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.
Definition at line 89 of file petsc_parallel_sparse_matrix.cc.
SparseMatrix & SparseMatrix< number >::operator= | ( | const value_type | d | ) |
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 matrix=0
, which sets all elements of the matrix to zero, but keep the sparsity pattern previously used.
Definition at line 122 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::copy_from | ( | const SparseMatrix & | other | ) |
Make a copy of the PETSc matrix other
. It is assumed that both matrices have the same SparsityPattern.
Definition at line 129 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::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 , |
||
const size_type | n_offdiag_nonzero_per_row = 0 |
||
) |
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.
reinit
is deprecated: please use the overload with a sparsity pattern argument instead. Definition at line 142 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::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 , |
||
const std::vector< size_type > & | offdiag_row_lengths = std::vector<size_type>() |
||
) |
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.
reinit
is deprecated: please use the overload with a sparsity pattern argument instead. Definition at line 165 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit | ( | const MPI_Comm & | communicator, |
const SparsityPatternType & | 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 |
||
) |
Initialize using the given sparsity pattern with communication happening over the provided 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 preset_nonzero_locations
flag is 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.
Definition at line 190 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< SparsityPatternType >::reinit | ( | const IndexSet & | local_rows, |
const IndexSet & | local_columns, | ||
const SparsityPatternType & | sparsity_pattern, | ||
const MPI_Comm & | communicator | ||
) |
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 ascending, 1:1 IndexSets are supported.
Definition at line 212 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::reinit | ( | const SparseMatrix & | other | ) |
Initialize this matrix to have the same structure as other
. This will not copy the values of the other matrix, but you can use copy_from() for this.
Definition at line 106 of file petsc_parallel_sparse_matrix.cc.
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inlinevirtual |
Return a reference to the MPI communicator object in use with this matrix.
Implements PETScWrappers::MatrixBase.
Definition at line 500 of file petsc_parallel_sparse_matrix.h.
PetscScalar SparseMatrix< number >::matrix_norm_square | ( | const Vector & | v | ) | const |
Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e. \(\left(v^\ast,Mv\right)\). 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 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.
Definition at line 644 of file petsc_parallel_sparse_matrix.cc.
PetscScalar SparseMatrix< number >::matrix_scalar_product | ( | const Vector & | u, |
const Vector & | v | ||
) | const |
Compute the matrix scalar product \(\left(u^\ast,Mv\right)\).
The implementation of this function is not as efficient as the one in the 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.
Definition at line 653 of file petsc_parallel_sparse_matrix.cc.
IndexSet SparseMatrix< number >::locally_owned_domain_indices | ( | ) | const |
Return the partitioning of the domain space of this matrix, i.e., the partitioning of the vectors this matrix has to be multiplied with.
Definition at line 663 of file petsc_parallel_sparse_matrix.cc.
IndexSet SparseMatrix< number >::locally_owned_range_indices | ( | ) | const |
Return the partitioning of the range space of this matrix, i.e., the partitioning of the vectors that result from matrix-vector products.
Definition at line 687 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::mmult | ( | SparseMatrix & | C, |
const SparseMatrix & | B, | ||
const MPI::Vector & | V = MPI::Vector() |
||
) | const |
Perform the matrix-matrix multiplication \(C = AB\), or, \(C = A \text{diag}(V) B\) given a compatible vector \(V\).
This function calls MatrixBase::mmult() to do the actual work.
Definition at line 711 of file petsc_parallel_sparse_matrix.cc.
void SparseMatrix< number >::Tmmult | ( | SparseMatrix & | C, |
const SparseMatrix & | B, | ||
const MPI::Vector & | V = MPI::Vector() |
||
) | const |
Perform the matrix-matrix multiplication with the transpose of this
, i.e., \(C = A^T B\), or, \(C = A^T \text{diag}(V) B\) given a compatible vector \(V\).
This function calls MatrixBase::Tmmult() to do the actual work.
Definition at line 722 of file petsc_parallel_sparse_matrix.cc.
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private |
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.
do_reinit
is deprecated: please use the overload with a sparsity pattern argument instead. Definition at line 227 of file petsc_parallel_sparse_matrix.cc.
|
private |
Same as previous function.
do_reinit
is deprecated: please use the overload with a sparsity pattern argument instead. Definition at line 260 of file petsc_parallel_sparse_matrix.cc.
|
private |
Same as previous functions.
Definition at line 458 of file petsc_parallel_sparse_matrix.cc.
|
private |
Same as previous functions.
Definition at line 321 of file petsc_parallel_sparse_matrix.cc.
|
friend |
To allow calling protected prepare_add() and prepare_set().
Definition at line 491 of file petsc_parallel_sparse_matrix.h.
|
private |
Copy of the communicator object to be used for this parallel vector.
Definition at line 436 of file petsc_parallel_sparse_matrix.h.