def init():
# Set some SIE lens-model parameters and pack them into an array:
l_amp = lamp # Einstein radius
l_xcen = -2.5 # x position of center
l_ycen = 2.5 # y position of center
l_axrat = lax # minor-to-major axis ratio
l_pa = lpa # major-axis position angle (degrees) c.c.w. from x axis
lpar = np.asarray([l_amp, l_xcen, l_ycen, l_axrat, l_pa])
lenspar = np.asarray([l_amp, lsig, l_xcen, l_ycen, l_axrat, l_pa])
# The following lines will plot the un-lensed and lensed images side by side:
(xg, yg) = ldf.sie_grad(x, y, lpar)
g_lensimage = ldf.gauss_2d(x - xg, y - yg, gpar)
lens_source = ldf.gauss_2d(x, y, lenspar)
lens_source[lens_source < 0.6] = np.nan
ax2.imshow(g_lensimage, **myargs, clim=(vmin, vmax))
lens = ax2.imshow(lens_source, **lensargs, clim=(vmin, vmax))
ax2.set_yticklabels([])
ax2.set_xticklabels([])
ax2.set_yticks([])
ax2.set_xticks([])
txt = ax2.text(20, 457, 'Lensed Image', size=15, color='w', zorder=5)
txt.set_path_effects(
[PathEffects.withStroke(linewidth=5, foreground='k')])
return lens,
def update(val):
g_axrat = sgaxrat.val
g_xcen = sgxcen.val
g_ycen = sgycen.val
g_pa = sgpa.val
g_sig = sgsig.val
l_axrat = slaxrat.val
gpar = np.asarray([g_amp, g_sig, g_xcen, g_ycen, g_axrat, g_pa])
lpar = np.asarray([l_amp, l_xcen, l_ycen, l_axrat, l_pa])
#g_image = ldf.gauss_2d(x, y, gpar)
(xg, yg) = ldf.sie_grad(x, y, lpar)
g_lensimage = ldf.gauss_2d(x-xg, y-yg, gpar)
f.set_data(g_lensimage)
fig.canvas.draw_idle()
def lens_object(lax,lamp=1.5,lsig=0.05,lx=0.,ly=0.,lpa=0.): # Set some SIE lens-model parameters and pack them into an array: l_amp = lamp # Einstein radius l_xcen = lx # x position of center l_ycen = ly # y position of center l_axrat = lax # minor-to-major axis ratio l_pa = lpa # major-axis position angle (degrees) c.c.w. from x axis lpar = np.asarray([l_amp, l_xcen, l_ycen, l_axrat, l_pa]) lpar2 = np.asarray([l_amp, l_xcen, l_ycen, 2., l_pa]) # rax of 2. lenspar = np.asarray([l_amp, lsig, l_xcen, l_ycen, l_axrat, l_pa]) # The following lines will plot the un-lensed and lensed images side by side: (xg, yg) = ldf.sie_grad(x, y, lpar) g_lensimage = ldf.gauss_2d(x-xg, y-yg, gpar) lens_source = ldf.gauss_2d(x, y, lenspar) lens_source[lens_source < 0.6] = np.nan return g_lensimage,lens_source
xhilo = [-2.5, 2.5] yhilo = [-2.5, 2.5] x = (xhilo[1] - xhilo[0]) * np.outer(np.ones(ny), np.arange(nx)) / float(nx-1) + xhilo[0] y = (yhilo[1] - yhilo[0]) * np.outer(np.arange(ny), np.ones(nx)) / float(ny-1) + yhilo[0] # Set some SIE lens-model parameters and pack them into an array: l_amp = 1.5 # Einstein radius l_xcen = 0. # x position of center l_ycen = 0. # y position of center l_axrat = 1. # minor-to-major axis ratio l_pa = 0. # major-axis position angle (degrees) c.c.w. from x axis lpar = np.asarray([l_amp, l_xcen, l_ycen, l_axrat, l_pa]) lenspar = np.asarray([l_amp, 0.05, l_xcen, l_ycen, l_axrat, l_pa]) # The following lines will plot the un-lensed and lensed images side by side: (xg, yg) = ldf.sie_grad(x, y, lpar) plt.figure(figsize=(8,4)) gs1 = gridspec.GridSpec(1,2) gs1.update(wspace=0.03) cmap = plt.cm.viridis cir = plt.Circle((250,250),150,fill=False,ls='--',color='C0') ax1 = plt.subplot(gs1[0]) im = ax1.imshow(xg,**myargs)#,clim=(0.5,2.2)) # set to make the lens the same always vmin, vmax = im.get_clim() ax1.add_artist(cir) ax1.set_yticklabels([]); ax1.set_xticklabels([]) ax1.set_yticks([]); ax1.set_xticks([]) txt = ax1.text(20,457,'x deflection', size=15, color='w')
def lookup(par):
"""
PURPOSE: Calculate the flux received in a SDSSIII fiber over the intrinsic flux as a
function of impact parameter, Einstein radius, axis ratio, size, etc...
