LaguerreLaplaceConvolution: function LaguerreLaplaceConvolution

In LaplaceDeconv: Laplace Deconvolution with Noisy Discrete Non-Equally Spaced Observations on a Finite Time Interval

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)

LaplaceDeconv documentation built on May 2, 2019, 11:12 a.m.