MFEM  v4.1.0 Finite element discretization library
matrix.hpp
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1 // Copyright (c) 2010-2020, Lawrence Livermore National Security, LLC. Produced
3 // LICENSE and NOTICE for details. LLNL-CODE-806117.
4 //
5 // This file is part of the MFEM library. For more information and source code
6 // availability visit https://mfem.org.
7 //
8 // MFEM is free software; you can redistribute it and/or modify it under the
9 // terms of the BSD-3 license. We welcome feedback and contributions, see file
10 // CONTRIBUTING.md for details.
11
12 #ifndef MFEM_MATRIX
13 #define MFEM_MATRIX
14
15 #include "../general/array.hpp"
16 #include "../general/globals.hpp"
17 #include "operator.hpp"
18
19 namespace mfem
20 {
21
22 // Abstract data types matrix, inverse matrix
23
24 class MatrixInverse;
25
26 /// Abstract data type matrix
27 class Matrix : public Operator
28 {
29  friend class MatrixInverse;
30 public:
31  //// Defines matrix diagonal policy upon elimination of rows and/or columns.
33  {
34  DIAG_ZERO, ///< Set the diagonal value to zero
35  DIAG_ONE, ///< Set the diagonal value to one
36  DIAG_KEEP ///< Keep the diagonal value
37  };
38
39  /// Creates a square matrix of size s.
40  explicit Matrix(int s) : Operator(s) { }
41
42  /// Creates a matrix of the given height and width.
43  explicit Matrix(int h, int w) : Operator(h, w) { }
44
45  /// Returns whether the matrix is a square matrix.
46  bool IsSquare() const { return (height == width); };
47
48  /// Returns reference to a_{ij}.
49  virtual double &Elem(int i, int j) = 0;
50
51  /// Returns constant reference to a_{ij}.
52  virtual const double &Elem(int i, int j) const = 0;
53
54  /// Returns a pointer to (an approximation) of the matrix inverse.
55  virtual MatrixInverse *Inverse() const = 0;
56
57  /// Finalizes the matrix initialization.
58  virtual void Finalize(int) { }
59
60  /// Prints matrix to stream out.
61  virtual void Print (std::ostream & out = mfem::out, int width_ = 4) const;
62
63  /// Destroys matrix.
64  virtual ~Matrix() { }
65 };
66
67
68 /// Abstract data type for matrix inverse
69 class MatrixInverse : public Solver
70 {
71 public:
73
74  /// Creates approximation of the inverse of square matrix
75  MatrixInverse(const Matrix &mat)
76  : Solver(mat.height, mat.width) { }
77 };
78
79 /// Abstract data type for sparse matrices
81 {
82 public:
83  /// Creates a square matrix of the given size.
84  explicit AbstractSparseMatrix(int s = 0) : Matrix(s) { }
85
86  /// Creates a matrix of the given height and width.
87  explicit AbstractSparseMatrix(int h, int w) : Matrix(h, w) { }
88
89  /// Returns the number of non-zeros in a matrix
90  virtual int NumNonZeroElems() const = 0;
91
92  /// Gets the columns indexes and values for row *row*.
93  /** Returns:
94  - 0 if @a cols and @a srow are copies of the values in the matrix.
95  - 1 if @a cols and @a srow are views of the values in the matrix. */
96  virtual int GetRow(const int row, Array<int> &cols, Vector &srow) const = 0;
97
98  /** @brief If the matrix is square, this method will place 1 on the diagonal
99  (i,i) if row i has "almost" zero l1-norm.
100
101  If entry (i,i) does not belong to the sparsity pattern of A, then an
102  error will occur. */
103  virtual void EliminateZeroRows(const double threshold = 1e-12) = 0;
104
105  /// Matrix-Vector Multiplication y = A*x
106  virtual void Mult(const Vector &x, Vector &y) const = 0;
107  /// Matrix-Vector Multiplication y = y + val*A*x
108  virtual void AddMult(const Vector &x, Vector &y,
109  const double val = 1.) const = 0;
110  /// MatrixTranspose-Vector Multiplication y = A'*x
111  virtual void MultTranspose(const Vector &x, Vector &y) const = 0;
112  /// MatrixTranspose-Vector Multiplication y = y + val*A'*x
113  virtual void AddMultTranspose(const Vector &x, Vector &y,
114  const double val = 1.) const = 0;
115
116  /// Destroys AbstractSparseMatrix.
117  virtual ~AbstractSparseMatrix() { }
118 };
119
120 }
121
122 #endif
virtual void Finalize(int)
Finalizes the matrix initialization.
Definition: matrix.hpp:58
virtual MatrixInverse * Inverse() const =0
Returns a pointer to (an approximation) of the matrix inverse.
Set the diagonal value to zero.
Definition: matrix.hpp:34
virtual ~AbstractSparseMatrix()
Destroys AbstractSparseMatrix.
Definition: matrix.hpp:117
Abstract data type for sparse matrices.
Definition: matrix.hpp:80
virtual void AddMult(const Vector &x, Vector &y, const double val=1.) const =0
Matrix-Vector Multiplication y = y + val*A*x.
Abstract data type for matrix inverse.
Definition: matrix.hpp:69
virtual void Print(std::ostream &out=mfem::out, int width_=4) const
Prints matrix to stream out.
Definition: matrix.cpp:22
virtual int NumNonZeroElems() const =0
Returns the number of non-zeros in a matrix.
AbstractSparseMatrix(int h, int w)
Creates a matrix of the given height and width.
Definition: matrix.hpp:87
virtual void MultTranspose(const Vector &x, Vector &y) const =0
MatrixTranspose-Vector Multiplication y = A&#39;*x.
bool IsSquare() const
Returns whether the matrix is a square matrix.
Definition: matrix.hpp:46
Matrix(int h, int w)
Creates a matrix of the given height and width.
Definition: matrix.hpp:43
Keep the diagonal value.
Definition: matrix.hpp:36
virtual ~Matrix()
Destroys matrix.
Definition: matrix.hpp:64
Abstract data type matrix.
Definition: matrix.hpp:27
virtual double & Elem(int i, int j)=0
Returns reference to a_{ij}.
virtual int GetRow(const int row, Array< int > &cols, Vector &srow) const =0
Gets the columns indexes and values for row row.
virtual void Mult(const Vector &x, Vector &y) const =0
Matrix-Vector Multiplication y = A*x.
MatrixInverse(const Matrix &mat)
Creates approximation of the inverse of square matrix.
Definition: matrix.hpp:75
Set the diagonal value to one.
Definition: matrix.hpp:35
virtual void EliminateZeroRows(const double threshold=1e-12)=0
If the matrix is square, this method will place 1 on the diagonal (i,i) if row i has &quot;almost&quot; zero l1...
int height
Dimension of the output / number of rows in the matrix.
Definition: operator.hpp:27
Matrix(int s)
Creates a square matrix of size s.
Definition: matrix.hpp:40
virtual void AddMultTranspose(const Vector &x, Vector &y, const double val=1.) const =0
MatrixTranspose-Vector Multiplication y = y + val*A&#39;*x.
Vector data type.
Definition: vector.hpp:48
Base class for solvers.
Definition: operator.hpp:500
OutStream out(std::cout)
Global stream used by the library for standard output. Initially it uses the same std::streambuf as s...
Definition: globals.hpp:66
Abstract operator.
Definition: operator.hpp:24
AbstractSparseMatrix(int s=0)
Creates a square matrix of the given size.
Definition: matrix.hpp:84
int width
Dimension of the input / number of columns in the matrix.
Definition: operator.hpp:28