Create a quadratic functionΒΆ

In this example we are going to create a quadratic function of the form

f : \underline{X} \mapsto \underline{\underline{A}} ( \underline{X} - \underline{b} ) + \underline{c} + \frac{1}{2} \underline{X}^T \times \underline{\underline{\underline{M}}} \times \underline{X}

[2]:

from __future__ import print_function
import openturns as ot
import math as m

[9]:

# create a quadratic function
inputDimension = 3
outputDimension = 2
center = [1.0] * inputDimension
constant = [-1.0, 2.0] # c
linear = ot.Matrix(inputDimension, outputDimension) # A
quadratic = ot.SymmetricTensor(inputDimension, outputDimension) # M
quadratic[0,0,1] = 3.0
function = ot.QuadraticFunction(center, constant, linear, quadratic)
x = [7.0, 8.0, 9.0]
print(function(x))

[-1,56]

[7]:

# draw y1 with x1=2.0, x2=1.0, x0 in [0, 2]
ot.ParametricFunction(function, [1, 2], [2.0, 1.0]).getMarginal(1).draw(0.0, 2.0)

[7]:
../../_images/examples_functional_modeling_quadratic_function_4_0.svg