## Converts CPL parameters (0 to 1) into hinge (x,y) coordinates (date and pdf) that describe a model

### Description

Converts either a vector of parameters, or a matrix of many parameter sets to CPL-model hinges (date and pdf coordinates).

### Usage

CPLparsToHinges(pars, years)

### Arguments

 pars Either a vector of one parameter set, or a matrix of several parameter sets (one set per row). years A vector of years.

### Details

The CPL model requires pars to be of odd length, each between 0 and 1. A n-CPL model has $$2n-1$$ parameters ($$n-1$$ x-parameters and $$n$$ y-parameters) that are mapped to $$n+1$$ PD coordinates (x,y pairs) using a modified Stick Breaking Dirichlet Process. The first and last x-coordinate are set as $$x_{min}$$ and $$x_{max}$$, and the remaining internal x-coordinates are converted from their respective x-parameters using the Beta distribution CDF (where $$\alpha = 1$$ and $$\beta =$$ the number of pieces still to be broken). The y-parameters (between 0 and 1) are converted to y-coordinates in two steps. Firstly, they are mapped from the parameter range (0,1) to the coordinate range (0, $$\infty$$) using the formula $$\frac{1}{(1 - y)^2} - 1$$, and the single remaining y-coordinate is set as $$\frac{1}{(1 - 0.5)^2} - 1$$. Secondly, they are normalised by the total area under the curve, calculated as the sum of the areas under all $$n$$ pieces: $Area = \sum_{i=1}^{n} (\frac{y_i + y_{i+1}}{2})(x_{i+1} - x_i)$

### Examples

	# convert a single random 6-CPL parameter set
x <- CPLparsToHinges(pars=runif(11), years=5500:7500)