minPenalty  R Documentation 
This function minimizes
0.5*sum[j=m+1][g] (Delta^m a[j])^2
with respect to a[1],...,a[g] under the constraints
sum[j=1][g] c[j]mu[j] = 0
and
sum[j=1][g] c[j](mu[j]^2 + sigma0^2) = 1,
where
c[j] = exp(a[j])/sum[l=1][g]exp(a[l])
with one of a's fixed to zero.
Note that the minimum is always zero. We are thus mainly interested in the point where the minimum is reached.
minPenalty(knots = NULL, dist.range = c(6, 6), by.knots = 0.3, sdspline = NULL, difforder = 3, init.c, maxiter = 200, rel.tolerance = 1e10, toler.chol = 1e15, toler.eigen = 1e3, maxhalf = 10, debug = 0, info = TRUE)
knots 
A vector of knots mu[1], ..., mu[g]. 
dist.range 
Approximate minimal and maximal knot. If not given by 
by.knots 
The distance between the two knots used when building a vector of knots if these
are not given by 
sdspline 
Standard deviation sigma0^2 of the basis
Gspline (here it appeares only in the variance constraint).
If not given it is determined as 2/3 times the maximal distance between the two knots. If

difforder 
The order of the finite difference used in the penalty term. 
init.c 
Optional vector of the initial values for the Gspline coefficients c, all values must lie between 0 and 1 and must sum up to 1. 
maxiter 
Maximum number of NewtonRaphson iterations. 
rel.tolerance 
(Relative) tolerance to declare the convergence. For this
function, the convergence is declared if absolute value of the
penalty is lower than 
toler.chol 
Tolerance to declare Cholesky decomposition singular. 
toler.eigen 
Tolerance to declare an eigen value of a matrix to be zero. 
maxhalf 
Maximum number of stephalving steps if updated estimate leads to a decrease of the objective function. 
debug 
If nonzero print debugging information. 
info 
If TRUE information concerning the iteration process is printed during the computation to the standard output. 
A list with the components “spline”, “penalty”, “warning”, “fail”.
spline 
A data frame with columns named “Knot”, “SD basis”,
“c coef.” and “a coef.” which gives the optimal values of
c[1],...,c[g] and
a[1],...,a[g] in the latter two columns. This
data.frame can be further worked out using the function 
penalty 
The value of the penalty term when declaring convergence. 
warning 
Possible warnings concerning the convergence. 
fail 
Failure indicator. It is zero if everything went OK. 
Arnošt Komárek arnost.komarek@mff.cuni.cz
optimum < minPenalty(knots=seq(4.2, 4.2, by = 0.3), sdspline=0.2, difforder=3) where < optimum$spline print(where) show < eval.Gspline(where, seq(4.2, 4.2, by=0.05)) plot(show, type="l", bty="n", lwd=2)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.