/*******************************************************************************
* Copyright (c) 2020 Konduit, K.K.
*
* 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
******************************************************************************/
//
// @author GS <sgazeos@gmail.com>
//
#include <op_boilerplate.h>
#include <NDArray.h>
#include <execution/Threads.h>
#include <ConstantTadHelper.h>
#include "../triangular_solve.h"
namespace nd4j {
namespace ops {
namespace helpers {
/*
* lower triangular process for system of linear equations
* x_1 = b_1/a_1,1
* x_2 = (b_2 - a_2,1 * x_1) / a_2,2
* x_3 = (b_3 - a_3,1 * x_1 - a_3,2 * x_2) / a_3,3
* ...
* x_M = (b_M - a_M,1 * x_1 - ... a_M,M-1 * x_M-1)/ a_M,M
*
* output == x
* a == leftInput
* b == rightInput
*
* */
template <typename T>
static __device__ void lowerTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
T const* rightInput, Nd4jLong const* rightInputShape,
bool const adjoint, T* output, Nd4jLong* outputShape,
Nd4jLong rows) {
for (auto r = 0; r < rows; r++) {
Nd4jLong posY[] = {r, 0};
Nd4jLong posX[] = {r, r};
auto xIndex = shape::getOffset(leftInputShape, posX, 0);
auto yIndex = shape::getOffset(rightInputShape, posY, 0);
auto zIndex = shape::getOffset(outputShape, posY, 0);
auto sum = rightInput[yIndex];
for (auto c = 0; c < r; c++) {
Nd4jLong posZ[] = {c, 0};
Nd4jLong pos[] = {r, c};
auto xcIndex = shape::getOffset(leftInputShape, pos, 0);
auto zcIndex = shape::getOffset(outputShape, posZ, 0);
sum -= leftInput[xcIndex] * output[zcIndex];
}
output[zIndex] = sum / leftInput[xIndex];
}
}
/*
* upper triangular process for system of linear equations
* x_M = b_M/a_M,M
* x_M-1 = (b_M-1 - a_M-1,M-2 * x_M) / a_M-1,M-1
* x_M-2 = (b_M-2 - a_M-2,M-3 * x_M-2 - a_M-2,M-1 * x_M) / a_3,3
* ...
* x_1 = (b_1 - a_1,2 * x_2 - ... a_1,M * x_M)/ a_1,1
*
* output == x
* a == leftInput
* b == rightInput
*
* */
template <typename T>
static __device__ void upperTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
T const* rightInput, Nd4jLong const* rightInputShape, bool const adjoint, T* output,
Nd4jLong* outputShape, Nd4jLong rows) {
for (auto r = rows; r > 0; r--) {
Nd4jLong posY[] = {r - 1, 0};
Nd4jLong posX[] = {r - 1, r - 1};
auto xIndex = shape::getOffset(leftInputShape, posX, 0);
auto yIndex = shape::getOffset(rightInputShape, posY, 0);
auto zIndex = shape::getOffset(outputShape, posY, 0);
auto sum = rightInput[yIndex];
for (auto c = r; c < rows; c++) {
Nd4jLong posZ[] = {c, 0};
Nd4jLong pos[] = {r - 1, c};
auto zcIndex = shape::getOffset(outputShape, posZ, 0);
auto xcIndex = shape::getOffset(leftInputShape, pos, 0);
sum -= leftInput[xcIndex] * output[zcIndex];
}
output[zIndex] = sum / leftInput[xIndex];
}
}
template <typename T>
static __global__ void triangularSolveKernel(T const* leftInput, Nd4jLong const* leftPartShape,
T const* rightInput, Nd4jLong const* rightPartShape, bool const lower, bool const adjoint, T* output,
Nd4jLong* outputShape, Nd4jLong* tadLeftShape, Nd4jLong* tadLeftOffset, Nd4jLong* tadRightShape,
Nd4jLong* tadRightOffset, Nd4jLong* tadOutputShape, Nd4jLong* tadOutputOffset, Nd4jLong batchNum) {
__shared__ Nd4jLong rows;
if (threadIdx.x == 0) {
rows = shape::sizeAt(leftPartShape, -2);
}
__syncthreads();
auto start = blockIdx.x * blockDim.x + threadIdx.x;
auto stop = batchNum;
auto increment = blockDim.x * gridDim.x;
for (auto i = start; i < stop; i += increment) {
auto pLeftPart = leftInput + tadLeftOffset[i];
auto pRightPart = rightInput + tadRightOffset[i];
auto pOutputPart = output + tadOutputOffset[i];
if (lower) {
lowerTriangularSolve<T>(pLeftPart, tadLeftShape, pRightPart, tadRightShape, adjoint, pOutputPart, tadOutputShape, rows);
} else {
upperTriangularSolve<T>(pLeftPart, tadLeftShape, pRightPart, tadRightShape, adjoint, pOutputPart, tadOutputShape, rows);
}
}
}
template <typename T>
static int triangularSolveFunctor_(nd4j::LaunchContext * context, NDArray* leftInput, NDArray* rightInput,
bool lower, bool adjoint, NDArray* output) {
NDArray::prepareSpecialUse({output}, {leftInput, rightInput});
