/*************************************************************************
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 >>>
*************************************************************************/
#pragma warning disable 162
#pragma warning disable 219
using System;
public partial class alglib
{
/*************************************************************************
*************************************************************************/
public class densesolverreport
{
//
// Public declarations
//
public double r1 { get { return _innerobj.r1; } set { _innerobj.r1 = value; } }
public double rinf { get { return _innerobj.rinf; } set { _innerobj.rinf = value; } }
public densesolverreport()
{
_innerobj = new densesolver.densesolverreport();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private densesolver.densesolverreport _innerobj;
public densesolver.densesolverreport innerobj { get { return _innerobj; } }
public densesolverreport(densesolver.densesolverreport obj)
{
_innerobj = obj;
}
}
/*************************************************************************
*************************************************************************/
public class densesolverlsreport
{
//
// Public declarations
//
public double r2 { get { return _innerobj.r2; } set { _innerobj.r2 = value; } }
public double[,] cx { get { return _innerobj.cx; } set { _innerobj.cx = value; } }
public int n { get { return _innerobj.n; } set { _innerobj.n = value; } }
public int k { get { return _innerobj.k; } set { _innerobj.k = value; } }
public densesolverlsreport()
{
_innerobj = new densesolver.densesolverlsreport();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private densesolver.densesolverlsreport _innerobj;
public densesolver.densesolverlsreport innerobj { get { return _innerobj; } }
public densesolverlsreport(densesolver.densesolverlsreport obj)
{
_innerobj = obj;
}
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolve(double[,] a, int n, double[] b, out int info, out densesolverreport rep, out double[] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0];
densesolver.rmatrixsolve(a, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolvem(double[,] a, int n, double[,] b, int m, bool rfs, out int info, out densesolverreport rep, out double[,] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0,0];
densesolver.rmatrixsolvem(a, n, b, m, rfs, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixlusolve(double[,] lua, int[] p, int n, double[] b, out int info, out densesolverreport rep, out double[] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0];
densesolver.rmatrixlusolve(lua, p, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixlusolvem(double[,] lua, int[] p, int n, double[,] b, int m, out int info, out densesolverreport rep, out double[,] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0,0];
densesolver.rmatrixlusolvem(lua, p, n, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixmixedsolve(double[,] a, double[,] lua, int[] p, int n, double[] b, out int info, out densesolverreport rep, out double[] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0];
densesolver.rmatrixmixedsolve(a, lua, p, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixmixedsolvem(double[,] a, double[,] lua, int[] p, int n, double[,] b, int m, out int info, out densesolverreport rep, out double[,] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0,0];
densesolver.rmatrixmixedsolvem(a, lua, p, n, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixsolvem(complex[,] a, int n, complex[,] b, int m, bool rfs, out int info, out densesolverreport rep, out complex[,] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0,0];
densesolver.cmatrixsolvem(a, n, b, m, rfs, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixsolve(complex[,] a, int n, complex[] b, out int info, out densesolverreport rep, out complex[] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0];
densesolver.cmatrixsolve(a, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixlusolvem(complex[,] lua, int[] p, int n, complex[,] b, int m, out int info, out densesolverreport rep, out complex[,] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0,0];
densesolver.cmatrixlusolvem(lua, p, n, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixlusolve(complex[,] lua, int[] p, int n, complex[] b, out int info, out densesolverreport rep, out complex[] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0];
densesolver.cmatrixlusolve(lua, p, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixmixedsolvem(complex[,] a, complex[,] lua, int[] p, int n, complex[,] b, int m, out int info, out densesolverreport rep, out complex[,] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0,0];
densesolver.cmatrixmixedsolvem(a, lua, p, n, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixmixedsolve(complex[,] a, complex[,] lua, int[] p, int n, complex[] b, out int info, out densesolverreport rep, out complex[] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0];
densesolver.cmatrixmixedsolve(a, lua, p, n, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixsolvem(double[,] a, int n, bool isupper, double[,] b, int m, out int info, out densesolverreport rep, out double[,] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0,0];
densesolver.spdmatrixsolvem(a, n, isupper, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixsolve(double[,] a, int n, bool isupper, double[] b, out int info, out densesolverreport rep, out double[] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0];
densesolver.spdmatrixsolve(a, n, isupper, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixcholeskysolvem(double[,] cha, int n, bool isupper, double[,] b, int m, out int info, out densesolverreport rep, out double[,] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0,0];
densesolver.spdmatrixcholeskysolvem(cha, n, isupper, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixcholeskysolve(double[,] cha, int n, bool isupper, double[] b, out int info, out densesolverreport rep, out double[] x)
{
info = 0;
rep = new densesolverreport();
x = new double[0];
densesolver.spdmatrixcholeskysolve(cha, n, isupper, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixsolvem(complex[,] a, int n, bool isupper, complex[,] b, int m, out int info, out densesolverreport rep, out complex[,] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0,0];
densesolver.hpdmatrixsolvem(a, n, isupper, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixsolve(complex[,] a, int n, bool isupper, complex[] b, out int info, out densesolverreport rep, out complex[] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0];
densesolver.hpdmatrixsolve(a, n, isupper, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixcholeskysolvem(complex[,] cha, int n, bool isupper, complex[,] b, int m, out int info, out densesolverreport rep, out complex[,] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0,0];
densesolver.hpdmatrixcholeskysolvem(cha, n, isupper, b, m, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixcholeskysolve(complex[,] cha, int n, bool isupper, complex[] b, out int info, out densesolverreport rep, out complex[] x)
{
info = 0;
rep = new densesolverreport();
x = new complex[0];
densesolver.hpdmatrixcholeskysolve(cha, n, isupper, b, ref info, rep.innerobj, ref x);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolvels(double[,] a, int nrows, int ncols, double[] b, double threshold, out int info, out densesolverlsreport rep, out double[] x)
{
info = 0;
rep = new densesolverlsreport();
x = new double[0];
densesolver.rmatrixsolvels(a, nrows, ncols, b, threshold, ref info, rep.innerobj, ref x);
return;
}
}
public partial class alglib
{
/*************************************************************************
This object stores state of the LinLSQR method.
You should use ALGLIB functions to work with this object.
*************************************************************************/
public class linlsqrstate
{
//
// Public declarations
//
public linlsqrstate()
{
_innerobj = new linlsqr.linlsqrstate();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private linlsqr.linlsqrstate _innerobj;
public linlsqr.linlsqrstate innerobj { get { return _innerobj; } }
public linlsqrstate(linlsqr.linlsqrstate obj)
{
_innerobj = obj;
}
}
/*************************************************************************
*************************************************************************/
public class linlsqrreport
{
//
// Public declarations
//
public int iterationscount { get { return _innerobj.iterationscount; } set { _innerobj.iterationscount = value; } }
public int nmv { get { return _innerobj.nmv; } set { _innerobj.nmv = value; } }
public int terminationtype { get { return _innerobj.terminationtype; } set { _innerobj.terminationtype = value; } }
public linlsqrreport()
{
_innerobj = new linlsqr.linlsqrreport();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private linlsqr.linlsqrreport _innerobj;
public linlsqr.linlsqrreport innerobj { get { return _innerobj; } }
public linlsqrreport(linlsqr.linlsqrreport obj)
{
_innerobj = obj;
}
}
/*************************************************************************
This function initializes linear LSQR Solver. This solver is used to solve
non-symmetric (and, possibly, non-square) problems. Least squares solution
is returned for non-compatible systems.
USAGE:
1. User initializes algorithm state with LinLSQRCreate() call
2. User tunes solver parameters with LinLSQRSetCond() and other functions
3. User calls LinLSQRSolveSparse() function which takes algorithm state
and SparseMatrix object.
4. User calls LinLSQRResults() to get solution
5. Optionally, user may call LinLSQRSolveSparse() again to solve another
problem with different matrix and/or right part without reinitializing
LinLSQRState structure.
INPUT PARAMETERS:
M - number of rows in A
N - number of variables, N>0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrcreate(int m, int n, out linlsqrstate state)
{
state = new linlsqrstate();
linlsqr.linlsqrcreate(m, n, state.innerobj);
return;
}
/*************************************************************************
This function changes preconditioning settings of LinLSQQSolveSparse()
function. By default, SolveSparse() uses diagonal preconditioner, but if
you want to use solver without preconditioning, you can call this function
which forces solver to use unit matrix for preconditioning.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetprecunit(linlsqrstate state)
{
linlsqr.linlsqrsetprecunit(state.innerobj);
return;
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. LinCGSolveSparse() will use diagonal of the system matrix as
preconditioner. This preconditioning mode is active by default.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetprecdiag(linlsqrstate state)
{
linlsqr.linlsqrsetprecdiag(state.innerobj);
return;
}
/*************************************************************************
This function sets optional Tikhonov regularization coefficient.
It is zero by default.
INPUT PARAMETERS:
LambdaI - regularization factor, LambdaI>=0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetlambdai(linlsqrstate state, double lambdai)
{
linlsqr.linlsqrsetlambdai(state.innerobj, lambdai);
return;
}
/*************************************************************************
Procedure for solution of A*x=b with sparse A.
INPUT PARAMETERS:
State - algorithm state
A - sparse M*N matrix in the CRS format (you MUST contvert it
to CRS format by calling SparseConvertToCRS() function
BEFORE you pass it to this function).
B - right part, array[M]
RESULT:
This function returns no result.
You can get solution by calling LinCGResults()
NOTE: this function uses lightweight preconditioning - multiplication by
inverse of diag(A). If you want, you can turn preconditioning off by
calling LinLSQRSetPrecUnit(). However, preconditioning cost is low
and preconditioner is very important for solution of badly scaled
problems.
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsolvesparse(linlsqrstate state, sparsematrix a, double[] b)
{
linlsqr.linlsqrsolvesparse(state.innerobj, a.innerobj, b);
return;
}
/*************************************************************************
This function sets stopping criteria.
INPUT PARAMETERS:
EpsA - algorithm will be stopped if ||A^T*Rk||/(||A||*||Rk||)<=EpsA.
EpsB - algorithm will be stopped if ||Rk||<=EpsB*||B||
MaxIts - algorithm will be stopped if number of iterations
more than MaxIts.
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: if EpsA,EpsB,EpsC and MaxIts are zero then these variables will
be setted as default values.
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetcond(linlsqrstate state, double epsa, double epsb, int maxits)
{
linlsqr.linlsqrsetcond(state.innerobj, epsa, epsb, maxits);
return;
}
/*************************************************************************
LSQR solver: results.
This function must be called after LinLSQRSolve
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[N], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* 1 ||Rk||<=EpsB*||B||
* 4 ||A^T*Rk||/(||A||*||Rk||)<=EpsA
* 5 MaxIts steps was taken
* 7 rounding errors prevent further progress,
X contains best point found so far.
(sometimes returned on singular systems)
* Rep.IterationsCount contains iterations count
* NMV countains number of matrix-vector calculations
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrresults(linlsqrstate state, out double[] x, out linlsqrreport rep)
{
x = new double[0];
rep = new linlsqrreport();
linlsqr.linlsqrresults(state.innerobj, ref x, rep.innerobj);
return;
}
/*************************************************************************
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 MinCGOptimize().
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetxrep(linlsqrstate state, bool needxrep)
{
linlsqr.linlsqrsetxrep(state.innerobj, needxrep);
return;
}
}
public partial class alglib
{
/*************************************************************************
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!
*************************************************************************/
public class lincgstate
{
//
// Public declarations
//
public lincgstate()
{
_innerobj = new lincg.lincgstate();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private lincg.lincgstate _innerobj;
public lincg.lincgstate innerobj { get { return _innerobj; } }
public lincgstate(lincg.lincgstate obj)
{
_innerobj = obj;
}
}
/*************************************************************************
*************************************************************************/
public class lincgreport
{
//
// Public declarations
//
public int iterationscount { get { return _innerobj.iterationscount; } set { _innerobj.iterationscount = value; } }
public int nmv { get { return _innerobj.nmv; } set { _innerobj.nmv = value; } }
public int terminationtype { get { return _innerobj.terminationtype; } set { _innerobj.terminationtype = value; } }
public double r2 { get { return _innerobj.r2; } set { _innerobj.r2 = value; } }
public lincgreport()
{
_innerobj = new lincg.lincgreport();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private lincg.lincgreport _innerobj;
public lincg.lincgreport innerobj { get { return _innerobj; } }
public lincgreport(lincg.lincgreport obj)
{
_innerobj = obj;
}
}
/*************************************************************************
This function initializes linear CG Solver. This solver is used to solve
symmetric positive definite problems. If you want to solve nonsymmetric
(or non-positive definite) problem you may use LinLSQR solver provided by
ALGLIB.
USAGE:
1. User initializes algorithm state with LinCGCreate() call
2. User tunes solver parameters with LinCGSetCond() and other functions
3. Optionally, user sets starting point with LinCGSetStartingPoint()
4. User calls LinCGSolveSparse() function which takes algorithm state and
SparseMatrix object.
5. User calls LinCGResults() to get solution
6. Optionally, user may call LinCGSolveSparse() again to solve another
problem with different matrix and/or right part without reinitializing
LinCGState structure.
INPUT PARAMETERS:
N - problem dimension, N>0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgcreate(int n, out lincgstate state)
{
state = new lincgstate();
lincg.lincgcreate(n, state.innerobj);
return;
}
/*************************************************************************
This function sets starting point.
By default, zero starting point is used.
INPUT PARAMETERS:
X - starting point, array[N]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetstartingpoint(lincgstate state, double[] x)
{
lincg.lincgsetstartingpoint(state.innerobj, x);
return;
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. By default, SolveSparse() uses diagonal preconditioner, but if
you want to use solver without preconditioning, you can call this function
which forces solver to use unit matrix for preconditioning.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetprecunit(lincgstate state)
{
lincg.lincgsetprecunit(state.innerobj);
return;
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. LinCGSolveSparse() will use diagonal of the system matrix as
preconditioner. This preconditioning mode is active by default.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetprecdiag(lincgstate state)
{
lincg.lincgsetprecdiag(state.innerobj);
return;
}
/*************************************************************************
This function sets stopping criteria.
INPUT PARAMETERS:
EpsF - algorithm will be stopped if norm of residual is less than
EpsF*||b||.
MaxIts - algorithm will be stopped if number of iterations is more
than MaxIts.
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
If both EpsF and MaxIts are zero then small EpsF will be set to small
value.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetcond(lincgstate state, double epsf, int maxits)
{
lincg.lincgsetcond(state.innerobj, epsf, maxits);
return;
}
/*************************************************************************
Procedure for solution of A*x=b with sparse A.
INPUT PARAMETERS:
State - algorithm state
A - sparse matrix in the CRS format (you MUST contvert it to
CRS format by calling SparseConvertToCRS() function).
IsUpper - whether upper or lower triangle of A is used:
* IsUpper=True => only upper triangle is used and lower
triangle is not referenced at all
* IsUpper=False => only lower triangle is used and upper
triangle is not referenced at all
B - right part, array[N]
RESULT:
This function returns no result.
You can get solution by calling LinCGResults()
NOTE: this function uses lightweight preconditioning - multiplication by
inverse of diag(A). If you want, you can turn preconditioning off by
calling LinCGSetPrecUnit(). However, preconditioning cost is low and
preconditioner is very important for solution of badly scaled
problems.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsolvesparse(lincgstate state, sparsematrix a, bool isupper, double[] b)
{
lincg.lincgsolvesparse(state.innerobj, a.innerobj, isupper, b);
return;
}
/*************************************************************************
CG-solver: results.
