Hello.
I am trying to invert a matrix, and I am finding that I can get different
answers depending on whether I set LAPACK true or false using "qr". I had
understood that LAPACK is, in general more robust and faster than LINPACK,
so I am confused as to why I am getting what seems to be invalid answers.
The matrix is ostensibly the Hessian for a function I am optimizing. I want
to get the parameter correlations, so I need to invert the matrix. There
are times where the standard "solve(X)" returns an error, but "solve(qr(X,
LAPACK=TRUE))" returns values. However, there are times, where the latter
returns what seems to be bizarre results.
For example, an example matrix is PLLH (Pareto LogLikelihood Hessian)
alpha theta
alpha 1144.6262175141619082 -0.012907777205604828788
theta -0.0129077772056048 0.000000155437688485563
Running plain "solve (PLLH)" or "solve (qr(PLLH))" returns:
[,1] [,2]
alpha 0.0137466171688024 1141.53956787721
theta 1141.5395678772131305 101228592.41439932585
However, running "solve(qr(PLLH, LAPACK=TRUE)) returns:
[,1] [,2]
[1,] 0.0137466171688024 0.0137466171688024
[2,] 1141.5395678772131305 1141.5395678772131305
which seems wrong as the original matrix had identical entries on the off
diagonals.
I am neither a programmer nor an expert in matrix calculus, so I do not
understand why I should be getting different answers using different
libraries to perform the ostensibly same function. I understand the
extremely small value of d²X/d(theta)² (PLLH[2,2]) may be contributing to
the error, but I would appreciate confirmation, or correction, from the
experts on this list.
Thank you very much,
--Avraham Adler
PS: For completeness, the QR decompositions per "R" under LINPACK and
LAPACK are shown below:
> qr(PLLH)
$qr
alpha theta
alpha -1144.6262175869414932095 0.01290777720653695122277
theta -0.0000112768491646264 0.00000000987863187747112
$rank
[1] 2
$qraux
[1] 1.99999999993641619511209 0.00000000987863187747112
$pivot
[1] 1 2
attr(,"class")
[1] "qr"
>
> qr(PLLH, LAPACK=TRUE)
$qr
alpha theta
alpha -1144.62621758694149320945 0.01290777720653695122277
theta -0.00000563842458249248 0.00000000987863187747112
$rank
[1] 2
$qraux
[1] 1.99999999993642 0.00000000000000
$pivot
[1] 1 2
attr(,"useLAPACK")
[1] TRUE
attr(,"class")
[1] "qr"
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