r""" UTPM == Univariate Taylor Polynomial of Matrices This class implements univariate Taylor arithmetic on matrices, i.e. [A]_D = \sum_{

Taylor coefficients Tc. One can propagate more than one direction at a time (called vector mode) by initializing with mytc = Tc(x0, [[x11

The CGraph (short for Computational Graph) represents a computational procedure of elementary functions. It is a Directed Acylic Graph (D

UTPS == Univariate Taylor Polynomial on Scalars This class implements univariate Taylor arithmetic on real numbers, i.e. [x] = \sum_{d=0}

Class: Algorithmic differentiation

We implement the Computational Graph (CG) as Directed Graph The Graph of y = x1(x2+x3) looks like --- independent variables v1(x1):

Parse and compare numpy version strings. Numpy has the following versioning scheme (numbers given are examples; they can be >9) in principle)

UTP(X, vectorized=False) Univariate Taylor Polynomial (UTP) with coefficients that are arbitrary numpy.ndarrays Attributes ----

Sparse Matrix as Vertex List

An abstract base class in an attempt to follow the DRY principle. It implements the algebraic class of a ring as defined on http://e

Test nth derivatives of scalar functions that take auxiliary arguments.

Test scalar math identities involving only elementary functions in numpy.

Check the examples from the last slide of a talk by Warwick Tucker 2010. It is from Lecture 1 of the Automatic Differentiation Winter School

Test scalar math identities involving special functions in scipy.

Test the push forward class functions that operate directly on data.