diff --git a/contrib/lbfgs/solvers.h b/contrib/lbfgs/solvers.h deleted file mode 100755 index 2f7e1b5ae6f01b82158c67ec89a026cfb5700788..0000000000000000000000000000000000000000 --- a/contrib/lbfgs/solvers.h +++ /dev/null @@ -1,1353 +0,0 @@ -/************************************************************************* -Copyright (c) Sergey Bochkanov (ALGLIB project). - ->>> SOURCE LICENSE >>> -This program is free software; you can redistribute it and/or modify -it under the terms of the GNU General Public License as published by -the Free Software Foundation (www.fsf.org); either version 2 of the -License, or (at your option) any later version. - -This program is distributed in the hope that it will be useful, -but WITHOUT ANY WARRANTY; without even the implied warranty of -MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the -GNU General Public License for more details. - -A copy of the GNU General Public License is available at -http://www.fsf.org/licensing/licenses ->>> END OF LICENSE >>> -*************************************************************************/ -#ifndef _solvers_pkg_h -#define _solvers_pkg_h -#include "ap.h" -#include "alglibinternal.h" -#include "linalg.h" -#include "alglibmisc.h" - -///////////////////////////////////////////////////////////////////////// -// -// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (DATATYPES) -// -///////////////////////////////////////////////////////////////////////// -namespace alglib_impl -{ -typedef struct -{ - double r1; - double rinf; -} densesolverreport; -typedef struct -{ - double r2; - ae_matrix cx; - ae_int_t n; - ae_int_t k; -} densesolverlsreport; -typedef struct -{ - ae_int_t n; - ae_int_t m; - double epsf; - ae_int_t maxits; - ae_bool xrep; - double stpmax; - ae_vector x; - double f; - ae_vector fi; - ae_matrix j; - ae_bool needf; - ae_bool needfij; - ae_bool xupdated; - rcommstate rstate; - ae_int_t repiterationscount; - ae_int_t repnfunc; - ae_int_t repnjac; - ae_int_t repterminationtype; - ae_vector xbase; - double fbase; - double fprev; - ae_vector candstep; - ae_vector rightpart; - ae_vector cgbuf; -} nleqstate; -typedef struct -{ - ae_int_t iterationscount; - ae_int_t nfunc; - ae_int_t njac; - ae_int_t terminationtype; -} nleqreport; - -} - -///////////////////////////////////////////////////////////////////////// -// -// THIS SECTION CONTAINS C++ INTERFACE -// -///////////////////////////////////////////////////////////////////////// -namespace alglib -{ - -/************************************************************************* - -*************************************************************************/ -class _densesolverreport_owner -{ -public: - _densesolverreport_owner(); - _densesolverreport_owner(const _densesolverreport_owner &rhs); - _densesolverreport_owner& operator=(const _densesolverreport_owner &rhs); - virtual ~_densesolverreport_owner(); - alglib_impl::densesolverreport* c_ptr(); - alglib_impl::densesolverreport* c_ptr() const; -protected: - alglib_impl::densesolverreport *p_struct; -}; -class densesolverreport : public _densesolverreport_owner -{ -public: - densesolverreport(); - densesolverreport(const densesolverreport &rhs); - densesolverreport& operator=(const densesolverreport &rhs); - virtual ~densesolverreport(); - double &r1; - double &rinf; - -}; - - -/************************************************************************* - -*************************************************************************/ -class _densesolverlsreport_owner -{ -public: - _densesolverlsreport_owner(); - _densesolverlsreport_owner(const _densesolverlsreport_owner &rhs); - _densesolverlsreport_owner& operator=(const _densesolverlsreport_owner &rhs); - virtual ~_densesolverlsreport_owner(); - alglib_impl::densesolverlsreport* c_ptr(); - alglib_impl::densesolverlsreport* c_ptr() const; -protected: - alglib_impl::densesolverlsreport *p_struct; -}; -class densesolverlsreport : public _densesolverlsreport_owner -{ -public: - densesolverlsreport(); - densesolverlsreport(const densesolverlsreport &rhs); - densesolverlsreport& operator=(const densesolverlsreport &rhs); - virtual ~densesolverlsreport(); - double &r2; - real_2d_array cx; - ae_int_t &n; - ae_int_t &k; - -}; - -/************************************************************************* - -*************************************************************************/ -class _nleqstate_owner -{ -public: - _nleqstate_owner(); - _nleqstate_owner(const _nleqstate_owner &rhs); - _nleqstate_owner& operator=(const _nleqstate_owner &rhs); - virtual ~_nleqstate_owner(); - alglib_impl::nleqstate* c_ptr(); - alglib_impl::nleqstate* c_ptr() const; -protected: - alglib_impl::nleqstate *p_struct; -}; -class nleqstate : public _nleqstate_owner -{ -public: - nleqstate(); - nleqstate(const nleqstate &rhs); - nleqstate& operator=(const nleqstate &rhs); - virtual ~nleqstate(); - ae_bool &needf; - ae_bool &needfij; - ae_bool &xupdated; - double &f; - real_1d_array fi; - real_2d_array j; - real_1d_array x; - -}; - - -/************************************************************************* - -*************************************************************************/ -class _nleqreport_owner -{ -public: - _nleqreport_owner(); - _nleqreport_owner(const _nleqreport_owner &rhs); - _nleqreport_owner& operator=(const _nleqreport_owner &rhs); - virtual ~_nleqreport_owner(); - alglib_impl::nleqreport* c_ptr(); - alglib_impl::nleqreport* c_ptr() const; -protected: - alglib_impl::nleqreport *p_struct; -}; -class nleqreport : public _nleqreport_owner -{ -public: - nleqreport(); - nleqreport(const nleqreport &rhs); - nleqreport& operator=(const nleqreport &rhs); - virtual ~nleqreport(); - ae_int_t &iterationscount; - ae_int_t &nfunc; - ae_int_t &njac; - ae_int_t &terminationtype; - -}; - -/************************************************************************* -Dense solver. - -This subroutine solves a system A*x=b, where A is NxN non-denegerate -real matrix, x and b are vectors. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(N^3) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - return code: - * -3 A is singular, or VERY close to singular. - X is filled by zeros in such cases. - * -1 N<=0 was passed - * 1 task is solved (but matrix A may be ill-conditioned, - check R1/RInf parameters for condition numbers). - Rep - solver report, see below for more info - X - array[0..N-1], it contains: - * solution of A*x=b if A is non-singular (well-conditioned - or ill-conditioned, but not very close to singular) - * zeros, if A is singular or VERY close to singular - (in this case Info=-3). - -SOLVER REPORT - -Subroutine sets following fields of the Rep structure: -* R1 reciprocal of condition number: 1/cond(A), 1-norm. -* RInf reciprocal of condition number: 1/cond(A), inf-norm. - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixsolve(const real_2d_array &a, const ae_int_t n, const real_1d_array &b, ae_int_t &info, densesolverreport &rep, real_1d_array &x); - - -/************************************************************************* -Dense solver. - -Similar to RMatrixSolve() but solves task with multiple right parts (where -b and x are NxM matrices). - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* optional iterative refinement -* O(N^3+M*N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - RFS - iterative refinement switch: - * True - refinement is used. - Less performance, more precision. - * False - refinement is not used. - More performance, less precision. - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixsolvem(const real_2d_array &a, const ae_int_t n, const real_2d_array &b, const ae_int_t m, const bool rfs, ae_int_t &info, densesolverreport &rep, real_2d_array &x); - - -/************************************************************************* -Dense solver. - -This subroutine solves a system A*X=B, where A is NxN non-denegerate -real matrix given by its LU decomposition, X and B are NxM real matrices. - -Algorithm features: -* automatic detection of degenerate cases -* O(N^2) complexity -* condition number estimation - -No iterative refinement is provided because exact form of original matrix -is not known to subroutine. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - LUA - array[0..N-1,0..N-1], LU decomposition, RMatrixLU result - P - array[0..N-1], pivots array, RMatrixLU result - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixlusolve(const real_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const real_1d_array &b, ae_int_t &info, densesolverreport &rep, real_1d_array &x); - - -/************************************************************************* -Dense solver. - -Similar to RMatrixLUSolve() but solves task with multiple right parts -(where b and x are NxM matrices). - -Algorithm features: -* automatic detection of degenerate cases -* O(M*N^2) complexity -* condition number estimation - -No iterative refinement is provided because exact form of original matrix -is not known to subroutine. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - LUA - array[0..N-1,0..N-1], LU decomposition, RMatrixLU result - P - array[0..N-1], pivots array, RMatrixLU result - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixlusolvem(const real_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const real_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, real_2d_array &x); - - -/************************************************************************* -Dense solver. - -This subroutine solves a system A*x=b, where BOTH ORIGINAL A AND ITS -LU DECOMPOSITION ARE KNOWN. You can use it if for some reasons you have -both A and its LU decomposition. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - LUA - array[0..N-1,0..N-1], LU decomposition, RMatrixLU result - P - array[0..N-1], pivots array, RMatrixLU result - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolveM - Rep - same as in RMatrixSolveM - X - same as in RMatrixSolveM - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixmixedsolve(const real_2d_array &a, const real_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const real_1d_array &b, ae_int_t &info, densesolverreport &rep, real_1d_array &x); - - -/************************************************************************* -Dense solver. - -Similar to RMatrixMixedSolve() but solves task with multiple right parts -(where b and x are NxM matrices). - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(M*N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - LUA - array[0..N-1,0..N-1], LU decomposition, RMatrixLU result - P - array[0..N-1], pivots array, RMatrixLU result - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolveM - Rep - same as in RMatrixSolveM - X - same as in RMatrixSolveM - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void rmatrixmixedsolvem(const real_2d_array &a, const real_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const real_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, real_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolveM(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(N^3+M*N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - RFS - iterative refinement switch: - * True - refinement is used. - Less performance, more precision. - * False - refinement is not used. - More performance, less precision. - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixsolvem(const complex_2d_array &a, const ae_int_t n, const complex_2d_array &b, const ae_int_t m, const bool rfs, ae_int_t &info, densesolverreport &rep, complex_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolve(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(N^3) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixsolve(const complex_2d_array &a, const ae_int_t n, const complex_1d_array &b, ae_int_t &info, densesolverreport &rep, complex_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolveM(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* O(M*N^2) complexity -* condition number estimation - -No iterative refinement is provided because exact form of original matrix -is not known to subroutine. Use CMatrixSolve or CMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - LUA - array[0..N-1,0..N-1], LU decomposition, RMatrixLU result - P - array[0..N-1], pivots array, RMatrixLU result - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixlusolvem(const complex_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const complex_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, complex_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolve(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* O(N^2) complexity -* condition number estimation - -No iterative refinement is provided because exact form of original matrix -is not known to subroutine. Use CMatrixSolve or CMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - LUA - array[0..N-1,0..N-1], LU decomposition, CMatrixLU result - P - array[0..N-1], pivots array, CMatrixLU result - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixlusolve(const complex_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const complex_1d_array &b, ae_int_t &info, densesolverreport &rep, complex_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixMixedSolveM(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(M*N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - LUA - array[0..N-1,0..N-1], LU decomposition, CMatrixLU result - P - array[0..N-1], pivots array, CMatrixLU result - N - size of A - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolveM - Rep - same as in RMatrixSolveM - X - same as in RMatrixSolveM - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixmixedsolvem(const complex_2d_array &a, const complex_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const