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- abc.ABC(builtins.object)
-
- RecursivePolynomial
-
- IntegratedLegendrePolynomials
- JacobiPolynomials
- LegendrePolynomials
- Monomials
class IntegratedLegendrePolynomials(RecursivePolynomial) |
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- Method resolution order:
- IntegratedLegendrePolynomials
- RecursivePolynomial
- abc.ABC
- builtins.object
Methods defined here:
- __init__(self)
- Initialize self. See help(type(self)) for accurate signature.
Data and other attributes defined here:
- __abstractmethods__ = frozenset()
Methods inherited from RecursivePolynomial:
- evaluate(self, x, n)
- Evaluate the recursive polynomial of degree n for all values of x.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of length len(x) containing the values of the polynomial
evaluated at each value of x.
- evaluate_all(self, x, n)
- Evaluates the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of shape (len(x), n+1 ) containing the values of the polynomial
evaluated at each value of x up to degree n.
- plot_all(self, x, n)
- Plots the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Data descriptors inherited from RecursivePolynomial:
- __dict__
- dictionary for instance variables
- __weakref__
- list of weak references to the object
Data and other attributes inherited from RecursivePolynomial:
- rec_coeff = None
- starter = None
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class JacobiPolynomials(RecursivePolynomial) |
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JacobiPolynomials(alpha, beta)
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- Method resolution order:
- JacobiPolynomials
- RecursivePolynomial
- abc.ABC
- builtins.object
Methods defined here:
- __init__(self, alpha, beta)
- Initialize self. See help(type(self)) for accurate signature.
Data and other attributes defined here:
- __abstractmethods__ = frozenset()
- alpha = None
- beta = None
Methods inherited from RecursivePolynomial:
- evaluate(self, x, n)
- Evaluate the recursive polynomial of degree n for all values of x.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of length len(x) containing the values of the polynomial
evaluated at each value of x.
- evaluate_all(self, x, n)
- Evaluates the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of shape (len(x), n+1 ) containing the values of the polynomial
evaluated at each value of x up to degree n.
- plot_all(self, x, n)
- Plots the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Data descriptors inherited from RecursivePolynomial:
- __dict__
- dictionary for instance variables
- __weakref__
- list of weak references to the object
Data and other attributes inherited from RecursivePolynomial:
- rec_coeff = None
- starter = None
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class LegendrePolynomials(RecursivePolynomial) |
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- Method resolution order:
- LegendrePolynomials
- RecursivePolynomial
- abc.ABC
- builtins.object
Methods defined here:
- __init__(self)
- Initialize self. See help(type(self)) for accurate signature.
Data and other attributes defined here:
- __abstractmethods__ = frozenset()
Methods inherited from RecursivePolynomial:
- evaluate(self, x, n)
- Evaluate the recursive polynomial of degree n for all values of x.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of length len(x) containing the values of the polynomial
evaluated at each value of x.
- evaluate_all(self, x, n)
- Evaluates the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of shape (len(x), n+1 ) containing the values of the polynomial
evaluated at each value of x up to degree n.
- plot_all(self, x, n)
- Plots the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Data descriptors inherited from RecursivePolynomial:
- __dict__
- dictionary for instance variables
- __weakref__
- list of weak references to the object
Data and other attributes inherited from RecursivePolynomial:
- rec_coeff = None
- starter = None
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class Monomials(RecursivePolynomial) |
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- Method resolution order:
- Monomials
- RecursivePolynomial
- abc.ABC
- builtins.object
Methods defined here:
- __init__(self)
- Initialize self. See help(type(self)) for accurate signature.
Data and other attributes defined here:
- __abstractmethods__ = frozenset()
Methods inherited from RecursivePolynomial:
- evaluate(self, x, n)
- Evaluate the recursive polynomial of degree n for all values of x.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of length len(x) containing the values of the polynomial
evaluated at each value of x.
- evaluate_all(self, x, n)
- Evaluates the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of shape (len(x), n+1 ) containing the values of the polynomial
evaluated at each value of x up to degree n.
- plot_all(self, x, n)
- Plots the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Data descriptors inherited from RecursivePolynomial:
- __dict__
- dictionary for instance variables
- __weakref__
- list of weak references to the object
Data and other attributes inherited from RecursivePolynomial:
- rec_coeff = None
- starter = None
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class RecursivePolynomial(abc.ABC) |
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Abstract base class for recursive polynomial evaluation.
Polynomials are evaluated using the following recursion:
* d "starter" (given functions)
* P_i(x) = s_i(x) for i < d
* recursion formulate for i >= d:
* P_i(x) = sum_{j=0}^{d-1} c_j(i,x) P_{i-d+j}(x)
Attributes:
-----------
starter : list
List of starter functions.
rec_coeff : list
List of recursive coefficients.
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- Method resolution order:
- RecursivePolynomial
- abc.ABC
- builtins.object
Methods defined here:
- __init__(self)
- Initialize self. See help(type(self)) for accurate signature.
- evaluate(self, x, n)
- Evaluate the recursive polynomial of degree n for all values of x.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of length len(x) containing the values of the polynomial
evaluated at each value of x.
- evaluate_all(self, x, n)
- Evaluates the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Returns:
--------
vals : ndarray
Array of shape (len(x), n+1 ) containing the values of the polynomial
evaluated at each value of x up to degree n.
- plot_all(self, x, n)
- Plots the recursive polynomial for all values of x up to n.
Parameters:
-----------
x : array_like
Array of values to evaluate the polynomial at.
n : int
Maximum degree of the polynomial to evaluate.
Data descriptors defined here:
- __dict__
- dictionary for instance variables
- __weakref__
- list of weak references to the object
Data and other attributes defined here:
- __abstractmethods__ = frozenset({'__init__'})
- rec_coeff = None
- starter = None
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