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//
// Copyright (C) 2004 - 2016 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 dealii__petsc_matrix_base_h
#define dealii__petsc_matrix_base_h
#include <deal.II/base/config.h>
#ifdef DEAL_II_WITH_PETSC
# include <deal.II/base/subscriptor.h>
# include <deal.II/lac/full_matrix.h>
# include <deal.II/lac/exceptions.h>
# include <deal.II/lac/vector.h>
# include <petscmat.h>
# include <deal.II/base/std_cxx11/shared_ptr.h>
# include <vector>
# include <cmath>
DEAL_II_NAMESPACE_OPEN
template <typename Matrix> class BlockMatrixBase;
namespace PETScWrappers
{
// forward declarations
class VectorBase;
class MatrixBase;
namespace MatrixIterators
{
/**
* This class acts as an iterator walking over the elements of PETSc
* matrices. Since PETSc offers a uniform interface for all types of
* matrices, this iterator can be used to access both sparse and full
* matrices.
*
* Note that PETSc does not give any guarantees as to the order of
* elements within each row. Note also that accessing the elements of a
* full matrix surprisingly only shows the nonzero elements of the matrix,
* not all elements.
*
* @ingroup PETScWrappers
* @author Guido Kanschat, Roy Stogner, Wolfgang Bangerth, 2004
*/
class const_iterator
{
private:
/**
* Accessor class for iterators
*/
class Accessor
{
public:
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Constructor. Since we use accessors only for read access, a const
* matrix pointer is sufficient.
*/
Accessor (const MatrixBase *matrix,
const size_type row,
const size_type index);
/**
* Copy constructor.
*/
Accessor (const Accessor &a);
/**
* Row number of the element represented by this object.
*/
size_type row() const;
/**
* Index in row of the element represented by this object.
*/
size_type index() const;
/**
* Column number of the element represented by this object.
*/
size_type column() const;
/**
* Value of this matrix entry.
*/
PetscScalar value() const;
/**
* Exception
*/
DeclException0 (ExcBeyondEndOfMatrix);
/**
* Exception
*/
DeclException3 (ExcAccessToNonlocalRow,
int, int, int,
<< "You tried to access row " << arg1
<< " of a distributed matrix, but only rows "
<< arg2 << " through " << arg3
<< " are stored locally and can be accessed.");
private:
/**
* The matrix accessed.
*/
mutable MatrixBase *matrix;
/**
* Current row number.
*/
size_type a_row;
/**
* Current index in row.
*/
size_type a_index;
/**
* Cache where we store the column indices of the present row. This is
* necessary, since PETSc makes access to the elements of its matrices
* rather hard, and it is much more efficient to copy all column
* entries of a row once when we enter it than repeatedly asking PETSc
* for individual ones. This also makes some sense since it is likely
* that we will access them sequentially anyway.
*
* In order to make copying of iterators/accessor of acceptable
* performance, we keep a shared pointer to these entries so that more
* than one accessor can access this data if necessary.
*/
std_cxx11::shared_ptr<const std::vector<size_type> > colnum_cache;
/**
* Similar cache for the values of this row.
*/
std_cxx11::shared_ptr<const std::vector<PetscScalar> > value_cache;
/**
* Discard the old row caches (they may still be used by other
* accessors) and generate new ones for the row pointed to presently
* by this accessor.
*/
void visit_present_row ();
/**
* Make enclosing class a friend.
*/
friend class const_iterator;
};
public:
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Constructor. Create an iterator into the matrix @p matrix for the
* given row and the index within it.
*/
const_iterator (const MatrixBase *matrix,
const size_type row,
const size_type index);
/**
* Prefix increment.
*/
const_iterator &operator++ ();
/**
* Postfix increment.
*/
const_iterator operator++ (int);
/**
* Dereferencing operator.
*/
const Accessor &operator* () const;
/**
* Dereferencing operator.
*/
const Accessor *operator-> () const;
/**
* Comparison. True, if both iterators point to the same matrix
* position.