complex_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, complex_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixMixedSolve(), but for complex matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* iterative refinement -* O(N^2) complexity - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - LUA - array[0..N-1,0..N-1], LU decomposition, CMatrixLU result - P - array[0..N-1], pivots array, CMatrixLU result - N - size of A - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolveM - Rep - same as in RMatrixSolveM - X - same as in RMatrixSolveM - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void cmatrixmixedsolve(const complex_2d_array &a, const complex_2d_array &lua, const integer_1d_array &p, const ae_int_t n, const complex_1d_array &b, ae_int_t &info, densesolverreport &rep, complex_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolveM(), but for symmetric positive definite -matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* O(N^3+M*N^2) complexity -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - IsUpper - what half of A is provided - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve. - Returns -3 for non-SPD matrices. - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void spdmatrixsolvem(const real_2d_array &a, const ae_int_t n, const bool isupper, const real_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, real_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolve(), but for SPD matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* O(N^3) complexity -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - IsUpper - what half of A is provided - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Returns -3 for non-SPD matrices. - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void spdmatrixsolve(const real_2d_array &a, const ae_int_t n, const bool isupper, const real_1d_array &b, ae_int_t &info, densesolverreport &rep, real_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolveM(), but for SPD matrices represented -by their Cholesky decomposition. - -Algorithm features: -* automatic detection of degenerate cases -* O(M*N^2) complexity -* condition number estimation -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - CHA - array[0..N-1,0..N-1], Cholesky decomposition, - SPDMatrixCholesky result - N - size of CHA - IsUpper - what half of CHA is provided - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void spdmatrixcholeskysolvem(const real_2d_array &cha, const ae_int_t n, const bool isupper, const real_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, real_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolve(), but for SPD matrices represented -by their Cholesky decomposition. - -Algorithm features: -* automatic detection of degenerate cases -* O(N^2) complexity -* condition number estimation -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - CHA - array[0..N-1,0..N-1], Cholesky decomposition, - SPDMatrixCholesky result - N - size of A - IsUpper - what half of CHA is provided - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void spdmatrixcholeskysolve(const real_2d_array &cha, const ae_int_t n, const bool isupper, const real_1d_array &b, ae_int_t &info, densesolverreport &rep, real_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolveM(), but for Hermitian positive definite -matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* O(N^3+M*N^2) complexity -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - IsUpper - what half of A is provided - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve. - Returns -3 for non-HPD matrices. - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void hpdmatrixsolvem(const complex_2d_array &a, const ae_int_t n, const bool isupper, const complex_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, complex_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixSolve(), but for Hermitian positive definite -matrices. - -Algorithm features: -* automatic detection of degenerate cases -* condition number estimation -* O(N^3) complexity -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - A - array[0..N-1,0..N-1], system matrix - N - size of A - IsUpper - what half of A is provided - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Returns -3 for non-HPD matrices. - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void hpdmatrixsolve(const complex_2d_array &a, const ae_int_t n, const bool isupper, const complex_1d_array &b, ae_int_t &info, densesolverreport &rep, complex_1d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolveM(), but for HPD matrices represented -by their Cholesky