from __future__ import division
"""
Data manipulations for 2D data sets.
Using the meta data information, various types of averaging
are performed in Q-space

To test this module use:

cd test

"""
#####################################################################
# This software was developed by the University of Tennessee as part of the
# Distributed Data Analysis of Neutron Scattering Experiments (DANSE)
# project funded by the US National Science Foundation.
# copyright 2008, University of Tennessee
######################################################################

# TODO: copy the meta data from the 2D object to the resulting 1D object
import math
import numpy as np
import sys

#from data_info import plottable_2D
from .data_info import Data1D

[docs]def get_q(dx, dy, det_dist, wavelength):
"""
:param dx: x-distance from beam center [mm]
:param dy: y-distance from beam center [mm]
:return: q-value at the given position
"""
# Distance from beam center in the plane of detector
plane_dist = math.sqrt(dx * dx + dy * dy)
# Half of the scattering angle
theta = 0.5 * math.atan(plane_dist / det_dist)
return (4.0 * math.pi / wavelength) * math.sin(theta)

[docs]def get_q_compo(dx, dy, det_dist, wavelength, compo=None):
"""
This reduces tiny error at very large q.
Implementation of this func is not started yet.<--ToDo
"""
if dy == 0:
if dx >= 0:
angle_xy = 0
else:
angle_xy = math.pi
else:
angle_xy = math.atan(dx / dy)

if compo == "x":
out = get_q(dx, dy, det_dist, wavelength) * math.cos(angle_xy)
elif compo == "y":
out = get_q(dx, dy, det_dist, wavelength) * math.sin(angle_xy)
else:
out = get_q(dx, dy, det_dist, wavelength)
return out

[docs]def flip_phi(phi):
"""
Correct phi to within the 0 <= to <= 2pi range

:return: phi in >=0 and <=2Pi
"""
Pi = math.pi
if phi < 0:
phi_out = phi + (2 * Pi)
elif phi > (2 * Pi):
phi_out = phi - (2 * Pi)
else:
phi_out = phi
return phi_out

[docs]def get_pixel_fraction_square(x, xmin, xmax):
"""
Return the fraction of the length
from xmin to x.::

A            B
+-----------+---------+
xmin        x         xmax

:param x: x-value
:param xmin: minimum x for the length considered
:param xmax: minimum x for the length considered
:return: (x-xmin)/(xmax-xmin) when xmin < x < xmax

"""
if x <= xmin:
return 0.0
if x > xmin and x < xmax:
return (x - xmin) / (xmax - xmin)
else:
return 1.0

[docs]def get_intercept(q, q_0, q_1):
"""
Returns the fraction of the side at which the
q-value intercept the pixel, None otherwise.
The values returned is the fraction ON THE SIDE
OF THE LOWEST Q. ::

A           B
+-----------+--------+    <--- pixel size
0                    1
Q_0 -------- Q ----- Q_1   <--- equivalent Q range
if Q_1 > Q_0, A is returned
if Q_1 < Q_0, B is returned
if Q is outside the range of [Q_0, Q_1], None is returned

"""
if q_1 > q_0:
if q > q_0 and q <= q_1:
return (q - q_0) / (q_1 - q_0)
else:
if q > q_1 and q <= q_0:
return (q - q_1) / (q_0 - q_1)
return None

[docs]def get_pixel_fraction(qmax, q_00, q_01, q_10, q_11):
"""
Returns the fraction of the pixel defined by
the four corners (q_00, q_01, q_10, q_11) that
has q < qmax.::

q_01                q_11
y=1         +--------------+
|              |
|              |
|              |
y=0         +--------------+
q_00                q_10

x=0            x=1

"""
# y side for x = minx
x_0 = get_intercept(qmax, q_00, q_01)
# y side for x = maxx
x_1 = get_intercept(qmax, q_10, q_11)

