EngineerMath


1   package JSci.maths;
2   
3   /**
4   * This class is dedicated to engineering methods applied to arrays including
5   * signal processing.
6   * All methods here are safe, that is, they create copies of arrays whenever
7   * necessary.
8   * This makes for slower methods, but the programmer can always
9   * define his own methods optimized for performance.
10  * @author Daniel Lemire
11  */
12  public final class EngineerMath extends AbstractMath {
13          private EngineerMath() {}
14  
15          /**
16          * Return a running average over the data.
17          * The returned array has the same size as the input array.
18          * It is often used in signal processing to estimate the baseline.
19          * @param v the data.
20          * @param width width of the average.
21          * @exception IllegalArgumentException if v.length < width
22          * @exception IllegalArgumentException if width is even
23          * @exception IllegalArgumentException if v.length = 0
24          */
25          public static double[] runningAverage(double[] v, int width) {
26      if(v.length<width)
27        throw new IllegalArgumentException  ("Array must be at least as long as the required width : "+v.length+" < "+width);
28      if((width&1)==0)
29        throw new IllegalArgumentException  ("The parameter 'width' must be odd : "+width);
30      if(v.length==0)
31        throw new IllegalArgumentException  ("Empty array, nothing to compute!");
32      int halfsize=width >> 1;
33      double[] ans=new double[v.length];
34      ans[0]=ArrayMath.mean(ArrayMath.extract(0,width-1,v));
35      for(int k=1;k<halfsize;k++) {
36         ans[k]=ans[0];
37      }
38      for(int k=halfsize;k<v.length-halfsize-1;k++) {
39        ans[k]=ArrayMath.mean(ArrayMath.extract(k-halfsize,k+halfsize,v));
40      }
41  
42      ans[v.length-halfsize-1]=ArrayMath.mean(ArrayMath.extract(v.length-1-width+1,v.length-1,v));
43      for(int k=v.length-halfsize;k<v.length;k++) {
44        ans[k]=ans[v.length-halfsize-1];
45      }
46      return(ans);
47    }
48          /**
49          * Return a running median over the data.
50          * The returned array has the same size as the input array.
51          * It is often used in signal processing to estimate the baseline.
52          * Safer than the running average, but somewhat more costly computationally.
53          * @param v the data
54          * @param width width of the average
55          * @exception IllegalArgumentException if v.length < width
56          * @exception IllegalArgumentException if width is even
57          */
58          public static double[] runningMedian(double[] v, int width) {
59      if(v.length<width)
60        throw new IllegalArgumentException  ("Array must be at least as long as the required width : "+v.length+" < "+width);
61      if((width&1)==0)
62        throw new IllegalArgumentException  ("The parameter 'width' must be odd : "+width);
63      if(v.length==0)
64        throw new IllegalArgumentException  ("Empty array, nothing to compute!");
65      int halfsize=width >> 1;
66      double[] ans=new double[v.length];
67      ans[0]=ArrayMath.median(ArrayMath.extract(0,width-1,v));
68      for(int k=1;k<halfsize;k++) {
69         ans[k]=ans[0];
70      }
71      for(int k=halfsize;k<v.length-halfsize-1;k++) {
72        ans[k]=ArrayMath.median(ArrayMath.extract(k-halfsize,k+halfsize,v));
73      }
74  
75      ans[v.length-halfsize-1]=ArrayMath.median(ArrayMath.extract(v.length-1-width+1,v.length-1,v));
76      for(int k=v.length-halfsize;k<v.length;k++) {
77        ans[k]=ans[v.length-halfsize-1];
78      }
79      return(ans);
80    }
81  
82      /**
83      * Shannon entropy of an array.
84          * Please check that the mass of the array is 1 before using this method.
85          * Use the method "entropy" otherwise.
86          * @jsci.planetmath ShannonsTheoremEntropy
87          */
88      public static double icf(double[] v) {
89          double ans=0;
90          for(int j=0;j<v.length;j++) {
91              if(v[j]!=0) {
92                  if (v[j]<0) {
93                      throw new IllegalArgumentException  ("You cannot take the ICF of a array having negative components : v ["+j+"] = "+v[j]+" < 0");
94                  }
95                  ans-=v[j]*Math.log(v[j]);
96              }
97          }
98          return(ans);
99      }
100 
101     /**
102     * Compute the entropy of an array.
103         * The entropy as defined using the absolute value.
104         */
105     public static double entropy(double[] v) {
106         double[] temp=ArrayMath.abs(v);
107         double m=ArrayMath.mass(temp);
108         if(m==0) return(0);
109         temp=ArrayMath.scalarMultiply(1/m, temp);
110         return(icf(temp));
111 
112     }
113 
114     /**
115     * Compute the entropy of an array.
116         * The entropy as defined using the absolute value.
117         */
118     public static double entropy(int[] v) {
119         int[] temp=ArrayMath.abs(v);
120         int m=ArrayMath.mass(temp);
121         if(m==0) return(0);
122         double[] t2=ArrayMath.scalarMultiply(1.0/m, temp);
123         return(icf(t2));
124     }
125     /**
126     * Set an array to the specified length resampling using linear interpolation.
127         */
128     public static double[] resample(double[] data, final int newLength) {
129                 if(newLength<=0)
130                         throw new IllegalArgumentException  ("New length must be strictly positive : "+newLength+" <=0 ");
131                 double[] ans=new double[newLength];
132                 for(int k=0;k<newLength;k++) {
133             double pos = ((double)k/(double)(newLength-1))*(data.length-1);
134                         int base1 = (int) Math.floor(pos);
135                         int base2 = (int) Math.ceil(pos);
136                         double mod = pos-base1;
137                         ans[k]=data[base1]*mod+data[base2]*(1.0-mod);
138                 }
139         return(ans);
140     }
141 }
142 
143
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