Reference documentation for deal.II version Git 9c5841c5ee 20191111 14:05:52 0700

#include <deal.II/lac/petsc_matrix_base.h>
Public Types  
using  const_iterator = MatrixIterators::const_iterator 
using  size_type = types::global_dof_index 
using  value_type = PetscScalar 
Public Member Functions  
MatrixBase ()  
MatrixBase (const MatrixBase &)=delete  
MatrixBase &  operator= (const MatrixBase &)=delete 
virtual  ~MatrixBase () override 
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 
virtual const MPI_Comm &  get_mpi_communicator () const =0 
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.e12) 
PetscBool  is_hermitian (const double tolerance=1.e12) 
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 (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 ::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) 
Protected Member Functions  
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  
Mat  matrix 
VectorOperation::values  last_action 
Private Attributes  
std::vector< PetscInt >  column_indices 
std::vector< PetscScalar >  column_values 
Base class for all matrix classes that are implemented on top of the PETSc matrix types. Since in PETSc all matrix types (i.e. sequential and parallel, sparse, blocked, etc.) are built by filling the contents of an abstract object that is only referenced through a pointer of a type that is independent of the actual matrix type, we can implement almost all functionality of matrices in this base class. Derived classes will then only have to provide the functionality to create one or the other kind of matrix.
The interface of this class is modeled after the existing SparseMatrix class in deal.II. It has almost the same member functions, and is often exchangeable. However, since PETSc only supports a single scalar type (either double, float, or a complex data type), it is not templated, and only works with whatever your PETSc installation has defined the data type PetscScalar to.
Note that PETSc only guarantees that operations do what you expect if the functions MatAssemblyBegin
and MatAssemblyEnd
have been called after matrix assembly. Therefore, you need to call SparseMatrix::compress() before you actually use the matrix. This also calls MatCompress
that compresses the storage format for sparse matrices by discarding unused elements. PETSc allows to continue with assembling the matrix after calls to these functions, but since there are no more free entries available after that any more, it is better to only call SparseMatrix::compress() once at the end of the assembly stage and before the matrix is actively used.
Definition at line 284 of file petsc_matrix_base.h.
Declare an alias for the iterator class.
Definition at line 290 of file petsc_matrix_base.h.
Declare type for container size.
Definition at line 295 of file petsc_matrix_base.h.
using PETScWrappers::MatrixBase::value_type = PetscScalar 
Declare an alias in analogy to all the other container classes.
Definition at line 300 of file petsc_matrix_base.h.
PETScWrappers::MatrixBase::MatrixBase  (  ) 
Default constructor.
Definition at line 75 of file petsc_matrix_base.cc.

delete 
Copy constructor. It is deleted as copying this base class without knowing the concrete kind of matrix stored may both miss important details and be expensive if the matrix is large.

overridevirtual 
Destructor. Made virtual so that one can use pointers to this class.
Definition at line 82 of file petsc_matrix_base.cc.

delete 
Copy operator. It is deleted as copying this base class without knowing the concrete kind of matrix stored may both miss important details and be expensive if the matrix is large.
MatrixBase & PETScWrappers::MatrixBase::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 keeps the sparsity pattern previously used.
Definition at line 109 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::clear  (  ) 
Release all memory and return to a state just like after having called the default constructor.
Definition at line 90 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::set  (  const size_type  i, 
const size_type  j,  
const PetscScalar  value  
) 
Set the element (i,j) to value
.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value
is not a finite number an exception is thrown.
void PETScWrappers::MatrixBase::set  (  const std::vector< size_type > &  indices, 
const FullMatrix< PetscScalar > &  full_matrix,  
const bool  elide_zero_values = false 

) 
Set all elements given in a FullMatrix<double> into the sparse matrix locations given by indices
. In other words, this function writes the elements in full_matrix
into the calling matrix, using the localtoglobal indexing specified by indices
for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.
void PETScWrappers::MatrixBase::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 

) 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.
void PETScWrappers::MatrixBase::set  (  const size_type  row, 
const std::vector< size_type > &  col_indices,  
const std::vector< PetscScalar > &  values,  
const bool  elide_zero_values = false 

) 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.
void PETScWrappers::MatrixBase::set  (  const size_type  row, 
const size_type  n_cols,  
const size_type *  col_indices,  
const PetscScalar *  values,  
const bool  elide_zero_values = false 

