1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
|
/*=========================================================================
*
* Copyright NumFOCUS
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* https://www.apache.org/licenses/LICENSE-2.0.txt
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
*=========================================================================*/
#ifndef VNLIterativeSparseSolverTraits_h
#define VNLIterativeSparseSolverTraits_h
#include "vnl/vnl_vector.h"
#include "vnl/vnl_sparse_matrix.h"
#include "vnl/vnl_sparse_matrix_linear_system.h"
#include "vnl/algo/vnl_lsqr.h"
/** \class VNLIterativeSparseSolverTraits
* \brief Generic interface for iterative sparse linear solver.
*
* This generic interface (common to several sparse solvers), allow to
* interchange solver solutions when dealing with sparse linear system. See
* itk::ParameterizationQuadEdgeMeshFilter for reference.
*
* It internally uses the VNL library to represent and deal with vectors
* (vnl_vector) and sparse matrices (vnl_sparse_matrix). The solver by itself
* is an iterative one see vnl_sparse_matrix_linear_system for more details on
* the method used.
*
* \ingroup ITKCommon
*
* \sa VNLSparseLUSolverTraits
*/
template <typename T = double>
class VNLIterativeSparseSolverTraits
{
public:
using ValueType = T;
using MatrixType = vnl_sparse_matrix<ValueType>;
using VectorType = vnl_vector<ValueType>;
using SolverType = vnl_lsqr;
/** \return false (it is not a direct solver, it is an iterative solver) */
static bool
IsDirectSolver()
{
return false;
}
/** \brief initialize a square sparse matrix of size iN x iN */
static MatrixType
InitializeSparseMatrix(const unsigned int & iN)
{
return MatrixType(iN, iN);
}
/** \brief initialize a sparse matrix of size iRow x iCol */
static MatrixType
InitializeSparseMatrix(const unsigned int & iRow, const unsigned int & iCol)
{
return MatrixType(iRow, iCol);
}
/** \brief initialize a vector of size iN */
static VectorType
InitializeVector(const unsigned int & iN)
{
return VectorType(iN);
}
/** \brief iA[iR][iC] = iV */
static void
FillMatrix(MatrixType & iA, const unsigned int & iR, const unsigned int & iC, const ValueType & iV)
{
iA(iR, iC) = iV;
}
/** \brief iA[iR][iC] += iV */
static void
AddToMatrix(MatrixType & iA, const unsigned int & iR, const unsigned int & iC, const ValueType & iV)
{
iA(iR, iC) += iV;
}
/** \brief Solve the linear system \f$ iA \cdot oX = iB \f$ */
static bool
Solve(const MatrixType & iA, const VectorType & iB, VectorType & oX)
{
using SparseLinearSystemType = vnl_sparse_matrix_linear_system<ValueType>;
SparseLinearSystemType system(iA, iB);
SolverType solver(system);
return solver.minimize(oX);
}
/** \brief Solve the linear systems: \f$ iA \cdot oX = iBx \f$, \f$ iA \cdot oY = iBy \f$, \f$ iA \cdot oZ = iBz \f$
*/
static bool
Solve(const MatrixType & iA,
const VectorType & iBx,
const VectorType & iBy,
const VectorType & iBz,
VectorType & oX,
VectorType & oY,
VectorType & oZ)
{
bool result1 = Solve(iA, iBx, 100000, oX);
bool result2 = Solve(iA, iBy, 100000, oY);
bool result3 = Solve(iA, iBz, 100000, oZ);
return (result1 && result2 && result3);
}
/** \brief Solve the linear systems: \f$ iA \cdot oX = iBx \f$, \f$ iA \cdot oY = iBy \f$ */
static bool
Solve(const MatrixType & iA, const VectorType & iBx, const VectorType & iBy, VectorType & oX, VectorType & oY)
{
bool result1 = Solve(iA, iBx, oX);
bool result2 = Solve(iA, iBy, oY);
return (result1 && result2);
}
/** \brief Solve the linear systems: \f$ iA \cdot oX = iBx \f$ in N iterations */
static bool
Solve(const MatrixType & iA, const VectorType & iB, const long & iNbIter, VectorType & oX)
{
using SparseLinearSystemType = vnl_sparse_matrix_linear_system<ValueType>;
SparseLinearSystemType system(iA, iB);
SolverType solver(system);
solver.set_max_iterations(iNbIter);
return solver.minimize(oX);
}
};
#endif
|
