Clover coverage report - baseCode - 0.2.5 Coverage timestamp: Tue Apr 12 2005 11:31:58 EDT FRAMES NO FRAMES |
file stats: | LOC: | 253 |  | Methods: | 12
| NCLOC: | 124 |  | Classes: | 1
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Source file | Conditionals | Statements | Methods | TOTAL
CorrelationStats.java | 10% | 13.2% | 25% | 13.6% |

1 |  |
     package baseCode.math;
2 |  |
3 |  |
     import cern.colt.list.DoubleArrayList;
4 |  |
     import cern.colt.matrix.DoubleMatrix2D;
5 |  |
     import cern.colt.matrix.impl.SparseDoubleMatrix2D;
6 |  |
     import cern.jet.math.Arithmetic;
7 |  |
     import cern.jet.stat.Probability;
8 |  |
9 |  |
     /**
10 |  |
      * Statistical evaluation and transformation tools for correlations.
11 |  |
      * <p>
12 |  |
      * Copyright (c) 2004
13 |  |
      * </p>
14 |  |
      * <p>
15 |  |
      * Institution:: Columbia University
16 |  |
      * </p>
17 |  |
      *
18 |  |
      * @author Paul Pavlidis
19 |  |
      * @version $Id: CorrelationStats.java,v 1.11 2005/01/05 17:59:19 pavlidis Exp $
20 |  |
      */
21 |  |
     public class CorrelationStats {
22 |  |
23 |  |
        private static DoubleMatrix2D correlationPvalLookup;
24 |  |
        private static final double BINSIZE = 0.005; // resolution of correlation.
25 |  |
        // Differences smaller than this
26 |  |
        // are considered meaningless.
27 |  |
        private static final double STEPSIZE = BINSIZE * 2; // this MUST be more than
28 |  |
        // the binsize.
29 |  |
        private static final int MAXCOUNT = 1000; // maximum number of things.
30 |  |
        private static final double PVALCHOP = 8.0; // value by which log(pvalues)
31 |  |
        // are scaled before storing as
32 |  |
        // bytes. Values less than
33 |  |
        // 10^e-256/PVALCHOP are
34 |  |
        // 'clipped'.
35 |  |
36 |  |
        static {
37 | 1 |
           int numbins = ( int ) Math.ceil( 1.0 / BINSIZE );
38 | 1 |
           correlationPvalLookup = new SparseDoubleMatrix2D( numbins, MAXCOUNT + 1 );
39 |  |
        }
40 |  |
41 |  |
        /**
42 |  |
         * @param correl Pearson correlation.
43 |  |
         * @param count Number of items used to calculate the correlation. NOT the degrees of freedom.
44 |  |
         * @return double
45 |  |
         */
46 | 0 |
        public static double pvalue( double correl, int count ) {
47 |  |
48 | 0 |
           double acorrel = Math.abs( correl );
49 |  |
50 | 0 |
           if ( acorrel == 1.0 ) {
51 | 0 |
              return 0.0;
52 |  |
           }
53 |  |
54 | 0 |
           if ( acorrel == 0.0 ) {
55 | 0 |
              return 1.0;
56 |  |
           }
57 |  |
58 | 0 |
           int dof = count - 2;
59 |  |
60 | 0 |
           if ( dof <= 0 ) {
61 | 0 |
              return 1.0;
62 |  |
           }
63 |  |
64 | 0 |
           int bin = ( int ) Math.ceil( acorrel / BINSIZE );
65 | 0 |
           if ( count <= MAXCOUNT
66 |  |
                 && correlationPvalLookup.getQuick( bin, dof ) != 0.0 ) {
67 | 0 |
              return correlationPvalLookup.getQuick( bin, dof );
68 |  |
           }
69 | 0 |
           double t = correlationTstat( acorrel, dof );
70 | 0 |
           double p = Probability.studentT( dof, -t );
71 | 0 |
           if ( count < MAXCOUNT ) {
72 | 0 |
              correlationPvalLookup.setQuick( bin, dof, p );
73 |  |
           }
74 | 0 |
           return p;
75 |  |
76 |  |
        }
77 |  |
78 |  |
        /**
79 |  |
         * @param correl double
80 |  |
         * @return int
81 |  |
         */
82 | 0 |
        public static int correlAsByte( double correl ) {
83 | 0 |
           if ( correl == -1.0 ) {
84 | 0 |
              return 0;
85 |  |
           }
86 |  |
87 | 0 |
           return ( int ) ( Math.ceil( ( correl + 1.0 ) * 128 ) - 1 );
88 |  |
        }
89 |  |
90 |  |
        /**
91 |  |
         * Reverse the Fisher z-transform of correlations.
