Getting Started

Getting Started

First, import the package.

julia> using LsqFit

Define a two-parameter exponential decay model, where $t$ is a one-element independent variable, $p_1$ and $p_2$ are parameters.

The model function is:

\[m(t, \boldsymbol{p}) = p_1 \exp(-p_2 t)\]
julia> # t: array of independent variable
julia> # p: array of model parameters
julia> model(t, p) = p[1] * exp.(-p[2] * t)

For illustration purpose, we generate some fake data.

julia> # tdata: data of independent variable
julia> # ydata: data of dependent variable
julia> tdata = linspace(0,10,20)
julia> ydata = model(tdata, [1.0 2.0]) + 0.01*randn(length(tdata))

Before fitting the data, we also need a initial value of parameters for curve_fit().

julia> p0 = [0.5, 0.5]

Run curve_fit() to fit the data and get the estimated parameters.

julia> fit = curve_fit(model, tdata, ydata, p0)
julia> param = fit.param
2-element Array{Float64,1}:

LsqFit.jl also provides functions to exam the goodness of fit. estimate_covar(fit) computes the estimated covariance matrix.

julia> cov = estimate_covar(fit)
2×2 Array{Float64,2}:
 0.000116545  0.000174633
 0.000174633  0.00258261

standard_error(fit) returns the standard error of each parameter.

julia> se = standard_error(fit)
2-element Array{Float64,1}:

To get the confidence interval at 10% significance level, run confidence_interval(fit, alpha), which essentially computes the estimate parameter value ± (standard error * critical value from t-distribution).

julia> confidence_interval = confidence_interval(fit, 0.1)
2-element Array{Tuple{Float64,Float64},1}:
 (0.992333, 1.02977)
 (1.98537, 2.16162)

For more details of LsqFit.jl, check Tutorial and API References section.