*/
bool operator == (const const_iterator &) const;
/**
* Inverse of <tt>==</tt>.
*/
bool operator != (const const_iterator &) const;
/**
* Comparison operator. Result is true if either the first row number is
* smaller or if the row numbers are equal and the first index is
* smaller.
*/
bool operator < (const const_iterator &) const;
/**
* Exception
*/
DeclException2 (ExcInvalidIndexWithinRow,
int, int,
<< "Attempt to access element " << arg2
<< " of row " << arg1
<< " which doesn't have that many elements.");
private:
/**
* Store an object of the accessor class.
*/
Accessor accessor;
};
}
/**
* 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 @p MatAssemblyBegin and @p MatAssemblyEnd have been called
* after matrix assembly. Therefore, you need to call
* SparseMatrix::compress() before you actually use the matrix. This also
* calls @p 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.
*
* @ingroup PETScWrappers
* @ingroup Matrix1
* @author Wolfgang Bangerth, 2004
*/
class MatrixBase : public Subscriptor
{
public:
/**
* Declare a typedef for the iterator class.
*/
typedef MatrixIterators::const_iterator const_iterator;
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Declare a typedef in analogy to all the other container classes.
*/
typedef PetscScalar value_type;
/**
* Default constructor.
*/
MatrixBase ();
/**
* Destructor. Made virtual so that one can use pointers to this class.
*/
virtual ~MatrixBase ();
/**
* 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 keeps the sparsity pattern
* previously used.
*/
MatrixBase &
operator = (const value_type d);
/**
* Release all memory and return to a state just like after having called
* the default constructor.
*/
void clear ();
/**
* Set the element (<i>i,j</i>) to @p 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 <tt>value</tt> is
* not a finite number an exception is thrown.
*/
void set (const size_type i,
const size_type j,
const PetscScalar value);
/**
* Set all elements given in a FullMatrix<double> into the sparse matrix
* locations given by <tt>indices</tt>. In other words, this function
* writes the elements in <tt>full_matrix</tt> into the calling matrix,
* using the local-to-global indexing specified by <tt>indices</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be inserted anyway or they should be
* filtered away. The default value is <tt>false</tt>, i.e., even zero
* values are inserted/replaced.
*/
void set (const std::vector<size_type> &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 local-to-global indexing on
* rows and columns, respectively.
*/
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);
/**
* Set several elements in the specified row of the matrix with column
* indices as given by <tt>col_indices</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be inserted anyway or they should be
* filtered away. The default value is <tt>false</tt>, i.e., even zero
* values are inserted/replaced.
*/
void 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 to values given by <tt>values</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be inserted anyway or they should be
* filtered away. The default value is <tt>false</tt>, i.e., even zero
* values are inserted/replaced.
*/
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);
/**
* Add @p value to the element (<i>i,j</i>).
*
* 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 <tt>value</tt> is
* not a finite number an exception is thrown.
*/
void add (const size_type i,
const size_type j,
const PetscScalar value);
/**
* Add all elements given in a FullMatrix<double> into sparse matrix
* locations given by <tt>indices</tt>. In other words, this function adds
* the elements in <tt>full_matrix</tt> to the respective entries in
* calling matrix, using the local-to-global indexing specified by
* <tt>indices</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be added anyway or these should be
* filtered away and only non-zero data is added. The default value is
* <tt>true</tt>, i.e., zero values won't be added into the matrix.
*/
void add (const std::vector<size_type> &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 local-to-global indexing on
* rows and columns, respectively.
*/
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);
/**
* Set several elements in the specified row of the matrix with column
* indices as given by <tt>col_indices</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be added anyway or these should be
* filtered away and only non-zero data is added. The default value is
* <tt>true</tt>, i.e., zero values won't be added into the matrix.
*/
void add (const size_type row,
const std::vector<size_type> &col_indices,
const std::vector<PetscScalar> &values,
const bool elide_zero_values = true);
/**
* Add an array of values given by <tt>values</tt> 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 <tt>elide_zero_values</tt> can be used to
* specify whether zero values should be added anyway or these should be
* filtered away and only non-zero data is added. The default value is
* <tt>true</tt>, i.e., zero values won't be added into the matrix.
