-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathBrownian.java
201 lines (187 loc) · 6.69 KB
/
Brownian.java
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
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
// Author: Valentin Debarnot, Léo Martire.
// Description: This class implements the decomposition along
// the non-normalised Faber-Schauder system
// (often called the Lévy decomposition) of the
// Brownian motion.
// Last modified: See file metadata.
// Usage: TODO.
// Notes: N/A.
package BrownianGenerator;
import java.util.Arrays; // useful ?
import java.util.Random; // for gaussian vectors
public class Brownian{
// Attributes //---------------------------------------------
private int len; // number of time index discretisation points
private int dim; // Brownian motion dimension
private int n; // cut parameter (information about the generation)
private double c; // scaling (information about the generation)
private double[] start; // Brownian motion starting point
private double[][] BrownianPath; // Brownian motion values
//-----------------------------------------------------------
// Constructors //-------------------------------------------
public Brownian(int Kt){
// Constructor : basic.
this(Kt, 1, 1.0, 15);
}
public Brownian(int Kt, int dimension){
// Constructor : default.
this(Kt, dimension, 1.0, 15);
}
public Brownian(int Kt, int dimension, double c){
// Constructor : scale.
this(Kt, dimension, c, 15);
}
public Brownian(int Kt, int dimension, int N){
// Constructor : cut.
this(Kt, dimension, 1.0, N);
}
public Brownian(int Kt, int dimension, double c, int N){
// Constructor : complete.
// Errors :
if(Kt<=0){
System.err.println("Error : interval discretisation is impossible (Kt="+Kt+").");
System.exit(-1);
}
if(c<=0){
System.err.println("Error : dimension is incorrect (d="+dimension+").");
System.exit(-1);
}
if(c<=0){
System.err.println("Error : interval length is incorrect (c="+c+").");
System.exit(-1);
}
if(c<=0){
System.err.println("Error : cut index is incorrect (N="+N+").");
System.exit(-1);
}
// Warnings :
if(Kt<=10){
System.err.println("Warning : interval discretisation is very small (Kt="+Kt+"), beware.");
}
if(c<=1e-12){
System.err.println("Warning : interval length is very small (c="+c+"), numerical singularities may occur.");
}
if(N<=5){
System.err.println("Warning : cut point is very small (N="+N+"), beware.");
}
// Construction :
this.len=Kt;
this.dim=dimension;
this.c=c;
this.n=N;
this.start=new double[dimension];
SchauderWavelet sw=new SchauderWavelet(this.len);
this.BrownianPath=this.getBrownian(sw, this.dim, N);
for(int i=0; i<this.dim; i++){ // ensure the starting point is O
this.start[i]=0;
}
this.scale(c);
}
//-----------------------------------------------------------
// Methods //------------------------------------------------
private void scale(double c){
// Scales the [0, 1]-based Brownian motion.
// @param c the scaling parameter
// @return void.
double coef=Math.sqrt(c);
for(int i=0; i<this.len; i++){
for(int j=0; j<this.dim; j++){
this.BrownianPath[j][i]=coef*this.BrownianPath[j][i];
}
}
}
private double[][] getBrownian(SchauderWavelet w, int dimension, int N){
// Generates an approximation of the Brownian motion using the non-normalised Faber-Schauder system.
// @param w the SchauderWavelet object used in the approximation
// @param dimension the dimension of the wanted Brownian motion
// @param N the cut parameter of the approximation
// @return a double-index table representing the wanted Brownian motion approximation
double[][] B=new double[dimension][this.len];
double[] tmp;
double[] g;
int wSt;
while(!(w.hasToStop() || w.getOrder()>N)){
tmp=w.getValues();
g=getGaussians(dimension);
wSt=w.getStart();
for(int i=wSt; i<=w.getEnd(); i++){
for(int j=0; j<dimension; j++){
B[j][i]+=g[j]*tmp[i-wSt];
}
}
//w.printStatus(); // Debugging : show all used wavelets when they are used.
w.iterate();
}
w.reinitialize();
return(B);
}
private double[] getGaussians(int number){
// Builds a Gaussian vector.
// @param number size of the wanted Gaussian vector
// @return a Gaussian vector
if(number<=0){
System.err.println("Error : invalid number of Gaussians requested ("+number+" requested).");
System.exit(-1);
}
double[] g=new double[number];
Random r=new Random();
for(int i=0; i<number; i++){
g[i]=r.nextGaussian();
}
return(g);
}
public void changeStartPoint(double[] coordinates){
// Changes the starting point of the Brownian motion.
// @param coordinates a table of coordinates for the new starting point
// @return void
if(coordinates.length!=this.dim){
System.err.println("Error : dimension of requested starting point is invalid (dimension : "+coordinates.length+", Brownian motion dimension : "+this.dim+").");
System.exit(-1);
}
for(int i=0; i<this.len; i++){
for(int j=0; j<this.dim; j++){
this.BrownianPath[j][i]-=this.start[j]; // remove the previous starting point
this.BrownianPath[j][i]+=coordinates[j]; // add the new starting point
}
}
this.start=coordinates;
}
public double[] get(int t){
// Returns the t-th coordinate.
if(t<0 || t>=this.len){
System.err.println("Error : index requested is invalid (t="+t+", Kt="+this.len+").");
System.exit(-1);
}
double[] r=new double[this.dim];
for(int i=0; i<this.dim; i++){
r[i]=this.BrownianPath[i][t];
}
return(r);
}
public int getLength(){
return(this.len);
}
public int getDim(){
return(this.dim);
}
public String getCharacteristics(){
return("kt="+this.len+"; d="+this.dim+"; c="+c+"; n="+n+"; startPoint="+Arrays.toString(this.start));
}
//-----------------------------------------------------------
// toString redefinition //----------------------------------
public String toString(){
// toString redefinition.
String str="";
str+="Brownian motion "+this.hashCode()+" ("+this.getCharacteristics()+") :\n";
for(int i=0; i<this.len; i++){
str+="[";
for(int j=0; j<this.dim; j++){
str+=Util.formatDouble(this.BrownianPath[j][i]);
if(j<this.dim-1){str+=", ";}
}
str+="]\n";
}
return(str);
}
//-----------------------------------------------------------
}