) 
Set several elements to values given by values
in a given row in columns given by col_indices into the sparse matrix.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be inserted anyway or they should be filtered away. The default value is false
, i.e., even zero values are inserted/replaced.
void PETScWrappers::MatrixBase::add  (  const size_type  i, 
const size_type  j,  
const PetscScalar  value  
) 
Add value
to the element (i,j).
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds a new entry to the matrix if it didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist. If value
is not a finite number an exception is thrown.
void PETScWrappers::MatrixBase::add  (  const std::vector< size_type > &  indices, 
const FullMatrix< PetscScalar > &  full_matrix,  
const bool  elide_zero_values = true 

) 
Add all elements given in a FullMatrix<double> into sparse matrix locations given by indices
. In other words, this function adds the elements in full_matrix
to the respective entries in calling matrix, using the localtoglobal indexing specified by indices
for both the rows and the columns of the matrix. This function assumes a quadratic sparse matrix and a quadratic full_matrix, the usual situation in FE calculations.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.
void PETScWrappers::MatrixBase::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 

) 
Same function as before, but now including the possibility to use rectangular full_matrices and different localtoglobal indexing on rows and columns, respectively.
void PETScWrappers::MatrixBase::add  (  const size_type  row, 
const std::vector< size_type > &  col_indices,  
const std::vector< PetscScalar > &  values,  
const bool  elide_zero_values = true 

) 
Set several elements in the specified row of the matrix with column indices as given by col_indices
to the respective value.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.
void PETScWrappers::MatrixBase::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 

) 
Add an array of values given by values
in the given global matrix row at columns specified by col_indices in the sparse matrix.
If the present object (from a derived class of this one) happens to be a sparse matrix, then this function adds some new entries to the matrix if they didn't exist before, very much in contrast to the SparseMatrix class which throws an error if the entry does not exist.
The optional parameter elide_zero_values
can be used to specify whether zero values should be added anyway or these should be filtered away and only nonzero data is added. The default value is true
, i.e., zero values won't be added into the matrix.
void PETScWrappers::MatrixBase::clear_row  (  const size_type  row, 
const PetscScalar  new_diag_value = 0 

) 
Remove all elements from this row
by setting them to zero. The function does not modify the number of allocated nonzero entries, it only sets some entries to zero. It may drop them from the sparsity pattern, though (but retains the allocated memory in case new entries are again added later).
This operation is used in eliminating constraints (e.g. due to hanging nodes) and makes sure that we can write this modification to the matrix without having to read entries (such as the locations of nonzero elements) from it – without this operation, removing constraints on parallel matrices is a rather complicated procedure.
The second parameter can be used to set the diagonal entry of this row to a value different from zero. The default is to set it to zero.
Definition at line 125 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::clear_rows  (  const std::vector< size_type > &  rows, 
const PetscScalar  new_diag_value = 0 

