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Create a stationary covariance modelΒΆ
This use case illustrates how the User can create a covariance function from parametric models. The library implements the multivariate Exponential model as a parametric model for the covariance function where the spatial covariance function writes:
It is possible to define the exponential model from the spatial covariance matrix rather than the correlation matrix :
with:
We call the amplitude vector and the scale vector.
The library implements the multivariate exponential model thanks to the object ExponentialModel which is created from:
the scale and amplitude vectors : in that case, by default ;
the scale and amplitude vectors and the spatial correlation matrix ;
the scale and amplitude vectors and the spatial covariance matrix ; Then is mapped into the associated correlation matrix and the previous constructor is used.
import openturns as ot
ot.Log.Show(ot.Log.NONE)
Create the amplitude vector (output dimension 3)
amplitude = [1.0, 2.0, 3.0]
# Scale vector (input dimension 1)
scale = [4.0]
# spatialCorrelation
spatialCorrelation = ot.CorrelationMatrix(3)
spatialCorrelation[0, 1] = 0.8
spatialCorrelation[0, 2] = 0.6
spatialCorrelation[1, 2] = 0.1
# spatialCovariance
spatialCovariance = ot.CovarianceMatrix(3)
spatialCovariance[0, 0] = 4.0
spatialCovariance[1, 1] = 5.0
spatialCovariance[2, 2] = 6.0
spatialCovariance[0, 1] = 1.2
spatialCovariance[0, 2] = 0.9
spatialCovariance[1, 2] = -0.2
Create the covariance model from the amplitude and scale, no spatial correlation
ot.ExponentialModel(scale, amplitude)
or from the amplitude, scale and spatialCovariance
ot.ExponentialModel(scale, amplitude, spatialCorrelation)
or from the scale and spatialCovariance
ot.ExponentialModel(scale, spatialCovariance)