DT/LaplacianMatrix.cpp at master · tgbudd/DT · GitHub

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
146
147
148
149
150
151
152
153
154
155
156
157
#include <map>

#include "LaplacianMatrix.h"

LaplacianMatrix::LaplacianMatrix(const Triangulation * const triangulation) : Matrix(triangulation->NumberOfVertices() ) {
	boost::array<double,3> unitmeasure = {1.0,1.0,1.0};
	std::vector<boost::array<double,3> > edgemeasure(triangulation->NumberOfTriangles(),unitmeasure);
	Initialize(triangulation,edgemeasure);
}

LaplacianMatrix::LaplacianMatrix(const Triangulation * const triangulation, const std::vector<boost::array<double,3> > & edge_measure) : Matrix(edge_measure.size()) {
	Initialize(triangulation,edge_measure);
}

void LaplacianMatrix::Initialize(const Triangulation * const triangulation, const std::vector<boost::array<double,3> > & edge_measure)
{
	laplacianRules_.resize(triangulation->NumberOfVertices());
	for(int i=0;i<triangulation->NumberOfTriangles();i++)
	{
		Triangle * triangle = triangulation->getTriangle(i);
		for(int j=0;j<3;j++)
		{
			Edge * edge = triangle->getEdge(j);
			int start = edge->getNext()->getOpposite()->getId();
			int end = edge->getPrevious()->getOpposite()->getId();

			std::pair<std::map<int,double>::iterator,bool> insertion;
			insertion = laplacianRules_[start].insert(std::pair<int,double>(end,-edge_measure[i][j]));
			if( !insertion.second )
			{
				insertion.first->second -= edge_measure[i][j];
			}
			insertion = laplacianRules_[start].insert(std::pair<int,double>(start,edge_measure[i][j]));
			if( !insertion.second )
			{
				insertion.first->second += edge_measure[i][j];
			}
		}
	}
}

void LaplacianMatrix::MultiplyVector(const std::vector<double> & from, std::vector<double> & to) const
{
	for(int i=0;i<static_cast<int>(from.size());i++)
	{
		to[i] = 0.0;
		for(std::map<int,double>::const_iterator it = laplacianRules_[i].begin(); it != laplacianRules_[i].end(); it++)
		{
			to[i] += it->second * from[it->first];
		}
	}
}


DomainLaplacianMatrix::DomainLaplacianMatrix(const Triangulation * const triangulation, const std::vector<const Vertex*> & vertices, const std::vector<const Vertex*> & fixed)
	: Matrix(vertices.size()),
	vertices_(vertices)
{
	boost::array<double,3> unitmeasure = {1.0,1.0,1.0};
	std::vector<boost::array<double,3> > edgemeasure(triangulation->NumberOfTriangles(),unitmeasure);
	Initialize(triangulation,edgemeasure,vertices,fixed);
}

DomainLaplacianMatrix::DomainLaplacianMatrix(const Triangulation * const triangulation, const std::vector<boost::array<double,3> > & edge_measure, const std::vector<const Vertex*> & vertices, const std::vector<const Vertex*> & fixed)
	: Matrix(vertices.size() ),
	vertices_(vertices)
{
	Initialize(triangulation,edge_measure,vertices,fixed);
}

void DomainLaplacianMatrix::Initialize(const Triangulation * const triangulation, const std::vector<boost::array<double,3> > & edge_measure, const std::vector<const Vertex*> & vertices, const std::vector<const Vertex*> & fixed)
{
	int NotInSet = vertices.size()+1;
	std::vector<int> type(triangulation->NumberOfVertices(),NotInSet);
	for(int i=0,endi=vertices.size();i<endi;i++)
	{
		type[vertices[i]->getId()] = i;
	}
	for(int i=0,endi=fixed.size();i<endi;i++)
	{
		type[fixed[i]->getId()] = -i-1;
	}

	laplacianRules_.resize(vertices.size());
	targetRules_.resize(vertices.size());
	for(int i=0;i<triangulation->NumberOfTriangles();i++)
	{
		Triangle * triangle = triangulation->getTriangle(i);
		for(int j=0;j<3;j++)
		{
			Edge * edge = triangle->getEdge(j);
			int start = edge->getNext()->getOpposite()->getId();
			int end = edge->getPrevious()->getOpposite()->getId();

			if( type[start] >= 0 && type[start] != NotInSet )
			{
				std::pair<std::map<int,double>::iterator,bool> insertion;
				insertion = laplacianRules_[type[start]].insert(std::pair<int,double>(type[start],edge_measure[i][j]));
				if( !insertion.second )
				{
					insertion.first->second += edge_measure[i][j];
				}
				if( type[end] >= 0 && type[end] != NotInSet )
				{
					insertion = laplacianRules_[type[start]].insert(std::pair<int,double>(type[end],-edge_measure[i][j]));
					if( !insertion.second )
					{
						insertion.first->second -= edge_measure[i][j];
					}
				} else
				{
					insertion = targetRules_[type[start]].insert(std::pair<int,double>(fixed[-type[end]-1]->getId(),edge_measure[i][j]));
					if( !insertion.second )
					{
						insertion.first->second += edge_measure[i][j];
					}
				}
			}
		}
	}
}

void DomainLaplacianMatrix::MultiplyVector(const std::vector<double> & from, std::vector<double> & to) const
{
	for(int i=0;i<static_cast<int>(from.size());i++)
	{
		to[i] = 0.0;
		for(std::map<int,double>::const_iterator it = laplacianRules_[i].begin(); it != laplacianRules_[i].end(); it++)
		{
			to[i] += it->second * from[it->first];
		}
	}
}

bool DomainLaplacianMatrix::FindHarmonic(std::vector<double> & x, double eps, int maxIterations )
{
	std::vector<double> target(targetRules_.size());
	GetTarget(x,target);
	std::vector<double> xsub(vertices_.size());
	for(int i=0,endi=vertices_.size();i<endi;i++)
	{
		xsub[i] = x[vertices_[i]->getId()];
	}
	return ConjugateGradientSolve(target,xsub,eps,maxIterations);
}

void DomainLaplacianMatrix::GetTarget(const std::vector<double> & x, std::vector<double> & target)
{
	for(int i=0;i<static_cast<int>(targetRules_.size());i++)
	{
		target[i] = 0.0;
		for(std::map<int,double>::const_iterator it = targetRules_[i].begin(); it != targetRules_[i].end(); it++)
		{
			target[i] += it->second * x[it->first];
		}
	}
}