# Routine plosurfs

Graphical comparison between reference, validation and estimation data (to analyze tracker results only).

### Description

This routine displays a graphical comparison between reference & validation samples $\left\{y_k\in\mathbb{R}, k\in [1, N]\right\}$ & $\left\{y_k\in\mathbb{R}, k\in [1, N_v]\right\}$ obtained for different values $\left\{x_k\in\mathbb{R}^n,k \in [1, N]\right\}$ & $\left\{x_k\in\mathbb{R}^n,k \in [1, N_v]\right\}$ of some explanatory variables $x$, and an associated approximating function $f:\mathbb{R}^n\rightarrow\mathbb{R}$. The local approximation error $f(x_k)-y_k$ and the root-mean-square error are also computed to evaluate the accuracy of the approximation (see errapprox for a complete description).

### Syntax

plosurfs(pop,best,X,Y,names,Xv,Yv,{options})

### Input arguments

The first seven input arguments are mandatory:

 pop Structure containing the main information about the individuals of the final population (as provided by tracker) nbindiv: number of individuals in the population nbinputs: number of explanatory variables (including fictitious variables if any) nbfinputs: number of fictitious variables added to get simpler trees f2nfinputs: row vector (1 x $nbfinputs$) containing the numbers of the explanatory variables associated to the fictitious variables (only if $nbfvar~=0$) degfinputs: row vector (1 x $nbfinputs$) containing the relative degrees of the explanatory variables associated to the fictitious variables (only if $nbfvar~=0$) indiv: cell vector containing a representation of the parse trees associated to the individuals of the population (each component includes 2 cells of char containing the chromosomes associated to the numerator $Pop.indiv\{i\}(1)$ and denominator $Pop.indiv\{i\}(2)$) fitness: vector containing the fitnesses of the individuals of the population nbnodes: vector containing the numbers of nodes of the individuals of the population param: cell vector containing the monomials coefficients (vector) for the individuals of the population ordered as follows: $param\{i\}(1)$ = constant term of the numerator for the $i^{th}$ individual of the population $param\{i\}(2:l+1)$ = coefficients associated to the $l$ numerator monomials for the $i^{th}$ individual of the population (apart from the constant term)$param\{i\}(l+2:l+m+1)$ = coefficients associated to the $m$ denominator monomials for the $i^{th}$ individual of the population (apart from the constant term frozen to 1) nbreg: vector containing the number of regressors associated to any individual in the population ($l+m$) degmax: vector containing the max degree of the regressors associated to any individual in the populationsumdeg: vector containing the total degree associated to any individual in the population best Index of the best individual in the final population, w.r.t. fitness (as provided by tracker) X Values $\left\{x_k\in\mathbb{R}^n,k \in [1, N]\right\}$ of the explanatory variables $x$ used for optimization ($n\times N$ array, where X(:,k) corresponds to $x_k$). Note that $n$ can only be equal to 2 in this routine. Y Samples $\left\{y_k\in\mathbb{R}, k\in [1, N]\right\}$ used for optimization ($1\times N$ array where Y(k) corresponds to $y_k$). names Names of the explanatory variables $x$ ($1\times n$ cell array of strings). Xv Values $\left\{x_k\in\mathbb{R}^n,k \in [1, N_v]\right\}$ of the explanatory variables $x$ used for validation ($n\times N_v$ array, where X(:,k) corresponds to $x_k$). Note that $n$ can only be equal to 2 in this routine. Yv Samples $\left\{y_k\in\mathbb{R}, k\in [1, N_v]\right\}$ used for validation ($1\times N_v$ array where Y(k) corresponds to $y_k$).

The eigth input argument Options is an optional structured variable with fields:

 axlim Row vector [1x6] containing a set of user-defined axis limits corresponding to the Matlab axis comand viewpoint This option is applicable only if 3-D graphs are to be displayed ($n=2$). The row vector [1x2] represents the deviation with respect to the default viewpoint [-145 30] options.viewpoint(1) is the horizontal rotation in degrees about the z-axis, with positive values indicating counter-clockwise rotation options.viewpoint(2) is the vertical elevation in degrees with positive values corresponding to moving above the graphs. The default value is [0 0]

lsapprox
olsapprox
qpapprox
tracker
koala
errapprox
plotapprox
plosurfaces
plofronts