decomposition. - -Algorithm features: -* automatic detection of degenerate cases -* O(M*N^2) complexity -* condition number estimation -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - CHA - array[0..N-1,0..N-1], Cholesky decomposition, - HPDMatrixCholesky result - N - size of CHA - IsUpper - what half of CHA is provided - B - array[0..N-1,0..M-1], right part - M - right part size - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void hpdmatrixcholeskysolvem(const complex_2d_array &cha, const ae_int_t n, const bool isupper, const complex_2d_array &b, const ae_int_t m, ae_int_t &info, densesolverreport &rep, complex_2d_array &x); - - -/************************************************************************* -Dense solver. Same as RMatrixLUSolve(), but for HPD matrices represented -by their Cholesky decomposition. - -Algorithm features: -* automatic detection of degenerate cases -* O(N^2) complexity -* condition number estimation -* matrix is represented by its upper or lower triangle - -No iterative refinement is provided because such partial representation of -matrix does not allow efficient calculation of extra-precise matrix-vector -products for large matrices. Use RMatrixSolve or RMatrixMixedSolve if you -need iterative refinement. - -INPUT PARAMETERS - CHA - array[0..N-1,0..N-1], Cholesky decomposition, - SPDMatrixCholesky result - N - size of A - IsUpper - what half of CHA is provided - B - array[0..N-1], right part - -OUTPUT PARAMETERS - Info - same as in RMatrixSolve - Rep - same as in RMatrixSolve - X - same as in RMatrixSolve - - -- ALGLIB -- - Copyright 27.01.2010 by Bochkanov Sergey -*************************************************************************/ -void hpdmatrixcholeskysolve(const complex_2d_array &cha, const ae_int_t n, const bool isupper, const complex_1d_array &b, ae_int_t &info, densesolverreport &rep, complex_1d_array &x); - - -/************************************************************************* -Dense solver. - -This subroutine finds solution of the linear system A*X=B with non-square, -possibly degenerate A. System is solved in the least squares sense, and -general least squares solution X = X0 + CX*y which minimizes |A*X-B| is -returned. If A is non-degenerate, solution in the usual sense is returned - -Algorithm features: -* automatic detection of degenerate cases -* iterative refinement -* O(N^3) complexity - -INPUT PARAMETERS - A - array[0..NRows-1,0..NCols-1], system matrix - NRows - vertical size of A - NCols - horizontal size of A - B - array[0..NCols-1], right part - Threshold- a number in [0,1]. Singular values beyond Threshold are - considered zero. Set it to 0.0, if you don't understand - what it means, so the solver will choose good value on its - own. - -OUTPUT PARAMETERS - Info - return code: - * -4 SVD subroutine failed - * -1 if NRows<=0 or NCols<=0 or Threshold<0 was passed - * 1 if task is solved - Rep - solver report, see below for more info - X - array[0..N-1,0..M-1], it contains: - * solution of A*X=B if A is non-singular (well-conditioned - or ill-conditioned, but not very close to singular) - * zeros, if A is singular or VERY close to singular - (in this case Info=-3). - -SOLVER REPORT - -Subroutine sets following fields of the Rep structure: -* R2 reciprocal of condition number: 1/cond(A), 2-norm. -* N = NCols -* K dim(Null(A)) -* CX array[0..N-1,0..K-1], kernel of A. - Columns of CX store such vectors that A*CX[i]=0. - - -- ALGLIB -- - Copyright 24.08.2009 by Bochkanov Sergey -*************************************************************************/ -void rmatrixsolvels(const real_2d_array &a, const ae_int_t nrows, const ae_int_t ncols, const real_1d_array &b, const double threshold, ae_int_t &info, densesolverlsreport &rep, real_1d_array &x); - -/************************************************************************* - LEVENBERG-MARQUARDT-LIKE NONLINEAR SOLVER - -DESCRIPTION: -This algorithm solves system of nonlinear equations - F[0](x[0], ..., x[n-1]) = 0 - F[1](x[0], ..., x[n-1]) = 0 - ... - F[M-1](x[0], ..., x[n-1]) = 0 -with M/N do not necessarily coincide. Algorithm converges quadratically -under following conditions: - * the solution set XS is nonempty - * for some xs in XS there exist such neighbourhood N(xs) that: - * vector function F(x) and its Jacobian J(x) are continuously - differentiable on N - * ||F(x)|| provides local error bound on N, i.e. there exists such - c1, that ||F(x)||>c1*distance(x,XS) -Note that these conditions are much more weaker than usual non-singularity -conditions. For example, algorithm will converge for any affine function -F (whether its Jacobian singular or not). - - -REQUIREMENTS: -Algorithm will request following information during its operation: -* function vector F[] and Jacobian matrix at given point X -* value of merit function f(x)=F[0]^2(x)+...