[R] solve computationally singular

[xchen]

Hi uRsers,

when inverting a 2 by 2 matrix using solve, I encountered a error message:
solve.default(sigma, tol = 1e-07) :
system is computationally singular: reciprocal condition number
= 1.7671e-017

and then I test the determinant of this matrix: 6.341393e-06.

In my program, I have a condition block that whether a matrix is
invertible like this:
if(det(sigma)<1e-7) return NULL;

but this seems doesnot work to prevent the singularity when inverting a
matrix. I am some confused about the relationship between "reciprocal
condition number" and determinant. Can anybody give me some idea how to
prevent this situation?

Thanks a lot!

Xiaohui

[xchen]

Hi uRsers,

when inverting a 2 by 2 matrix using solve, I encountered a error message:
solve.default(sigma, tol = 1e-07) :
system is computationally singular: reciprocal condition number
= 1.7671e-017

and then I test the determinant of this matrix: 6.341393e-06.

In my program, I have a condition block that whether a matrix is
invertible like this:
if(det(sigma)<1e-7) return NULL;

but this seems doesnot work to prevent the singularity when inverting a
matrix. I am some confused about the relationship between "reciprocal
condition number" and determinant. Can anybody give me some idea how to
prevent this situation?

Thanks a lot!

Xiaohui

[xchen]

Hi uRsers,

when inverting a 2 by 2 matrix using solve, I encountered a error message:
solve.default(sigma, tol = 1e-07) :
system is computationally singular: reciprocal condition number
= 1.7671e-017

and then I test the determinant of this matrix: 6.341393e-06.

In my program, I have a condition block that whether a matrix is
invertible like this:
if(det(sigma)<1e-7) return NULL;

but this seems doesnot work to prevent the singularity when inverting a
matrix. I am some confused about the relationship between "reciprocal
condition number" and determinant. Can anybody give me some idea how to
prevent this situation?

Thanks a lot!

Xiaohui

[Simon Wood]

Post by xchen
Hi uRsers,
system is computationally singular: reciprocal condition number
= 1.7671e-017
and then I test the determinant of this matrix: 6.341393e-06.
In my program, I have a condition block that whether a matrix is
if(det(sigma)<1e-7) return NULL;

- the determinant isn' t the best way of testing for computational
singularity.

For example, in the following `a' is computationally singular (it has a
condition number of 1e18, but it has a determinant of 1e-6)

a<- diag(c(1e6,1e-12))

Post by xchen
a

[,1] [,2]
[1,] 1e+06 0e+00
[2,] 0e+00 1e-12

Post by xchen
det(a)

[1] 1e-06

Post by xchen
solve(a)

Error in solve.default(a) : system is computationally singular: reciprocal
condition number = 1e-18

If you are really only interested in small matrices, then calculation of the
condition number as the ratio of largest to smallest singular values is the
most reliable thing to do (or you could just trap the `solve' errors). See
e.g. Golub and van Loan "Matrix Computations" for efficient condition number
estimators, for larger matrices.

Simon

Post by xchen
but this seems doesnot work to prevent the singularity when inverting a
matrix. I am some confused about the relationship between "reciprocal
condition number" and determinant. Can anybody give me some idea how to
prevent this situation?
Thanks a lot!
Xiaohui
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-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of xchen
Sent: Tuesday, November 07, 2006 2:46 PM
To: r-help at stat.math.ethz.ch
Subject: [R] solve computationally singular

Hi uRsers,

when inverting a 2 by 2 matrix using solve, I encountered a error message:
solve.default(sigma, tol = 1e-07) :
system is computationally singular: reciprocal condition number
= 1.7671e-017

and then I test the determinant of this matrix: 6.341393e-06.

In my program, I have a condition block that whether a matrix is
invertible like this:
if(det(sigma)<1e-7) return NULL;

but this seems doesnot work to prevent the singularity when inverting a
matrix. I am some confused about the relationship between "reciprocal
condition number" and determinant. Can anybody give me some idea how to
prevent this situation?

Thanks a lot!

Xiaohui