def refineCTF(radial_array,
angle_array,
amp_con,
z1,
z2,
angle_astig,
normPSD,
cs,
wavelength,
refineFlags=(1, 1, 1, 1),
weights=None,
msg=True):
"""
take a 2D normalized PSB and refines all CTF parameters
using a linear least squares
all values in meters
"""
print "BEFORE ac=%.3f, z1=%.3e, z2=%.3e, astig=%.1f" % (amp_con, z1, z2,
angle_astig)
print cs, wavelength
print "resolution limits %.2f <> %.2f" % (1.0e10 / radial_array.max(),
1.0e10 / radial_array.min())
### convert parameters
C = math.sin(math.asin(amp_con) - math.pi / 4.)
D = math.sqrt(1 - C**2)
zavg = (z1 + z2) / 2.0
zdiff = z2 - z1
if abs(zdiff) < 1e-9:
# this prevents singular matrices
zdiff = 1e-9
astigrad = math.radians(angle_astig)
### create astigmatic gamma function
radialsq_array = radial_array**2
astigcos_array = numpy.cos(2.0 * (angle_array - astigrad))
defocus_array = zavg - zdiff / 2.0 * astigcos_array
gamma_array = (-0.5 * math.pi * cs * wavelength**3 * radialsq_array**2 +
math.pi * wavelength * radialsq_array * defocus_array)
del defocus_array, radial_array
### create refinement vectors
cosvec = numpy.cos(2 * gamma_array) #C
sinvec = numpy.sin(2 * gamma_array) #D
dCTFdGamma_array = -2 * C * sinvec + 2 * D * cosvec
onevec = numpy.ones(radialsq_array.shape)
zavgvec = wavelength * math.pi * radialsq_array * dCTFdGamma_array
zdiffvec = -0.5 * zavgvec * astigcos_array
zastigvec = zavgvec * zdiff * numpy.sin(2.0 * (angle_array - astigrad))
del gamma_array, astigcos_array, dCTFdGamma_array
### create X data matrix and adjust y values
#X = numpy.array([cosvec, sinvec]).transpose()
X = numpy.vstack([cosvec, sinvec])
if refineFlags[0] == 1:
X = numpy.vstack([X, zavgvec])
if refineFlags[1] == 1:
X = numpy.vstack([X, zdiffvec])
if refineFlags[2] == 1:
X = numpy.vstack([X, zastigvec])
X = numpy.vstack([X, onevec, radialsq_array])
X = X.transpose()
del cosvec, sinvec, zavgvec, zdiffvec, zastigvec, angle_array
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = 2 * normPSD - 1
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
index = 0
C = beta[index]
index += 1
D = beta[index]
index += 1
if refineFlags[0] == 1:
dzavg = beta[index]
print "dzavg", dzavg
index += 1
else:
dzavg = 0
if refineFlags[1] == 1:
dzdiff = beta[index]
index += 1
print "dzdiff", dzdiff
else:
dzdiff = 0
if refineFlags[2] == 1:
dtheta = beta[index] % 2 * math.pi
index += 1
print "dtheta", dtheta
else:
dtheta = 0
constant = beta[index]
index += 1
sqterm = beta[index]
index += 1
if refineFlags[3] == 1:
psi = 0.5 * math.atan2(C, D)
phi = psi + math.pi / 4
amp_con = math.sin(phi)
zavg += dzavg
zdiff += dzdiff
if zdiff < 0:
zdiff = 0
z1 = zavg - zdiff / 2
z2 = zavg + zdiff / 2.