# x side for y = miny
y_0 = get_intercept(qmax, q_00, q_10)
# x side for y = maxy
y_1 = get_intercept(qmax, q_01, q_11)

# surface fraction for a 1x1 pixel
frac_max = 0

if x_0 and x_1:
frac_max = (x_0 + x_1) / 2.0
elif y_0 and y_1:
frac_max = (y_0 + y_1) / 2.0
elif x_0 and y_0:
if q_00 < q_10:
frac_max = x_0 * y_0 / 2.0
else:
frac_max = 1.0 - x_0 * y_0 / 2.0
elif x_0 and y_1:
if q_00 < q_10:
frac_max = x_0 * y_1 / 2.0
else:
frac_max = 1.0 - x_0 * y_1 / 2.0
elif x_1 and y_0:
if q_00 > q_10:
frac_max = x_1 * y_0 / 2.0
else:
frac_max = 1.0 - x_1 * y_0 / 2.0
elif x_1 and y_1:
if q_00 < q_10:
frac_max = 1.0 - (1.0 - x_1) * (1.0 - y_1) / 2.0
else:
frac_max = (1.0 - x_1) * (1.0 - y_1) / 2.0

# If we make it here, there is no intercept between
# this pixel and the constant-q ring. We only need
# to know if we have to include it or exclude it.
elif (q_00 + q_01 + q_10 + q_11) / 4.0 < qmax:
frac_max = 1.0

return frac_max

[docs]def get_dq_data(data2D):
'''
Get the dq for resolution averaging
The pinholes and det. pix contribution present
in both direction of the 2D which must be subtracted when
converting to 1D: dq_overlap should calculated ideally at
q = 0. Note This method works on only pinhole geometry.
Extrapolate dqx(r) and dqy(phi) at q = 0, and take an average.
'''
z_max = max(data2D.q_data)
z_min = min(data2D.q_data)
dqx_at_z_max = data2D.dqx_data[np.argmax(data2D.q_data)]
dqx_at_z_min = data2D.dqx_data[np.argmin(data2D.q_data)]
dqy_at_z_max = data2D.dqy_data[np.argmax(data2D.q_data)]
dqy_at_z_min = data2D.dqy_data[np.argmin(data2D.q_data)]
# Find qdx at q = 0
dq_overlap_x = (dqx_at_z_min * z_max - dqx_at_z_max * z_min) / (z_max - z_min)
# when extrapolation goes wrong
if dq_overlap_x > min(data2D.dqx_data):
dq_overlap_x = min(data2D.dqx_data)
dq_overlap_x *= dq_overlap_x
# Find qdx at q = 0
dq_overlap_y = (dqy_at_z_min * z_max - dqy_at_z_max * z_min) / (z_max - z_min)
# when extrapolation goes wrong
if dq_overlap_y > min(data2D.dqy_data):
dq_overlap_y = min(data2D.dqy_data)
# get dq at q=0.
dq_overlap_y *= dq_overlap_y

dq_overlap = np.sqrt((dq_overlap_x + dq_overlap_y) / 2.0)
# Final protection of dq
if dq_overlap < 0:
dq_overlap = dqy_at_z_min
dqx_data = data2D.dqx_data[np.isfinite(data2D.data)]
dqy_data = data2D.dqy_data[np.isfinite(
data2D.data)] - dq_overlap
# def; dqx_data = dq_r dqy_data = dq_phi
# Convert dq 2D to 1D here
dq_data = np.sqrt(dqx_data**2 + dqx_data**2)
return dq_data

################################################################################

"""
to new Data2D format
This is mainly used by the Readers

:param data2d: 2d array of Data2D object
:return: 1d arrays of Data2D object

"""
if data2d.data is None or data2d.x_bins is None or data2d.y_bins is None:
raise ValueError("Can't convert this data: data=None...")
new_x = np.tile(data2d.x_bins, (len(data2d.y_bins), 1))
new_y = np.tile(data2d.y_bins, (len(data2d.x_bins), 1))
new_y = new_y.swapaxes(0, 1)

new_data = data2d.data.flatten()
qx_data = new_x.flatten()
qy_data = new_y.flatten()
q_data = np.sqrt(qx_data * qx_data + qy_data * qy_data)
if data2d.err_data is None or np.any(data2d.err_data <= 0):
new_err_data = np.sqrt(np.abs(new_data))
else:
new_err_data = data2d.err_data.flatten()