*/
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);
/**
* Remove all elements from this <tt>row</tt> 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 non-zero
* 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.
*/
void clear_row (const size_type row,
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.
*/
void clear_rows (const std::vector<size_type> &rows,
const PetscScalar new_diag_value = 0);
/**
* 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
* @ref GlossCompress "Compressing distributed objects"
* for more information.
*/
void compress (const VectorOperation::values operation);
/**
* Return the value of the entry (<i>i,j</i>). 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 @p 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 <tt>el()</tt>
* function.
*/
PetscScalar operator () (const size_type i,
const size_type j) const;
/**
* Return the value of the matrix entry (<i>i,j</i>). 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.
*/
PetscScalar el (const size_type i,
const size_type j) const;
/**
* Return the main diagonal element in the <i>i</i>th 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.
*/
PetscScalar diag_element (const size_type i) const;
/**
* Return the number of rows in this matrix.
*/
size_type m () const;
/**
* Return the number of columns in this matrix.
*/
size_type n () 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().
*/
size_type local_size () 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
* <tt>n=local_size()</tt>.
*/
std::pair<size_type, size_type>
local_range () const;
/**
* Return whether @p index is in the local range or not, see also
* local_range().
*/
bool in_local_range (const size_type index) const;
/**
* Return a reference to the MPI communicator object in use with this
* matrix. This function has to be implemented in derived classes.
*/
virtual const MPI_Comm &get_mpi_communicator () const = 0;
/**
* 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.
*/
size_type n_nonzero_elements () const;
/**
* Number of entries in a specific row.
*/
size_type row_length (const size_type row) const;
/**
* Return the l1-norm 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 l1-norm for vectors, i.e.
* $|Mv|_1\leq |M|_1 |v|_1$. (cf. Haemmerlin-Hoffmann: Numerische
* Mathematik)
*/
PetscReal l1_norm () const;
/**
* Return the linfty-norm 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 linfty-norm of vectors, i.e.
* $|Mv|_infty \leq |M|_infty |v|_infty$. (cf. Haemmerlin-Hoffmann:
* Numerische Mathematik)
*/
PetscReal linfty_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.
*/
PetscReal frobenius_norm () 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 @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.
*
* 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.
*/
PetscScalar matrix_norm_square (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 @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.
*
* 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.
*/
PetscScalar matrix_scalar_product (const VectorBase &u,
const VectorBase &v) const;
#if DEAL_II_PETSC_VERSION_GTE(3,1,0)
/**
* Return the trace of the matrix, i.e. the sum of all diagonal entries in
* the matrix.
*/
PetscScalar trace () const;
#endif
/**
* Multiply the entire matrix by a fixed factor.
*/
MatrixBase &operator *= (const PetscScalar factor);
/**
* Divide the entire matrix by a fixed factor.
*/
MatrixBase &operator /= (const PetscScalar factor);
/**
* Add the matrix @p other scaled by the factor @p factor to the current
* matrix.
*/
MatrixBase &add (const MatrixBase &other,
const PetscScalar factor);
/**
* Matrix-vector multiplication: let <i>dst = M*src</i> with <i>M</i>
* 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.
*/
void vmult (VectorBase &dst,
const VectorBase &src) const;
/**
* Matrix-vector multiplication: let <i>dst = M<sup>T</sup>*src</i> with
* <i>M</i> 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.
*/
void Tvmult (VectorBase &dst,
const VectorBase &src) const;
/**
* Adding Matrix-vector multiplication. Add <i>M*src</i> on <i>dst</i>
* with <i>M</i> 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.
*/
void vmult_add (VectorBase &dst,
const VectorBase &src) const;
/**
* Adding Matrix-vector multiplication. Add <i>M<sup>T</sup>*src</i> to
* <i>dst</i> with <i>M</i> 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.
