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arthus701Max Schanner
arthus701
and
Max Schanner
authored
Add betainc C implementation (#798)
Co-authored-by: Max Schanner <arthus@gfz-potsdam.de>
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‎pytensor/scalar/c_code/incbet.c‎

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/* adapted from file incbet.c, obtained from the Cephes library (MIT License)
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Cephes Math Library, Release 2.8: June, 2000
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Copyright 1984, 1995, 2000 by Stephen L. Moshier
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*/
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//For GPU support
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#ifdef __CUDACC__
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#define DEVICE __device__
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#else
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#define DEVICE
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#endif
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#include <float.h>
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#include <math.h>
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#include <stdio.h>
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#include <numpy/npy_math.h>
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#define MINLOG -170.0
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#define MAXLOG +170.0
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#define MAXGAM 171.624376956302725
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#define EPSILON 2.2204460492503131e-16
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DEVICE static double pseries(double, double, double);
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DEVICE static double incbcf(double, double, double);
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DEVICE static double incbd(double, double, double);
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static double big = 4.503599627370496e15;
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static double biginv = 2.22044604925031308085e-16;
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DEVICE double BetaInc(double a, double b, double x)
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{
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double xc, y, w, t;
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/* check function arguments */
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if (a <= 0.0) return NPY_NAN;
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if (b <= 0.0) return NPY_NAN;
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if (x < 0.0) return NPY_NAN;
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if (1.0 < x) return NPY_NAN;
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/* some special cases */
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if (x == 0.0) return 0.0;
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if (x == 1.0) return 1.0;
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if ( (b * x) <= 1.0 && x <= 0.95)
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{
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return pseries(a, b, x);
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}
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xc = 1.0 - x;
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/* reverse a and b if x is greater than the mean */
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if (x > (a / (a + b)))
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{
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t = BetaInc(b, a, xc);
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if (t <= EPSILON) return 1.0 - EPSILON;
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return 1.0 - t;
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}
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/* Choose expansion for better convergence. */
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y = x * (a+b-2.0) - (a-1.0);
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if( y < 0.0 )
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w = incbcf( a, b, x );
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else
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w = incbd( a, b, x ) / xc;
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y = a * log(x);
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t = b * log(xc);
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if( (a+b) < MAXGAM && fabs(y) < MAXLOG && fabs(t) < MAXLOG )
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{
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t = pow(xc, b);
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t *= pow(x, a);
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t /= a;
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t *= w;
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t *= tgamma(a + b) / (tgamma(a) * tgamma(b));
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return t;
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}
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/* Resort to logarithms. */
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y += t + lgamma(a+b) - lgamma(a) - lgamma(b);
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y += log(w / a);
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if( y < MINLOG )
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t = 0.0;
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else
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t = exp(y);
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return t;
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}
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/* Continued fraction expansion #1
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* for incomplete beta integral
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*/
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DEVICE static double incbcf(double a, double b, double x)
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{
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double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
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double k1, k2, k3, k4, k5, k6, k7, k8;
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double r, t, ans, thresh;
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int n;
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k1 = a;
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k2 = a + b;
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k3 = a;
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k4 = a + 1.0;
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k5 = 1.0;
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k6 = b - 1.0;
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k7 = k4;
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k8 = a + 2.0;
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pkm2 = 0.0;
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qkm2 = 1.0;
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pkm1 = 1.0;
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qkm1 = 1.0;
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ans = 1.0;
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r = 1.0;
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n = 0;
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thresh = 3.0 * EPSILON;
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do
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{
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xk = -( x * k1 * k2 ) / ( k3 * k4 );
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pk = pkm1 + pkm2 * xk;
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qk = qkm1 + qkm2 * xk;
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pkm2 = pkm1;
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pkm1 = pk;
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qkm2 = qkm1;
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qkm1 = qk;
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xk = ( x * k5 * k6 ) / ( k7 * k8 );
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pk = pkm1 + pkm2 * xk;
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qk = qkm1 + qkm2 * xk;
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pkm2 = pkm1;
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pkm1 = pk;
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qkm2 = qkm1;
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qkm1 = qk;
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if( qk != 0.0 )
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r = pk/qk;
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if( r != 0.0 )
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{
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t = fabs( (ans - r) / r );
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ans = r;
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}
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else
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t = 1.0;
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if( t < thresh )
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break;
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k1 += 1.0;
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k2 += 1.0;
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k3 += 2.0;
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k4 += 2.0;
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k5 += 1.0;
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k6 -= 1.0;
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k7 += 2.0;
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k8 += 2.0;
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if( (fabs(qk) + fabs(pk)) > big )
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{
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pkm2 *= biginv;
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pkm1 *= biginv;
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qkm2 *= biginv;
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qkm1 *= biginv;
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}
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if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
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{