# TODO: make sense of the following two lines...
#output = Data2D()
output = data2d
output.data = new_data
output.err_data = new_err_data
output.qx_data = qx_data
output.qy_data = qy_data
output.q_data = q_data

return output

################################################################################

[docs]class Binning(object):
'''
This class just creates a binning object
either linear or log
'''

def __init__(self, min_value, max_value, n_bins, base=None):
'''
if base is None: Linear binning
'''
self.min = min_value if min_value > 0 else 0.0001
self.max = max_value
self.n_bins = n_bins
self.base = base

[docs]    def get_bin_index(self, value):
'''
The general formula logarithm binning is:
bin = floor(N * (log(x) - log(min)) / (log(max) - log(min)))
'''
if self.base:
temp_x = self.n_bins * (math.log(value, self.base) - math.log(self.min, self.base))
temp_y = math.log(self.max, self.base) - math.log(self.min, self.base)
else:
temp_x = self.n_bins * (value - self.min)
temp_y = self.max - self.min
# Bin index calulation
return int(math.floor(temp_x / temp_y))

################################################################################

class _Slab(object):
"""
Compute average I(Q) for a region of interest
"""

def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0,
y_max=0.0, bin_width=0.001, fold = False):
# Minimum Qx value [A-1]
self.x_min = x_min
# Maximum Qx value [A-1]
self.x_max = x_max
# Minimum Qy value [A-1]
self.y_min = y_min
# Maximum Qy value [A-1]
self.y_max = y_max
# Bin width (step size) [A-1]
self.bin_width = bin_width
# If True, I(|Q|) will be return, otherwise,
# negative q-values are allowed
self.fold = fold

def __call__(self, data2D):
return NotImplemented

def _avg(self, data2D, maj):
"""
Compute average I(Q_maj) for a region of interest.
The major axis is defined as the axis of Q_maj.
The minor axis is the axis that we average over.

:param data2D: Data2D object
:param maj_min: min value on the major axis
:return: Data1D object
"""
if len(data2D.detector) > 1:
msg = "_Slab._avg: invalid number of "
msg += " detectors: %g" % len(data2D.detector)
raise RuntimeError(msg)

# Get data
data = data2D.data[np.isfinite(data2D.data)]
err_data = data2D.err_data[np.isfinite(data2D.data)]
qx_data = data2D.qx_data[np.isfinite(data2D.data)]
qy_data = data2D.qy_data[np.isfinite(data2D.data)]

# Build array of Q intervals
if maj == 'x':
if self.fold:
x_min = 0
else:
x_min = self.x_min
nbins = int(math.ceil((self.x_max - x_min) / self.bin_width))
elif maj == 'y':
if self.fold:
y_min = 0
else:
y_min = self.y_min
nbins = int(math.ceil((self.y_max - y_min) / self.bin_width))
else:
raise RuntimeError("_Slab._avg: unrecognized axis %s" % str(maj))

x = np.zeros(nbins)
y = np.zeros(nbins)
err_y = np.zeros(nbins)
y_counts = np.zeros(nbins)

# Average pixelsize in q space
for npts in range(len(data)):
# ignore points that are masked
continue
# default frac
frac_x = 0
frac_y = 0
# get ROI
if self.x_min <= qx_data[npts] and self.x_max > qx_data[npts]:
frac_x = 1
if self.y_min <= qy_data[npts] and self.y_max > qy_data[npts]:
frac_y = 1
frac = frac_x * frac_y

if frac == 0:
continue
# binning: find axis of q
if maj == 'x':
q_value = qx_data[npts]
min_value = x_min
if maj == 'y':
q_value = qy_data[npts]
min_value = y_min
if self.fold and q_value < 0:
q_value = -q_value
# bin
i_q = int(math.ceil((q_value - min_value) / self.bin_width)) - 1

# skip outside of max bins
if i_q < 0 or i_q >= nbins:
continue

# TODO: find better definition of x[i_q] based on q_data
# min_value + (i_q + 1) * self.bin_width / 2.0
x[i_q] += frac * q_value
y[i_q] += frac * data[npts]

if err_data is None or err_data[npts] == 0.0:
if data[npts] < 0:
data[npts] = -data[npts]
err_y[i_q] += frac * frac * data[npts]
else:
err_y[i_q] += frac * frac * err_data[npts] * err_data[npts]
y_counts[i_q] += frac

