/*
* ******************************************************************************
* *
* *
* * 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 GS <sgazeos@gmail.com>
//
#include <system/op_boilerplate.h>
#include <array/NDArray.h>
#include <execution/Threads.h>
#include <helpers/ConstantTadHelper.h>
#include "../triangular_solve.h"
namespace sd {
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 _CUDA_HD void lowerTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
T const* rightInput, Nd4jLong const* rightInputShape,
bool const unitOnDiag, T* output, const Nd4jLong* outputShape,
Nd4jLong rows, Nd4jLong cols) {
for (auto r = 0; r < rows; r++) {
for (auto j = 0; j < cols; j++) {
Nd4jLong posY[] = {r, j};
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, j};
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] = unitOnDiag?sum: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 _CUDA_HD void upperTriangularSolve(T const* leftInput, Nd4jLong const* leftInputShape,
T const* rightInput, Nd4jLong const* rightInputShape, bool const unitOnDiag, T* output,
const Nd4jLong* outputShape, Nd4jLong rows, Nd4jLong cols) {
for (auto r = rows; r > 0; r--) {
for (auto j = 0; j < cols; j++) {
Nd4jLong posY[] = {r - 1, j};
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, j};
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] = unitOnDiag?sum: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 unitsOnDiag, T* output,
const Nd4jLong* outputShape, const Nd4jLong* tadLeftShape, const Nd4jLong* tadLeftOffset, const Nd4jLong* tadRightShape,
const Nd4jLong* tadRightOffset, const Nd4jLong* tadOutputShape, const Nd4jLong* tadOutputOffset, Nd4jLong batchNum) {
__shared__ Nd4jLong rows;
__shared__ Nd4jLong cols;
if (threadIdx.x == 0) {
rows = shape::sizeAt(leftPartShape, -2);
cols = shape::sizeAt(rightPartShape, -1);
}
__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, unitsOnDiag, pOutputPart, tadOutputShape, rows, cols);
} else {
upperTriangularSolve<T>(pLeftPart, tadLeftShape, pRightPart, tadRightShape, unitsOnDiag, pOutputPart, tadOutputShape, rows, cols);
}
}
}
template <typename T>
static int triangularSolveFunctor_(sd::LaunchContext * context, NDArray* leftInput, NDArray* rightInput,
bool lower, bool unitsOnDiag, NDArray* output) {
NDArray::prepareSpecialUse({output}, {leftInput, rightInput});
auto leftTads = ConstantTadHelper::getInstance().tadForDimensions(leftInput->shapeInfo(), {-2, -1});
auto rightTads = ConstantTadHelper::getInstance().tadForDimensions(rightInput->shapeInfo(), {-2, -1});
auto outputTads = ConstantTadHelper::getInstance().tadForDimensions(output->shapeInfo(), {-2, -1});
auto stream = context->getCudaStream();
T const* leftBuf = reinterpret_cast<T const*>(leftInput->specialBuffer());
T const* rightBuf = reinterpret_cast<T const*>(rightInput->specialBuffer());
T* outputBuf = reinterpret_cast<T*>(output->specialBuffer());
triangularSolveKernel<T><<<128, 128, 256, *stream>>>(leftBuf, leftInput->specialShapeInfo(),
rightBuf, rightInput->specialShapeInfo(), lower, unitsOnDiag, 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();
}
/// triangularSolve2D - 2D implementation of triangularSolveFunctor
/// \tparam T - type of NDArray output
/// \param context - launch context pointer
/// \param leftInput - T matrix of equation Tx = b
/// \param rightInput - b vector of equation Tx = b
/// \param lower - lower or upper triangular matrix
/// \param unitsOnDiag - solve for case when only units (1.0) on diagonal is assumed
/// \param output - output vector (x on equation Tx = b)
///
template <typename T>
void triangularSolve2D(sd::LaunchContext* context, const NDArray& leftInput, const NDArray& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output) {
triangularSolveFunctor_<T>(context, const_cast<NDArray*>(&leftInput), const_cast<NDArray*>(&rightInput), lower, unitsOnDiag, &output);
// leftInput.syncToHost(); rightInput.syncToHost(); output.syncToHost();
// T const* pLeftPart = (T const*)leftInput.getBuffer();
// T const* pRightPart = (T const*)rightInput.getBuffer();
// T* pOutputPart = (T*)output.buffer();
// auto rows = leftInput.rows();
// auto cols = leftInput.columns();
// if (lower) {
