150 lines
4.9 KiB
C++
150 lines
4.9 KiB
C++
/* ******************************************************************************
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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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// Created by Yurii Shyrma on 11.01.2018
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//
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#include <helpers/hhColPivQR.h>
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#include <helpers/householder.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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HHcolPivQR::HHcolPivQR(const NDArray& matrix) {
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_qr = matrix.dup();
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_diagSize = math::nd4j_min<int>(matrix.sizeAt(0), matrix.sizeAt(1));
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_coeffs = NDArray(matrix.ordering(), {1, _diagSize}, matrix.dataType(), matrix.getContext());
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_permut = NDArray(matrix.ordering(), {matrix.sizeAt(1), matrix.sizeAt(1)}, matrix.dataType(), matrix.getContext());
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evalData();
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}
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void HHcolPivQR::evalData() {
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BUILD_SINGLE_SELECTOR(_qr.dataType(), _evalData, (), FLOAT_TYPES);
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}
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//////////////////////////////////////////////////////////////////////////
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template <typename T>
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void HHcolPivQR::_evalData() {
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const int rows = _qr.sizeAt(0);
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const int cols = _qr.sizeAt(1);
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NDArray transp(_qr.ordering(), {cols}/*{1, cols}*/, _qr.dataType(), _qr.getContext());
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NDArray normsUpd(_qr.ordering(), {cols}/*{1, cols}*/, _qr.dataType(), _qr.getContext());
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NDArray normsDir(_qr.ordering(), {cols}/*{1, cols}*/, _qr.dataType(), _qr.getContext());
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int transpNum = 0;
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for (int k = 0; k < cols; ++k)
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normsDir.r<T>(k) = normsUpd.r<T>(k) = _qr({0,0, k,k+1}).reduceNumber(reduce::Norm2).t<T>(0);
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T normScaled = (normsUpd.reduceNumber(reduce::Max)).t<T>(0) * DataTypeUtils::eps<T>();
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T threshold1 = normScaled * normScaled / (T)rows;
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T threshold2 = math::nd4j_sqrt<T,T>(DataTypeUtils::eps<T>());
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T nonZeroPivots = _diagSize;
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T maxPivot = 0.;
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for(int k = 0; k < _diagSize; ++k) {
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int biggestColIndex = normsUpd({k,-1}).indexReduceNumber(indexreduce::IndexMax).e<int>(0);
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T biggestColNorm = normsUpd({k,-1}).reduceNumber(reduce::Max).t<T>(0);
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T biggestColSqNorm = biggestColNorm * biggestColNorm;
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biggestColIndex += k;
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if(nonZeroPivots == (T)_diagSize && biggestColSqNorm < threshold1 * (T)(rows-k))
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nonZeroPivots = k;
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transp.r<T>(k) = (T)biggestColIndex;
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if(k != biggestColIndex) {
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NDArray temp1(_qr({0,0, k,k+1}));
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NDArray temp2(_qr({0,0, biggestColIndex,biggestColIndex+1}));
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temp1.swapUnsafe(temp2);
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math::nd4j_swap<T>(normsUpd.r<T>(k), normsUpd.r<T>(biggestColIndex));
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math::nd4j_swap<T>(normsDir.r<T>(k), normsDir.r<T>(biggestColIndex));
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++transpNum;
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}
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T normX, c;
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NDArray qrBlock = _qr({k,rows, k,k+1});
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Householder<T>::evalHHmatrixDataI(qrBlock, c, normX);
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_coeffs.r<T>(k) = c;
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_qr.r<T>(k,k) = normX;
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T max = math::nd4j_abs<T>(normX);
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if(max > maxPivot)
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maxPivot = max;
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if(k < rows && (k+1) < cols) {
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NDArray qrBlock = _qr({k,rows, k+1,cols}, true);
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NDArray tail = _qr({k+1,rows, k, k+1}, true);
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Householder<T>::mulLeft(qrBlock, tail, _coeffs.t<T>(k));
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}
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for (int j = k + 1; j < cols; ++j) {
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if (normsUpd.t<T>(j) != (T)0.f) {
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T temp = math::nd4j_abs<T>(_qr.t<T>(k, j)) / normsUpd.t<T>(j);
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temp = ((T)1. + temp) * ((T)1. - temp);
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temp = temp < (T)0. ? (T)0. : temp;
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T temp2 = temp * normsUpd.t<T>(j) * normsUpd.t<T>(j) / (normsDir.t<T>(j)*normsDir.t<T>(j));
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if (temp2 <= threshold2) {
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if(k+1 < rows && j < cols)
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normsDir.r<T>(j) = _qr({k+1,rows, j,j+1}).reduceNumber(reduce::Norm2).t<T>(0);
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normsUpd.r<T>(j) = normsDir.t<T>(j);
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}
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else
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normsUpd.r<T>(j) = normsUpd.t<T>(j) * math::nd4j_sqrt<T, T>(temp);
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}
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}
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}
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_permut.setIdentity();
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for(int k = 0; k < _diagSize; ++k) {
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int idx = transp.e<int>(k);
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NDArray temp1 = _permut({0,0, k, k+1});
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NDArray temp2 = _permut({0,0, idx,idx+1});
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temp1.swapUnsafe(temp2);
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}
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}
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BUILD_SINGLE_TEMPLATE(template void HHcolPivQR::_evalData, (), FLOAT_TYPES);
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}
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}
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}
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