Unexpected failure of Cholesky docomposition

My understanding is that a Cholesky decomposition should work on any
square, positive definite matrix.  I am encountering an issue where chol()
fails and give the error: "the leading minor of order 3 is not positive
definite"

This occurs on multiple machines and version of R.

Here is a minimal reproducible example:

# initialize matrix
values = c(1,0.725,0,0,0.725,1,0.692,0,0,0.692,1,0.644,0,0,0.664,1)
B = matrix(values, 4,4)

# show that singular values are positive
svd(B)$d

# show that matrix is symmetric
isSymmetric(B)

# B is symmetric positive definite, but Cholesky still fails
chol(B)

Is this a numerical stability issue?  How can I predict which matrices
will fail?

- Gabriel






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