implementation of the Gamma function and log10 Binomial / Multinomial coefficients. Unit tests for gamma and binomial passed with honors.
git-svn-id: file:///humgen/gsa-scr1/gsa-engineering/svn_contents/trunk@6056 348d0f76-0448-11de-a6fe-93d51630548a
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droazen
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3392c67e0f
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@ -1018,7 +1018,7 @@ public class MathUtils {
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return softMax(a,x2);
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}
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static public double softMax(final double x, final double y) {
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static public double softMax(final double x, final double y) {
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if (Double.isInfinite(x))
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return y;
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@ -1056,19 +1056,236 @@ public class MathUtils {
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// return Math.log10(Math.pow(10.0,x) + Math.pow(10.0,y));
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}
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static public double phredScaleToProbability (byte q) {
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public static double phredScaleToProbability (byte q) {
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return Math.pow(10,(-q)/10.0);
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}
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static public double phredScaleToLog10Probability (byte q) {
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public static double phredScaleToLog10Probability (byte q) {
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return ((-q)/10.0);
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}
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static public byte probabilityToPhredScale (double p) {
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public static byte probabilityToPhredScale (double p) {
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return (byte) ((-10) * Math.log10(p));
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}
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static public double log10ProbabilityToPhredScale (double log10p) {
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public static double log10ProbabilityToPhredScale (double log10p) {
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return (-10) * log10p;
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}
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}
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/**
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* Converts LN to LOG10
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* @param ln log(x)
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* @return log10(x)
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*/
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public static double lnToLog10 (double ln) {
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return ln * Math.log10(Math.exp(1));
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}
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/**
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* Constants to simplify the log gamma function calculation.
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*/
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private static final double
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zero = 0.0,
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one = 1.0,
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half = .5,
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a0 = 7.72156649015328655494e-02,
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a1 = 3.22467033424113591611e-01,
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a2 = 6.73523010531292681824e-02,
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a3 = 2.05808084325167332806e-02,
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a4 = 7.38555086081402883957e-03,
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a5 = 2.89051383673415629091e-03,
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a6 = 1.19270763183362067845e-03,
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a7 = 5.10069792153511336608e-04,
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a8 = 2.20862790713908385557e-04,
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a9 = 1.08011567247583939954e-04,
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a10 = 2.52144565451257326939e-05,
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a11 = 4.48640949618915160150e-05,
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tc = 1.46163214496836224576e+00,
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tf = -1.21486290535849611461e-01,
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tt = -3.63867699703950536541e-18,
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t0 = 4.83836122723810047042e-01,
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t1 = -1.47587722994593911752e-01,
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t2 = 6.46249402391333854778e-02,
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t3 = -3.27885410759859649565e-02,
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t4 = 1.79706750811820387126e-02,
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t5 = -1.03142241298341437450e-02,
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t6 = 6.10053870246291332635e-03,
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t7 = -3.68452016781138256760e-03,
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t8 = 2.25964780900612472250e-03,
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t9 = -1.40346469989232843813e-03,
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t10 = 8.81081882437654011382e-04,
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t11 = -5.38595305356740546715e-04,
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t12 = 3.15632070903625950361e-04,
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t13 = -3.12754168375120860518e-04,
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t14 = 3.35529192635519073543e-04,
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u0 = -7.72156649015328655494e-02,
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u1 = 6.32827064025093366517e-01,
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u2 = 1.45492250137234768737e+00,
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u3 = 9.77717527963372745603e-01,
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u4 = 2.28963728064692451092e-01,
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u5 = 1.33810918536787660377e-02,
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v1 = 2.45597793713041134822e+00,
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v2 = 2.12848976379893395361e+00,
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v3 = 7.69285150456672783825e-01,
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v4 = 1.04222645593369134254e-01,
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v5 = 3.21709242282423911810e-03,
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s0 = -7.72156649015328655494e-02,
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s1 = 2.14982415960608852501e-01,
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s2 = 3.25778796408930981787e-01,
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s3 = 1.46350472652464452805e-01,
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s4 = 2.66422703033638609560e-02,
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s5 = 1.84028451407337715652e-03,
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s6 = 3.19475326584100867617e-05,
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r1 = 1.39200533467621045958e+00,
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r2 = 7.21935547567138069525e-01,
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r3 = 1.71933865632803078993e-01,
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r4 = 1.86459191715652901344e-02,
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r5 = 7.77942496381893596434e-04,
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r6 = 7.32668430744625636189e-06,
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w0 = 4.18938533204672725052e-01,
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w1 = 8.33333333333329678849e-02,
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w2 = -2.77777777728775536470e-03,
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w3 = 7.93650558643019558500e-04,
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w4 = -5.95187557450339963135e-04,
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w5 = 8.36339918996282139126e-04,
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w6 = -1.63092934096575273989e-03;
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/**
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* Efficient rounding functions to simplify the log gamma function calculation
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* double to long with 32 bit shift
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*/
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private static final int HI(double x) {
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return (int)(Double.doubleToLongBits(x) >> 32);
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}
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/**
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* Efficient rounding functions to simplify the log gamma function calculation
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* double to long without shift
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*/
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private static final int LO(double x) {
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return (int)Double.doubleToLongBits(x);
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}
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/**
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* Most efficent implementation of the lnGamma (FDLIBM)
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* Use via the log10Gamma wrapper method.
