def deflections(self, xin, yin):
from numpy import ones, arctan as atan, arctanh as atanh
from math import cos, sin, pi
from numpy import arcsin as asin, arcsinh as asinh
x, y = self.align_coords(xin, yin)
q = self.q
if q == 1.:
q = 1. - 1e-7 # Avoid divide-by-zero errors
eps = (1. - q**2)**0.5
if self.eta == 1.:
# SIE models
r = (x**2 + y**2)**0.5
r[r == 0.] = 1e-9
xout = self.b * asinh(eps * x / q / r) * q**0.5 / eps
yout = self.b * asin(eps * y / r) * q**0.5 / eps
else:
from powerlaw import powerlawdeflections as pld
b, eta = self.b, self.eta
s = 1e-7
if x.ndim > 1:
yout, xout = pld(-1 * y.ravel(), x.ravel(), b, eta, s, q)
xout, yout = xout.reshape(x.shape), -1 * yout.reshape(y.shape)
else:
yout, xout = pld(-1 * y, x, b, eta, s, q)
yout = -1 * yout
theta = -(self.theta - pi / 2.)
ctheta = cos(theta)
stheta = sin(theta)
x = xout * ctheta + yout * stheta
y = yout * ctheta - xout * stheta
return x, y
def deflections(self, xin, yin):
from numpy import ones, arctan as atan, arctanh as atanh
from math import cos, sin, pi
from numpy import arcsin as asin, arcsinh as asinh
x, y = self.align_coords(xin, yin)
q = self.q
if q == 1.:
q = 1. - 1e-7 # Avoid divide-by-zero errors
eps = (1. - q**2)**0.5
if self.eta == 1.:
# SIE models
r = (x**2 + y**2)**0.5
r[r == 0.] = 1e-9
xout = self.b * asinh(eps * x / q / r) * q**0.5 / eps
yout = self.b * asin(eps * y / r) * q**0.5 / eps
else:
from powerlaw import powerlawdeflections as pld
b, eta = self.b, self.eta
s = 1e-7
if x.ndim > 1:
yout, xout = pld(-1 * y.ravel(), x.ravel(), b, eta, s, q)
xout, yout = xout.reshape(x.shape), -1 * yout.reshape(y.shape)
else:
yout, xout = pld(-1 * y, x, b, eta, s, q)
yout = -1 * yout
theta = -(self.theta - pi / 2.)
ctheta = cos(theta)
stheta = sin(theta)
x = xout * ctheta + yout * stheta
y = yout * ctheta - xout * stheta
return x, y
def deflections(self, xin, yin, d=1):
b = self.b * d
from numpy import ones, arctan as atan, arctanh as atanh
from math import cos, sin, pi
from numpy import arcsin as asin, arcsinh as asinh
x, y = self.align_coords(xin, yin, False)
q = self.q
if q == 1.:
q = 1. - 1e-7 # Avoid divide-by-zero errors
eps = (1. - q**2)**0.5
if self.eta == 1.:
# SIE models
r = (x**2 + y**2)**0.5
r[r == 0.] = 1e-9
# xout = self.b*asinh(eps*x/q/r)*q**0.5/eps
# yout = self.b*asin(eps*y/r)*q**0.5/eps
xout = b * asinh(eps * y / q / r) * q**0.5 / eps
yout = b * asin(eps * -x / r) * q**0.5 / eps
xout, yout = -yout, xout
x, y = self.align_coords(xout, yout, False, revert=True)
return x - self.x, y - self.y
theta = 2 - self.theta #-(self.theta - pi/2.)
ctheta = cos(theta)
stheta = sin(theta)
x = xout * ctheta + yout * stheta
y = yout * ctheta - xout * stheta
return x, y
else:
from powerlaw import powerlawdeflections as pld
b, eta = b, self.eta
s = 1e-4
if x.ndim > 1:
# yout,xout = pld(-1*y.ravel(),x.ravel(),b,eta,s,q)
# xout,yout = xout.reshape(x.shape),-1*yout.reshape(y.shape)
xout, yout = pld(x.ravel(), y.ravel(), b, eta, s, q)
xout, yout = xout.reshape(x.shape), yout.reshape(y.shape)
else:
xout, yout = pld(x, y, b, eta, s, q)
