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cavis/libnd4j/include/ops/declarable/helpers/cpu/betaInc.cpp

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Eclipse Migration Initial Commit
2019-06-06 14:21:15 +02:00
/*******************************************************************************
* Copyright (c) 2015-2018 Skymind, Inc.
*
* This program and the accompanying materials are made available under the
* terms of the Apache License, Version 2.0 which is available at
* https://www.apache.org/licenses/LICENSE-2.0.
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
* License for the specific language governing permissions and limitations
* under the License.
*
* SPDX-License-Identifier: Apache-2.0
******************************************************************************/
//
// Created by Yurii Shyrma on 11.12.2017
//
#include<cmath>
#include <DataTypeUtils.h>
#include<ops/declarable/helpers/betaInc.h>
#include <NDArrayFactory.h>
namespace nd4j {
namespace ops {
namespace helpers {
const int maxIter = 10000; // max number of loop iterations in function for continued fractions
const int maxValue = 3000; // if a and b are both > maxValue, then apply Gauss-Legendre quadrature.
// 18 values of abscissas and weights for 36-point Gauss-Legendre integration,
// take a note - weights and abscissas are symmetric around the midpoint of the range of integration: 36/2 = 18
const double abscissas[18] = {0.0021695375159141994,
0.011413521097787704,0.027972308950302116,0.051727015600492421,
0.082502225484340941, 0.12007019910960293,0.16415283300752470,
0.21442376986779355, 0.27051082840644336, 0.33199876341447887,
0.39843234186401943, 0.46931971407375483, 0.54413605556657973,
0.62232745288031077, 0.70331500465597174, 0.78649910768313447,
0.87126389619061517, 0.95698180152629142};
const double weights[18] = {0.0055657196642445571,
0.012915947284065419,0.020181515297735382,0.027298621498568734,
0.034213810770299537,0.040875750923643261,0.047235083490265582,
0.053244713977759692,0.058860144245324798,0.064039797355015485,
0.068745323835736408,0.072941885005653087,0.076598410645870640,
0.079687828912071670,0.082187266704339706,0.084078218979661945,
0.085346685739338721,0.085983275670394821};
///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// modified Lentz’s algorithm for continued fractions,
// reference: Lentz, W.J. 1976, “Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions,”
template <typename T>
static T continFract(const T a, const T b, const T x) {
const T min = DataTypeUtils::min<T>() / DataTypeUtils::eps<T>();
const T amu = a - (T)1.;
const T apu = a + (T)1.;
const T apb = a + b;
// first iteration
T coeff1 = (T)1.;
T coeff2 = (T)1. - apb * x / apu;
if(math::nd4j_abs<T>(coeff2) < min)
coeff2 = min;
coeff2 = (T)1./coeff2;
T result = coeff2;
T val, delta;
int i2;
// rest iterations
for(int i=1; i <= maxIter; i+=2) {
i2 = 2*i;
// even step
val = i * (b - (T)i) * x / ((amu + (T)i2) * (a + (T)i2));
coeff2 = (T)(1.) + val * coeff2;
if(math::nd4j_abs<T>(coeff2) < min)
coeff2 = min;
coeff2 = (T)1. / coeff2;
coeff1 = (T)(1.) + val / coeff1;
if(math::nd4j_abs<T>(coeff1) < min)
coeff1 = min;
result *= coeff1 * coeff2;
//***********************************************//
// odd step
val = -(a + (T)i) * (apb + (T)i) * x / ((a + (T)i2) * (apu + (T)i2));
coeff2 = (T)(1.) + val * coeff2;
if(math::nd4j_abs<T>(coeff2) < min)
coeff2 = min;
coeff2 = (T)1. / coeff2;
coeff1 = (T)(1.) + val / coeff1;
if(math::nd4j_abs<T>(coeff1) < min)
coeff1 = min;
delta = coeff1 * coeff2;
result *= delta;
// condition to stop loop
if(math::nd4j_abs<T>(delta - (T)1.) <= DataTypeUtils::eps<T>())
break;
}
return result;
}
///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// evaluates incomplete beta integral using Gauss-Legendre quadrature method
template <typename T>
static T gausLegQuad(const T a, const T b, const T x) {
T upLim, t, result;
T sum = (T)0.;
T amu = a - (T)1.;
T bmu = b - (T)1.;
T rat = a / (a + b);
T lnrat = math::nd4j_log<T,T>(rat);
T lnratm = math::nd4j_log<T,T>((T)1. - rat);
t = math::nd4j_sqrt<T,T>(a * b /((a + b) * (a + b) * (a + b + (T)1.)));
if (x > rat) {
if (x >= (T)1.)
