Cascades


1   
2   package JSci.maths.wavelet;
3   
4   import JSci.maths.*;
5   
6   /****************************************
7   * This class is a standard implementation
8   * of the Cascades algorithm.
9   * @author Daniel Lemire
10  *****************************************/
11  public final class Cascades extends AbstractMath {
12      private Cascades(){}
13  
14      /****************************************
15    * This method return the number of "scaling"
16    * functions at the previous scale given a
17    * number of scaling functions. The answer
18    * is always smaller than the provided value
19    * (about half since this is a dyadic
20    * implementation). This relates to the same idea
21    * as the "filter type".
22      *****************************************/
23      public static int previousDimension (int filtretype, int k) {
24          int i=(int) Math.round((k+filtretype)/2d);
25          if(2*i-filtretype==k) {
26              return(i);
27          } else {
28              if(2*Math.round(k/2d)==k) {
29                  throw new IllegalScalingException("Odd number of values into an even filter! Change the number of values/iterations: "+k);
30              } else {
31                  throw new IllegalScalingException("Even number of values into an odd filter! Change the number of values/iterations: "+k);
32              }
33          }
34      }
35  
36      public static double[] evalScaling (Filter filtre,int n0, int j1, int k) {
37          if (j1>20) {
38              throw new IllegalArgumentException  ("Too many iterations : "+j1);
39          }
40          if(n0<=0) {
41              throw new IllegalArgumentException  ("Must have a positive number of scaling functions : "+n0+" < 0.");
42          }
43          double[] init=new double[n0];
44          if((k>=init.length)||(k<0)) {
45              throw new IllegalArgumentException  ("There are "+init.length+" scaling functions going from 0 to "+(init.length-1)+" and you are trying to get the "+k+"th function.");
46  
47          }
48          init[k]=1;/* initialisation */
49          return(evaluation(filtre, j1, init));
50      }
51  
52  
53      public static double[] evalWavelet (Filter filtre, int filtretype, int n0, int j1, int k) {
54          if (j1>20) {
55              throw new IllegalArgumentException  ("Too many iterations : "+j1);
56          }
57          if(n0-filtretype<=0) {
58              throw new IllegalArgumentException  ("With "+n0+" scaling functions and a filter of type "+filtretype+", you are left with no wavelets. Please change the number of scaling functions, the multiresolution or the number of iterations");
59          }
60          double[] init=new double[n0-filtretype];
61          if((k>=init.length)||(k<0)) {
62              throw new IllegalArgumentException  ("There are "+init.length+" wavelets going from 0 to "+(init.length-1)+" and you are trying to get to the "+k+"th wavelet.");
63          }
64          init[k]=1;
65          double[] filtreWavelet=filtre.highpass(init);
66          return(evaluation(filtre,j1,filtreWavelet));
67      }
68  
69      public static double[] evalWavelet (Filter filtre,int n0, int j1, int k) {
70          return(evalWavelet(filtre,1,n0,j1,k));
71      }
72  
73      public static double[] evalWaveletHaar (Filter filtre,int n0, int j1, int k) {
74          return(evalWavelet(filtre,0,n0,j1,k));
75      }
76  
77      public static double[] evalWaveletQuadratic (Filter filtre, int n0, int j1, int k) {
78          return(evalWavelet(filtre,2,n0,j1,k));
79      }
80  
81      public static int PowerOf2(int pwrOf2) {
82          if(pwrOf2<0) {
83              throw new IllegalArgumentException  ("This parametre must be positive : "+pwrOf2+" < 0");
84          }
85          int reponse=1;
86          for(int i=pwrOf2;i>0;i--) {
87              reponse=reponse*2;
88          }
89          return(reponse);
90      }
91  
92  
93      /************************************************
94      * method used to oversample according to
95      * the lazy (Dirac Delta Function) interpolation
96      *************************************************/
97      public static double[] oversample(double data[]) {
98          double answer[]=new double[2*data.length-1];
99          for(int i=0;i<data.length-1;i++) {
100             answer[2*i]=data[i];
101         }
102         answer[2*data.length-2]=data[data.length-1];
103         return answer;
104     }
105 
106     /*********************************************
107     * Method used to oversample according to the
108     * Haar transform
109     **********************************************/
110     public static double[] doublesample(double data[]) {
111         int Nombre=data.length;
112         double answer[]=new double[2*Nombre];
113         for(int i=0;i<Nombre;i++) {
114             answer[2*i+1]=data[i];
115         }
116         return answer;
117         }
118     /**************************************************
119     * Special oversampling for the linear spline
120     * interpolation
121     ***************************************************/
122     public static double[] supersample(double data[]) {
123         int Nombre=data.length;
124         double answer[]=new double[2*Nombre+1];
125         for(int i=0;i<Nombre;i++) {
126             answer[2*i+1]=data[i];
127         }
128         return answer;
129         }
130   /**********************************
131   * Special oversampling for the
132   * quadratic spline interpolation
133   ***********************************/
134     public static double[] quadraticOversample( double[] v) {
135         double[] ans=new double[2*v.length-2];
136         ans[0]=v[0];
137         ans[ans.length-1]=v[v.length-1];
138         for(int k=1;k<v.length-1;k++) {
139             ans[2*k-1]=v[k];
140         }
141         return(ans);
142     }
143   /****************************************************
144   * Starting with n0 scaling functions and
145   * going jfin scales ahead (iterating jfin times),
146   * tells you how many scaling functions you'll have.
147   * (Dyadic multiresolutions of type filtretype.)
148   * @param filtertype filter type
149   * @param n0 number of scaling functions initially
150   * @param jfin number of iterations
151   ******************************************************/
152     public static int dimension(int n0, int jfin, int filtertype) {
153         return(PowerOf2(jfin)*(n0-filtertype)+filtertype);
154 
155     }
156 
157   /****************************************************
158   * Starting with n0 scaling functions and
159   * going jfin scales ahead (iterating jfin times),
160   * tells you how many scaling functions you'll have.
161   * (Linear spline and dyadic multiresolution of type 1.)
162   * @param n0 number of scaling functions initially
163   * @param jfin number of iterations
164   ******************************************************/
165     public static int dimension(int n0, int jfin) {
166         return(Cascades.PowerOf2(jfin)*(n0-1)+1);
167     }
168   /****************************************************
169   * Starting with n0 scaling functions and
170   * going jfin scales ahead (iterating jfin times),
171   * tells you how many scaling functions you'll have.
172   * (Haar and dyadic multiresolution of type 0.)
173   * @param n0 number of scaling functions initially
174   * @param jfin number of iterations
175   ******************************************************/
176     public static int dimensionHaar(int n0, int jfin) {
177         return(Cascades.PowerOf2(jfin)*(n0));
178     }
179 
180     public static double[] evaluation (Filter filtre, int j1, double[] init) {
181         if (j1<0) {
182             throw new IllegalArgumentException  ("Incorrect parameters : "+j1+" < 0 ");
183         }
184         if (j1>20) {
185             throw new IllegalArgumentException  ("Excessive number of iterations: "+j1);
186         }
187         double[] data=init;
188         for (int j=0;j<j1;j++){
189             data=filtre.lowpass(data);
190         }
191         return(data);
192     }
193 
194 }
195
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