This function must be called after LinCGSolve
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[N], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -5 input matrix is either not positive definite,
too large or too small
* -4 overflow/underflow during solution
(ill conditioned problem)
* 1 ||residual||<=EpsF*||b||
* 5 MaxIts steps was taken
* 7 rounding errors prevent further progress,
best point found is returned
* Rep.IterationsCount contains iterations count
* NMV countains number of matrix-vector calculations
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgresults(lincgstate state, out double[] x, out lincgreport rep)
{
x = new double[0];
rep = new lincgreport();
lincg.lincgresults(state.innerobj, ref x, rep.innerobj);
return;
}
/*************************************************************************
This function sets restart frequency. By default, algorithm is restarted
after N subsequent iterations.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetrestartfreq(lincgstate state, int srf)
{
lincg.lincgsetrestartfreq(state.innerobj, srf);
return;
}
/*************************************************************************
This function sets frequency of residual recalculations.
Algorithm updates residual r_k using iterative formula, but recalculates
it from scratch after each 10 iterations. It is done to avoid accumulation
of numerical errors and to stop algorithm when r_k starts to grow.
Such low update frequence (1/10) gives very little overhead, but makes
algorithm a bit more robust against numerical errors. However, you may
change it
INPUT PARAMETERS:
Freq - desired update frequency, Freq>=0.
Zero value means that no updates will be done.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetrupdatefreq(lincgstate state, int freq)
{
lincg.lincgsetrupdatefreq(state.innerobj, freq);
return;
}
/*************************************************************************
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 MinCGOptimize().
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetxrep(lincgstate state, bool needxrep)
{
lincg.lincgsetxrep(state.innerobj, needxrep);
return;
}
}
public partial class alglib
{
/*************************************************************************
*************************************************************************/
public class nleqstate
{
//
// Public declarations
//
public bool needf { get { return _innerobj.needf; } set { _innerobj.needf = value; } }
public bool needfij { get { return _innerobj.needfij; } set { _innerobj.needfij = value; } }
public bool xupdated { get { return _innerobj.xupdated; } set { _innerobj.xupdated = value; } }
public double f { get { return _innerobj.f; } set { _innerobj.f = value; } }
public double[] fi { get { return _innerobj.fi; } }
public double[,] j { get { return _innerobj.j; } }
public double[] x { get { return _innerobj.x; } }
public nleqstate()
{
_innerobj = new nleq.nleqstate();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private nleq.nleqstate _innerobj;
public nleq.nleqstate innerobj { get { return _innerobj; } }
public nleqstate(nleq.nleqstate obj)
{
_innerobj = obj;
}
}
/*************************************************************************
*************************************************************************/
public class nleqreport
{
//
// Public declarations
//
public int iterationscount { get { return _innerobj.iterationscount; } set { _innerobj.iterationscount = value; } }
public int nfunc { get { return _innerobj.nfunc; } set { _innerobj.nfunc = value; } }
public int njac { get { return _innerobj.njac; } set { _innerobj.njac = value; } }
public int terminationtype { get { return _innerobj.terminationtype; } set { _innerobj.terminationtype = value; } }
public nleqreport()
{
_innerobj = new nleq.nleqreport();
}
//
// Although some of declarations below are public, you should not use them
// They are intended for internal use only
//
private nleq.nleqreport _innerobj;
public nleq.nleqreport innerobj { get { return _innerobj; } }
public nleqreport(nleq.nleqreport obj)
{
_innerobj = obj;
}
}
/*************************************************************************
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
*************************************************************************/
public static void nleqcreatelm(int n, int m, double[] x, out nleqstate state)
{
state = new nleqstate();
nleq.nleqcreatelm(n, m, x, state.innerobj);
return;
}
public static void nleqcreatelm(int m, double[] x, out nleqstate state)
{
int n;
state = new nleqstate();
n = ap.len(x);
nleq.nleqcreatelm(n, m, x, state.innerobj);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqsetcond(nleqstate state, double epsf, int maxits)
{
nleq.nleqsetcond(state.innerobj, epsf, maxits);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqsetxrep(nleqstate state, bool needxrep)
{
nleq.nleqsetxrep(state.innerobj, needxrep);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqsetstpmax(nleqstate state, double stpmax)
{
nleq.nleqsetstpmax(state.innerobj, stpmax);
return;
}
/*************************************************************************
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
*************************************************************************/
public static bool nleqiteration(nleqstate state)
{
bool result = nleq.nleqiteration(state.innerobj);
return result;
}
/*************************************************************************
This family of functions is used to launcn iterations of nonlinear solver
These functions accept following parameters:
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
obj - optional object which is passed to func/grad/hess/jac/rep
can be null
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
public static void nleqsolve(nleqstate state, ndimensional_func func, ndimensional_jac jac, ndimensional_rep rep, object obj)
{
if( func==null )
throw new alglibexception("ALGLIB: error in 'nleqsolve()' (func is null)");
if( jac==null )
throw new alglibexception("ALGLIB: error in 'nleqsolve()' (jac is null)");
while( alglib.nleqiteration(state) )
{
if( state.needf )
{
func(state.x, ref state.innerobj.f, obj);
continue;
}
if( state.needfij )
{
jac(state.x, state.innerobj.fi, state.innerobj.j, obj);
continue;
}
if( state.innerobj.xupdated )
{
if( rep!=null )
rep(state.innerobj.x, state.innerobj.f, obj);
continue;
}
throw new alglibexception("ALGLIB: error in 'nleqsolve' (some derivatives were not provided?)");
}
}
/*************************************************************************
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
*************************************************************************/
public static void nleqresults(nleqstate state, out double[] x, out nleqreport rep)
{
x = new double[0];
rep = new nleqreport();
nleq.nleqresults(state.innerobj, ref x, rep.innerobj);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqresultsbuf(nleqstate state, ref double[] x, nleqreport rep)
{
nleq.nleqresultsbuf(state.innerobj, ref x, rep.innerobj);
return;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqrestartfrom(nleqstate state, double[] x)
{
nleq.nleqrestartfrom(state.innerobj, x);
return;
}
}
public partial class alglib
{
public class densesolver
{
public class densesolverreport : apobject
{
public double r1;
public double rinf;
public densesolverreport()
{
init();
}
public override void init()
{
}
public override alglib.apobject make_copy()
{
densesolverreport _result = new densesolverreport();
_result.r1 = r1;
_result.rinf = rinf;
return _result;
}
};
public class densesolverlsreport : apobject
{
public double r2;
public double[,] cx;
public int n;
public int k;
public densesolverlsreport()
{
init();
}
public override void init()
{
cx = new double[0,0];
}
public override alglib.apobject make_copy()
{
densesolverlsreport _result = new densesolverlsreport();
_result.r2 = r2;
_result.cx = (double[,])cx.Clone();
_result.n = n;
_result.k = k;
return _result;
}
};
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolve(double[,] a,
int n,
double[] b,
ref int info,
densesolverreport rep,
ref double[] x)
{
double[,] bm = new double[0,0];
double[,] xm = new double[0,0];
int i_ = 0;
info = 0;
x = new double[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new double[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
rmatrixsolvem(a, n, bm, 1, true, ref info, rep, ref xm);
x = new double[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolvem(double[,] a,
int n,
double[,] b,
int m,
bool rfs,
ref int info,
densesolverreport rep,
ref double[,] x)
{
double[,] da = new double[0,0];
double[,] emptya = new double[0,0];
int[] p = new int[0];
double scalea = 0;
int i = 0;
int j = 0;
int i_ = 0;
info = 0;
x = new double[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
da = new double[n, n];
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=0; j<=n-1; j++)
{
scalea = Math.Max(scalea, Math.Abs(a[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
for(i=0; i<=n-1; i++)
{
for(i_=0; i_<=n-1;i_++)
{
da[i,i_] = a[i,i_];
}
}
trfac.rmatrixlu(ref da, n, n, ref p);
if( rfs )
{
rmatrixlusolveinternal(da, p, scalea, n, a, true, b, m, ref info, rep, ref x);
}
else
{
rmatrixlusolveinternal(da, p, scalea, n, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void rmatrixlusolve(double[,] lua,
int[] p,
int n,
double[] b,
ref int info,
densesolverreport rep,
ref double[] x)
{
double[,] bm = new double[0,0];
double[,] xm = new double[0,0];
int i_ = 0;
info = 0;
x = new double[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new double[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
rmatrixlusolvem(lua, p, n, bm, 1, ref info, rep, ref xm);
x = new double[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixlusolvem(double[,] lua,
int[] p,
int n,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
double[,] emptya = new double[0,0];
int i = 0;
int j = 0;
double scalea = 0;
info = 0;
x = new double[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|U[i,j]|)
// we assume that LU is in its normal form, i.e. |L[i,j]|<=1
// 2. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=i; j<=n-1; j++)
{
scalea = Math.Max(scalea, Math.Abs(lua[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
rmatrixlusolveinternal(lua, p, scalea, n, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void rmatrixmixedsolve(double[,] a,
double[,] lua,
int[] p,
int n,
double[] b,
ref int info,
densesolverreport rep,
ref double[] x)
{
double[,] bm = new double[0,0];
double[,] xm = new double[0,0];
int i_ = 0;
info = 0;
x = new double[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new double[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
rmatrixmixedsolvem(a, lua, p, n, bm, 1, ref info, rep, ref xm);
x = new double[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixmixedsolvem(double[,] a,
double[,] lua,
int[] p,
int n,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
double scalea = 0;
int i = 0;
int j = 0;
info = 0;
x = new double[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=0; j<=n-1; j++)
{
scalea = Math.Max(scalea, Math.Abs(a[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
rmatrixlusolveinternal(lua, p, scalea, n, a, true, b, m, ref info, rep, ref 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
*************************************************************************/
public static void cmatrixsolvem(complex[,] a,
int n,
complex[,] b,
int m,
bool rfs,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
complex[,] da = new complex[0,0];
complex[,] emptya = new complex[0,0];
int[] p = new int[0];
double scalea = 0;
int i = 0;
int j = 0;
int i_ = 0;
info = 0;
x = new complex[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
da = new complex[n, n];
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=0; j<=n-1; j++)
{
scalea = Math.Max(scalea, math.abscomplex(a[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
for(i=0; i<=n-1; i++)
{
for(i_=0; i_<=n-1;i_++)
{
da[i,i_] = a[i,i_];
}
}
trfac.cmatrixlu(ref da, n, n, ref p);
if( rfs )
{
cmatrixlusolveinternal(da, p, scalea, n, a, true, b, m, ref info, rep, ref x);
}
else
{
cmatrixlusolveinternal(da, p, scalea, n, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void cmatrixsolve(complex[,] a,
int n,
complex[] b,
ref int info,
densesolverreport rep,
ref complex[] x)
{
complex[,] bm = new complex[0,0];
complex[,] xm = new complex[0,0];
int i_ = 0;
info = 0;
x = new complex[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new complex[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
cmatrixsolvem(a, n, bm, 1, true, ref info, rep, ref xm);
x = new complex[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixlusolvem(complex[,] lua,
int[] p,
int n,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
complex[,] emptya = new complex[0,0];
int i = 0;
int j = 0;
double scalea = 0;
info = 0;
x = new complex[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|U[i,j]|)
// we assume that LU is in its normal form, i.e. |L[i,j]|<=1
// 2. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=i; j<=n-1; j++)
{
scalea = Math.Max(scalea, math.abscomplex(lua[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
cmatrixlusolveinternal(lua, p, scalea, n, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void cmatrixlusolve(complex[,] lua,
int[] p,
int n,
complex[] b,
ref int info,
densesolverreport rep,
ref complex[] x)
{
complex[,] bm = new complex[0,0];
complex[,] xm = new complex[0,0];
int i_ = 0;
info = 0;
x = new complex[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new complex[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
cmatrixlusolvem(lua, p, n, bm, 1, ref info, rep, ref xm);
x = new complex[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void cmatrixmixedsolvem(complex[,] a,
complex[,] lua,
int[] p,
int n,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
double scalea = 0;
int i = 0;
int j = 0;
info = 0;
x = new complex[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
scalea = 0;
for(i=0; i<=n-1; i++)
{
for(j=0; j<=n-1; j++)
{
scalea = Math.Max(scalea, math.abscomplex(a[i,j]));
}
}
if( (double)(scalea)==(double)(0) )
{
scalea = 1;
}
scalea = 1/scalea;
cmatrixlusolveinternal(lua, p, scalea, n, a, true, b, m, ref info, rep, ref 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
*************************************************************************/
public static void cmatrixmixedsolve(complex[,] a,
complex[,] lua,
int[] p,
int n,
complex[] b,
ref int info,
densesolverreport rep,
ref complex[] x)
{
complex[,] bm = new complex[0,0];
complex[,] xm = new complex[0,0];
int i_ = 0;
info = 0;
x = new complex[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new complex[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
