def deflect(self, xim, yim, lens):
"""
Calculate deflection following Keeton,Mao,Witt 2000.
Parameters:
xim, yim
2D Arrays of image coordinates we're going to lens,
probably generated by np.meshgrid.
lens
A lens object; we use this to shift the coordinate system
to be centered on the lens.
"""
ximage, yimage = xim.copy(), yim.copy()
ximage -= lens.x['value']
yimage -= lens.y['value']
if not np.isclose(lens.PA['value'], 0.):
r, theta = cart2pol(ximage, yimage)
ximage, yimage = pol2cart(r, theta - (lens.PA['value'] * deg2rad))
# KMW2000, altered for our coordinate convention.
g, thg = self.shear['value'], (self.shearangle['value'] -
lens.PA['value']) * deg2rad
dxs = -g * np.cos(2 * thg) * ximage - g * np.sin(2 * thg) * yimage
dys = -g * np.sin(2 * thg) * ximage + g * np.cos(2 * thg) * yimage
if not np.isclose(lens.PA['value'], 0.):
r, theta = cart2pol(dxs, dys)
dxs, dys = pol2cart(r, theta + (lens.PA['value'] * deg2rad))
self.deflected_x = dxs
self.deflected_y = dys
def deflect(self,xim,yim,lens):
"""
Calculate deflection following Keeton,Mao,Witt 2000.
Parameters:
xim, yim
2D Arrays of image coordinates we're going to lens,
probably generated by np.meshgrid.
lens
A lens object; we use this to shift the coordinate system
to be centered on the lens.
"""
ximage,yimage = xim.copy(), yim.copy()
ximage -= lens.x['value']; yimage -= lens.y['value']
if not np.isclose(lens.PA['value'], 0.):
r,theta = cart2pol(ximage,yimage)
ximage,yimage = pol2cart(r,theta-(lens.PA['value']*deg2rad))
# KMW2000, altered for our coordinate convention.
g,thg = self.shear['value'], (self.shearangle['value']-lens.PA['value'])*deg2rad
dxs = -g*np.cos(2*thg)*ximage - g*np.sin(2*thg)*yimage
dys = -g*np.sin(2*thg)*ximage + g*np.cos(2*thg)*yimage
if not np.isclose(lens.PA['value'], 0.):
r,theta = cart2pol(dxs,dys)
dxs,dys = pol2cart(r,theta+(lens.PA['value']*deg2rad))
self.deflected_x = dxs; self.deflected_y = dys
def deflect(self, xim, yim, Dd, Ds, Dds):
"""
Follow Kormann+1994 for the lensing deflections.
Parameters:
xim, yim
2D Arrays of image coordinates we're going to lens,
probably generated by np.meshgrid.
Dd, Ds, Dds
Distances to the lens, source and between the source
and lens (units don't matter as long as they're the
same). Can't be calculated only from lens due to source
distances.
"""
if self._altered: # Only redo if something is new.
ximage, yimage = xim.copy(), yim.copy() # for safety.
f = 1. - self.e['value']
fprime = np.sqrt(1. - f**2.)
# K+94 parameterizes in terms of LOS velocity dispersion and then
# basically the Einstein radius.
sigma = ((self.M['value'] * Ds * G * Msun * c**2.) /
(4 * np.pi**2. * Dd * Dds * Mpc))**(1 / 4.)
Xi0 = 4 * np.pi * (sigma / c)**2. * (Dd * Dds / Ds)
# Flip units, the recenter and rotate grid to lens center and major axis
ximage *= arcsec2rad
yimage *= arcsec2rad
ximage -= (self.x['value'] * arcsec2rad)
yimage -= (self.y['value'] * arcsec2rad)
if not np.isclose(self.PA['value'], 0.):
r, theta = cart2pol(ximage, yimage)
ximage, yimage = pol2cart(r,
theta - (self.PA['value'] * deg2rad))
phi = np.arctan2(yimage, ximage)
