/************************************************************************* 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 { /************************************************************************* *************************************************************************/ 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 { public double r1; public double rinf; }; public class densesolverlsreport { public double r2; public double[,] cx; public int n; public int k; public densesolverlsreport() { cx = new double[0,0]; } }; /************************************************************************* 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( i0 ) { 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]; 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](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]; 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](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=0; i--) { if( i0 ) { 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=0; i--) { if( i0 ) { 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 nleq { public class nleqstate { 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() { 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 class nleqreport { public int iterationscount; public int nfunc; public int njac; public int terminationtype; }; public const int armijomaxfev = 20; /************************************************************************* 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) { ap.assert(n>=1, "NLEQCreateLM: N<1!"); ap.assert(m>=1, "NLEQCreateLM: M<1!"); ap.assert(ap.len(x)>=n, "NLEQCreateLM: Length(X)=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) { ap.assert(math.isfinite(epsf), "NLEQSetCond: EpsF is not finite number!"); ap.assert((double)(epsf)>=(double)(0), "NLEQSetCond: negative EpsF!"); 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) { ap.assert(math.isfinite(stpmax), "NLEQSetStpMax: StpMax is not finite!"); 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( ap.len(x)=state.n, "NLEQRestartFrom: Length(X)(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; } } } }