# Average the sums
for n in range(nbins):
err_y[n] = math.sqrt(err_y[n])

err_y = err_y / y_counts
y = y / y_counts
x = x / y_counts
idx = (np.isfinite(y) & np.isfinite(x))

if not idx.any():
msg = "Average Error: No points inside ROI to average..."
raise ValueError(msg)
return Data1D(x=x[idx], y=y[idx], dy=err_y[idx])

[docs]class SlabY(_Slab):
"""
Compute average I(Qy) for a region of interest
"""

def __call__(self, data2D):
"""
Compute average I(Qy) for a region of interest

:param data2D: Data2D object
:return: Data1D object
"""
return self._avg(data2D, 'y')

[docs]class SlabX(_Slab):
"""
Compute average I(Qx) for a region of interest
"""

def __call__(self, data2D):
"""
Compute average I(Qx) for a region of interest
:param data2D: Data2D object
:return: Data1D object
"""
return self._avg(data2D, 'x')

################################################################################

[docs]class Boxsum(object):
"""
Perform the sum of counts in a 2D region of interest.
"""

def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
# Minimum Qx value [A-1]
self.x_min = x_min
# Maximum Qx value [A-1]
self.x_max = x_max
# Minimum Qy value [A-1]
self.y_min = y_min
# Maximum Qy value [A-1]
self.y_max = y_max

def __call__(self, data2D):
"""
Perform the sum in the region of interest

:param data2D: Data2D object
:return: number of counts, error on number of counts,
number of points summed
"""
y, err_y, y_counts = self._sum(data2D)

# Average the sums
counts = 0 if y_counts == 0 else y
error = 0 if y_counts == 0 else math.sqrt(err_y)

# Added y_counts to return, SMK & PDB, 04/03/2013
return counts, error, y_counts

def _sum(self, data2D):
"""
Perform the sum in the region of interest

:param data2D: Data2D object
:return: number of counts,
error on number of counts, number of entries summed
"""
if len(data2D.detector) > 1:
msg = "Circular averaging: invalid number "
msg += "of detectors: %g" % len(data2D.detector)
raise RuntimeError(msg)
# Get data
data = data2D.data[np.isfinite(data2D.data)]
err_data = data2D.err_data[np.isfinite(data2D.data)]
qx_data = data2D.qx_data[np.isfinite(data2D.data)]
qy_data = data2D.qy_data[np.isfinite(data2D.data)]

y = 0.0
err_y = 0.0
y_counts = 0.0

# Average pixelsize in q space
for npts in range(len(data)):
# ignore points that are masked
continue
# default frac
frac_x = 0
frac_y = 0

# get min and max at each points
qx = qx_data[npts]
qy = qy_data[npts]

# get the ROI
if self.x_min <= qx and self.x_max > qx:
frac_x = 1
if self.y_min <= qy and self.y_max > qy:
frac_y = 1
# Find the fraction along each directions
frac = frac_x * frac_y
if frac == 0:
continue
y += frac * data[npts]
if err_data is None or err_data[npts] == 0.0:
if data[npts] < 0:
data[npts] = -data[npts]
err_y += frac * frac * data[npts]
else:
err_y += frac * frac * err_data[npts] * err_data[npts]
y_counts += frac
return y, err_y, y_counts

[docs]class Boxavg(Boxsum):
"""
Perform the average of counts in a 2D region of interest.
"""

def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
super(Boxavg, self).__init__(x_min=x_min, x_max=x_max,
y_min=y_min, y_max=y_max)

def __call__(self, data2D):
"""
Perform the sum in the region of interest

:param data2D: Data2D object
:return: average counts, error on average counts

"""
y, err_y, y_counts = self._sum(data2D)

# Average the sums
counts = 0 if y_counts == 0 else y / y_counts
error = 0 if y_counts == 0 else math.sqrt(err_y) / y_counts

return counts, error

################################################################################

[docs]class CircularAverage(object):
"""
Perform circular averaging on 2D data

The data returned is the distribution of counts
as a function of Q
"""

def __init__(self, r_min=0.0, r_max=0.0, bin_width=0.0005):
# Minimum radius included in the average [A-1]
self.r_min = r_min
# Maximum radius included in the average [A-1]
self.r_max = r_max
# Bin width (step size) [A-1]
self.bin_width = bin_width

