def sphere_model_pattern(Nx, Ny, diameter, intensity, wavelength, pixel_size, detector_distance, x0=0, y0=0, detector_adu_photon=1., detector_quantum_efficiency=1., material='water', downsampling=1):
s = (Ny, Nx)
img = np.zeros(shape=s)
msk = np.ones(shape=s, dtype='bool')
Y,X = spimage.grid(s, (0,0)) # Non-centered grid vectors in [px]
# Center grid
Xc = X - x0 # Centered grid x vectors in [px]
Yc = Y - y0 # Centered grid y vectors in [px]
# Grid to q-space (but we keep units in px)
Xc = spimage.x_to_qx(Xc,pixel_size,detector_distance)
Yc = spimage.y_to_qy(Yc,pixel_size,detector_distance)
Rc = np.sqrt(Xc**2+Yc**2)
size = sphere_model_convert_diameter_to_size(diameter, wavelength, pixel_size, detector_distance)
scaling = sphere_model_convert_intensity_to_scaling(intensity, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
I_fit = I_sphere_diffraction(scaling, Rc, size)
return I_fit
def fit_sphere_intensity_radial(r, img_r, diameter, intensity, wavelength, pixel_size, detector_distance, full_output=False, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', maxfev=1000):
"""
...
usage:
======
...
Parameters:
===========
...
"""
R = numpy.array(r, dtype="float")
R = spimage.x_to_qx(R, pixel_size, detector_distance)
size = sphere_model_convert_diameter_to_size(diameter, wavelength, pixel_size, detector_distance)
I_fit_m = lambda i: I_sphere_diffraction(sphere_model_convert_intensity_to_scaling(i, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, detector_adu_photon, material),R,size)
E_fit_m = lambda i: I_fit_m(i) - img_r
if len(img_r):
[intensity], cov, infodict, mesg, ier = leastsq(E_fit_m, intensity, maxfev=maxfev, xtol=1e-3, full_output=True)
# Reduced Chi-squared and normalised mean difference and standard error
chisquared = (E_fit_m(intensity)**2).sum()/(img_r.size - 1)
nmerr = abs( E_fit_m(intensity) ).sum() / (img_r.size - 1) / abs(img_r).sum()
#### EXPERIMENTAL
#flin = lambda m, c: m*r + c
#ferr = lambda v: E_fit_m(intensity) - flin(v[0], v[1])
#sphericity = scipy.optimize.leastsq(ferr,(0,img_r[0]))[0][0]
#### ---
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = numpy.nan
else:
infodict={}
pcov = None
chisquared = 0
error
if full_output:
infodict['chisquared'] = chisquared
infodict['error'] = nmerr
infodict['pcov'] = pcov
#infodict['sphericity'] = sphericity
return intensity, infodict
else:
return intensity
def fit_sphere_intensity_radial(r, img_r, diameter, intensity, wavelength, pixel_size, detector_distance, full_output=False, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', maxfev=1000):
"""
...
usage:
======
...
Parameters:
===========
...
"""
R = np.array(r, dtype="float")
R = spimage.x_to_qx(R, pixel_size, detector_distance)
size = sphere_model_convert_diameter_to_size(diameter, wavelength, pixel_size, detector_distance)
I_fit_m = lambda i: I_sphere_diffraction(sphere_model_convert_intensity_to_scaling(i, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, detector_adu_photon, material),R,size)
E_fit_m = lambda i: I_fit_m(i) - img_r
if len(img_r):
[intensity], cov, infodict, mesg, ier = leastsq(E_fit_m, intensity, maxfev=maxfev, xtol=1e-3, full_output=True)
# Reduced Chi-squared and normalised mean difference and standard error
chisquared = (E_fit_m(intensity)**2).sum()/(img_r.size - 1)
nmerr = abs( E_fit_m(intensity) ).sum() / (img_r.size - 1) / abs(img_r).sum()
#### EXPERIMENTAL
#flin = lambda m, c: m*r + c
#ferr = lambda v: E_fit_m(intensity) - flin(v[0], v[1])
#sphericity = scipy.optimize.leastsq(ferr,(0,img_r[0]))[0][0]
#### ---
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = np.nan
else:
infodict={}
pcov = None
chisquared = 0
error
if full_output:
infodict['chisquared'] = chisquared
infodict['error'] = nmerr
infodict['pcov'] = pcov
#infodict['sphericity'] = sphericity
return intensity, infodict
else:
return intensity
def fit_sphere_diameter_radial(r, img_r, diameter, intensity, wavelength, pixel_size, detector_distance, full_output=False, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', maxfev=1000, do_brute_evals=0,dlim=None):
if len(img_r.shape) > 1 or len(r.shape) > 1:
print "Error: Inputs have to be one-dimensional."
