If, as reported, the behaviour is fundamentally similar on MacOS X,
Linux and IRIX then it would appear that this is a feature(bug?) of
the LAPACK reference implementation and that whoever wrote the Windows
version saw fit to improve on it. I don't think LAPACK ever pretended
to properly handle NaNs.
Although both Linux and OSX produce an error the behavior of LAPACK is
not similar.
(It would be nice if someone using Windows could try the following test
too)
(1) Compile the following C code
void testdgesv(long* N, long* NRHS, double* A, long* LDA, long* IPIVOT,
double* B, long* LDB, long* INFO)
{
DGESV(N, NRHS, A, LDA, IPIVOT, B, LDB, INFO);
}
(you will have to use the right combination of case and _s)
(2) Run these commands in R:
dyn.load("test.so")
N <- as.integer(3)
NRHS <- as.integer(3)
A <- matrix(as.double(NaN), 3, 3)
LDA <- as.integer(3)
IPIVOT <- integer(3)
B <- diag(3)
storage.mode(B) <- "double"
LDB <- as.integer(3)
INFO <- as.integer(0)
.C("testdgesv", N = N, NRHS = NRHS, A = A, LDA = LDA, IPIVOT = IPIVOT,
B = B, LDB = LDB, INFO = INFO, NAOK = TRUE)
$N
[1] 3
$NRHS
[1] 3
$A
[,1] [,2] [,3]
[1,] NaN NaN NaN
[2,] NaN NaN NaN
[3,] NaN NaN NaN
$LDA
[1] 3
$IPIVOT
[1] 1 2 3
$B
[,1] [,2] [,3]
[1,] 1 0 0
[2,] 0 1 0
[3,] 0 0 1
$LDB
[1] 3
$INFO
[1] 3
//////////////////
On my Mac mini this exits with no errors or warnings (other than INFO =
3 anyway). However,
solve(A)
generates the error:
Error in solve.default(A) : Lapack routine dgesv: system is exactly
singular
This behavior seems to suggest that error is generated somewhere in R,
not in LAPACK.
Okay, now for the weird bit.
When I run this in Linux I get:
> .C("testdgesv", N = N, NRHS = NRHS, A = A, LDA = LDA, IPIVOT =
IPIVOT, B = B, LDB = LDB, INFO = INFO, NAOK = TRUE)
$N
[1] 3
$NRHS
[1] 3
$A
[,1] [,2] [,3]
[1,] NaN NaN NaN
[2,] NaN NaN NaN
[3,] NaN NaN NaN
$LDA
[1] 3
$IPIVOT
[1] 3 2 3
$B
[,1] [,2] [,3]
[1,] NaN NaN NaN
[2,] NaN NaN NaN
[3,] NaN NaN NaN
$LDB
[1] 3
$INFO
[1] 0
where INFO == 0 indicates "successful exit" but
> solve(A)
Error in solve.default(A) : system is computationally singular:
reciprocal condition number = 0
In case it is important:
platform powerpc-apple-darwin7.8.0
arch powerpc
os darwin7.8.0
system powerpc, darwin7.8.0
status
major 2
minor 0.1
year 2004
month 11
day 15
language R
and
platform i686-pc-linux-gnu
arch i686
os linux-gnu
system i686, linux-gnu
status
major 2
minor 0.1
year 2004
month 11
day 15
language R
prompt> more Makevars
PKG_LIBS=${LAPACK_LIBS} ${BLAS_LIBS} ${FLIBS}