Create a symbolic function

In this example we are going to create a function from mathematical formulas:

Analytical expressions of the gradient and hessian are automatically computed except if the function is not differentiable everywhere. In that case a finite difference method is used.

import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
import math as m
ot.Log.Show(ot.Log.NONE)

create a symbolic function

function = ot.SymbolicFunction(['x0', 'x1'],
                               ['-(6 + x0^2 - x1)'])
print(function)

Out:

[x0,x1]->[-(6 + x0^2 - x1)]

evaluate function

x = [2.0, 3.0]
print('x=', x, 'f(x)=', function(x))

Out:

x= [2.0, 3.0] f(x)= [-7]

show gradient

print(function.getGradient())

Out:

| d(y0) / d(x0) = -2*x0
| d(y0) / d(x1) = 1

use gradient

print('x=', x, 'df(x)=', function.gradient(x))

Out:

x= [2.0, 3.0] df(x)= [[ -4 ]
 [  1 ]]

draw isocontours of f around [2,3]

graph = function.draw(0, 1, 0, [2.0, 3.0], [1.5, 2.5], [2.5, 3.5])
view = viewer.View(graph)
plt.show()