235 lines
12 KiB
Plaintext
235 lines
12 KiB
Plaintext
/*******************************************************************************
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* Copyright (c) 2020 Konduit, K.K.
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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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// @author GS <sgazeos@gmail.com>
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//
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#include <system/op_boilerplate.h>
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#include <array/NDArray.h>
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#include <execution/Threads.h>
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#include <helpers/ConstantTadHelper.h>
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#include "../triangular_solve.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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* lower triangular process for system of linear equations
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* x_1 = b_1/a_1,1
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* x_2 = (b_2 - a_2,1 * x_1) / a_2,2
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* x_3 = (b_3 - a_3,1 * x_1 - a_3,2 * x_2) / a_3,3
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* ...
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* x_M = (b_M - a_M,1 * x_1 - ... a_M,M-1 * x_M-1)/ a_M,M
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*
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* output == x
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* a == leftInput
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* b == rightInput
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*
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* */
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template <typename T>
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static __device__ void lowerTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
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T const* rightInput, Nd4jLong const* rightInputShape,
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bool const adjoint, T* output, Nd4jLong* outputShape,
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Nd4jLong rows, Nd4jLong cols) {
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for (auto r = 0; r < rows; r++) {
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for (auto j = 0; j < cols; j++) {
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Nd4jLong posY[] = {r, j};
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Nd4jLong posX[] = {r, r};
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auto xIndex = shape::getOffset(leftInputShape, posX, 0);
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auto yIndex = shape::getOffset(rightInputShape, posY, 0);
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auto zIndex = shape::getOffset(outputShape, posY, 0);
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auto sum = rightInput[yIndex];
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for (auto c = 0; c < r; c++) {
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Nd4jLong posZ[] = {c, j};
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Nd4jLong pos[] = {r, c};
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auto xcIndex = shape::getOffset(leftInputShape, pos, 0);
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auto zcIndex = shape::getOffset(outputShape, posZ, 0);
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sum -= leftInput[xcIndex] * output[zcIndex];
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}
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output[zIndex] = sum / leftInput[xIndex];
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}
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}
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}
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/*
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* upper triangular process for system of linear equations
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* x_M = b_M/a_M,M
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* x_M-1 = (b_M-1 - a_M-1,M-2 * x_M) / a_M-1,M-1
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* x_M-2 = (b_M-2 - a_M-2,M-3 * x_M-2 - a_M-2,M-1 * x_M) / a_3,3
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* ...
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* x_1 = (b_1 - a_1,2 * x_2 - ... a_1,M * x_M)/ a_1,1
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*
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* output == x
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* a == leftInput
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* b == rightInput
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*
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* */
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template <typename T>
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static __device__ void upperTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
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T const* rightInput, Nd4jLong const* rightInputShape, bool const adjoint, T* output,
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Nd4jLong* outputShape, Nd4jLong rows, Nd4jLong cols) {
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for (auto r = rows; r > 0; r--) {
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for (auto j = 0; j < cols; j++) {
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Nd4jLong posY[] = {r - 1, j};
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Nd4jLong posX[] = {r - 1, r - 1};
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auto xIndex = shape::getOffset(leftInputShape, posX, 0);
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auto yIndex = shape::getOffset(rightInputShape, posY, 0);
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auto zIndex = shape::getOffset(outputShape, posY, 0);
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auto sum = rightInput[yIndex];
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for (auto c = r; c < rows; c++) {
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Nd4jLong posZ[] = {c, j};
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Nd4jLong pos[] = {r - 1, c};
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auto zcIndex = shape::getOffset(outputShape, posZ, 0);
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auto xcIndex = shape::getOffset(leftInputShape, pos, 0);
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sum -= leftInput[xcIndex] * output[zcIndex];
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}
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output[zIndex] = sum / leftInput[xIndex];
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}
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}
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}
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template <typename T>
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static __global__ void triangularSolveKernel(T const* leftInput, Nd4jLong const* leftPartShape,
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T const* rightInput, Nd4jLong const* rightPartShape, bool const lower, bool const adjoint, T* output,
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Nd4jLong* outputShape, Nd4jLong* tadLeftShape, Nd4jLong* tadLeftOffset, Nd4jLong* tadRightShape,
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Nd4jLong* tadRightOffset, Nd4jLong* tadOutputShape, Nd4jLong* tadOutputOffset, Nd4jLong batchNum) {
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__shared__ Nd4jLong rows;
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__shared__ Nd4jLong cols;
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if (threadIdx.x == 0) {
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rows = shape::sizeAt(leftPartShape, -2);
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cols = shape::sizeAt(rightPartShape, -1);
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}
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__syncthreads();
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auto start = blockIdx.x * blockDim.x + threadIdx.x;
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auto stop = batchNum;
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auto increment = blockDim.x * gridDim.x;
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for (auto i = start; i < stop; i += increment) {
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auto pLeftPart = leftInput + tadLeftOffset[i];
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auto pRightPart = rightInput + tadRightOffset[i];
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auto pOutputPart = output + tadOutputOffset[i];
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if (lower) {