auto leftTads = ConstantTadHelper::getInstance()->tadForDimensions(leftInput->getShapeInfo(), {-2, -1});
auto rightTads = ConstantTadHelper::getInstance()->tadForDimensions(rightInput->getShapeInfo(), {-2, -1});
auto outputTads = ConstantTadHelper::getInstance()->tadForDimensions(output->shapeInfo(), {-2, -1});
auto stream = context->getCudaStream();
T const* leftBuf = reinterpret_cast<T const*>(leftInput->getSpecialBuffer());
T const* rightBuf = reinterpret_cast<T const*>(rightInput->getSpecialBuffer());
T* outputBuf = reinterpret_cast<T*>(output->specialBuffer());
triangularSolveKernel<T><<<128, 128, 256, *stream>>>(leftBuf, leftInput->getSpecialShapeInfo(),
rightBuf, rightInput->getSpecialShapeInfo(), lower, adjoint, outputBuf, output->specialShapeInfo(),
leftTads.specialShapeInfo(), leftTads.specialOffsets(), rightTads.specialShapeInfo(),
rightTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets(),
leftTads.numberOfTads());
NDArray::registerSpecialUse({output}, {leftInput, rightInput});
return Status::OK();
}
int triangularSolveFunctor(nd4j::LaunchContext * context, NDArray* leftInput, NDArray* rightInput, bool lower, bool adjoint, NDArray* output) {
BUILD_SINGLE_SELECTOR(leftInput->dataType(), return triangularSolveFunctor_, (context, leftInput, rightInput, lower, adjoint, output), FLOAT_NATIVE);
}
template <typename T>
static __global__ void upperAdjointKernel(T const* input, T* output,
Nd4jLong batchSize, Nd4jLong rows, Nd4jLong columns,
Nd4jLong* inputTads, Nd4jLong* inputOffsets, Nd4jLong* outputTads, Nd4jLong* outputOffsets) {
for (auto b = blockIdx.x; b < batchSize; b += gridDim.x) {
auto inputPart = input + inputOffsets[b];
auto outputPart = output + outputOffsets[b];
for (auto r = threadIdx.x; r < rows; r += blockDim.x) {
for (auto c = threadIdx.y; c <= r; c += blockDim.y) {
Nd4jLong zPos[] = {r, c};
Nd4jLong xPos[] = {c, r};
auto zIndex = shape::getOffset(outputTads, zPos);
auto xIndex = shape::getOffset(inputTads, xPos);
outputPart[zIndex] = inputPart[xIndex];
}
}
}
}
template <typename T>
static __global__ void lowerAdjointKernel(T const* input, T* output,
Nd4jLong batchSize, Nd4jLong rows, Nd4jLong columns,
Nd4jLong* inputTads, Nd4jLong* inputOffsets, Nd4jLong* outputTads, Nd4jLong* outputOffsets) {
for (auto b = blockIdx.x; b < batchSize; b += gridDim.x) {
auto inputPart = input + inputOffsets[b];
auto outputPart = output + outputOffsets[b];
for (auto r = threadIdx.x; r < rows; r += blockDim.x) {
for (auto c = r + threadIdx.y; c < columns; c += blockDim.y) {
Nd4jLong zPos[] = {r, c};
Nd4jLong xPos[] = {c, r};
auto zIndex = shape::getOffset(outputTads, zPos);
auto xIndex = shape::getOffset(inputTads, xPos);
outputPart[zIndex] = inputPart[xIndex];
}
}
}
}
template <typename T>
static void adjointTriangularMatrix_(nd4j::LaunchContext* context, NDArray const* input, bool const lower,
NDArray* output) {
auto inputTads = ConstantTadHelper::getInstance()->tadForDimensions(input->getShapeInfo(), {-2, -1});
auto outputTads = ConstantTadHelper::getInstance()->tadForDimensions(output->getShapeInfo(), {-2, -1});
auto stream = context->getCudaStream();
auto inputBuf = reinterpret_cast<T const*>(input->getSpecialBuffer());
auto outputBuf = reinterpret_cast<T*>(output->specialBuffer());
auto rows = input->sizeAt(-2);
auto columns = input->sizeAt(-1);
if (lower) {
lowerAdjointKernel<T><<<128, 256, 256, *stream>>>(inputBuf, outputBuf, outputTads.numberOfTads(), rows, columns, inputTads.specialShapeInfo(), inputTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets());
} else {
upperAdjointKernel<T><<<128, 256, 256, *stream>>>(inputBuf, outputBuf, outputTads.numberOfTads(), rows, columns, inputTads.specialShapeInfo(), inputTads.specialOffsets(), outputTads.specialShapeInfo(), outputTads.specialOffsets());
}
}
void adjointMatrix(nd4j::LaunchContext* context, NDArray const* input, bool const lower, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), adjointTriangularMatrix_, (context, input, lower, output), FLOAT_NATIVE);
}
}
}
}