+F[M-1]^2(x) at given point X - - -USAGE: -1. User initializes algorithm state with NLEQCreateLM() call -2. User tunes solver parameters with NLEQSetCond(), NLEQSetStpMax() and - other functions -3. User calls NLEQSolve() function which takes algorithm state and - pointers (delegates, etc.) to callback functions which calculate merit - function value and Jacobian. -4. User calls NLEQResults() to get solution -5. Optionally, user may call NLEQRestartFrom() to solve another problem - with same parameters (N/M) but another starting point and/or another - function vector. NLEQRestartFrom() allows to reuse already initialized - structure. - - -INPUT PARAMETERS: - N - space dimension, N>1: - * if provided, only leading N elements of X are used - * if not provided, determined automatically from size of X - M - system size - X - starting point - - -OUTPUT PARAMETERS: - State - structure which stores algorithm state - - -NOTES: -1. you may tune stopping conditions with NLEQSetCond() function -2. if target function contains exp() or other fast growing functions, and - optimization algorithm makes too large steps which leads to overflow, - use NLEQSetStpMax() function to bound algorithm's steps. -3. this algorithm is a slightly modified implementation of the method - described in 'Levenberg-Marquardt method for constrained nonlinear - equations with strong local convergence properties' by Christian Kanzow - Nobuo Yamashita and Masao Fukushima and further developed in 'On the - convergence of a New Levenberg-Marquardt Method' by Jin-yan Fan and - Ya-Xiang Yuan. - - - -- ALGLIB -- - Copyright 20.08.2009 by Bochkanov Sergey -*************************************************************************/ -void nleqcreatelm(const ae_int_t n, const ae_int_t m, const real_1d_array &x, nleqstate &state); -void nleqcreatelm(const ae_int_t m, const real_1d_array &x, nleqstate &state); - - -/************************************************************************* -This function sets stopping conditions for the nonlinear solver - -INPUT PARAMETERS: - State - structure which stores algorithm state - EpsF - >=0 - The subroutine finishes its work if on k+1-th iteration - the condition ||F||<=EpsF is satisfied - MaxIts - maximum number of iterations. If MaxIts=0, the number of - iterations is unlimited. - -Passing EpsF=0 and MaxIts=0 simultaneously will lead to automatic -stopping criterion selection (small EpsF). - -NOTES: - - -- ALGLIB -- - Copyright 20.08.2010 by Bochkanov Sergey -*************************************************************************/ -void nleqsetcond(const nleqstate &state, const double epsf, const ae_int_t maxits); - - -/************************************************************************* -This function turns on/off reporting. - -INPUT PARAMETERS: - State - structure which stores algorithm state - NeedXRep- whether iteration reports are needed or not - -If NeedXRep is True, algorithm will call rep() callback function if it is -provided to NLEQSolve(). - - -- ALGLIB -- - Copyright 20.08.2010 by Bochkanov Sergey -*************************************************************************/ -void nleqsetxrep(const nleqstate &state, const bool needxrep); - - -/************************************************************************* -This function sets maximum step length - -INPUT PARAMETERS: - State - structure which stores algorithm state - StpMax - maximum step length, >=0. Set StpMax to 0.0, if you don't - want to limit step length. - -Use this subroutine when target function contains exp() or other fast -growing functions, and algorithm makes too large steps which lead to -overflow. This function allows us to reject steps that are too large (and -therefore expose us to the possible overflow) without actually calculating -function value at the x+stp*d. - - -- ALGLIB -- - Copyright 20.08.2010 by Bochkanov Sergey -*************************************************************************/ -void nleqsetstpmax(const nleqstate &state, const double stpmax); - - -/************************************************************************* -This function provides reverse communication interface -Reverse communication interface is not documented or recommended to use. -See below for functions which provide better documented API -*************************************************************************/ -bool