ClassEqSys - Wrj4P5 Wiki - Wrj4P5

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