What you show below is only a representation of the matrix to 7dp. If you look
at that, though, the condition number is suspiciously large (i.e. the matrix is
very ill-conditioned):
> txt <- textConnection("
+ 0.99252358 0.93715047 0.7540535 0.4579895
+ 0.01607797 0.09616267 0.2452471 0.3088614
+ 0.09772828 0.58451468 1.4907090 1.8773815
+ -0.01000000 0.00000000 0.0900000 0.1700000
+ ")
> mat <- matrix(scan(txt, quiet = TRUE), ncol = 4, byrow = TRUE)
> close(txt)
>
> with(svd(mat), d[1]/d[4])
[1] 82473793
With this representation, though, the matrix does seem to allow inversion on a
windows 32 bit machine:
> solve(mat)
[,1] [,2] [,3] [,4]
[1,] 1.4081192 -7826819 1287643 21.5115344
[2,] -0.3987761 18796863 -3092403 -25.7757002
[3,] -0.1208272 -18836093 3098860 -0.9159397
[4,] 0.1467979 9511648 -1564829 7.6326466
>
and horrible as it is (look closely at columns 2 and 3) it does check out
pretty well:
> mat %*% solve(mat)
[,1] [,2] [,3] [,4]
[1,] 1.000000e+00 -3.060450e-10 1.108447e-10 -1.025872e-15
[2,] 3.571091e-18 1.000000e+00 -5.269385e-11 -1.840975e-16
[3,] 8.201989e-17 2.559318e-09 1.000000e+00 -1.284563e-15
[4,] -3.203479e-18 -8.867573e-11 1.813305e-11 1.000000e+00
>
but a generalized inverse (with default tolerances) is very different
> library(MASS)
> ginv(mat)
[,1] [,2] [,3] [,4]
[1,] 1.27299552 -0.2800302 -1.7022000 16.38665
[2,] -0.07426349 0.1804989 1.0971974 -13.46780
[3,] -0.44601712 0.2273789 1.3821521 -13.24953
[4,] 0.31100880 -0.1368457 -0.8318576 13.86073
>
which emphasises the delicacy of dealing with an ill-conditioned matrix.
Incidently this also checks out fairly well according to the definition of a
ginverse:
> range(mat - mat %*% ginv(mat) %*% mat)
[1] -2.132894e-08 2.128452e-08
>
When dealing with numerical matrices you have to be prepared for the unexpected.
Bill Venables.
-----Original Message-----
From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On
Behalf Of Noah Silverman
Sent: Sunday, 21 November 2010 2:56 PM
To: r-help@r-project.org
Subject: [R] Can't invert matrix
Hi,
I'm trying to use the solve() function in R to invert a matrix. I get
the following error, "Lapack routine dgesv: system is exactly singular"
However, My matrix doesn't appear to be singular.
[,1] [,2] [,3] [,4]
[1,] 0.99252358 0.93715047 0.7540535 0.4579895
[2,] 0.01607797 0.09616267 0.2452471 0.3088614
[3,] 0.09772828 0.58451468 1.4907090 1.8773815
[4,] -0.01000000 0.00000000 0.0900000 0.1700000
Can anyone help me understand what is happening here?
Thanks!
-N
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and provide commented, minimal, self-contained, reproducible code.