"""
Perform circular averaging on the data

:param data2D: Data2D object
:return: Data1D object
"""
# Get data W/ finite values
data = data2D.data[np.isfinite(data2D.data)]
q_data = data2D.q_data[np.isfinite(data2D.data)]
err_data = data2D.err_data[np.isfinite(data2D.data)]

dq_data = None
if data2D.dqx_data is not None and data2D.dqy_data is not None:
dq_data = get_dq_data(data2D)

if len(q_data) == 0:
msg = "Circular averaging: invalid q_data: %g" % data2D.q_data
raise RuntimeError(msg)

# Build array of Q intervals
nbins = int(math.ceil((self.r_max - self.r_min) / self.bin_width))

x = np.zeros(nbins)
y = np.zeros(nbins)
err_y = np.zeros(nbins)
err_x = np.zeros(nbins)
y_counts = np.zeros(nbins)

for npt in range(len(data)):

continue

frac = 0

# q-value at the pixel (j,i)
q_value = q_data[npt]
data_n = data[npt]

# No need to calculate the frac when all data are within range
if self.r_min >= self.r_max:
raise ValueError("Limit Error: min > max")

if self.r_min <= q_value and q_value <= self.r_max:
frac = 1
if frac == 0:
continue
i_q = int(math.floor((q_value - self.r_min) / self.bin_width))

# Take care of the edge case at phi = 2pi.
if i_q == nbins:
i_q = nbins - 1
y[i_q] += frac * data_n
# Take dqs from data to get the q_average
x[i_q] += frac * q_value
if err_data is None or err_data[npt] == 0.0:
if data_n < 0:
data_n = -data_n
err_y[i_q] += frac * frac * data_n
else:
err_y[i_q] += frac * frac * err_data[npt] * err_data[npt]
if dq_data is not None:
# To be consistent with dq calculation in 1d reduction,
# we need just the averages (not quadratures) because
# it should not depend on the number of the q points
# in the qr bins.
err_x[i_q] += frac * dq_data[npt]
else:
err_x = None
y_counts[i_q] += frac

# Average the sums
for n in range(nbins):
if err_y[n] < 0:
err_y[n] = -err_y[n]
err_y[n] = math.sqrt(err_y[n])
# if err_x is not None:
#    err_x[n] = math.sqrt(err_x[n])

err_y = err_y / y_counts
err_y[err_y == 0] = np.average(err_y)
y = y / y_counts
x = x / y_counts
idx = (np.isfinite(y)) & (np.isfinite(x))

if err_x is not None:
d_x = err_x[idx] / y_counts[idx]
else:
d_x = None

if not idx.any():
msg = "Average Error: No points inside ROI to average..."
raise ValueError(msg)

return Data1D(x=x[idx], y=y[idx], dy=err_y[idx], dx=d_x)

################################################################################

[docs]class Ring(object):
"""
Defines a ring on a 2D data set.
The ring is defined by r_min, r_max, and
the position of the center of the ring.

The data returned is the distribution of counts
around the ring as a function of phi.

Phi_min and phi_max should be defined between 0 and 2*pi
in anti-clockwise starting from the x- axis on the left-hand side
"""
# Todo: remove center.

def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0, nbins=36):
self.r_min = r_min
self.r_max = r_max
# Center of the ring in x
self.center_x = center_x
# Center of the ring in y
self.center_y = center_y
# Number of angular bins
self.nbins_phi = nbins

def __call__(self, data2D):
"""
Apply the ring to the data set.
Returns the angular distribution for a given q range

:param data2D: Data2D object

:return: Data1D object
"""
if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
raise RuntimeError("Ring averaging only take plottable_2D objects")

Pi = math.pi

# Get data
data = data2D.data[np.isfinite(data2D.data)]
q_data = data2D.q_data[np.isfinite(data2D.data)]
err_data = data2D.err_data[np.isfinite(data2D.data)]
qx_data = data2D.qx_data[np.isfinite(data2D.data)]
qy_data = data2D.qy_data[np.isfinite(data2D.data)]

# Set space for 1d outputs
phi_bins = np.zeros(self.nbins_phi)
phi_counts = np.zeros(self.nbins_phi)
phi_values = np.zeros(self.nbins_phi)
phi_err = np.zeros(self.nbins_phi)

