Cond with 1 or inf norm returns 1 for a matrix of all zeros

[btracey]

package main

import (
    "fmt"
    "math"

    "github.com/gonum/matrix/mat64"
)

func main() {
    a := mat64.NewDense(1, 1, nil)
    fmt.Println(mat64.Cond(a, 1))
    fmt.Println(mat64.Cond(a, 2))
    fmt.Println(mat64.Cond(a, math.Inf(1)))
}

This may be a bizarre quirk of the lapack function, but this should not be the final output from mat64.

[kortschak]

Should Cond(zero, 2) be NaN or Inf? I can see arguments both ways. Also note that 1 is only returned for square matrices; non-square return Inf.

[kortschak]

There is a trivial fix and I believe this is a bug in LAPACK. DGECON returns early if anorm == 1 and so does the native Gecon as we would expect given the provenance. If this early exit is removed, +Inf is returned by mat64.Cond(zero, .... Presumably we should be returning 0 here instead.

[kortschak]

Also note that native Trcon returns 1 for n=0 where Gecon returns 0. Presumably these should agree.

[kortschak]

Whooops.

I was just about to file an issue with NETLIB and no. The issue is a transcription error, one that explains the difference between Gecon and Trcon. The PR above will now reflect that discovery.

[btracey]

Ah, sorry.

I would think that it should return Inf. It's very convenient to have comparisons work correctly (with a specific condition number), and I don't see any usefulness in NaN relative to Inf.

[kortschak]

No worries. It presumably will return Inf when SVD is fixed to use lapack routines. I think the LAPACK behaviour for zero sized matrices is wrong, but we don't see that in mat64 because we panic anyway.