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pkm2 *= big;
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pkm1 *= big;
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qkm2 *= big;
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qkm1 *= big;
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}
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}
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while( ++n < 300 );
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return ans;
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}
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/* Continued fraction expansion #2
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* for incomplete beta integral
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*/
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DEVICE static double incbd(double a, double b, double x)
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{
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double xk, pk, pkm1, pkm2, qk, qkm1, qkm2;
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double k1, k2, k3, k4, k5, k6, k7, k8;
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double r, t, ans, z, thresh;
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int n;
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k1 = a;
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k2 = b - 1.0;
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k3 = a;
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k4 = a + 1.0;
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k5 = 1.0;
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k6 = a + b;
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k7 = a + 1.0;;
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k8 = a + 2.0;
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pkm2 = 0.0;
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qkm2 = 1.0;
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pkm1 = 1.0;
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qkm1 = 1.0;
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z = x / (1.0-x);
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ans = 1.0;
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r = 1.0;
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n = 0;
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thresh = 3.0 * EPSILON;
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do
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{
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xk = -( z * k1 * k2 ) / ( k3 * k4 );
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pk = pkm1 + pkm2 * xk;
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qk = qkm1 + qkm2 * xk;
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pkm2 = pkm1;
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pkm1 = pk;
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qkm2 = qkm1;
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qkm1 = qk;
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xk = ( z * k5 * k6 ) / ( k7 * k8 );
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pk = pkm1 + pkm2 * xk;
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qk = qkm1 + qkm2 * xk;
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pkm2 = pkm1;
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pkm1 = pk;
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qkm2 = qkm1;
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qkm1 = qk;
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if( qk != 0 )
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r = pk/qk;
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if( r != 0 )
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{
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t = fabs( (ans - r) / r );
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ans = r;
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}
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else
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t = 1.0;
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if( t < thresh )
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break;
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k1 += 1.0;
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k2 -= 1.0;
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k3 += 2.0;
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k4 += 2.0;
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k5 += 1.0;
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k6 += 1.0;
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k7 += 2.0;
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k8 += 2.0;
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if( (fabs(qk) + fabs(pk)) > big )
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{
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pkm2 *= biginv;
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pkm1 *= biginv;
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qkm2 *= biginv;
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qkm1 *= biginv;
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}
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if( (fabs(qk) < biginv) || (fabs(pk) < biginv) )
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{
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pkm2 *= big;
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pkm1 *= big;
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qkm2 *= big;
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qkm1 *= big;
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}
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}
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while( ++n < 300 );
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return ans;
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}
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/* Power series for incomplete beta integral.
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Use when b*x is small and x not too close to 1. */
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DEVICE static double pseries(double a, double b, double x)
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{
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double s, t, u, v, n, t1, z, ai;
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ai = 1.0 / a;
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u = (1.0 - b) * x;
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v = u / (a + 1.0);
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t1 = v;
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t = u;
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n = 2.0;
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s = 0.0;
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z = EPSILON * ai;
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while( fabs(v) > z )
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{
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u = (n - b) * x / n;
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t *= u;
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v = t / (a + n);
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s += v;
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n += 1.0;
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}
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s += t1;
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s += ai;
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u = a * log(x);
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if( (a+b) < MAXGAM && fabs(u) < MAXLOG )
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{
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t = tgamma(a + b) / (tgamma(a) * tgamma(b));
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s = s * t * pow(x,a);
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}
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else
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{
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t = lgamma(a + b) - lgamma(a) - lgamma(b) + u + log(s);
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if( t < MINLOG )
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s = 0.0;
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else
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s = exp(t);
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}
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return s;
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}

‎pytensor/scalar/math.py‎

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Original file line numberDiff line numberDiff line change
@@ -1495,8 +1495,25 @@ def grad(self, inp, grads):
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),
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]
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def c_code(self, *args, **kwargs):
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raise NotImplementedError()
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def c_support_code(self, **kwargs):
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with open(os.path.join(os.path.dirname(__file__), "c_code", "incbet.c")) as f:
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raw = f.read()
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return raw
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def c_code(self, node, name, inp, out, sub):
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(a, b, x) = inp
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(z,) = out
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if (
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node.inputs[0].type in float_types
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and node.inputs[1].type in float_types
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and node.inputs[2].type in float_types
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):
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return f"""{z} = BetaInc({a}, {b}, {x});"""
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raise NotImplementedError("type not supported", type)
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def c_code_cache_version(self):
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return (1,)
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betainc = BetaInc(upgrade_to_float_no_complex, name="betainc")

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