Description Usage Arguments Details Value Examples
This function generates M decreasing eigenvalues.
1 |
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:
ν_m = (M+1-m)/m.
"exponential":
The eigenvalues start at 1 and decrease
exponentially towards 0:
ν_m = exp(-(m-1)/2).
"wiener":
The eigenvalues correspond to the eigenvalues of the Wiener
process:
ν_m = (pi/2 * (2m-1))^(-2)
A vector containing the M
decreasing eigenvalues.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | 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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