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solvers.h
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solvers.h
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/*************************************************************************
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
{
normestimatorstate nes;
ae_vector rx;
ae_vector b;
ae_int_t n;
ae_int_t m;
ae_int_t prectype;
ae_vector ui;
ae_vector uip1;
ae_vector vi;
ae_vector vip1;
ae_vector omegai;
ae_vector omegaip1;
double alphai;
double alphaip1;
double betai;
double betaip1;
double phibari;
double phibarip1;
double phii;
double rhobari;
double rhobarip1;
double rhoi;
double ci;
double si;
double theta;
double lambdai;
ae_vector d;
double anorm;
double bnorm2;
double dnorm;
double r2;
ae_vector x;
ae_vector mv;
ae_vector mtv;
double epsa;
double epsb;
double epsc;
ae_int_t maxits;
ae_bool xrep;
ae_bool xupdated;
ae_bool needmv;
ae_bool needmtv;
ae_bool needmv2;
ae_bool needvmv;
ae_bool needprec;
ae_int_t repiterationscount;
ae_int_t repnmv;
ae_int_t repterminationtype;
ae_bool running;
ae_vector tmpd;
ae_vector tmpx;
rcommstate rstate;
} linlsqrstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nmv;
ae_int_t terminationtype;
} linlsqrreport;
typedef struct
{
ae_vector rx;
ae_vector b;
ae_int_t n;
ae_int_t prectype;
ae_vector cx;
ae_vector cr;
ae_vector cz;
ae_vector p;
ae_vector r;
ae_vector z;
double alpha;
double beta;
double r2;
double meritfunction;
ae_vector x;
ae_vector mv;
ae_vector pv;
double vmv;
ae_vector startx;
double epsf;
ae_int_t maxits;
ae_int_t itsbeforerestart;
ae_int_t itsbeforerupdate;
ae_bool xrep;
ae_bool xupdated;
ae_bool needmv;
ae_bool needmtv;
ae_bool needmv2;
ae_bool needvmv;
ae_bool needprec;
ae_int_t repiterationscount;
ae_int_t repnmv;
ae_int_t repterminationtype;
ae_bool running;
ae_vector tmpd;
rcommstate rstate;
} lincgstate;
typedef struct
{
ae_int_t iterationscount;
ae_int_t nmv;
ae_int_t terminationtype;
double r2;
} lincgreport;
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;
};
/*************************************************************************
This object stores state of the LinLSQR method.
You should use ALGLIB functions to work with this object.
*************************************************************************/
class _linlsqrstate_owner
{
public:
_linlsqrstate_owner();
_linlsqrstate_owner(const _linlsqrstate_owner &rhs);
_linlsqrstate_owner& operator=(const _linlsqrstate_owner &rhs);
virtual ~_linlsqrstate_owner();
alglib_impl::linlsqrstate* c_ptr();
alglib_impl::linlsqrstate* c_ptr() const;
protected:
alglib_impl::linlsqrstate *p_struct;
};
class linlsqrstate : public _linlsqrstate_owner
{
public:
linlsqrstate();
linlsqrstate(const linlsqrstate &rhs);
linlsqrstate& operator=(const linlsqrstate &rhs);
virtual ~linlsqrstate();
};
/*************************************************************************
*************************************************************************/
class _linlsqrreport_owner
{
public:
_linlsqrreport_owner();
_linlsqrreport_owner(const _linlsqrreport_owner &rhs);
_linlsqrreport_owner& operator=(const _linlsqrreport_owner &rhs);
virtual ~_linlsqrreport_owner();
alglib_impl::linlsqrreport* c_ptr();
alglib_impl::linlsqrreport* c_ptr() const;
protected:
alglib_impl::linlsqrreport *p_struct;
};
class linlsqrreport : public _linlsqrreport_owner
{
public:
linlsqrreport();
linlsqrreport(const linlsqrreport &rhs);
linlsqrreport& operator=(const linlsqrreport &rhs);
virtual ~linlsqrreport();
ae_int_t &iterationscount;
ae_int_t &nmv;
ae_int_t &terminationtype;
};
/*************************************************************************
This object stores state of the linear CG method.
You should use ALGLIB functions to work with this object.
Never try to access its fields directly!
*************************************************************************/
class _lincgstate_owner
{
public:
_lincgstate_owner();
_lincgstate_owner(const _lincgstate_owner &rhs);
_lincgstate_owner& operator=(const _lincgstate_owner &rhs);
virtual ~_lincgstate_owner();
alglib_impl::lincgstate* c_ptr();
alglib_impl::lincgstate* c_ptr() const;
protected:
alglib_impl::lincgstate *p_struct;
};
class lincgstate : public _lincgstate_owner
{
public:
lincgstate();
lincgstate(const lincgstate &rhs);
lincgstate& operator=(const lincgstate &rhs);
virtual ~lincgstate();
};
/*************************************************************************
*************************************************************************/
class _lincgreport_owner
{
public:
_lincgreport_owner();
_lincgreport_owner(const _lincgreport_owner &rhs);
_lincgreport_owner& operator=(const _lincgreport_owner &rhs);
virtual ~_lincgreport_owner();
alglib_impl::lincgreport* c_ptr();
alglib_impl::lincgreport* c_ptr() const;
protected:
alglib_impl::lincgreport *p_struct;
};
class lincgreport : public _lincgreport_owner
{
public:
lincgreport();
lincgreport(const lincgreport &rhs);
lincgreport& operator=(const lincgreport &rhs);
virtual ~lincgreport();
ae_int_t &iterationscount;
ae_int_t &nmv;
ae_int_t &terminationtype;
double &r2;
};
/*************************************************************************
*************************************************************************/
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
*************************************************************************/