if refineFlags[2] == 1:
astigrad += dtheta
angle_astig = math.degrees(astigrad)
print "AFTER ac=%.3f, z1=%.3e, z2=%.3e, astig=%.1f" % (amp_con, z1, z2,
angle_astig)
if msg is True:
from matplotlib import pyplot
args = numpy.argsort(radialsq_array)
radialsq_array = radialsq_array[args]
yprime = yprime[args]
pyplot.clf()
yprime2 = yprime - constant - sqterm * radialsq_array
yprime2 /= numpy.abs(yprime2).max()
newGamma = (-0.5 * math.pi * cs * wavelength**3 * radialsq_array**2 +
math.pi * wavelength * radialsq_array * zavg)
newB = math.sqrt(1 - amp_con**2)
adjctf1 = 2 * numpy.power(
amp_con * numpy.cos(newGamma) + newB * numpy.sin(newGamma), 2) - 1
pyplot.plot(radialsq_array, yprime2, '.', color="gray")
#pyplot.plot(radialsq_array, yprime2, 'k-',)
pyplot.plot(
radialsq_array,
adjctf1,
'b--',
)
pyplot.title("CTF Refine 2D Fit")
pyplot.subplots_adjust(
wspace=0.05,
hspace=0.05,
bottom=0.05,
left=0.05,
top=0.95,
right=0.95,
)
pyplot.show()
if amp_con < 0.0:
apDisplay.printWarning(
"amp contrast is negative (reduce defocus): %.4f" % (amp_con))
#return None
if amp_con > 0.5:
apDisplay.printWarning(
"amp contrast is too large (increase defocus): %.8f" % (amp_con))
#return None
return amp_con, z1, z2, angle_astig
def refineCTFOneDimension(radial_array,
amp_con,
zavg,
normPSD,
cs,
wavelength,
weights=None,
msg=True):
"""
take a 2D normalized PSB and refines all CTF parameters
using a linear least squares
all values in meters
"""
apDisplay.printColor("BEFORE ac=%.3f, zavg=%.3e" % (amp_con, zavg), "cyan")
print cs, wavelength
print "resolution limits %.2f <> %.2f" % (1.0e10 / radial_array.max(),
1.0e10 / radial_array.min())
### convert parameters
C = math.sin(math.asin(amp_con) - math.pi / 4.)
D = math.sqrt(1 - C**2)
### create astigmatic gamma function
radialsq_array = radial_array**2
gamma_array = (-0.5 * math.pi * cs * wavelength**3 * radialsq_array**2 +
math.pi * wavelength * radialsq_array * zavg)
### create refinement vectors
cosvec = numpy.cos(2 * gamma_array) #C
sinvec = numpy.sin(2 * gamma_array) #D
onevec = numpy.ones(radialsq_array.shape)
dCTFdGamma_array = -2 * C * sinvec + 2 * D * cosvec
zavgvec = wavelength * math.pi * radialsq_array * dCTFdGamma_array
### create X data matrix and adjust
X = numpy.array([cosvec, sinvec, zavgvec, onevec,
radialsq_array]).transpose()
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = (normPSD - normPSD.mean())
yprime /= numpy.abs(yprime).max()
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
C = beta[0]
D = beta[1]
dzavg = beta[2]
constant = beta[3]
sqterm = beta[4]
print beta
psi = 0.5 * math.atan2(C, D)
print "psi=", psi
phi = psi + math.pi / 4
print "phi=", phi
amp_con = math.sin(phi)
if dzavg / zavg > 1:
apDisplay.printWarning("Bad defocus change: %.4e --> %.4e" %
(zavg, zavg + dzavg))
return None
zavg += dzavg
print "AFTER ac=%.3f, zavg=%.3e" % (amp_con, zavg)
apDisplay.printColor("AFTER ac=%.3f, zavg=%.3e" % (amp_con, zavg), "cyan")
newGamma = (-0.5 * math.pi * cs * wavelength**3 * radialsq_array**2 +
math.pi * wavelength * radialsq_array * zavg)