*/
void Tvmult_add (VectorBase &dst,
const VectorBase &src) const;
/**
* Compute the residual of an equation <i>Mx=b</i>, where the residual is
* defined to be <i>r=b-Mx</i>. Write the residual into @p dst. The
* <i>l<sub>2</sub></i> norm of the residual vector is returned.
*
* Source <i>x</i> and destination <i>dst</i> 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.
*/
PetscScalar residual (VectorBase &dst,
const VectorBase &x,
const VectorBase &b) const;
/**
* Iterator starting at the first entry.
*/
const_iterator begin () const;
/**
* Final iterator.
*/
const_iterator end () const;
/**
* Iterator starting at the first entry of row @p 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
* <tt>end(r)</tt>. Note also that the iterator may not be dereferencable
* in that case.
*/
const_iterator begin (const size_type r) const;
/**
* Final iterator of row <tt>r</tt>. It points to the first element past
* the end of line @p r, or past the end of the entire sparsity pattern.
*
* Note that the end iterator is not necessarily dereferencable. This is
* in particular the case if it is the end iterator for the last row of a
* matrix.
*/
const_iterator end (const size_type r) 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 read-only operations into the
* matrix.
*/
operator Mat () const;
/**
* Make an in-place transpose of a matrix.
*/
void transpose ();
/**
* Test whether a matrix is symmetric. Default tolerance is
* $1000\times32$-bit machine precision.
*/
#if DEAL_II_PETSC_VERSION_LT(3,2,0)
PetscTruth
#else
PetscBool
#endif
is_symmetric (const double tolerance = 1.e-12);
/**
* Test whether a matrix is Hermitian, i.e. it is the complex conjugate of
* its transpose. Default tolerance is $1000\times32$-bit machine
* precision.
*/
#if DEAL_II_PETSC_VERSION_LT(3,2,0)
PetscTruth
#else
PetscBool
#endif
is_hermitian (const double tolerance = 1.e-12);
/**
* Print the PETSc matrix object values using PETSc internal matrix viewer
* function <tt>MatView</tt>. The default format prints the non- zero
* matrix elements. For other valid view formats, consult
* http://www.mcs.anl.gov/petsc/petsc-
* current/docs/manualpages/Mat/MatView.html
*/
void write_ascii (const PetscViewerFormat format = PETSC_VIEWER_DEFAULT);
/**
* Print the elements of a matrix to the given output stream.
*
* @param[in,out] out The output stream to which to write.
* @param[in] alternative_output This argument is ignored. It exists for
* compatibility with similar functions in other matrix classes.
*/
void print (std::ostream &out,
const bool alternative_output = false) const;
/**
* Returns the number bytes consumed by this matrix on this CPU.
*/
std::size_t memory_consumption() const;
/**
* Exception
*/
DeclException1 (ExcPETScError,
int,
<< "An error with error number " << arg1
<< " occurred while calling a PETSc function");
/**
* Exception
*/
DeclException0 (ExcSourceEqualsDestination);
/**
* Exception.
*/
DeclException2 (ExcWrongMode,
int, int,
<< "You tried to do a "
<< (arg1 == 1 ?
"'set'" :
(arg1 == 2 ?
"'add'" : "???"))
<< " operation but the matrix is currently in "
<< (arg2 == 1 ?
"'set'" :
(arg2 == 2 ?
"'add'" : "???"))
<< " mode. You first have to call 'compress()'.");
protected:
/**
* A generic matrix object in PETSc. The actual type, a sparse matrix, is
* set in the constructor.
*/
Mat matrix;
/**
* Store whether the last action was a write or add operation.
*/
VectorOperation::values last_action;
/**
* 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.
*/
void prepare_action(const VectorOperation::values new_action);
/**
* 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.
*/
void assert_is_compressed();
/**
* 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.
*/
void prepare_add();
/**
* Same as prepare_add() but prepare the matrix for setting elements if
* the representation of elements in this class requires such an
* operation.
