Stig's "infamous" Example Matrix
Stig Mortensen wrote on Oct 22, 2007 to the authors of the Matrix
package with subject “Strange result from expm”.
There, he presented the following 8 * 8 matrix for
which the Matrix expm() gave a “strange” result.
As we later researched, the result indeed was wrong: the correct
entries were wrongly permuted. The reason has been in the underlying
source code in Octave from which it had been ported to Matrix.
data(matStig)
Martin Maechler
data(matStig) as(matStig, "sparseMatrix") # since that prints more nicely. ## For more compact printing: op <- options(digits = 4) E1 <- expm(matStig, "Ward77", preconditioning="buggy") # the wrong result as(E1, "sparseMatrix") str(E2 <- expm(matStig, "Pade"))# the correct one (has "accuracy" attribute) as(E2, "sparseMatrix") attr(E2,"accuracy") <- NULL # don't want it below E3 <- expm(matStig, "R_Eigen") # even that is fine here all.equal(E1,E2) # not at all equal (rel.difference >~= 1.) stopifnot(all.equal(E3,E2)) # == ##________ The "proof" that "Ward77" is wrong _________ M <- matStig Et1 <- expm(t(M), "Ward77", precond= "buggy") Et2 <- expm(t(M), "Pade"); attr(Et2,"accuracy") <- NULL all.equal(Et1, t(E1)) # completely different (rel.diff ~ 1.7 (platform dep.)) stopifnot(all.equal(Et2, t(E2))) # the same (up to tolerance) options(op)
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