qnm.angular¶
Solve the angular Teukolsky equation via spectral decomposition.
TODO Documentation.
Functions
C_and_sep_const_closest(A0, s, c, m, l_max) |
Get a single eigenvalue and eigenvector of decomposition matrix, where the eigenvalue is closest to some guess A0. |
M_matrix(s, c, m, l_max) |
Spherical-spheroidal decomposition matrix truncated at l_max. |
M_matrix_elem(s, c, m, l, lprime) |
The (l, lprime) matrix element from the spherical-spheroidal decomposition matrix from Eq. |
calA(s, l, m) |
Eq. |
calB(s, l, m) |
Eq. |
calC(s, l, m) |
Eq. |
calD(s, l, m) |
Eq. |
calE(s, l, m) |
Eq. |
calF(s, l, m) |
Eq. |
calG(s, l, m) |
Eq. |
calH(s, l, m) |
Eq. |
give_M_matrix_elem_ufunc(s, c, m) |
Gives ufunc that implements matrix elements of the spherical-spheroidal decomposition matrix. |
l_min(s, m) |
Minimum allowed value of l for a given s, m. |
sep_const_closest(A0, s, c, m, l_max) |
Gives the separation constant that is closest to A0. |
sep_consts(s, c, m, l_max) |
Finds eigenvalues of decomposition matrix, i.e. |
swsphericalh_A(s, l, m) |
Angular separation constant at a=0. |
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qnm.angular.C_and_sep_const_closest(A0, s, c, m, l_max)[source]¶ Get a single eigenvalue and eigenvector of decomposition matrix, where the eigenvalue is closest to some guess A0.
Parameters: - A0: complex
Value close to the desired separation constant.
- s: int
Spin-weight of interest
- c: complex
Oblateness of spheroidal harmonic
- m: int
Magnetic quantum number
- l_max: int
Maximum angular quantum number
Returns: - complex, complex ndarray
The first element of the tuple is the eigenvalue that is closest in value to A0. The second element of the tuple is the corresponding eigenvector.
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qnm.angular.M_matrix(s, c, m, l_max)[source]¶ Spherical-spheroidal decomposition matrix truncated at l_max.
Parameters: - s: int
Spin-weight of interest
- c: complex
Oblateness of the spheroidal harmonic
- m: int
Magnetic quantum number
- l_max: int
Maximum angular quantum number
Returns: - complex ndarray
Decomposition matrix
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qnm.angular.M_matrix_elem(s, c, m, l, lprime)[source]¶ The (l, lprime) matrix element from the spherical-spheroidal decomposition matrix from Eq. (55).
Parameters: - s: int
Spin-weight of interest
- c: complex
Oblateness of the spheroidal harmonic
- m: int
Magnetic quantum number
- l: int
Angular quantum number of interest
- lprime: int
Primed quantum number of interest
Returns: - complex
Matrix element M_{l, lprime}
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qnm.angular.give_M_matrix_elem_ufunc(s, c, m)[source]¶ Gives ufunc that implements matrix elements of the spherical-spheroidal decomposition matrix.
Parameters: - s: int
Spin-weight of interest
- c: complex
Oblateness of the spheroidal harmonic
- m: int
Magnetic quantum number
Returns: - ufunc
Implements elements of M matrix
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qnm.angular.l_min(s, m)[source]¶ Minimum allowed value of l for a given s, m.
The formula is l_min = max(|m|,|s|).
Parameters: - s: int
Spin-weight of interest
- m: int
Magnetic quantum number
Returns: - int
l_min
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qnm.angular.sep_const_closest(A0, s, c, m, l_max)[source]¶ Gives the separation constant that is closest to A0.
Parameters: - A0: complex
Value close to the desired separation constant.
- s: int
Spin-weight of interest
- c: complex
Oblateness of spheroidal harmonic
- m: int
Magnetic quantum number
- l_max: int
Maximum angular quantum number
Returns: - complex
Separation constant that is the closest to A0.
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qnm.angular.sep_consts(s, c, m, l_max)[source]¶ Finds eigenvalues of decomposition matrix, i.e. the separation constants, As.
Parameters: - s: int
Spin-weight of interest
- c: complex
Oblateness of spheroidal harmonic
- m: int
Magnetic quantum number
- l_max: int
Maximum angular quantum number
Returns: - complex ndarray
Eigenvalues of spherical-spheroidal decomposition matrix
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qnm.angular.swsphericalh_A(s, l, m)[source]¶ Angular separation constant at a=0.
- Eq. (50). Has no dependence on m. The formula is
- A_0 = l(l+1) - s(s+1)
Parameters: - s: int
Spin-weight of interest
- l: int
Angular quantum number of interest
- m: int
Magnetic quantum number, ignored
Returns: - int
Value of A(a=0) = l(l+1) - s(s+1)