// lowerTriangularSolve<T>(pLeftPart, leftInput.shapeInfo(), pRightPart, rightInput.shapeInfo(), unitsOnDiag, pOutputPart, output.shapeInfo(), rows, cols);
// } else {
// upperTriangularSolve<T>(pLeftPart, leftInput.shapeInfo(), pRightPart, rightInput.shapeInfo(), unitsOnDiag, pOutputPart, output.shapeInfo(), rows, cols);
// }
// output.syncToDevice();
}
BUILD_SINGLE_TEMPLATE(template void triangularSolve2D, (sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output), FLOAT_TYPES);
// template void triangularSolve2D<float>(sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output);
// template void triangularSolve2D<bfloat16>(sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output);
// template void triangularSolve2D<float16>(sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output);
// template void triangularSolve2D<double>(sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output);
int triangularSolveFunctor(sd::LaunchContext * context, NDArray* leftInput, NDArray* rightInput, bool lower, bool unitsOnDiag, NDArray* output) {
BUILD_SINGLE_SELECTOR(leftInput->dataType(), return triangularSolveFunctor_, (context, leftInput, rightInput, lower, unitsOnDiag, output), FLOAT_NATIVE);
}
template <typename T>
static __global__ void upperAdjointKernel(T const* input, T* output,
Nd4jLong batchSize, Nd4jLong rows, Nd4jLong columns,
Nd4jLong const* inputTads, Nd4jLong const* inputOffsets, Nd4jLong const* outputTads, Nd4jLong const* 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 const* inputTads, Nd4jLong const* inputOffsets, Nd4jLong const* outputTads, Nd4jLong const* 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_(sd::LaunchContext* context, NDArray const* input, bool const lower,
NDArray* output) {
auto inputTads = ConstantTadHelper::getInstance().tadForDimensions(input->shapeInfo(), {-2, -1});
auto outputTads = ConstantTadHelper::getInstance().tadForDimensions(output->shapeInfo(), {-2, -1});
auto stream = context->getCudaStream();
auto inputBuf = reinterpret_cast<T const*>(input->specialBuffer());
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(sd::LaunchContext* context, NDArray const* input, bool const lower, NDArray* output) {
BUILD_SINGLE_SELECTOR(input->dataType(), adjointTriangularMatrix_, (context, input, lower, output), FLOAT_NATIVE);
}
/*
//////////////////////////////////////////////////////////////////////////
template <typename T>
void triangularSolve2D(sd::LaunchContext* context, NDArray const& A, NDArray const& b, bool const lower, bool const unitsOnDiag, NDArray& x) {
if(A.rankOf() != 2)
throw std::runtime_error("triangularSolve2D: input matrix A must be 2D !");
int temp;
const bool isBvector = b.isCommonVector(temp);
const bool isXvector = x.isCommonVector(temp);
if(A.sizeAt(0) != (isBvector ? b.lengthOf() : b.sizeAt(0)))
throw std::runtime_error("triangularSolve2D: A and b must have the same number of rows !");
if(A.sizeAt(1) != (isXvector ? x.lengthOf() : x.sizeAt(0)))
throw std::runtime_error("triangularSolve2D: columns number of array A must be equal to rows number of array x !");
if(isBvector) {
if(lower) {
for (int i = 0; i < A.sizeAt(0); ++i) {
T sum = b.t<T>(i);
for (int j = 0; j < i; ++j)
sum -= A.t<T>(i,j) * x.t<T>(j);
x.r<T>(i) = unitsOnDiag ? sum : sum / A.t<T>(i,i);
}
}
else {
for (int i = A.sizeAt(0) - 1; i >= 0; --i) {
T sum = b.t<T>(i);
for (int j = i + 1; j < A.sizeAt(1); ++j)
sum -= A.t<T>(i,j) * x.t<T>(j);
x.r<T>(i) = unitsOnDiag ? sum : sum / A.t<T>(i,i);
}
}
}
else {
if(lower) {
for (int bCol = 0; bCol < b.sizeAt(1); ++bCol) {
for (int i = 0; i < A.sizeAt(0); ++i) {
T sum = b.t<T>(i, bCol);
for (int j = 0; j < i; ++j)
sum -= A.t<T>(i,j) * x.t<T>(j, bCol);
x.r<T>(i, bCol) = unitsOnDiag ? sum : sum / A.t<T>(i,i);
}
}
}
else {
for (int bCol = 0; bCol < b.sizeAt(1); ++bCol) {
for (int i = A.sizeAt(0) - 1; i >= 0; --i) {
T sum = b.t<T>(i, bCol);
for (int j = i + 1; j < A.sizeAt(1); ++j)
sum -= A.t<T>(i,j) * x.t<T>(j, bCol);
x.r<T>(i, bCol) = unitsOnDiag ? sum : sum / A.t<T>(i,i);
}
}
}
}
}
BUILD_SINGLE_TEMPLATE(template void triangularSolve2D, (sd::LaunchContext* context, NDArray const& leftInput, NDArray const& rightInput, bool const lower, bool const unitsOnDiag, NDArray& output), FLOAT_TYPES);
*/
}
}
}