eVal | R Documentation |
This function generates M
decreasing eigenvalues.
eVal(M, type)
M |
An integer, the number of eigenvalues to be generated. |
type |
A character string specifying the type of eigenvalues that should be calculated. See Details. |
The function implements three types of eigenvalues:
"linear":
The eigenvalues start at 1
and decrease linearly
towards 0
:
\nu_m = \frac{M+1-m}{m}.
"exponential":
The eigenvalues start at 1
and decrease
exponentially towards 0
:
\nu_m =
\exp\left(-\frac{m-1}{2}\right).
"wiener":
The eigenvalues correspond to the eigenvalues of the Wiener
process:
\nu_m = \frac{1}{(\pi/2 \cdot (2m-1))^2}.
A vector containing the M
decreasing eigenvalues.
oldpar <- par(no.readonly = TRUE)
# simulate M = 10 eigenvalues
M <- 10
eLin <- eVal(M = M, type = "linear")
eExp <- eVal(M = M, type = "exponential")
eWien <- eVal(M = M, type = "wiener")
par(mfrow = c(1,1))
plot(1:M, eLin, pch = 20, xlab = "m", ylab = expression(nu[m]), ylim = c(0,1))
points(1:M, eExp, pch = 20, col = 3)
points(1:M, eWien, pch = 20, col = 4)
legend("topright", legend = c("linear", "exponential", "wiener"), pch = 20, col = c(1,3,4))
par(oldpar)
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