) 
Same as clear_row(), except that it works on a number of rows at once.
The second parameter can be used to set the diagonal entries of all cleared rows to something different from zero. Note that all of these diagonal entries get the same value – if you want different values for the diagonal entries, you have to set them by hand.
Definition at line 134 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::compress  (  const VectorOperation::values  operation  ) 
PETSc matrices store their own sparsity patterns. So, in analogy to our own SparsityPattern class, this function compresses the sparsity pattern and allows the resulting matrix to be used in all other operations where before only assembly functions were allowed. This function must therefore be called once you have assembled the matrix.
See Compressing distributed objects for more information.
Definition at line 191 of file petsc_matrix_base.cc.
Return the value of the entry (i,j). This may be an expensive operation and you should always take care where to call this function. In contrast to the respective function in the MatrixBase
class, we don't throw an exception if the respective entry doesn't exist in the sparsity pattern of this class, since PETSc does not transmit this information.
This function is therefore exactly equivalent to the el()
function.
Return the value of the matrix entry (i,j). If this entry does not exist in the sparsity pattern, then zero is returned. While this may be convenient in some cases, note that it is simple to write algorithms that are slow compared to an optimal solution, since the sparsity of the matrix is not used.
Definition at line 163 of file petsc_matrix_base.cc.
PetscScalar PETScWrappers::MatrixBase::diag_element  (  const size_type  i  )  const 
Return the main diagonal element in the ith row. This function throws an error if the matrix is not quadratic.
Since we do not have direct access to the underlying data structure, this function is no faster than the elementwise access using the el() function. However, we provide this function for compatibility with the SparseMatrix class.
Definition at line 179 of file petsc_matrix_base.cc.
MatrixBase::size_type PETScWrappers::MatrixBase::m  (  )  const 
Return the number of rows in this matrix.
Definition at line 235 of file petsc_matrix_base.cc.
MatrixBase::size_type PETScWrappers::MatrixBase::n  (  )  const 
Return the number of columns in this matrix.
Definition at line 248 of file petsc_matrix_base.cc.
MatrixBase::size_type PETScWrappers::MatrixBase::local_size  (  )  const 
Return the local dimension of the matrix, i.e. the number of rows stored on the present MPI process. For sequential matrices, this number is the same as m(), but for parallel matrices it may be smaller.
To figure out which elements exactly are stored locally, use local_range().
Definition at line 261 of file petsc_matrix_base.cc.
std::pair< MatrixBase::size_type, MatrixBase::size_type > PETScWrappers::MatrixBase::local_range  (  )  const 
Return a pair of indices indicating which rows of this matrix are stored locally. The first number is the index of the first row stored, the second the index of the one past the last one that is stored locally. If this is a sequential matrix, then the result will be the pair (0,m()), otherwise it will be a pair (i,i+n), where n=local_size()
.
Definition at line 274 of file petsc_matrix_base.cc.
bool PETScWrappers::MatrixBase::in_local_range  (  const size_type  index  )  const 
Return whether index
is in the local range or not, see also local_range().

