qnm.contfrac

Infinite continued fractions via Lentz’s method.

TODO Documentation.

Functions

lentz(a, b[, tol, N_min, N_max, tiny])	Compute a continued fraction via modified Lentz’s method.
lentz_gen(a, b[, tol, N_min, N_max, tiny])	Compute a continued fraction via modified Lentz’s method, using generators rather than functions.

qnm.contfrac.lentz(a, b, tol=1e-10, N_min=0, N_max=inf, tiny=1e-30)

Compute a continued fraction via modified Lentz’s method.

This implementation is by the book [1].

Parameters:

a: callable returning numeric.

b: callable returning numeric.

tol: float [default: 1.e-10]

Tolerance for termination of evaluation.

N_min: int [default: 0]

Minimum number of iterations to evaluate.

N_max: int or comparable [default: np.Inf]

Maximum number of iterations to evaluate.

tiny: float [default: 1.e-30]

Very small number to control convergence of Lentz’s method when there is cancellation in a denominator.

Returns:

(float, float, int)

The first element of the tuple is the value of the continued fraction. The second element is the estimated error. The third element is the number of iterations.

References

[1]	(1, 2) WH Press, SA Teukolsky, WT Vetterling, BP Flannery, “Numerical Recipes,” 3rd Ed., Cambridge University Press 2007, ISBN 0521880688, 9780521880688 .

qnm.contfrac.lentz_gen(a, b, tol=1e-10, N_min=0, N_max=inf, tiny=1e-30)

Compute a continued fraction via modified Lentz’s method, using generators rather than functions.

This implementation is by the book [1].

Parameters:

a: generator yielding numeric.

b: generator yielding numeric.

tol: float [default: 1.e-10]

Tolerance for termination of evaluation.

N_min: int [default: 0]

Minimum number of iterations to evaluate.

N_max: int or comparable [default: np.Inf]

Maximum number of iterations to evaluate.

tiny: float [default: 1.e-30]

Very small number to control convergence of Lentz’s method when there is cancellation in a denominator.

Returns:

(float, float, int)

The first element of the tuple is the value of the continued fraction. The second element is the estimated error. The third element is the number of iterations.

References

[1]	(1, 2) WH Press, SA Teukolsky, WT Vetterling, BP Flannery, “Numerical Recipes,” 3rd Ed., Cambridge University Press 2007, ISBN 0521880688, 9780521880688 .