Package gmisclib :: Module ortho_poly :: Class ortho_poly
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Class ortho_poly

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Virtual base class. This is a superclass of all orthorgonal polynomials. This does the recurrence [Abramowitz and Stegun p.782], and ensures that the generated polynomials are all orthonormal to each other. The derived classed need to specify two functions: recurse() and wt_(). Recurse() is the recursion relation from P(i) and P(i-1) to P(i+1), and wt_() is the weighting function for the polynomial. Wt_() is needed to check orthogonality, and really defines the polynomial. These polynomials are guarenteed to be orthogonal to eachother when summed over the supplied set of x points. Thus, if you change x_() or wt_(), you get a different set of functions.

Instance Methods
 
__init__(self, n=None, x=None)
Argument n is how many points you want the polynomials evaluated at.
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P(self, i)
Self.P(i) is the ith orthogonal polynomial.
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recurse(self, n, fn, fnm1)
Does the recurrence relation, evaluating f_(n+1) as a function of n, f_n, and f_(n-1).
source code
 
compute(self, n) source code
 
expand(self, c) (Inherited from gmisclib.ortho_poly.ortho) source code
 
wt(self)
Weighting function to get orthonormality. (Inherited from gmisclib.ortho_poly.ortho)
source code
 
wt_(self) (Inherited from gmisclib.ortho_poly.ortho) source code
 
x_(self, m)
Calculates the points at which the function is evaluated, if you want m evenly spaced points. (Inherited from gmisclib.ortho_poly.ortho)
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Class Variables
  __doc__ = """Virtual base cla...
  registry = {} (Inherited from gmisclib.ortho_poly.ortho)
Method Details

__init__(self, n=None, x=None)
(Constructor)

source code 

Argument n is how many points you want the polynomials evaluated at. The ordinates of the points are placed in self.x. You may alternatively specify the points as argument x, in which case the x_() function will never be called.

Overrides: ortho.__init__
(inherited documentation)

P(self, i)

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Self.P(i) is the ith orthogonal polynomial. The result is normalized so that numpy.sum(self.P(i)**2) == 1.

Overrides: ortho.P

recurse(self, n, fn, fnm1)

source code 

Does the recurrence relation, evaluating f_(n+1) as a function of n, f_n, and f_(n-1). For n=0 and n=1, fn and fnm1 may be None.

compute(self, n)

source code 
Overrides: ortho.compute

Class Variable Details

__doc__

Value:
"""Virtual base class.
		This is a superclass of all orthorgonal polynomials.
		This does the recurrence [Abramowitz and Stegun p.782],
		and ensures that the generated polynomials are all
		orthonormal to each other.
		The derived classed need to specify two functions:
		recurse() and wt_().
		Recurse() is the recursion relation from P(i) and P(i-1)
...