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*/
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private static double lnGamma(double x) {
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double t,y,z,p,p1,p2,p3,q,r,w;
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int i;
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int hx = HI(x);
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int lx = LO(x);
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/* purge off +-inf, NaN, +-0, and negative arguments */
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int ix = hx&0x7fffffff;
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if (ix >= 0x7ff00000) return Double.POSITIVE_INFINITY;
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if ((ix|lx)==0 || hx < 0) return Double.NaN;
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if (ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
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return -Math.log(x);
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}
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/* purge off 1 and 2 */
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if((((ix-0x3ff00000)|lx)==0)||(((ix-0x40000000)|lx)==0)) r = 0;
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/* for x < 2.0 */
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else if(ix<0x40000000) {
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if(ix<=0x3feccccc) { /* lgamma(x) = lgamma(x+1)-log(x) */
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r = -Math.log(x);
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if(ix>=0x3FE76944) {y = one-x; i= 0;}
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else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;}
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else {y = x; i=2;}
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} else {
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r = zero;
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if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */
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else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */
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else {y=x-one;i=2;}
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}
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switch(i) {
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case 0:
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z = y*y;
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p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10))));
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p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11)))));
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p = y*p1+p2;
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r += (p-0.5*y); break;
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case 1:
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z = y*y;
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w = z*y;
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p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */
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p2 = t1+w*(t4+w*(t7+w*(t10+w*t13)));
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p3 = t2+w*(t5+w*(t8+w*(t11+w*t14)));
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p = z*p1-(tt-w*(p2+y*p3));
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r += (tf + p); break;
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case 2:
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p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5)))));
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p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5))));
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r += (-0.5*y + p1/p2);
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}
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}
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else if(ix<0x40200000) { /* x < 8.0 */
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i = (int)x;
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t = zero;
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y = x-(double)i;
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p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6))))));
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q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6)))));
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r = half*y+p/q;
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z = one; /* lgamma(1+s) = log(s) + lgamma(s) */
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switch(i) {
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case 7: z *= (y+6.0); /* FALLTHRU */
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case 6: z *= (y+5.0); /* FALLTHRU */
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case 5: z *= (y+4.0); /* FALLTHRU */
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case 4: z *= (y+3.0); /* FALLTHRU */
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case 3: z *= (y+2.0); /* FALLTHRU */
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r += Math.log(z); break;
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}
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/* 8.0 <= x < 2**58 */
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} else if (ix < 0x43900000) {
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t = Math.log(x);
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z = one/x;
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y = z*z;
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w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6)))));
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r = (x-half)*(t-one)+w;
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} else
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/* 2**58 <= x <= inf */
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r = x*(Math.log(x)-one);
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return r;
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}
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/**
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* Calculates the log10 of the gamma function for x using the efficient FDLIBM
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* implementation to avoid overflows and guarantees high accuracy even for large
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* numbers.
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*
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* @param x the x parameter
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* @return the log10 of the gamma function at x.
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*/
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public static double log10Gamma(double x) {
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return lnToLog10(lnGamma(x));
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}
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/**
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* Calculates the log10 of the binomial coefficient avoiding overflows
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*
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* @param n total number of samples
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* @param k number of successes
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* @return the log10 of the binomial coefficient
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*/
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public static double log10BinomialCoefficient (double n, double k) {
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return log10Gamma(n+1) - log10Gamma(k+1) - log10Gamma(n-k+1);
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}
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/**
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* Calculates the log10 of the multinomial coefficient avoiding overflows
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*
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* @param n total number of samples
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* @param k array of any size with the number of successes for each grouping (k1, k2, k3, ..., km)
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* @return
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*/
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public static double log10MultinomialCoefficient (double n, double [] k) {
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double denominator = 0.0;
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for (double x : k) {
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denominator += log10Gamma(x+1);
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}
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return log10Gamma(n+1) - denominator;
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}
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}
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@ -137,5 +137,22 @@ public class MathUtilsUnitTest extends BaseTest {
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Assert.assertTrue(r.mean()- 3224.625 < 2e-10 );
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Assert.assertTrue(r.stddev()-9072.6515881128 < 2e-10);
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}
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@Test
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public void testLog10Gamma() {
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logger.warn("Executing testLog10Gamma");
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10Gamma(4.0), 0.7781513) == 0);
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10Gamma(10), 5.559763) == 0);
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10Gamma(10654), 38280.53, 1e-2) == 0);
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}
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@Test
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public void testLog10BinomialCoefficient() {
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logger.warn("Executing testLog10BinomialCoefficient");
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10BinomialCoefficient(4, 2), 0.7781513) == 0);
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10BinomialCoefficient(10,3), 2.079181) == 0);
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Assert.assertTrue(MathUtils.compareDoubles(MathUtils.log10BinomialCoefficient(103928, 119 ), 400.2156, 1e-4) == 0);
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}
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}
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