def smooth_image(input_file=None,
output_file=None,
final_res=None,
clobber=True,
verbose=True):
''' Smooths an image to a desired resolution in arcsec.
'''
# import external modules
from scipy.ndimage.filters import gaussian_filter as smooth
import pyfits as pf
import numpy as np
# Load fits file
image, header = pf.getdata(input_file, header=True)
print input_file, image.shape
# Smooth the image
# convert from degrees/pix to "/pix
fwhm = final_res / (header['CDELT2'] * 3600.)
if image.ndim > 2:
image_smooth = np.zeros(image.shape)
for i in range(image.shape[0]):
image_smooth[i, :, :] = smooth(image[i, :, :],
sigma=(fwhm / 2., fwhm / 2.))
else:
image_smooth = smooth(image, sigma=(fwhm / 2., fwhm / 2.))
# Write out the fits file
pf.writeto(output_file, image_smooth, header=header, clobber=clobber)
def get_bubble_from_signal(sig_x,
sig_y,
sig_z,
calib_radius_func,
sigma=1,
flip_signal=False,
verbose=False):
if flip_signal:
sig_z = np.flip(sig_z, axis=0)
sig_z = smooth(sig_z, sigma=sigma)
first_peak_arg, second_peak_arg = get_salient_peaks(sig_z)
radius = calib_radius_func(np.abs(second_peak_arg - first_peak_arg) / 2)
max_peak_x = sig_x[first_peak_arg]
if verbose:
print("first_peak_arg:", first_peak_arg)
print("second_peak_arg", second_peak_arg)
if np.isnan(second_peak_arg):
return Circle(0, 0, 1)
else:
second_peak_x = sig_x[second_peak_arg]
if verbose:
print("max_peak_x", max_peak_x)
print("second_peak_x", second_peak_x)
cent_x = (max_peak_x + second_peak_x) / 2
cent_y = sig_y[0]
return Circle(cent_x, cent_y, radius)
def test_autocorrelation():
x = []
for ii in range(10):
n = np.random.random_integers(300, 500)
t = np.arange(n) / 100.
x += [smooth(np.random.normal(0, 1, t.shape), sigma=3)]
acorr, t, psd, f = autocorrelation(x, fs=100)
fig, axs = plt.subplots(3, 1)
axs[0].plot(x[0])
axs[0].plot(x[1])
axs[0].plot(x[2])
axs[1].plot(f, psd)
axs[2].plot(t, acorr)
def smooth_image(input_file=None, output_file=None, final_res=None,
clobber=True, verbose=True):
''' Smooths an image to a desired resolution in arcsec.
'''
# import external modules
from scipy.ndimage.filters import gaussian_filter as smooth
import pyfits as pf
# Load fits file
image, header = pf.getdata(input_file, header=True)
# Smooth the image
# convert from degrees/pix to "/pix
fwhm = final_res / (header['CDELT2'] * 3600.)
image_smooth = smooth(image,sigma=(fwhm/2.,fwhm/2.))
# Write out the fits file
pf.writeto(output_file, image_smooth, header=header, clobber=clobber)
def add_timepoints(self, models, session, heading_smoothing=1):
# get smoothed headings
hxyz = smooth(self.hxyz, heading_smoothing)
# add timepoints
for tp_ctr in xrange(self.ts + 1):
tp = models.Timepoint()
tp.hxyz = hxyz[tp_ctr]
tp.xidx, tp.yidx, tp.zidx = self.pos_idx[tp_ctr]
tp.odor = self.odor[tp_ctr]
tp.detected_odor = self.detected_odor[tp_ctr]
tp.src_entropy = self.entropies[tp_ctr]
session.add(tp)
# get timepoint start and end ids if first iteration
if tp_ctr == 0:
session.flush()
self.start_tp_id = tp.id
self.end_tp_id = self.start_tp_id + self.ts
def get_candidate_signals(img,
signal_len,
left_offset=5,
threshold_abs=50,
min_distance=2,
smooth_img=False,
verbose=False):
if smooth_img:
img = smooth(img, sigma=1, axis=0)
local_max = peak_local_max(img,
min_distance=min_distance,
threshold_abs=threshold_abs,
exclude_border=True)
signals_z = []
signals_x = []
signals_y = []
for idx, lm in enumerate(local_max):
xmin_offset = lm[1] - left_offset
if xmin_offset < 0:
xmin_offset = 0
xmax_offset = lm[1] + signal_len - left_offset
if xmax_offset > img.shape[1]:
xmax_offset = img.shape[1] - 1
sz = img[lm[0], xmin_offset:xmax_offset]
sx = np.arange(xmin_offset, xmax_offset, 1)
sy = np.ones(sz.shape) * lm[0]
if len(sz) == len(sx):
signals_z.append(sz)
signals_x.append(sx)
signals_y.append(sy)
return signals_x, signals_y, signals_z
