[R] Unexpected failure of Cholesky docomposition

[Hoffman, Gabriel]

There was a typo in my example.  Here is the fixed version:

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


# It turns out the the *eigen* values are mixed sign.
# That explains the issue
eigen(B)$values

Thanks for you help, especially Bert.

- Gabriel


From: William Dunlap <wdunlap using tibco.com<mailto:wdunlap using tibco.com>>
Date: Tuesday, November 13, 2018 at 12:31 PM
To: Gabriel Hoffman <gabriel.hoffman using mssm.edu<mailto:gabriel.hoffman using mssm.edu>>
Cc: "r-help using r-project.org<mailto:r-help using r-project.org>" <r-help using r-project.org<mailto:r-help using r-project.org>>
Subject: Re: [R] Unexpected failure of Cholesky docomposition

Aren't singular values always positive or zero?  Look at eigen(B)$values to check for positive definiteness.

Fix your example - your B is not symmetric.

Bill Dunlap
TIBCO Software
wdunlap tibco.com<https://urldefense.proofpoint.com/v2/url?u=http-3A__tibco.com&d=DwMFaQ&c=shNJtf5dKgNcPZ6Yh64b-A&r=KdYcmw5SdXylMrTGSuNVkNJulowod64k0PTDC5BHZkk&m=Vq3YaG1EYDN2Fp8XpmcP8kVgEmHvlDEIwLveBpn4R4Q&s=1NN3MX73Jjmlphkfkm-NlTB-XWOrrMMN3zOGzX3y0RE&e=>

On Tue, Nov 13, 2018 at 7:30 AM, Hoffman, Gabriel <gabriel.hoffman using mssm.edu<mailto:gabriel.hoffman using mssm.edu>> wrote:
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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