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// $Id: petsc_matrix_base.h 20745 2010-03-07 12:50:06Z young $
// Version: $Name$
//
// Copyright (C) 2004, 2005, 2006, 2007, 2008, 2009 by the deal.II authors
//
// This file is subject to QPL and may not be distributed
// without copyright and license information. Please refer
// to the file deal.II/doc/license.html for the text and
// further information on this license.
//
//---------------------------------------------------------------------------
#ifndef __deal2__petsc_matrix_base_h
#define __deal2__petsc_matrix_base_h
#include <base/config.h>
#ifdef DEAL_II_USE_PETSC
# include <base/subscriptor.h>
# include <lac/full_matrix.h>
# include <lac/exceptions.h>
# include <petscmat.h>
# include <base/std_cxx1x/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
{
/**
* STL conforming iterator. 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:
/**
* Constructor. Since we use
* accessors only for read
* access, a const matrix
* pointer is sufficient.
*/
Accessor (const MatrixBase *matrix,
const unsigned int row,
const unsigned int index);
/**
* Row number of the element
* represented by this
* object.
*/
unsigned int row() const;
/**
* Index in row of the element
* represented by this
* object.
*/
unsigned int index() const;
/**
* Column number of the
* element represented by
* this object.
*/
unsigned int 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.
*/
unsigned int a_row;
/**
* Current index in row.
*/
unsigned int 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_cxx1x::shared_ptr<const std::vector<unsigned int> > colnum_cache;
/**
* Similar cache for the values
* of this row.
*/
std_cxx1x::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:
/**
* Constructor. Create an iterator
* into the matrix @p matrix for the
* given row and the index within it.
*/
const_iterator (const MatrixBase *matrix,
const unsigned int row,
const unsigned int 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 exchangable. 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 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 unsigned int i,
const unsigned int 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<unsigned int> &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<unsigned int> &row_indices,
const std::vector<unsigned int> &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 unsigned int row,
const std::vector<unsigned int> &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 unsigned int row,
const unsigned int n_cols,
const unsigned int *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 unsigned int i,
const unsigned int 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<unsigned int> &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<unsigned int> &row_indices,
const std::vector<unsigned int> &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 unsigned int row,
const std::vector<unsigned int> &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 unsigned int row,
const unsigned int n_cols,
const unsigned int *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 unsigned int 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<unsigned int> &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.
* more information.
*/
void compress ();
/**
* 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 unsigned int i,
const unsigned int 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 unsigned int i,
const unsigned int 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 unsigned int i) const;
/**
* Return the number of rows in this
* matrix.
*/
unsigned int m () const;
/**
* Return the number of columns in this
* matrix.
*/
unsigned int 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().
*/
unsigned int 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<unsigned int, unsigned int>
local_range () const;
/**
* Return whether @p index is
* in the local range or not,
* see also local_range().
*/
bool in_local_range (const unsigned int 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.
*/
unsigned int n_nonzero_elements () const;
/**
* Number of entries in a specific row.
*/
unsigned int row_length (const unsigned int 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;
/**
* 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);
/**
* 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;
/**
* 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;
/**
* 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;
/**
* STL-like iterator with the
* first entry.
*/
const_iterator begin () const;
/**
* Final iterator.
*/
const_iterator end () const;
/**
* STL-like iterator with 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 unsigned int 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 unsigned int 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 const Mat () const;
/**
* Make an in-place transpose of a
* matrix.
*/
void transpose ();
/**
* Test whether a matrix is symmetric.
* Default tolerance is zero.
*/
PetscTruth is_symmetric (const double tol = 0.0);
#if DEAL_II_PETSC_VERSION_GTE(2,3,0)
/**
* Test whether a matrix is Hermitian,
* i.e. it is the complex conjugate
* of its transpose. Default tolerance
* is zero.
*/
PetscTruth is_hermitian (const double tol = 0.0);
#endif
/*
* Abstract PETSc object that helps view
* in ASCII other PETSc objects. Currently
* this function simply writes non-zero
* elements of a matrix to the terminal.
*/
void write_ascii ();
/**
* Returns the number bytes consumed
* by this matrix on this CPU.
*/
unsigned int memory_consumption() const;
/**
* Exception
*/
DeclException1 (ExcPETScError,
int,
<< "An error with error number " << arg1
<< " occured while calling a PETSc function");
/**
* Exception
*/
DeclException0 (ExcSourceEqualsDestination);
protected:
/**
* A generic matrix object in
* PETSc. The actual type, a sparse
* matrix, is set in the constructor.
*/
Mat matrix;
/**
* PETSc doesn't allow to mix additions
* to matrix entries and overwriting
* them (to make synchronisation of
* parallel computations
* simpler). Since the interface of the
* existing classes don't support the
* notion of not interleaving things,
* we have to emulate this
* ourselves. The way we do it is to,
* for each access operation, store
* whether it is an insertion or an
* addition. If the previous one was of
* different type, then we first have
* to flush the PETSc buffers;
* otherwise, we can simply go on.
*
* The following structure and variable
* declare and store the previous
* state.
*/
struct LastAction
{
enum Values { none, insert, add };
};
/**
* Store whether the last action was a
* write or add operation.
