285 lines
10 KiB
C++
285 lines
10 KiB
C++
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// Copyright (C) 2008-2015 National ICT Australia (NICTA)
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//
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// This Source Code Form is subject to the terms of the Mozilla Public
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// License, v. 2.0. If a copy of the MPL was not distributed with this
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// file, You can obtain one at http://mozilla.org/MPL/2.0/.
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// -------------------------------------------------------------------
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//
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// Written by Conrad Sanderson - http://conradsanderson.id.au
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// Written by James Sanders
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// Written by Eric Jon Sundstrom
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//! \addtogroup auxlib
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//! @{
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//! interface functions for accessing decompositions in LAPACK and ATLAS
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class auxlib
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{
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public:
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template<const uword row, const uword col>
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struct pos
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{
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static const uword n2 = row + col*2;
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static const uword n3 = row + col*3;
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static const uword n4 = row + col*4;
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};
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//
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// inv
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template<typename eT, typename T1>
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inline static bool inv(Mat<eT>& out, const Base<eT,T1>& X);
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template<typename eT>
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inline static bool inv(Mat<eT>& out, const Mat<eT>& A);
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template<typename eT>
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inline static bool inv_noalias_tinymat(Mat<eT>& out, const Mat<eT>& X, const uword N);
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template<typename eT>
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inline static bool inv_inplace_lapack(Mat<eT>& out);
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//
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// inv_tr
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template<typename eT, typename T1>
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inline static bool inv_tr(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
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//
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// inv_sym
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template<typename eT, typename T1>
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inline static bool inv_sym(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
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//
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// inv_sympd
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template<typename eT, typename T1>
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inline static bool inv_sympd(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
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//
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// det
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template<typename eT, typename T1>
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inline static eT det(const Base<eT,T1>& X);
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template<typename eT>
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inline static eT det_tinymat(const Mat<eT>& X, const uword N);
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template<typename eT>
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inline static eT det_lapack(const Mat<eT>& X, const bool make_copy);
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//
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// log_det
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template<typename eT, typename T1>
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inline static bool log_det(eT& out_val, typename get_pod_type<eT>::result& out_sign, const Base<eT,T1>& X);
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//
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// lu
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template<typename eT, typename T1>
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inline static bool lu(Mat<eT>& L, Mat<eT>& U, podarray<blas_int>& ipiv, const Base<eT,T1>& X);
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template<typename eT, typename T1>
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inline static bool lu(Mat<eT>& L, Mat<eT>& U, Mat<eT>& P, const Base<eT,T1>& X);
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template<typename eT, typename T1>
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inline static bool lu(Mat<eT>& L, Mat<eT>& U, const Base<eT,T1>& X);
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//
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// eig_gen
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template<typename T1>
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inline static bool eig_gen(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base<typename T1::pod_type,T1>& expr);
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template<typename T1>
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inline static bool eig_gen(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base< std::complex<typename T1::pod_type>, T1 >& expr);
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template<typename T1>
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inline static bool eig_gen_dual(Mat< std::complex<typename T1::pod_type> >& vals, Mat<typename T1::pod_type>& vecs_l, Mat<typename T1::pod_type>& vecs_r, const Base<typename T1::pod_type,T1>& expr);
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template<typename T1>
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inline static bool eig_gen_dual(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs_l, Mat< std::complex<typename T1::pod_type> >& vecs_r, const Base< std::complex<typename T1::pod_type>, T1 >& expr);
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//
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// eig_pair
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template<typename T1, typename T2>
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inline static bool eig_pair(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base<typename T1::pod_type,T1>& A_expr, const Base<typename T1::pod_type,T2>& B_expr);
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template<typename T1, typename T2>
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inline static bool eig_pair(Mat< std::complex<typename T1::pod_type> >& vals, Mat< std::complex<typename T1::pod_type> >& vecs, const uword mode, const Base< std::complex<typename T1::pod_type>, T1 >& A_expr, const Base< std::complex<typename T1::pod_type>, T2 >& B_expr);
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//
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// eig_sym
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template<typename eT, typename T1>
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inline static bool eig_sym(Col<eT>& eigval, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool eig_sym(Col<T>& eigval, const Base<std::complex<T>,T1>& X);
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template<typename eT, typename T1>
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inline static bool eig_sym(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool eig_sym(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
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template<typename eT, typename T1>
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inline static bool eig_sym_dc(Col<eT>& eigval, Mat<eT>& eigvec, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool eig_sym_dc(Col<T>& eigval, Mat< std::complex<T> >& eigvec, const Base<std::complex<T>,T1>& X);