# yout,xout = pld(-1*y,x,b,eta,s,q)
# yout = -1*yout
# theta = -(self.theta - pi/2.)
# ctheta = cos(theta)
# stheta = sin(theta)
# x = xout*ctheta+yout*stheta
# y = yout*ctheta-xout*stheta
# return x,y
x, y = self.align_coords(xout, yout, False, revert=True)
return x - self.x, y - self.y
def deflections(self, xin, yin):
if self.NoFreeParams == True:
try:
return self.deflx, self.defly
except:
pass
x, y = self.align_coords(xin, yin)
q = self.q
if q == 1.:
q = 1. - 1e-7 # Avoid divide-by-zero errors
eps = (1. - q**2)**0.5
if self.eta == 1.:
# SIE models
r = (x**2 + y**2)**0.5
r[r == 0.] = 1e-9
xout = self.b * np.arcsinh(eps * x / q / r) * q**0.5 / eps
yout = self.b * np.arcsin(eps * y / r) * q**0.5 / eps
else:
from powerlaw import powerlawdeflections as pld
b, eta = self.b, self.eta
s = 1e-7
if x.ndim > 1:
yout, xout = pld(-1 * y.ravel(), x.ravel(), b, eta, s, q)
xout, yout = xout.reshape(x.shape), -1 * yout.reshape(y.shape)
else:
yout, xout = pld(-1 * y, x, b, eta, s, q)
yout = -1 * yout
theta = -(self.theta - np.pi / 2.)
ctheta = np.cos(theta)
stheta = np.sin(theta)
x = xout * ctheta + yout * stheta
y = yout * ctheta - xout * stheta
self.deflx = x
self.defly = y
return x, y
def caustic(self):
if self.eta != 1:
from powerlaw import powerlawmag as plm, powerlawdeflections as pld
import numpy
from scipy import interpolate
q = self.q
b, eta = self.b, self.eta
gam = eta * 0.5
q0 = (1.0 - gam) * b**(2.0 * gam) / (q**gam)
r = numpy.linspace(q0 / 2., q0 * 2, 100)
x0, y0, mag = plm(r, r * 0., b, eta, 1e-4, q)
if mag[0] > 0:
r = numpy.linspace(1e-7, q0 * 2, 200)
x0, y0, mag = plm(r, r * 0., b, eta, 1e-4, q)
while mag[-1] < 0:
q0 *= 2
r = numpy.linspace(q0 / 2., q0 * 2, 100)
x0, y0, mag = plm(r, r * 0., b, eta, 1e-4, q)
tmp = interpolate.splrep(r, mag)
root = interpolate.sproot(tmp, 1)[0]
theta = numpy.linspace(0, numpy.pi / 2, 500)
ctheta = numpy.cos(theta)
stheta = numpy.sin(theta)
rvals = theta * 0. + root
for i in range(1, theta.size):
r = numpy.linspace(root * 0.9, root * 1.1, 20)
x = r * ctheta[i]
y = r * stheta[i]
x0, y0, mag = plm(x, y, b, eta, 1e-4, q)
while mag[0] > 0:
root *= 0.9
r = numpy.linspace(root * 0.9, root * 1.1, 20)
x = r * ctheta[i]
y = r * stheta[i]
x0, y0, mag = plm(x, y, b, eta, 1e-4, q)
while mag[-1] < 0:
root *= 1.1
r = numpy.linspace(root * 0.9, root * 1.1, 20)
x = r * ctheta[i]
y = r * stheta[i]
x0, y0, mag = plm(x, y, b, eta, 1e-4, q)
tmp = interpolate.splrep(r, mag)
root = interpolate.sproot(tmp, 1)[0]
rvals[i] = root
x, y = rvals * ctheta, rvals * stheta
x = numpy.concatenate(
(x, -1 * x[::-1][1:], -1 * x[1:], x[::-1][1:]))
y = numpy.concatenate(
(y, y[::-1][1:], -1 * y[1:], -1 * y[::-1][1:]))
x0, y0 = pld(x, y, b, eta, 1e-4, q)
x0, y0 = self.align_coords(x - x0, y - y0, False, revert=True)
return x0, y0
from numpy import ones, arctan as atan, arctanh as atanh
from numpy import cos, sin, pi, linspace
from numpy import arcsin as asin, arcsinh as asinh
q = self.q
if q == 1.:
q = 1. - 1e-7 # Avoid divide-by-zero errors
eps = (1. - q**2)**0.5
theta = linspace(0, 2 * pi, 5000)
ctheta = cos(theta)
stheta = sin(theta)
delta = (ctheta**2 + q**2 * stheta**2)**0.5
xout = ctheta * q**0.5 / delta - asinh(eps * ctheta / q) * q**0.5 / eps
yout = stheta * q**0.5 / delta - asin(eps * stheta) * q**0.5 / eps
xout, yout = xout * self.b, yout * self.b
theta = -(self.theta - pi / 2.)
ctheta = cos(theta)
stheta = sin(theta)
x = xout * ctheta + yout * stheta
y = yout * ctheta - xout * stheta
return x + self.x, y + self.y