Complex scalar transforms

[plw0315]

Hi Nathanael,

You make a note in the following page that "SHTns only deals with real spatial data", but you do have two subroutines SH_to_spat_cplx and spat_cplx_to_SH which deal with complex scalar synthesis and analysis. I guess your note about dealing with only real spatial data is outdated, am I right? https://users.isterre.fr/nschaeff/SHTns/spec.html

My second question is about the input and output variables z and alm of the subroutines SH_to_spat_cplx and spat_cplx_to_SH. How do I call them from fortran code? I didn't find the corresponding subroutines in the fortran API. All my following questions are within the context of fortran. You indicate that alm[l*(l+1)+m] is the SH coefficient of order l and degree m (with -l <= m <= l). Do you imply that the indices of alm start at 0? Because for l=0 and m=0, the coefficient is alm(0). Also it is unclear to me what kind of arrary is z? Is it a two dimension array or one dimension? Do the indices start at 0 or 1?

Any help will be greatly appreciated!

[Nathanaël Schaeffer]

Hello,

1) Indeed, this part of the doc is outdated.

2) The Fortran interface is included, but was not documented. From Fortran, you should have access to subroutines shtns_sh_to_spat_cplx(alm, z) and shtns_spat_cplx_to_sh(z, alm).

3) Usage: the doc is for C, which has arrays starting from 0. Simply add 1 to the indices to have Fortran-base indexing: in a Fortran code, you would use alm( l*(l+1)+m+1 ) to access complex coeficient of degree l and order m.

Assuming you use layout = SHT_PHI_CONTIGUOUS (see Fortran example), z is a 2D array defined by z(1:nphi, 1:nlat)

Note that both alm and z are complex-valued arrays. I hope this clarifies the situation, do not hesitate to ask further questions.

[plw0315]

Thanks again!

You have clarified all the questions I have so far. I also successfully called the two subroutines SH_to_spat_cplx and spat_cplx_to_SH. You may already know that your work is very valuable to atomic physics, because in many cases one needs to expand the electron wave function in spherical harmonics.