fluiddyn.calcul.sphericalharmo

Spherical harmonics operators (fluiddyn.calcul.sphericalharmo)

This module requires the C library shtns. To install it, run something like:

./configure --enable-openmp --enable-python
make && make install

class fluiddyn.calcul.sphericalharmo.EasySHT(lmax=15, mmax=None, mres=1, norm=None, nlat=None, nlon=None, flags=None, polar_opt=1e-08, nl_order=2, radius=6367470.0)

Bases: object

Simple possibilities of shtns.

Less possibilities but very simple to use… It has been written specially for atmospheric applications.

Creation of a default instance:

esh = EasySHT(lmax=15)

Parameters:

lmaxnumber {15}

Truncation degree.

mmax{None, int}

If is None, triangular truncation.

mres1

Azimutal symmetry coefficient (see shtns documentation).

norm=shtns.sht_fourpi

For SH with quadratic mean equal to unity.

nlat{None, int}

If None, computed by shtns to avoid aliasing.

nlon{None, int}

If None, computed by shtns to avoid aliasing.

flags{sht_quick_init|SHT_PHI_CONTIGUOUS|SHT_SOUTH_POLE_FIRST, int}

Option flag for shtns.

polar_opt{1.0e-8, float}

Polar optimization threshold.

nl_order{2, int}

Nonlinear order of the equations (used to compute nlat and nlon).

radius{radius_earth, number}

Radius of the sphere (in meters)

Notes

In contrast as with shtns, with easypysht the meridional unit vector points towards the North if shtns.SHT_SOUTH_POLE_FIRST is used (this is the default) and it points towards the South if shtns.SHT_SOUTH_POLE_FIRST is not given in flags (thus there is a change of sign in the meridional velocity).

easypysht has been written for atmospheric applications thus some usual notations are used.

Here are some definitions useful to understand the code:

• l denotes the degree of the spherical harmonic functions

• m denotes the order of the spherical harmonic functions

• SH denotes spherical harmonic (spectral array)

• spat denotes spatial array

• lat denotes latitude

• lon denotes longitude

• kh denotes horizontal wavenumber

• u denotes longitudinal velocity

• v denotes meridional velocity (the sign depends on the used base)

• hdiv denotes horizontal divergence

• hrot denotes vertical vorticity (curl on the sphere)

• grad denotes the horizontal gradient

Variables and functions about spectral space array: lmax, mmax, mres, nlm, idx_lm(), l_idx, m_idx, l2_idx

Variables about grid and real space array: nlat, nlon, lats, lons, sin_lats, LATS, LONS

Variables for spectra: l2_l, kh_l

self.sh is the instance of the class sht defined in shtns.py. All functions and variables of this class can be used directly from this instance, for example:

esh.sh.sh_to_point(f_lm, cost, phi)

where t is the colatitude and phi is the longitude.

produce_str_describing_oper()

Produce a string describing the operator.

idx_lm(self, l, m)

create_array_sh(value=None, dtype=<class 'complex'>)

Create an array representing a field in spectral space.

create_array_spat(value=None)

Create an array representing a field in spatial space.

sh_from_spat(field, field_lm=None)

Spherical harmonic transform.

examples: f_lm = sh_from_spat(f)

or if f_lm already exists: sh_from_spat(f, f_lm)

spat_from_sh(field_lm, field=None)

Inverse spherical harmonic transform.

chrono_sht(nb_sht=10)

Microbenchmark forward and inverse SHT, and vorticity, divergence <-> u, v transformations.

uv_from_hdivrotsh(hdiv_lm, hrot_lm, uu=None, vv=None)

u, v from div, rot (u and v are overwritten)

hdivrotsh_from_uv(uu, vv, hdiv_lm=None, hrot_lm=None)

Compute hdivrotsh from uuvv.

(div_lm and rot_lm are overwritten)

uv_from_uDuRsh(uD_lm, uR_lm, uu=None, vv=None)

Compute velocities uu, vv from uD, uR (uu and vv are overwritten).

uDuRsh_from_uv(uu, vv, uD_lm=None, uR_lm=None)

Compute helmholtz decomposition of the velocities from uu, vv. (uD_lm and uR_lm are overwritten).

hdivrotsh_from_uDuRsh(uD_lm, uR_lm, hdiv_lm=None, hrot_lm=None)

Compute horizontal divergence and vertical vorticity spherical harmonics from velocity vector spherical harmonics (hdiv_lm and hrot_lm are overwritten).

uDuRsh_from_hdivrotsh(hdiv_lm, hrot_lm, uD_lm=None, uR_lm=None)

Compute velocity vector spherical harmonics from horizontal divergence and vertical vorticity spherical harmonics (uD_lm and uR_lm are overwritten).

gradf_from_fsh(f_lm, gradf_lon=None, gradf_lat=None)

gradf from fsh.

Compute the gradient of a function f from its spherical harmonic coeff f_lm (gradf_lon and gradf_lat are overwritten)

sum_wavenumbers(field_lm)

Convenient function to look more like a pseudo-spectral Operators

_spectrum_from_array_desh(array_desh)

Compute spectrum(l) from array_desh(ilm)

_array_desh_from_sh(field_lm, key_field)

Compute the array_desh (density of energy) from an field_lm

spectrum_from_sh(field_lm, key_field)

compute spectrum from field_lm

cospectrum_from_2fieldssh(f_lm, g_lm)

compute cospectrum(l) from f_lm(ilm) and g_lm(ilm)

cospectrum_from_2vectorssh(f_lon_lm, f_lat_lm, g_lon_lm, g_lat_lm)

compute cospectrum(l)…

cospectrum_from_2fieldssh2(f_lm, g_lm)

compute cospectrum(l)…

cospectrum_from_2divrotsh(hdiva_lm, hrota_lm, hdivb_lm, hrotb_lm)

compute cospectrum(l)…

dealiasing(field_lm)

Convenient function for fluidsim

Functions

bin_int(n, width)
compute_lmax(nlat[, nl_order])
compute_nlatnlon(lmax[, nl_order])

Classes

EasySHT([lmax, mmax, mres, norm, nlat, ...])

Simple possibilities of shtns.