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ClassEqSys : Model of the General Equation System

test applet and code is here

  1. /*[class] EqSys 5/20/2008 by Classiclll
  2. *
  3. *Model of multi-value Vector Functions, the Equation System
  4. * f(x) = [ fi(x) | fi : R^n -> R^m ]
  5. * can solve the multi-value non-linear equation, with Simplex(Nelder) and Newton
  6. * f(x) = 0
  7. */
  8. EqSys(int dom, int rng) //constructor with dimension of domain & codomain.
  9. int domDim() //dimension of the domain (n)
  10. int rngDim() //dimension of the range (m)
  11. abstract Vec valueAt(Vec x) //value of the equation system(R^n -> R^m) at x
  12. //Jacobian at x, if not continuouse, you can return diffAt(x,d)
  13. abstract Mat jacobAt(Vec x)
  14. /* [Sample] Jacobian of f(x) = { x+y+z-1, y+z-1, x+z-1 }
  15. double[][] jacobi = { {1, 1, 1}, // { {dxf0(X), dyf0(X), dzf0(X)}
  16. {0, 1, 1}, // {dxf1(X), dyf1(X), dzf1(X)}
  17. {1, 0, 1} }; // {dxf2(X), dyf2(X), dzf2(X)} }
  18. */
  19. Vec diffAt(Vec x, Vec d) // overwride if needed
  20. Vec solveByNewton(Vec x0) // find the solution by the newton, start at x0
  21. Vec solveBySimplex(Vec x0, int limit)
  22. // find the solution by the simplex, start at x0
  23. Vec solveBySimplex(Vec x0, int limit, int tryal)
  24. // find the solution by the simplex, start at x0