R devel - Dec 2012 - Catching errors from solve() with near-singular matrices

Dear all,

The background is that I'm trying to fix this bug in the geometry
package:
https://r-forge.r-project.org/tracker/index.php?func=detail&aid=1993&group_id=1149&atid=4552

Boiled down, the problem is that there exists at least one matrix X for
which det(X) != 0 and for which solve(X) fails giving the error "system
is computationally singular: reciprocal condition number = ..." (see
appended code & attached file). I don't want my function that calls
solve(X) to return an error.

I can think of two strategies for dealing with this problem:

Strategy 1: Some code like this:
   if (det(X) < epsilon) {
      warning("Near singular matrix") 
      return(NULL) 
   }
   return(solve(X))

The problem is then to find what epsilon should be.

Strategy 2: Catch the error thrown by solve(X) like this:

        f <- function(X) {
          invX <- tryCatch(solve(X), error=function(e) {
            warning(e)
            error.flag <<- TRUE})
          if (error.flag) return(NULL)
          return(invX)
        }
        
This works OK if called without a surrounding try() 
        
        ret  <- f(matrix(0, 2, 2))      ## Gives warning
        
However, if I encase the call to f() in a try statement, I get an error: 

        ret1 <- try(f(matrix(0, 2, 2))) ## Gives error "Lapack routine
dgesv: system is exactly singular"

This is undesirable.

Advice on how to solve the problem with either strategy would be much
appreciated - as indeed would be a completely different solution.

All the best,

David.

* * *

Code to throw an error in solve():
> X = as.matrix(read.csv("X.csv"))
> det(X)
[1] 2.32721e-21
> solve(X)
Error in solve.default(X) : 
  system is computationally singular: reciprocal condition number = 1.79977e-16


-- 
David C Sterratt, Research Fellow http://homepages.inf.ed.ac.uk/sterratt
Institute for Adaptive and Neural Computation     tel: +44 131 651 1739
School of Informatics, University of Edinburgh    fax: +44 131 650 6899
Informatics Forum, 10 Crichton Street, Edinburgh EH8 9AB, Scotland  
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
NEW BOOK: Principles of Computational Modelling in Neuroscience
Sterratt, Graham, Gillies & Willshaw (CUP, 2011).
http://www.compneuroprinciples.org  

The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.

Dear David,

I can think of two strategies for dealing with this
problem:
>
> Strategy 1: Some code like this:
>    if (det(X) < epsilon) {
>       warning("Near singular matrix")
>       return(NULL)
>    }
>    return(solve(X))

This solution is probably the easiest one to take, but to match
solve.default, the test should be

  if (rcond(X) < .Machine$double.eps)

Catching that case should avoid the error. I hope this helps.

All the best,
Jon

	[[alternative HTML version deleted]]

I am not sure that this query is appropriate for r-devel, it seems to be more
appropriate for r-help.

In any case,  you might want to try MASS::ginv instead of solve(), if you expect
ill-conditioning.  Here is one possible solution:

        f <- function(X) {
          invX <- tryCatch(ginv(X, tol=.Machine$double.eps),
error=function(e) {
            warning(e)
            error.flag <- TRUE})  # you should avoid the global assignment
`<<-'
          if (error.flag) return(NULL)
          return(invX)
        }

      n <- 14
        A <- matrix(NA, n, n)
for (i in 1:n) for (j in 1:n) A[i,j] <- 1/(i+j-1)

ret  <- f(A)               
ret1 <- try(f(A)) 

Hope this helps,
Ravi

-----Original Message-----
From: r-devel-bounces at r-project.org [mailto:r-devel-bounces at r-project.org]
On Behalf Of David Sterratt
Sent: Tuesday, December 11, 2012 10:14 AM
To: r-devel at r-project.org
Subject: [Rd] Catching errors from solve() with near-singular matrices

Dear all,

The background is that I'm trying to fix this bug in the geometry
package:
https://r-forge.r-project.org/tracker/index.php?func=detail&aid=1993&group_id=1149&atid=4552

Boiled down, the problem is that there exists at least one matrix X for which
det(X) != 0 and for which solve(X) fails giving the error "system is
computationally singular: reciprocal condition number = ..." (see appended
code & attached file). I don't want my function that calls
solve(X) to return an error.

I can think of two strategies for dealing with this problem:

Strategy 1: Some code like this:
   if (det(X) < epsilon) {
      warning("Near singular matrix") 
      return(NULL) 
   }
   return(solve(X))

The problem is then to find what epsilon should be.

Strategy 2: Catch the error thrown by solve(X) like this:

        f <- function(X) {
          invX <- tryCatch(solve(X), error=function(e) {
            warning(e)
            error.flag <<- TRUE})
          if (error.flag) return(NULL)
          return(invX)
        }
        
This works OK if called without a surrounding try() 
        
        ret  <- f(matrix(0, 2, 2))      ## Gives warning
        
However, if I encase the call to f() in a try statement, I get an error: 

        ret1 <- try(f(matrix(0, 2, 2))) ## Gives error "Lapack routine
dgesv: system is exactly singular"

This is undesirable.

Advice on how to solve the problem with either strategy would be much
appreciated - as indeed would be a completely different solution.

All the best,

David.

* * *

Code to throw an error in solve():
> X = as.matrix(read.csv("X.csv"))
> det(X)
[1] 2.32721e-21
> solve(X)
Error in solve.default(X) : 
  system is computationally singular: reciprocal condition number = 1.79977e-16


--
David C Sterratt, Research Fellow http://homepages.inf.ed.ac.uk/sterratt
Institute for Adaptive and Neural Computation     tel: +44 131 651 1739
School of Informatics, University of Edinburgh    fax: +44 131 650 6899
Informatics Forum, 10 Crichton Street, Edinburgh EH8 9AB, Scotland
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * NEW
BOOK: Principles of Computational Modelling in Neuroscience Sterratt, Graham,
Gillies & Willshaw (CUP, 2011).
http://www.compneuroprinciples.org  

The University of Edinburgh is a charitable body, registered in Scotland, with
registration number SC005336.