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ClassEqSys : Model of the General Equation System

test applet and code is here

/*[class] EqSys              5/20/2008 by Classiclll
  *
  *Model of multi-value Vector Functions, the Equation System
  *		f(x) = [ fi(x) | fi : R^n -> R^m ]
  * can solve the multi-value non-linear equation, with Simplex(Nelder) and Newton
  * 		f(x) = 0
  */
    EqSys(int dom, int rng) //constructor with dimension of domain & codomain.

    int domDim()		//dimension of the domain (n)
    int rngDim()		//dimension of the range (m)
    
    abstract Vec valueAt(Vec x)	//value of the equation system(R^n -> R^m) at x
		//Jacobian at x, if not continuouse, you can return diffAt(x,d)
    abstract Mat jacobAt(Vec x)
/*	 [Sample]  Jacobian of f(x) = { x+y+z-1, y+z-1, x+z-1 }
   double[][] jacobi = { {1, 1, 1},	// { {dxf0(X), dyf0(X), dzf0(X)}
                         {0, 1, 1},	//   {dxf1(X), dyf1(X), dzf1(X)}
		         {1, 0, 1} };	//   {dxf2(X), dyf2(X), dzf2(X)} }
*/
    Vec diffAt(Vec x, Vec d)		// overwride if needed

    Vec solveByNewton(Vec x0)		// find the solution by the newton, start at x0
    Vec solveBySimplex(Vec x0, int limit) 
                   // find the solution by the simplex, start at x0
    Vec solveBySimplex(Vec x0, int limit, int tryal)
		// find the solution by the simplex, start at x0