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// $Id: matrix_out.h 31932 2013-12-08 02:15:54Z heister $
//
// Copyright (C) 2001 - 2013 by the deal.II authors
//
// This file is part of the deal.II library.
//
// The deal.II library is free software; you can use it, redistribute
// it, and/or modify it under the terms of the GNU Lesser General
// Public License as published by the Free Software Foundation; either
// version 2.1 of the License, or (at your option) any later version.
// The full text of the license can be found in the file LICENSE at
// the top level of the deal.II distribution.
//
// ---------------------------------------------------------------------
#ifndef __deal2__matrix_out_h
#define __deal2__matrix_out_h
#include <deal.II/base/config.h>
#include <deal.II/base/data_out_base.h>
#include <deal.II/lac/sparse_matrix.h>
#include <deal.II/lac/block_sparse_matrix.h>
DEAL_II_NAMESPACE_OPEN
/**
* Output a matrix in graphical form using the generic format
* independent output routines of the base class. The matrix is
* converted into a list of patches on a 2d domain where the height is
* given by the elements of the matrix. The functions of the base
* class can then write this "mountain representation" of the matrix
* in a variety of graphical output formats. The coordinates of the
* matrix output are that the columns run with increasing x-axis, as
* usual, starting from zero, while the rows run into the negative
* y-axis, also starting from zero. Note that due to some internal
* restrictions, this class can only output one matrix at a time,
* i.e. it can not take advantage of the multiple dataset capabilities
* of the base class.
*
* A typical usage of this class would be as follows:
* @code
* FullMatrix<double> M;
* ... // fill matrix M with some values
*
* // now write out M:
* MatrixOut matrix_out;
* std::ofstream out ("M.gnuplot");
* matrix_out.build_patches (M, "M");
* matrix_out.write_gnuplot (out);
* @endcode
* Of course, you can as well choose a different graphical output
* format. Also, this class supports any matrix, not only of type
* FullMatrix, as long as it satisfies a number of requirements,
* stated with the member functions of this class.
*
* The generation of patches through the build_patches() function
* can be modified by giving it an object holding certain flags. See
* the documentation of the members of the Options class for a
* description of these flags.
*
*
* <h3>Internals</h3>
*
* To avoid a compiler error in Sun's Forte compiler, we derive
* privately from DataOutBase. Since the base class
* DataOutInterface does so as well, this does no harm, but
* calms the compiler which is suspecting an access control conflict
* otherwise. Testcase here:
* @code
* template <typename T> class V {};
*
* struct B1 {
* template <int dim> struct X {
* int i[dim];
* };
* };
*
* struct B2 : private B1 {};
*
* struct D : public B2, private B1 {
* ~D () {};
* typedef B1::X<2> X;
* V<X> x;
* };
*
* D d;
* @endcode
*
* @ingroup output
* @author Wolfgang Bangerth, 2001
*/
class MatrixOut : public DataOutInterface<2,2>
{
public:
/**
* Declare type for container size.
*/
typedef types::global_dof_index size_type;
/**
* Class holding various
* variables which are used to
* modify the output of the
* MatrixOut class.
*/
struct Options
{
/**
* If @p true, only show the
* absolute values of the
* matrix entries, rather
* than their true values
* including the
* sign. Default value is
* @p false.
*/
bool show_absolute_values;
/**
* If larger than one, do not
* show each element of the
* matrix, but rather an
* average over a number of
* entries. The number of
* output patches is
* accordingly smaller. This
* flag determines how large
* each shown block shall be
* (in rows/columns). For
* example, if it is two,
* then always four entries
* are collated into one.
*
* Default value is one.
*/
unsigned int block_size;
/**
* If true, plot
* discontinuous patches, one
* for each entry.
*/
bool discontinuous;
/**
* Default constructor. Set
* all elements of this
* structure to their default
* values.
