karhunen_loeve_generator#

class arte.utils.karhunen_loeve_generator.KarhunenLoeveGenerator(pupil, covariance_matrix)#

Bases: object

Generator of KL polynomials departing from a covariance matrix and a user defined base of polynomials.

The user can specify the diameter of the pupil pupil or specify a CircularMask

In the case a scalar real value is passed as pupil argument, The shape of the returned array cannot be specified: it is a square array of size ceil(pupil_diameter). The center of the unit disk cannot be specified and it is the central pixel of the array (if the array size is odd) or the corner of the 4 central pixels (if the array size is even).

In the case a CircularMask is passed as pupil argument, the mask is used as unit disk over which the polynomial are computed. Non-integer center coordinates and radius are properly managed.

Parameters:

pupil (real or CircularMask) – If a scalar value, the argument is used as pupil diameter in pixels. If a CircularMask, the argument is used as mask representing the unit disk.
covariance_matrix (array of shape (nModes, nModes) representing) – the phenomenon covariance matrix

Examples

Create a KL polynomial using Zernike description of Kolmogorov turbulence >>> from arte.atmo.utils import getFullKolmogorovCovarianceMatrix >>> from arte.utils.zernike_generator import ZernikeGenerator >>> from arte.utils.kl_generator import KLGenerator >>> from arte.types.mask import CircularMask >>> import numpy as np >>> import matplotlib.pyplot as plt

>>> mask = CircularMask((128,128), 64, (64,64))
>>> zz = ZernikeGenerator(mask)
>>> nmodes=100
>>> kolm_covar = getFullKolmogorovCovarianceMatrix(nmodes)
>>> zbase = np.rollaxis(np.ma.masked_array([zz.getZernike(n)
                                        for n in range(2,nmodes+2)]),0,3)
>>> generator = KLGenerator(mask, kolm_covar)
>>> generator.generateFromBase(zbase)
>>> kl =generator.getKL(2)
>>> plt.imshow(kl)

Methods

`cartesian_coordinates`()	Return X, Y maps of cartesian coordinates
`center`()	Y, X coordinates of the unit disk center
`first_mode`()	First mode index
`radius`()	Radius of the unit disk

degree
generateFromBase
getCube
getDerivativeX
getDerivativeXDict
getDerivativeY
getDerivativeYDict
getKL
getKLDict
getModesDict

cartesian_coordinates()#

Return X, Y maps of cartesian coordinates

The KL polynomials and derivatives are evaluated over a grid of points, whose coordinates are accessible through cartesian_coordinates

Returns:: X,Y – coordinates of points of the unit disk where the polynomials are evaluated
Return type:: array

Examples

Create KL polynomials on a unit disk defined over 4 pixels. The returned arrays have (4,4) shape (corresponding to the coords [-0.75, -0.25, 0.25, 0.75])

>>> zg = KLGenerator(4)
>>> x, y = zg.cartesian_coordinates()
>>> x[0]
array([-0.75, -0.25,  0.25,  0.75])

As above with 3 pixels

>>> zg = KLGenerator(3)
>>> x, y = zg.cartesian_coordinates()
>>> x[0]
array([-0.666, 0,  0.666])

In case of non-integer diameter, the array size is rounded up to the next integer

>>> zg = KLGenerator(2.5)
>>> x, y = zg.cartesian_coordinates()
>>> x[0]
array([-0.8, 0,  0.8])

center()#

Y, X coordinates of the unit disk center

Returns:: center – Y, X coordinate of the unit disk center in the array reference system
Return type:: array of shape (2,)

classmethod degree(index)#

first_mode()#: First mode index

generateFromBase(inBase)#

getCube()#

getDerivativeX(index)#

getDerivativeXDict(indexVector)#

getDerivativeY(index)#

getDerivativeYDict(indexVector)#

getKL(index)#

getKLDict(indexVector)#

getModesDict(indexVector)#

radius()#

Radius of the unit disk

Returns:: radius – unit disk radius in pixel
Return type:: real