def sort_trials(trialsfile, sortedfile):
# Load trials
trials, ntrials = load_trials(trialsfile)
# Preferred targets
preferred_targets = get_preferred_targets(trials)
# Smoothing parameter
t = trials[0]['t']
dt = t[1] - t[0]
sigma_smooth = int(50 / dt)
#-------------------------------------------------------------------------------------
# Sort
#-------------------------------------------------------------------------------------
sortby = [
'all', 'choice', 'motion_choice', 'colour_choice', 'context_choice'
]
sorted_trials = {s: {} for s in sortby}
ncorrect = 0
for i, trial in enumerate(trials):
choice = get_choice(trial)
if choice == 0:
target = +1
else:
target = -1
for s in ['all']:
sorted_trial = sort_func(s, preferred_targets, target, trial)
for unit, cond in enumerate(sorted_trial):
sorted_trials[s].setdefault(cond, []).append((i, unit))
if choice == trial['info']['choice']:
ncorrect += 1
for s in sortby:
if s in ['all']:
continue
sorted_trial = sort_func(s, preferred_targets, target, trial)
for unit, cond in enumerate(sorted_trial):
sorted_trials[s].setdefault(cond, []).append((i, unit))
print("[ {}.sort_trials ] {:.2f}% correct.".format(
THIS, 100 * ncorrect / ntrials))
#-------------------------------------------------------------------------------------
# Average within conditions
#-------------------------------------------------------------------------------------
nunits, ntime = trial['r'].shape
for s in sorted_trials:
# Average
for cond, i_unit in sorted_trials[s].items():
r = np.zeros((nunits, ntime))
n = np.zeros(nunits)
for i, unit in i_unit:
r[unit] += trials[i]['r'][unit]
n[unit] += 1
r = r * np.tile(safe_divide(n), (ntime, 1)).T
sorted_trials[s][cond] = smooth(r, sigma_smooth, axis=1)
# Normalize
X = 0
X2 = 0
n = 0
for cond, r in sorted_trials[s].items():
X += np.sum(r, axis=1)
X2 += np.sum(r**2, axis=1)
n += r.shape[1]
mean = X / n
std = np.sqrt(X2 / n - mean**2)
mean = np.tile(mean, (ntime, 1)).T
std = np.tile(std, (ntime, 1)).T
for cond, r in sorted_trials[s].items():
sorted_trials[s][cond] = (r - mean) / std
#-------------------------------------------------------------------------------------
# Save
#-------------------------------------------------------------------------------------
with open(sortedfile, 'wb') as f:
pickle.dump((t, sorted_trials), f, pickle.HIGHEST_PROTOCOL)
print("[ {}.sort_trials ] Sorted trials saved to {}".format(
THIS, sortedfile))
def calculate_yy(bin_edges,arrays,region,version,cov_versions,beam_version,
effective_freq,overwrite,maxval,unsanitized_beam=False,do_weights=False,
pa1_shift = None,
pa2_shift = None,
pa3_150_shift = None,
pa3_090_shift = None,
no_act_color_correction=False, ccor_exp = -1,
sim_splits=None,unblind=False,all_analytic=False,beta_samples=None):
"""
We calculate the yy power spectrum as follows.
We restrict the Fourier modes in our analysis to those within bin_edges.
This way we don't carry irrelevant pixels and thus speed up the ability to MC.
We accept two covariance versions in cov_versions, which correspond to
[act_covariance_from_split_0,act_covariance_from_split_1,other_covs].
Thus the ACT auto covariances are pre-calculated
"""
arrays = arrays.split(',')
narrays = len(arrays)
if sim_splits is not None: assert not(unblind)
def warn(): print("WARNING: no bandpass file found. Assuming array ",dm.c['id']," has no response to CMB, tSZ and CIB.")
aspecs = tutils.ASpecs().get_specs
bandpasses = not(effective_freq)
savedir = tutils.get_save_path(version,region)
assert len(cov_versions)==3
covdirs = [tutils.get_save_path(cov_versions[i],region) for i in range(3)]
for covdir in covdirs: assert os.path.exists(covdir)
if not(overwrite):
assert not(os.path.exists(savedir)), \
"This version already exists on disk. Please use a different version identifier."
