addit package

Submodules

addit.dit module

addit.dit.rundit(S, nu_lines, beta, gammaL, nu_grid, beta_grid, gammaL_grid)

run DIT

Parameters

  • S – line strength (Nlines)

  • nu_lines – line center (Nlines)

  • beta – Gaussian STD (Nlines)

  • gammaL – Lorentian half width (Nlines)

  • nu_grid – linear wavenumber grid

  • beta_grid – beta grid

  • gammaL_grid – gammaL grid

Returns

Cross section

addit.dit.voigt_kernel(k, beta, gammaL)

Fourier Kernel of the Voigt Profile

Parameters

  • k – conjugated of wavenumber

  • beta – Gaussian standard deviation

  • gammaL – Lorentian Half Width

Returns

kernel (N_x,N_beta,N_gammaL)

Note

Conversions to the (full) width, wG and wL are as follows: wG=2*sqrt(2*ln2) beta wL=2*gamma

addit.interpolate module

addit.interpolate.interp2d(x, y, xp, yp, fp)

interpolation of a 2D function f(x,y) from given precomputed x,y,f arrays.

Parameters

  • x – x value to be evaluated

  • y – y value to be evaluated

  • xp – Arrays defining the data point coordinates for x

  • yp – Arrays defining the data point coordinates for y

  • fp – 2D array of the function to interpolate at the data points.

Returns

f(x,y)

addit.ncf module

Neighbouring Contribution Function

  • Assume a given x-grid xv[k], and a value x. For a 1D case, the Neighbouring Contribution Function gives ncf(k,x) = (x-xv[s])/dv for k=s, (xv[s]-x)/dv for k=s+1, and 0 elsewhere, where s is the nearest index of xv[k] to x but xv[k]<x.

  • For a 2D case, NCF gives the non-zero values for 4 points around (x,y)

addit.ncf.conti(i, x, xv)

neighbouring contribution function for index i.

Parameters

  • i – index

  • x – x value

  • xv – x-grid

Returns

neighbouring contribution function of x to the i-th component of the array with the same dimension as xv.

addit.ncf.inc2D(w, x, y, xv, yv)

integrated neighbouring contribution function for 2D (memory reduced sum).

Parameters

  • w – weight (N)

  • x – x values (N)

  • y – y values (N)

  • xv – x grid

  • yv – y grid

Returns

integrated neighbouring contribution function

Note

This function computes sum_n w_n fx_n otimes fy_n, where w_n is the weight, fx_n and fy_n are the n-th NCFs for 1D. A direct sum uses huge RAM. In this function, we use jax.lax.scan to compute the sum

Example

>>> N=10000
>>> xv=jnp.linspace(0,1,11) #grid
>>> yv=jnp.linspace(0,1,13) #grid
>>> w=np.logspace(1.0,3.0,N)
>>> x=np.random.rand(N)
>>> y=np.random.rand(N)
>>> val=inc2D(w,x,y,xv,yv)
>>> #the comparision with the direct sum
>>> valdirect=jnp.sum(nc2D(x,y,xv,yv)*w,axis=2)
>>> #maximum deviation
>>> print(jnp.max(jnp.abs((val-valdirect)/jnp.mean(valdirect)))*100,"%") #%
>>> 5.196106e-05 %
>>> #mean deviation
>>> print(jnp.sqrt(jnp.mean((val-valdirect)**2))/jnp.mean(valdirect)*100,"%") #%
>>> 1.6135311e-05 %
addit.ncf.inc3D(w, x, y, z, xv, yv, zv)

integrated neighbouring contribution for 3D (memory reduced sum).

Parameters

  • w – weight (N)

  • x – x values (N)

  • y – y values (N)

  • z – z values (N)

  • xv – x grid

  • yv – y grid

  • zv – z grid

Returns

integrated neighbouring contribution

Note

This function computes sum_n w_n fx_n otimes fy_n otimes fz_n, where w_n is the weight, fx_n, fy_n, and fz_n are the n-th NCFs for 1D. A direct sum uses huge RAM. In this function, we use jax.lax.scan to compute the sum

Example

>>> N=10000
>>> xv=jnp.linspace(0,1,11) #grid
>>> yv=jnp.linspace(0,1,13) #grid
>>> zv=jnp.linspace(0,1,17) #grid
>>> w=np.logspace(1.0,3.0,N)
>>> x=np.random.rand(N)
>>> y=np.random.rand(N)
>>> z=np.random.rand(N)
>>> val=inc3D(w,x,y,z,xv,yv,zv)
>>> #the comparision with the direct sum
>>> valdirect=jnp.sum(nc3D(x,y,z,xv,yv,zv)*w,axis=3)
>>> #maximum deviation
>>> print(jnp.max(jnp.abs((val-valdirect)/jnp.mean(valdirect)))*100,"%") #%
>>> 5.520862e-05 %
>>> #mean deviation
>>> print(jnp.sqrt(jnp.mean((val-valdirect)**2))/jnp.mean(valdirect)*100,"%") #%
>>> 8.418057e-06 %
addit.ncf.nc1D(x, xv)

neighbouring contribution function for 1D.

Parameters

  • x – x value

  • xv – x grid

Returns

neighbouring contribution function

Example

>>> xv=jnp.linspace(0,1,11) #grid
>>> print(nc1D(0.23,xv))
>>> [0.         0.         0.70000005 0.29999995 0.         0.  0.         0.         0.         0.         0.        ]
addit.ncf.nc2D(x, y, xv, yv)

neighbouring contribution function for 2D.

Parameters

  • x – x value

  • y – y value

  • xv – x grid

  • yv – y grid

Returns

2D neighbouring contribution function

addit.ncf.nc3D(x, y, z, xv, yv, zv)

neighbouring contribution function for 3D.

Note

See Fig. 1 in van den Bekerom and Pannier (2021) JQSR 261, 107476

Parameters

  • x – x value

  • y – y value

  • z – z value

  • xv – x grid

  • yv – y grid

  • zv – z grid

Returns

3D neighbouring contribution function

Module contents