92 |  |
         *
93 |  |
         * @param r
94 |  |
         * @return
95 |  |
         */
96 | 0 |
        public static double unFisherTransform( double r ) {
97 | 0 |
           return Math.exp( 2.0 * r - 1.0 ) / Math.exp( 2.0 * r + 1.0 );
98 |  |
        }
99 |  |
100 |  |
        /**
101 |  |
         * Compute the Fisher z transform of the Pearson correlation.
102 |  |
         *
103 |  |
         * @param r Correlation coefficient.
104 |  |
         * @return Fisher transform of the Correlation.
105 |  |
         */
106 | 100 |
        public static double fisherTransform( double r ) {
107 | 100 |
           if ( !isValidPearsonCorrelation( r ) ) {
108 | 0 |
              throw new IllegalArgumentException( "Invalid correlation " + r );
109 |  |
           }
110 |  |
111 | 100 |
           return 0.5 * Math.log( ( 1.0 + r ) / ( 1.0 - r ) );
112 |  |
        }
113 |  |
114 |  |
        /**
115 |  |
         * Fisher-transform a list of correlations.
116 |  |
         *
117 |  |
         * @param e
118 |  |
         * @return
119 |  |
         */
120 | 5 |
        public static DoubleArrayList fisherTransform( DoubleArrayList e ) {
121 | 5 |
           DoubleArrayList r = new DoubleArrayList( e.size() );
122 | 5 |
           for ( int i = 0; i < e.size(); i++ ) {
123 | 100 |
              r.add( CorrelationStats.fisherTransform( e.getQuick( i ) ) );
124 |  |
           }
125 | 5 |
           return r;
126 |  |
        }
127 |  |
128 |  |
        /**
129 |  |
         * Conver a correlation p value into a value between 0 and 255 inclusive. This is done by taking the log, multiplying
130 |  |
         * it by a fixed value (currently 8). This means that pvalues less than 10^-32 are rounded to 10^-32.
131 |  |
         *
132 |  |
         * @param correl double
133 |  |
         * @param count int
134 |  |
         * @return int
135 |  |
         */
136 | 0 |
        public static int pvalueAsByte( double correl, int count ) {
137 | 0 |
           int p = -( int ) Math.floor( PVALCHOP
138 |  |
                 * Arithmetic.log10( pvalue( correl, count ) ) );
139 |  |
140 | 0 |
           if ( p < 0 ) {
141 | 0 |
              return 0;
142 | 0 |
           } else if ( p > 255 ) {
143 | 0 |
              return 255;
144 |  |
           }
145 | 0 |
           return p;
146 |  |
        }
147 |  |
148 |  |
        /**
149 |  |
         * @param pvalByte int
150 |  |
         * @return double
151 |  |
         */
152 | 0 |
        public static double byteToPvalue( int pvalByte ) {
153 | 0 |
           return Math.pow( 10.0, -( double ) pvalByte / PVALCHOP );
154 |  |
        }
155 |  |
156 |  |
        /**
157 |  |
         * @param correlByte int
158 |  |
         * @return double
159 |  |
         */
160 | 0 |
        public static double byteToCorrel( int correlByte ) {
161 | 0 |
           return correlByte / 128.0 - 1.0;
162 |  |
        }
163 |  |
164 |  |
        /**
165 |  |
         * Compute the t-statistic associated with a Pearson correlation.