cmatrixmixedsolvem(a, lua, p, n, bm, 1, ref info, rep, ref xm);
x = new complex[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixsolvem(double[,] a,
int n,
bool isupper,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
double[,] da = new double[0,0];
double sqrtscalea = 0;
int i = 0;
int j = 0;
int j1 = 0;
int j2 = 0;
int i_ = 0;
info = 0;
x = new double[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
da = new double[n, n];
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
sqrtscalea = 0;
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(j=j1; j<=j2; j++)
{
sqrtscalea = Math.Max(sqrtscalea, Math.Abs(a[i,j]));
}
}
if( (double)(sqrtscalea)==(double)(0) )
{
sqrtscalea = 1;
}
sqrtscalea = 1/sqrtscalea;
sqrtscalea = Math.Sqrt(sqrtscalea);
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(i_=j1; i_<=j2;i_++)
{
da[i,i_] = a[i,i_];
}
}
if( !trfac.spdmatrixcholesky(ref da, n, isupper) )
{
x = new double[n, m];
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
spdmatrixcholeskysolveinternal(da, sqrtscalea, n, isupper, a, true, b, m, ref info, rep, ref 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
*************************************************************************/
public static void spdmatrixsolve(double[,] a,
int n,
bool isupper,
double[] b,
ref int info,
densesolverreport rep,
ref double[] x)
{
double[,] bm = new double[0,0];
double[,] xm = new double[0,0];
int i_ = 0;
info = 0;
x = new double[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new double[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
spdmatrixsolvem(a, n, isupper, bm, 1, ref info, rep, ref xm);
x = new double[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void spdmatrixcholeskysolvem(double[,] cha,
int n,
bool isupper,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
double[,] emptya = new double[0,0];
double sqrtscalea = 0;
int i = 0;
int j = 0;
int j1 = 0;
int j2 = 0;
info = 0;
x = new double[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|U[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
sqrtscalea = 0;
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(j=j1; j<=j2; j++)
{
sqrtscalea = Math.Max(sqrtscalea, Math.Abs(cha[i,j]));
}
}
if( (double)(sqrtscalea)==(double)(0) )
{
sqrtscalea = 1;
}
sqrtscalea = 1/sqrtscalea;
spdmatrixcholeskysolveinternal(cha, sqrtscalea, n, isupper, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void spdmatrixcholeskysolve(double[,] cha,
int n,
bool isupper,
double[] b,
ref int info,
densesolverreport rep,
ref double[] x)
{
double[,] bm = new double[0,0];
double[,] xm = new double[0,0];
int i_ = 0;
info = 0;
x = new double[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new double[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
spdmatrixcholeskysolvem(cha, n, isupper, bm, 1, ref info, rep, ref xm);
x = new double[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixsolvem(complex[,] a,
int n,
bool isupper,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
complex[,] da = new complex[0,0];
double sqrtscalea = 0;
int i = 0;
int j = 0;
int j1 = 0;
int j2 = 0;
int i_ = 0;
info = 0;
x = new complex[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
da = new complex[n, n];
//
// 1. scale matrix, max(|A[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
sqrtscalea = 0;
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(j=j1; j<=j2; j++)
{
sqrtscalea = Math.Max(sqrtscalea, math.abscomplex(a[i,j]));
}
}
if( (double)(sqrtscalea)==(double)(0) )
{
sqrtscalea = 1;
}
sqrtscalea = 1/sqrtscalea;
sqrtscalea = Math.Sqrt(sqrtscalea);
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(i_=j1; i_<=j2;i_++)
{
da[i,i_] = a[i,i_];
}
}
if( !trfac.hpdmatrixcholesky(ref da, n, isupper) )
{
x = new complex[n, m];
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
hpdmatrixcholeskysolveinternal(da, sqrtscalea, n, isupper, a, true, b, m, ref info, rep, ref 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
*************************************************************************/
public static void hpdmatrixsolve(complex[,] a,
int n,
bool isupper,
complex[] b,
ref int info,
densesolverreport rep,
ref complex[] x)
{
complex[,] bm = new complex[0,0];
complex[,] xm = new complex[0,0];
int i_ = 0;
info = 0;
x = new complex[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new complex[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
hpdmatrixsolvem(a, n, isupper, bm, 1, ref info, rep, ref xm);
x = new complex[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void hpdmatrixcholeskysolvem(complex[,] cha,
int n,
bool isupper,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
complex[,] emptya = new complex[0,0];
double sqrtscalea = 0;
int i = 0;
int j = 0;
int j1 = 0;
int j2 = 0;
info = 0;
x = new complex[0,0];
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
//
// 1. scale matrix, max(|U[i,j]|)
// 2. factorize scaled matrix
// 3. solve
//
sqrtscalea = 0;
for(i=0; i<=n-1; i++)
{
if( isupper )
{
j1 = i;
j2 = n-1;
}
else
{
j1 = 0;
j2 = i;
}
for(j=j1; j<=j2; j++)
{
sqrtscalea = Math.Max(sqrtscalea, math.abscomplex(cha[i,j]));
}
}
if( (double)(sqrtscalea)==(double)(0) )
{
sqrtscalea = 1;
}
sqrtscalea = 1/sqrtscalea;
hpdmatrixcholeskysolveinternal(cha, sqrtscalea, n, isupper, emptya, false, b, m, ref info, rep, ref 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
*************************************************************************/
public static void hpdmatrixcholeskysolve(complex[,] cha,
int n,
bool isupper,
complex[] b,
ref int info,
densesolverreport rep,
ref complex[] x)
{
complex[,] bm = new complex[0,0];
complex[,] xm = new complex[0,0];
int i_ = 0;
info = 0;
x = new complex[0];
if( n<=0 )
{
info = -1;
return;
}
bm = new complex[n, 1];
for(i_=0; i_<=n-1;i_++)
{
bm[i_,0] = b[i_];
}
hpdmatrixcholeskysolvem(cha, n, isupper, bm, 1, ref info, rep, ref xm);
x = new complex[n];
for(i_=0; i_<=n-1;i_++)
{
x[i_] = xm[i_,0];
}
}
/*************************************************************************
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
*************************************************************************/
public static void rmatrixsolvels(double[,] a,
int nrows,
int ncols,
double[] b,
double threshold,
ref int info,
densesolverlsreport rep,
ref double[] x)
{
double[] sv = new double[0];
double[,] u = new double[0,0];
double[,] vt = new double[0,0];
double[] rp = new double[0];
double[] utb = new double[0];
double[] sutb = new double[0];
double[] tmp = new double[0];
double[] ta = new double[0];
double[] tx = new double[0];
double[] buf = new double[0];
double[] w = new double[0];
int i = 0;
int j = 0;
int nsv = 0;
int kernelidx = 0;
double v = 0;
double verr = 0;
bool svdfailed = new bool();
bool zeroa = new bool();
int rfs = 0;
int nrfs = 0;
bool terminatenexttime = new bool();
bool smallerr = new bool();
int i_ = 0;
info = 0;
x = new double[0];
if( (nrows<=0 || ncols<=0) || (double)(threshold)<(double)(0) )
{
info = -1;
return;
}
if( (double)(threshold)==(double)(0) )
{
threshold = 1000*math.machineepsilon;
}
//
// Factorize A first
//
svdfailed = !svd.rmatrixsvd(a, nrows, ncols, 1, 2, 2, ref sv, ref u, ref vt);
zeroa = (double)(sv[0])==(double)(0);
if( svdfailed || zeroa )
{
if( svdfailed )
{
info = -4;
}
else
{
info = 1;
}
x = new double[ncols];
for(i=0; i<=ncols-1; i++)
{
x[i] = 0;
}
rep.n = ncols;
rep.k = ncols;
rep.cx = new double[ncols, ncols];
for(i=0; i<=ncols-1; i++)
{
for(j=0; j<=ncols-1; j++)
{
if( i==j )
{
rep.cx[i,j] = 1;
}
else
{
rep.cx[i,j] = 0;
}
}
}
rep.r2 = 0;
return;
}
nsv = Math.Min(ncols, nrows);
if( nsv==ncols )
{
rep.r2 = sv[nsv-1]/sv[0];
}
else
{
rep.r2 = 0;
}
rep.n = ncols;
info = 1;
//
// Iterative refinement of xc combined with solution:
// 1. xc = 0
// 2. calculate r = bc-A*xc using extra-precise dot product
// 3. solve A*y = r
// 4. update x:=x+r
// 5. goto 2
//
// This cycle is executed until one of two things happens:
// 1. maximum number of iterations reached
// 2. last iteration decreased error to the lower limit
//
utb = new double[nsv];
sutb = new double[nsv];
x = new double[ncols];
tmp = new double[ncols];
ta = new double[ncols+1];
tx = new double[ncols+1];
buf = new double[ncols+1];
for(i=0; i<=ncols-1; i++)
{
x[i] = 0;
}
kernelidx = nsv;
for(i=0; i<=nsv-1; i++)
{
if( (double)(sv[i])<=(double)(threshold*sv[0]) )
{
kernelidx = i;
break;
}
}
rep.k = ncols-kernelidx;
nrfs = densesolverrfsmaxv2(ncols, rep.r2);
terminatenexttime = false;
rp = new double[nrows];
for(rfs=0; rfs<=nrfs; rfs++)
{
if( terminatenexttime )
{
break;
}
//
// calculate right part
//
if( rfs==0 )
{
for(i_=0; i_<=nrows-1;i_++)
{
rp[i_] = b[i_];
}
}
else
{
smallerr = true;
for(i=0; i<=nrows-1; i++)
{
for(i_=0; i_<=ncols-1;i_++)
{
ta[i_] = a[i,i_];
}
ta[ncols] = -1;
for(i_=0; i_<=ncols-1;i_++)
{
tx[i_] = x[i_];
}
tx[ncols] = b[i];
xblas.xdot(ta, tx, ncols+1, ref buf, ref v, ref verr);
rp[i] = -v;
smallerr = smallerr && (double)(Math.Abs(v))<(double)(4*verr);
}
if( smallerr )
{
terminatenexttime = true;
}
}
//
// solve A*dx = rp
//
for(i=0; i<=ncols-1; i++)
{
tmp[i] = 0;
}
for(i=0; i<=nsv-1; i++)
{
utb[i] = 0;
}
for(i=0; i<=nrows-1; i++)
{
v = rp[i];
for(i_=0; i_<=nsv-1;i_++)
{
utb[i_] = utb[i_] + v*u[i,i_];
}
}
for(i=0; i<=nsv-1; i++)
{
if( i<kernelidx )
{
sutb[i] = utb[i]/sv[i];
}
else
{
sutb[i] = 0;
}
}
for(i=0; i<=nsv-1; i++)
{
v = sutb[i];
for(i_=0; i_<=ncols-1;i_++)
{
tmp[i_] = tmp[i_] + v*vt[i,i_];
}
}
//
// update x: x:=x+dx
//
for(i_=0; i_<=ncols-1;i_++)
{
x[i_] = x[i_] + tmp[i_];
}
}
//
// fill CX
//
if( rep.k>0 )
{
rep.cx = new double[ncols, rep.k];
for(i=0; i<=rep.k-1; i++)
{
for(i_=0; i_<=ncols-1;i_++)
{
rep.cx[i_,i] = vt[kernelidx+i,i_];
}
}
}
}
/*************************************************************************
Internal LU solver
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void rmatrixlusolveinternal(double[,] lua,
int[] p,
double scalea,
int n,
double[,] a,
bool havea,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
int i = 0;
int j = 0;
int k = 0;
int rfs = 0;
int nrfs = 0;
double[] xc = new double[0];
double[] y = new double[0];
double[] bc = new double[0];
double[] xa = new double[0];
double[] xb = new double[0];
double[] tx = new double[0];
double v = 0;
double verr = 0;
double mxb = 0;
double scaleright = 0;
bool smallerr = new bool();
bool terminatenexttime = new bool();
int i_ = 0;
info = 0;
x = new double[0,0];
alglib.ap.assert((double)(scalea)>(double)(0));
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
for(i=0; i<=n-1; i++)
{
if( p[i]>n-1 || p[i]<i )
{
info = -1;
return;
}
}
x = new double[n, m];
y = new double[n];
xc = new double[n];
bc = new double[n];
tx = new double[n+1];
xa = new double[n+1];
xb = new double[n+1];
//
// estimate condition number, test for near singularity
//
rep.r1 = rcond.rmatrixlurcond1(lua, n);
rep.rinf = rcond.rmatrixlurcondinf(lua, n);
if( (double)(rep.r1)<(double)(rcond.rcondthreshold()) || (double)(rep.rinf)<(double)(rcond.rcondthreshold()) )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
//
// solve
//
for(k=0; k<=m-1; k++)
{
//
// copy B to contiguous storage
//
for(i_=0; i_<=n-1;i_++)
{
bc[i_] = b[i_,k];
}
//
// Scale right part:
// * MX stores max(|Bi|)
// * ScaleRight stores actual scaling applied to B when solving systems
// it is chosen to make |scaleRight*b| close to 1.
//
mxb = 0;
for(i=0; i<=n-1; i++)
{
mxb = Math.Max(mxb, Math.Abs(bc[i]));
}
if( (double)(mxb)==(double)(0) )
{
mxb = 1;
}
scaleright = 1/mxb;
//
// First, non-iterative part of solution process.
// We use separate code for this task because
// XDot is quite slow and we want to save time.
//
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = scaleright*bc[i_];
}
rbasiclusolve(lua, p, scalea, n, ref xc, ref tx);
//
// Iterative refinement of xc:
// * calculate r = bc-A*xc using extra-precise dot product
// * solve A*y = r
// * update x:=x+r
//
// This cycle is executed until one of two things happens:
// 1. maximum number of iterations reached
// 2. last iteration decreased error to the lower limit
//
if( havea )
{
nrfs = densesolverrfsmax(n, rep.r1, rep.rinf);
terminatenexttime = false;
for(rfs=0; rfs<=nrfs-1; rfs++)
{
if( terminatenexttime )
{
break;
}
//
// generate right part
//
smallerr = true;
for(i_=0; i_<=n-1;i_++)
{
xb[i_] = xc[i_];
}
for(i=0; i<=n-1; i++)
{
for(i_=0; i_<=n-1;i_++)
{
xa[i_] = scalea*a[i,i_];
}
xa[n] = -1;
xb[n] = scaleright*bc[i];
xblas.xdot(xa, xb, n+1, ref tx, ref v, ref verr);
y[i] = -v;
smallerr = smallerr && (double)(Math.Abs(v))<(double)(4*verr);
}
if( smallerr )
{
terminatenexttime = true;
}
//
// solve and update
//
rbasiclusolve(lua, p, scalea, n, ref y, ref tx);
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = xc[i_] + y[i_];
}
}
}
//
// Store xc.
// Post-scale result.
//
v = scalea*mxb;
for(i_=0; i_<=n-1;i_++)
{
x[i_,k] = v*xc[i_];
}
}
}
/*************************************************************************
Internal Cholesky solver
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void spdmatrixcholeskysolveinternal(double[,] cha,
double sqrtscalea,
int n,
bool isupper,
double[,] a,
bool havea,
double[,] b,
int m,
ref int info,
densesolverreport rep,
ref double[,] x)
{
int i = 0;
int j = 0;
int k = 0;
double[] xc = new double[0];
double[] y = new double[0];
double[] bc = new double[0];
double[] xa = new double[0];
double[] xb = new double[0];
double[] tx = new double[0];
double v = 0;
double mxb = 0;
double scaleright = 0;
int i_ = 0;
info = 0;
x = new double[0,0];
alglib.ap.assert((double)(sqrtscalea)>(double)(0));
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
x = new double[n, m];
y = new double[n];
xc = new double[n];
bc = new double[n];
tx = new double[n+1];
xa = new double[n+1];
xb = new double[n+1];
//
// estimate condition number, test for near singularity
//
rep.r1 = rcond.spdmatrixcholeskyrcond(cha, n, isupper);
rep.rinf = rep.r1;
if( (double)(rep.r1)<(double)(rcond.rcondthreshold()) )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
//
// solve
//
for(k=0; k<=m-1; k++)
{
//
// copy B to contiguous storage
//
for(i_=0; i_<=n-1;i_++)
{
bc[i_] = b[i_,k];
}
//
// Scale right part:
// * MX stores max(|Bi|)
// * ScaleRight stores actual scaling applied to B when solving systems
// it is chosen to make |scaleRight*b| close to 1.
//
mxb = 0;
for(i=0; i<=n-1; i++)
{
mxb = Math.Max(mxb, Math.Abs(bc[i]));
}
if( (double)(mxb)==(double)(0) )
{
mxb = 1;
}
scaleright = 1/mxb;
//
// First, non-iterative part of solution process.
// We use separate code for this task because
// XDot is quite slow and we want to save time.
//
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = scaleright*bc[i_];
}
spdbasiccholeskysolve(cha, sqrtscalea, n, isupper, ref xc, ref tx);
//
// Store xc.
// Post-scale result.
