Thanks for the explanation.
I'm taking a class (in grad school these days) on advanced derivatives
(financial, not calculus). One of the valuation strategies involves
building two matrices and then solving. This matrix is for the
particular group of call options I selected based on other criteria. It
is strange that all of the other ones I've tried will solve, but this
one won't Perhaps it is a function of my OS or R version. (I'm using
32bit R on a Mac. ).
Thanks!
-N
On 11/20/10 9:24 PM, bill.venab...@csiro.au wrote:
> 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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