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Last data update: 2014.03.03

R: function LaguerreLaplaceConvolution

LaguerreLaplaceConvolution

R Documentation

function LaguerreLaplaceConvolution

Description

computes the Laplace convolution of two functions f and g observed at discrete times t. Use trapezoidal formula and an expansion of f in the Laguerre function basis.

Usage

LaguerreLaplaceConvolution(t, g, f.coef, a)

Arguments

`t,`	numeric vector, the observation times
`g,`	numeric vector, the observed values of the known Laplace convolution kernel at the observation times
`f.coef,`	numeric vector, the coefficients in the Laguerre function basis of the function f to convole with g
`a,`	numeric, the scale of the Laguerre functions basis

Value

return the Laplace convolution of f and g using Trapezoidal formula and expansion of f in the Laguerre function basis

Author(s)

Y. Rozenholc and M. Pensky

Examples

## Not run: 

 library(LaplaceDeconv)
 a = 1/2
 t = seq(0,10,l=100)
 g = exp(-5*t)
 f.coef = c(1,0.25,0.1)
 # compute the Laplace convolution from g, kernel computed at times t, and the function described by
 # its decomposition in Laguerre function basis with scale a
 fg = LaguerreLaplaceConvolution(t,g,f.coef,a)
 matplot(t,cbind(MakeLaguerreMatrix(a,3)(t)%*%f.coef,g,fg),lty=1,type='l',ylab='')
 legend('topright',lty=1,legend=c('f','g','fxg'),col=1:3)
 
## End(Not run)