source: sasview/src/sas/sascalc/dataloader/manipulations.py @ f84d793

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
PYTHONPATH=../src/ python2  -m sasdataloader.test.utest_averaging DataInfoTests.test_sectorphi_quarter
```
"""
#####################################################################
# 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.
# See the license text in license.txt
# 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


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)


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


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

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

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

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

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

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

def reader2D_converter(data2d=None):
    """
    convert old 2d format opened by IhorReader or danse_reader
    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()
    mask = np.ones(len(new_data), dtype=bool)

    # TODO: make sense of the following two lines...
    #from sas.sascalc.dataloader.data_info import Data2D
    #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
    output.mask = mask

    return output

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

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

    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):
        # 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 = False

    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)):
            # 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])


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')


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')

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

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)):
            # 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


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

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

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

    def __call__(self, data2D, ismask=False):
        """
        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)]
        mask_data = data2D.mask[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)):

            if ismask and not mask_data[npt]:
                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)

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

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):
        # Minimum radius
        self.r_min = r_min
        # Maximum radius
        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)):
            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)):

            # 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
        for i in range(self.nbins):
            y[i] = y[i] / y_counts[i]
            y_err[i] = math.sqrt(y_err[i]) / y_counts[i]

            # The type of averaging: phi,q2, or q
            # Calculate x[i]should be at the center of the bin
            if run.lower() == 'phi':
                x[i] = (self.phi_max - self.phi_min) / self.nbins * \
                    (1.0 * i + 0.5) + self.phi_min
            else:
                # We take the center of ring area, not radius.
                # This is more accurate than taking the radial center of ring.
                # delta_r = (self.r_max - self.r_min) / self.nbins
                # r_inner = self.r_min + delta_r * i
                # r_outer = r_inner + delta_r
                # x[i] = math.sqrt((r_inner * r_inner + r_outer * r_outer) / 2)
                x[i] = x[i] / y_counts[i]
        y_err[y_err == 0] = np.average(y_err)
        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)


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')


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')

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

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):
        # Minimum radius
        self.r_min = r_min
        # Maximum radius
        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

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

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
        """
        mask = self._find(data2D)

        return mask

    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

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

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
        """
        mask = self._find(data2D)

        return mask

    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