Solves automatic numerical differentiation problems in one or more variables.
Project description
Suite of tools written in _Python to solve automatic numerical differentiation problems in one or more variables. Finite differences are used in an adaptive manner, coupled with a Romberg extrapolation methodology to provide a maximally accurate result. The user can configure many options like; changing the order of the method or the extrapolation, even allowing the user to specify whether complexstep, central, forward or backward differences are used.
The methods provided are:
Derivative: Compute the derivatives of order 1 through 10 on any scalar function.
Gradient: Compute the gradient vector of a scalar function of one or more variables.
Jacobian: Compute the Jacobian matrix of a vector valued function of one or more variables.
Hessian: Compute the Hessian matrix of all 2nd partial derivatives of a scalar function of one or more variables.
Hessdiag: Compute only the diagonal elements of the Hessian matrix
All of these methods also produce error estimates on the result.
The documentation for numdifftools is available here http://numdifftools.readthedocs.org/
To test if the toolbox is working paste the following in an interactive python session:
import numdifftools as nd nd.test(coverage=True, doctests=True)
Examples
Compute 1’st and 2’nd derivative of exp(x), at x == 1:
>>> import numpy as np >>> import numdifftools as nd >>> fd = nd.Derivative(np.exp) # 1'st derivative >>> fdd = nd.Derivative(np.exp, n=2) # 2'nd derivative >>> fd(1) array([ 2.71828183])
Nonlinear least squares:
>>> xdata = np.reshape(np.arange(0,1,0.1),(1,1)) >>> ydata = 1+2*np.exp(0.75*xdata) >>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata)  ydata)**2 >>> Jfun = nd.Jacobian(fun) >>> np.abs(Jfun([1,2,0.75])) < 1e14 # should be numerically zero array([[ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True], [ True, True, True]], dtype=bool)
Compute gradient of sum(x**2):
>>> fun = lambda x: np.sum(x**2) >>> dfun = nd.Gradient(fun) >>> dfun([1,2,3]) array([ 2., 4., 6.])
See also
scipy.misc.derivative
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