//
v = math.sqr(sqrtscalea)*mxb;
for(i_=0; i_<=n-1;i_++)
{
x[i_,k] = v*xc[i_];
}
}
}
/*************************************************************************
Internal LU solver
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void cmatrixlusolveinternal(complex[,] lua,
int[] p,
double scalea,
int n,
complex[,] a,
bool havea,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
int i = 0;
int j = 0;
int k = 0;
int rfs = 0;
int nrfs = 0;
complex[] xc = new complex[0];
complex[] y = new complex[0];
complex[] bc = new complex[0];
complex[] xa = new complex[0];
complex[] xb = new complex[0];
complex[] tx = new complex[0];
double[] tmpbuf = new double[0];
complex v = 0;
double verr = 0;
double mxb = 0;
double scaleright = 0;
bool smallerr = new bool();
bool terminatenexttime = new bool();
int i_ = 0;
info = 0;
x = new complex[0,0];
alglib.ap.assert((double)(scalea)>(double)(0));
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
for(i=0; i<=n-1; i++)
{
if( p[i]>n-1 || p[i]<i )
{
info = -1;
return;
}
}
x = new complex[n, m];
y = new complex[n];
xc = new complex[n];
bc = new complex[n];
tx = new complex[n];
xa = new complex[n+1];
xb = new complex[n+1];
tmpbuf = new double[2*n+2];
//
// estimate condition number, test for near singularity
//
rep.r1 = rcond.cmatrixlurcond1(lua, n);
rep.rinf = rcond.cmatrixlurcondinf(lua, n);
if( (double)(rep.r1)<(double)(rcond.rcondthreshold()) || (double)(rep.rinf)<(double)(rcond.rcondthreshold()) )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
//
// solve
//
for(k=0; k<=m-1; k++)
{
//
// copy B to contiguous storage
//
for(i_=0; i_<=n-1;i_++)
{
bc[i_] = b[i_,k];
}
//
// Scale right part:
// * MX stores max(|Bi|)
// * ScaleRight stores actual scaling applied to B when solving systems
// it is chosen to make |scaleRight*b| close to 1.
//
mxb = 0;
for(i=0; i<=n-1; i++)
{
mxb = Math.Max(mxb, math.abscomplex(bc[i]));
}
if( (double)(mxb)==(double)(0) )
{
mxb = 1;
}
scaleright = 1/mxb;
//
// First, non-iterative part of solution process.
// We use separate code for this task because
// XDot is quite slow and we want to save time.
//
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = scaleright*bc[i_];
}
cbasiclusolve(lua, p, scalea, n, ref xc, ref tx);
//
// Iterative refinement of xc:
// * calculate r = bc-A*xc using extra-precise dot product
// * solve A*y = r
// * update x:=x+r
//
// This cycle is executed until one of two things happens:
// 1. maximum number of iterations reached
// 2. last iteration decreased error to the lower limit
//
if( havea )
{
nrfs = densesolverrfsmax(n, rep.r1, rep.rinf);
terminatenexttime = false;
for(rfs=0; rfs<=nrfs-1; rfs++)
{
if( terminatenexttime )
{
break;
}
//
// generate right part
//
smallerr = true;
for(i_=0; i_<=n-1;i_++)
{
xb[i_] = xc[i_];
}
for(i=0; i<=n-1; i++)
{
for(i_=0; i_<=n-1;i_++)
{
xa[i_] = scalea*a[i,i_];
}
xa[n] = -1;
xb[n] = scaleright*bc[i];
xblas.xcdot(xa, xb, n+1, ref tmpbuf, ref v, ref verr);
y[i] = -v;
smallerr = smallerr && (double)(math.abscomplex(v))<(double)(4*verr);
}
if( smallerr )
{
terminatenexttime = true;
}
//
// solve and update
//
cbasiclusolve(lua, p, scalea, n, ref y, ref tx);
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = xc[i_] + y[i_];
}
}
}
//
// Store xc.
// Post-scale result.
//
v = scalea*mxb;
for(i_=0; i_<=n-1;i_++)
{
x[i_,k] = v*xc[i_];
}
}
}
/*************************************************************************
Internal Cholesky solver
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void hpdmatrixcholeskysolveinternal(complex[,] cha,
double sqrtscalea,
int n,
bool isupper,
complex[,] a,
bool havea,
complex[,] b,
int m,
ref int info,
densesolverreport rep,
ref complex[,] x)
{
int i = 0;
int j = 0;
int k = 0;
complex[] xc = new complex[0];
complex[] y = new complex[0];
complex[] bc = new complex[0];
complex[] xa = new complex[0];
complex[] xb = new complex[0];
complex[] tx = new complex[0];
double v = 0;
double mxb = 0;
double scaleright = 0;
int i_ = 0;
info = 0;
x = new complex[0,0];
alglib.ap.assert((double)(sqrtscalea)>(double)(0));
//
// prepare: check inputs, allocate space...
//
if( n<=0 || m<=0 )
{
info = -1;
return;
}
x = new complex[n, m];
y = new complex[n];
xc = new complex[n];
bc = new complex[n];
tx = new complex[n+1];
xa = new complex[n+1];
xb = new complex[n+1];
//
// estimate condition number, test for near singularity
//
rep.r1 = rcond.hpdmatrixcholeskyrcond(cha, n, isupper);
rep.rinf = rep.r1;
if( (double)(rep.r1)<(double)(rcond.rcondthreshold()) )
{
for(i=0; i<=n-1; i++)
{
for(j=0; j<=m-1; j++)
{
x[i,j] = 0;
}
}
rep.r1 = 0;
rep.rinf = 0;
info = -3;
return;
}
info = 1;
//
// solve
//
for(k=0; k<=m-1; k++)
{
//
// copy B to contiguous storage
//
for(i_=0; i_<=n-1;i_++)
{
bc[i_] = b[i_,k];
}
//
// Scale right part:
// * MX stores max(|Bi|)
// * ScaleRight stores actual scaling applied to B when solving systems
// it is chosen to make |scaleRight*b| close to 1.
//
mxb = 0;
for(i=0; i<=n-1; i++)
{
mxb = Math.Max(mxb, math.abscomplex(bc[i]));
}
if( (double)(mxb)==(double)(0) )
{
mxb = 1;
}
scaleright = 1/mxb;
//
// First, non-iterative part of solution process.
// We use separate code for this task because
// XDot is quite slow and we want to save time.
//
for(i_=0; i_<=n-1;i_++)
{
xc[i_] = scaleright*bc[i_];
}
hpdbasiccholeskysolve(cha, sqrtscalea, n, isupper, ref xc, ref tx);
//
// Store xc.
// Post-scale result.
//
v = math.sqr(sqrtscalea)*mxb;
for(i_=0; i_<=n-1;i_++)
{
x[i_,k] = v*xc[i_];
}
}
}
/*************************************************************************
Internal subroutine.
Returns maximum count of RFS iterations as function of:
1. machine epsilon
2. task size.
3. condition number
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static int densesolverrfsmax(int n,
double r1,
double rinf)
{
int result = 0;
result = 5;
return result;
}
/*************************************************************************
Internal subroutine.
Returns maximum count of RFS iterations as function of:
1. machine epsilon
2. task size.
3. norm-2 condition number
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static int densesolverrfsmaxv2(int n,
double r2)
{
int result = 0;
result = densesolverrfsmax(n, 0, 0);
return result;
}
/*************************************************************************
Basic LU solver for ScaleA*PLU*x = y.
This subroutine assumes that:
* L is well-scaled, and it is U which needs scaling by ScaleA.
* A=PLU is well-conditioned, so no zero divisions or overflow may occur
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void rbasiclusolve(double[,] lua,
int[] p,
double scalea,
int n,
ref double[] xb,
ref double[] tmp)
{
int i = 0;
double v = 0;
int i_ = 0;
for(i=0; i<=n-1; i++)
{
if( p[i]!=i )
{
v = xb[i];
xb[i] = xb[p[i]];
xb[p[i]] = v;
}
}
for(i=1; i<=n-1; i++)
{
v = 0.0;
for(i_=0; i_<=i-1;i_++)
{
v += lua[i,i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[n-1] = xb[n-1]/(scalea*lua[n-1,n-1]);
for(i=n-2; i>=0; i--)
{
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = scalea*lua[i,i_];
}
v = 0.0;
for(i_=i+1; i_<=n-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = (xb[i]-v)/(scalea*lua[i,i]);
}
}
/*************************************************************************
Basic Cholesky solver for ScaleA*Cholesky(A)'*x = y.
This subroutine assumes that:
* A*ScaleA is well scaled
* A is well-conditioned, so no zero divisions or overflow may occur
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void spdbasiccholeskysolve(double[,] cha,
double sqrtscalea,
int n,
bool isupper,
ref double[] xb,
ref double[] tmp)
{
int i = 0;
double v = 0;
int i_ = 0;
//
// A = L*L' or A=U'*U
//
if( isupper )
{
//
// Solve U'*y=b first.
//
for(i=0; i<=n-1; i++)
{
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
if( i<n-1 )
{
v = xb[i];
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
for(i_=i+1; i_<=n-1;i_++)
{
xb[i_] = xb[i_] - v*tmp[i_];
}
}
}
//
// Solve U*x=y then.
//
for(i=n-1; i>=0; i--)
{
if( i<n-1 )
{
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
v = 0.0;
for(i_=i+1; i_<=n-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
}
}
else
{
//
// Solve L*y=b first
//
for(i=0; i<=n-1; i++)
{
if( i>0 )
{
for(i_=0; i_<=i-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
v = 0.0;
for(i_=0; i_<=i-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
}
//
// Solve L'*x=y then.
//
for(i=n-1; i>=0; i--)
{
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
if( i>0 )
{
v = xb[i];
for(i_=0; i_<=i-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
for(i_=0; i_<=i-1;i_++)
{
xb[i_] = xb[i_] - v*tmp[i_];
}
}
}
}
}
/*************************************************************************
Basic LU solver for ScaleA*PLU*x = y.
This subroutine assumes that:
* L is well-scaled, and it is U which needs scaling by ScaleA.
* A=PLU is well-conditioned, so no zero divisions or overflow may occur
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void cbasiclusolve(complex[,] lua,
int[] p,
double scalea,
int n,
ref complex[] xb,
ref complex[] tmp)
{
int i = 0;
complex v = 0;
int i_ = 0;
for(i=0; i<=n-1; i++)
{
if( p[i]!=i )
{
v = xb[i];
xb[i] = xb[p[i]];
xb[p[i]] = v;
}
}
for(i=1; i<=n-1; i++)
{
v = 0.0;
for(i_=0; i_<=i-1;i_++)
{
v += lua[i,i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[n-1] = xb[n-1]/(scalea*lua[n-1,n-1]);
for(i=n-2; i>=0; i--)
{
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = scalea*lua[i,i_];
}
v = 0.0;
for(i_=i+1; i_<=n-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = (xb[i]-v)/(scalea*lua[i,i]);
}
}
/*************************************************************************
Basic Cholesky solver for ScaleA*Cholesky(A)'*x = y.
This subroutine assumes that:
* A*ScaleA is well scaled
* A is well-conditioned, so no zero divisions or overflow may occur
-- ALGLIB --
Copyright 27.01.2010 by Bochkanov Sergey
*************************************************************************/
private static void hpdbasiccholeskysolve(complex[,] cha,
double sqrtscalea,
int n,
bool isupper,
ref complex[] xb,
ref complex[] tmp)
{
int i = 0;
complex v = 0;
int i_ = 0;
//
// A = L*L' or A=U'*U
//
if( isupper )
{
//
// Solve U'*y=b first.
//
for(i=0; i<=n-1; i++)
{
xb[i] = xb[i]/(sqrtscalea*math.conj(cha[i,i]));
if( i<n-1 )
{
v = xb[i];
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = sqrtscalea*math.conj(cha[i,i_]);
}
for(i_=i+1; i_<=n-1;i_++)
{
xb[i_] = xb[i_] - v*tmp[i_];
}
}
}
//
// Solve U*x=y then.
//
for(i=n-1; i>=0; i--)
{
if( i<n-1 )
{
for(i_=i+1; i_<=n-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
v = 0.0;
for(i_=i+1; i_<=n-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
}
}
else
{
//
// Solve L*y=b first
//
for(i=0; i<=n-1; i++)
{
if( i>0 )
{
for(i_=0; i_<=i-1;i_++)
{
tmp[i_] = sqrtscalea*cha[i,i_];
}
v = 0.0;
for(i_=0; i_<=i-1;i_++)
{
v += tmp[i_]*xb[i_];
}
xb[i] = xb[i]-v;
}
xb[i] = xb[i]/(sqrtscalea*cha[i,i]);
}
//
// Solve L'*x=y then.
//
for(i=n-1; i>=0; i--)
{
xb[i] = xb[i]/(sqrtscalea*math.conj(cha[i,i]));
if( i>0 )
{
v = xb[i];
for(i_=0; i_<=i-1;i_++)
{
tmp[i_] = sqrtscalea*math.conj(cha[i,i_]);
}
for(i_=0; i_<=i-1;i_++)
{
xb[i_] = xb[i_] - v*tmp[i_];
}
}
}
}
}
}
public class linlsqr
{
/*************************************************************************
This object stores state of the LinLSQR method.
You should use ALGLIB functions to work with this object.
*************************************************************************/
public class linlsqrstate : apobject
{
public normestimator.normestimatorstate nes;
public double[] rx;
public double[] b;
public int n;
public int m;
public int prectype;
public double[] ui;
public double[] uip1;
public double[] vi;
public double[] vip1;
public double[] omegai;
public double[] omegaip1;
public double alphai;
public double alphaip1;
public double betai;
public double betaip1;
public double phibari;
public double phibarip1;
public double phii;
public double rhobari;
public double rhobarip1;
public double rhoi;
public double ci;
public double si;
public double theta;
public double lambdai;
public double[] d;
public double anorm;
public double bnorm2;
public double dnorm;
public double r2;
public double[] x;
public double[] mv;
public double[] mtv;
public double epsa;
public double epsb;
public double epsc;
public int maxits;
public bool xrep;
public bool xupdated;
public bool needmv;
public bool needmtv;
public bool needmv2;
public bool needvmv;
public bool needprec;
public int repiterationscount;
public int repnmv;
public int repterminationtype;
public bool running;
public double[] tmpd;
public double[] tmpx;
public rcommstate rstate;
public linlsqrstate()
{
init();
}
public override void init()
{
nes = new normestimator.normestimatorstate();
rx = new double[0];
b = new double[0];
ui = new double[0];
uip1 = new double[0];
vi = new double[0];
vip1 = new double[0];
omegai = new double[0];
omegaip1 = new double[0];
d = new double[0];
x = new double[0];
mv = new double[0];
mtv = new double[0];
tmpd = new double[0];
tmpx = new double[0];
rstate = new rcommstate();
}
public override alglib.apobject make_copy()
{
linlsqrstate _result = new linlsqrstate();
_result.nes = (normestimator.normestimatorstate)nes.make_copy();
_result.rx = (double[])rx.Clone();
_result.b = (double[])b.Clone();
_result.n = n;
_result.m = m;
_result.prectype = prectype;
_result.ui = (double[])ui.Clone();
_result.uip1 = (double[])uip1.Clone();
_result.vi = (double[])vi.Clone();
_result.vip1 = (double[])vip1.Clone();
_result.omegai = (double[])omegai.Clone();
_result.omegaip1 = (double[])omegaip1.Clone();
_result.alphai = alphai;
_result.alphaip1 = alphaip1;
_result.betai = betai;
_result.betaip1 = betaip1;
_result.phibari = phibari;
_result.phibarip1 = phibarip1;
_result.phii = phii;
_result.rhobari = rhobari;
_result.rhobarip1 = rhobarip1;
_result.rhoi = rhoi;
_result.ci = ci;
_result.si = si;
_result.theta = theta;
_result.lambdai = lambdai;
_result.d = (double[])d.Clone();
_result.anorm = anorm;
_result.bnorm2 = bnorm2;
_result.dnorm = dnorm;
_result.r2 = r2;
_result.x = (double[])x.Clone();
_result.mv = (double[])mv.Clone();
_result.mtv = (double[])mtv.Clone();
_result.epsa = epsa;
_result.epsb = epsb;
_result.epsc = epsc;
_result.maxits = maxits;
_result.xrep = xrep;
_result.xupdated = xupdated;
_result.needmv = needmv;
_result.needmtv = needmtv;
_result.needmv2 = needmv2;
_result.needvmv = needvmv;
_result.needprec = needprec;
_result.repiterationscount = repiterationscount;
_result.repnmv = repnmv;
_result.repterminationtype = repterminationtype;
_result.running = running;
_result.tmpd = (double[])tmpd.Clone();
_result.tmpx = (double[])tmpx.Clone();
_result.rstate = (rcommstate)rstate.make_copy();
return _result;
}
};
public class linlsqrreport : apobject
{
public int iterationscount;
public int nmv;
public int terminationtype;
public linlsqrreport()
{
init();
}
public override void init()
{
}
public override alglib.apobject make_copy()
{
linlsqrreport _result = new linlsqrreport();
_result.iterationscount = iterationscount;
_result.nmv = nmv;
_result.terminationtype = terminationtype;
return _result;
}
};
public const double atol = 1.0E-6;
public const double btol = 1.0E-6;
/*************************************************************************
This function initializes linear LSQR Solver. This solver is used to solve
non-symmetric (and, possibly, non-square) problems. Least squares solution
is returned for non-compatible systems.
