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ddmu.expr <- function (x)
{
if (dist == "Pythagoras" || dist == "Clark")
{ dist.text <- deparse (dist.expr)[3]
dist.text <- paste ("-0.5", dist.text, sep = "*")
dist.text <- gsub ("xik", x, dist.text)
dist.text <- gsub ("xjk", "mu", dist.text)
dist.expression <- parse (text = dist.text)
AA <- D(dist.expression,"mu")
}
if(dist == "SqrtL1") AA <- expression(-(sign(x-mu)))
return(AA)
}
The derivative of any newly defined distance function must also be specified in a
function ddmu.expr according to the example code given above. The built-in R function
D is then called recursively to obtain the expression for the second-order derivative
as discussed in Section 5.4.2.1 before the integral (5.16) is numerically solved using
my.integrate , a slightly modified version of the built-in R function integrate .
Value
A list with the following components:
1
2 d ij }
The n
×
n matrix
{−
.
D
A matrix with n rows and five columns containing the details of each
sample point to be plotted: two-dimensional coordinates, plotting
character, colour, line type.
Z
A list with each component a matrix containing the details of a
biplot axis to be plotted: two-dimensional coordinates, marker
value, indicator if value is shown as a calibration on the biplot
axis.
Z.axes
All the eigenvalues (squared singular values).
e.vals
Overall quality of two-dimensional biplot display.
quality
Sample predictions for samples specified in predictions.samples .
Only available if straight = TRUE when dist =
"Pythagoras" . Use function CircularNonLinear.
predictions described below to obtain sample predictions for
nonlinear biplots in general.
predictions
Coordinates of the point of concurrency of biplot trajectories.
O.co
5.6.2 Function CircularNonLinear.predictions
This function calculates the predictions on all variables for any point in the display space
of a two-dimensional nonlinear biplot.
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