# CMPFit

`mpfit`

library (MINPACK minimization).

A Julia wrapper for the
The `CMPFit.jl`

package is a wrapper for the `mpfit`

C-library by Craig Markwardt, providing access to the the MINPACK implementation of the
Levenberg-Marquardt algorithm, and allowing simple and quick solutions to Least Squares minimization problems in Julia.

**This is a wrapper for a C library, hence it require to download the C code and compile it.**
Check the LsqFit package for a pure Julia solution.

## Installation

To install `CMPFit`

your machine should be equipped with `CMake`

and a C compiler. In the Julia REPL type:

`] add CMPFit`

This will automaticaly download the `cmpfit`

library (v1.3) from Craig's webpage and compile it.

## Usage

Usage is very simple: given a set of observed data and uncertainties, define a (whatever complex) Julia function to evaluate a model to be compared with the data, and ask `cmpfit`

to find the model parameter values which best fit the data.

Example:

```
using CMPFit
# Independent variable
x = [-1.7237128E+00,1.8712276E+00,-9.6608055E-01,
-2.8394297E-01,1.3416969E+00,1.3757038E+00,
-1.3703436E+00,4.2581975E-02,-1.4970151E-01,
8.2065094E-01]
# Observed data
y = [-4.4494256E-02,8.7324673E-01,7.4443483E-01,
4.7631559E+00,1.7187297E-01,1.1639182E-01,
1.5646480E+00,5.2322268E+00,4.2543168E+00,
6.2792623E-01]
# Data uncertainties
e = fill(0., size(y)) .+ 0.5
# Define a model (actually a Gaussian curve)
function GaussModel(x::Vector{Float64}, p::Vector{Float64})
sig2 = p[4] * p[4]
xc = @. x - p[3]
model = @. p[2] * exp(-0.5 * xc * xc / sig2) + p[1]
return model
end
# Guess model parameters
param = [0.0, 1.0, 1.0, 1.0]
# Call `cmpfit` and print the results:
res = cmpfit(x, y, e, GaussModel, param);
println(res)
```

The value returned by `cmpfit`

is a Julia structure. You may look at its content with:

`dump(res)`

Specifically, the best fit parameter values and their 1-sigma uncertainties are:

```
println(res.param)
println(res.perror)
```

`CMPFit`

mirrors all the facilities provided by the underlying C-library, e.g. a parameter can be fixed during the fit, or its value limited to a specific range. Moreover, the whole fitting process may be customized for, e.g., limiting the maximum number of model evaluation, or change the relative chi-squared convergence criterium. E.g.:

```
# Set guess parameters
param = [0.5, 4.5, 1.0, 1.0]
# Create the `parinfo` structures for the 4 parameters used in the
# example above:
pinfo = CMPFit.Parinfo(4)
# Fix the value of the 1st parameter:
pinfo[1].fixed = 1
# Set a lower (4) and upper limit (5) for the 2nd parameter
pinfo[2].limited = (1,1)
pinfo[2].limits = (4, 5)
# Create a `config` structure
config = CMPFit.Config()
# Limit the maximum function evaluation to 200
config.maxfev = 200
# Change the chi-squared convergence criterium:
config.ftol = 1.e-5
# Re-run the minimization process
res = cmpfit(x, y, e, GaussModel, param, parinfo=pinfo, config=config);
println(res)
```

See Craig's webpage for further documentation on the `config`

and `parinfo`

structures.