USAGE:
1. User initializes algorithm state with LinLSQRCreate() call
2. User tunes solver parameters with LinLSQRSetCond() and other functions
3. User calls LinLSQRSolveSparse() function which takes algorithm state
and SparseMatrix object.
4. User calls LinLSQRResults() to get solution
5. Optionally, user may call LinLSQRSolveSparse() again to solve another
problem with different matrix and/or right part without reinitializing
LinLSQRState structure.
INPUT PARAMETERS:
M - number of rows in A
N - number of variables, N>0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrcreate(int m,
int n,
linlsqrstate state)
{
int i = 0;
alglib.ap.assert(m>0, "LinLSQRCreate: M<=0");
alglib.ap.assert(n>0, "LinLSQRCreate: N<=0");
state.m = m;
state.n = n;
state.prectype = 0;
state.epsa = atol;
state.epsb = btol;
state.epsc = 1/Math.Sqrt(math.machineepsilon);
state.maxits = 0;
state.lambdai = 0;
state.xrep = false;
state.running = false;
//
// * allocate arrays
// * set RX to NAN (just for the case user calls Results() without
// calling SolveSparse()
// * set B to zero
//
normestimator.normestimatorcreate(m, n, 2, 2, state.nes);
state.rx = new double[state.n];
state.ui = new double[state.m+state.n];
state.uip1 = new double[state.m+state.n];
state.vip1 = new double[state.n];
state.vi = new double[state.n];
state.omegai = new double[state.n];
state.omegaip1 = new double[state.n];
state.d = new double[state.n];
state.x = new double[state.m+state.n];
state.mv = new double[state.m+state.n];
state.mtv = new double[state.n];
state.b = new double[state.m];
for(i=0; i<=n-1; i++)
{
state.rx[i] = Double.NaN;
}
for(i=0; i<=m-1; i++)
{
state.b[i] = 0;
}
state.rstate.ia = new int[1+1];
state.rstate.ra = new double[0+1];
state.rstate.stage = -1;
}
/*************************************************************************
This function sets right part. By default, right part is zero.
INPUT PARAMETERS:
B - right part, array[N].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetb(linlsqrstate state,
double[] b)
{
int i = 0;
alglib.ap.assert(!state.running, "LinLSQRSetB: you can not change B when LinLSQRIteration is running");
alglib.ap.assert(state.m<=alglib.ap.len(b), "LinLSQRSetB: Length(B)<M");
alglib.ap.assert(apserv.isfinitevector(b, state.m), "LinLSQRSetB: B contains infinite or NaN values");
state.bnorm2 = 0;
for(i=0; i<=state.m-1; i++)
{
state.b[i] = b[i];
state.bnorm2 = state.bnorm2+b[i]*b[i];
}
}
/*************************************************************************
This function changes preconditioning settings of LinLSQQSolveSparse()
function. By default, SolveSparse() uses diagonal preconditioner, but if
you want to use solver without preconditioning, you can call this function
which forces solver to use unit matrix for preconditioning.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetprecunit(linlsqrstate state)
{
alglib.ap.assert(!state.running, "LinLSQRSetPrecUnit: you can not change preconditioner, because function LinLSQRIteration is running!");
state.prectype = -1;
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. LinCGSolveSparse() will use diagonal of the system matrix as
preconditioner. This preconditioning mode is active by default.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetprecdiag(linlsqrstate state)
{
alglib.ap.assert(!state.running, "LinLSQRSetPrecDiag: you can not change preconditioner, because function LinCGIteration is running!");
state.prectype = 0;
}
/*************************************************************************
This function sets optional Tikhonov regularization coefficient.
It is zero by default.
INPUT PARAMETERS:
LambdaI - regularization factor, LambdaI>=0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetlambdai(linlsqrstate state,
double lambdai)
{
alglib.ap.assert(!state.running, "LinLSQRSetLambdaI: you can not set LambdaI, because function LinLSQRIteration is running");
alglib.ap.assert(math.isfinite(lambdai) && (double)(lambdai)>=(double)(0), "LinLSQRSetLambdaI: LambdaI is infinite or NaN");
state.lambdai = lambdai;
}
/*************************************************************************
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static bool linlsqriteration(linlsqrstate state)
{
bool result = new bool();
int summn = 0;
double bnorm = 0;
int i = 0;
int i_ = 0;
//
// Reverse communication preparations
// I know it looks ugly, but it works the same way
// anywhere from C++ to Python.
//
// This code initializes locals by:
// * random values determined during code
// generation - on first subroutine call
// * values from previous call - on subsequent calls
//
if( state.rstate.stage>=0 )
{
summn = state.rstate.ia[0];
i = state.rstate.ia[1];
bnorm = state.rstate.ra[0];
}
else
{
summn = -983;
i = -989;
bnorm = -834;
}
if( state.rstate.stage==0 )
{
goto lbl_0;
}
if( state.rstate.stage==1 )
{
goto lbl_1;
}
if( state.rstate.stage==2 )
{
goto lbl_2;
}
if( state.rstate.stage==3 )
{
goto lbl_3;
}
if( state.rstate.stage==4 )
{
goto lbl_4;
}
if( state.rstate.stage==5 )
{
goto lbl_5;
}
if( state.rstate.stage==6 )
{
goto lbl_6;
}
//
// Routine body
//
alglib.ap.assert(alglib.ap.len(state.b)>0, "LinLSQRIteration: using non-allocated array B");
bnorm = Math.Sqrt(state.bnorm2);
state.running = true;
state.repnmv = 0;
clearrfields(state);
state.repiterationscount = 0;
summn = state.m+state.n;
state.r2 = state.bnorm2;
//
//estimate for ANorm
//
normestimator.normestimatorrestart(state.nes);
lbl_7:
if( !normestimator.normestimatoriteration(state.nes) )
{
goto lbl_8;
}
if( !state.nes.needmv )
{
goto lbl_9;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.nes.x[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmv = true;
state.rstate.stage = 0;
goto lbl_rcomm;
lbl_0:
state.needmv = false;
for(i_=0; i_<=state.m-1;i_++)
{
state.nes.mv[i_] = state.mv[i_];
}
goto lbl_7;
lbl_9:
if( !state.nes.needmtv )
{
goto lbl_11;
}
for(i_=0; i_<=state.m-1;i_++)
{
state.x[i_] = state.nes.x[i_];
}
//
//matrix-vector multiplication
//
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmtv = true;
state.rstate.stage = 1;
goto lbl_rcomm;
lbl_1:
state.needmtv = false;
for(i_=0; i_<=state.n-1;i_++)
{
state.nes.mtv[i_] = state.mtv[i_];
}
goto lbl_7;
lbl_11:
goto lbl_7;
lbl_8:
normestimator.normestimatorresults(state.nes, ref state.anorm);
//
//initialize .RX by zeros
//
for(i=0; i<=state.n-1; i++)
{
state.rx[i] = 0;
}
//
//output first report
//
if( !state.xrep )
{
goto lbl_13;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
clearrfields(state);
state.xupdated = true;
state.rstate.stage = 2;
goto lbl_rcomm;
lbl_2:
state.xupdated = false;
lbl_13:
//
// LSQR, Step 0.
//
// Algorithm outline corresponds to one which was described at p.50 of
// "LSQR - an algorithm for sparse linear equations and sparse least
// squares" by C.Paige and M.Saunders with one small addition - we
// explicitly extend system matrix by additional N lines in order
// to handle non-zero lambda, i.e. original A is replaced by
// [ A ]
// A_mod = [ ]
// [ lambda*I ].
//
// Step 0:
// x[0] = 0
// beta[1]*u[1] = b
// alpha[1]*v[1] = A_mod'*u[1]
// w[1] = v[1]
// phiBar[1] = beta[1]
// rhoBar[1] = alpha[1]
// d[0] = 0
//
// NOTE:
// There are three criteria for stopping:
// (S0) maximum number of iterations
// (S1) ||Rk||<=EpsB*||B||;
// (S2) ||A^T*Rk||/(||A||*||Rk||)<=EpsA.
// It is very important that S2 always checked AFTER S1. It is necessary
// to avoid division by zero when Rk=0.
//
state.betai = bnorm;
if( (double)(state.betai)==(double)(0) )
{
//
// Zero right part
//
state.running = false;
state.repterminationtype = 1;
result = false;
return result;
}
for(i=0; i<=summn-1; i++)
{
if( i<state.m )
{
state.ui[i] = state.b[i]/state.betai;
}
else
{
state.ui[i] = 0;
}
state.x[i] = state.ui[i];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmtv = true;
state.rstate.stage = 3;
goto lbl_rcomm;
lbl_3:
state.needmtv = false;
for(i=0; i<=state.n-1; i++)
{
state.mtv[i] = state.mtv[i]+state.lambdai*state.ui[state.m+i];
}
state.alphai = 0;
for(i=0; i<=state.n-1; i++)
{
state.alphai = state.alphai+state.mtv[i]*state.mtv[i];
}
state.alphai = Math.Sqrt(state.alphai);
if( (double)(state.alphai)==(double)(0) )
{
//
// Orthogonality stopping criterion is met
//
state.running = false;
state.repterminationtype = 4;
result = false;
return result;
}
for(i=0; i<=state.n-1; i++)
{
state.vi[i] = state.mtv[i]/state.alphai;
state.omegai[i] = state.vi[i];
}
state.phibari = state.betai;
state.rhobari = state.alphai;
for(i=0; i<=state.n-1; i++)
{
state.d[i] = 0;
}
state.dnorm = 0;
//
// Steps I=1, 2, ...
//
lbl_15:
if( false )
{
goto lbl_16;
}
//
// At I-th step State.RepIterationsCount=I.
//
state.repiterationscount = state.repiterationscount+1;
//
// Bidiagonalization part:
// beta[i+1]*u[i+1] = A_mod*v[i]-alpha[i]*u[i]
// alpha[i+1]*v[i+1] = A_mod'*u[i+1] - beta[i+1]*v[i]
//
// NOTE: beta[i+1]=0 or alpha[i+1]=0 will lead to successful termination
// in the end of the current iteration. In this case u/v are zero.
// NOTE2: algorithm won't fail on zero alpha or beta (there will be no
// division by zero because it will be stopped BEFORE division
// occurs). However, near-zero alpha and beta won't stop algorithm
// and, although no division by zero will happen, orthogonality
// in U and V will be lost.
//
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.vi[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmv = true;
state.rstate.stage = 4;
goto lbl_rcomm;
lbl_4:
state.needmv = false;
for(i=0; i<=state.n-1; i++)
{
state.mv[state.m+i] = state.lambdai*state.vi[i];
}
state.betaip1 = 0;
for(i=0; i<=summn-1; i++)
{
state.uip1[i] = state.mv[i]-state.alphai*state.ui[i];
state.betaip1 = state.betaip1+state.uip1[i]*state.uip1[i];
}
if( (double)(state.betaip1)!=(double)(0) )
{
state.betaip1 = Math.Sqrt(state.betaip1);
for(i=0; i<=summn-1; i++)
{
state.uip1[i] = state.uip1[i]/state.betaip1;
}
}
for(i_=0; i_<=state.m-1;i_++)
{
state.x[i_] = state.uip1[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmtv = true;
state.rstate.stage = 5;
goto lbl_rcomm;
lbl_5:
state.needmtv = false;
for(i=0; i<=state.n-1; i++)
{
state.mtv[i] = state.mtv[i]+state.lambdai*state.uip1[state.m+i];
}
state.alphaip1 = 0;
for(i=0; i<=state.n-1; i++)
{
state.vip1[i] = state.mtv[i]-state.betaip1*state.vi[i];
state.alphaip1 = state.alphaip1+state.vip1[i]*state.vip1[i];
}
if( (double)(state.alphaip1)!=(double)(0) )
{
state.alphaip1 = Math.Sqrt(state.alphaip1);
for(i=0; i<=state.n-1; i++)
{
state.vip1[i] = state.vip1[i]/state.alphaip1;
}
}
//
// Build next orthogonal transformation
//
state.rhoi = apserv.safepythag2(state.rhobari, state.betaip1);
state.ci = state.rhobari/state.rhoi;
state.si = state.betaip1/state.rhoi;
state.theta = state.si*state.alphaip1;
state.rhobarip1 = -(state.ci*state.alphaip1);
state.phii = state.ci*state.phibari;
state.phibarip1 = state.si*state.phibari;
//
// Update .RNorm
//
// This tricky formula is necessary because simply writing
// State.R2:=State.PhiBarIP1*State.PhiBarIP1 does NOT guarantees
// monotonic decrease of R2. Roundoff error combined with 80-bit
// precision used internally by Intel chips allows R2 to increase
// slightly in some rare, but possible cases. This property is
// undesirable, so we prefer to guard against R increase.
//
state.r2 = Math.Min(state.r2, state.phibarip1*state.phibarip1);
//
// Update d and DNorm, check condition-related stopping criteria
//
for(i=0; i<=state.n-1; i++)
{
state.d[i] = 1/state.rhoi*(state.vi[i]-state.theta*state.d[i]);
state.dnorm = state.dnorm+state.d[i]*state.d[i];
}
if( (double)(Math.Sqrt(state.dnorm)*state.anorm)>=(double)(state.epsc) )
{
state.running = false;
state.repterminationtype = 7;
result = false;
return result;
}
//
// Update x, output report
//
for(i=0; i<=state.n-1; i++)
{
state.rx[i] = state.rx[i]+state.phii/state.rhoi*state.omegai[i];
}
if( !state.xrep )
{
goto lbl_17;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
clearrfields(state);
state.xupdated = true;
state.rstate.stage = 6;
goto lbl_rcomm;
lbl_6:
state.xupdated = false;
lbl_17:
//
// Check stopping criteria
// 1. achieved required number of iterations;
// 2. ||Rk||<=EpsB*||B||;
// 3. ||A^T*Rk||/(||A||*||Rk||)<=EpsA;
//
if( state.maxits>0 && state.repiterationscount>=state.maxits )
{
//
// Achieved required number of iterations
//
state.running = false;
state.repterminationtype = 5;
result = false;
return result;
}
if( (double)(state.phibarip1)<=(double)(state.epsb*bnorm) )
{
//
// ||Rk||<=EpsB*||B||, here ||Rk||=PhiBar
//
state.running = false;
state.repterminationtype = 1;
result = false;
return result;
}
if( (double)(state.alphaip1*Math.Abs(state.ci)/state.anorm)<=(double)(state.epsa) )
{
//
// ||A^T*Rk||/(||A||*||Rk||)<=EpsA, here ||A^T*Rk||=PhiBar*Alpha[i+1]*|.C|
//
state.running = false;
state.repterminationtype = 4;
result = false;
return result;
}
//
// Update omega
//
for(i=0; i<=state.n-1; i++)
{
state.omegaip1[i] = state.vip1[i]-state.theta/state.rhoi*state.omegai[i];
}
//
// Prepare for the next iteration - rename variables:
// u[i] := u[i+1]
// v[i] := v[i+1]
// rho[i] := rho[i+1]
// ...
