```
# NOT RUN {
# create a set of independent signals S, glued together by a mixing matrix A
# (note the notation and matrix multiplication direction as we are dealing with
# row rather than column vectors)
set.seed(100)
S <- matrix(runif(10000), 5000, 2)
A <- matrix(c(1, 1, -1, 2), 2, 2, byrow = TRUE)
# the mixed signal X
X = S %*% t(A)
# The function centers and whitens (by the eigenvalue decomposition of the
# unconditional covariance matrix) the data before applying the theICA algorithm.
IC <- fastica(X, n.comp = 2, approach = "symmetric", gfun = "tanh", trace = TRUE,
A.init = diag(2))
# demeaned data:
X_bar = scale(X, scale = FALSE)
# whitened data:
X_white = X_bar %*% t(IC$whiteningMatrix)
# check whitening:
# check correlations are zero
cor(X_white)
# check diagonals are 1 in covariance
cov(X_white)
# check that the estimated signals(S) multiplied by the
# estimated mxing matrix (A) are the same as the original dataset (X)
round(head(IC$S %*% t(IC$A)), 12) == round(head(X), 12)
# do some plots:
par(mfrow = c(1, 3))
plot(IC$S %*% t(IC$A), main = "Pre-processed data")
plot(X_white, main = "Whitened and Centered components")
plot(IC$S, main = "ICA components")
# }
```

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