141 lines
4.6 KiB
C++
141 lines
4.6 KiB
C++
/*******************************************************************************
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* Copyright (c) 2015-2018 Skymind, Inc.
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*
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* This program and the accompanying materials are made available under the
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* terms of the Apache License, Version 2.0 which is available at
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* https://www.apache.org/licenses/LICENSE-2.0.
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
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* License for the specific language governing permissions and limitations
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* under the License.
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*
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* SPDX-License-Identifier: Apache-2.0
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******************************************************************************/
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//
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// Created by Yurii Shyrma on 11.12.2017
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//
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#include<cmath>
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#include <array/DataTypeUtils.h>
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#include <ops/declarable/helpers/betaInc.h>
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#include <array/NDArrayFactory.h>
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#include <execution/Threads.h>
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namespace sd {
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namespace ops {
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namespace helpers {
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///////////////////////////////////////////////////////////////////
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// modified Lentz’s algorithm for continued fractions,
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// reference: Lentz, W.J. 1976, “Generating Bessel Functions in Mie Scattering Calculations Using Continued Fractions”
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template <typename T>
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static T continuedFraction(const T a, const T b, const T x) {
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const T min = DataTypeUtils::min<T>() / DataTypeUtils::eps<T>();
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const T aPlusb = a + b;
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T val, aPlus2i;
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T t2 = 1;
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T t1 = static_cast<T>(1) - aPlusb * x / (a + static_cast<T>(1));
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if(math::nd4j_abs<T>(t1) < min)
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t1 = min;
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t1 = static_cast<T>(1) / t1;
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T result = t1;
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for(uint i = 1; i <= maxIter; ++i) {
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aPlus2i = a + static_cast<T>(2*i);
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val = i * (b - i) * x / ((aPlus2i - static_cast<T>(1)) * aPlus2i);
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// t1
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t1 = static_cast<T>(1) + val * t1;
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if(math::nd4j_abs<T>(t1) < min)
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t1 = min;
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t1 = static_cast<T>(1) / t1;
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// t2
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t2 = static_cast<T>(1) + val / t2;
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if(math::nd4j_abs<T>(t2) < min)
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t2 = min;
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// result
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result *= t2 * t1;
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val = -(a + i) * (aPlusb + i) * x / ((aPlus2i + static_cast<T>(1)) * aPlus2i);
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// t1
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t1 = static_cast<T>(1) + val * t1;
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if(math::nd4j_abs<T>(t1) < min)
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t1 = min;
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t1 = static_cast<T>(1) / t1;
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// t2
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t2 = static_cast<T>(1) + val / t2;
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if(math::nd4j_abs<T>(t2) < min)
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t2 = min;
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// result
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val = t2 * t1;
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result *= val;
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// condition to stop loop
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if(math::nd4j_abs<T>(val - static_cast<T>(1)) <= DataTypeUtils::eps<T>())
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return result;
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}
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return DataTypeUtils::infOrMax<T>(); // no convergence, more iterations is required, return infinity
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}
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///////////////////////////////////////////////////////////////////
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// evaluates incomplete beta function for positive a and b, and x between 0 and 1.
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template <typename T>
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static T betaIncCore(T a, T b, T x) {
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// if (a <= (T)0. || b <= (T)0.)
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// throw("betaInc function: a and b must be > 0 !");
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// if (x < (T)0. || x > (T)1.)
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// throw("betaInc function: x must be within (0, 1) interval !");
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// t^{n-1} * (1 - t)^{n-1} is symmetric function with respect to x = 0.5
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if(a == b && x == static_cast<T>(0.5))
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return static_cast<T>(0.5);
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if (x == static_cast<T>(0) || x == static_cast<T>(1))
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return x;
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const T gammaPart = lgamma(a) + lgamma(b) - lgamma(a + b);
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const T front = math::nd4j_exp<T,T>(math::nd4j_log<T, T>(x) * a + math::nd4j_log<T, T>(1.f - x) * b - gammaPart);
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if (x <= (a + static_cast<T>(1)) / (a + b + static_cast<T>(2)))
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return front * continuedFraction<T>(a, b, x) / a;
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else // symmetry relation
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return static_cast<T>(1) - front * continuedFraction<T>(b, a, static_cast<T>(1) - x) / b;
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}
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///////////////////////////////////////////////////////////////////
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template<typename T>
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static void betaIncForArray(sd::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x, NDArray& output) {
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int xLen = x.lengthOf();
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auto func = PRAGMA_THREADS_FOR {
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for (auto i = start; i < stop; i++)
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output.t<T>(i) = betaIncCore<T>(a.t<T>(i), b.t<T>(i), x.t<T>(i));
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};
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sd::Threads::parallel_for(func, 0, xLen);
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}
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///////////////////////////////////////////////////////////////////
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// overload betaInc for arrays, shapes of a, b and x must be the same !!!
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void betaInc(sd::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x, NDArray& output) {
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auto xType = a.dataType();
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BUILD_SINGLE_SELECTOR(xType, betaIncForArray, (context, a, b, x, output), FLOAT_TYPES);
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}
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BUILD_SINGLE_TEMPLATE(template void betaIncForArray, (sd::LaunchContext * context, const NDArray& a, const NDArray& b, const NDArray& x, NDArray& output), FLOAT_TYPES);
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}
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}
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}
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