Complex number version

[joecomp]

Hi all

Do you plan to do a complex version of your package ?

Thanks in advance for your answer.

Regards

[xinxing02]

Hi,

For points in complex space, I think the current method cannot do it. If you mean a complex function with points in real space, one temporary solution could be to manually split your kernel function into real and complex parts, and split the matrix vector multiplication into four corresponding parts. A simple wrapper function for matvec should be good.

So far we don't have specific plan to extend to complex kernel function yet, but it's definitely doable. We will let you know once we decided or worked it out.

Xin

[joecomp]

Hi Xin

Thanks for your quick answer

This is my matrix A that is made of complex number (a + ib)

I was interested by the HSS factorization and solve.

Regards

[xinxing02]

I think it is also doable to have HSS factorization and solve for complex kernel matrices if your kernel function is symmetric or hermitian.

Simply changing the current general data type 'DTYPE' to 'complex' cannot work because (1) DTYPE is used for both coordinates and matrix entries, and (2) if you are concerned about Hermitian matrix, then admissible blocks B_ij = B_ji* and this requires additional modifications in H2Pack, since presently, H2Pack always assumes B_ij = B_ji^T.

In order to support complex matrices, we will need to (1) split the data type for coordinates and matrix entries, and (2) add flag and corresponding operations for Hermitian matvec/factorization/solve. Right now, I'm not sure when we would work on it.

Thanks,
Xin.

[xinxing02]

Also, we may also need to take conjugate of the basis matrices Ui in some operations for Hermitian H2/HSS matrices.