Package PyDSTool :: Package PyCont :: Module TestFunc :: Class DiscreteMap
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Class DiscreteMap

source code

object --+    
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  Function --+
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            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)

Instance Methods [hide private]
 
__init__(self, F, period=1)
x.__init__(...) initializes x; see x.__class__.__doc__ for signature
source code
 
func(self, X) source code
 
diff(self, X, ind=None) source code

Inherited from Function: __call__, __getitem__, __setitem__, findzero, numhess

Inherited from object: __delattr__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __repr__, __setattr__, __str__

Properties [hide private]

Inherited from object: __class__

Method Details [hide private]

__init__(self, F, period=1)
(Constructor)

source code 

x.__init__(...) initializes x; see x.__class__.__doc__ for signature

Overrides: object.__init__
(inherited documentation)

diff(self, X, ind=None)

source code 
Overrides: Function.diff