return (T)1.0;
upLim = math::nd4j_min<T>((T)1., math::nd4j_max<T>(rat + (T)1.*t, x + (T)5.*t));
}
else {
if (x <= (T)0.)
return (T)0.;
upLim = math::nd4j_max<T>(0., math::nd4j_min<T>(rat - (T)10.*t, x - (T)5.*t));
}
// Gauss-Legendre
PRAGMA_OMP_SIMD_SUM(sum)
for (int i = 0; i < 18; ++i) {
auto t = x + (upLim - x) * (T)abscissas[i];
sum += (T)weights[i] * math::nd4j_exp<T,T>(amu * (math::nd4j_log<T,T>(t) - lnrat) + bmu * (math::nd4j_log<T,T>((T)1. - t) - lnratm));
}
if (std::is_same<T, double>::value) {
result = sum * (upLim - x) * math::nd4j_exp<T,T>(amu * lnrat - lgamma(static_cast<double>(a)) + bmu * lnratm - lgamma(static_cast<double>(b)) + lgamma(static_cast<double>(a + b)));
} else {
result = sum * (upLim - x) * math::nd4j_exp<T,T>(amu * lnrat - lgamma((float) a) + bmu * lnratm - lgamma((float) b) + lgamma(static_cast<float>(a + b)));
}
if(result > (T)0.)
return (T)1. - result;
return -result;
}
///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// evaluates incomplete beta function for positive a and b, and x between 0 and 1.
template <typename T>
static T betaIncTA(T a, T b, T x) {
// if (a <= (T)0. || b <= (T)0.)
// throw("betaInc function: a and b must be > 0 !");
// if (x < (T)0. || x > (T)1.)
// throw("betaInc function: x must be within (0, 1) interval !");
// t^{n-1} * (1 - t)^{n-1} is symmetric function with respect to x = 0.5
if(a == b && x == (T)0.5)
return (T)0.5;
if (x == (T)0. || x == (T)1.)
return x;
if (a > (T)maxValue && b > (T)maxValue)
return gausLegQuad<T>(a, b, x);
T front = math::nd4j_exp<T,T>( lgamma(static_cast<double>(a + b)) - lgamma(static_cast<double>(a)) - lgamma(static_cast<double>(b)) + a * math::nd4j_log<T, T>(x) + b * math::nd4j_log<T, T>((T)1. - x));
// continued fractions
if (x < (a + (T)1.) / (a + b + (T)2.))
return front * continFract(a, b, x) / a;
// symmetry relation
else
return (T)1. - front * continFract(b, a, (T)1. - x) / b;
}
template<typename T>
NDArray betaIncT(nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x) {
auto result = NDArray(&x, false, x.getContext());
int xLen = x.lengthOf();
PRAGMA_OMP_PARALLEL_FOR_IF(xLen > Environment::getInstance()->elementwiseThreshold())
for(int i = 0; i < xLen; ++i) {
result.p(i, betaIncTA<T>(a.e<T>(i), b.e<T>(i), x.e<T>(i)));
}
return result;
}
///////////////////////////////////////////////////////////////////
///////////////////////////////////////////////////////////////////
// overload betaInc for arrays, shapes of a, b and x must be the same !!!
NDArray betaInc(nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x) {
auto xType = a.dataType();
BUILD_SINGLE_SELECTOR(xType, return betaIncT, (context,a, b, x), FLOAT_TYPES);
return a;
}
template float continFract<float> (const float a, const float b, const float x);
template float16 continFract<float16>(const float16 a, const float16 b, const float16 x);
template bfloat16 continFract<bfloat16>(const bfloat16 a, const bfloat16 b, const bfloat16 x);
template double continFract<double> (const double a, const double b, const double x);
template float gausLegQuad<float> (const float a, const float b, const float x);
template float16 gausLegQuad<float16>(const float16 a, const float16 b, const float16 x);
template bfloat16 gausLegQuad<bfloat16>(const bfloat16 a, const bfloat16 b, const bfloat16 x);
template double gausLegQuad<double> (const double a, const double b, const double x);
template float betaIncTA<float> (const float a, const float b, const float x);
template float16 betaIncTA<float16>(const float16 a, const float16 b, const float16 x);
template bfloat16 betaIncTA<bfloat16>(const bfloat16 a, const bfloat16 b, const bfloat16 x);
template double betaIncTA<double> (const double a, const double b, const double x);
template NDArray betaIncT<float> (nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x);
template NDArray betaIncT<float16>(nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x);
template NDArray betaIncT<bfloat16>(nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x);
template NDArray betaIncT<double> (nd4j::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x);
}
}
}