# Routine plosurfaces

Graphical comparison between reference, validation and estimation data (to analyze koala 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

plosurfaces(fsym,X,Y,names,Xv,Yv,Vloo{,CI,options})

### Input arguments

The first seven input arguments are mandatory:

 fsym Symbolic representation of the rational function $f$ (symbolic object), as provided by koala 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 $y_k$). Vloo Variance of a given output (Leave-One-Out type) as computed by koala on the estimation data X ($1\times N$ array).

The eigth and ninth input arguments are optional ones.

 CI Confidence Interval (99%) of a given output as computed by koala on the data options.Xci ($1\times P$ array). options 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 ($n=2$). This $1\times 2$ row vector 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 options.viewpoint=[0 0].

lsapprox
olsapprox
qpapprox
tracker
koala
errapprox
plotapprox
plosurfs
plofronts