nleqiteration(const nleqstate &state); - - -/************************************************************************* -This family of functions is used to launcn iterations of nonlinear solver - -These functions accept following parameters: - state - algorithm state - func - callback which calculates function (or merit function) - value func at given point x - jac - callback which calculates function vector fi[] - and Jacobian jac at given point x - rep - optional callback which is called after each iteration - can be NULL - ptr - optional pointer which is passed to func/grad/hess/jac/rep - can be NULL - - - -- ALGLIB -- - Copyright 20.03.2009 by Bochkanov Sergey - -*************************************************************************/ -void nleqsolve(nleqstate &state, - void (*func)(const real_1d_array &x, double &func, void *ptr), - void (*jac)(const real_1d_array &x, real_1d_array &fi, real_2d_array &jac, void *ptr), - void (*rep)(const real_1d_array &x, double func, void *ptr) = NULL, - void *ptr = NULL); - - -/************************************************************************* -NLEQ solver results - -INPUT PARAMETERS: - State - algorithm state. - -OUTPUT PARAMETERS: - X - array[0..N-1], solution - Rep - optimization report: - * Rep.TerminationType completetion code: - * -4 ERROR: algorithm has converged to the - stationary point Xf which is local minimum of - f=F[0]^2+...+F[m-1]^2, but is not solution of - nonlinear system. - * 1 sqrt(f)<=EpsF. - * 5 MaxIts steps was taken - * 7 stopping conditions are too stringent, - further improvement is impossible - * Rep.IterationsCount contains iterations count - * NFEV countains number of function calculations - * ActiveConstraints contains number of active constraints - - -- ALGLIB -- - Copyright 20.08.2009 by Bochkanov Sergey -*************************************************************************/ -void nleqresults(const nleqstate &state, real_1d_array &x, nleqreport &rep); - - -/************************************************************************* -NLEQ solver results - -Buffered implementation of NLEQResults(), which uses pre-allocated buffer -to store X[]. If buffer size is too small, it resizes buffer. It is -intended to be used in the inner cycles of performance critical algorithms -where array reallocation penalty is too large to be ignored. - - -- ALGLIB -- - Copyright 20.08.2009 by Bochkanov Sergey -*************************************************************************/ -void nleqresultsbuf(const nleqstate &state, real_1d_array &x, nleqreport &rep); - - -/************************************************************************* -This subroutine restarts CG algorithm from new point. All optimization -parameters are left unchanged. - -This function allows to solve multiple optimization problems (which -must have same number of dimensions) without object reallocation penalty. - -INPUT PARAMETERS: - State - structure used for reverse communication previously - allocated with MinCGCreate call. - X - new starting point. - BndL - new lower bounds - BndU - new upper bounds - - -- ALGLIB -- - Copyright 30.07.2010 by Bochkanov Sergey -*************************************************************************/ -void nleqrestartfrom(const nleqstate &state, const real_1d_array &x); -} - -///////////////////////////////////////////////////////////////////////// -// -// THIS SECTION CONTAINS COMPUTATIONAL CORE DECLARATIONS (FUNCTIONS) -// -///////////////////////////////////////////////////////////////////////// -namespace alglib_impl -{ -void rmatrixsolve(/* Real */ ae_matrix* a, - ae_int_t n, - /* Real */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -void rmatrixsolvem(/* Real */ ae_matrix* a, - ae_int_t n, - /* Real */ ae_matrix* b, - ae_int_t m, - ae_bool rfs, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_matrix* x, - ae_state *_state); -void rmatrixlusolve(/* Real */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Real */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -void rmatrixlusolvem(/* Real */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Real */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_matrix* x, - ae_state *_state); -void rmatrixmixedsolve(/* Real */ ae_matrix* a, - /* Real */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Real */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -void rmatrixmixedsolvem(/* Real */ ae_matrix* a, - /* Real */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Real */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_matrix* x, - ae_state *_state); -void