View source: R/alphafrontier.3d.r
alphafrontier.3d | R Documentation |
3d representation of alpha-quantile frontier for a set of reference points (xobs,yobs) in the case of two input and one output. No representation yet for hyperbolic direction.
alphafrontier.3d(xobs, yobs, type="output",alpha=0.95, digits=4,
box.leg=TRUE, palette=heat_hcl, rgl=FALSE, n.class=NULL, ...)
xobs |
a matrix of size |
yobs |
a matrix of size |
type |
a character, "output" or "input" direction |
alpha |
a scalar |
digits |
a precision parameter to compute the alpha-frontier |
box.leg |
representation of a legend-box on the plot with the values of frontier |
palette |
function to use for colors in case where option |
rgl |
a boolean, for output direction, representation of the graphic in 3d if TRUE |
n.class |
a numeric, for output direction, the number of class |
... |
usual parameters of function |
In "input" direction:
You choose a value of output in the legend box, the efficiency-frontier of the input is represented with the corresponding color on the 2d graphic.
In "output" direction :
For calculate the alpha-quantile efficiency output frontier everywhere, we have
constructed a grid of size n \times n
by drawing vertical and horizontal lines
which intersect each reference observations. Then, we have calculated for each cell C_k
k=1,...,n^2
the prediction of the alpha-quantile output
efficiency frontier which correspond to the \alpha^{th}
elements of the suite
\{y_j\}_{j=1,...,n_k}
where reference observations j,
j=1,...,n_k
verify
\ x^1_j\leq\inf_{(x^1,x^2) \in C_k}x^1
and
x^2\leq\inf_{(x_1,x_2) \in C_k}x^2
.
We propose to use an algorithm which filled up cells with colors depending on the values
taken by the alpha-quantile output efficiency frontier. The algorithm attach the row
and vary the column as the folling figure can show it.
no values
The algorithm used is certainly not optimized. For a data set of 61 observations, the function necessits 15.17s on an Optiplex GX745 2 duo 2.13GHz under Windows Vista and probably bugs beyond a certain number of observation
Abdelaati Daouia and Thibault Laurent
alphascore
data(spain)
xyn <- cbind(spain[, 3:4],spain[, 1])
xtab <- as.matrix(xyn[, c(1,2)])
ytab <- matrix(xyn[, 3])
# representation in 2-d
op <- par(no.readonly = TRUE) # the whole list of settable par's.
alphafrontier.3d(xtab, ytab, type = "output", alpha = 0.6, xlab = "input 1",
ylab = "input 2", main = "blabla")
points(xtab, pch = 16)
par(op)
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