Integration functions

Functions are available in integration.jl to be able to integrate the area under a region of a spectrum, or to integrate the area under Gaussian, Lorentzian or other peaks built from the functions provided in functions.jl.

Function trapz

At the moment, only two functions are available. trapz is an implementation in Julia of the trapezoïdal integration function available in Matlab for instance. Call it as:

area = trapz(x, y)

INPUTS:

x: Vector{Float64} containing the x values;

y: Vector{Float64} containing the y values;

OUTPUTS:

area: Float64, the trapezoidal integration value

This function is particularly helpful to calculate the area under a portion of a spectrum, and can be used for various purposes (normalisation, area comparison, etc.).

Function gaussianarea

gaussianarea allows to calculate the area under a gaussian peak from its half-width at half maximum (hwhm) and its amplitude, with the possibility of calculating the error based on the inputs of the errors on hwhm and amplitude. Call it as:

area, esearea = gaussianarea(Amplitude,HWHM; eseAmplitude = [0.0], eseHWHM = [0.0])

INPUTS:

Amplitude: Array{Float64} containing the amplitudes

HWHM: Array{Float64} containing the half width at half maximum of the peaks

eseAmplitude: Array{Float64} containing the errors affecting Amplitude

eseHWHM: Array{Float64} containing the errors affecting HWHM

OUTPUTS:

area: Array{Float64} contaning the areas

esearea: Array{Float64} contaning the propagated errors affecting the areas calculations. If eseAmplitude and eseHWHM are not indicated, the function will return 0.0 for esearea, the error made on the area calculation.