//
for(i_=0; i_<=summn-1;i_++)
{
state.ui[i_] = state.uip1[i_];
}
for(i_=0; i_<=state.n-1;i_++)
{
state.vi[i_] = state.vip1[i_];
}
for(i_=0; i_<=state.n-1;i_++)
{
state.omegai[i_] = state.omegaip1[i_];
}
state.alphai = state.alphaip1;
state.betai = state.betaip1;
state.phibari = state.phibarip1;
state.rhobari = state.rhobarip1;
goto lbl_15;
lbl_16:
result = false;
return result;
//
// Saving state
//
lbl_rcomm:
result = true;
state.rstate.ia[0] = summn;
state.rstate.ia[1] = i;
state.rstate.ra[0] = bnorm;
return result;
}
/*************************************************************************
Procedure for solution of A*x=b with sparse A.
INPUT PARAMETERS:
State - algorithm state
A - sparse M*N matrix in the CRS format (you MUST contvert it
to CRS format by calling SparseConvertToCRS() function
BEFORE you pass it to this function).
B - right part, array[M]
RESULT:
This function returns no result.
You can get solution by calling LinCGResults()
NOTE: this function uses lightweight preconditioning - multiplication by
inverse of diag(A). If you want, you can turn preconditioning off by
calling LinLSQRSetPrecUnit(). However, preconditioning cost is low
and preconditioner is very important for solution of badly scaled
problems.
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsolvesparse(linlsqrstate state,
sparse.sparsematrix a,
double[] b)
{
int n = 0;
int i = 0;
int j = 0;
int t0 = 0;
int t1 = 0;
double v = 0;
n = state.n;
alglib.ap.assert(!state.running, "LinLSQRSolveSparse: you can not call this function when LinLSQRIteration is running");
alglib.ap.assert(alglib.ap.len(b)>=state.m, "LinLSQRSolveSparse: Length(B)<M");
alglib.ap.assert(apserv.isfinitevector(b, state.m), "LinLSQRSolveSparse: B contains infinite or NaN values");
//
// Allocate temporaries
//
apserv.rvectorsetlengthatleast(ref state.tmpd, n);
apserv.rvectorsetlengthatleast(ref state.tmpx, n);
//
// Compute diagonal scaling matrix D
//
if( state.prectype==0 )
{
//
// Default preconditioner - inverse of column norms
//
for(i=0; i<=n-1; i++)
{
state.tmpd[i] = 0;
}
t0 = 0;
t1 = 0;
while( sparse.sparseenumerate(a, ref t0, ref t1, ref i, ref j, ref v) )
{
state.tmpd[j] = state.tmpd[j]+math.sqr(v);
}
for(i=0; i<=n-1; i++)
{
if( (double)(state.tmpd[i])>(double)(0) )
{
state.tmpd[i] = 1/Math.Sqrt(state.tmpd[i]);
}
else
{
state.tmpd[i] = 1;
}
}
}
else
{
//
// No diagonal scaling
//
for(i=0; i<=n-1; i++)
{
state.tmpd[i] = 1;
}
}
//
// Solve.
//
// Instead of solving A*x=b we solve preconditioned system (A*D)*(inv(D)*x)=b.
// Transformed A is not calculated explicitly, we just modify multiplication
// by A or A'. After solution we modify State.RX so it will store untransformed
// variables
//
linlsqrsetb(state, b);
linlsqrrestart(state);
while( linlsqriteration(state) )
{
if( state.needmv )
{
for(i=0; i<=n-1; i++)
{
state.tmpx[i] = state.tmpd[i]*state.x[i];
}
sparse.sparsemv(a, state.tmpx, ref state.mv);
}
if( state.needmtv )
{
sparse.sparsemtv(a, state.x, ref state.mtv);
for(i=0; i<=n-1; i++)
{
state.mtv[i] = state.tmpd[i]*state.mtv[i];
}
}
}
for(i=0; i<=n-1; i++)
{
state.rx[i] = state.tmpd[i]*state.rx[i];
}
}
/*************************************************************************
This function sets stopping criteria.
INPUT PARAMETERS:
EpsA - algorithm will be stopped if ||A^T*Rk||/(||A||*||Rk||)<=EpsA.
EpsB - algorithm will be stopped if ||Rk||<=EpsB*||B||
MaxIts - algorithm will be stopped if number of iterations
more than MaxIts.
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTE: if EpsA,EpsB,EpsC and MaxIts are zero then these variables will
be setted as default values.
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetcond(linlsqrstate state,
double epsa,
double epsb,
int maxits)
{
alglib.ap.assert(!state.running, "LinLSQRSetCond: you can not call this function when LinLSQRIteration is running");
alglib.ap.assert(math.isfinite(epsa) && (double)(epsa)>=(double)(0), "LinLSQRSetCond: EpsA is negative, INF or NAN");
alglib.ap.assert(math.isfinite(epsb) && (double)(epsb)>=(double)(0), "LinLSQRSetCond: EpsB is negative, INF or NAN");
alglib.ap.assert(maxits>=0, "LinLSQRSetCond: MaxIts is negative");
if( ((double)(epsa)==(double)(0) && (double)(epsb)==(double)(0)) && maxits==0 )
{
state.epsa = atol;
state.epsb = btol;
state.maxits = state.n;
}
else
{
state.epsa = epsa;
state.epsb = epsb;
state.maxits = maxits;
}
}
/*************************************************************************
LSQR solver: results.
This function must be called after LinLSQRSolve
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[N], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* 1 ||Rk||<=EpsB*||B||
* 4 ||A^T*Rk||/(||A||*||Rk||)<=EpsA
* 5 MaxIts steps was taken
* 7 rounding errors prevent further progress,
X contains best point found so far.
(sometimes returned on singular systems)
* Rep.IterationsCount contains iterations count
* NMV countains number of matrix-vector calculations
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrresults(linlsqrstate state,
ref double[] x,
linlsqrreport rep)
{
int i_ = 0;
x = new double[0];
alglib.ap.assert(!state.running, "LinLSQRResult: you can not call this function when LinLSQRIteration is running");
if( alglib.ap.len(x)<state.n )
{
x = new double[state.n];
}
for(i_=0; i_<=state.n-1;i_++)
{
x[i_] = state.rx[i_];
}
rep.iterationscount = state.repiterationscount;
rep.nmv = state.repnmv;
rep.terminationtype = state.repterminationtype;
}
/*************************************************************************
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 MinCGOptimize().
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrsetxrep(linlsqrstate state,
bool needxrep)
{
state.xrep = needxrep;
}
/*************************************************************************
This function restarts LinLSQRIteration
-- ALGLIB --
Copyright 30.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void linlsqrrestart(linlsqrstate state)
{
state.rstate.ia = new int[1+1];
state.rstate.ra = new double[0+1];
state.rstate.stage = -1;
clearrfields(state);
}
/*************************************************************************
Clears request fileds (to be sure that we don't forgot to clear something)
*************************************************************************/
private static void clearrfields(linlsqrstate state)
{
state.xupdated = false;
state.needmv = false;
state.needmtv = false;
state.needmv2 = false;
state.needvmv = false;
state.needprec = false;
}
}
public class lincg
{
/*************************************************************************
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!
*************************************************************************/
public class lincgstate : apobject
{
public double[] rx;
public double[] b;
public int n;
public int prectype;
public double[] cx;
public double[] cr;
public double[] cz;
public double[] p;
public double[] r;
public double[] z;
public double alpha;
public double beta;
public double r2;
public double meritfunction;
public double[] x;
public double[] mv;
public double[] pv;
public double vmv;
public double[] startx;
public double epsf;
public int maxits;
public int itsbeforerestart;
public int itsbeforerupdate;
public bool xrep;
public bool xupdated;
public bool needmv;
public bool needmtv;
public bool needmv2;
public bool needvmv;
public bool needprec;
public int repiterationscount;
public int repnmv;
public int repterminationtype;
public bool running;
public double[] tmpd;
public rcommstate rstate;
public lincgstate()
{
init();
}
public override void init()
{
rx = new double[0];
b = new double[0];
cx = new double[0];
cr = new double[0];
cz = new double[0];
p = new double[0];
r = new double[0];
z = new double[0];
x = new double[0];
mv = new double[0];
pv = new double[0];
startx = new double[0];
tmpd = new double[0];
rstate = new rcommstate();
}
public override alglib.apobject make_copy()
{
lincgstate _result = new lincgstate();
_result.rx = (double[])rx.Clone();
_result.b = (double[])b.Clone();
_result.n = n;
_result.prectype = prectype;
_result.cx = (double[])cx.Clone();
_result.cr = (double[])cr.Clone();
_result.cz = (double[])cz.Clone();
_result.p = (double[])p.Clone();
_result.r = (double[])r.Clone();
_result.z = (double[])z.Clone();
_result.alpha = alpha;
_result.beta = beta;
_result.r2 = r2;
_result.meritfunction = meritfunction;
_result.x = (double[])x.Clone();
_result.mv = (double[])mv.Clone();
_result.pv = (double[])pv.Clone();
_result.vmv = vmv;
_result.startx = (double[])startx.Clone();
_result.epsf = epsf;
_result.maxits = maxits;
_result.itsbeforerestart = itsbeforerestart;
_result.itsbeforerupdate = itsbeforerupdate;
_result.xrep = xrep;
_result.xupdated = xupdated;
_result.needmv = needmv;
_result.needmtv = needmtv;
_result.needmv2 = needmv2;
_result.needvmv = needvmv;
_result.needprec = needprec;
_result.repiterationscount = repiterationscount;
_result.repnmv = repnmv;
_result.repterminationtype = repterminationtype;
_result.running = running;
_result.tmpd = (double[])tmpd.Clone();
_result.rstate = (rcommstate)rstate.make_copy();
return _result;
}
};
public class lincgreport : apobject
{
public int iterationscount;
public int nmv;
public int terminationtype;
public double r2;
public lincgreport()
{
init();
}
public override void init()
{
}
public override alglib.apobject make_copy()
{
lincgreport _result = new lincgreport();
_result.iterationscount = iterationscount;
_result.nmv = nmv;
_result.terminationtype = terminationtype;
_result.r2 = r2;
return _result;
}
};
public const double defaultprecision = 1.0E-6;
/*************************************************************************
This function initializes linear CG Solver. This solver is used to solve
symmetric positive definite problems. If you want to solve nonsymmetric
(or non-positive definite) problem you may use LinLSQR solver provided by
ALGLIB.
USAGE:
1. User initializes algorithm state with LinCGCreate() call
2. User tunes solver parameters with LinCGSetCond() and other functions
3. Optionally, user sets starting point with LinCGSetStartingPoint()
4. User calls LinCGSolveSparse() function which takes algorithm state and
SparseMatrix object.
5. User calls LinCGResults() to get solution
6. Optionally, user may call LinCGSolveSparse() again to solve another
problem with different matrix and/or right part without reinitializing
LinCGState structure.
INPUT PARAMETERS:
N - problem dimension, N>0
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgcreate(int n,
lincgstate state)
{
int i = 0;
alglib.ap.assert(n>0, "LinCGCreate: N<=0");
state.n = n;
state.prectype = 0;
state.itsbeforerestart = n;
state.itsbeforerupdate = 10;
state.epsf = defaultprecision;
state.maxits = 0;
state.xrep = false;
state.running = false;
//
// * allocate arrays
// * set RX to NAN (just for the case user calls Results() without
// calling SolveSparse()
// * set starting point to zero
// * we do NOT initialize B here because we assume that user should
// initializate it using LinCGSetB() function. In case he forgets
// to do so, exception will be thrown in the LinCGIteration().
//
state.rx = new double[state.n];
state.startx = new double[state.n];
state.b = new double[state.n];
for(i=0; i<=state.n-1; i++)
{
state.rx[i] = Double.NaN;
state.startx[i] = 0.0;
state.b[i] = 0;
}
state.cx = new double[state.n];
state.p = new double[state.n];
state.r = new double[state.n];
state.cr = new double[state.n];
state.z = new double[state.n];
state.cz = new double[state.n];
state.x = new double[state.n];
state.mv = new double[state.n];
state.pv = new double[state.n];
updateitersdata(state);
state.rstate.ia = new int[0+1];
state.rstate.ra = new double[2+1];
state.rstate.stage = -1;
}
/*************************************************************************
This function sets starting point.
By default, zero starting point is used.
INPUT PARAMETERS:
X - starting point, array[N]
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetstartingpoint(lincgstate state,
double[] x)
{
int i_ = 0;
alglib.ap.assert(!state.running, "LinCGSetStartingPoint: you can not change starting point because LinCGIteration() function is running");
alglib.ap.assert(state.n<=alglib.ap.len(x), "LinCGSetStartingPoint: Length(X)<N");
alglib.ap.assert(apserv.isfinitevector(x, state.n), "LinCGSetStartingPoint: X contains infinite or NaN values!");
for(i_=0; i_<=state.n-1;i_++)
{
state.startx[i_] = x[i_];
}
}
/*************************************************************************
This function sets right part. By default, right part is zero.
INPUT PARAMETERS:
B - right part, array[N].
OUTPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetb(lincgstate state,
double[] b)
{
int i_ = 0;
alglib.ap.assert(!state.running, "LinCGSetB: you can not set B, because function LinCGIteration is running!");
alglib.ap.assert(alglib.ap.len(b)>=state.n, "LinCGSetB: Length(B)<N");
alglib.ap.assert(apserv.isfinitevector(b, state.n), "LinCGSetB: B contains infinite or NaN values!");
for(i_=0; i_<=state.n-1;i_++)
{
state.b[i_] = b[i_];
}
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. By default, SolveSparse() uses diagonal preconditioner, but if
you want to use solver without preconditioning, you can call this function
which forces solver to use unit matrix for preconditioning.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetprecunit(lincgstate state)
{
alglib.ap.assert(!state.running, "LinCGSetPrecUnit: you can not change preconditioner, because function LinCGIteration is running!");
state.prectype = -1;
}
/*************************************************************************
This function changes preconditioning settings of LinCGSolveSparse()
function. LinCGSolveSparse() will use diagonal of the system matrix as
preconditioner. This preconditioning mode is active by default.
INPUT PARAMETERS:
State - structure which stores algorithm state
-- ALGLIB --
Copyright 19.11.2012 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetprecdiag(lincgstate state)
{
alglib.ap.assert(!state.running, "LinCGSetPrecDiag: you can not change preconditioner, because function LinCGIteration is running!");
state.prectype = 0;
}
/*************************************************************************
This function sets stopping criteria.
INPUT PARAMETERS:
EpsF - algorithm will be stopped if norm of residual is less than
EpsF*||b||.
MaxIts - algorithm will be stopped if number of iterations is more
than MaxIts.
