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object --+ | Function --+ | DiscreteMap
Turns a function into a map composed with itself period times. Chain rule gives jacobian. Note that F: R^n+m --> R^n, where m is the number of free parameters. Thus, we transform to G: R^n+m --> R^n+m given by G(x,p) = [F(x,p), p], where x is state variable and p parameters. This gives DG = [ DF_x DF_p ] [ 0 I ] Chain rule on F gives DF^n = DF(F^n-1)*DF(F^n-2)*...*DF(F)*DF(X). Chain rule on G gives the same thing as F, and when you keep track of the upper left and upper right blocks of DG composed with itself, you arrive at DF^n_x = DF_x(F^n-1)*DF_x(F^n-2)*...*DF_x(F)*DF_x(X) DF^n_a = DF_x(F^n-1)*DF_a(F^n-2) + DF_a(F^n-1) (defined recursively with F^0 = X, F^-1 = 0)
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Inherited from Inherited from |
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x.__init__(...) initializes x; see x.__class__.__doc__ for signature
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