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lowerTriangularSolve<T>(pLeftPart, tadLeftShape, pRightPart, tadRightShape, adjoint, pOutputPart, tadOutputShape, rows, cols);
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} else {
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upperTriangularSolve<T>(pLeftPart, tadLeftShape, pRightPart, tadRightShape, adjoint, pOutputPart, tadOutputShape, rows, cols);
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}
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}
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}
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template <typename T>
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static int triangularSolveFunctor_(sd::LaunchContext * context, NDArray* leftInput, NDArray* rightInput,
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bool lower, bool adjoint, NDArray* output) {
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NDArray::prepareSpecialUse({output}, {leftInput, rightInput});
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auto leftTads = ConstantTadHelper::getInstance()->tadForDimensions(leftInput->getShapeInfo(), {-2, -1});
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auto rightTads = ConstantTadHelper::getInstance()->tadForDimensions(rightInput->getShapeInfo(), {-2, -1});
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auto outputTads = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {-2, -1});
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auto stream = context->getCudaStream();
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T const* leftBuf = reinterpret_cast<T const*>(leftInput->getSpecialBuffer());
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T const* rightBuf = reinterpret_cast<T const*>(rightInput->getSpecialBuffer());
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T* outputBuf = reinterpret_cast<T*>(output->specialBuffer());
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triangularSolveKernel<T><<<128, 128, 256, *stream>>>(leftBuf, leftInput->getSpecialShapeInfo(),
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rightBuf, rightInput->getSpecialShapeInfo(), lower, adjoint, outputBuf, output->specialShapeInfo(),
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leftTads.specialShapeInfo(), leftTads.specialOffsets(), rightTads.specialShapeInfo(),
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rightTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets(),
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leftTads.numberOfTads());
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NDArray::registerSpecialUse({output}, {leftInput, rightInput});
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return Status::OK();
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}
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int triangularSolveFunctor(sd::LaunchContext * context, NDArray* leftInput, NDArray* rightInput, bool lower, bool adjoint, NDArray* output) {
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BUILD_SINGLE_SELECTOR(leftInput->dataType(), return triangularSolveFunctor_, (context, leftInput, rightInput, lower, adjoint, output), FLOAT_NATIVE);
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}
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template <typename T>
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static __global__ void upperAdjointKernel(T const* input, T* output,
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Nd4jLong batchSize, Nd4jLong rows, Nd4jLong columns,
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Nd4jLong* inputTads, Nd4jLong* inputOffsets, Nd4jLong* outputTads, Nd4jLong* outputOffsets) {
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for (auto b = blockIdx.x; b < batchSize; b += gridDim.x) {
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auto inputPart = input + inputOffsets[b];
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auto outputPart = output + outputOffsets[b];
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for (auto r = threadIdx.x; r < rows; r += blockDim.x) {
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for (auto c = threadIdx.y; c <= r; c += blockDim.y) {
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Nd4jLong zPos[] = {r, c};
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Nd4jLong xPos[] = {c, r};
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auto zIndex = shape::getOffset(outputTads, zPos);
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auto xIndex = shape::getOffset(inputTads, xPos);
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outputPart[zIndex] = inputPart[xIndex];
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}
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}
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}
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}
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template <typename T>
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static __global__ void lowerAdjointKernel(T const* input, T* output,
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Nd4jLong batchSize, Nd4jLong rows, Nd4jLong columns,
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Nd4jLong* inputTads, Nd4jLong* inputOffsets, Nd4jLong* outputTads, Nd4jLong* outputOffsets) {
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for (auto b = blockIdx.x; b < batchSize; b += gridDim.x) {
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auto inputPart = input + inputOffsets[b];
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auto outputPart = output + outputOffsets[b];
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for (auto r = threadIdx.x; r < rows; r += blockDim.x) {
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for (auto c = r + threadIdx.y; c < columns; c += blockDim.y) {
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Nd4jLong zPos[] = {r, c};
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Nd4jLong xPos[] = {c, r};
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auto zIndex = shape::getOffset(outputTads, zPos);
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auto xIndex = shape::getOffset(inputTads, xPos);
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outputPart[zIndex] = inputPart[xIndex];
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}
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}
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}
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}
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template <typename T>
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static void adjointTriangularMatrix_(sd::LaunchContext* context, NDArray const* input, bool const lower,
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NDArray* output) {
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auto inputTads = ConstantTadHelper::getInstance()->tadForDimensions(input->getShapeInfo(), {-2, -1});
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auto outputTads = ConstantTadHelper::getInstance()->tadForDimensions(output->getShapeInfo(), {-2, -1});
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auto stream = context->getCudaStream();
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auto inputBuf = reinterpret_cast<T const*>(input->getSpecialBuffer());
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auto outputBuf = reinterpret_cast<T*>(output->specialBuffer());
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auto rows = input->sizeAt(-2);
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auto columns = input->sizeAt(-1);
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if (lower) {
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lowerAdjointKernel<T><<<128, 256, 256, *stream>>>(inputBuf, outputBuf, outputTads.numberOfTads(), rows, columns, inputTads.specialShapeInfo(), inputTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets());
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} else {
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upperAdjointKernel<T><<<128, 256, 256, *stream>>>(inputBuf, outputBuf, outputTads.numberOfTads(), rows, columns, inputTads.specialShapeInfo(), inputTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets());
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}
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}
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void adjointMatrix(sd::LaunchContext* context, NDArray const* input, bool const lower, NDArray* output) {
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BUILD_SINGLE_SELECTOR(input->dataType(), adjointTriangularMatrix_, (context, input, lower, output), FLOAT_NATIVE);
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}
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}
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}
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}
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