fitctf1 = C * cosvec + D * sinvec
fitctf1b = numpy.sin(2 * gamma_array + 2 * psi)
fitctf2 = numpy.sin(2 * newGamma + 2 * psi)
newB = math.sqrt(1 - amp_con**2)
# need to do the y' = 2 y - 1
adjctf1 = 2 * numpy.power(
amp_con * numpy.cos(newGamma) + newB * numpy.sin(newGamma), 2) - 1
crosscorr = scipy.stats.pearsonr(fitctf2, adjctf1)[0]
if crosscorr < -0.6:
print "likely 180 degree out of phase"
apDisplay.printWarning("Bad angle translation: %.8f" % (amp_con))
if msg is True:
from matplotlib import pyplot
pyplot.clf()
yprime2 = yprime - constant - sqterm * radialsq_array
yprime2 /= numpy.abs(yprime2).max()
pyplot.plot(radialsq_array, yprime2, '.', color="gray")
pyplot.plot(
radialsq_array,
yprime2,
'k-',
)
pyplot.plot(
radialsq_array,
fitctf1b,
'r--',
)
pyplot.plot(
radialsq_array,
fitctf2,
'g--',
)
pyplot.plot(
radialsq_array,
adjctf1,
'b--',
)
conf1 = scipy.stats.pearsonr(yprime2, fitctf1b)[0]
conf2 = scipy.stats.pearsonr(yprime2, adjctf1)[0]
conf3 = scipy.stats.pearsonr(yprime2, fitctf2)[0]
#pyplot.ylim(ymin=-1.05, ymax=1.05)
pyplot.title("CTF Refine 1D Fit (%.2f, %.2f, %.2f) CC=%.3f" %
(conf1, conf2, conf3, crosscorr))
pyplot.subplots_adjust(
wspace=0.05,
hspace=0.05,
bottom=0.05,
left=0.05,
top=0.95,
right=0.95,
)
pyplot.show()
if crosscorr < 0.5:
apDisplay.printWarning("Bad angle translation: %.8f" % (amp_con))
return None
if zavg > 20e-6 or zavg < 0.1e-6:
apDisplay.printWarning("Bad defocus change: %.4e --> %.4e" %
(zavg - dzavg, zavg))
return None
if amp_con < 0.0:
apDisplay.printWarning(
"amp contrast is negative (reduce defocus): %.4f" % (amp_con))
#return None
if amp_con > 0.6:
apDisplay.printWarning(
"amp contrast is too large (increase defocus): %.8f" % (amp_con))
#return None
return amp_con, zavg
def refineAmplitudeContrast(radial_array,
defocus,
normPSD,
cs,
wavelength,
weights=None,
msg=True):
"""
takes elliptical average data and fits it to the equation
A cos(x) + B sin(x)
"""
if msg is True:
print "resolution limits %.2f <> %.2f" % (1.0e10 / radial_array.max(),
1.0e10 / radial_array.min())
# create X matrix
radialsq = radial_array**2
if msg is True:
print 1.0 / radial_array[-1], wavelength, defocus, cs
gamma = (-0.5 * math.pi * cs * wavelength**3 * radialsq**2 +
math.pi * wavelength * radialsq * defocus)
cosvec = numpy.cos(2 * gamma) #C
sinvec = numpy.sin(2 * gamma) #D
onevec = numpy.ones(gamma.shape) #extra constant
X = numpy.array([cosvec, sinvec, onevec, radialsq]).transpose()
#del cosvec, sinvec, gamma
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = (normPSD - normPSD.mean())
yprime /= numpy.abs(yprime).max()
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
C = beta[0]
D = beta[1]
constant = beta[2]
sqterm = beta[3]
if msg is True:
print beta, radial_array.shape
psi = 0.5 * math.atan2(C, D)
if msg is True:
print "psi=", psi
phi = psi + math.pi / 4
if msg is True:
print "phi=", phi
amp_con = math.sin(phi)
if msg is True:
apDisplay.printColor("amplitude contrast = %.8f" % (amp_con), "cyan")
fitctf1 = C * cosvec + D * sinvec
fitctf2 = numpy.sin(2 * gamma + 2 * psi)
