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# Class ortho_poly

source code

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. source code

 P(self, i) Self.P(i) is the ith orthogonal polynomial. source code

 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) source code
 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) `...` ```

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