Besseltools Module¶
python binding to besseltools library (part of CatAna)
SphericalBesselZeros¶
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class
catana.besseltools.
SphericalBesselZeros
(self: catana.besseltools.SphericalBesselZeros, l: int) → None¶ A root generator for spherical Bessel functions.
The class is initialized for a specific multipole l. The zeros are computed iteratively and the results are stored so that they only have to be computed once. I.e if the n-th zero is requested and it has not been computed before, start at the highest computed zero and compute all zeros up to the n-th.
Constructor
Parameters: l (int) – multipole of the spherical Bessel function -
__getitem__
(self: catana.besseltools.SphericalBesselZeros, n: int) → float¶ return n-th zero
Parameters: n (int) – index of zero crossing Returns: float – n-th root of the spherical Bessel function with multipole l
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compute_up_to
(self: catana.besseltools.SphericalBesselZeros, n: float) → None¶ precompute first n zeros
Parameters: n (int) – number of zeros to compute
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Spherical Bessel Integrator¶
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catana.besseltools.
double_sbessel_integrator
(*args, **kwargs)¶ Overloaded function.
- double_sbessel_integrator(w: Callable[[float], float], l: int, r_max: float, k1: numpy.ndarray[float64], k2: numpy.ndarray[float64]) -> object
Compute an integral containing 2 spherical Bessel functions with the same multipole.
Computes \(\int_0^{r_{max}} \; w(r) \; j_l(k_1 r) \; j_l(k_2 r) \;\; dr\)
Parameters: - w (callable) – function to integrate (see equation)
- l (int) – multipole of the spherical Bessel functions
- r_max (float) – upper boundary of integration
- k1 (float) – frequency of one spherical Bessel function
- k2 (float) – frequency of other spherical Bessel function
- double_sbessel_integrator(w: catana.basictypes.FunctionInterpolator, l: int, r_max: float, k1: numpy.ndarray[float64], k2: numpy.ndarray[float64]) -> object
Compute an integral containing 2 spherical Bessel functions with the same multipole, using a
FunctionInterpolator
Computes \(\int_0^{r_{max}} \; w(r) \; j_l(k_1 r) \; j_l(k_2 r) \;\; dr\)
Parameters: - fi (FunctionInterpolator) – function to integrate (see equation, fi(r) is an interpolator of w(r))
- l (int) – multipole of the spherical Bessel functions
- r_max (float) – upper boundary of integration
- k1 (float) – frequency of one spherical Bessel function
- k2 (float) – frequency of other spherical Bessel function