Legendre2D#
- class astropy.modeling.polynomial.Legendre2D(x_degree, y_degree, x_domain=None, x_window=None, y_domain=None, y_window=None, n_models=None, model_set_axis=None, name=None, meta=None, **params)[source]#
Bases:
OrthoPolynomialBase
Bivariate Legendre series.
Defined as:
\[P_{n_m}(x,y) = \sum_{n,m=0}^{n=d,m=d}C_{nm} L_n(x ) L_m(y)\]where
L_n(x)
andL_m(y)
are Legendre polynomials.For explanation of
x_domain
,y_domain
,x_window
andy_window
see Notes regarding usage of domain and window.- Parameters:
- x_degree
int
degree in x
- y_degree
int
degree in y
- x_domain
tuple
orNone
, optional domain of the x independent variable
- y_domain
tuple
orNone
, optional domain of the y independent variable
- x_window
tuple
orNone
, optional range of the x independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window
- y_window
tuple
orNone
, optional range of the y independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window
- **params
dict
keyword: value pairs, representing parameter_name: value
- x_degree
- Other Parameters:
- fixed
dict
, optional A dictionary
{parameter_name: boolean}
of parameters to not be varied during fitting. True means the parameter is held fixed. Alternatively thefixed
property of a parameter may be used.- tied
dict
, optional A dictionary
{parameter_name: callable}
of parameters which are linked to some other parameter. The dictionary values are callables providing the linking relationship. Alternatively thetied
property of a parameter may be used.- bounds
dict
, optional A dictionary
{parameter_name: value}
of lower and upper bounds of parameters. Keys are parameter names. Values are a list or a tuple of length 2 giving the desired range for the parameter. Alternatively, themin
andmax
properties of a parameter may be used.- eqcons
list
, optional A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqcons
list
, optional A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
- fixed
Notes
Model formula:
\[P(x) = \sum_{i=0}^{i=n}C_{i} * L_{i}(x)\]where
L_{i}
is the corresponding Legendre polynomial.This model does not support the use of units/quantities, because each term in the sum of Legendre polynomials is a polynomial in x - since the coefficients within each Legendre polynomial are fixed, we can’t use quantities for x since the units would not be compatible. For example, the third Legendre polynomial (P2) is 1.5x^2-0.5, but if x was specified with units, 1.5x^2 and -0.5 would have incompatible units.
Methods Summary
fit_deriv
(x, y, *params)Derivatives with respect to the coefficients.
Methods Documentation