Package numdifftools :: Module core :: Class Derivative
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Class Derivative

     object --+    
              |    
Common_diff_par --+
                  |
                 Derivative

Known Subclasses:
Gradient, Hessdiag, Hessian

Estimate n'th derivative of fun at x0, with error estimate


Input arguments
===============
fun = function to differentiate.

**kwds
------
derOrder : Integer from 1 to 4 defining derivative order. (Default 1)
metOrder : Integer from 1 to 4 defining order of basic method used.
             (For 'central' methods, it must be from the set [2,4].
             (Default 2)
method   : Method of estimation.  Valid options are:
              'central', 'forward' or 'backwards'.     (Default 'central')
numTerms : Number of Romberg terms used in the extrapolation.
             Must be an integer from 0 to 3.  (Default 2)
             Note: 0 disables the Romberg step completely.
stepFix  : If not None, it will define the maximum excursion from x0
             that is used and prevent the adaptive logic from working.
             This will be considerably faster, but not necessarily
             as accurate as allowing the adaptive logic to run.
            (Default: None)
stepMax  : Maximum allowed excursion from x0 as a multiple of x0. (Default 100)
stepRatio: Ratio used between sequential steps in the estimation
             of the derivative (Default 2)
vectorized : True  - if your function is vectorized.
               False - loop over the successive function calls (default).

Uses a semi-adaptive scheme to provide the best estimate of the
derivative by its automatic choice of a differencing interval. It uses
finite difference approximations of various orders, coupled with a
generalized (multiple term) Romberg extrapolation. This also yields the
error estimate provided. See the document DERIVEST.pdf for more explanation
of the algorithms behind the parameters.

 Note on metOrder: higher order methods will generally be more accurate,
         but may also suffer more from numerical problems. First order
         methods would usually not be recommended.
 Note on method: Central difference methods are usually the most accurate,
        but sometimes one can only allow evaluation in forward or backward
        direction.


Examples
--------
 # 1'st and 2'nd derivative of exp(x), at x == 1
 >>> import numpy as np
 >>> fd = Derivative(np.exp)              # 1'st derivative
 >>> fdd = Derivative(np.exp,derOrder=2)  # 2'nd derivative
 >>> fd(1)
 array([ 2.71828183])

 >>> d2 = fdd(1)
 >>> fdd.error_estimate # Get error estimate
 array([  5.95741234e-11])

 # 3'rd derivative of x.^3+x.^4, at x = [0,1]
 >>> fun = lambda x: x**3 + x**4
 >>> fd3 = Derivative(fun,derOrder=3)
 >>> fd3([0,1])          #  True derivatives: [6,30]
 array([  6.,  30.])

 >>> fd3.error_estimate
 array([  2.65282677e-14,   1.06113071e-13])

 See also
 --------
 Gradient,
 Hessdiag,
 Hessian,
 Jacobian

Method Summary
  __init__(self, fun, **kwds)
  __call__(self, x00)
  derivative(self, x00)
Return estimate of n'th derivative of fun at x0 using romberg extrapolation
  _derivative(self, x00)
  _fder(self, f_x0i, x0i, h)
Return derivative estimates of f at x0 for a sequence of stepsizes h...
  _fun(self, xi)
  _gradient(self, x00)
  _hessdiag(self, x00)
  _hessian(self, x00)
  _partial_der(self, x00)
Return partial derivatives
    Inherited from Common_diff_par
  _check_params(self)
check the parameters for acceptability
  _fdamat(self, parity, nterms)
Return matrix for fda derivation.
  _fdiff_b(self, f_x0i, x0i, h)
Return backward differences...
  _fdiff_c(self, f_x0i, x0i, h)
Return central differences...
  _fdiff_f(self, f_x0i, x0i, h)
Return forward differences...
  _rombextrap(self, der_init)
Return Romberg extrapolated derivatives and error estimates based on the initial derivative estimates...
  _set_all_der_par(self)
Set derivative parameters: stepsize, differention rule and romberg extrapolation
  _set_delta(self)
Set the steps to use in derivation.
  _set_fdarule(self)
Generate finite differencing rule in advance.
  _set_fdiff(self)
Set _fdiff fun according to method
  _set_rombexpon(self)
Member variables used...
    Inherited from object
  __delattr__(...)
x.__delattr__('name') <==> del x.name
  __getattribute__(...)
x.__getattribute__('name') <==> x.name
  __hash__(x)
x.__hash__() <==> hash(x)
  __reduce__(...)
helper for pickle
  __reduce_ex__(...)
helper for pickle
  __repr__(x)
x.__repr__() <==> repr(x)
  __setattr__(...)
x.__setattr__('name', value) <==> x.name = value
  __str__(x)
x.__str__() <==> str(x)
    Inherited from type
  __new__(T, S, ...)
T.__new__(S, ...) -> a new object with type S, a subtype of T

Method Details

derivative(self, x00)

Return estimate of n'th derivative of fun at x0 using romberg extrapolation

_fder(self, f_x0i, x0i, h)

Return derivative estimates of f at x0 for a sequence of stepsizes h

Member variables used
---------------------
derOrder
fdarule
numTerms

_partial_der(self, x00)

Return partial derivatives

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