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:
astropy.modeling.polynomial.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_degreeint
degree in x
- y_degreeint
degree in y
- x_domaintuple or None, optional
domain of the x independent variable
- y_domaintuple or None, optional
domain of the y independent variable
- x_windowtuple or None, optional
range of the x independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window
- y_windowtuple or None, optional
range of the y independent variable If None, it is set to (-1, 1) Fitters will remap the domain to this window
- **paramsdict
keyword: value pairs, representing parameter_name: value
- Other Parameters
- fixeda 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.- tieddict, 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.- boundsdict, 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.- eqconslist, optional
A list of functions of length
n
such thateqcons[j](x0,*args) == 0.0
in a successfully optimized problem.- ineqconslist, optional
A list of functions of length
n
such thatieqcons[j](x0,*args) >= 0.0
is a successfully optimized problem.
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
(self, x, y, *params)Derivatives with respect to the coefficients.
Methods Documentation
-
fit_deriv
(self, x, y, *params)[source]¶ Derivatives with respect to the coefficients. This is an array with Legendre polynomials:
Lx0Ly0 Lx1Ly0…LxnLy0…LxnLym
- Parameters
- xndarray
input
- yndarray
input
- paramsthrow away parameter
parameter list returned by non-linear fitters
- Returns
- resultndarray
The Vandermonde matrix