📄 matlib.h
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#include "matrix.hpp"
#ifndef __MATLIB_H
#define __MATLIB_H
int SolveSysEqa(matrix& a,matrix& c);
double SolveREqa(matrix& a,vector& v,vector& x);//col(a)=vlen(v),x*a=v,vlen(x)=mrow(a)
double SolevLEqa(matrix& a,vector& v,vector& x);//mrow(a)=vlen(v),a*x=v,vlen(x)=mcol(a)
int SysEig(matrix& a, matrix& p, vector& d);
int SelfCov(vector& x,vector& r,int n);
int qr(matrix& a);
int qr1(matrix& a);
matrix pinv(matrix& a,double eps=1.e-12);
int PartialCorrByLS(matrix& a,vector& pr);
double rndnorm(double mu, double sigma);
double rnduniform(double dmin, double dmax);
double cauchyrnd();
vector polyfit(vector& x,vector& y,int aicflag=0,int n=0);//aicflag<0,n-degree;aicflag=0,AIC;aicflag=1,BIC
vector polyval(vector& p,vector& x);
int SolveNewtonDir(matrix& a,vector& b);
// SysMatrix Canonical form
int SolveNewtonDir2(matrix& a,vector& b);
// Cholesky Decompose
int SolveNewtonDir3(matrix& a,vector& b);
int SysMatrixCanonical(matrix& a, matrix& p, vector& d); //
int CholeskyDecompose(matrix& A, matrix& L, vector& D,vector& E);// A+E=LDL'
// Q'AQ=LDL':A -> Q'AQ=H -> H=LDL', H- Tri-diag
int SolveMNewtonDir(matrix& a,vector& b);
// P'AP=LDL' P Altetnate Matrix
int SolveMNewtonDir1(matrix& a,vector& b);
//standard simplex algorithm, b>=0,x>=0, min c'x s.t. a*x<=b;
int lp_simplex(matrix& a, vector& b,vector& c, vector& x);
int lp_simplex(matrix& a, vector& b,vector& c,IntVector& js,vector& x);
//by affine inner point and dual
int lp_affineinner(matrix& a, vector& b,vector& c, vector& x);
int SolveSysEqa(matrix& a,vector& v,vector& x);
//inverse of matrix a by gauss principal elements
int dcinv(matrix& a);
//ll decomposite of sysmetric matrix
int dicll(matrix& a);
//LUdecomposite of matrix
int lu(matrix& a,IntVector& js);
//double GetLypExp(matrix& a);
#endif __MATLIB_H
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