qpms.tmatrices Namespace Reference

Data Structures
class	TMatrix

Functions
def	WignerD_mm (l, quat)
def	WignerD_mm_fromvector (l, vect)
def	WignerD_yy (lmax, quat)
def	WignerD_yy_fromvector (lmax, vect)
def	identity_yy (lmax)
def	identity_tyty (lmax)
def	xflip_yy (lmax)
def	xflip_tyy (lmax)
def	xflip_tyty (lmax)
def	yflip_yy (lmax)
def	yflip_tyy (lmax)
def	yflip_tyty (lmax)
def	zflip_yy (lmax)
def	zflip_tyy (lmax)
def	zflip_tyty (lmax)
def	zrotN_yy (N, lMax)
def	op_yy2tyty (yyop)
def	zrotN_tyty (N, lMax)
def	parity_yy (lmax)
def	loadScuffTMatrices (fileName, normalisation=1, version='old', freqscale=None, order=None)
def	apply_matrix_left (matrix, tensor, axis)
def	apply_ndmatrix_left (matrix, tensor, axes)
def	apply_ndmatrix_right (tensor, matrix, axes)
def	ndmatrix_Hconj (matrix)
def	symz_indexarrays (lMax, npart=1)
def	get_TMatrix_fromspec (tmatrix_spec)
def	perform_tmspecs (tmspecs)

Variables
bool	use_moble_quaternion = False
	ň = np.newaxis
	reCN = re.compile('(\d*)C(\d+)')

Detailed Description

Mostly legacy code, but still kept for reference.
Might be removed in future versions.

Function Documentation

apply_matrix_left()

def qpms.tmatrices.apply_matrix_left	(		matrix,
			tensor,
			axis
	)

TODO doc
Apply square matrix to a given axis of a tensor, so that the result retains the shape
of the original tensor. The summation goes over the second index of the matrix and the
given tensor axis.

apply_ndmatrix_left()

def qpms.tmatrices.apply_ndmatrix_left	(		matrix,
			tensor,
			axes
	)

Generalized apply_matrix_left, the matrix can have more (2N) abstract dimensions,
like M[i,j,k,...z,i,j,k,...,z]. N axes have to be specified in a tuple, corresponding
to the axes 0,1,...N-1 of the matrix

apply_ndmatrix_right()

def qpms.tmatrices.apply_ndmatrix_right	(		tensor,
			matrix,
			axes
	)

Right-side analogue of apply_ndmatrix_lift.
Multiplies a tensor with a 2N-dimensional matrix, conserving the axis order.

get_TMatrix_fromspec()

def qpms.tmatrices.get_TMatrix_fromspec

(

tmatrix_spec

)

 TODO doc 
returns (TMatrices, freqs, lMax)

identity_tyty()

def qpms.tmatrices.identity_tyty

(

lmax

)

TODO doc

identity_yy()

def qpms.tmatrices.identity_yy

(

lmax

)

TODO doc

loadScuffTMatrices()

def qpms.tmatrices.loadScuffTMatrices	(		fileName,
			normalisation = 1,
			version = 'old',
			freqscale = None,
			order = None
	)

TODO doc

version describes version of scuff-em. It is either 'old' or 'new'. 
default order is ('N','M') with 'old' version, ('M','N') with 'new'

ndmatrix_Hconj()

def qpms.tmatrices.ndmatrix_Hconj

(

matrix

)

For 2N-dimensional matrix, swap the first N and last N matrix, and complex conjugate.

op_yy2tyty()

def qpms.tmatrices.op_yy2tyty

(

yyop

)

Broadcasts an yy operator to tyty operator without considering mirroring effects.
Good (maybe only) for rotations.

parity_yy()

def qpms.tmatrices.parity_yy

(

lmax

)

Parity operator (flip in x,y,z)
parity = (-1)**l

perform_tmspecs()

def qpms.tmatrices.perform_tmspecs

(

tmspecs

)

Takes a sequence of TMatrixSpec or TMatrix instances and returns
a list of corresponding TMatrix instances

symz_indexarrays()

def qpms.tmatrices.symz_indexarrays	(		lMax,
			npart = 1
	)

Returns indices that are used for separating the in-plane E ('TE' in the photonic crystal
jargon) and perpendicular E ('TM' in the photonic crystal jargon) modes
in the z-mirror symmetric systems.

Parameters
----------
lMax : int
    The maximum degree cutoff for the T-matrix to which these indices will be applied.

npart : int
    Number of particles (TODO better description)

Returns
-------
TEč, TMč : (npart * 2 * nelem)-shaped bool ndarray
    Mask arrays corresponding to the 'TE' and 'TM' modes, respectively.

WignerD_mm()

def qpms.tmatrices.WignerD_mm	(		l,
			quat
	)

Calculates Wigner D matrix (as an numpy (2*l+1,2*l+1)-shaped array) 
for order l, and a rotation given by quaternion quat.

This represents the rotation of spherical vector basis
TODO doc

WignerD_mm_fromvector()

def qpms.tmatrices.WignerD_mm_fromvector	(		l,
			vect
	)

TODO doc

WignerD_yy()

def qpms.tmatrices.WignerD_yy	(		lmax,
			quat
	)

TODO doc

WignerD_yy_fromvector()

def qpms.tmatrices.WignerD_yy_fromvector	(		lmax,
			vect
	)

TODO doc

xflip_yy()

def qpms.tmatrices.xflip_yy

(

lmax

)

TODO doc
xflip = δ(m + m') δ(l - l')  
(i.e. ones on the (m' m) antidiagonal

yflip_yy()

def qpms.tmatrices.yflip_yy

(

lmax

)

TODO doc
yflip = rot(z,pi/2) * xflip * rot(z,-pi/2)
      = δ(m + m') δ(l - l') * (-1)**m

zflip_yy()

def qpms.tmatrices.zflip_yy

(

lmax

)

TODO doc
zflip = (-1)^(l+m)