*/
void prepare_set();
private:
/**
* purposefully not implemented
*/
MatrixBase(const MatrixBase &);
/**
* purposefully not implemented
*/
MatrixBase &operator=(const MatrixBase &);
/**
* An internal array of integer values that is used to store the column
* indices when adding/inserting local data into the (large) sparse
* matrix.
*/
std::vector<PetscInt> column_indices;
/**
* An internal array of double values that is used to store the column
* indices when adding/inserting local data into the (large) sparse
* matrix.
*/
std::vector<PetscScalar> column_values;
/**
* To allow calling protected prepare_add() and prepare_set().
*/
template <class> friend class dealii::BlockMatrixBase;
};
#ifndef DOXYGEN
// -------------------------- inline and template functions ----------------------
namespace MatrixIterators
{
inline
const_iterator::Accessor::
Accessor (const MatrixBase *matrix,
const size_type row,
const size_type index)
:
matrix(const_cast<MatrixBase *>(matrix)),
a_row(row),
a_index(index)
{
visit_present_row ();
}
inline
const_iterator::Accessor::
Accessor (const Accessor &a)
:
matrix(a.matrix),
a_row(a.a_row),
a_index(a.a_index),
colnum_cache (a.colnum_cache),
value_cache (a.value_cache)
{}
inline
const_iterator::Accessor::size_type
const_iterator::Accessor::row() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return a_row;
}
inline
const_iterator::Accessor::size_type
const_iterator::Accessor::column() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return (*colnum_cache)[a_index];
}
inline
const_iterator::Accessor::size_type
const_iterator::Accessor::index() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return a_index;
}
inline
PetscScalar
const_iterator::Accessor::value() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return (*value_cache)[a_index];
}
inline
const_iterator::
const_iterator(const MatrixBase *matrix,
const size_type row,
const size_type index)
:
accessor(matrix, row, index)
{}
inline
const_iterator &
const_iterator::operator++ ()
{
Assert (accessor.a_row < accessor.matrix->m(), ExcIteratorPastEnd());
++accessor.a_index;
// if at end of line: do one step, then
// cycle until we find a row with a
// nonzero number of entries
if (accessor.a_index >= accessor.colnum_cache->size())
{
accessor.a_index = 0;
++accessor.a_row;
while ((accessor.a_row < accessor.matrix->m())
&&
(accessor.matrix->row_length(accessor.a_row) == 0))
++accessor.a_row;
accessor.visit_present_row();
}
return *this;
}
inline
const_iterator
const_iterator::operator++ (int)
{
const const_iterator old_state = *this;
++(*this);
return old_state;
}
inline
const const_iterator::Accessor &
const_iterator::operator* () const
{
return accessor;
}
inline
const const_iterator::Accessor *
const_iterator::operator-> () const
{
return &accessor;
}
inline
bool
const_iterator::
operator == (const const_iterator &other) const
{
return (accessor.a_row == other.accessor.a_row &&
accessor.a_index == other.accessor.a_index);
}
inline
bool
const_iterator::
operator != (const const_iterator &other) const
{
return ! (*this == other);
}
inline
bool
const_iterator::
operator < (const const_iterator &other) const
{
return (accessor.row() < other.accessor.row() ||
(accessor.row() == other.accessor.row() &&
accessor.index() < other.accessor.index()));
}
}
// Inline the set() and add()
// functions, since they will be
// called frequently, and the
// compiler can optimize away
// some unnecessary loops when
// the sizes are given at
// compile time.