newB = math.sqrt(1 - amp_con**2)
# need to do the y' = 2 y - 1
adjctf1 = 2 * numpy.power(
amp_con * numpy.cos(gamma) + newB * numpy.sin(gamma), 2) - 1
#adjctf2 = 2 * numpy.power(numpy.sin(gamma + math.asin(amp_con)), 2) - 1
crosscorr = scipy.stats.pearsonr(fitctf2, adjctf1)[0]
yprime2 = yprime - constant - sqterm * radialsq
yprime2 /= numpy.abs(yprime2).max()
fitconf = scipy.stats.pearsonr(yprime2, fitctf2)[0]
if msg is True:
from matplotlib import pyplot
pyplot.clf()
pyplot.plot(radialsq, yprime2, '.', color="gray")
pyplot.plot(
radialsq,
yprime2,
'k-',
)
pyplot.plot(
radialsq,
fitctf1,
'r--',
)
pyplot.plot(
radialsq,
fitctf2,
'g--',
)
pyplot.plot(
radialsq,
adjctf1,
'b--',
)
conf1 = scipy.stats.pearsonr(yprime2, fitctf1)[0]
conf2 = scipy.stats.pearsonr(yprime2, adjctf1)[0]
conf3 = scipy.stats.pearsonr(yprime2, fitctf2)[0]
print "conf %.4f, %.4f, %.4f; cc = %.4f" % (conf1, conf2, conf3,
crosscorr)
#pyplot.ylim(ymin=-1.05, ymax=1.05)
pyplot.title("Amplitude Contrast Fit (%.2f, %.2f, %.2f) CC=%.3f" %
(conf1, conf2, conf3, crosscorr))
pyplot.subplots_adjust(
wspace=0.05,
hspace=0.05,
bottom=0.05,
left=0.05,
top=0.95,
right=0.95,
)
pyplot.show()
if crosscorr < -0.6:
print "likely 180 degree out of phase"
apDisplay.printWarning("Bad angle translation: %.8f" % (amp_con))
return None
if fitconf < 0.1 and amp_con > 0.4:
apDisplay.printWarning("Bad fit confidence %.3f, ac=%.8f" %
(fitconf, amp_con))
return None
if crosscorr < 0.5:
apDisplay.printWarning("Bad angle translation: %.8f" % (amp_con))
return None
if amp_con < 0.0:
apDisplay.printWarning(
"amp contrast is negative (reduce defocus): %.4f" % (amp_con))
#return None
if amp_con > 0.6:
apDisplay.printWarning(
"amp contrast is too large (increase defocus): %.8f" % (amp_con))
#return None
return amp_con
def refineCTF(radial_array, angle_array,
amp_con, z1, z2, angle_astig,
normPSD, cs, wavelength, refineFlags=(1,1,1,1), weights=None, msg=True):
"""
take a 2D normalized PSB and refines all CTF parameters
using a linear least squares
all values in meters
"""
print "BEFORE ac=%.3f, z1=%.3e, z2=%.3e, astig=%.1f"%(amp_con, z1, z2, angle_astig)
print cs, wavelength
print "resolution limits %.2f <> %.2f"%(1.0e10/radial_array.max(), 1.0e10/radial_array.min())
### convert parameters
C = math.sin(math.asin(amp_con) - math.pi/4.)
D = math.sqrt(1 - C**2)
zavg = (z1 + z2)/2.0
zdiff = z2 - z1
if abs(zdiff) < 1e-9:
# this prevents singular matrices
zdiff = 1e-9
astigrad = math.radians(angle_astig)
### create astigmatic gamma function
radialsq_array = radial_array**2
astigcos_array = numpy.cos(2.0*(angle_array - astigrad))
defocus_array = zavg - zdiff/2.0 * astigcos_array
gamma_array = ( -0.5*math.pi * cs * wavelength**3 * radialsq_array**2
+ math.pi * wavelength * radialsq_array * defocus_array )
del defocus_array, radial_array
### create refinement vectors
cosvec = numpy.cos(2*gamma_array) #C
sinvec = numpy.sin(2*gamma_array) #D
dCTFdGamma_array = -2*C*sinvec + 2*D*cosvec
onevec = numpy.ones(radialsq_array.shape)
