103 lines
2.9 KiB
C++
103 lines
2.9 KiB
C++
/*******************************************************************************
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* Copyright (c) 2020 Konduit K.K.
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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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// @author Yurii Shyrma (iuriish@yahoo.com)
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//
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#ifndef LIBND4J_HESSENBERGANDSCHUR_H
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#define LIBND4J_HESSENBERGANDSCHUR_H
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#include <array/NDArray.h>
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namespace sd {
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namespace ops {
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namespace helpers {
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// this class implements Hessenberg decomposition of square matrix using orthogonal similarity transformation
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// A = Q H Q^T
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// Q - orthogonal matrix
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// H - Hessenberg matrix
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template <typename T>
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class Hessenberg {
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// suppose we got input square NxN matrix
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public:
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NDArray _Q; // {N,N}
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NDArray _H; // {N,N}
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explicit Hessenberg(const NDArray& matrix);
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private:
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void evalData();
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};
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// this class implements real Schur decomposition of square matrix using orthogonal similarity transformation
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// A = U T U^T
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// T - real quasi-upper-triangular matrix - block upper triangular matrix where the blocks on the diagonal are 1×1 or 2×2 with complex eigenvalues
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// U - real orthogonal matrix
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template <typename T>
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class Schur {
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// suppose we got input square NxN matrix
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public:
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NDArray _T; // {N,N}
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NDArray _U; // {N,N}
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explicit Schur(const NDArray& matrix);
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void splitTwoRows(const int ind, const T shift);
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void calcShift(const int ind, const int iter, T& shift, NDArray& shiftInfo);
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void initFrancisQR(const int ind1, const int ind2, const NDArray& shiftVec, int& ind3, NDArray& householderVec);
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void doFrancisQR(const int ind1, const int ind2, const int ind3, const NDArray& householderVec);
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void calcFromHessenberg();
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private:
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static const int _maxItersPerRow = 40;
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void evalData(const NDArray& matrix);
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//////////////////////////////////////////////////////////////////////////
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FORCEINLINE int getSmallSubdiagEntry(const int inInd) {
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int outInd = inInd;
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while (outInd > 0) {
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T factor = math::nd4j_abs<T>(_T.t<T>(outInd-1, outInd-1)) + math::nd4j_abs<T>(_T.t<T>(outInd, outInd));
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if (math::nd4j_abs<T>(_T.t<T>(outInd, outInd-1)) <= DataTypeUtils::eps<T>() * factor)
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break;
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outInd--;
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}
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return outInd;
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}
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};
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}
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}
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}
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#endif //LIBND4J_HESSENBERGANDSCHUR_H
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