/* ****************************************************************************** * * * 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. * * See the NOTICE file distributed with this work for additional * information regarding copyright ownership. * 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 ******************************************************************************/ // // @author sgazeos@gmail.com // #include //#include #include //#include #include #include #include #include namespace sd { namespace ops { namespace helpers { /** * gammaLess - compute gamma distributed value for shapes (alpha) from 0 to 1 * @tparam T - any float types are acceptable * @param rng - random generator for uniformly vals * @param alpha - shape of distribution * @param beta - scale of distributed values * @return gamma distributed value */ template T gammaLess(graph::RandomGenerator& rng, T const alpha, T const beta) { auto d = T(1.0334f) - T(0.0766f) * math::p_exp(T(2.2942f) * alpha); auto a = math::p_pow(T(2.f), alpha) * math::p_pow(T(1.f) - math::p_exp(-d * T(0.5f)), alpha); auto b = alpha * math::p_pow(d, alpha - T(1.f)) * exp(-d); auto c = a + b; T rawX; static auto index = 0LL; const T underAlpha = T(1.f) / alpha; const T powerAlpha = math::p_pow(T(2.f), alpha - T(1.f)); for (;;) { auto u = rng.relativeT(index++, T(0.f), T(1.f)); if (u <= a / c) rawX = -T(2.f) * math::p_log(T(1.f) - T(0.5f) * math::p_pow(T(c * u), underAlpha)); else rawX = - math::p_log(c * (T(1.f) - u)/(alpha * math::p_pow(d, alpha - T(1.f)))); T v = rng.relativeT(index++, 0.f, 1.f); if (rawX <= d) { auto testVal = (math::p_pow(rawX, alpha - 1.f) * math::p_exp(-T(0.5f) * rawX)) / (powerAlpha * math::p_pow(T(1.f) - math::p_exp(-T(0.5f) * rawX), alpha - T(1.f))); if (testVal < v) continue; break; } else { if (v <= math::p_pow(d / rawX, T(1.f) - alpha)) break; continue; } } return rawX / beta; } /** * gammaGreat - generate gamma distributed value for shape (alpha) greater then 1 * @tparam T - given type (any float type is accepted.) * @param rng - random generator * @param alpha - shape of the gamma distribution (alpha) * @param beta - scale of the gamma distribution (beta) * @return - gamma distributed value with given params */ template T gammaGreat(graph::RandomGenerator& rng, T const alpha, T const beta) { auto decreasedAlpha = alpha - T(1.f/3.f); auto c = T(1.)/ math::p_sqrt(T(9.f) * decreasedAlpha); static auto index = 0LL; T x; auto normalDistributed = [](graph::RandomGenerator& rng, Nd4jLong& index) { auto v1 = rng.relativeT(index++, T(0.f), T(1.f)); auto v2 = rng.relativeT(index++, T(0.f), T(1.f)); return math::p_cos(T(2.f * 3.141592f) * v2) * math::p_sqrt(T(-2.f) * math::p_log(v1)); }; // const T underAlpha = T(1.f) / alpha; // const T powerAlpha = math::p_pow(T(2.f), alpha - T(1.f)); float normalizedVar; for(;;) { do { x = normalDistributed(rng, index); //printf("X = %f\n", x); normalizedVar = T(1.f) + c * x; } while(normalizedVar < T(0.f)); normalizedVar = normalizedVar * normalizedVar * normalizedVar; //v * v * v; auto u = rng.relativeT(index++, T(0.f), T(1.f)); //printf("UNI = %f\n", u); if( u < T(1.f) - T(.0331f) * (x * x) * (x * x) ) break; //return (d * v / b); if( log(u) < 0.5f * x * x + decreasedAlpha * (1. - normalizedVar + math::p_log(normalizedVar)) ) break; } return (decreasedAlpha * normalizedVar / beta); } template void fillRandomGamma_(LaunchContext* context, graph::RandomGenerator& rng, NDArray* alpha, NDArray* beta, NDArray* output) { auto broadcasted = alpha->shapeInfo(); if (beta != nullptr) { const Nd4jLong* broadcastedShape = nullptr; ShapeUtils::evalBroadcastShapeInfo(*alpha, *beta, true, broadcastedShape, context->getWorkspace()); broadcasted = broadcastedShape; } auto step = shape::length(broadcasted); auto shift = output->lengthOf() / step; auto copyAlpha = alpha; auto copyBeta = beta; if (beta != nullptr) { NDArray alphaBroadcasted(broadcasted, alpha->dataType(), false, context); NDArray betaBroadcasted(broadcasted, beta->dataType(), false, context); copyAlpha = new NDArray(alphaBroadcasted.applyTrueBroadcast(BroadcastOpsTuple::Assign(), *alpha)); copyBeta = new NDArray(betaBroadcasted.applyTrueBroadcast(BroadcastOpsTuple::Assign(), *beta)); } bool directOutput = output->ews() == 1 && output->ordering() == 'c'; T* outputBuf = output->dataBuffer()->primaryAsT(); PRAGMA_OMP_PARALLEL_FOR for (Nd4jLong k = 0; k < shift; k++) { auto pos = k * step; for (Nd4jLong e = 0; e < step; e++) if (directOutput) { outputBuf[pos + e] = copyAlpha->t(e) <= 1? gammaLess(rng, copyAlpha->t(e), beta?copyBeta->t(e):T(1.f)):gammaGreat(rng, copyAlpha->t(e), beta?copyBeta->t(e):T(1.f)); } else { output->r(pos + e) = copyAlpha->t(e) <= 1? gammaLess(rng, copyAlpha->t(e), beta?copyBeta->t(e):T(1.f)):gammaGreat(rng, copyAlpha->t(e), beta?copyBeta->t(e):T(1.f)); } } if (beta != nullptr) { delete copyAlpha; delete copyBeta; //delete broadcasted; } } void fillRandomGamma(LaunchContext* context, graph::RandomGenerator& rng, NDArray* alpha, NDArray* beta, NDArray* output) { BUILD_SINGLE_SELECTOR(output->dataType(), fillRandomGamma_, (context, rng, alpha, beta, output), FLOAT_NATIVE); } BUILD_SINGLE_TEMPLATE(template void fillRandomGamma_, (LaunchContext* context, graph::RandomGenerator& rng, NDArray* alpha, NDArray* beta, NDArray* output), FLOAT_NATIVE); /* * algorithm Poisson generator based upon the inversion by sequential search:[48]:505 init: Let x ← 0, p ← e−λ, s ← p. Generate uniform random number u in [0,1]. while u > s do: x ← x + 1. p ← p * λ / x. s ← s + p. return x. * */ template void fillRandomPoisson_(LaunchContext* context, graph::RandomGenerator& rng, NDArray* lambda, NDArray* output) { auto shift = output->lengthOf() / lambda->lengthOf(); auto step = lambda->lengthOf(); T* lambdaBuf = lambda->dataBuffer()->primaryAsT(); Z* outputBuf = output->dataBuffer()->primaryAsT(); bool directLa = lambda->ews() == 1 && lambda->ordering() == 'c'; bool directOut = output->ews() == 1 && output->ordering() == 'c'; PRAGMA_OMP_PARALLEL_FOR for (Nd4jLong k = 0; k < shift; k++) { auto pos = k * step; auto u = rng.relativeT(k, 0., 1.); for (Nd4jLong e = 0; e < step; e++) { auto p = math::nd4j_exp(-lambda->t(e)); auto s = p; auto x = Z(0.f); while (u > s) { x += 1.f; p *= directLa?lambdaBuf[e]/x:lambda->t(e) / x; s += p; } if (directOut) outputBuf[pos + e] = x; else output->r(pos + e) = x; } } } void fillRandomPoisson(LaunchContext* context, graph::RandomGenerator& rng, NDArray* lambda, NDArray* output) { BUILD_DOUBLE_SELECTOR(lambda->dataType(), output->dataType(), fillRandomPoisson_, (context, rng, lambda, output), FLOAT_TYPES, FLOAT_TYPES); } BUILD_DOUBLE_TEMPLATE(template void fillRandomPoisson_, (LaunchContext* context, graph::RandomGenerator& rng, NDArray* lambda, NDArray* output), FLOAT_TYPES, FLOAT_TYPES); template void fillRandomUniform_(LaunchContext* context, graph::RandomGenerator& rng, NDArray* min, NDArray* max, NDArray* output) { T minVal = T(0); T maxVal = DataTypeUtils::max(); if (min) minVal = min->t(0); if (max) maxVal = max->t(0); if (output->isR()) RandomLauncher::fillUniform(context, rng, output, minVal, maxVal); else { PRAGMA_OMP_PARALLEL_FOR for (Nd4jLong i = 0; i < output->lengthOf(); i++) { output->r(i) = rng.relativeT(i, minVal, maxVal); } } } void fillRandomUniform(LaunchContext* context, graph::RandomGenerator& rng, NDArray* min, NDArray* max, NDArray* output) { BUILD_SINGLE_SELECTOR(output->dataType(), fillRandomUniform_, (context, rng, min, max, output), NUMERIC_TYPES); } // used https://en.wikipedia.org/wiki/Categorical_distribution // methods: gumbel trick + softmax + argmax template void fillRandomMultiNomial_(LaunchContext* context, graph::RandomGenerator& rng, NDArray& input, NDArray& output, const Nd4jLong numOfSamples, const int dimC) { const Tx* x = input.bufferAsT(); Tz* z = output.bufferAsT(); Tx minVal = DataTypeUtils::min(); Tx maxVal = 1.0; auto dimA = (0 == dimC) ? 1 : 0; const Nd4jLong batchValue = output.sizeAt(dimC); const Nd4jLong numOfClassX = input.sizeAt(dimA); const Nd4jLong zDimAstride = output.stridesOf()[dimA]; const Nd4jLong xDimAstride = input.stridesOf()[dimA]; const Nd4jLong zDimCstride = output.stridesOf()[dimC]; const Nd4jLong xDimCstride = input.stridesOf()[dimC]; auto func = PRAGMA_THREADS_FOR_2D{ for (auto nBatchIndex = start_x; nBatchIndex < stop_x; nBatchIndex += inc_x) { for (auto nSampleIndexInBatch = start_y; nSampleIndexInBatch < stop_y; nSampleIndexInBatch += inc_y) { const Tx* xTad = x + (nBatchIndex * xDimCstride); Tz* zTad = z + (nBatchIndex * zDimCstride); Tz& arg = zTad[nSampleIndexInBatch * zDimAstride]; Tx Max = -minVal; auto nSamplesPerBatch = nBatchIndex * numOfClassX * numOfSamples; auto nClassesPerSample = nSampleIndexInBatch * numOfClassX; for (Nd4jLong nClass = 0; nClass < numOfClassX; nClass += 1) { auto nIndex = nSamplesPerBatch + nClassesPerSample + nClass; auto unifornLog = sd::math::nd4j_log(-sd::math::nd4j_log(rng.relativeT(nIndex, minVal, maxVal))); Tx tValue = (xTad[nClass * xDimAstride] - unifornLog); if (tValue > Max) { Max = tValue; arg = nClass; } } } } }; samediff::Threads::parallel_for(func, 0, batchValue, 1, 0, numOfSamples, 1); rng.rewindH(output.lengthOf()*numOfClassX); return; } void fillRandomMultiNomial(LaunchContext* context, graph::RandomGenerator& rng, NDArray& input, NDArray& output, const Nd4jLong numOfSamples, const int dimC) { BUILD_DOUBLE_SELECTOR(input.dataType(), output.dataType(), fillRandomMultiNomial_, (context, rng, input, output, numOfSamples, dimC), FLOAT_TYPES, INDEXING_TYPES); } } } }