OUTPUT PARAMETERS:
State - structure which stores algorithm state
NOTES:
If both EpsF and MaxIts are zero then small EpsF will be set to small
value.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetcond(lincgstate state,
double epsf,
int maxits)
{
alglib.ap.assert(!state.running, "LinCGSetCond: you can not change stopping criteria when LinCGIteration() is running");
alglib.ap.assert(math.isfinite(epsf) && (double)(epsf)>=(double)(0), "LinCGSetCond: EpsF is negative or contains infinite or NaN values");
alglib.ap.assert(maxits>=0, "LinCGSetCond: MaxIts is negative");
if( (double)(epsf)==(double)(0) && maxits==0 )
{
state.epsf = defaultprecision;
state.maxits = maxits;
}
else
{
state.epsf = epsf;
state.maxits = maxits;
}
}
/*************************************************************************
Reverse communication version of linear CG.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static bool lincgiteration(lincgstate state)
{
bool result = new bool();
int i = 0;
double uvar = 0;
double bnorm = 0;
double v = 0;
int i_ = 0;
//
// Reverse communication preparations
// I know it looks ugly, but it works the same way
// anywhere from C++ to Python.
//
// This code initializes locals by:
// * random values determined during code
// generation - on first subroutine call
// * values from previous call - on subsequent calls
//
if( state.rstate.stage>=0 )
{
i = state.rstate.ia[0];
uvar = state.rstate.ra[0];
bnorm = state.rstate.ra[1];
v = state.rstate.ra[2];
}
else
{
i = -983;
uvar = -989;
bnorm = -834;
v = 900;
}
if( state.rstate.stage==0 )
{
goto lbl_0;
}
if( state.rstate.stage==1 )
{
goto lbl_1;
}
if( state.rstate.stage==2 )
{
goto lbl_2;
}
if( state.rstate.stage==3 )
{
goto lbl_3;
}
if( state.rstate.stage==4 )
{
goto lbl_4;
}
if( state.rstate.stage==5 )
{
goto lbl_5;
}
if( state.rstate.stage==6 )
{
goto lbl_6;
}
if( state.rstate.stage==7 )
{
goto lbl_7;
}
//
// Routine body
//
alglib.ap.assert(alglib.ap.len(state.b)>0, "LinCGIteration: B is not initialized (you must initialize B by LinCGSetB() call");
state.running = true;
state.repnmv = 0;
clearrfields(state);
updateitersdata(state);
//
// Start 0-th iteration
//
for(i_=0; i_<=state.n-1;i_++)
{
state.rx[i_] = state.startx[i_];
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needvmv = true;
state.rstate.stage = 0;
goto lbl_rcomm;
lbl_0:
state.needvmv = false;
bnorm = 0;
state.r2 = 0;
state.meritfunction = 0;
for(i=0; i<=state.n-1; i++)
{
state.r[i] = state.b[i]-state.mv[i];
state.r2 = state.r2+state.r[i]*state.r[i];
state.meritfunction = state.meritfunction+state.mv[i]*state.rx[i]-2*state.b[i]*state.rx[i];
bnorm = bnorm+state.b[i]*state.b[i];
}
bnorm = Math.Sqrt(bnorm);
//
// Output first report
//
if( !state.xrep )
{
goto lbl_8;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
clearrfields(state);
state.xupdated = true;
state.rstate.stage = 1;
goto lbl_rcomm;
lbl_1:
state.xupdated = false;
lbl_8:
//
// Is x0 a solution?
//
if( !math.isfinite(state.r2) || (double)(Math.Sqrt(state.r2))<=(double)(state.epsf*bnorm) )
{
state.running = false;
if( math.isfinite(state.r2) )
{
state.repterminationtype = 1;
}
else
{
state.repterminationtype = -4;
}
result = false;
return result;
}
//
// Calculate Z and P
//
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.r[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needprec = true;
state.rstate.stage = 2;
goto lbl_rcomm;
lbl_2:
state.needprec = false;
for(i=0; i<=state.n-1; i++)
{
state.z[i] = state.pv[i];
state.p[i] = state.z[i];
}
//
// Other iterations(1..N)
//
state.repiterationscount = 0;
lbl_10:
if( false )
{
goto lbl_11;
}
state.repiterationscount = state.repiterationscount+1;
//
// Calculate Alpha
//
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.p[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needvmv = true;
state.rstate.stage = 3;
goto lbl_rcomm;
lbl_3:
state.needvmv = false;
if( !math.isfinite(state.vmv) || (double)(state.vmv)<=(double)(0) )
{
//
// a) Overflow when calculating VMV
// b) non-positive VMV (non-SPD matrix)
//
state.running = false;
if( math.isfinite(state.vmv) )
{
state.repterminationtype = -5;
}
else
{
state.repterminationtype = -4;
}
result = false;
return result;
}
state.alpha = 0;
for(i=0; i<=state.n-1; i++)
{
state.alpha = state.alpha+state.r[i]*state.z[i];
}
state.alpha = state.alpha/state.vmv;
if( !math.isfinite(state.alpha) )
{
//
// Overflow when calculating Alpha
//
state.running = false;
state.repterminationtype = -4;
result = false;
return result;
}
//
// Next step toward solution
//
for(i=0; i<=state.n-1; i++)
{
state.cx[i] = state.rx[i]+state.alpha*state.p[i];
}
//
// Calculate R:
// * use recurrent relation to update R
// * at every ItsBeforeRUpdate-th iteration recalculate it from scratch, using matrix-vector product
// in case R grows instead of decreasing, algorithm is terminated with positive completion code
//
if( !(state.itsbeforerupdate==0 || state.repiterationscount%state.itsbeforerupdate!=0) )
{
goto lbl_12;
}
//
// Calculate R using recurrent formula
//
for(i=0; i<=state.n-1; i++)
{
state.cr[i] = state.r[i]-state.alpha*state.mv[i];
state.x[i] = state.cr[i];
}
goto lbl_13;
lbl_12:
//
// Calculate R using matrix-vector multiplication
//
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.cx[i_];
}
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needmv = true;
state.rstate.stage = 4;
goto lbl_rcomm;
lbl_4:
state.needmv = false;
for(i=0; i<=state.n-1; i++)
{
state.cr[i] = state.b[i]-state.mv[i];
state.x[i] = state.cr[i];
}
//
// Calculating merit function
// Check emergency stopping criterion
//
v = 0;
for(i=0; i<=state.n-1; i++)
{
v = v+state.mv[i]*state.cx[i]-2*state.b[i]*state.cx[i];
}
if( (double)(v)<(double)(state.meritfunction) )
{
goto lbl_14;
}
for(i=0; i<=state.n-1; i++)
{
if( !math.isfinite(state.rx[i]) )
{
state.running = false;
state.repterminationtype = -4;
result = false;
return result;
}
}
//
//output last report
//
if( !state.xrep )
{
goto lbl_16;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
clearrfields(state);
state.xupdated = true;
state.rstate.stage = 5;
goto lbl_rcomm;
lbl_5:
state.xupdated = false;
lbl_16:
state.running = false;
state.repterminationtype = 7;
result = false;
return result;
lbl_14:
state.meritfunction = v;
lbl_13:
for(i_=0; i_<=state.n-1;i_++)
{
state.rx[i_] = state.cx[i_];
}
//
// calculating RNorm
//
// NOTE: monotonic decrease of R2 is not guaranteed by algorithm.
//
state.r2 = 0;
for(i=0; i<=state.n-1; i++)
{
state.r2 = state.r2+state.cr[i]*state.cr[i];
}
//
//output report
//
if( !state.xrep )
{
goto lbl_18;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.rx[i_];
}
clearrfields(state);
state.xupdated = true;
state.rstate.stage = 6;
goto lbl_rcomm;
lbl_6:
state.xupdated = false;
lbl_18:
//
//stopping criterion
//achieved the required precision
//
if( !math.isfinite(state.r2) || (double)(Math.Sqrt(state.r2))<=(double)(state.epsf*bnorm) )
{
state.running = false;
if( math.isfinite(state.r2) )
{
state.repterminationtype = 1;
}
else
{
state.repterminationtype = -4;
}
result = false;
return result;
}
if( state.repiterationscount>=state.maxits && state.maxits>0 )
{
for(i=0; i<=state.n-1; i++)
{
if( !math.isfinite(state.rx[i]) )
{
state.running = false;
state.repterminationtype = -4;
result = false;
return result;
}
}
//
//if X is finite number
//
state.running = false;
state.repterminationtype = 5;
result = false;
return result;
}
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = state.cr[i_];
}
//
//prepere of parameters for next iteration
//
state.repnmv = state.repnmv+1;
clearrfields(state);
state.needprec = true;
state.rstate.stage = 7;
goto lbl_rcomm;
lbl_7:
state.needprec = false;
for(i_=0; i_<=state.n-1;i_++)
{
state.cz[i_] = state.pv[i_];
}
if( state.repiterationscount%state.itsbeforerestart!=0 )
{
state.beta = 0;
uvar = 0;
for(i=0; i<=state.n-1; i++)
{
state.beta = state.beta+state.cz[i]*state.cr[i];
uvar = uvar+state.z[i]*state.r[i];
}
//
//check that UVar is't INF or is't zero
//
if( !math.isfinite(uvar) || (double)(uvar)==(double)(0) )
{
state.running = false;
state.repterminationtype = -4;
result = false;
return result;
}
//
//calculate .BETA
//
state.beta = state.beta/uvar;
//
//check that .BETA neither INF nor NaN
//
if( !math.isfinite(state.beta) )
{
state.running = false;
state.repterminationtype = -1;
result = false;
return result;
}
for(i=0; i<=state.n-1; i++)
{
state.p[i] = state.cz[i]+state.beta*state.p[i];
}
}
else
{
for(i_=0; i_<=state.n-1;i_++)
{
state.p[i_] = state.cz[i_];
}
}
//
//prepere data for next iteration
//
for(i=0; i<=state.n-1; i++)
{
//
//write (k+1)th iteration to (k )th iteration
//
state.r[i] = state.cr[i];
state.z[i] = state.cz[i];
}
goto lbl_10;
lbl_11:
result = false;
return result;
//
// Saving state
//
lbl_rcomm:
result = true;
state.rstate.ia[0] = i;
state.rstate.ra[0] = uvar;
state.rstate.ra[1] = bnorm;
state.rstate.ra[2] = v;
return result;
}
/*************************************************************************
Procedure for solution of A*x=b with sparse A.
INPUT PARAMETERS:
State - algorithm state
A - sparse matrix in the CRS format (you MUST contvert it to
CRS format by calling SparseConvertToCRS() function).
IsUpper - whether upper or lower triangle of A is used:
* IsUpper=True => only upper triangle is used and lower
triangle is not referenced at all
* IsUpper=False => only lower triangle is used and upper
triangle is not referenced at all
B - right part, array[N]
RESULT:
This function returns no result.
You can get solution by calling LinCGResults()
NOTE: this function uses lightweight preconditioning - multiplication by
inverse of diag(A). If you want, you can turn preconditioning off by
calling LinCGSetPrecUnit(). However, preconditioning cost is low and
preconditioner is very important for solution of badly scaled
problems.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsolvesparse(lincgstate state,
sparse.sparsematrix a,
bool isupper,
double[] b)
{
int n = 0;
int i = 0;
double v = 0;
double vmv = 0;
int i_ = 0;
n = state.n;
alglib.ap.assert(alglib.ap.len(b)>=state.n, "LinCGSetB: Length(B)<N");
alglib.ap.assert(apserv.isfinitevector(b, state.n), "LinCGSetB: B contains infinite or NaN values!");
//
// Allocate temporaries
//
apserv.rvectorsetlengthatleast(ref state.tmpd, n);
//
// Compute diagonal scaling matrix D
//
if( state.prectype==0 )
{
//
// Default preconditioner - inverse of matrix diagonal
//
for(i=0; i<=n-1; i++)
{
v = sparse.sparsegetdiagonal(a, i);
if( (double)(v)>(double)(0) )
{
state.tmpd[i] = 1/Math.Sqrt(v);
}
else
{
state.tmpd[i] = 1;
}
}
}
else
{
//
// No diagonal scaling
//
for(i=0; i<=n-1; i++)
{
state.tmpd[i] = 1;
}
}
//
// Solve
//
lincgrestart(state);
lincgsetb(state, b);
while( lincgiteration(state) )
{
//
// Process different requests from optimizer
//
if( state.needmv )
{
sparse.sparsesmv(a, isupper, state.x, ref state.mv);
}
if( state.needvmv )
{
sparse.sparsesmv(a, isupper, state.x, ref state.mv);
vmv = 0.0;
for(i_=0; i_<=state.n-1;i_++)
{
vmv += state.x[i_]*state.mv[i_];
}
state.vmv = vmv;
}
if( state.needprec )
{
for(i=0; i<=n-1; i++)
{
state.pv[i] = state.x[i]*math.sqr(state.tmpd[i]);
}
}
}
}
/*************************************************************************
CG-solver: results.
This function must be called after LinCGSolve
INPUT PARAMETERS:
State - algorithm state
OUTPUT PARAMETERS:
X - array[N], solution
Rep - optimization report:
* Rep.TerminationType completetion code:
* -5 input matrix is either not positive definite,
too large or too small
* -4 overflow/underflow during solution
(ill conditioned problem)
* 1 ||residual||<=EpsF*||b||
* 5 MaxIts steps was taken
* 7 rounding errors prevent further progress,
best point found is returned
* Rep.IterationsCount contains iterations count
* NMV countains number of matrix-vector calculations
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgresults(lincgstate state,
ref double[] x,
lincgreport rep)
{
int i_ = 0;
x = new double[0];
alglib.ap.assert(!state.running, "LinCGResult: you can not get result, because function LinCGIteration has been launched!");
if( alglib.ap.len(x)<state.n )
{
x = new double[state.n];
}
for(i_=0; i_<=state.n-1;i_++)
{
x[i_] = state.rx[i_];
}
rep.iterationscount = state.repiterationscount;
rep.nmv = state.repnmv;
rep.terminationtype = state.repterminationtype;
rep.r2 = state.r2;
}
/*************************************************************************
This function sets restart frequency. By default, algorithm is restarted
after N subsequent iterations.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetrestartfreq(lincgstate state,
int srf)
{
alglib.ap.assert(!state.running, "LinCGSetRestartFreq: you can not change restart frequency when LinCGIteration() is running");
alglib.ap.assert(srf>0, "LinCGSetRestartFreq: non-positive SRF");
state.itsbeforerestart = srf;
}
/*************************************************************************
This function sets frequency of residual recalculations.
Algorithm updates residual r_k using iterative formula, but recalculates
it from scratch after each 10 iterations. It is done to avoid accumulation
of numerical errors and to stop algorithm when r_k starts to grow.
Such low update frequence (1/10) gives very little overhead, but makes
algorithm a bit more robust against numerical errors. However, you may
change it
INPUT PARAMETERS:
Freq - desired update frequency, Freq>=0.
Zero value means that no updates will be done.
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetrupdatefreq(lincgstate state,
int freq)
{
alglib.ap.assert(!state.running, "LinCGSetRUpdateFreq: you can not change update frequency when LinCGIteration() is running");
alglib.ap.assert(freq>=0, "LinCGSetRUpdateFreq: non-positive Freq");
state.itsbeforerupdate = freq;
}
/*************************************************************************
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 MinCGOptimize().