*/
LastAction::Values last_action;
/**
* Flush buffers on all CPUs when
* switching between inserting and
* adding to elements, no-op otherwise.
* Should be called from all internal
* functions accessing matrix elements.
*/
void prepare_action(const LastAction::Values new_action);
/**
* 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:
/**
* An internal array of integer
* values that is used to store the
* column indices when
* adding/inserting local data into
* the (large) sparse matrix.
*/
#ifdef PETSC_USE_64BIT_INDICES
std::vector<PetscInt> column_indices;
#else
std::vector<int> column_indices;
#endif
/**
* 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 unsigned int row,
const unsigned int index)
:
matrix(const_cast<MatrixBase*>(matrix)),
a_row(row),
a_index(index)
{
visit_present_row ();
}
inline
unsigned int
const_iterator::Accessor::row() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return a_row;
}
inline
unsigned int
const_iterator::Accessor::column() const
{
Assert (a_row < matrix->m(), ExcBeyondEndOfMatrix());
return (*colnum_cache)[a_index];
}
inline
unsigned int
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 unsigned int row,
const unsigned int 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 unsigned int i,
const unsigned int j,
const PetscScalar value)
{
Assert (numbers::is_finite(value),
ExcMessage("The given value is not finite but either "
"infinite or Not A Number (NaN)"));
set (i, 1, &j, &value, false);
}
inline
void
MatrixBase::set (const std::vector<unsigned int> &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 (unsigned int 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<unsigned int> &row_indices,
const std::vector<unsigned int> &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 (unsigned int 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 unsigned int row,
const std::vector<unsigned int> &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 unsigned int row,
const unsigned int n_cols,
const unsigned int *col_indices,
const PetscScalar *values,
const bool elide_zero_values)
{
prepare_action(LastAction::insert);
#ifdef PETSC_USE_64BIT_INDICES
const PetscInt petsc_i = row;
PetscInt * col_index_ptr;
#else
const int petsc_i = row;
int * col_index_ptr;
#endif
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 (unsigned int j=0; j<n_cols; ++j)
{
const PetscScalar value = values[j];
Assert (numbers::is_finite(value),
ExcMessage("The given value is not finite but either "
"infinite or Not A Number (NaN)"));
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 unsigned int i,
const unsigned int j,
const PetscScalar value)
{
Assert (numbers::is_finite(value),
ExcMessage("The given value is not finite but either "
"infinite or Not A Number (NaN)"));
if (value == PetscScalar())
{
// we have to do checkings on 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(LastAction::add);
return;
}
else
add (i, 1, &j, &value, false);
}
inline
void
MatrixBase::add (const std::vector<unsigned int> &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 (unsigned int 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<unsigned int> &row_indices,
const std::vector<unsigned int> &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 (unsigned int 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 unsigned int row,
const std::vector<unsigned int> &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 unsigned int row,
const unsigned int n_cols,
const unsigned int *col_indices,
const PetscScalar *values,
const bool elide_zero_values,
const bool /*col_indices_are_sorted*/)
{
prepare_action(LastAction::add);
#ifdef PETSC_USE_64BIT_INDICES
const PetscInt petsc_i = row;
PetscInt * col_index_ptr;
#else
const int petsc_i = row;
int * col_index_ptr;
#endif
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 (unsigned int j=0; j<n_cols; ++j)
{
const PetscScalar value = values[j];
Assert (numbers::is_finite(value),
ExcMessage("The given value is not finite but either "
"infinite or Not A Number (NaN)"));
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);
Assert (ierr == 0, ExcPETScError(ierr));
}
inline
PetscScalar
MatrixBase::operator() (const unsigned int i,
const unsigned int 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 unsigned int 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 unsigned int 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 (unsigned int 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 unsigned int index) const
{
#ifdef PETSC_USE_64BIT_INDICES
PetscInt begin, end;
#else
int begin, end;
#endif
const int ierr = MatGetOwnershipRange (static_cast<const Mat &>(matrix),
&begin, &end);
AssertThrow (ierr == 0, ExcPETScError(ierr));
return ((index >= static_cast<unsigned int>(begin)) &&
(index < static_cast<unsigned int>(end)));
}
inline
void
MatrixBase::prepare_action(const LastAction::Values new_action)
{
// flush PETSc buffers when switching
// actions, otherwise just return.
if (last_action == new_action) return;
int ierr;
ierr = MatAssemblyBegin(matrix, MAT_FLUSH_ASSEMBLY);
AssertThrow (ierr == 0, ExcPETScError(ierr));
ierr = MatAssemblyEnd(matrix, MAT_FLUSH_ASSEMBLY);
AssertThrow (ierr == 0, ExcPETScError(ierr));
last_action = new_action;
}
inline
void
MatrixBase::prepare_add()
{
prepare_action(LastAction::add);
}
inline
void
MatrixBase::prepare_set()
{
prepare_action(LastAction::insert);
}
#endif // DOXYGEN
}
DEAL_II_NAMESPACE_CLOSE
#endif // DEAL_II_USE_PETSC
/*---------------------------- petsc_matrix_base.h ---------------------------*/
#endif
/*---------------------------- petsc_matrix_base.h ---------------------------*/
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