matrix: Interop between mat64 and cmat128

[btracey]

Not sure what the right place for this is, so here we are.

I'm looking in to the redesign of Eigen. I don't understand how the API surface is supposed to look so that they can interoperate.

The other factorization methods have methods on the extraction type to get the bounds. LFromLU, for example, is a method on *Dense. For Eigen, we want something like

func (c *cmat128.Dense) Eigenvalues(mat64.Eigen){...}

However, we can't add methods to cmat128.Dense in mat64, and I think the plan was to not have cmat128 import mat64. We have the conv routines, but I don't see how they solve this problem.

[kortschak]

For the Eigen values, it seems to me that the best way is to just use a []complex128. The Eigen vectors are the tricky bit.

[btracey]

Yes. Sorry, I meant Eigenvectors

[btracey]

This sort of interop should be determined though before stability. B = A^H * A is a mat64.SymDense; we'll want to pass matrices in both directions.

[kortschak]

This sort of interop should be determined though before stability.

Absolutely. That's why #134 and #283 are in API stability.

[btracey]

Understood.

[kortschak]

B = A^H * A is a mat64.SymDense

I don't think that we can do this nor that we should. If we start with A being complex then the result of that operation is complex, though with the imaginary component being zero. It should be up to the user to either know this or test for it and be able to take the cmat128.Matrix result and extract the real part - this is what conv does.

type symShim struct {
    Matrix
}

func (s simShim) Symmetric() int {
    r, c := s.Dims()
    if r != c {
        panic(mat64.ErrShape)
    }
    return r
}

and then

var tmp cmat128.Dense
tmp.Mul(a.H(), a)
n, _ := tmp.Dims()
b := mat64.NewSymDense(n, nil)
b.CopySym(symShim{conv.NewReal(&tmp)})

[btracey]

The plan is to merge cmat128 and mat64

[btracey]

This has been done.