bfieldtools.sphtools.SphBasis¶
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class
bfieldtools.sphtools.SphBasis(Np)¶ Constructs an object that describes unit sphere. Can be used to compute inner products and function sph spectra on the sphere.
TODO: mu0 might be missing!!!
Initialises the sphbasis object.
- Parameters
- Np: int
Mumber of points along theta and phi in spherical coordinates
- Returns
- self: sphbasis object
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initqp(self)¶ Initialises quadrature points on the sphere.
Default points are McLaren(10) so that we avoid singularities.
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innerproduct(self, fun1, fun2)¶ Inner product of vector functions fun1 and fun2. Defined as integration over a surface of unit sphere <C,D> = int C dot D dOmega. Quadrature rule defined in qp is used.
- Parameters
- fun1: Nx3 array
vector function 1
- fun2: Nx3 array
vector function 2
- Returns
- dotp: int
inner product of fun1 and fun2
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avsphspectra(self, fun, lmax)¶ Calculate the l,m-spectra (over r**l-terms) of vector function defined in quadrature points using the inner product.
- Parameters
- fun: Nx3 array
vector function computed at quadrature points self.sqp
- lmax: int
maximum degree l for which the spectra is computed
- Returns
- coeffs: lmax*(lmax+2)x1 arrays
spectral coefficients
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bvsphspectra(self, fun, lmax)¶ Calculate the l,m-spectra (over r**(-l)-terms) of vector function defined in quadrature points using the inner product.
- Parameters
- fun: Nx3 array
vector function computed at quadrature points self.sqp
- lmax: int
maximum degree l for which the spectra is computed
- Returns
- coeffs: lmax*(lmax+2)x1 arrays
spectral coefficients