[Rd] Catching errors from solve() with near-singular matrices

[Ravi Varadhan]

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


--
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