chore: import upstream snapshot with attribution
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/*
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* ******************************************************************************
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* *
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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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* * See the NOTICE file distributed with this work for additional
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* * information regarding copyright ownership.
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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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//
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// @author George A. Shulinok <sgazeos@gmail.com>
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//
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#include <array/NDArrayFactory.h>
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#include <execution/Threads.h>
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#include <helpers/MmulHelper.h>
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#include <ops/declarable/helpers/qr.h>
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#if NOT_EXCLUDED(OP_qr)
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namespace sd {
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namespace ops {
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namespace helpers {
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template <typename T>
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NDArray matrixMinor(NDArray& in, sd::LongType col) {
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NDArray* m = in.ulike();
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m->setIdentity();
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auto mRef = *m;
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auto view = mRef({col, m->rows(), col, m->columns()});
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auto inView = in({col, m->rows(), col, m->columns()});
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view->assign(inView);
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delete view;
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delete inView;
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delete m;
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return mRef;
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}
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/* m = I - v v^T */
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template <typename T>
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NDArray vmul(NDArray& v, int n) {
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std::vector<sd::LongType> nShape = {n,n};
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NDArray res('c', nShape, v.dataType(), v.getContext()); // x = matrix_new(n, n);
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T const* vBuf = v.getDataBuffer()->primaryAsT<T>();
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T* resBuf = res.dataBuffer()->primaryAsT<T>();
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auto interloop = PRAGMA_THREADS_FOR_2D {
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for (auto i = start_x; i < n; i += inc_x)
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for (auto j = start_y; j < n; j += inc_y) resBuf[i * n + j] = -2 * vBuf[i] * vBuf[j] + (i == j ? T(1) : T(0));
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};
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samediff::Threads::parallel_for(interloop, 0, n, 1, 0, n, 1);
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return res;
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}
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template <typename T>
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void qrSingle(NDArray* matrix, NDArray* Q, NDArray* R, bool const fullMatricies) {
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sd::LongType M = matrix->sizeAt(-2);
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sd::LongType N = matrix->sizeAt(-1);
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auto resQ = fullMatricies ? Q->ulike() : new NDArray(NDArrayFactory::create<T>(matrix->ordering(), {M, M}, Q->getContext()));
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auto resR = fullMatricies ? R->ulike() : matrix->ulike();
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std::vector<NDArray*> q(M, nullptr);
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std::vector<sd::LongType> mShape = {M};
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NDArray z = *matrix;
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NDArray e('c', mShape, DataTypeUtils::fromT<T>(), Q->getContext()); // two internal buffers and scalar for squared norm
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for (sd::LongType k = 0; k < N && k < M - 1; k++) { // loop for columns, but not further then row number
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e.nullify();
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z = matrixMinor<T>(z, k); // minor computing for current column with given matrix z (initally is a input matrix)
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std::vector<sd::LongType> zeroVec = {0};
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auto currentColumn = z({0, 0, k, k + 1}); // retrieve k column from z to x buffer
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auto *normPtr = currentColumn->reduceAlongDimension(reduce::Norm2,&zeroVec);
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NDArray norm = *normPtr;
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delete normPtr;
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if (matrix->t<T>(k, k) > T(0.f)) { // negate on positive matrix diagonal element
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NDArray *negNorm = norm * T(-1.f);
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norm.assign(negNorm);
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delete negNorm;
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}
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e.p(k, &norm);
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NDArray *ePlusColumn = e + (*currentColumn);
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e.assign(ePlusColumn);
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delete ePlusColumn;
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auto *normEPtr = e.reduceAlongDimension(reduce::Norm2, &zeroVec);
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NDArray *eDivNormE = e / (*normEPtr);
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e.assign(eDivNormE);
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delete eDivNormE;
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delete normEPtr;
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q[k] = new NDArray(vmul<T>(e, M));
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auto qQ = z.ulike();
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MmulHelper::matmul(q[k], &z, qQ, false, false, 0, 0, qQ);
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z = std::move(*qQ);
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delete currentColumn;
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}
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resQ->assign(q[0]); //
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for (sd::LongType i = 1; i < N && i < M - 1; i++) {
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auto tempResQ = resQ;
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MmulHelper::matmul(q[i], resQ, tempResQ, false, false, 0, 0, tempResQ); // use mmulMxM?
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resQ = std::move(tempResQ);
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}
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MmulHelper::matmul(resQ, matrix, resR, false, false, 0, 0, resR);
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// resR *= -1.f;
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resQ->transposei();
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if (fullMatricies) {
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Q->assign(resQ);
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R->assign(resR);
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} else {
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auto resQRef = *resQ;
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auto resRRef = *resR;
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auto resQView = resQRef({0, 0, 0, N});
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auto resRView = resRRef({0, N, 0, 0});
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Q->assign(resQView);
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R->assign(resRView);
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delete resQView;
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delete resRView;
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}
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// Clean up allocated NDArrays in q vector
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for (sd::LongType i = 0; i < M; i++) {
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if (q[i] != nullptr) {
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delete q[i];
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}
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}
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delete resQ;
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delete resR;
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}
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template <typename T>
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void qr_(NDArray * input, NDArray* outputQ, NDArray* outputR, bool const fullMatricies) {
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sd::LongType lastDim = input->rankOf() - 1;
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sd::LongType preLastDim = input->rankOf() - 2;
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ResultSet listOutQ(outputQ->allTensorsAlongDimension({(int)preLastDim, (int)lastDim}));
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ResultSet listOutR(outputR->allTensorsAlongDimension({(int)preLastDim, (int)lastDim}));
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ResultSet listInput(input->allTensorsAlongDimension({(int)preLastDim, (int)lastDim}));
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auto batching = PRAGMA_THREADS_FOR {
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for (auto batch = start; batch < stop; batch++) {
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// qr here
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qrSingle<T>(listInput.at(batch), listOutQ.at(batch), listOutR.at(batch), fullMatricies);
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}
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};
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samediff::Threads::parallel_tad(batching, 0, listOutQ.size(), 1);
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}
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void qr(sd::LaunchContext* context, NDArray * input, NDArray* outputQ, NDArray* outputR,
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bool const fullMatricies) {
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BUILD_SINGLE_SELECTOR(input->dataType(), qr_, (input, outputQ, outputR, fullMatricies), SD_FLOAT_TYPES);
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}
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} // namespace helpers
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} // namespace ops
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} // namespace sd
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#endif
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