fluidsht.sht2d.operators¶
Operators 2D (fluidfft.sht2d.operators
)¶
-
class
fluidsht.sht2d.operators.
OperatorsSphereHarmo2D
(nlat=None, nlon=None, lmax=15, norm='orthonormal', cs_phase=False, grid_type='gaussian', radius=1, sht=None)[source]¶ Bases:
object
Perform 2D SHT and operations on data.
- Parameters
- nlatint
Global dimension over the theta-axis (?? dimension for the real arrays).
- nlonint
Global dimension over the phi-axis (?? dimension for the real arrays).
- lmaxint
Truncation degree.
- normstr
Normalization for SHT transforms. See
options_norm
in the respective modules for available options.- cs_phasebool
Disable (default) or enables the Condon-Shortley phase factor to the associated Legendre functions;
- radiusfloat
Radius of the sphere
- sht: str or SHT classes
Name of module or string characterizing a method. It has to correspond to a module of fluidsht. The first part “fluidsht.” of the module “path” can be omitted.
Notes
Some of the class attributes and their equivalent mathematical definitions
\[\begin{split}\texttt{l2_idx} &= l(l+1) \\ \texttt{K2} &= \frac{l(l+1)}{r^2} &= -\Delta \\ \texttt{K2_r} &= \texttt{K2} \times r &= \frac{l(l+1)}{r} \\ \texttt{inv_K2_r} &= \texttt{K2_r}^{-1} &= \frac{r}{l(l+1)}\end{split}\]where, \(\Delta = \nabla^2 :=\) Laplacian operator.
-
nlm
: int = None¶
-
K2
: Af = None¶
-
inv_K2_not0
¶
-
K2_r
¶ Compute \(r \Delta = [l(l+1)] / r\)
-
inv_K2_r
¶ Compute \((r \Delta)^{-1} = r / [l(l+1)]\)
-
where_l2_idx_positive
¶
-
laplacian_sh
(self, a_lm: 'complex128[:]', negative: bool = False)[source]¶ Compute the Laplacian, \(\nabla^{n} a^{lm}\)
- Parameters
- a_lmndarray
- negative: bool, optional
Negative of the result.
-
invlaplacian_sh
(self, a_lm: 'complex128[:]', negative: bool = False)[source]¶ Compute the Laplacian, \(\nabla^{n} a^{lm}\)
- Parameters
- a_lmndarray
- negative: bool, optional
Negative of the result.
-
divrotsh_from_vsh
(self, uD_lm: 'complex128[:]', uR_lm: 'complex128[:]', div_lm: 'complex128[:] or None' = None, rot_lm: 'complex128[:] or None' = None)[source]¶ Compute divergence and curl from vector spherical harmonics uD, uR (
div_lm
androt_lm
are overwritten).
-
vsh_from_divrotsh
(self, div_lm: 'complex128[:]', rot_lm: 'complex128[:]', uD_lm: 'complex128[:] or None' = None, uR_lm: 'complex128[:] or None' = None)[source]¶ Compute VSH from divergence and curl spherical harmonics
div_lm
,rot_lm
(uD_lm
anduR_lm
are overwritten).
-
vec_from_divrotsh
(self, div_lm, rot_lm, u=None, v=None)[source]¶ Velocities u, v from horizontal divergence, and vertical vorticity (u and v are overwritten).
-
vec_from_rotsh
(self, rot_sh, u=None, v=None)[source]¶ Velocities u, v from vertical vorticity alone (u and v are overwritten).
Functions
|
Easily select an available SHT library. |
Classes
|
Perform 2D SHT and operations on data. |