qpms.qpms_p Namespace Reference

Functions
def	cart2sph (cart, axis=-1, allow2d=False)
def	sph2cart (sph, axis=-1)
def	sph_loccart2cart (loccart, sph, axis=-1)
def	sph_loccart_basis (sph, sphaxis=-1, cartaxis=None)
def	nelem2lMax (nelem)
def	lMax2nelem (lMax)
def	lpy (nmax, z)
def	lpy1 (nmax, z)
def	vswf_yr (pos_sph, lMax, J=1)
def	zJn (n, z, J=1)
def	π̃_zerolim (nmax)
def	π̃_pilim (nmax)
def	τ̃_zerolim (nmax)
def	τ̃_pilim (nmax)
def	get_π̃τ̃_y1 (θ, nmax)
def	vswf_yr1 (pos_sph, nmax, J=1)
def	zplane_pq_y (nmax, betap=0)
def	plane_pq_y (nmax, kdir_cart, E_cart)
def	ε_drude (ε_inf, ω_p, γ_p, ω)
def	mie_coefficients (a, nmax, k_i, k_e, μ_i=1, μ_e=1, J_ext=1, J_scat=3)
def	G_Mie_scat_precalc_cart_new (source_cart, dest_cart, RH, RV, a, nmax, k_i, k_e, μ_i=1, μ_e=1, J_ext=1, J_scat=3)
def	Grr_Delga (nmax, a, r, k, ε_m, ε_b)
def	G0_dip_1 (r_cart, k)
def	G0_analytical (r, k)
def	G0L_analytical (r, k)
def	G0T_analytical (r, k)
def	G0_sum_1_slow (source_cart, dest_cart, k, nmax)
def	loadWfile (fileName, lMax=None, fatForm=True, nparticles=2)
def	processWfiles_sameKs (freqfilenames, destfilename, nparticles=2, lMax=None, f='npz')
def	loadWfile_info (fileName, lMax=None, midk_halfwidth=None, freqlimits=None)
def	loadWfile_processed (fileName, lMax=None, fatForm=True, midk_halfwidth=None, midk_index=None, freqlimits=None, iteratechunk=None)

Variables
	ň = np.newaxis
	eV = e

Detailed Description

This file contains mostly legacy code, but is still kept for reference. Avoid using this.

Function Documentation

G0_dip_1()

def qpms.qpms_p.G0_dip_1	(		r_cart,
			k
	)

Free-space dyadic Green's function in terms of the spherical vector waves.
FIXME

G_Mie_scat_precalc_cart_new()

def qpms.qpms_p.G_Mie_scat_precalc_cart_new	(		source_cart,
			dest_cart,
			RH,
			RV,
			a,
			nmax,
			k_i,
			k_e,
			μ_i = 1,
			μ_e = 1,
			J_ext = 1,
			J_scat = 3
	)

Implementation according to Kristensson, page 50
My (Taylor's) basis functions are normalized to n*(n+1), whereas Kristensson's to 1
TODO: check possible -1 factors (cf. Kristensson's dagger notation)

get_π̃τ̃_y1()

def qpms.qpms_p.get_π̃τ̃_y1	(		θ,
			nmax
	)

(... TODO)

loadWfile()

def qpms.qpms_p.loadWfile	(		fileName,
			lMax = None,
			fatForm = True,
			nparticles = 2
	)

Load the translation operator lattice sums generated by hexlattice_ewald.c
fatForm has different indices (so that it can be easily multiplied with T-Matrix
and twice the size.

loadWfile_info()

def qpms.qpms_p.loadWfile_info	(		fileName,
			lMax = None,
			midk_halfwidth = None,
			freqlimits = None
	)

Returns all the relevant data from the W file except for the W values themselves

loadWfile_processed()

def qpms.qpms_p.loadWfile_processed	(		fileName,
			lMax = None,
			fatForm = True,
			midk_halfwidth = None,
			midk_index = None,
			freqlimits = None,
			iteratechunk = None
	)

midk_halfwidth: int
    if given, takes only the "middle" k-value by index nk//2 and midk_halfwidth values from both sides
midk_index: int
    if given, midk_index is taken as the "middle" value instad of nk//2
freqlimit: pair of doubles; 
    if given, only the values from the given frequency range (in Hz) are returned to save RAM
    N.B.: the frequencies in the processed file are expected to be sorted!
iteratechunk: positive int ; NI
    if given, this works as a generator with only iteratechunk frequencies processed and returned at each iteration to save memory

lpy1()

def qpms.qpms_p.lpy1	(		nmax,
			z
	)

Associated legendre function and its derivatative at z in the 'y-indexing'.
(Without Condon-Shortley phase AFAIK.)
NOT THOROUGHLY TESTED

Parameters
----------

nmax: int
    The maximum order to which the Legendre functions will be evaluated..
    
z: float
    The point at which the Legendre functions are evaluated.
    
output: (P_y, dP_y) TODO
    y-indexed legendre polynomials and their derivatives

mie_coefficients()

def qpms.qpms_p.mie_coefficients	(		a,
			nmax,
			k_i,
			k_e,
			μ_i = 1,
			μ_e = 1,
			J_ext = 1,
			J_scat = 3
	)

FIXME test the magnetic case
TODO description
RH concerns the N ("electric") part, RV the M ("magnetic") part
#

Parameters
----------
a : float
    Diameter of the sphere.
    
nmax : int
    To which order (inc. nmax) to compute the coefficients.