pure virtual 
Return a reference to the MPI communicator object in use with this matrix. This function has to be implemented in derived classes.
Implemented in PETScWrappers::MPI::SparseMatrix, PETScWrappers::SparseMatrix, PETScWrappers::MatrixFree, and PETScWrappers::FullMatrix.
MatrixBase::size_type PETScWrappers::MatrixBase::n_nonzero_elements  (  )  const 
Return the number of nonzero elements of this matrix. Actually, it returns the number of entries in the sparsity pattern; if any of the entries should happen to be zero, it is counted anyway.
Definition at line 288 of file petsc_matrix_base.cc.
MatrixBase::size_type PETScWrappers::MatrixBase::row_length  (  const size_type  row  )  const 
Number of entries in a specific row.
Definition at line 300 of file petsc_matrix_base.cc.
PetscReal PETScWrappers::MatrixBase::l1_norm  (  )  const 
Return the l1norm of the matrix, that is \(M_1=max_{all columns j}\sum_{all rows i} M_ij\), (max. sum of columns). This is the natural matrix norm that is compatible to the l1norm for vectors, i.e. \(Mv_1\leq M_1 v_1\). (cf. HaemmerlinHoffmann: Numerische Mathematik)
Definition at line 336 of file petsc_matrix_base.cc.
PetscReal PETScWrappers::MatrixBase::linfty_norm  (  )  const 
Return the linftynorm of the matrix, that is \(M_infty=max_{all rows i}\sum_{all columns j} M_ij\), (max. sum of rows). This is the natural matrix norm that is compatible to the linftynorm of vectors, i.e. \(Mv_infty \leq M_infty v_infty\). (cf. HaemmerlinHoffmann: Numerische Mathematik)
Definition at line 349 of file petsc_matrix_base.cc.
PetscReal PETScWrappers::MatrixBase::frobenius_norm  (  )  const 
Return the frobenius norm of the matrix, i.e. the square root of the sum of squares of all entries in the matrix.
Definition at line 362 of file petsc_matrix_base.cc.
PetscScalar PETScWrappers::MatrixBase::matrix_norm_square  (  const VectorBase &  v  )  const 
Return the square of the norm of the vector \(v\) with respect to the norm induced by this matrix, i.e. \(\left(v,Mv\right)\). 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.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then the given vector has to be a distributed vector as well. Conversely, if the matrix is not distributed, then neither may the vector be.
Definition at line 374 of file petsc_matrix_base.cc.
PetscScalar PETScWrappers::MatrixBase::matrix_scalar_product  (  const VectorBase &  u, 
const VectorBase &  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 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.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 383 of file petsc_matrix_base.cc.
PetscScalar PETScWrappers::MatrixBase::trace  (  )  const 
Return the trace of the matrix, i.e. the sum of all diagonal entries in the matrix.
Definition at line 393 of file petsc_matrix_base.cc.
MatrixBase & PETScWrappers::MatrixBase::operator*=  (  const PetscScalar  factor  ) 
Multiply the entire matrix by a fixed factor.
Definition at line 406 of file petsc_matrix_base.cc.
MatrixBase & PETScWrappers::MatrixBase::operator/=  (  const PetscScalar  factor  ) 
Divide the entire matrix by a fixed factor.
Definition at line 417 of file petsc_matrix_base.cc.
MatrixBase & PETScWrappers::MatrixBase::add  (  const PetscScalar  factor, 
const MatrixBase &  other  
) 
Add the matrix other
scaled by the factor factor
to the current matrix.
Definition at line 428 of file petsc_matrix_base.cc.
MatrixBase & PETScWrappers::MatrixBase::add  (  const MatrixBase &  other, 
const PetscScalar  factor  
) 
Add the matrix other
scaled by the factor factor
to the current matrix.
Definition at line 440 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::vmult  (  VectorBase &  dst, 
const VectorBase &  src  
)  const 
Matrixvector multiplication: let dst = M*src with M being this matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 447 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::Tvmult  (  VectorBase &  dst, 
const VectorBase &  src  
)  const 
Matrixvector multiplication: let dst = M^{T}*src with M being this matrix. This function does the same as vmult() but takes the transposed matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 458 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::vmult_add  (  VectorBase &  dst, 
const VectorBase &  src  
)  const 
Adding Matrixvector multiplication. Add M*src on dst with M being this matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 469 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::Tvmult_add  (  VectorBase &  dst, 
const VectorBase &  src  
)  const 
Adding Matrixvector multiplication. Add M^{T}*src to dst with M being this matrix. This function does the same as vmult_add() but takes the transposed matrix.
Source and destination must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then both vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 480 of file petsc_matrix_base.cc.
PetscScalar PETScWrappers::MatrixBase::residual  (  VectorBase &  dst, 
const VectorBase &  x,  
const VectorBase &  b  
)  const 
Compute the residual of an equation Mx=b, where the residual is defined to be r=bMx. Write the residual into dst
. The l_{2} norm of the residual vector is returned.
Source x and destination dst must not be the same vector.
Note that if the current object represents a parallel distributed matrix (of type PETScWrappers::MPI::SparseMatrix), then all vectors have to be distributed vectors as well. Conversely, if the matrix is not distributed, then neither of the vectors may be.
Definition at line 578 of file petsc_matrix_base.cc.
const_iterator PETScWrappers::MatrixBase::begin  (  )  const 
Iterator starting at the first entry. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of begin() taking a row number as an argument.
const_iterator PETScWrappers::MatrixBase::end  (  )  const 
Final iterator. This can only be called on a processor owning the entire matrix. In all other cases refer to the version of end() taking a row number as an argument.
const_iterator PETScWrappers::MatrixBase::begin  (  const size_type  r  )  const 
Iterator starting at the first entry of row r
.
Note that if the given row is empty, i.e. does not contain any nonzero entries, then the iterator returned by this function equals end(r)
. Note also that the iterator may not be dereferenceable in that case.
const_iterator PETScWrappers::MatrixBase::end  (  const size_type  r  )  const 
Final iterator of row r
. It points to the first element past the end of line r
, or past the end of the entire sparsity pattern.
Note that the end iterator is not necessarily dereferenceable. This is in particular the case if it is the end iterator for the last row of a matrix.
PETScWrappers::MatrixBase::operator Mat  (  )  const 
Conversion operator to gain access to the underlying PETSc type. If you do this, you cut this class off some information it may need, so this conversion operator should only be used if you know what you do. In particular, it should only be used for readonly operations into the matrix.
Definition at line 594 of file petsc_matrix_base.cc.
Mat & PETScWrappers::MatrixBase::petsc_matrix  (  ) 
Return a reference to the underlying PETSc type. It can be used to modify the underlying data, so use it only when you know what you are doing.
Definition at line 600 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::transpose  (  ) 
Make an inplace transpose of a matrix.
Definition at line 606 of file petsc_matrix_base.cc.
PetscBool PETScWrappers::MatrixBase::is_symmetric  (  const double  tolerance = 1.e12  ) 
Test whether a matrix is symmetric. Default tolerance is \(1000\times32\)bit machine precision.
Definition at line 618 of file petsc_matrix_base.cc.
PetscBool PETScWrappers::MatrixBase::is_hermitian  (  const double  tolerance = 1.e12  ) 
Test whether a matrix is Hermitian, i.e. it is the complex conjugate of its transpose. Default tolerance is \(1000\times32\)bit machine precision.
Definition at line 628 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::write_ascii  (  const PetscViewerFormat  format = PETSC_VIEWER_DEFAULT  ) 
Print the PETSc matrix object values using PETSc internal matrix viewer function MatView
. The default format prints the non zero matrix elements. For other valid view formats, consult http://www.mcs.anl.gov/petsc/petsccurrent/docs/manualpages/Mat/MatView.html
Definition at line 640 of file petsc_matrix_base.cc.
void PETScWrappers::MatrixBase::print  (  std::ostream &  out, 
const bool  alternative_output = false 