zavgvec = wavelength*math.pi*radialsq_array * dCTFdGamma_array
zdiffvec = -0.5*zavgvec * astigcos_array
zastigvec = zavgvec * zdiff * numpy.sin(2.0*(angle_array- astigrad))
del gamma_array, astigcos_array, dCTFdGamma_array
### create X data matrix and adjust y values
#X = numpy.array([cosvec, sinvec]).transpose()
X = numpy.vstack([cosvec, sinvec])
if refineFlags[0] == 1:
X = numpy.vstack([X, zavgvec])
if refineFlags[1] == 1:
X = numpy.vstack([X, zdiffvec])
if refineFlags[2] == 1:
X = numpy.vstack([X, zastigvec])
X = numpy.vstack([X, onevec, radialsq_array])
X = X.transpose()
del cosvec, sinvec, zavgvec, zdiffvec, zastigvec, angle_array
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = 2 * normPSD - 1
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
index = 0
C = beta[index]
index += 1
D = beta[index]
index += 1
if refineFlags[0] == 1:
dzavg = beta[index]
print "dzavg", dzavg
index += 1
else:
dzavg = 0
if refineFlags[1] == 1:
dzdiff = beta[index]
index += 1
print "dzdiff", dzdiff
else:
dzdiff = 0
if refineFlags[2] == 1:
dtheta = beta[index] % 2*math.pi
index += 1
print "dtheta", dtheta
else:
dtheta = 0
constant = beta[index]
index += 1
sqterm = beta[index]
index += 1
if refineFlags[3] == 1:
psi = 0.5*math.atan2(C,D)
phi = psi + math.pi/4
amp_con = math.sin(phi)
zavg += dzavg
zdiff += dzdiff
if zdiff < 0:
zdiff = 0
z1 = zavg - zdiff/2
z2 = zavg + zdiff/2.
if refineFlags[2] == 1:
astigrad += dtheta
angle_astig = math.degrees(astigrad)
print "AFTER ac=%.3f, z1=%.3e, z2=%.3e, astig=%.1f"%(amp_con, z1, z2, angle_astig)
if msg is True:
from matplotlib import pyplot
args = numpy.argsort(radialsq_array)
radialsq_array = radialsq_array[args]
yprime = yprime[args]
pyplot.clf()
yprime2 = yprime - constant - sqterm*radialsq_array
yprime2 /= numpy.abs(yprime2).max()
newGamma = ( -0.5*math.pi * cs * wavelength**3 * radialsq_array**2
+ math.pi * wavelength * radialsq_array * zavg )
newB = math.sqrt(1 - amp_con**2)
adjctf1 = 2 * numpy.power(amp_con*numpy.cos(newGamma) + newB*numpy.sin(newGamma), 2) - 1
pyplot.plot(radialsq_array, yprime2, '.', color="gray")
#pyplot.plot(radialsq_array, yprime2, 'k-',)
pyplot.plot(radialsq_array, adjctf1, 'b--',)
pyplot.title("CTF Refine 2D Fit")
pyplot.subplots_adjust(wspace=0.05, hspace=0.05,
bottom=0.05, left=0.05, top=0.95, right=0.95, )
pyplot.show()
if amp_con < 0.0:
apDisplay.printWarning("amp contrast is negative (reduce defocus): %.4f"%(amp_con))
#return None
if amp_con > 0.5:
apDisplay.printWarning("amp contrast is too large (increase defocus): %.8f"%(amp_con))
#return None
return amp_con, z1, z2, angle_astig
def refineCTFOneDimension(radial_array, amp_con, zavg, normPSD, cs, wavelength, weights=None, msg=True):
"""
take a 2D normalized PSB and refines all CTF parameters
using a linear least squares
all values in meters
"""
apDisplay.printColor("BEFORE ac=%.3f, zavg=%.3e"%(amp_con, zavg), "cyan")
print cs, wavelength
print "resolution limits %.2f <> %.2f"%(1.0e10/radial_array.max(), 1.0e10/radial_array.min())
### convert parameters
C = math.sin(math.asin(amp_con) - math.pi/4.)