try: os.makedirs(savedir)
except:
if overwrite: pass
else: raise
mask = enmap.read_map(covdir+"tilec_mask.fits")
from scipy.ndimage.filters import gaussian_filter as smooth
pm = enmap.read_map("/scratch/r/rbond/msyriac/data/planck/data/pr2/COM_Mask_Lensing_2048_R2.00_car_deep56_interp_order0.fits")
wcs = pm.wcs
mask = enmap.enmap(smooth(pm,sigma=10),wcs) * mask
shape,wcs = mask.shape,mask.wcs
Ny,Nx = shape
modlmap = enmap.modlmap(shape,wcs)
omodlmap = modlmap.copy()
ells = np.arange(0,modlmap.max())
minell = maps.minimum_ell(shape,wcs)
sel = np.where(np.logical_and(modlmap>=bin_edges[0]-minell,modlmap<=bin_edges[-1]+minell))
modlmap = modlmap[sel]
bps = []
lbeams = []
kbeams = []
shifts = []
cfreqs = []
lmins = []
lmaxs = []
names = []
for i,qid in enumerate(arrays):
dm = sints.models[sints.arrays(qid,'data_model')](region=mask,calibrated=True)
if dm.name=='act_mr3':
season,array1,array2 = sints.arrays(qid,'season'),sints.arrays(qid,'array'),sints.arrays(qid,'freq')
array = '_'.join([array1,array2])
elif dm.name=='planck_hybrid':
season,patch,array = None,None,sints.arrays(qid,'freq')
else:
raise ValueError
lmin,lmax,hybrid,radial,friend,cfreq,fgroup,wrfit = aspecs(qid)
lmins.append(lmin)
lmaxs.append(lmax)
names.append(qid)
cfreqs.append(cfreq)
if bandpasses:
try:
fname = dm.get_bandpass_file_name(array)
bps.append("data/"+fname)
if (pa1_shift is not None) and 'PA1' in fname:
shifts.append(pa1_shift)
elif (pa2_shift is not None) and 'PA2' in fname:
shifts.append(pa2_shift)
elif (pa3_150_shift is not None) and ('PA3' in fname) and ('150' in fname):
shifts.append(pa3_150_shift)
elif (pa3_090_shift is not None) and ('PA3' in fname) and ('090' in fname):
shifts.append(pa3_90_shift)
else:
shifts.append(0)
except:
warn()
bps.append(None)
else:
try: bps.append(cfreq)
except:
warn()
bps.append(None)
kbeam = tutils.get_kbeam(qid,modlmap,sanitize=not(unsanitized_beam),version=beam_version,planck_pixwin=True)
if dm.name=='act_mr3':
lbeam = tutils.get_kbeam(qid,ells,sanitize=not(unsanitized_beam),version=beam_version,planck_pixwin=False) # note no pixwin but doesnt matter since no ccorr for planck
elif dm.name=='planck_hybrid':
lbeam = None
else:
raise ValueError
lbeams.append(lbeam)
kbeams.append(kbeam.copy())
# Make responses
responses = {}
def _get_response(comp,param_override=None):
if bandpasses:
if no_act_color_correction:
r = tfg.get_mix_bandpassed(bps, comp, bandpass_shifts=shifts,
param_dict_override=param_override)
else:
r = tfg.get_mix_bandpassed(bps, comp, bandpass_shifts=shifts,
ccor_cen_nus=cfreqs, ccor_beams=lbeams,
ccor_exps = [ccor_exp] * narrays,
param_dict_override=param_override)
else:
r = tfg.get_mix(bps, comp,param_dict_override=param_override)
return r
for comp in ['tSZ','CMB','CIB']:
responses[comp] = _get_response(comp,None)
from tilec.utils import is_planck
ilcgens = []
okcoadds = []
for splitnum in range(2):
covdir = covdirs[splitnum]
kcoadds = []
for i,qid in enumerate(arrays):
lmin = lmins[i]
lmax = lmaxs[i]
if is_planck(qid):
dm = sints.models[sints.arrays(qid,'data_model')](region=mask,calibrated=True)
_,kcoadd,_ = kspace.process(dm,region,qid,mask,
skip_splits=True,
splits_fname=sim_splits[i] if sim_splits is not None else None,
inpaint=False,fn_beam = None,
plot_inpaint_path = None,
split_set=splitnum)
else:
kcoadd_name = covdir + "kcoadd_%s.npy" % qid
kcoadd = enmap.enmap(np.load(kcoadd_name),wcs)
kmask = maps.mask_kspace(shape,wcs,lmin=lmin,lmax=lmax)
dtype = kcoadd.dtype
kcoadds.append((kcoadd.copy()*kmask)[sel])
kcoadds = enmap.enmap(np.stack(kcoadds),wcs)
okcoadds.append(kcoadds.copy())
# Read Covmat
ctheory = ilc.CTheory(modlmap)
