Cadabra manual: Nevaluate

nevaluate

Numerically evaluate an expression.

Given a scalar expression of one or more variables, evaluate it for a range of values of those variables. This algorithm accepts a Cadabra expression and one or more numpy arrays containing the values of the variables, in the form of a dictionary. A simple example with an expression of one variable:

ex:= \cos(x) \exp(-x**2/4); import numpy as np xv = np.linspace(0, 3, 100) z = np.array( nevaluate(ex, {$x$: xv} ) )

$\displaystyle{}\cos{x} \exp\left( - \frac{1}{4}{x}^{2}\right)$

\cos(x) \exp( - 1/4 (x)**2)

z[0:10];

[1.         0.99931146 0.99724785 0.99381515 0.98902334 0.98288631
 0.97542182 0.96665142 0.95660038 0.94529757]

The nevaluate function thus takes as its second argument a Python dictionary which maps each variable in the expression to a list of values. For expressions of multiple variables, the logic is the same: just list all the variables in the dictionary, as in the example below.

ex:= \cos(x) \sin(y);

$\displaystyle{}\cos{x} \sin{y}$

\cos(x) \sin(y)

xv = np.linspace(0, np.pi, 100) yv = np.linspace(0, np.pi, 100)

z = np.array( nevaluate(ex, {$x$: xv, $y$: yv}) )

z[3,10];

0.3106205340965772