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72 lines
2.4 KiB
72 lines
2.4 KiB
1 year ago
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// This file is part of libigl, a simple c++ geometry processing library.
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//
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// Copyright (C) 2023 Alec Jacobson <alecjacobson@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla Public License
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// v. 2.0. If a copy of the MPL was not distributed with this file, You can
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// obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef IGL_SPECTRA_EIGS_H
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#define IGL_SPECTRA_EIGS_H
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#include "../igl_inline.h"
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#include "../eigs.h"
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#include <Eigen/Core>
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#include <Eigen/Sparse>
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#include <Eigen/SparseLU>
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namespace igl
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{
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namespace spectra
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{
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/// Act like MATLAB's eigs function. Compute the first/last k eigen pairs of
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/// the generalized eigen value problem:
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///
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/// A u = s B u
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///
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/// Solutions are approximate and sorted.
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///
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/// Ideally one should use ARPACK and the Eigen unsupported ARPACK module.
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/// This implementation does simple, naive power iterations.
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///
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/// @param[in] A #A by #A symmetric matrix
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/// @param[in] B #A by #A symmetric positive-definite matrix
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/// @param[in] k number of eigen pairs to compute
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/// @param[in] type whether to extract from the high or low end
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/// @param[out] sU #A by k list of sorted eigen vectors (descending)
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/// @param[out] sS k list of sorted eigen values (descending)
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///
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/// \bug only the 'sm' small magnitude eigen values are well supported
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///
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template <
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typename EigsScalar,
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typename DerivedU,
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typename DerivedS,
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typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>> >
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IGL_INLINE bool eigs(
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const Eigen::SparseMatrix<EigsScalar> & A,
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const Eigen::SparseMatrix<EigsScalar> & B,
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const int k,
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const igl::EigsType type,
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Eigen::PlainObjectBase<DerivedU> & U,
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Eigen::PlainObjectBase<DerivedS> & S);
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/// \overload
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/// @param[in] sigma shift to apply to A, as in A ← A + sigma B
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template <
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typename EigsScalar,
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typename DerivedU,
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typename DerivedS,
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typename Solver = Eigen::SparseLU<Eigen::SparseMatrix<EigsScalar>> >
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IGL_INLINE bool eigs(
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const Eigen::SparseMatrix<EigsScalar> & A,
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const Eigen::SparseMatrix<EigsScalar> & B,
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const int k,
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const EigsScalar sigma,
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Eigen::PlainObjectBase<DerivedU> & U,
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Eigen::PlainObjectBase<DerivedS> & S);
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}
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}
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#ifndef IGL_STATIC_LIBRARY
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#include "eigs.cpp"
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#endif
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#endif
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