Notes to cl-random

I failed to fully install cl-random on Mac OS X, although it is available via quicklisp, which makes things way easier. I mainly failed to get cl-rmath (a dependency of cl-random) working properly with libRmath. Although I succeded in compiling and installing libRmath.dylib for my architecture, CFFI gives me the message Unable to load foreign library (LIBRMATH). / Could not register handle for external module LIBRMATH: / no suitable image found. Did find: / /usr/lib/libRmath.dylib: mach-o, but wrong architecture. I have no clue why... Here is what I have achieved so far:

cl-rmath seems not to be needed to correctly draw samples from a multivariate normal distribution. Here is what I did:

• install the following dependencies with quicklisp: alexandria, anaphora, array-operations, cl-num-utils, cl-slice, let-plus, lla
• Loading lla needs blas and lapack to be installed. This blog entry describes how to install it
• If it doesn't find the foreign libraries for lla, you may have to give the path to its directory like this: (push #P"/usr/lib/" cffi:*foreign-library-directories*)
• download the source of cl-random
• you need to load the following files from the src/ folder: internals.lisp, package.lisp, random.lisp, multivariate.lisp as well as the function definition draw-standard-normal from univariate.lisp

You SHOULD now be able to draw random samples from a multivariate normal distribution:

CL-USER 1 > (setf distribution (cl-random::r-multivariate-normal #(1 2)
                                                                 (cl-random::mm t #2a((1 2)
                                                                                      (3 4)))))
#S(CL-RANDOM::R-MULTIVARIATE-NORMAL :N 2 :MEAN #(1 2) :VARIANCE-LEFT-SQRT #<CL-NUM-UTILS.MATRIX:LOWER-TRIANGULAR-MATRIX element-type DOUBLE-FLOAT
  3.16228       .
  4.42719 0.63246>)

CL-USER 2 > (cl-random:draw distribution)
#(0.20293392998246396D0 0.28948779023461224D0)

But if we generate some data and try to re-construct its mean and co-variance matrix, it doesn't fit...

CL-USER 3 > (setf data (loop repeat 1000 collect (coerce (cl-random:draw distribution) 'list)))
((2.777448778345402D0 5.218260204218044D0) (2.4401058735625983D0 4.318675829774026D0) (-3.1800525694534816D0 -2.5749326526079886D0) (3.289998442578751D0 6.533266966322055D0) ...)

CL-USER 4 > (setf lik (make-instance 'mlep:max-likelihood :data-set data))
#<MLEP:MAX-LIKELIHOOD 227B4C83>

CL-USER 5 > (mlep:run lik)
(#(0.7370068251772093D0 1.6190530720731782D0) #2A((9.490688560267179D0 13.240753178128449D0) (13.240753178128449D0 18.8576808919066D0)))

So, the co-variance matrix is clearly not wat we wanted to achieve. I've tested that against numpy.cov from Pythons numpy and got the same results. So mlep:max-likelihood works fine. The samples are drawn wrongly... If you succeed in getting this to work all right and/or know what I've done wrong, please report!

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