cmatrixsolvem(/* Complex */ ae_matrix* a, - ae_int_t n, - /* Complex */ ae_matrix* b, - ae_int_t m, - ae_bool rfs, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_matrix* x, - ae_state *_state); -void cmatrixsolve(/* Complex */ ae_matrix* a, - ae_int_t n, - /* Complex */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_vector* x, - ae_state *_state); -void cmatrixlusolvem(/* Complex */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Complex */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_matrix* x, - ae_state *_state); -void cmatrixlusolve(/* Complex */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Complex */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_vector* x, - ae_state *_state); -void cmatrixmixedsolvem(/* Complex */ ae_matrix* a, - /* Complex */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Complex */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_matrix* x, - ae_state *_state); -void cmatrixmixedsolve(/* Complex */ ae_matrix* a, - /* Complex */ ae_matrix* lua, - /* Integer */ ae_vector* p, - ae_int_t n, - /* Complex */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_vector* x, - ae_state *_state); -void spdmatrixsolvem(/* Real */ ae_matrix* a, - ae_int_t n, - ae_bool isupper, - /* Real */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_matrix* x, - ae_state *_state); -void spdmatrixsolve(/* Real */ ae_matrix* a, - ae_int_t n, - ae_bool isupper, - /* Real */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -void spdmatrixcholeskysolvem(/* Real */ ae_matrix* cha, - ae_int_t n, - ae_bool isupper, - /* Real */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_matrix* x, - ae_state *_state); -void spdmatrixcholeskysolve(/* Real */ ae_matrix* cha, - ae_int_t n, - ae_bool isupper, - /* Real */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -void hpdmatrixsolvem(/* Complex */ ae_matrix* a, - ae_int_t n, - ae_bool isupper, - /* Complex */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_matrix* x, - ae_state *_state); -void hpdmatrixsolve(/* Complex */ ae_matrix* a, - ae_int_t n, - ae_bool isupper, - /* Complex */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_vector* x, - ae_state *_state); -void hpdmatrixcholeskysolvem(/* Complex */ ae_matrix* cha, - ae_int_t n, - ae_bool isupper, - /* Complex */ ae_matrix* b, - ae_int_t m, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_matrix* x, - ae_state *_state); -void hpdmatrixcholeskysolve(/* Complex */ ae_matrix* cha, - ae_int_t n, - ae_bool isupper, - /* Complex */ ae_vector* b, - ae_int_t* info, - densesolverreport* rep, - /* Complex */ ae_vector* x, - ae_state *_state); -void rmatrixsolvels(/* Real */ ae_matrix* a, - ae_int_t nrows, - ae_int_t ncols, - /* Real */ ae_vector* b, - double threshold, - ae_int_t* info, - densesolverlsreport* rep, - /* Real */ ae_vector* x, - ae_state *_state); -ae_bool _densesolverreport_init(densesolverreport* p, ae_state *_state, ae_bool make_automatic); -ae_bool _densesolverreport_init_copy(densesolverreport* dst, densesolverreport* src, ae_state *_state, ae_bool make_automatic); -void _densesolverreport_clear(densesolverreport* p); -ae_bool _densesolverlsreport_init(densesolverlsreport* p, ae_state *_state, ae_bool make_automatic); -ae_bool _densesolverlsreport_init_copy(densesolverlsreport* dst, densesolverlsreport* src, ae_state *_state, ae_bool make_automatic); -void _densesolverlsreport_clear(densesolverlsreport* p); -void nleqcreatelm(ae_int_t n, - ae_int_t m, - /* Real */ ae_vector* x, - nleqstate* state, - ae_state *_state); -void nleqsetcond(nleqstate* state, - double epsf, - ae_int_t maxits, - ae_state *_state); -void nleqsetxrep(nleqstate* state, ae_bool needxrep, ae_state *_state); -void nleqsetstpmax(nleqstate* state, double stpmax, ae_state *_state); -ae_bool nleqiteration(nleqstate* state, ae_state *_state); -void nleqresults(nleqstate* state, - /* Real */ ae_vector* x, - nleqreport* rep, - ae_state *_state); -void nleqresultsbuf(nleqstate* state, - /* Real */ ae_vector* x, - nleqreport* rep, - ae_state *_state); -void nleqrestartfrom(nleqstate* state, - /* Real */ ae_vector* x, - ae_state *_state); -ae_bool _nleqstate_init(nleqstate* p, ae_state *_state, ae_bool make_automatic); -ae_bool _nleqstate_init_copy(nleqstate* dst, nleqstate* src, ae_state *_state, ae_bool make_automatic); -void _nleqstate_clear(nleqstate* p); -ae_bool _nleqreport_init(nleqreport* p, ae_state *_state, ae_bool make_automatic); -ae_bool _nleqreport_init_copy(nleqreport* dst, nleqreport* src, ae_state *_state, ae_bool make_automatic); -void _nleqreport_clear(nleqreport* p); - -} -#endif -