Complex scalar transforms for mmax<lmax

[plw0315]

Hi Nathanael,

Does the fortran subroutine

shtns_sh_to_spat_cplx(alm,z) and shtns_spat_cplx_to_SH(z,alm)

work for the case when mmax < lmax? If it does work, how is the SH coefficient stored in the array alm? Thanks!

[Nathanaël Schaeffer]

Hello,

That is a good question!

It turns out it works for mmax<lmax, but with the same storage convention as for mmax=lmax. This means that the storage for all coefficients up to m=lmax must be provided, but the coefficients for m>mmax are simply ignored. This is of course a huge waste of space when mmax << lmax. I never though about this issue, so I'm open to ideas for a better storage scheme.

[plw0315]

Hello,

It's good to know that it works for mmax<lmax. About storage scheme for the SH coefficients in fortran, I have the following suggetion:

for l =0, mmax
SH_coef( m, l ) = alm( l(l+1) + m +1 ),
for l = mmax+1, lmax
SH_coef( m, l ) = alm( (mmax+1)^2 + (2*mmax+1)*(l-mmax-1) + m+mmax+1 )

Is it easy to make such a change in your code?

[Nathanaël Schaeffer]

Hi,

Fairly easy. I just pushed a new commit with your storage scheme implemented. sht_func.c is the only file that has changed, and you can grab it here.

Please check that it works as intended, any feedback appreciated.

Cheers,

[plw0315]

Hi,

Have you resolved this error message yet? This is the error message when I set mmax<lmax. I only need mres=1, which is not a problem for me. Thanks!

[SHTns] Run-time error : complex SH requires lmax=mmax and mres=1.

[Nathanaël Schaeffer]

Yes, this error message is gone.

[plw0315]

By the way, are the subroutines and functions in your library thread-safe? I am thinking use them within a paralleled do loop.

[Nathanaël Schaeffer]

Yes, all the full-transform (which means function that have inverse counterparts) routines are guaranteed thread-safe. The routines that are not thread-safe are *_to_lat().

If you do this, don't forget to disable the internal use of threads, with a call to shtns_use_threads(1)

[plw0315]

Hello,

The updated version works fine as desired. Thank you very much!