nells = kcoadds[0].size
cov = np.zeros((narrays,narrays,nells))
for aindex1 in range(narrays):
for aindex2 in range(aindex1,narrays):
qid1 = names[aindex1]
qid2 = names[aindex2]
if is_planck(names[aindex1]) or is_planck(names[aindex2]) or all_analytic:
lmin,lmax,hybrid,radial,friend,f1,fgroup,wrfit = aspecs(qid1)
lmin,lmax,hybrid,radial,friend,f2,fgroup,wrfit = aspecs(qid2)
# If both are Planck and same array, get white noise from last bin
icov = ctheory.get_theory_cls(f1,f2,a_cmb=1,a_gal=0.8)*kbeams[aindex1]*kbeams[aindex2]
if aindex1==aindex2:
pcov = enmap.enmap(np.load(covdirs[2]+"tilec_hybrid_covariance_%s_%s.npy" % (names[aindex1],names[aindex2])),wcs)
pbin_edges = np.append(np.arange(500,3000,200) ,[3000,4000,5000,5800])
pbinner = stats.bin2D(omodlmap,pbin_edges)
w = pbinner.bin(pcov)[1][-1]
icov = icov + w
else:
icov = np.load(covdir+"tilec_hybrid_covariance_%s_%s.npy" % (names[aindex1],names[aindex2]))[sel]
if aindex1==aindex2:
icov[modlmap<lmins[aindex1]] = maxval
icov[modlmap>lmaxs[aindex1]] = maxval
cov[aindex1,aindex2] = icov
cov[aindex2,aindex1] = icov
assert np.all(np.isfinite(cov))
ilcgen = ilc.HILC(modlmap,np.stack(kbeams),cov=cov,responses=responses,invert=True)
ilcgens.append(ilcgen)
solutions = ['tSZ','tSZ-CMB','tSZ-CIB']
ypowers = {}
w2 = np.mean(mask**2.)
binner = stats.bin2D(modlmap,bin_edges)
np.random.seed(100)
blinding = np.random.uniform(0.8,1.2) if not(unblind) else 1
def _get_ypow(sname,dname,dresponse=None,dcmb=False):
if dresponse is not None:
assert dname is not None
for splitnum in range(2):
ilcgens[splitnum].add_response(dname,dresponse)
ykmaps = []
for splitnum in range(2):
if dcmb:
assert dname is not None
ykmap = ilcgens[splitnum].multi_constrained_map(okcoadds[splitnum],sname,[dname,"CMB"])
else:
if dname is None:
ykmap = ilcgens[splitnum].standard_map(okcoadds[splitnum],sname)
else:
ykmap = ilcgens[splitnum].constrained_map(okcoadds[splitnum],sname,dname)
ykmaps.append(ykmap.copy())
ypower = (ykmaps[0]*ykmaps[1].conj()).real / w2
return binner.bin(ypower)[1] * blinding
# The usual solutions
for solution in solutions:
sols = solution.split('-')
if len(sols)==2:
sname = sols[0]
dname = sols[1]
elif len(sols)==1:
sname = sols[0]
dname = None
else:
raise ValueError
ypowers[solution] = _get_ypow(sname,dname,dresponse=None)
# The CIB SED samples
if beta_samples is not None:
y_bsamples = []
y_bsamples_cmb = []
for beta in beta_samples:
pdict = tfg.default_dict.copy()
pdict['beta_CIB'] = beta
response = _get_response("CIB",param_override=pdict)
y_bsamples.append( _get_ypow("tSZ","iCIB",dresponse=response,dcmb=False) )
y_bsamples_cmb.append( _get_ypow("tSZ","iCIB",dresponse=response,dcmb=True) )
else:
y_bsamples = None
y_bsamples_cmb = None
return binner.centers,ypowers,y_bsamples,y_bsamples_cmb
fig = plt.figure(1, figsize=(12, 12))
labels = ['$x$', '$y$', '$z$', '$v_x$', '$v_y$', '$v_z$']
plt.clf()
for col in range(6):
for row in range(col + 1):
print(row, col)
ax = plt.axes([.05 + col * .15, .05 + row * .15, .15, .15])
if row == col:
x = h[row][col][1][1:]
y = h[row][col][0]
ax.plot(x, y, linewidth=.5)
plt.ylabel(labels[row], rotation=0)
else:
z = h[row][col][0]
z[z == 0] = min(z[z > 0])
z = smooth(z, 10)
ax.contour(np.log(z),
100,
linewidths=.2,
linestyles='solid',
colors='black',
alpha=.5)
ax.imshow(z, alpha=.8)
ax.set_xticks([])
ax.set_yticks([])
if row == 0:
plt.xlabel(labels[col])
#-------------------------------------- Marginals
d = len(coordinates)
print 'Data saved! Collecting more...' + 'You have %s minutes left.' %(str(recording_time*5))
print 'Tattoo done, making the images now...'