inline
void
MatrixBase::set (const size_type i,
const size_type j,
const PetscScalar value)
{
AssertIsFinite(value);
set (i, 1, &j, &value, false);
}
inline
void
MatrixBase::set (const std::vector<size_type> &indices,
const FullMatrix<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (indices.size() == values.m(),
ExcDimensionMismatch(indices.size(), values.m()));
Assert (values.m() == values.n(), ExcNotQuadratic());
for (size_type i=0; i<indices.size(); ++i)
set (indices[i], indices.size(), &indices[0], &values(i,0),
elide_zero_values);
}
inline
void
MatrixBase::set (const std::vector<size_type> &row_indices,
const std::vector<size_type> &col_indices,
const FullMatrix<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (row_indices.size() == values.m(),
ExcDimensionMismatch(row_indices.size(), values.m()));
Assert (col_indices.size() == values.n(),
ExcDimensionMismatch(col_indices.size(), values.n()));
for (size_type i=0; i<row_indices.size(); ++i)
set (row_indices[i], col_indices.size(), &col_indices[0], &values(i,0),
elide_zero_values);
}
inline
void
MatrixBase::set (const size_type row,
const std::vector<size_type> &col_indices,
const std::vector<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (col_indices.size() == values.size(),
ExcDimensionMismatch(col_indices.size(), values.size()));
set (row, col_indices.size(), &col_indices[0], &values[0],
elide_zero_values);
}
inline
void
MatrixBase::set (const size_type row,
const size_type n_cols,
const size_type *col_indices,
const PetscScalar *values,
const bool elide_zero_values)
{
(void)elide_zero_values;
prepare_action(VectorOperation::insert);
const PetscInt petsc_i = row;
PetscInt *col_index_ptr;
PetscScalar const *col_value_ptr;
int n_columns;
// If we don't elide zeros, the pointers are already available...
#ifndef PETSC_USE_64BIT_INDICES
if (elide_zero_values == false)
{
col_index_ptr = (int *)col_indices;
col_value_ptr = values;
n_columns = n_cols;
}
else
#endif
{
// Otherwise, extract nonzero values in each row and get the
// respective index.
if (column_indices.size() < n_cols)
{
column_indices.resize(n_cols);
column_values.resize(n_cols);
}
n_columns = 0;
for (size_type j=0; j<n_cols; ++j)
{
const PetscScalar value = values[j];
AssertIsFinite(value);
if (value != PetscScalar())
{
column_indices[n_columns] = col_indices[j];
column_values[n_columns] = value;
n_columns++;
}
}
Assert(n_columns <= (int)n_cols, ExcInternalError());
col_index_ptr = &column_indices[0];
col_value_ptr = &column_values[0];
}
const int ierr
= MatSetValues (matrix, 1, &petsc_i, n_columns, col_index_ptr,
col_value_ptr, INSERT_VALUES);
AssertThrow (ierr == 0, ExcPETScError(ierr));
}
inline
void
MatrixBase::add (const size_type i,
const size_type j,
const PetscScalar value)
{
AssertIsFinite(value);
if (value == PetscScalar())
{
// we have to check after using Insert/Add in any case to be
// consistent with the MPI communication model (see the comments in
// the documentation of TrilinosWrappers::Vector), but we can save
// some work if the addend is zero. However, these actions are done
// in case we pass on to the other function.
prepare_action(VectorOperation::add);
return;
}
else
add (i, 1, &j, &value, false);
}
inline
void
MatrixBase::add (const std::vector<size_type> &indices,
const FullMatrix<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (indices.size() == values.m(),
ExcDimensionMismatch(indices.size(), values.m()));
Assert (values.m() == values.n(), ExcNotQuadratic());
for (size_type i=0; i<indices.size(); ++i)
add (indices[i], indices.size(), &indices[0], &values(i,0),
elide_zero_values);
}
inline
void
MatrixBase::add (const std::vector<size_type> &row_indices,
const std::vector<size_type> &col_indices,
const FullMatrix<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (row_indices.size() == values.m(),
ExcDimensionMismatch(row_indices.size(), values.m()));
Assert (col_indices.size() == values.n(),
ExcDimensionMismatch(col_indices.size(), values.n()));
for (size_type i=0; i<row_indices.size(); ++i)
add (row_indices[i], col_indices.size(), &col_indices[0], &values(i,0),
elide_zero_values);
}
inline
void
MatrixBase::add (const size_type row,
const std::vector<size_type> &col_indices,
const std::vector<PetscScalar> &values,
const bool elide_zero_values)
{
Assert (col_indices.size() == values.size(),
ExcDimensionMismatch(col_indices.size(), values.size()));
add (row, col_indices.size(), &col_indices[0], &values[0],
elide_zero_values);
}
inline
void
MatrixBase::add (const size_type row,
const size_type n_cols,
const size_type *col_indices,
const PetscScalar *values,
const bool elide_zero_values,
const bool /*col_indices_are_sorted*/)
{
(void)elide_zero_values;
prepare_action(VectorOperation::add);
const PetscInt petsc_i = row;
PetscInt *col_index_ptr;
PetscScalar const *col_value_ptr;
int n_columns;
// If we don't elide zeros, the pointers are already available...