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgsetxrep(lincgstate state,
bool needxrep)
{
state.xrep = needxrep;
}
/*************************************************************************
Procedure for restart function LinCGIteration
-- ALGLIB --
Copyright 14.11.2011 by Bochkanov Sergey
*************************************************************************/
public static void lincgrestart(lincgstate state)
{
state.rstate.ia = new int[0+1];
state.rstate.ra = new double[2+1];
state.rstate.stage = -1;
clearrfields(state);
}
/*************************************************************************
Clears request fileds (to be sure that we don't forgot to clear something)
*************************************************************************/
private static void clearrfields(lincgstate state)
{
state.xupdated = false;
state.needmv = false;
state.needmtv = false;
state.needmv2 = false;
state.needvmv = false;
state.needprec = false;
}
/*************************************************************************
Clears request fileds (to be sure that we don't forgot to clear something)
*************************************************************************/
private static void updateitersdata(lincgstate state)
{
state.repiterationscount = 0;
state.repnmv = 0;
state.repterminationtype = 0;
}
}
public class nleq
{
public class nleqstate : apobject
{
public int n;
public int m;
public double epsf;
public int maxits;
public bool xrep;
public double stpmax;
public double[] x;
public double f;
public double[] fi;
public double[,] j;
public bool needf;
public bool needfij;
public bool xupdated;
public rcommstate rstate;
public int repiterationscount;
public int repnfunc;
public int repnjac;
public int repterminationtype;
public double[] xbase;
public double fbase;
public double fprev;
public double[] candstep;
public double[] rightpart;
public double[] cgbuf;
public nleqstate()
{
init();
}
public override void init()
{
x = new double[0];
fi = new double[0];
j = new double[0,0];
rstate = new rcommstate();
xbase = new double[0];
candstep = new double[0];
rightpart = new double[0];
cgbuf = new double[0];
}
public override alglib.apobject make_copy()
{
nleqstate _result = new nleqstate();
_result.n = n;
_result.m = m;
_result.epsf = epsf;
_result.maxits = maxits;
_result.xrep = xrep;
_result.stpmax = stpmax;
_result.x = (double[])x.Clone();
_result.f = f;
_result.fi = (double[])fi.Clone();
_result.j = (double[,])j.Clone();
_result.needf = needf;
_result.needfij = needfij;
_result.xupdated = xupdated;
_result.rstate = (rcommstate)rstate.make_copy();
_result.repiterationscount = repiterationscount;
_result.repnfunc = repnfunc;
_result.repnjac = repnjac;
_result.repterminationtype = repterminationtype;
_result.xbase = (double[])xbase.Clone();
_result.fbase = fbase;
_result.fprev = fprev;
_result.candstep = (double[])candstep.Clone();
_result.rightpart = (double[])rightpart.Clone();
_result.cgbuf = (double[])cgbuf.Clone();
return _result;
}
};
public class nleqreport : apobject
{
public int iterationscount;
public int nfunc;
public int njac;
public int terminationtype;
public nleqreport()
{
init();
}
public override void init()
{
}
public override alglib.apobject make_copy()
{
nleqreport _result = new nleqreport();
_result.iterationscount = iterationscount;
_result.nfunc = nfunc;
_result.njac = njac;
_result.terminationtype = terminationtype;
return _result;
}
};
/*************************************************************************
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
*************************************************************************/
public static void nleqcreatelm(int n,
int m,
double[] x,
nleqstate state)
{
alglib.ap.assert(n>=1, "NLEQCreateLM: N<1!");
alglib.ap.assert(m>=1, "NLEQCreateLM: M<1!");
alglib.ap.assert(alglib.ap.len(x)>=n, "NLEQCreateLM: Length(X)<N!");
alglib.ap.assert(apserv.isfinitevector(x, n), "NLEQCreateLM: X contains infinite or NaN values!");
//
// Initialize
//
state.n = n;
state.m = m;
nleqsetcond(state, 0, 0);
nleqsetxrep(state, false);
nleqsetstpmax(state, 0);
state.x = new double[n];
state.xbase = new double[n];
state.j = new double[m, n];
state.fi = new double[m];
state.rightpart = new double[n];
state.candstep = new double[n];
nleqrestartfrom(state, x);
}
/*************************************************************************
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
*************************************************************************/
public static void nleqsetcond(nleqstate state,
double epsf,
int maxits)
{
alglib.ap.assert(math.isfinite(epsf), "NLEQSetCond: EpsF is not finite number!");
alglib.ap.assert((double)(epsf)>=(double)(0), "NLEQSetCond: negative EpsF!");
alglib.ap.assert(maxits>=0, "NLEQSetCond: negative MaxIts!");
if( (double)(epsf)==(double)(0) && maxits==0 )
{
epsf = 1.0E-6;
}
state.epsf = epsf;
state.maxits = 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
*************************************************************************/
public static void nleqsetxrep(nleqstate state,
bool needxrep)
{
state.xrep = 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
*************************************************************************/
public static void nleqsetstpmax(nleqstate state,
double stpmax)
{
alglib.ap.assert(math.isfinite(stpmax), "NLEQSetStpMax: StpMax is not finite!");
alglib.ap.assert((double)(stpmax)>=(double)(0), "NLEQSetStpMax: StpMax<0!");
state.stpmax = stpmax;
}
/*************************************************************************
-- ALGLIB --
Copyright 20.03.2009 by Bochkanov Sergey
*************************************************************************/
public static bool nleqiteration(nleqstate state)
{
bool result = new bool();
int n = 0;
int m = 0;
int i = 0;
double lambdaup = 0;
double lambdadown = 0;
double lambdav = 0;
double rho = 0;
double mu = 0;
double stepnorm = 0;
bool b = new bool();
int i_ = 0;
//
// Reverse communication preparations
// I know it looks ugly, but it works the same way
// anywhere from C++ to Python.
//
// This code initializes locals by:
// * random values determined during code
// generation - on first subroutine call
// * values from previous call - on subsequent calls
//
if( state.rstate.stage>=0 )
{
n = state.rstate.ia[0];
m = state.rstate.ia[1];
i = state.rstate.ia[2];
b = state.rstate.ba[0];
lambdaup = state.rstate.ra[0];
lambdadown = state.rstate.ra[1];
lambdav = state.rstate.ra[2];
rho = state.rstate.ra[3];
mu = state.rstate.ra[4];
stepnorm = state.rstate.ra[5];
}
else
{
n = -983;
m = -989;
i = -834;
b = false;
lambdaup = -287;
lambdadown = 364;
lambdav = 214;
rho = -338;
mu = -686;
stepnorm = 912;
}
if( state.rstate.stage==0 )
{
goto lbl_0;
}
if( state.rstate.stage==1 )
{
goto lbl_1;
}
if( state.rstate.stage==2 )
{
goto lbl_2;
}
if( state.rstate.stage==3 )
{
goto lbl_3;
}
if( state.rstate.stage==4 )
{
goto lbl_4;
}
//
// Routine body
//
//
// Prepare
//
n = state.n;
m = state.m;
state.repterminationtype = 0;
state.repiterationscount = 0;
state.repnfunc = 0;
state.repnjac = 0;
//
// Calculate F/G, initialize algorithm
//
clearrequestfields(state);
state.needf = true;
state.rstate.stage = 0;
goto lbl_rcomm;
lbl_0:
state.needf = false;
state.repnfunc = state.repnfunc+1;
for(i_=0; i_<=n-1;i_++)
{
state.xbase[i_] = state.x[i_];
}
state.fbase = state.f;
state.fprev = math.maxrealnumber;
if( !state.xrep )
{
goto lbl_5;
}
//
// progress report
//
clearrequestfields(state);
state.xupdated = true;
state.rstate.stage = 1;
goto lbl_rcomm;
lbl_1:
state.xupdated = false;
lbl_5:
if( (double)(state.f)<=(double)(math.sqr(state.epsf)) )
{
state.repterminationtype = 1;
result = false;
return result;
}
//
// Main cycle
//
lambdaup = 10;
lambdadown = 0.3;
lambdav = 0.001;
rho = 1;
lbl_7:
if( false )
{
goto lbl_8;
}
//
// Get Jacobian;
// before we get to this point we already have State.XBase filled
// with current point and State.FBase filled with function value
// at XBase
//
clearrequestfields(state);
state.needfij = true;
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xbase[i_];
}
state.rstate.stage = 2;
goto lbl_rcomm;
lbl_2:
state.needfij = false;
state.repnfunc = state.repnfunc+1;
state.repnjac = state.repnjac+1;
ablas.rmatrixmv(n, m, state.j, 0, 0, 1, state.fi, 0, ref state.rightpart, 0);
for(i_=0; i_<=n-1;i_++)
{
state.rightpart[i_] = -1*state.rightpart[i_];
}
//
// Inner cycle: find good lambda
//
lbl_9:
if( false )
{
goto lbl_10;
}
//
// Solve (J^T*J + (Lambda+Mu)*I)*y = J^T*F
// to get step d=-y where:
// * Mu=||F|| - is damping parameter for nonlinear system
// * Lambda - is additional Levenberg-Marquardt parameter
// for better convergence when far away from minimum
//
for(i=0; i<=n-1; i++)
{
state.candstep[i] = 0;
}
fbls.fblssolvecgx(state.j, m, n, lambdav, state.rightpart, ref state.candstep, ref state.cgbuf);
//
// Normalize step (it must be no more than StpMax)
//
stepnorm = 0;
for(i=0; i<=n-1; i++)
{
if( (double)(state.candstep[i])!=(double)(0) )
{
stepnorm = 1;
break;
}
}
linmin.linminnormalized(ref state.candstep, ref stepnorm, n);
if( (double)(state.stpmax)!=(double)(0) )
{
stepnorm = Math.Min(stepnorm, state.stpmax);
}
//
// Test new step - is it good enough?
// * if not, Lambda is increased and we try again.
// * if step is good, we decrease Lambda and move on.
//
// We can break this cycle on two occasions:
// * step is so small that x+step==x (in floating point arithmetics)
// * lambda is so large
//
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xbase[i_];
}
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.x[i_] + stepnorm*state.candstep[i_];
}
b = true;
for(i=0; i<=n-1; i++)
{
if( (double)(state.x[i])!=(double)(state.xbase[i]) )
{
b = false;
break;
}
}
if( b )
{
//
// Step is too small, force zero step and break
//
stepnorm = 0;
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xbase[i_];
}
state.f = state.fbase;
goto lbl_10;
}
clearrequestfields(state);
state.needf = true;
state.rstate.stage = 3;
goto lbl_rcomm;
lbl_3:
state.needf = false;
state.repnfunc = state.repnfunc+1;
if( (double)(state.f)<(double)(state.fbase) )
{
//
// function value decreased, move on
//
decreaselambda(ref lambdav, ref rho, lambdadown);
goto lbl_10;
}
if( !increaselambda(ref lambdav, ref rho, lambdaup) )
{
//
// Lambda is too large (near overflow), force zero step and break
//
stepnorm = 0;
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xbase[i_];
}
state.f = state.fbase;
goto lbl_10;
}
goto lbl_9;
lbl_10:
//
// Accept step:
// * new position
// * new function value
//
state.fbase = state.f;
for(i_=0; i_<=n-1;i_++)
{
state.xbase[i_] = state.xbase[i_] + stepnorm*state.candstep[i_];
}
state.repiterationscount = state.repiterationscount+1;
//
// Report new iteration
//
if( !state.xrep )
{
goto lbl_11;
}
clearrequestfields(state);
state.xupdated = true;
state.f = state.fbase;
for(i_=0; i_<=n-1;i_++)
{
state.x[i_] = state.xbase[i_];
}
state.rstate.stage = 4;
goto lbl_rcomm;
lbl_4:
state.xupdated = false;
lbl_11:
//
// Test stopping conditions on F, step (zero/non-zero) and MaxIts;
// If one of the conditions is met, RepTerminationType is changed.
//
if( (double)(Math.Sqrt(state.f))<=(double)(state.epsf) )
{
state.repterminationtype = 1;
}
if( (double)(stepnorm)==(double)(0) && state.repterminationtype==0 )
{
state.repterminationtype = -4;
}
if( state.repiterationscount>=state.maxits && state.maxits>0 )
{
state.repterminationtype = 5;
}
if( state.repterminationtype!=0 )
{
goto lbl_8;
}
//
// Now, iteration is finally over
//
goto lbl_7;
lbl_8:
result = false;
return result;
//
// Saving state
//
lbl_rcomm:
result = true;
state.rstate.ia[0] = n;
state.rstate.ia[1] = m;
state.rstate.ia[2] = i;
state.rstate.ba[0] = b;
state.rstate.ra[0] = lambdaup;
state.rstate.ra[1] = lambdadown;
state.rstate.ra[2] = lambdav;
state.rstate.ra[3] = rho;
state.rstate.ra[4] = mu;
state.rstate.ra[5] = stepnorm;
return result;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqresults(nleqstate state,
ref double[] x,
nleqreport rep)
{
x = new double[0];
nleqresultsbuf(state, ref x, 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
*************************************************************************/
public static void nleqresultsbuf(nleqstate state,
ref double[] x,
nleqreport rep)
{
int i_ = 0;
if( alglib.ap.len(x)<state.n )
{
x = new double[state.n];
}
for(i_=0; i_<=state.n-1;i_++)
{
x[i_] = state.xbase[i_];
}
rep.iterationscount = state.repiterationscount;
rep.nfunc = state.repnfunc;
rep.njac = state.repnjac;
rep.terminationtype = state.repterminationtype;
}
/*************************************************************************
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
*************************************************************************/
public static void nleqrestartfrom(nleqstate state,
double[] x)
{
int i_ = 0;
alglib.ap.assert(alglib.ap.len(x)>=state.n, "NLEQRestartFrom: Length(X)<N!");
alglib.ap.assert(apserv.isfinitevector(x, state.n), "NLEQRestartFrom: X contains infinite or NaN values!");
for(i_=0; i_<=state.n-1;i_++)
{
state.x[i_] = x[i_];
}
state.rstate.ia = new int[2+1];
state.rstate.ba = new bool[0+1];
state.rstate.ra = new double[5+1];
state.rstate.stage = -1;
clearrequestfields(state);
}
/*************************************************************************
Clears request fileds (to be sure that we don't forgot to clear something)
*************************************************************************/
private static void clearrequestfields(nleqstate state)
{
state.needf = false;
state.needfij = false;
state.xupdated = false;
}
/*************************************************************************
Increases lambda, returns False when there is a danger of overflow
*************************************************************************/
private static bool increaselambda(ref double lambdav,
ref double nu,
double lambdaup)
{
bool result = new bool();
double lnlambda = 0;
double lnnu = 0;
double lnlambdaup = 0;
double lnmax = 0;
result = false;
lnlambda = Math.Log(lambdav);
lnlambdaup = Math.Log(lambdaup);
lnnu = Math.Log(nu);
lnmax = 0.5*Math.Log(math.maxrealnumber);
if( (double)(lnlambda+lnlambdaup+lnnu)>(double)(lnmax) )
{
return result;
}
if( (double)(lnnu+Math.Log(2))>(double)(lnmax) )
{
return result;
}
lambdav = lambdav*lambdaup*nu;
nu = nu*2;
result = true;
return result;
}
/*************************************************************************
Decreases lambda, but leaves it unchanged when there is danger of underflow.
*************************************************************************/
private static void decreaselambda(ref double lambdav,
ref double nu,
double lambdadown)
{
nu = 1;
if( (double)(Math.Log(lambdav)+Math.Log(lambdadown))<(double)(Math.Log(math.minrealnumber)) )
{
lambdav = math.minrealnumber;
}
else
{
lambdav = lambdav*lambdadown;
}
}
}
}