USAGE: f_f/f_i = lookup(par[b, q_l, P.A_l, amp, sigma_s, xcen_s, ycen_s,q_s, P.A_s])
ARGUMENTS:
pars:
par[0]: Einstein Radius
par[1]: Axis ratio of lens
par[2]: Position angle of lens (c.c.w. major-axis rotation w.r.t. x-axis)
par[3]: Amplitude of source galaxy
par[4]: Intermediate-axis sigma of source galaxy
par[5]: x coordinate of source galaxy
par[6]: y coordinate of source galaxy
par[7]: Axis ratio of source
par[8]: Position angle of source (c.c.w. major-axis rotation w.r.t. x-axis)
RETURNS: Ratio of flux in fiber w.r.t intrinsic flux
WRITTEN: Ryan A. Arneson, U. of Utah, 2010
"""
#Define the pixel scale to be 0.01"/pixel
myargs = {
'interpolation': 'nearest',
'origin': 'lower',
'cmap': cm.gray,
'hold': False
}
psf = g.gauss2d(800, 150)
nx = 1600.
ny = 1600.
ximg = n.outer(n.ones(ny), n.arange(nx, dtype='float')) - 800.
yimg = n.outer(n.arange(ny, dtype='float'), n.ones(nx)) - 800.
#lpar_guess = n.asarray([b, xcen, ycen, q, P.A.])
lpar_guess = n.asarray([par[0], 0.0, 0.0, par[1], par[2]])
#gpar_guess = n.asarray([amp., sigma, xcen, ycen, q, P.A.])
gpar_guess = n.asarray([par[3], par[4], par[5], par[6], par[7], par[8]])
xg, yg = ldf.sie_grad(ximg, yimg, lpar_guess)
lmodel = ldf.gauss_2d(ximg - xg, yimg - yg, gpar_guess)
#lmodel = signal.fftconvolve(lmodel, psf, mode='same')
#lmodel = lmodel[1:1601,1:1601]
fiber = yimg
for i in range(0, 1600):
for j in range(0, 1600):
fiber[i, j] = n.sqrt(fiber[i, j]**2 + (j - 800.)**2)
for i in range(0, 1600):
for j in range(0, 1600):
if fiber[i, j] <= 100:
fiber[i, j] = 1.0
else:
fiber[i, j] = 0.0
fiber = signal.fftconvolve(fiber, psf, mode='same')
fiber = fiber[1:1601, 1:1601]
f_f = n.sum(lmodel * fiber)
#calculate the intrinisic flux (i.e. b=0)
lpar_guess[0] = 0.0
ximg = n.outer(n.ones(ny), n.arange(nx, dtype='float')) - 800.
yimg = n.outer(n.arange(ny, dtype='float'), n.ones(nx)) - 800.
xg, yg = ldf.sie_grad(ximg, yimg, lpar_guess)
lmodel2 = ldf.gauss_2d(ximg - xg, yimg - yg, gpar_guess)
#lmodel2 = signal.fftconvolve(lmodel2, psf, mode='same')
#lmodel2 = lmodel2[1:1601,1:1601]
f_i = n.sum(lmodel2 * fiber)
mag = f_f / f_i
#p.imshow(n.hstack((lmodel*fiber,lmodel2*fiber)),**myargs)
return mag
g_xcen = 0.0 # x position of center g_ycen = 0.0 # y position of center g_axrat = 1.0 # minor-to-major axis ratio g_pa = 0.0 # major-axis position angle (degrees) c.c.w. from x axis gpar = np.asarray([g_amp, g_sig, g_xcen, g_ycen, g_axrat, g_pa]) # Set some SIE lens-model parameters and pack them into an array: l_amp = 1.5 # Einstein radius l_xcen = 0.0 # x position of center l_ycen = 0.0 # y position of center l_axrat = 1.0 # minor-to-major axis ratio l_pa = 0.0 # major-axis position angle (degrees) c.c.w. from x axis lpar = np.asarray([l_amp, l_xcen, l_ycen, l_axrat, l_pa]) #g_image = ldf.gauss_2d(x, y, gpar) (xg, yg) = ldf.sie_grad(x, y, lpar) g_lensimage = ldf.gauss_2d(x-xg, y-yg, gpar) f = plt.imshow(g_lensimage, **myargs) ax = plt.axes([0.25,0.1,0.65,0.03]) slaxrat = Slider(ax, 'Lens Axis Ratio', 0.0, 5.0, valinit=l_axrat) ax = plt.axes([0.25,0.15,0.65,0.03]) sgaxrat = Slider(ax, 'Gaussian Axis Ratio', 0.0, 5.0, valinit=g_axrat) ax = plt.axes([0.25,0.20,0.65,0.03]) sgpa = Slider(ax, 'Gaussian Major-Axis Angle', 0.0, 360.0, valinit=g_pa) ax = plt.axes([0.25,0.25,0.65,0.03]) sgxcen = Slider(ax, 'Gaussian X-center', -1.5, 1.5, valinit=g_xcen)