#ifndef PETSC_USE_64BIT_INDICES
if (elide_zero_values == false)
{
col_index_ptr = (int *)col_indices;
col_value_ptr = values;
n_columns = n_cols;
}
else
#endif
{
// Otherwise, extract nonzero values in each row and get the
// respective index.
if (column_indices.size() < n_cols)
{
column_indices.resize(n_cols);
column_values.resize(n_cols);
}
n_columns = 0;
for (size_type j=0; j<n_cols; ++j)
{
const PetscScalar value = values[j];
AssertIsFinite(value);
if (value != PetscScalar())
{
column_indices[n_columns] = col_indices[j];
column_values[n_columns] = value;
n_columns++;
}
}
Assert(n_columns <= (int)n_cols, ExcInternalError());
col_index_ptr = &column_indices[0];
col_value_ptr = &column_values[0];
}
const int ierr
= MatSetValues (matrix, 1, &petsc_i, n_columns, col_index_ptr,
col_value_ptr, ADD_VALUES);
AssertThrow (ierr == 0, ExcPETScError(ierr));
}
inline
PetscScalar
MatrixBase::operator() (const size_type i,
const size_type j) const
{
return el(i,j);
}
inline
MatrixBase::const_iterator
MatrixBase::begin() const
{
return const_iterator(this, 0, 0);
}
inline
MatrixBase::const_iterator
MatrixBase::end() const
{
return const_iterator(this, m(), 0);
}
inline
MatrixBase::const_iterator
MatrixBase::begin(const size_type r) const
{
Assert (r < m(), ExcIndexRange(r, 0, m()));
if (row_length(r) > 0)
return const_iterator(this, r, 0);
else
return end (r);
}
inline
MatrixBase::const_iterator
MatrixBase::end(const size_type r) const
{
Assert (r < m(), ExcIndexRange(r, 0, m()));
// place the iterator on the first entry
// past this line, or at the end of the
// matrix
for (size_type i=r+1; i<m(); ++i)
if (row_length(i) > 0)
return const_iterator(this, i, 0);
// if there is no such line, then take the
// end iterator of the matrix
return end();
}
inline
bool
MatrixBase::in_local_range (const size_type index) const
{
PetscInt begin, end;
const int ierr = MatGetOwnershipRange (static_cast<const Mat &>(matrix),
&begin, &end);
AssertThrow (ierr == 0, ExcPETScError(ierr));
return ((index >= static_cast<size_type>(begin)) &&
(index < static_cast<size_type>(end)));
}
inline
void
MatrixBase::prepare_action(const VectorOperation::values new_action)
{
if (last_action == VectorOperation::unknown)
last_action = new_action;
Assert (last_action == new_action, ExcWrongMode (last_action, new_action));
}
inline
void
MatrixBase::assert_is_compressed ()
{
// compress() sets the last action to none, which allows us to check if there
// are pending add/insert operations:
AssertThrow (last_action == VectorOperation::unknown,
ExcMessage("Error: missing compress() call."));
}
inline
void
MatrixBase::prepare_add()
{
prepare_action(VectorOperation::add);
}
inline
void
MatrixBase::prepare_set()
{
prepare_action(VectorOperation::insert);
}
#endif // DOXYGEN
}
DEAL_II_NAMESPACE_CLOSE
#endif // DEAL_II_WITH_PETSC
/*---------------------------- petsc_matrix_base.h ---------------------------*/
#endif
/*---------------------------- petsc_matrix_base.h ---------------------------*/
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