Exponential covariance function over a grid

Description

This function computes the discretisation of an exponential covariance function of the form:

C( s, t ) = α e^{ - β | s - t | }

over a 1D grid [t_0, t_1, …, t_{P-1}], thus obtaining the P \times P matrix of values:

C_{i,j} = C( t_i, t_j ) = α e^{ - β | t_i - t_j | } .

Usage

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Arguments

grid

a vector of time points.

alpha

the alpha parameter in the exponential covariance formula.

beta

the beta parameter in the exponential covariance formula.

See Also

generate_gauss_fdata, generate_gauss_mfdata

Examples

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grid = seq( 0, 1, length.out = 5e2 )

alpha = 0.2
beta = 0.3

dev.new()
image( exp_cov_function( grid, alpha, beta ),
       main = 'Exponential covariance function',
       xlab = 'grid', ylab = 'grid')

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