*/
Options (const bool show_absolute_values = false,
const unsigned int block_size = 1,
const bool discontinuous = false);
};
/**
* Destructor. Declared in order
* to make it virtual.
*/
virtual ~MatrixOut ();
/**
* Generate a list of patches
* from the given matrix and use
* the given string as the name
* of the data set upon writing
* to a file. Once patches have
* been built, you can use the
* functions of the base class to
* write the data into a files,
* using one of the supported
* output formats.
*
* You may give a structure
* holding various options. See
* the description of the fields
* of this structure for more
* information.
*
* Note that this function
* requires that we can extract
* elements of the matrix, which
* is done using the
* get_element() function
* declared below. By adding
* specializations, you can
* extend this class to other
* matrix classes which are not
* presently
* supported. Furthermore, we
* need to be able to extract the
* size of the matrix, for which
* we assume that the matrix type
* offers member functions
* <tt>m()</tt> and <tt>n()</tt>, which
* return the number of rows and
* columns, respectively.
*/
template <class Matrix>
void build_patches (const Matrix &matrix,
const std::string &name,
const Options options = Options(false, 1, false));
private:
/**
* Abbreviate the somewhat
* lengthy name for the dealii::DataOutBase::Patch
* class.
*
* Note that we have to indicate the
* global scope in front of DataOutBase,
* since otherwise the C++ rules specify
* that this here indicates the
* DataOutBase base class of this
* class. Since that is a private base
* class, we cannot access its members,
* and so access to the local Patch type
* would be forbidden.
*/
typedef dealii::DataOutBase::Patch<2,2> Patch;
/**
* This is a list of patches that
* is created each time
* build_patches() is
* called. These patches are used
* in the output routines of the
* base classes.
*/
std::vector<Patch> patches;
/**
* Name of the matrix to be
* written.
*/
std::string name;
/**
* Function by which the base
* class's functions get to know
* what patches they shall write
* to a file.
*/
virtual const std::vector<Patch> &
get_patches () const;
/**
* Virtual function through which
* the names of data sets are
* obtained by the output
* functions of the base class.
*/
virtual std::vector<std::string> get_dataset_names () const;
/**
* Return the element with given
* indices of a sparse matrix.
*/
template <typename number>
static double get_element (const SparseMatrix<number> &matrix,
const size_type i,
const size_type j);
/**
* Return the element with given
* indices of a block sparse
* matrix.
*/
template <typename number>
static double get_element (const BlockSparseMatrix<number> &matrix,
const size_type i,
const size_type j);
/**
* Return the element with given
* indices from any matrix type
* for which no specialization of
* this function was declared
* above. This will call
* <tt>operator()</tt> on the matrix.
*/
template <class Matrix>
static double get_element (const Matrix &matrix,
const size_type i,
const size_type j);
/**
* Get the value of the matrix at
* gridpoint <tt>(i,j)</tt>. Depending
* on the given flags, this can
* mean different things, for
* example if only absolute
* values shall be shown then the
* absolute value of the matrix
* entry is taken. If the block
* size is larger than one, then
* an average of several matrix
* entries is taken.