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//
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// chol
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template<typename eT, typename T1>
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inline static bool chol(Mat<eT>& out, const Base<eT,T1>& X, const uword layout);
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//
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// qr
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template<typename eT, typename T1>
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inline static bool qr(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
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template<typename eT, typename T1>
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inline static bool qr_econ(Mat<eT>& Q, Mat<eT>& R, const Base<eT,T1>& X);
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//
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// svd
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template<typename eT, typename T1>
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inline static bool svd(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
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template<typename T, typename T1>
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inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
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template<typename eT, typename T1>
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inline static bool svd(Col<eT>& S, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool svd(Col<T>& S, const Base<std::complex<T>, T1>& X);
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template<typename eT, typename T1>
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inline static bool svd(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool svd(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
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template<typename eT, typename T1>
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inline static bool svd_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X, const char mode);
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template<typename T, typename T1>
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inline static bool svd_econ(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X, const char mode);
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template<typename eT, typename T1>
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inline static bool svd_dc(Col<eT>& S, const Base<eT,T1>& X, uword& n_rows, uword& n_cols);
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template<typename T, typename T1>
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inline static bool svd_dc(Col<T>& S, const Base<std::complex<T>, T1>& X, uword& n_rows, uword& n_cols);
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template<typename eT, typename T1>
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inline static bool svd_dc(Col<eT>& S, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool svd_dc(Col<T>& S, const Base<std::complex<T>, T1>& X);
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template<typename eT, typename T1>
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inline static bool svd_dc(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool svd_dc(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
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template<typename eT, typename T1>
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inline static bool svd_dc_econ(Mat<eT>& U, Col<eT>& S, Mat<eT>& V, const Base<eT,T1>& X);
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template<typename T, typename T1>
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inline static bool svd_dc_econ(Mat< std::complex<T> >& U, Col<T>& S, Mat< std::complex<T> >& V, const Base< std::complex<T>, T1>& X);
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//
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// solve
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template<typename T1>
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inline static bool solve_square_fast(Mat<typename T1::elem_type>& out, Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr);
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template<typename T1>
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inline static bool solve_square_refine(Mat<typename T1::pod_type>& out, typename T1::pod_type& out_rcond, Mat<typename T1::pod_type>& A, const Base<typename T1::pod_type,T1>& B_expr, const bool equilibrate);
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template<typename T1>
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inline static bool solve_square_refine(Mat< std::complex<typename T1::pod_type> >& out, typename T1::pod_type& out_rcond, Mat< std::complex<typename T1::pod_type> >& A, const Base<std::complex<typename T1::pod_type>,T1>& B_expr, const bool equilibrate);
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template<typename T1>
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inline static bool solve_approx_fast(Mat<typename T1::elem_type>& out, Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr);
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template<typename T1>
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inline static bool solve_approx_svd(Mat<typename T1::pod_type>& out, Mat<typename T1::pod_type>& A, const Base<typename T1::pod_type,T1>& B_expr);
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template<typename T1>
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inline static bool solve_approx_svd(Mat< std::complex<typename T1::pod_type> >& out, Mat< std::complex<typename T1::pod_type> >& A, const Base<std::complex<typename T1::pod_type>,T1>& B_expr);
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template<typename T1>
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inline static bool solve_tri(Mat<typename T1::elem_type>& out, const Mat<typename T1::elem_type>& A, const Base<typename T1::elem_type,T1>& B_expr, const uword layout);
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//
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// Schur decomposition
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template<typename eT, typename T1>
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inline static bool schur(Mat<eT>& U, Mat<eT>& S, const Base<eT,T1>& X, const bool calc_U = true);
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template<typename T, typename T1>
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inline static bool schur(Mat<std::complex<T> >& U, Mat<std::complex<T> >& S, const Base<std::complex<T>,T1>& X, const bool calc_U = true);
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//
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// syl (solution of the Sylvester equation AX + XB = C)
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template<typename eT>
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inline static bool syl(Mat<eT>& X, const Mat<eT>& A, const Mat<eT>& B, const Mat<eT>& C);
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//
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// QZ decomposition
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template<typename T, typename T1, typename T2>
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inline static bool qz(Mat<T>& A, Mat<T>& B, Mat<T>& vsl, Mat<T>& vsr, const Base<T,T1>& X_expr, const Base<T,T2>& Y_expr);
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template<typename T, typename T1, typename T2>
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inline static bool qz(Mat< std::complex<T> >& A, Mat< std::complex<T> >& B, Mat< std::complex<T> >& vsl, Mat< std::complex<T> >& vsr, const Base< std::complex<T>, T1 >& X_expr, const Base< std::complex<T>, T2 >& Y_expr);
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//
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// rcond
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template<typename T1>
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inline static typename T1::pod_type rcond(const Base<typename T1::pod_type,T1>& A_expr);
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template<typename T1>
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inline static typename T1::pod_type rcond(const Base<std::complex<typename T1::pod_type>,T1>& A_expr);
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};
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//! @}
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