# Calculate the deflections, account for e=0 (the SIS), which has
# cancelling infinities. K+94 eq 27a.
if np.isclose(f, 1.):
dxs = -(Xi0 / Dd) * np.cos(phi)
dys = -(Xi0 / Dd) * np.sin(phi)
else:
dxs = -(Xi0 / Dd) * (np.sqrt(f) / fprime) * np.arcsinh(
np.cos(phi) * fprime / f)
dys = -(Xi0 / Dd) * (np.sqrt(f) / fprime) * np.arcsin(
np.sin(phi) * fprime)
# Rotate and shift back to sky frame
if not np.isclose(self.PA['value'], 0.):
r, theta = cart2pol(dxs, dys)
dxs, dys = pol2cart(r, theta + (self.PA['value'] * deg2rad))
dxs *= rad2arcsec
dys *= rad2arcsec
self.deflected_x = dxs
self.deflected_y = dys
self._altered = False
def deflect(self,xim,yim,Dd,Ds,Dds):
"""
Follow Kormann+1994 for the lensing deflections.
Parameters:
xim, yim
2D Arrays of image coordinates we're going to lens,
probably generated by np.meshgrid.
Dd, Ds, Dds
Distances to the lens, source and between the source
and lens (units don't matter as long as they're the
same). Can't be calculated only from lens due to source
distances.
"""
if self._altered: # Only redo if something is new.
ximage, yimage = xim.copy(), yim.copy() # for safety.
f = 1. - self.e['value']
fprime = np.sqrt(1. - f**2.)
# K+94 parameterizes in terms of LOS velocity dispersion and then
# basically the Einstein radius.
sigma = ((self.M['value']*Ds*G*Msun*c**2.)/(4*np.pi**2. * Dd*Dds*Mpc))**(1/4.)
Xi0 = 4*np.pi * (sigma/c)**2. * (Dd*Dds/Ds)
# Flip units, the recenter and rotate grid to lens center and major axis
ximage *= arcsec2rad; yimage *= arcsec2rad
ximage -= (self.x['value']*arcsec2rad)
yimage -= (self.y['value']*arcsec2rad)
if not np.isclose(self.PA['value'], 0.):
r,theta = cart2pol(ximage,yimage)
ximage,yimage = pol2cart(r,theta-(self.PA['value']*deg2rad))
phi = np.arctan2(yimage,ximage)
# Calculate the deflections, account for e=0 (the SIS), which has
# cancelling infinities. K+94 eq 27a.
if np.isclose(f, 1.):
dxs = -(Xi0/Dd)*np.cos(phi)
dys = -(Xi0/Dd)*np.sin(phi)
else:
dxs = -(Xi0/Dd)*(np.sqrt(f)/fprime)*np.arcsinh(np.cos(phi)*fprime/f)
dys = -(Xi0/Dd)*(np.sqrt(f)/fprime)*np.arcsin(np.sin(phi)*fprime)
# Rotate and shift back to sky frame
if not np.isclose(self.PA['value'], 0.):
r,theta = cart2pol(dxs,dys)
dxs,dys = pol2cart(r,theta+(self.PA['value']*deg2rad))
dxs *= rad2arcsec; dys *= rad2arcsec
self.deflected_x = dxs
self.deflected_y = dys
self._altered = False
def Zphase_MahajanOSA(self): phasemap = np.zeros((self.PARAMS['1'],self.PARAMS['1'])) phasemap = phasemap + phasemap*1j sizeoffield = self.PARAMS['4'] B = 0.2 # fraction if the diffuse component; A = 1 - B # raction of directed component; peakx = 0 # normalized location of peak reflectance in x-direction peaky = 0 # normalized location of peak reflectance in x-direction p = 0 # 0.047 # set to zero to turn off the amplitude factor (Values from Burns et al in mm^(-2) self.PARAMS['6'] = 0 # ----------Joel's Method -------------------------------- nx = z_adjust(np.arange(1, self.PARAMS['1'] + 1), sizeoffield, self.PARAMS['1']) ny = z_adjust(np.arange(1, self.PARAMS['1'] + 1), sizeoffield, self.PARAMS['1']) xx, yy = np.meshgrid(nx, ny) angle, norm_radius = utils.cart2pol(xx,yy) norm_radius = norm_radius / (float(self.PARAMS['2']) / 2.) r = norm_radius phase = utils.computePhase(self.c, angle, r) d = np.sqrt((peakx - xx)**2 + (peaky - yy)**2); SCfactor = B + A * 10**(-p * ((self.PARAMS['2'])**2) * d**2) phase_result = SCfactor * np.exp(-1j * 2 * np.pi * phase / self.PARAMS['5']) phasemap[np.where(norm_radius <= 1)] = phase_result[np.where(norm_radius <= 1)] self.PARAMS['6'] = np.sum((norm_radius <= 1).astype(int)) # #-------- Austin's Method --------------------------------- # newsize = self.PARAMS['1'] # for ny in np.arange(1, self.PARAMS['1'] + 1): # for nx in np.arange(1, self.PARAMS['1'] + 1): # xpos = (((float(nx) - 1.) * (float(sizeoffield) / float(newsize))) - (sizeoffield / 2.)) # ypos = (((float(ny) - 1.) * (float(sizeoffield) / float(newsize))) - (sizeoffield / 2.)) # angle, norm_radius = utils.cart2pol(xpos,ypos) # norm_radius = float(norm_radius) / (float(self.PARAMS['2']) / 2.) # r = norm_radius # if norm_radius > 1: # pass # else: # phase = utils.computePhase(self.c, angle, r) # d = np.sqrt((peakx - xpos)**2 + (peaky - ypos)**2); # SCfactor = B + A * 10**(-p * ((self.PARAMS['2'])**2) * d**2) # phasemap[nx,ny] = SCfactor * np.exp(-1j * 2 * np.pi * phase / self.PARAMS['5']) # self.PARAMS['6'] += 1 return phasemap
def update(self, steering):
"""
Update the positions and headings
steering: vector of (x, y) steering
"""
self.accelerations = steering * self.dt
# old heading
_, old_headings = cart2pol(self.velocities)
new_velocities = self.velocities + self.accelerations * self.dt
# new velocity in polar coordinates
speeds, new_headings = cart2pol(new_velocities)
# calculate heading diff
headings_diff = np.radians(
180 -
(180 - np.degrees(new_headings) + np.degrees(old_headings)) % 360)
# if the heading diff is too big, we cut the turn at max_turn or min_turn
# use np.where
new_headings = np.where(headings_diff < -self.max_turn,
old_headings - self.max_turn, new_headings)
new_headings = np.where(self.max_turn < headings_diff,
old_headings + self.max_turn, new_headings)
# if the speed is too slow or too big, we adjust it
# use np.where
speeds = np.where(speeds < self.min_speed, self.min_speed, speeds)
speeds = np.where(speeds > self.max_speed, self.max_speed, speeds)
# set the new velocity
# modify pol2cart
self.velocities = pol2cart(speeds, new_headings)
self.headings = new_headings
# move
self.positions += self.velocities * self.dt
self.adjust_positions_to_boundaries()
def Zwave_MahajanOSA(self):
newsize = np.ceil(self.PARAMS['7']*self.PARAMS['2']).astype(int)
waveabermap = np.zeros((newsize, newsize))
sizeoffield = self.PARAMS['2']
self.PARAMS['6'] = 0
#------ Joel's Method -------------------------------------------------------------
nx = z_adjust(np.arange(1, newsize+1), sizeoffield, newsize)
ny = z_adjust(np.arange(1, newsize+1), sizeoffield, newsize)
xx, yy = np.meshgrid(nx, ny)
angle, norm_radius = utils.cart2pol(xx,yy)
norm_radius = norm_radius / (self.PARAMS['3'] / 2)
r = norm_radius
phase = utils.computePhase(self.c, angle, r)