# Plot the raw data
plt.plot(range(len(all_data)), all_data)
plt.title("Oscilloscope Channel 1")
plt.ylabel("Voltage (V)")
plt.xlabel("Time")
plt.savefig('%s/%s/%s_raw.pdf' %(current_dir,file_name,file_name),dpi=1000)
# Plot fancy data
all_data = np.array(all_data)
noise = np.random.normal(np.mean(all_data),(np.std(all_data)/3),len(all_data))
all_data = all_data + noise
x = smooth(all_data,sigma = np.std(all_data)*10)
grid = x.reshape(ort,-1)
figure(1)
imshow(grid, cmap = 'spectral', interpolation='gaussian')
plt.savefig('%s/%s/%s_fancy.pdf' %(current_dir,file_name,file_name),dpi=1000)
# Make movie!
def write_movie(data, fps=5):
global x
global current_dir
global file_name
print 'Making movie! Might take a bit of time (10-15 minutes). Be patient :)'
name = 0
for i in range(data.shape[0]):
for j in range(data.shape[1]):
name = name+1
"""
from __future__ import division
import numpy as np
from numpy import concatenate as cc
from scipy.signal import fftconvolve
from scipy.stats import pearsonr
from scipy import stats
from scipy.ndimage.filters import gaussian_filter1d as smooth
import matplotlib.pyplot as plt
from math_tools import stats as mt_stats
# TEST SIGNALS
T = np.arange(300)
X = smooth((np.random.uniform(0, 1, 300) > .95).astype(float), 5)
HT = np.arange(-20, 20)
H = np.exp(-HT / 7.)
H[H > 1] = 0
Y = np.convolve(X, H, mode='same')
T1 = np.array([1, 1, 0, 0, 1, 1, 0, 0, 1, 1])
def fftxcorr(x, y, dt=1.):
"""Calculate the cross correlation between two signals using fft.
Returns:
time vector, cross correlation vector
"""
def sort_trials(trialsfile, sortedfile):
# Load trials
trials, ntrials = load_trials(trialsfile)
# Preferred targets
preferred_targets = get_preferred_targets(trials)
# Smoothing parameter
t = trials[0]['t']
dt = t[1] - t[0]
sigma_smooth = int(50/dt)
#-------------------------------------------------------------------------------------
# Sort
#-------------------------------------------------------------------------------------
sortby = ['all', 'choice', 'motion_choice', 'colour_choice', 'context_choice']
sorted_trials = {s: {} for s in sortby}
ncorrect = 0
for i, trial in enumerate(trials):
choice = get_choice(trial)
if choice == 0:
target = +1
else:
target = -1
for s in ['all']:
sorted_trial = sort_func(s, preferred_targets, target, trial)
for unit, cond in enumerate(sorted_trial):
sorted_trials[s].setdefault(cond, []).append((i, unit))
if choice == trial['info']['choice']:
ncorrect += 1
for s in sortby:
if s in ['all']:
continue
sorted_trial = sort_func(s, preferred_targets, target, trial)
for unit, cond in enumerate(sorted_trial):
sorted_trials[s].setdefault(cond, []).append((i, unit))
print("[ {}.sort_trials ] {:.2f}% correct.".format(THIS, 100*ncorrect/ntrials))
#-------------------------------------------------------------------------------------
# Average within conditions
#-------------------------------------------------------------------------------------
nunits, ntime = trial['r'].shape
for s in sorted_trials:
# Average
for cond, i_unit in sorted_trials[s].items():
r = np.zeros((nunits, ntime))
n = np.zeros(nunits)
for i, unit in i_unit:
r[unit] += trials[i]['r'][unit]
n[unit] += 1
