Commit 6cf5eab3 authored by Martin Bauer's avatar Martin Bauer
Browse files

Added documentation

parent eb7c6efb
......@@ -69,9 +69,10 @@ def multi_differentiation(generating_function, index, symbols):
Computes moment from moment-generating function or cumulant from cumulant-generating function,
by differentiating the generating function, as specified by index and evaluating the derivative at symbols=0
:param generating_function: function with is differentiated
:param index: the i'th index specifies how often to differentiate w.r.t. to symbols[i]
:param symbols: symbol to differentiate
Args:
generating_function: function with is differentiated
index: the i'th index specifies how often to differentiate w.r.t. to symbols[i]
symbols: symbol to differentiate
"""
assert len(index) == len(symbols), "Length of index and length of symbols has to match"
......@@ -119,9 +120,10 @@ def __continuous_moment_or_cumulant(func, moment, symbols, generating_function):
def continuous_moment(func, moment, symbols=None):
"""Computes moment of given function.
:param func: function to compute moments of
:param moment: tuple or polynomial describing the moment
:param symbols: if moment is given as polynomial, pass the moment symbols, i.e. the dof of the polynomial
Args:
func: function to compute moments of
moment: tuple or polynomial describing the moment
symbols: if moment is given as polynomial, pass the moment symbols, i.e. the dof of the polynomial
"""
return __continuous_moment_or_cumulant(func, moment, symbols, moment_generating_function)
......
......@@ -43,7 +43,7 @@ def __partition(collection):
def __cumulant_raw_moment_transform(index, dependent_var_dict, outer_function, default_prefix, centralized):
"""Function to express cumulants as function of moments as vice versa.
"""Function to express cumulants as function of moments and vice versa.
Uses multivariate version of Faa di Bruno's formula.
......
......@@ -199,6 +199,24 @@ def get_moments_of_discrete_maxwellian_equilibrium(stencil, moments,
def compressible_to_incompressible_moment_value(term, rho, u):
"""Compressible to incompressible equilibrium moments
Transforms so-called compressible equilibrium moments (as obtained from the continuous Maxwellian) by
removing the density factor in all monomials where velocity components are multiplied to the density.
Examples:
>>> rho, *u = sp.symbols("rho u_:2")
>>> compressible_to_incompressible_moment_value(rho + rho * u[0] + rho * u[0]*u[1], rho, u)
rho + u_0*u_1 + u_0
Args:
term: compressible equilibrium value
rho: symbol for density
u: symbol for velocity
Returns:
incompressible equilibrium value
"""
term = sp.sympify(term)
term = term.expand()
if term.func != sp.Add:
......
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