223 lines
6.2 KiB
C++
223 lines
6.2 KiB
C++
/*******************************************************************************
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* Copyright (c) 2015-2018 Skymind, Inc.
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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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// Created by Yurii Shyrma on 18.12.2017
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//
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#include <householder.h>
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#include <NDArrayFactory.h>
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namespace nd4j {
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namespace ops {
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namespace helpers {
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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NDArray Householder<T>::evalHHmatrix(const NDArray& x) {
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// input validation
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if(!x.isVector() && !x.isScalar())
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throw std::runtime_error("ops::helpers::Householder::evalHHmatrix method: input array must be vector or scalar!");
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auto w = NDArrayFactory::create(x.ordering(), {(int)x.lengthOf(), 1}, x.dataType(), x.getContext()); // column-vector
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auto wT = NDArrayFactory::create(x.ordering(), {1, (int)x.lengthOf()}, x.dataType(), x.getContext()); // row-vector (transposed w)
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T coeff;
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T normX = x.reduceNumber(reduce::Norm2).e<T>(0);
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if(normX*normX - x.e<T>(0) * x.e<T>(0) <= DataTypeUtils::min<T>() || x.lengthOf() == 1) {
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normX = x.e<T>(0);
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coeff = 0.f;
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w = 0.f;
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}
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else {
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if(x.e<T>(0) >= (T)0.f)
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normX = -normX; // choose opposite sign to lessen roundoff error
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T u0 = x.e<T>(0) - normX;
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coeff = -u0 / normX;
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w.assign(x / u0);
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}
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w.p(Nd4jLong(0), 1.f);
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wT.assign(&w);
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auto identity = NDArrayFactory::create(x.ordering(), {(int)x.lengthOf(), (int)x.lengthOf()}, x.dataType(), x.getContext());
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identity.setIdentity(); // identity matrix
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return identity - mmul(w, wT) * coeff;
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}
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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void Householder<T>::evalHHmatrixData(const NDArray& x, NDArray& tail, T& coeff, T& normX) {
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// input validation
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if(!x.isVector() && !x.isScalar())
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throw std::runtime_error("ops::helpers::Householder::evalHHmatrixData method: input array must be vector or scalar!");
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if(!x.isScalar() && x.lengthOf() != tail.lengthOf() + 1)
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throw std::runtime_error("ops::helpers::Householder::evalHHmatrixData method: input tail vector must have length less than unity compared to input x vector!");
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normX = x.reduceNumber(reduce::Norm2, nullptr).e<T>(0);
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if(normX*normX - x.e<T>(0) * x.e<T>(0) <= DataTypeUtils::min<T>() || x.lengthOf() == 1) {
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normX = x.e<T>(0);
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coeff = (T)0.f;
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tail = (T)0.f;
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}
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else {
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if(x.e<T>(0) >= (T)0.f)
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normX = -normX; // choose opposite sign to lessen roundoff error
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T u0 = x.e<T>(0) - normX;
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coeff = -u0 / normX;
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if(x.isRowVector())
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tail.assign(x({0,0, 1,-1}) / u0);
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else
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tail.assign(x({1,-1, 0,0,}) / u0);
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}
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}
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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void Householder<T>::evalHHmatrixDataI(const NDArray& x, T& coeff, T& normX) {
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int rows = (int)x.lengthOf()-1;
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int num = 1;
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if(rows == 0) {
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rows = 1;
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num = 0;
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}
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auto tail = NDArrayFactory::create(x.ordering(), {rows, 1}, x.dataType(), x.getContext());
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evalHHmatrixData(x, tail, coeff, normX);
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if(x.isRowVector()) {
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auto temp = x({0,0, num, x.sizeAt(1)}, true);
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temp.assign(tail);
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}
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else {
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auto temp = x({num,x.sizeAt(0), 0,0}, true);
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temp.assign(tail);
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}
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}
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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void Householder<T>::mulLeft(NDArray& matrix, const NDArray& tail, const T coeff) {
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// if(matrix.rankOf() != 2)
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// throw "ops::helpers::Householder::mulLeft method: input array must be 2D matrix !";
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if(matrix.sizeAt(0) == 1) {
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matrix *= (T) 1.f - coeff;
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}
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else if(coeff != (T)0.f) {
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auto bottomPart = new NDArray(matrix({1,matrix.sizeAt(0), 0,0}, true));
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auto bottomPartCopy = *bottomPart;
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if(tail.isColumnVector()) {
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auto column = tail;
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auto row = tail.transpose();
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auto resultingRow = mmul(row, bottomPartCopy);
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auto fistRow = matrix({0,1, 0,0}, true);
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resultingRow += fistRow;
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fistRow -= resultingRow * coeff;
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*bottomPart -= mmul(column, resultingRow) * coeff;
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}
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else {
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auto row = tail;
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auto column = tail.transpose();
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auto resultingRow = mmul(row, bottomPartCopy);
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auto fistRow = matrix({0,1, 0,0}, true);
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resultingRow += fistRow;
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fistRow -= resultingRow * coeff;
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*bottomPart -= mmul(column, resultingRow) * coeff;
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}
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delete bottomPart;
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}
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}
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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void Householder<T>::mulRight(NDArray& matrix, const NDArray& tail, const T coeff) {
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// if(matrix.rankOf() != 2)
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// throw "ops::helpers::Householder::mulRight method: input array must be 2D matrix !";
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if(matrix.sizeAt(1) == 1)
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matrix *= (T)1.f - coeff;
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else if(coeff != (T)0.f) {
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auto rightPart = new NDArray(matrix({0,0, 1,matrix.sizeAt(1)}, true));
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auto rightPartCopy = *rightPart;
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auto fistCol = new NDArray(matrix({0,0, 0,1}, true));
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if(tail.isColumnVector()) {
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auto column = tail;
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auto row = tail.transpose();
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auto resultingCol = mmul(rightPartCopy, column);
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resultingCol += *fistCol;
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*fistCol -= resultingCol * coeff;
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*rightPart -= mmul(resultingCol, row) * coeff;
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}
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else {
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auto row = tail;
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auto column = tail.transpose();
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auto resultingCol = mmul(rightPartCopy, column);
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resultingCol += *fistCol;
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*fistCol -= resultingCol * coeff;
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*rightPart -= mmul(resultingCol, row) * coeff;
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}
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delete rightPart;
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delete fistCol;
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}
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}
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template class ND4J_EXPORT Householder<float>;
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template class ND4J_EXPORT Householder<float16>;
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template class ND4J_EXPORT Householder<bfloat16>;
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template class ND4J_EXPORT Householder<double>;
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}
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}
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}
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