__author__ = 'sibirrer'
import numpy as np
import numpy.polynomial.hermite as hermite
import math
import lenstronomy.Util.util as util
from lenstronomy.Util.package_util import exporter
export, __all__ = exporter()
[docs]@export
class Shapelets(object):
"""
"""
param_names = ['amp', 'beta', 'n1', 'n2', 'center_x', 'center_y']
lower_limit_default = {'amp': 0, 'beta': 0, 'n1': 0, 'n2': 0, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'amp': 100, 'beta': 100, 'n1': 150, 'n2': 150, 'center_x': 100, 'center_y': 100}
def __init__(self, interpolation=False, precalc=False, stable_cut=True, cut_scale=5):
"""
load interpolation of the Hermite polynomials in a range [-30,30] in order n<= 150
:return:
"""
self._interpolation = interpolation
self._precalc = precalc
self._stable_cut = stable_cut
self._cut_scale = cut_scale
if interpolation:
n_order = 50
self.H_interp = [[] for i in range(0, n_order)]
self.x_grid = np.linspace(-50, 50, 6000)
for k in range(0, n_order):
n_array = np.zeros(k+1)
n_array[k] = 1
values = self.hermval(self.x_grid, n_array)
self.H_interp[k] = values
[docs] def hermval(self, x, n_array, tensor=True):
"""
computes the Hermit polynomial as numpy.polynomial.hermite.hermval
difference: for values more than sqrt(n_max + 1) * cut_scale, the value is set to zero
this should be faster and numerically stable
:param x: array of values
:param n_array: list of coeffs in H_n
:param cut_scale: scale where the polynomial will be set to zero
:return: see numpy.polynomial.hermite.hermval
"""
if not self._stable_cut:
return hermite.hermval(x, n_array, tensor=tensor)
else:
n_max = len(n_array)
x_cut = np.sqrt(n_max + 1) * self._cut_scale
if isinstance(x, int) or isinstance(x, float):
if x >= x_cut:
return 0
else:
return hermite.hermval(x, n_array)
else:
out = np.zeros_like(x)
out[x < x_cut] = hermite.hermval(x[x < x_cut], n_array, tensor=tensor)
return out
[docs] def function(self, x, y, amp, beta, n1, n2, center_x, center_y):
"""
:param amp: amplitude of shapelet
:param beta: scale factor of shapelet
:param n1: x-order
:param n2: y-order
:param center_x: center in x
:param center_y: center in y
:return:
"""
if self._precalc:
return amp * x[n1] * y[n2]# / beta
x_ = x - center_x
y_ = y - center_y
return np.nan_to_num(amp * self.phi_n(n1, x_/beta) * self.phi_n(n2, y_/beta))#/beta
[docs] def H_n(self, n, x):
"""
constructs the Hermite polynomial of order n at position x (dimensionless)
:param n: The n'the basis function.
:type name: int.
:param x: 1-dim position (dimensionless)
:type state: float or numpy array.
:returns: array-- H_n(x).
:raises: AttributeError, KeyError
"""
if not self._interpolation:
n_array = np.zeros(n+1)
n_array[n] = 1
return self.hermval(x, n_array, tensor=False) # attention, this routine calculates every single hermite polynomial and multiplies it with zero (exept the right one)
else:
return np.interp(x, self.x_grid, self.H_interp[n])
[docs] def phi_n(self, n, x):
"""
constructs the 1-dim basis function (formula (1) in Refregier et al. 2001)
:param n: The n'the basis function.
:type name: int.
:param x: 1-dim position (dimensionless)
:type state: float or numpy array.
:returns: array-- phi_n(x).
:raises: AttributeError, KeyError
"""
prefactor = 1./np.sqrt(2**n*np.sqrt(np.pi)*math.factorial(n))
return prefactor*self.H_n(n, x)*np.exp(-x**2/2.)
[docs] def pre_calc(self, x, y, beta, n_order, center_x, center_y):
"""
calculates the H_n(x) and H_n(y) for a given x-array and y-array
:param x:
:param y:
:param amp:
:param beta:
:param n_order:
:param center_x:
:param center_y:
:return: list of H_n(x) and H_n(y)
"""
x_ = x - center_x
y_ = y - center_y
n = len(np.atleast_1d(x))
H_x = np.empty((n_order+1, n))
H_y = np.empty((n_order+1, n))
if n_order > 170:
raise ValueError('polynomial order to large', n_order)
for n in range(0, n_order+1):
prefactor = 1./np.sqrt(2**n*np.sqrt(np.pi)*math.factorial(n))
n_array = np.zeros(n+1)
n_array[n] = 1
H_x[n] = self.hermval(x_/beta, n_array, tensor=False) * prefactor * np.exp(-(x_/beta)**2/2.)