# Shift to apply to calculated phi values in order
# to center first bin at zero
phi_shift = Pi / self.nbins_phi

for npt in range(len(data)):
# ignore points that are masked
continue
frac = 0
# q-value at the point (npt)
q_value = q_data[npt]
data_n = data[npt]

# phi-value at the point (npt)
phi_value = math.atan2(qy_data[npt], qx_data[npt]) + Pi

if self.r_min <= q_value and q_value <= self.r_max:
frac = 1
if frac == 0:
continue
# binning
i_phi = int(math.floor((self.nbins_phi) *
(phi_value + phi_shift) / (2 * Pi)))

# Take care of the edge case at phi = 2pi.
if i_phi >= self.nbins_phi:
i_phi = 0
phi_bins[i_phi] += frac * data[npt]

if err_data is None or err_data[npt] == 0.0:
if data_n < 0:
data_n = -data_n
phi_err[i_phi] += frac * frac * math.fabs(data_n)
else:
phi_err[i_phi] += frac * frac * err_data[npt] * err_data[npt]
phi_counts[i_phi] += frac

for i in range(self.nbins_phi):
phi_bins[i] = phi_bins[i] / phi_counts[i]
phi_err[i] = math.sqrt(phi_err[i]) / phi_counts[i]
phi_values[i] = 2.0 * math.pi / self.nbins_phi * (1.0 * i)

idx = (np.isfinite(phi_bins))

if not idx.any():
msg = "Average Error: No points inside ROI to average..."
raise ValueError(msg)
# elif len(phi_bins[idx])!= self.nbins_phi:
#    print "resulted",self.nbins_phi- len(phi_bins[idx])
#,"empty bin(s) due to tight binning..."
return Data1D(x=phi_values[idx], y=phi_bins[idx], dy=phi_err[idx])

class _Sector(object):
"""
Defines a sector region on a 2D data set.
The sector is defined by r_min, r_max, phi_min, phi_max,
and the position of the center of the ring
where phi_min and phi_max are defined by the right
and left lines wrt central line
and phi_max could be less than phi_min.

Phi is defined between 0 and 2*pi in anti-clockwise
starting from the x- axis on the left-hand side
"""

def __init__(self, r_min, r_max, phi_min=0, phi_max=2 * math.pi, nbins=20,
base=None):
'''
:param base: must be a valid base for an algorithm, i.e.,
a positive number
'''
self.r_min = r_min
self.r_max = r_max
self.phi_min = phi_min
self.phi_max = phi_max
self.nbins = nbins
self.base = base

def _agv(self, data2D, run='phi'):
"""
Perform sector averaging.

:param data2D: Data2D object
:param run:  define the varying parameter ('phi' , 'q' , or 'q2')

:return: Data1D object
"""
if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
raise RuntimeError("Ring averaging only take plottable_2D objects")

# Get the all data & info
data = data2D.data[np.isfinite(data2D.data)]
q_data = data2D.q_data[np.isfinite(data2D.data)]
err_data = data2D.err_data[np.isfinite(data2D.data)]
qx_data = data2D.qx_data[np.isfinite(data2D.data)]
qy_data = data2D.qy_data[np.isfinite(data2D.data)]

dq_data = None
if data2D.dqx_data is not None and data2D.dqy_data is not None:
dq_data = get_dq_data(data2D)

# set space for 1d outputs
x = np.zeros(self.nbins)
y = np.zeros(self.nbins)
y_err = np.zeros(self.nbins)
x_err = np.zeros(self.nbins)
y_counts = np.zeros(self.nbins)  # Cycle counts (for the mean)

