5.1.6.4. numdifftools.nd_algopy.Hessdiag

class Hessdiag(f, method='forward', full_output=False)

Calculate Hessian diagonal with Algorithmic Differentiation method

Parameters

fun: function

function of one array fun(x, *args, **kwds)

method: string, optional {‘forward’, ‘reverse’}

defines method used in the approximation

Returns

hessdiagndarray

Hessian diagonal array of partial second order derivatives.

See also

Derivative

Gradient

Jacobian

Hessian

Notes

Algorithmic differentiation is a set of techniques to numerically evaluate the derivative of a function specified by a computer program. AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition, subtraction, multiplication, division, etc.) and elementary functions (exp, log, sin, cos, etc.). By applying the chain rule repeatedly to these operations, derivatives of arbitrary order can be computed automatically, accurately to working precision, and using at most a small constant factor more arithmetic operations than the original program.

References

Sebastian F. Walter and Lutz Lehmann 2013, “Algorithmic differentiation in Python with AlgoPy”, in Journal of Computational Science, vol 4, no 5, pp 334 - 344, http://www.sciencedirect.com/science/article/pii/S1877750311001013

https://en.wikipedia.org/wiki/Automatic_differentiation

Examples

>>> import numpy as np
>>> import numdifftools.nd_algopy as nda

# Rosenbrock function, minimized at [1,1]

>>> rosen = lambda x : (1.-x[0])**2 + 105*(x[1]-x[0]**2)**2
>>> Hfun = nda.Hessdiag(rosen)
>>> h = Hfun([1, 1]) #  h =[ 842, 210]
>>> np.allclose(h, [ 842.,  210.])
True

# cos(x-y), at (0,0)

>>> cos = np.cos
>>> fun = lambda xy : cos(xy[0]-xy[1])
>>> Hfun2 = nda.Hessdiag(fun)
>>> h2 = Hfun2([0, 0]) # h2 = [-1, -1]
>>> np.allclose(h2, [-1., -1.])
True

>>> Hfun3 = nda.Hessdiag(fun, method='reverse')
>>> h3 = Hfun3([0, 0]) # h2 = [-1, -1];
>>> np.allclose(h3, [-1., -1.])
True

Methods

__call__: callable with the following parameters:

x: array_like value at which function derivative is evaluated args: tuple Arguments for function fun. kwds: dict Keyword arguments for function fun.

__init__(f, method='forward', full_output=False)

Methods

__init__(f[, method, full_output])
computational_graph(x, *args, **kwds)

Attributes

fun