Package gmisclib :: Module ortho_poly :: Class Chebyshev

Class Chebyshev

Chebyshev polynomials of the first kind, orthonormal over (-1, 1) with weight (1-x^2)^(-1/2). These are the equi-ripple polynomials. Called Tn(x) in Abramowitz and Stegun.

Instance Methods

__init__(self, n=None, x=None)
Argument n is how many points you want the polynomials evaluated at.

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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).

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wt_(self)

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P(self, i)
Self.P(i) is the ith orthogonal polynomial. (Inherited from gmisclib.ortho_poly.ortho_poly)

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compute(self, n) (Inherited from gmisclib.ortho_poly.ortho_poly)

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expand(self, c) (Inherited from gmisclib.ortho_poly.ortho)

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wt(self)
Weighting function to get orthonormality. (Inherited from gmisclib.ortho_poly.ortho)

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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__ = `"""Chebyshev polynomials of the first ki...`
	name = `'Chebyshev'`
	registry = `{}` (Inherited from gmisclib.ortho_poly.ortho)

Method Details

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

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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)

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.

Overrides: ortho_poly.recurse: (inherited documentation)

wt_(self)

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Overrides: ortho.wt_

Class Variable Details

doc

Value:

"""Chebyshev polynomials of the first kind,
		orthonormal over (-1, 1) with weight (1-x^2)^(-1/2).
		These are the equi-ripple polynomials.
		Called Tn(x) in Abramowitz and Stegun.
		"""

Class Chebyshev

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

recurse(self, n, fn, fnm1)

wt_(self)

__doc__

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

doc