D = math.sqrt(1 - C**2)
### create astigmatic gamma function
radialsq_array = radial_array**2
gamma_array = ( -0.5*math.pi * cs * wavelength**3 * radialsq_array**2
+ math.pi * wavelength * radialsq_array * zavg )
### create refinement vectors
cosvec = numpy.cos(2*gamma_array) #C
sinvec = numpy.sin(2*gamma_array) #D
onevec = numpy.ones(radialsq_array.shape)
dCTFdGamma_array = -2*C*sinvec + 2*D*cosvec
zavgvec = wavelength*math.pi*radialsq_array * dCTFdGamma_array
### create X data matrix and adjust
X = numpy.array([cosvec, sinvec, zavgvec, onevec, radialsq_array]).transpose()
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = (normPSD - normPSD.mean())
yprime /= numpy.abs(yprime).max()
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
C = beta[0]
D = beta[1]
dzavg = beta[2]
constant = beta[3]
sqterm = beta[4]
print beta
psi = 0.5*math.atan2(C,D)
print "psi=", psi
phi = psi + math.pi/4
print "phi=", phi
amp_con = math.sin(phi)
if dzavg/zavg > 1:
apDisplay.printWarning("Bad defocus change: %.4e --> %.4e"%(zavg, zavg+dzavg))
return None
zavg += dzavg
print "AFTER ac=%.3f, zavg=%.3e"%(amp_con, zavg)
apDisplay.printColor("AFTER ac=%.3f, zavg=%.3e"%(amp_con, zavg), "cyan")
newGamma = ( -0.5*math.pi * cs * wavelength**3 * radialsq_array**2
+ math.pi * wavelength * radialsq_array * zavg )
fitctf1 = C*cosvec + D*sinvec
fitctf1b = numpy.sin(2*gamma_array + 2*psi)
fitctf2 = numpy.sin(2*newGamma + 2*psi)
newB = math.sqrt(1 - amp_con**2)
# need to do the y' = 2 y - 1
adjctf1 = 2 * numpy.power(amp_con*numpy.cos(newGamma) + newB*numpy.sin(newGamma), 2) - 1
crosscorr = scipy.stats.pearsonr(fitctf2, adjctf1)[0]
if crosscorr < -0.6:
print "likely 180 degree out of phase"
apDisplay.printWarning("Bad angle translation: %.8f"%(amp_con))
if msg is True:
from matplotlib import pyplot
pyplot.clf()
yprime2 = yprime - constant - sqterm*radialsq_array
yprime2 /= numpy.abs(yprime2).max()
pyplot.plot(radialsq_array, yprime2, '.', color="gray")
pyplot.plot(radialsq_array, yprime2, 'k-',)
pyplot.plot(radialsq_array, fitctf1b, 'r--',)
pyplot.plot(radialsq_array, fitctf2, 'g--',)
pyplot.plot(radialsq_array, adjctf1, 'b--',)
conf1 = scipy.stats.pearsonr(yprime2, fitctf1b)[0]
conf2 = scipy.stats.pearsonr(yprime2, adjctf1)[0]
conf3 = scipy.stats.pearsonr(yprime2, fitctf2)[0]
#pyplot.ylim(ymin=-1.05, ymax=1.05)
pyplot.title("CTF Refine 1D Fit (%.2f, %.2f, %.2f) CC=%.3f"%(conf1, conf2, conf3, crosscorr))
pyplot.subplots_adjust(wspace=0.05, hspace=0.05,
bottom=0.05, left=0.05, top=0.95, right=0.95, )
pyplot.show()
if crosscorr < 0.5:
apDisplay.printWarning("Bad angle translation: %.8f"%(amp_con))
return None
if zavg > 20e-6 or zavg < 0.1e-6:
apDisplay.printWarning("Bad defocus change: %.4e --> %.4e"%(zavg-dzavg, zavg))
return None
if amp_con < 0.0:
apDisplay.printWarning("amp contrast is negative (reduce defocus): %.4f"%(amp_con))
#return None
if amp_con > 0.6:
apDisplay.printWarning("amp contrast is too large (increase defocus): %.8f"%(amp_con))
#return None
return amp_con, zavg
def refineAmplitudeContrast(radial_array, defocus, normPSD, cs, wavelength, weights=None, msg=True):
"""
takes elliptical average data and fits it to the equation