return
S = sphere_model_convert_intensity_to_scaling(intensity, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
R = numpy.array(r, dtype="float")
R = spimage.x_to_qx(R, pixel_size, detector_distance)
I_fit_m = lambda d: I_sphere_diffraction(S,R,sphere_model_convert_diameter_to_size(d, wavelength, pixel_size, detector_distance))
def E_fit_m(d):
if not (img_r.std() and I_fit_m(d).std()): return 1.
else: return 1-scipy.stats.pearsonr(I_fit_m(d), img_r)[0]
# Start with brute force with a sensible range
# We'll assume at least 20x oversampling
if do_brute_evals:
if dlim is None:
dmin = sphere_model_convert_size_to_diameter(1./(img_r.size*2), wavelength, pixel_size, detector_distance)
dmax = dmin*img_r.size*2/20
else:
(dmin,dmax) = dlim
diameter = scipy.optimize.brute(E_fit_m, [(dmin, dmax)], Ns=do_brute_evals)
# End with least square
[diameter], cov, infodict, mesg, ier = leastsq(E_fit_m, diameter, maxfev=maxfev, xtol=1e-5, full_output=True)
diameter = abs(diameter)
# Reduced Chi-squared and standard error
chisquared = ((I_fit_m(diameter) - img_r)**2).sum()/(img_r.size - 1)
nmerr = abs( I_fit_m(diameter) - img_r ).sum() / (img_r.size - 1) / abs(img_r).sum()
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = numpy.nan
if full_output:
infodict['chisquared'] = chisquared
infodict['error'] = nmerr
infodict['pcov'] = pcov
infodict['img_r'] = img_r
infodict['I_fit_m'] = I_fit_m(diameter)
return diameter, infodict
else:
return diameter
def _prepare_for_fitting(img, msk, x0, y0, rmax, downsampling, adup, do_photon_counting, pixel_size, detector_distance):
if rmax is None: rmax = max(img.shape)/2 # Handle default of rmax
s = img.shape # Shape of image
Mr = spimage.rmask(s, rmax, (x0,y0)) # Radial mask
msk = msk * Mr # Merge mask and radial mask
img = img[::downsampling, ::downsampling]
msk = msk[::downsampling, ::downsampling]
Y,X = spimage.grid(s, (0,0)) # Non-centered grid vectors in [px]
# Center grid
Xc = X - x0 # Centered grid x vectors in [px]
Yc = Y - y0 # Centered grid y vectors in [px]
# Grid to q-space (but we keep units in px)
Xc = spimage.x_to_qx(Xc,pixel_size,detector_distance)
Yc = spimage.y_to_qy(Yc,pixel_size,detector_distance)
Xmc = Xc[msk] # Centered and masked grid x vectors in [px]
Ymc = Yc[msk] # Centered and masked grid y vectors in [px]
img = img / adup
if do_photon_counting: img = numpy.round(img) * (img > 0)
return Xmc, Ymc, img, msk
def fit_sphere_diameter_radial(r, img_r, diameter, intensity, wavelength, pixel_size, detector_distance, full_output=False, detector_adu_photon=1, detector_quantum_efficiency=1, material='water', maxfev=1000, do_brute_evals=0,dlim=None):
if len(img_r.shape) > 1 or len(r.shape) > 1:
print("Error: Inputs have to be one-dimensional.")
