Create a linear least squares modelΒΆ

In this example we are going to create a global approximation of a model response using a linear function:

\underline{y} \, \approx \, \widehat{h}(\underline{x}) \,
= \, \sum_{j=0}^{n_X} \; a_j \; \psi_j(\underline{x})

Here

h(x) = [cos(x_1 + x_2), (x2 + 1)* e^{x_1 - 2* x_2}]

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

# Prepare an input sample
x = [[0.5, 0.5], [-0.5, -0.5], [-0.5, 0.5], [0.5, -0.5]]
x += [[0.25, 0.25], [-0.25, -0.25], [-0.25, 0.25], [0.25, -0.25]]

Compute the output sample from the input sample and a function.

formulas = ['cos(x1 + x2)', '(x2 + 1) * exp(x1 - 2 * x2)']
model = ot.SymbolicFunction(['x1', 'x2'], formulas)
y = model(x)

Create a linear least squares model.

algo = ot.LinearLeastSquares(x, y)
algo.run()

get the linear term

algo.getLinear()

[[ 9.93014e-17 0.998189 ]
[ 4.96507e-17 -0.925648 ]]



get the constant term

algo.getConstant()

[0.854471,1.05305]



get the metamodel

responseSurface = algo.getMetaModel()

plot 2nd output of our model with x1=0.5

graph = ot.ParametricFunction(
    responseSurface, [0], [0.5]).getMarginal(1).draw(-0.5, 0.5)
graph.setLegends(['linear LS'])
curve = ot.ParametricFunction(model, [0], [0.5]).getMarginal(
    1).draw(-0.5, 0.5).getDrawable(0)
curve.setColor('red')
curve.setLegend('model')
graph.add(curve)
graph.setLegendPosition('topright')
view = viewer.View(graph)
plt.show()
y1 as a function of x1

Total running time of the script: ( 0 minutes 0.067 seconds)

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