# Get the min and max into the region: 0 <= phi < 2Pi
phi_min = flip_phi(self.phi_min)
phi_max = flip_phi(self.phi_max)

#  binning object
if run.lower() == 'phi':
binning = Binning(self.phi_min, self.phi_max, self.nbins, self.base)
else:
binning = Binning(self.r_min, self.r_max, self.nbins, self.base)

for n in range(len(data)):
# ignore points that are masked
continue

# q-value at the pixel (j,i)
q_value = q_data[n]
data_n = data[n]

# Is pixel within range?
is_in = False

# phi-value of the pixel (j,i)
phi_value = math.atan2(qy_data[n], qx_data[n]) + math.pi

# No need to calculate: data outside of the radius
if self.r_min > q_value or q_value > self.r_max:
continue

# In case of two ROIs (symmetric major and minor regions)(for 'q2')
if run.lower() == 'q2':
# For minor sector wing
# Calculate the minor wing phis
phi_min_minor = flip_phi(phi_min - math.pi)
phi_max_minor = flip_phi(phi_max - math.pi)
# Check if phis of the minor ring is within 0 to 2pi
if phi_min_minor > phi_max_minor:
is_in = (phi_value > phi_min_minor or
phi_value < phi_max_minor)
else:
is_in = (phi_value > phi_min_minor and
phi_value < phi_max_minor)

# For all cases(i.e.,for 'q', 'q2', and 'phi')
# Find pixels within ROI
if phi_min > phi_max:
is_in = is_in or (phi_value > phi_min or
phi_value < phi_max)
else:
is_in = is_in or (phi_value >= phi_min and
phi_value < phi_max)

# data oustide of the phi range
if not is_in:
continue

# Get the binning index
if run.lower() == 'phi':
i_bin = binning.get_bin_index(phi_value)
else:
i_bin = binning.get_bin_index(q_value)

# Take care of the edge case at phi = 2pi.
if i_bin == self.nbins:
i_bin = self.nbins - 1

# Get the total y
y[i_bin] += data_n
x[i_bin] += q_value
if err_data[n] is None or err_data[n] == 0.0:
if data_n < 0:
data_n = -data_n
y_err[i_bin] += data_n
else:
y_err[i_bin] += err_data[n]**2

if dq_data is not None:
# To be consistent with dq calculation in 1d reduction,
# we need just the averages (not quadratures) because
# it should not depend on the number of the q points
# in the qr bins.
x_err[i_bin] += dq_data[n]
else:
x_err = None
y_counts[i_bin] += 1

# Organize the results
with np.errstate(divide='ignore', invalid='ignore'):
y = y/y_counts
y_err = np.sqrt(y_err)/y_counts
# The type of averaging: phi, q2, or q
# Calculate x values at the center of the bin
if run.lower() == 'phi':
step = (self.phi_max - self.phi_min) / self.nbins
x = (np.arange(self.nbins) + 0.5) * step + self.phi_min
else:
# set q to the average of the q values within each bin
x = x/y_counts

### Alternate algorithm
## We take the center of ring area, not radius.
## This is more accurate than taking the radial center of ring.
#step = (self.r_max - self.r_min) / self.nbins
#r_inner = self.r_min + step * np.arange(self.nbins)
#x = math.sqrt((r_inner**2 + (r_inner + step)**2) / 2)

idx = (np.isfinite(y) & np.isfinite(y_err))
if x_err is not None:
d_x = x_err[idx] / y_counts[idx]
else:
d_x = None
if not idx.any():
msg = "Average Error: No points inside sector of ROI to average..."
raise ValueError(msg)
# elif len(y[idx])!= self.nbins:
#    print "resulted",self.nbins- len(y[idx]),
# "empty bin(s) due to tight binning..."
return Data1D(x=x[idx], y=y[idx], dy=y_err[idx], dx=d_x)

[docs]class SectorPhi(_Sector):
"""
Sector average as a function of phi.
I(phi) is return and the data is averaged over Q.

A sector is defined by r_min, r_max, phi_min, phi_max.
The number of bin in phi also has to be defined.
"""

def __call__(self, data2D):
"""
Perform sector average and return I(phi).

:param data2D: Data2D object
:return: Data1D object
"""
return self._agv(data2D, 'phi')

[docs]class SectorQ(_Sector):
"""
Sector average as a function of Q for both symatric wings.
I(Q) is return and the data is averaged over phi.

A sector is defined by r_min, r_max, phi_min, phi_max.
r_min, r_max, phi_min, phi_max >0.
The number of bin in Q also has to be defined.
"""

def __call__(self, data2D):
"""
Perform sector average and return I(Q).

:param data2D: Data2D object

:return: Data1D object
"""
return self._agv(data2D, 'q2')

################################################################################

[docs]class Ringcut(object):
"""
Defines a ring on a 2D data set.
The ring is defined by r_min, r_max, and
the position of the center of the ring.