166 |  |
         *
167 |  |
         * @param correl Pearson correlation
168 |  |
         * @param dof Degrees of freedom (n - 2)
169 |  |
         * @return double
170 |  |
         */
171 | 0 |
        public static double correlationTstat( double correl, int dof ) {
172 | 0 |
           return correl / Math.sqrt( ( 1.0 - correl * correl ) / dof );
173 |  |
        }
174 |  |
175 |  |
        /**
176 |  |
         * Statistical comparison of two correlations. Assumes data are bivariate normal. Null hypothesis is that the two
177 |  |
         * correlations are equal. See Zar (Biostatistics)
178 |  |
         *
179 |  |
         * @param correl1 First correlation
180 |  |
         * @param n1 Number of values used to compute correl1
181 |  |
         * @param correl2 Second correlation
182 |  |
         * @param n2 Number of values used to compute correl2
183 |  |
         * @return double p value.
184 |  |
         */
185 | 0 |
        public static double compare( double correl1, int n1, double correl2, int n2 ) {
186 |  |
187 | 0 |
           double Z;
188 | 0 |
           double sigma;
189 | 0 |
           double p;
190 |  |
191 | 0 |
           sigma = Math.sqrt( ( 1 / ( ( double ) n1 - 3 ) )
192 |  |
                 + ( 1 / ( ( double ) n2 - 3 ) ) );
193 |  |
194 | 0 |
           Z = Math.abs( correl1 - correl2 ) / sigma;
195 |  |
196 | 0 |
           p = Probability.normal( -Z ); // upper tail.
197 |  |
198 | 0 |
           if ( p > 0.5 ) {
199 | 0 |
              return 1.0 - p;
200 |  |
           }
201 | 0 |
           return p;
202 |  |
        }
203 |  |
204 |  |
        /**
205 |  |
         * Find the approximate correlation required to meet a particular pvalue. This works by simple gradient descent.
206 |  |
         *
207 |  |
         * @param pval double
208 |  |
         * @param count int
209 |  |
         * @return double
210 |  |
         */
211 | 0 |
        public static double correlationForPvalue( double pval, int count ) {
212 | 0 |
           double stop = pval / 100.0;
213 | 0 |
           double err = 1.0;
214 | 0 |
           double corrguess = 1.0;
215 | 0 |
           double step = STEPSIZE;
216 | 0 |
           double preverr = 0.0;
217 | 0 |
           int maxiter = 1000;
218 | 0 |
           int iter = 0;
219 | 0 |
           while ( Math.abs( err ) > stop && step >= BINSIZE ) {
220 | 0 |
              double guess = pvalue( corrguess, count );
221 | 0 |
              if ( guess > pval ) {
222 | 0 |
                 corrguess += step;
223 |  |
              } else {
224 | 0 |
                 corrguess -= step;
225 |  |
              }
226 |  |
227 | 0 |
              if ( preverr * err < 0 ) { // opposite signs. Means we missed. Make
228 |  |
                 // step smaller and keep going.
229 | 0 |
                 step /= 2;
230 |  |
              }
231 |  |
232 | 0 |
              preverr = err;
233 | 0 |
              err = pval - guess;
234 | 0 |
              iter++;
235 |  |
236 | 0 |
              if ( iter > maxiter ) {
237 | 0 |
                 throw new IllegalStateException( "Too many iterations" );
238 |  |
              }
239 |  |
           }
240 | 0 |
           return ( corrguess );
241 |  |
        }
242 |  |
243 |  |
        /**
244 |  |
         * Test if a value is a reasonable Pearson correlation (in the range -1 to 1; values outside of this
245 |  |
         * range are acceptable within a small roundoff.
246 |  |
         * @param r
247 |  |
         * @return
248 |  |
         */
249 | 180 |
        public static boolean isValidPearsonCorrelation( double r ) {
250 | 180 |
           return ( r + Constants.SMALL >= -1.0 && r - Constants.SMALL <= 1.0 );
251 |  |
        }
252 |  |
253 |  |
     }