-                      r9dda8cc
+                      rccc7192
     return phi_out
-def reader2D_converter(data2d=None):
-    """
-    convert old 2d format opened by IhorReader or danse_reader
-    to new Data2D format
-    :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 _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
 def get_pixel_fraction_square(x, xmin, xmax):
     """
 …
         return 1.0
+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
+        # Get the dq for resolution averaging
+        if data2D.dqx_data != None and data2D.dqy_data != None:
+            # 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)
+            x_max = data2D.dqx_data[data2D.q_data[z_max]]
+            x_min = data2D.dqx_data[data2D.q_data[z_min]]
+            y_max = data2D.dqy_data[data2D.q_data[z_max]]
+            y_min = data2D.dqy_data[data2D.q_data[z_min]]
+            # Find qdx at q = 0
+            dq_overlap_x = (x_min * z_max - x_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 = (y_min * z_max - y_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 = y_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
+            dqx = dqx_data * dqx_data
+            dqy = dqy_data * dqy_data
+            dq_data = np.add(dqx, dqy)
+            dq_data = np.sqrt(dq_data)
+        #q_data_max = np.max(q_data)
+        if len(data2D.q_data) == None:
+            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 != 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 != 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 != 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])
+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
+                    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):
 …
     return frac_max
+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
+                    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)
+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)
+    x_max = data2D.dqx_data[data2D.q_data[z_max]]
+    x_min = data2D.dqx_data[data2D.q_data[z_min]]
+    y_max = data2D.dqy_data[data2D.q_data[z_max]]
+    y_min = data2D.dqy_data[data2D.q_data[z_min]]
+    # Find qdx at q = 0
+    dq_overlap_x = (x_min * z_max - x_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 = (y_min * z_max - y_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 = y_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:
+        if q > q_1 and q <= q_0:
+            return (q - q_1) / (q_0 - q_1)
+    return None
+        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 _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 != None and data2D.dqy_data != None:
+            dq_data = get_dq_data(data2D)
+        #q_data_max = np.max(q_data)
+        if len(data2D.q_data) == None:
+            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 != 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 != 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 != 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):
 …
         if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
             raise RuntimeError("Ring averaging only take plottable_2D objects")
-        Pi = math.pi
         # Get the all data & info
 …
         qx_data = data2D.qx_data[np.isfinite(data2D.data)]
         qy_data = data2D.qy_data[np.isfinite(data2D.data)]
         dq_data = None
-        # Get the dq for resolution averaging
         if data2D.dqx_data != None and data2D.dqy_data != None:
+            # 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.
+            # Extrapolate dqy(perp) at q = 0
+            z_max = max(data2D.q_data)
+            z_min = min(data2D.q_data)
+            x_max = data2D.dqx_data[data2D.q_data[z_max]]
+            x_min = data2D.dqx_data[data2D.q_data[z_min]]
+            y_max = data2D.dqy_data[data2D.q_data[z_max]]
+            y_min = data2D.dqy_data[data2D.q_data[z_min]]
+            # Find qdx at q = 0
+            dq_overlap_x = (x_min * z_max - x_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 = (y_min * z_max - y_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)
+            if dq_overlap < 0:
+                dq_overlap = y_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
+            dqx = dqx_data * dqx_data
+            dqy = dqy_data * dqy_data
+            dq_data = np.add(dqx, dqy)
+            dq_data = np.sqrt(dq_data)
+            dq_data = get_dq_data(data2D)
         # set space for 1d outputs
 …
         for n in range(len(data)):
-            frac = 0
             # q-value at the pixel (j,i)
 …
             # phi-value of the pixel (j,i)
             phi_value = math.atan2(qy_data[n], qx_data[n]) + Pi
+            phi_value = math.atan2(qy_data[n], qx_data[n]) + math.pi
             # No need to calculate the frac when all data are within range
+            if self.r_min <= q_value and q_value <= self.r_max:
+                frac = 1
+            if frac == 0:
+            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 - Pi)
                 phi_max_minor = flip_phi(phi_max - Pi)
+                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:
 …
             if not is_in:
-                frac = 0
-            if frac == 0:
                 continue
             # Check which type of averaging we need
 …
             # Get the total y
             y[i_bin] += frac * data_n
             x[i_bin] += frac * q_value
+            y[i_bin] += data_n
+            x[i_bin] += q_value
             if err_data[n] == None or err_data[n] == 0.0:
                 if data_n < 0:
                     data_n = -data_n
                 y_err[i_bin] += frac * frac * data_n
+                y_err[i_bin] +=  data_n
             else:
                 y_err[i_bin] += frac * frac * err_data[n] * err_data[n]
+                y_err[i_bin] += err_data[n] * err_data[n]
             if dq_data != None:
 …
                 # it should not depend on the number of the q points
                 # in the qr bins.
                 x_err[i_bin] += frac * dq_data[n]
+                x_err[i_bin] += dq_data[n]
             else:
                 x_err = None
             y_counts[i_bin] += frac
+            y_counts[i_bin] += 1
         # Organize the results
 …
         return self._agv(data2D, 'q2')
+################################################################################
 class Ringcut(object):
 …
         return out
+################################################################################
 class Boxcut(object):
 …
         return outx & outy
+################################################################################
 class Sectorcut(object):

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SasView

Changeset ccc7192 in sasview for src/sas/sascalc

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src/sas/sascalc/dataloader/manipulations.py

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