ppmd.coulomb.wigner module

ppmd.coulomb.wigner.R_y(p, x)

matrix to apply to complex vector of p moments to rotate the basis functions used to compute the moments around the y-axis by angle x.

ppmd.coulomb.wigner.R_z(p, x)

matrix to apply to complex vector of p moments to rotate the basis functions used to compute the moments around the z-axis by angle x.

ppmd.coulomb.wigner.R_z_vec(p, x)

matrix to apply to complex vector of p moments to rotate the basis functions used to compute the moments around the z-axis by angle x.

ppmd.coulomb.wigner.R_zy(p, alpha, beta)

ppmd.coulomb.wigner.R_zyz(p, alpha, beta, gamma)

ppmd.coulomb.wigner.R_zyz_given_y(p, alpha, beta, gamma, m1)

ppmd.coulomb.wigner.Ry_set(p, beta, dtype)

Returns the set of matrices needed to rotate all p moments by beta around the y axis.

ppmd.coulomb.wigner.Rzyz_set(p, alpha, beta, gamma, dtype)

ppmd.coulomb.wigner.Rzyz_set_2(p, alpha, beta, gamma, dtype)

Returns the set of matrices needed to rotate all p moments by beta around the y axis.

ppmd.coulomb.wigner.Rzyz_set_orig(p, alpha, beta, gamma, dtype)

Returns the set of matrices needed to rotate all p moments by beta around the y axis.

ppmd.coulomb.wigner.eps_m(m)

ppmd.coulomb.wigner.wigner_d(j, mp, m, beta)

Compute the Wigner d-matrix d_{m’, m}^j(eta) using Jacobi polynomials. Taken from wikipedia which claims Wigner, E.P. 1931 as a source. Matches the recursion based method in wigner_d_rec.

ppmd.coulomb.wigner.wigner_d_rec(j, mp, m, beta)

Compute the Wigner d-matrix d_{m’, m}^j(eta) using recursion relations Uses recursion relations in:

“A fast and stable method for rotating spherical harmonic expansions”, Z. Gimbutas, L.Greengard

Corrections: Equation (11), last term, numerator in square root should be: (n-m)(n-m-1) not (n-m)(n-m+1) to match the Jacobi Polynomial version.