A cos(x) + B sin(x)
"""
if msg is True:
print "resolution limits %.2f <> %.2f"%(1.0e10/radial_array.max(), 1.0e10/radial_array.min())
# create X matrix
radialsq = radial_array**2
if msg is True:
print 1.0/radial_array[-1], wavelength, defocus, cs
gamma = ( -0.5 * math.pi * cs * wavelength**3 * radialsq**2
+ math.pi * wavelength * radialsq * defocus )
cosvec = numpy.cos(2*gamma) #C
sinvec = numpy.sin(2*gamma) #D
onevec = numpy.ones(gamma.shape) #extra constant
X = numpy.array([cosvec, sinvec, onevec, radialsq]).transpose()
#del cosvec, sinvec, gamma
# create weighted matrix
if weights is None:
# make an identity matrix for no weights
weights = numpy.ones(normPSD.shape[0])
# adjust y values
yprime = (normPSD - normPSD.mean())
yprime /= numpy.abs(yprime).max()
## solve it
beta = leastsq.totalLeastSquares(X, yprime, weights)
if beta is None:
beta = leastsq.numpyLeastSquares(X, yprime)
del X, weights
if beta is None:
apDisplay.printWarning("Least squares failed")
return None
#translate the values
C = beta[0]
D = beta[1]
constant = beta[2]
sqterm = beta[3]
if msg is True:
print beta, radial_array.shape
psi = 0.5*math.atan2(C,D)
if msg is True:
print "psi=", psi
phi = psi + math.pi/4
if msg is True:
print "phi=", phi
amp_con = math.sin(phi)
if msg is True:
apDisplay.printColor("amplitude contrast = %.8f"%(amp_con), "cyan")
fitctf1 = C*cosvec + D*sinvec
fitctf2 = numpy.sin(2*gamma + 2*psi)
newB = math.sqrt(1 - amp_con**2)
# need to do the y' = 2 y - 1
adjctf1 = 2 * numpy.power(amp_con*numpy.cos(gamma) + newB*numpy.sin(gamma), 2) - 1
#adjctf2 = 2 * numpy.power(numpy.sin(gamma + math.asin(amp_con)), 2) - 1
crosscorr = scipy.stats.pearsonr(fitctf2, adjctf1)[0]
yprime2 = yprime - constant - sqterm*radialsq
yprime2 /= numpy.abs(yprime2).max()
fitconf = scipy.stats.pearsonr(yprime2, fitctf2)[0]
if msg is True:
from matplotlib import pyplot
pyplot.clf()
pyplot.plot(radialsq, yprime2, '.', color="gray")
pyplot.plot(radialsq, yprime2, 'k-',)
pyplot.plot(radialsq, fitctf1, 'r--',)
pyplot.plot(radialsq, fitctf2, 'g--',)
pyplot.plot(radialsq, adjctf1, 'b--',)
conf1 = scipy.stats.pearsonr(yprime2, fitctf1)[0]
conf2 = scipy.stats.pearsonr(yprime2, adjctf1)[0]
conf3 = scipy.stats.pearsonr(yprime2, fitctf2)[0]
print "conf %.4f, %.4f, %.4f; cc = %.4f"%(conf1, conf2, conf3, crosscorr)
#pyplot.ylim(ymin=-1.05, ymax=1.05)
pyplot.title("Amplitude Contrast Fit (%.2f, %.2f, %.2f) CC=%.3f"%(conf1, conf2, conf3, crosscorr))
pyplot.subplots_adjust(wspace=0.05, hspace=0.05,
bottom=0.05, left=0.05, top=0.95, right=0.95, )
pyplot.show()
if crosscorr < -0.6:
print "likely 180 degree out of phase"
apDisplay.printWarning("Bad angle translation: %.8f"%(amp_con))
return None
if fitconf < 0.1 and amp_con > 0.4:
apDisplay.printWarning("Bad fit confidence %.3f, ac=%.8f"%(fitconf, amp_con))
return None
if crosscorr < 0.5:
apDisplay.printWarning("Bad angle translation: %.8f"%(amp_con))
return None
if amp_con < 0.0:
apDisplay.printWarning("amp contrast is negative (reduce defocus): %.4f"%(amp_con))
#return None
if amp_con > 0.6:
apDisplay.printWarning("amp contrast is too large (increase defocus): %.8f"%(amp_con))
#return None
return amp_con