waveabermap[np.where(norm_radius > self.PARAMS['2']/self.PARAMS['3'])] = float('nan')
waveabermap[np.where(norm_radius <= self.PARAMS['2']/self.PARAMS['3'])] = phase[np.where(norm_radius <= self.PARAMS['2']/self.PARAMS['3'])]
# #---- Austin's Method --------------------------------------------------------------
# for ny in range(newsize):
# for nx in range(newsize):
# xpos = ((nx - 1) * (sizeoffield / newsize) - (sizeoffield / 2))
# print(xpos)
# ypos = ((ny - 1) * (sizeoffield / newsize) - (sizeoffield / 2))
# angle, norm_radius = utils.cart2pol(xpos,ypos)
# norm_radius = norm_radius / (self.PARAMS['3'] / 2)
# r = norm_radius
# if norm_radius > self.PARAMS['2']/self.PARAMS['3']:
# waveabermap[nx,ny] = float('nan')
# else:
# phase = utils.computePhase(self.c, angle, r)
# waveabermap[nx,ny] = phase
# self.PARAMS['6'] += 1
return waveabermap
vecY = np.array([0])
vecSd = np.array([0.5])
mdlPrms = rmp_deg_pixel_x_y_s(vecY, vecX, vecSd, (int(pix), int(pix)),
-fovHeight / 2., fovHeight / 2., -fovHeight / 2.,
fovHeight / 2.)
mdlPrms = np.stack(mdlPrms, axis=1)
prf_ntr = crt_2D_gauss(pix, pix, mdlPrms[:, 0], mdlPrms[:, 1], mdlPrms[:, 2])
# %% apply gradient tp prf
gridX, gridY = np.meshgrid(
np.linspace(-pix / 2., pix / 2., pix, endpoint=False),
np.linspace(-pix / 2., pix / 2., pix, endpoint=False))
_, gridRad = cart2pol(gridX, gridY)
gradOtw = np.copy(np.ones(gridRad.shape) * gridRad.max() - gridRad)
gradInw = np.copy(gridRad)
gradOtw = np.divide(gradOtw, np.sum(gradOtw, axis=(0, 1)))
gradInw = np.divide(gradInw, np.sum(gradInw, axis=(0, 1)))
prf_otw = cnvl_grad_prf(prf_ntr, gradOtw, Normalize=True)
prf_inw = cnvl_grad_prf(prf_ntr, gradInw, Normalize=True)
# %% save new prfs to disk
fig, ax = plt.subplots()
cax = plt.imshow(prf_otw, cmap="viridis")
varFigName = os.path.join("/media/sf_D_DRIVE/MotDepPrf/Presentation/figures",
"Figure_prfshift", "prf_otw" + ".svg")
import itertools
import os
import numpy as np
import config_MotDepPrf as cfg
from PIL import Image
from utils import createBinCircleMask, getDistIma, assignBorderVals, cart2pol
# %% create the radial sine wave pattern
# get cartesian coordinates which are needed to define the textures
x, y = np.meshgrid(
np.linspace(-cfg.fovHeight / 2., cfg.fovHeight / 2., cfg.pix / 2.),
np.linspace(-cfg.fovHeight / 2., cfg.fovHeight / 2., cfg.pix / 2.))
# get polar coordinates which are needed to define the textures
theta, radius = cart2pol(x, y)
# define the phase for inward/outward conditin
phase = np.linspace(0., 2. * np.pi, cfg.nFrames / cfg.cycPerSec)
# get the array that divides field in angular cycles
polCycles = np.sin(cfg.angularCycles * theta)
polCycles[np.greater_equal(polCycles, 0)] = 1
polCycles[np.less(polCycles, 0)] = -1
# get radial sine wave gratings for main conditions
stimTexture = np.zeros(
(cfg.pix / 2., cfg.pix / 2., cfg.nFrames / cfg.cycPerSec))
for ind, ph in enumerate(phase):
ima = np.sin(cfg.spatFreq * 2. * np.pi * radius - ph)
stimTexture[..., ind] = ima
def test_cart_pol_conv():
print(ut.pol2cart((2, np.pi / 2)))
print(ut.cart2pol((5, 5)))