H_y[n] = self.hermval(y_/beta, n_array, tensor=False) * prefactor * np.exp(-(y_/beta)**2/2.)
return H_x, H_y
[docs]@export
class ShapeletSet(object):
"""
class to operate on entire shapelet set
"""
param_names = ['amp', 'n_max', 'beta', 'center_x', 'center_y']
lower_limit_default = {'beta': 0, 'center_x': -100, 'center_y': -100}
upper_limit_default = {'beta': 100, 'center_x': 100, 'center_y': 100}
def __init__(self):
self.shapelets = Shapelets(precalc=True)
[docs] def function(self, x, y, amp, n_max, beta, center_x=0, center_y=0):
"""
:param x:
:param y:
:param amp:
:param beta:
:param center_x:
:param center_y:
:return:
"""
num_param = int((n_max+1)*(n_max+2)/2)
f_ = np.zeros(len(np.atleast_1d(x)))
n1 = 0
n2 = 0
H_x, H_y = self.shapelets.pre_calc(x, y, beta, n_max, center_x, center_y)
for i in range(num_param):
kwargs_source_shapelet = {'center_x': center_x, 'center_y': center_y, 'n1': n1, 'n2': n2, 'beta': beta, 'amp': amp[i]}
out = self.shapelets.function(H_x, H_y, **kwargs_source_shapelet)
f_ += out
if n1 == 0:
n1 = n2 + 1
n2 = 0
else:
n1 -= 1
n2 += 1
try: len(x)
except: f_ = f_[0]
#if isinstance(x, int) or isinstance(x, float):
# f_ = f_[0]
return np.nan_to_num(f_)
[docs] def function_split(self, x, y, amp, n_max, beta, center_x=0, center_y=0):
num_param = int((n_max+1)*(n_max+2)/2)
A = []
n1 = 0
n2 = 0
H_x, H_y = self.shapelets.pre_calc(x, y, beta, n_max, center_x, center_y)
for i in range(num_param):
kwargs_source_shapelet = {'center_x': center_x, 'center_y': center_y, 'n1': n1, 'n2': n2, 'beta': beta, 'amp': amp[i]}
A.append(self.shapelets.function(H_x, H_y, **kwargs_source_shapelet))
if n1 == 0:
n1 = n2 + 1
n2 = 0
else:
n1 -= 1
n2 += 1
return A
[docs] def shapelet_basis_2d(self, num_order, beta, numPix, deltaPix=1, center_x=0, center_y=0):
"""
:param num_order: max shapelet order
:param beta: shapelet scale
:param numPix: number of pixel of the grid
:return: list of shapelets drawn on pixel grid, centered.
"""
num_param = int((num_order+2)*(num_order+1)/2)
kernel_list = []
x_grid, y_grid = util.make_grid(numPix, deltapix=deltaPix, subgrid_res=1)
n1 = 0
n2 = 0
H_x, H_y = self.shapelets.pre_calc(x_grid, y_grid, beta, num_order, center_x=center_x, center_y=center_y)
for i in range(num_param):
kwargs_source_shapelet = {'center_x': 0, 'center_y': 0, 'n1': n1, 'n2': n2, 'beta': beta, 'amp': 1}
kernel = self.shapelets.function(H_x, H_y, **kwargs_source_shapelet)
kernel = util.array2image(kernel)
kernel_list.append(kernel)
if n1 == 0:
n1 = n2 + 1
n2 = 0
else:
n1 -= 1
n2 += 1
return kernel_list
[docs] def decomposition(self, image, x, y, n_max, beta, deltaPix, center_x=0, center_y=0):
"""
decomposes an image into the shapelet coefficients in same order as for the function call
:param image:
:param x:
:param y:
:param n_max:
:param beta:
:param center_x:
:param center_y:
:return:
"""
num_param = int((n_max+1)*(n_max+2)/2)
param_list = np.zeros(num_param)
amp_norm = 1./beta**2*deltaPix**2
n1 = 0
n2 = 0
H_x, H_y = self.shapelets.pre_calc(x, y, beta, n_max, center_x, center_y)
for i in range(num_param):
kwargs_source_shapelet = {'center_x': center_x, 'center_y': center_y, 'n1': n1, 'n2': n2, 'beta': beta, 'amp': amp_norm}
base = self.shapelets.function(H_x, H_y, **kwargs_source_shapelet)
param = np.sum(image*base)
param_list[i] = param
if n1 == 0:
n1 = n2 + 1
n2 = 0
else:
n1 -= 1
n2 += 1
return param_list