Error: stack overflow when solving linear system for different types

[andreasnoack]

I am puzzled by

randn(3,3)\complex(randn(3))
error: stack overflow

as I cannot understand why it is not returning a "no method" error.

[vtjnash]

It looks like these two generic definitions are getting involved:

\(x,y) = y/x
(/)(A::StridedVecOrMat, B::StridedVecOrMat) = (B' \ A')'

(for your reference, found using which( \ , randn(3,3), complex(randn(3)) ) )

[andreasnoack]

Thank you. In particular for pointing to which.

Is it right to have right division as the fall back behaviour for left division? I would think of it more as a special feature for numbers maybe. If it is right, I can fix the matrix devision to catch this issue.

[ViralBShah]

Yes, we should really just implement this case by calling LAPACK, rather than depending on the fallback. It would also end up having better performance, due to avoiding the transpose.

While fixing this, it is also worthwhile to implement the various ldiv/rdiv transpose operators, by dispatching to LAPACK and avoiding the computation of the transposes.

A_ldiv_Bc
A_ldiv_Bt
Ac_ldiv_B
Ac_ldiv_Bc
At_ldiv_B
At_ldiv_Bt
A_rdiv_Bc
A_rdiv_Bt
Ac_rdiv_B
Ac_rdiv_Bc
At_rdiv_B
At_rdiv_Bt

[andreasnoack]

I shall give it a try, but I would like to hear the argument for having (x::Any,y::Any)=x/y and not restricting it to (x::Number,y::Number)=x/y.

[vtjnash]

Note that it is actually defined as x\y == y/x, which is true for all types by the definition of Julia's left division operator. (I made the same mistake when I first saw that definition and almost suggested the same thing)

[JeffBezanson]

The idea is that there is a set of "core operators" (sounds ilke something to document!) that are the minimal ones to implement, and other operators can be derived from those if necessary. / is a core operator, \ is not.

[andreasnoack]

But is it necessary to have these core operators defined for Any? Maybe I do not get it, but I think that they are only core for number types. Could they be restricted to numbers?

[StefanKarpinski]

I think that is probably the right thing to do.

[ViralBShah]

Yes, it does seem sensible to restrict to Number.

[johnmyleswhite]

I think restricting this to Number is definitely the right way to go.

[andreasnoack]

Pull request #1427 solves this issue.