ω : float
    Frequency of the radiation

ε_i, ε_e, μ_i, μ_e : complex
    Relative permittivities and permeabilities of the sphere (_i)
    and the environment (_e)
    MAGNETIC (μ_i, μ_e != 1)  CASE UNTESTED AND PROBABLY BUGGY

J_ext, J_scat : 1, 2, 3, or 4 (must be different)
    Specifies the species of the Bessel/Hankel functions in which
    the external incoming (J_ext) and scattered (J_scat) fields
    are represented. 1,2,3,4 correspond to j,y,h(1),h(2), respectively.
    The returned coefficients are always with respect to the decomposition
    of the "external incoming" wave.

Returns
-------
RV == a/p, RH == b/q, TV = d/p, TH = c/q
TODO 
what does it return on index 0???
FIXME permeabilities

nelem2lMax()

def qpms.qpms_p.nelem2lMax

(

nelem

)

Auxiliary inverse function to nelem(lMax) = (lMax + 2) * lMax. Returns 0 if
it nelem does not come from positive integer lMax.

plane_pq_y()

def qpms.qpms_p.plane_pq_y	(		nmax,
			kdir_cart,
			E_cart
	)

The plane wave expansion coefficients for any direction kdir_cart
and amplitude vector E_cart (which might be complex, depending on
the phase and polarisation state). If E_cart and kdir_cart are
not orthogonal, the result should correspond to the k-normal part
of E_cart.

The Taylor's convention on the expansion is used; therefore,
the electric field is expressed as
E(r) = E_cart * exp(1j * k ∙ r)
     = -1j * ∑_y ( p_y * Ñ_y(|k| * r) + q_y * M̃_y(|k| * r))
(note the -1j factor).

Parameters
----------
nmax: int
    The order of the expansion.
kdir_cart: (...,3)-shaped real array
    The wave vector (its magnitude does not play a role).
E_cart: (...,3)-shaped complex array
    Amplitude of the plane wave

Returns
-------
p_y, q_y:
    The expansion coefficients for the electric (Ñ) and magnetic
    (M̃) waves, respectively.

processWfiles_sameKs()

def qpms.qpms_p.processWfiles_sameKs	(		freqfilenames,
			destfilename,
			nparticles = 2,
			lMax = None,
			f = 'npz'
	)

Processes translation operator data in different files; each file is supposed to contain one frequency.
The Ks in the different files are expected to be exactly the same and in the same order; 
the result is sorted by frequencies and saved to npz file;
The representation is always "thin", i.e. the elements which are zero due to z-symmetry are skipped
F is either 'npz' or 'd' 
'npz' creates npz archive, 'd' creates a directory with individual npy files, where the W-matrix data
are writen using memmap.

sph_loccart2cart()

def qpms.qpms_p.sph_loccart2cart	(		loccart,
			sph,
			axis = -1
	)

Transformation of vector specified in local orthogonal coordinates 
(tangential to spherical coordinates – basis r̂,θ̂,φ̂) to global cartesian
coordinates (basis x̂,ŷ,ẑ)
SLOW FOR SMALL ARRAYS

Parameters
----------
loccart: ... TODO
    the transformed vector in the local orthogonal coordinates
    
sph: ... TODO
    the point (in spherical coordinates) at which the locally
    orthogonal basis is evaluated
    
Returns
-------
output: ... TODO
    The coordinates of the vector in global cartesian coordinates

sph_loccart_basis()

def qpms.qpms_p.sph_loccart_basis	(		sph,
			sphaxis = -1,
			cartaxis = None
	)

Returns the local cartesian basis in terms of global cartesian basis.
sphaxis refers to the original dimensions
TODO doc

vswf_yr()

def qpms.qpms_p.vswf_yr	(		pos_sph,
			lMax,
			J = 1
	)

Normalized vector spherical wavefunctions $\widetilde{M}_{mn}^{j}$,
$\widetilde{N}_{mn}^{j}$ as in [1, (2.40)].

Parameters
----------

pos_sph : np.array(dtype=float, shape=(someshape,3))
    The positions where the spherical vector waves are to be
    evaluated. The last axis corresponds to the individual
    points (r,θ,φ). The radial coordinate r is dimensionless,
    assuming that it has already been multiplied by the
    wavenumber.

nmax : int
    The maximum order to which the VSWFs are evaluated.
    
Returns
-------

output : np.array(dtype=complex, shape=(someshape,nmax*nmax + 2*nmax,3))
    Spherical vector wave functions evaluated at pos_sph,
    in the local basis (r̂,θ̂,φ̂). The last indices correspond
    to m, n (in the ordering given by mnindex()), and basis 
    vector index, respectively.
    
[1] Jonathan M. Taylor. Optical Binding Phenomena: Observations and
Mechanisms.

vswf_yr1()

def qpms.qpms_p.vswf_yr1	(		pos_sph,
			nmax,
			J = 1
	)

As vswf_yr, but evaluated only at single position (i.e. pos_sph has
to have shape=(3))

zplane_pq_y()

def qpms.qpms_p.zplane_pq_y	(		nmax,
			betap = 0
	)

The z-propagating plane wave expansion coefficients as in [1, (1.12)]

Taylor's normalization

(... TODO)

π̃_pilim()

def qpms.qpms_p.π̃_pilim

(

nmax

)

lim_{θ→ π+} π̃(cos θ)

π̃_zerolim()

def qpms.qpms_p.π̃_zerolim

(

nmax

)

lim_{θ→ 0-} π̃(cos θ)

τ̃_pilim()

def qpms.qpms_p.τ̃_pilim

(

nmax

)

lim_{θ→  π+} τ̃(cos θ)

τ̃_zerolim()

def qpms.qpms_p.τ̃_zerolim

(

nmax

)

lim_{θ→ 0-} τ̃(cos θ)