Create Random Matrices
Create random matrices or random points in a unit circle (Matlab style).
rand(n = 1, m = n) randn(n = 1, m = n) randi(imax, n = 1, m = n) randsample(n, k, w = NULL, replacement = FALSE) rands(n = 1, N = 1, r = 1) randp(n = 1, r = 1)
n, m |
integers specifying the size of the matrix |
imax |
integer or pair of integers |
k |
number of elements to return. |
w |
weight vector, used for discrete probabilities. |
replacement |
logical; sampling with or without replacement. |
N |
dimension of a shere, N=1 for the unit circle |
r |
radius of circle, default 1. |
rand(), randn(), randi() create random matrices of
size n x m, where the default is square matrices if m is
missing.
rand() uses the uniform distribution on ]0, 1[, while
randn() uses the normal distribution with mean 0 and standard
deviation 1.
randi() generates integers between imax[1] and imax[2]
resp. 1 and imax, if imax is a scalar.
randsample() samples k elements from 1:n, with or
without replacement, or returns a weighted sample (with replacement),
using the weight vector w for probabilities.
rands() generates uniformly random points on an N-sphere in
the N+1-dimensional space. To generate uniformly random points in the
N-dim. unit cube, take points in S^{N-1} und multiply with
unif(n)^(1/(N-1)).
randp() generates uniformly random points in the unit circle (or in
a circle of radius r).
Matrices of size nxm resp. a vector of length n.
randp() returns a pair of values representing a point in the circle,
or a matrix of size (n,2). rands() returns a matrix of size
(n, N+1) with all rows being vectors of length 1.
The Matlab style of setting a seed is not available; use R style
set.seed(...).
Knuth, D. (1981). The Art of Computer programming; Vol. 2: Seminumerical Algorithms; Chapt. 3: Random Numbers. Addison-Wesley, Reading.
rand(3) randn(1, 5) randi(c(1,6), 1, 10) randsample(10, 5, replacement = TRUE, w = c(0,0,0, 1, 1, 1, 1, 0,0,0)) P <- rands(1000, N = 1, r = 2) U <- randp(1000, 2) ## Not run: plot(U[, 1], U[, 2], pch = "+", asp = 1) points(P, pch = ".") ## End(Not run) #-- v is 2 independent normally distributed elements # u <- randp(1); r <- t(u) %*% u # v <- sqrt(-2 * log(r)/r) * u n <- 5000; U <- randp(n) R <- apply(U*U, 1, sum) P <- sqrt(-2 * log(R)/R) * U # rnorm(2*n) ## Not run: hist(c(P)) ## End(Not run)
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