r = r*np.tile(safe_divide(n), (ntime, 1)).T
sorted_trials[s][cond] = smooth(r, sigma_smooth, axis=1)
# Normalize
X = 0
X2 = 0
n = 0
for cond, r in sorted_trials[s].items():
X += np.sum(r, axis=1)
X2 += np.sum(r**2, axis=1)
n += r.shape[1]
mean = X/n
std = np.sqrt(X2/n - mean**2)
mean = np.tile(mean, (ntime, 1)).T
std = np.tile(std, (ntime, 1)).T
for cond, r in sorted_trials[s].items():
sorted_trials[s][cond] = (r - mean)/std
#-------------------------------------------------------------------------------------
# Save
#-------------------------------------------------------------------------------------
with open(sortedfile, 'wb') as f:
pickle.dump((t, sorted_trials), f, pickle.HIGHEST_PROTOCOL)
print("[ {}.sort_trials ] Sorted trials saved to {}".format(THIS, sortedfile))
gamts = np.zeros((szg,szg))
nadv = szx/szg
for i in range(szg):
for j in range(szg):
gamts[i,j] = gamt[nadv*i:nadv*(i+1),nadv*j:nadv*(j+1)].mean()
m,c,r,p,stderr = stats.linregress(gamts.ravel(),gamr.ravel())
gamr = (gamr-c)/m
diff = gamts-gamr
print 'mc',m,c
print 'rp',r,p
print 'SN',np.abs(gamt).mean()/diff.std()
if len(sys.argv)>2:
smth = float(sys.argv[2])
gamts = smooth(gamts,smth)
gamr = smooth(gamr,smth)
##plt.figure('In')
###plt.imshow(gamt,origin='lower',extent=(-600,600,-600,600),interpolation='nearest')
plt.figure('In small')
plt.pcolor(xs,xs,gamts)
plt.figure('out')
plt.pcolor(xs,xs,gamr)
plt.figure('in vs out')
plt.plot(gamts.ravel(),gamr.ravel(),'.')
plt.show()
from orphics import maps,io,cosmology,stats,mpi
from pixell import enmap,curvedsky
from enlib import bench
import numpy as np
import os,sys,shutil
from tilec import fg as tfg,ilc,kspace,utils as tutils
from soapack import interfaces as sints
from szar import foregrounds as fgs
import healpy as hp
from actsims.util import seed_tracker
from scipy.ndimage.filters import gaussian_filter as smooth
pm = enmap.read_map("/scratch/r/rbond/msyriac/data/planck/data/pr2/COM_Mask_Lensing_2048_R2.00_car_deep56_interp_order0.fits")
wcs = pm.wcs
pmask = enmap.enmap(smooth(pm,sigma=10),wcs)
region = "deep56"
arrays = "p04,p05,p06,p07,p08".split(',')
mask = sints.get_act_mr3_crosslinked_mask(region) * pmask
# io.hplot(mask,"pmask.png")
# sys.exit()
w2 = np.mean(mask**2.)
modlmap = mask.modlmap()
lmax = 5500
ells = np.arange(0,lmax,1)
ctheory = ilc.CTheory(ells)
aspecs = tutils.ASpecs().get_specs
rho = np.sqrt(uu**2+vv**2)
umax = u.max()
upix = np.gradient(u)[0]
nd,xb,yb = np.histogram2d(b1,b2,bins=np.linspace(-szx*pix/2,szx*pix/2,szk+1))
fov = nd>0
gamr = np.fft.fftshift(np.fft.ifftn(np.fft.ifftshift(fgamr))).real
if (szx/szk)%2==0:
gamt = np.pad(gamt[:-(szx/(2*szk)),:-(szx/(2*szk))],((szx/(2*szk),0),(szx/(2*szk),0)),'constant')
gamt = gamt.reshape(szk,szx/szk,szk,-1).mean((1,3))
x = np.linspace(-szx*pix/2,szx*pix/2,szk)
xx,yy = np.meshgrid(x,x,sparse=1)
gamr = smooth(gamr,sfac)
gamt = smooth(gamt,sfac)
m,c,r,p,stderr = stats.linregress(gamt[fov],gamr[fov])
gamr -= c
gamr /= m
gamr *= fov
gamt *= fov
diff = gamr-gamt
print 'Real space'
print 'mc',m,c
print 'rps',r,p,stderr
print 'SN',diff.std()/gamt.std()
print '...'
fm,fc,fr,fp,fstderr = stats.linregress(fgamt[rho<=umax],fgamr[rho<=umax])