)  const 
Print the elements of a matrix to the given output stream.
[in,out]  out  The output stream to which to write. 
[in]  alternative_output  This argument is ignored. It exists for compatibility with similar functions in other matrix classes. 
Definition at line 655 of file petsc_matrix_base.cc.
std::size_t PETScWrappers::MatrixBase::memory_consumption  (  )  const 
Return the number bytes consumed by this matrix on this CPU.
Definition at line 686 of file petsc_matrix_base.cc.

protected 
Ensure that the add/set mode that is required for actions following this call is compatible with the current mode. Should be called from all internal functions accessing matrix elements.

protected 
Internal function that checks that there are no pending insert/add operations. Throws an exception otherwise. Useful before calling any PETSc internal functions modifying the matrix.

protected 
For some matrix storage formats, in particular for the PETSc distributed blockmatrices, set and add operations on individual elements can not be freely mixed. Rather, one has to synchronize operations when one wants to switch from setting elements to adding to elements. BlockMatrixBase automatically synchronizes the access by calling this helper function for each block. This function ensures that the matrix is in a state that allows adding elements; if it previously already was in this state, the function does nothing.

protected 
Same as prepare_add() but prepare the matrix for setting elements if the representation of elements in this class requires such an operation.

protected 
Base function to perform the matrixmatrix multiplication \(C = AB\), or, if a vector \(V\) whose size is compatible with B is given, \(C = A \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.
This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.
The content as well as the sparsity pattern of the matrix \(C\) will be reset by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.
Definition at line 562 of file petsc_matrix_base.cc.

protected 
Base function to perform the matrixmatrix multiplication with the transpose of this
, i.e., \(C = A^T B\), or, if an optional vector \(V\) whose size is compatible with \(B\) is given, \(C = A^T \text{diag}(V) B\), where \(\text{diag}(V)\) defines a diagonal matrix with the vector entries.
This function assumes that the calling matrix \(A\) and \(B\) have compatible sizes. The size of \(C\) will be set within this function.
The content as well as the sparsity pattern of the matrix \(C\) will be changed by this function, so make sure that the sparsity pattern is not used somewhere else in your program. This is an expensive operation, so think twice before you use this function.
Definition at line 570 of file petsc_matrix_base.cc.

protected 
A generic matrix object in PETSc. The actual type, a sparse matrix, is set in the constructor.
Definition at line 968 of file petsc_matrix_base.h.

protected 
Store whether the last action was a write or add operation.
Definition at line 973 of file petsc_matrix_base.h.

mutableprivate 
An internal array of integer values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.
This variable does not store any "state" of the matrix object. Rather, it is only used as a temporary buffer by some of the member functions of this class. As with all mutable
member variables, the use of this variable is not threadsafe unless guarded by a mutex. However, since PETSc matrix operations are not threadsafe anyway, there is no need to attempt to make things threadsafe, and so there is no mutex associated with this variable.
Definition at line 1063 of file petsc_matrix_base.h.

mutableprivate 
An internal array of double values that is used to store the column indices when adding/inserting local data into the (large) sparse matrix.
The same comment as for the column_indices
variable above applies.
Definition at line 1073 of file petsc_matrix_base.h.