The data returned is the region inside the ring

Phi_min and phi_max should be defined between 0 and 2*pi
in anti-clockwise starting from the x- axis on the left-hand side
"""

def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0):
self.r_min = r_min
self.r_max = r_max
# Center of the ring in x
self.center_x = center_x
# Center of the ring in y
self.center_y = center_y

def __call__(self, data2D):
"""
Apply the ring to the data set.
Returns the angular distribution for a given q range

:param data2D: Data2D object

:return: index array in the range
"""
if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
raise RuntimeError("Ring cut only take plottable_2D objects")

# Get data
qx_data = data2D.qx_data
qy_data = data2D.qy_data
q_data = np.sqrt(qx_data * qx_data + qy_data * qy_data)

# check whether or not the data point is inside ROI
out = (self.r_min <= q_data) & (self.r_max >= q_data)
return out

################################################################################

[docs]class Boxcut(object):
"""
Find a rectangular 2D region of interest.
"""

def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
# Minimum Qx value [A-1]
self.x_min = x_min
# Maximum Qx value [A-1]
self.x_max = x_max
# Minimum Qy value [A-1]
self.y_min = y_min
# Maximum Qy value [A-1]
self.y_max = y_max

def __call__(self, data2D):
"""
Find a rectangular 2D region of interest.

:param data2D: Data2D object
:return: mask, 1d array (len = len(data))
with Trues where the data points are inside ROI, otherwise False
"""

def _find(self, data2D):
"""
Find a rectangular 2D region of interest.

:param data2D: Data2D object

:return: out, 1d array (length = len(data))
with Trues where the data points are inside ROI, otherwise Falses
"""
if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
raise RuntimeError("Boxcut take only plottable_2D objects")
# Get qx_ and qy_data
qx_data = data2D.qx_data
qy_data = data2D.qy_data

# check whether or not the data point is inside ROI
outx = (self.x_min <= qx_data) & (self.x_max > qx_data)
outy = (self.y_min <= qy_data) & (self.y_max > qy_data)

return outx & outy

################################################################################

[docs]class Sectorcut(object):
"""
Defines a sector (major + minor) region on a 2D data set.
The sector is defined by phi_min, phi_max,
where phi_min and phi_max are defined by the right
and left lines wrt central line.

Phi_min and phi_max are given in units of radian
and (phi_max-phi_min) should not be larger than pi
"""

def __init__(self, phi_min=0, phi_max=math.pi):
self.phi_min = phi_min
self.phi_max = phi_max

def __call__(self, data2D):
"""
Find a rectangular 2D region of interest.

:param data2D: Data2D object

:return: mask, 1d array (len = len(data))

with Trues where the data points are inside ROI, otherwise False
"""

def _find(self, data2D):
"""
Find a rectangular 2D region of interest.

:param data2D: Data2D object

:return: out, 1d array (length = len(data))

with Trues where the data points are inside ROI, otherwise Falses
"""
if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
raise RuntimeError("Sectorcut take only plottable_2D objects")
Pi = math.pi
# Get data
qx_data = data2D.qx_data
qy_data = data2D.qy_data

# get phi from data
phi_data = np.arctan2(qy_data, qx_data)

# Get the min and max into the region: -pi <= phi < Pi
phi_min_major = flip_phi(self.phi_min + Pi) - Pi
phi_max_major = flip_phi(self.phi_max + Pi) - Pi
# check for major sector
if phi_min_major > phi_max_major:
out_major = (phi_min_major <= phi_data) + \
(phi_max_major > phi_data)
else:
out_major = (phi_min_major <= phi_data) & (
phi_max_major > phi_data)

# minor sector
# Get the min and max into the region: -pi <= phi < Pi
phi_min_minor = flip_phi(self.phi_min) - Pi
phi_max_minor = flip_phi(self.phi_max) - Pi

# check for minor sector
if phi_min_minor > phi_max_minor:
out_minor = (phi_min_minor <= phi_data) + \
(phi_max_minor >= phi_data)
else:
out_minor = (phi_min_minor <= phi_data) & \
(phi_max_minor >= phi_data)
out = out_major + out_minor

return out