*/
template <class Matrix>
static double get_gridpoint_value (const Matrix &matrix,
const size_type i,
const size_type j,
const Options &options);
};
/* ---------------------- Template and inline functions ------------- */
template <typename number>
inline
double
MatrixOut::get_element (const SparseMatrix<number> &matrix,
const size_type i,
const size_type j)
{
return matrix.el(i,j);
}
template <typename number>
inline
double
MatrixOut::get_element (const BlockSparseMatrix<number> &matrix,
const size_type i,
const size_type j)
{
return matrix.el(i,j);
}
template <class Matrix>
inline
double
MatrixOut::get_element (const Matrix &matrix,
const size_type i,
const size_type j)
{
return matrix(i,j);
}
template <class Matrix>
inline
double
MatrixOut::get_gridpoint_value (const Matrix &matrix,
const size_type i,
const size_type j,
const Options &options)
{
// special case if block size is
// one since we then don't need all
// that loop overhead
if (options.block_size == 1)
{
if (options.show_absolute_values == true)
return std::fabs(get_element (matrix, i, j));
else
return get_element (matrix, i, j);
}
// if blocksize greater than one,
// then compute average of elements
double average = 0;
size_type n_elements = 0;
for (size_type row=i*options.block_size;
row < std::min(size_type(matrix.m()),
size_type((i+1)*options.block_size)); ++row)
for (size_type col=j*options.block_size;
col < std::min(size_type(matrix.m()),
size_type((j+1)*options.block_size)); ++col, ++n_elements)
if (options.show_absolute_values == true)
average += std::fabs(get_element (matrix, row, col));
else
average += get_element (matrix, row, col);
average /= n_elements;
return average;
}
template <class Matrix>
void
MatrixOut::build_patches (const Matrix &matrix,
const std::string &name,
const Options options)
{
size_type
gridpoints_x = (matrix.n() / options.block_size
+
(matrix.n() % options.block_size != 0 ? 1 : 0)),
gridpoints_y = (matrix.m() / options.block_size
+
(matrix.m() % options.block_size != 0 ? 1 : 0));
// If continuous, the number of
// plotted patches is matrix size-1
if (!options.discontinuous)
{
--gridpoints_x;
--gridpoints_y;
}
// first clear old data and set it
// to virgin state
patches.clear ();
patches.resize ((gridpoints_x) * (gridpoints_y));
// now build the patches
size_type index=0;
for (size_type i=0; i<gridpoints_y; ++i)
for (size_type j=0; j<gridpoints_x; ++j, ++index)
{
// within each patch, order
// the points in such a way
// that if some graphical
// output program (such as
// gnuplot) plots the
// quadrilaterals as two
// triangles, then the
// diagonal of the
// quadrilateral which cuts
// it into the two printed
// triangles is parallel to
// the diagonal of the
// matrix, rather than
// perpendicular to it. this
// has the advantage that,
// for example, the unit
// matrix is plotted as a
// straight rim, rather than
// as a series of bumps and
// valleys along the diagonal
patches[index].vertices[0](0) = j;
patches[index].vertices[0](1) = static_cast<signed int>(-i);
patches[index].vertices[1](0) = j;
patches[index].vertices[1](1) = static_cast<signed int>(-i-1);
patches[index].vertices[2](0) = j+1;
patches[index].vertices[2](1) = static_cast<signed int>(-i);
patches[index].vertices[3](0) = j+1;
patches[index].vertices[3](1) = static_cast<signed int>(-i-1);
// next scale all the patch
// coordinates by the block
// size, to get original
// coordinates
for (unsigned int v=0; v<4; ++v)
patches[index].vertices[v] *= options.block_size;
patches[index].n_subdivisions = 1;
patches[index].data.reinit (1,4);
if (options.discontinuous)
{
patches[index].data(0,0) = get_gridpoint_value(matrix, i, j, options);
patches[index].data(0,1) = get_gridpoint_value(matrix, i, j, options);
patches[index].data(0,2) = get_gridpoint_value(matrix, i, j, options);
patches[index].data(0,3) = get_gridpoint_value(matrix, i, j, options);
}
else
{
patches[index].data(0,0) = get_gridpoint_value(matrix, i, j, options);
patches[index].data(0,1) = get_gridpoint_value(matrix, i+1, j, options);
patches[index].data(0,2) = get_gridpoint_value(matrix, i, j+1, options);
patches[index].data(0,3) = get_gridpoint_value(matrix, i+1, j+1, options);
}
};
// finally set the name
this->name = name;
}
/*---------------------------- matrix_out.h ---------------------------*/
DEAL_II_NAMESPACE_CLOSE
#endif
/*---------------------------- matrix_out.h ---------------------------*/
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