return
S = sphere_model_convert_intensity_to_scaling(intensity, diameter, wavelength, pixel_size, detector_distance, detector_quantum_efficiency, 1, material)
R = np.array(r, dtype="float")
R = spimage.x_to_qx(R, pixel_size, detector_distance)
I_fit_m = lambda d: I_sphere_diffraction(S,R,sphere_model_convert_diameter_to_size(d, wavelength, pixel_size, detector_distance))
def E_fit_m(d):
if not (img_r.std() and I_fit_m(d).std()): return 1.
else: return 1-scipy.stats.pearsonr(I_fit_m(d), img_r)[0]
# Start with brute force with a sensible range
# We'll assume at least 20x oversampling
if do_brute_evals:
if dlim is None:
dmin = sphere_model_convert_size_to_diameter(1./(img_r.size*2), wavelength, pixel_size, detector_distance)
dmax = dmin*img_r.size*2/20
else:
(dmin,dmax) = dlim
diameter = scipy.optimize.brute(E_fit_m, [(dmin, dmax)], Ns=do_brute_evals)
# End with least square
[diameter], cov, infodict, mesg, ier = leastsq(E_fit_m, diameter, maxfev=maxfev, xtol=1e-5, full_output=True)
diameter = abs(diameter)
# Reduced Chi-squared and standard error
chisquared = ((I_fit_m(diameter) - img_r)**2).sum()/(img_r.size - 1)
nmerr = abs( I_fit_m(diameter) - img_r ).sum() / (img_r.size - 1) / abs(img_r).sum()
if cov is not None:
pcov = cov[0,0]*chisquared
else:
pcov = np.nan
if full_output:
infodict['chisquared'] = chisquared
infodict['error'] = nmerr
infodict['pcov'] = pcov
infodict['img_r'] = img_r
infodict['I_fit_m'] = I_fit_m(diameter)
return diameter, infodict
else:
return diameter
def _prepare_for_fitting(img, msk, x0, y0, rmax, downsampling, adup, do_photon_counting, pixel_size, detector_distance):
if rmax is None: rmax = max(img.shape)/2 # Handle default of rmax
s = img.shape # Shape of image
Mr = spimage.rmask(s, rmax, (x0,y0)) # Radial mask
msk = msk * Mr # Merge mask and radial mask
img = img[::downsampling, ::downsampling]
msk = msk[::downsampling, ::downsampling]
Y,X = spimage.grid(s, (0,0)) # Non-centered grid vectors in [px]
# Center grid
Xc = X - x0 # Centered grid x vectors in [px]
Yc = Y - y0 # Centered grid y vectors in [px]
# Grid to q-space (but we keep units in px)
Xc = spimage.x_to_qx(Xc,pixel_size,detector_distance)
Yc = spimage.y_to_qy(Yc,pixel_size,detector_distance)
Xmc = Xc[msk] # Centered and masked grid x vectors in [px]
Ymc = Yc[msk] # Centered and masked grid y vectors in [px]
img = img / adup
if do_photon_counting: img = np.round(img) * (img > 0)
return Xmc, Ymc, img, msk
return confmap, dlim, ilim
# Radial mask
def rmask(r, sh, cx, cy):
ny, nx = sh
xx, yy = np.meshgrid(np.arange(nx), np.arange(ny))
return (xx - cx)**2 + (yy - cy)**2 > (r**2)
infile = "../data/r%04d_lowq.h5" % args.run
with sparse.SmallFrame(infile, geometry="../geometry/b3_lowq.geom",
mode="r+") as f:
mask = f.activepixels[:300, :300]
sh = mask.shape
qr = spimage.x_to_qx(np.arange(0, sh[0] / 2.), pixelsize / downsampling,
distance)
def model(p, q):
diameter, intensity = p
A = spimage.sphere_model_convert_intensity_to_scaling(
intensity,
diameter,
wavelength,
pixelsize,
distance,
material=material)
s = spimage.sphere_model_convert_diameter_to_size(
diameter, wavelength, pixelsize, distance)
I = spimage.I_sphere_diffraction(A, q, s)
return I
