source: sasview/DataLoader/manipulations.py @ 330c63b

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

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


#TODO: copy the meta data from the 2D object to the resulting 1D object

from data_info import plottable_2D, Data1D
import math
import numpy

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)*cos(angle_xy)
    elif compo=="y":
        out=get_q(dx, dy, det_dist, wavelength)*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 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==None or data2d.x_bins==None or data2d.y_bins==None:
        raise ValueError,"Can't convert this data: data=None..."
    
    from DataLoader.data_info import Data2D

    new_x = numpy.tile(data2d.x_bins, (len(data2d.y_bins),1))
    new_y = numpy.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 = numpy.sqrt(qx_data*qx_data+qy_data*qy_data)
    if data2d.err_data == None or numpy.any(data2d.err_data<=0): 
        new_err_data = numpy.sqrt(numpy.abs(new_data))
    else:
        new_err_data = data2d.err_data.flatten()
    mask    = numpy.ones(len(new_data), dtype = bool)

    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:
            raise RuntimeError, "_Slab._avg: invalid number of detectors: %g" % len(data2D.detector)
        
        # Get data 
        data = data2D.data[numpy.isfinite(data2D.data)]
        q_data = data2D.q_data[numpy.isfinite(data2D.data)]
        err_data = data2D.err_data[numpy.isfinite(data2D.data)]
        qx_data = data2D.qx_data[numpy.isfinite(data2D.data)] 
        qy_data = data2D.qy_data[numpy.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))
            qbins = self.bin_width*numpy.arange(nbins)+ x_min
        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))
            qbins = self.bin_width*numpy.arange(nbins)+ y_min          
        else:
            raise RuntimeError, "_Slab._avg: unrecognized axis %s" % str(maj)
                                
        x  = numpy.zeros(nbins)
        y  = numpy.zeros(nbins)
        err_y = numpy.zeros(nbins)
        y_counts = numpy.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 = x_min 
            if maj=='y': 
                q_value = qy_data[npts] 
                min = y_min 
            if self.fold and q_value<0: q_value = -q_value   
            
            # bin
            i_q = int(math.ceil((q_value-min)/self.bin_width)) - 1
            
            # skip outside of max bins
            if i_q<0 or i_q>=nbins: continue
            
            # give it full weight
            #frac = 1 
            
            #TODO: find better definition of x[i_q] based on q_data
            x[i_q]         = min +(i_q+1)*self.bin_width/2.0
            y[i_q]         += frac * data[npts]
            
            if err_data == 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
        
        idx = (numpy.isfinite(y)& numpy.isfinite(x)) 
        
        if not idx.any(): 
            raise ValueError, "Average Error: No points inside ROI to average..." 
        elif len(y[idx])!= nbins:
            print "resulted",nbins- len(y[idx]),"empty bin(s) due to tight binning..."
        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
        
        """
        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)
        
        return counts, error
        
    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:
            raise RuntimeError, "Circular averaging: invalid number of detectors: %g" % len(data2D.detector)
        
        # Get data 
        data = data2D.data[numpy.isfinite(data2D.data)]
        q_data = data2D.q_data[numpy.isfinite(data2D.data)]
        err_data = data2D.err_data[numpy.isfinite(data2D.data)]
        qx_data = data2D.qx_data[numpy.isfinite(data2D.data)] 
        qy_data = data2D.qy_data[numpy.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 == 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 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


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):
        """
        Perform circular averaging on the data
        
        :param data2D: Data2D object
        
        :return: Data1D object
        """
        # Get data
        data = data2D.data[numpy.isfinite(data2D.data)]
        q_data = data2D.q_data[numpy.isfinite(data2D.data)]
        err_data = data2D.err_data[numpy.isfinite(data2D.data)]
   
        q_data_max = numpy.max(q_data)

        if len(data2D.q_data) == None:
            raise RuntimeError, "Circular averaging: invalid q_data: %g" % data2D.q_data

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

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

        for npt in range(len(data)):          
            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

            if err_data == 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]
            y_counts[i_q]  += frac
        
        ## x should be the center value of each bins        
        x = qbins+self.bin_width/2  
        
        # 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])
                      
        err_y = err_y/y_counts
        y    = y/y_counts
        idx = (numpy.isfinite(y))&(numpy.isfinite(x)) 
        
        if not idx.any(): 
            raise ValueError, "Average Error: No points inside ROI to average..." 
        elif len(y[idx])!= nbins:
            print "resulted",nbins- len(y[idx]),"empty bin(s) due to tight binning..."
        
        return Data1D(x=x[idx], y=y[idx], dy=err_y[idx])
    

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=20 ):
        # 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[numpy.isfinite(data2D.data)]
        q_data = data2D.q_data[numpy.isfinite(data2D.data)]
        err_data = data2D.err_data[numpy.isfinite(data2D.data)]
        qx_data = data2D.qx_data[numpy.isfinite(data2D.data)] 
        qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
        
        q_data_max = numpy.max(q_data)
        
        # Set space for 1d outputs
        phi_bins   = numpy.zeros(self.nbins_phi)
        phi_counts = numpy.zeros(self.nbins_phi)
        phi_values = numpy.zeros(self.nbins_phi)
        phi_err    = numpy.zeros(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/(2*Pi)))
            
            # Take care of the edge case at phi = 2pi. 
            if i_phi == self.nbins_phi:  
                i_phi =  self.nbins_phi -1 
                                             
            phi_bins[i_phi] += frac * data[npt]
            
            if err_data == 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 + 0.5)
            
        idx = (numpy.isfinite(phi_bins)) 

        if not idx.any(): 
            raise ValueError, "Average Error: No points inside ROI to average..." 
        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_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_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
     
class _Sector:
    """
    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):
        self.r_min = r_min
        self.r_max = r_max
        self.phi_min = phi_min
        self.phi_max = phi_max
        self.nbins = nbins
        
    
    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"
        Pi = math.pi

        # Get the all data & info
        data = data2D.data[numpy.isfinite(data2D.data)]
        q_data = data2D.q_data[numpy.isfinite(data2D.data)]
        err_data = data2D.err_data[numpy.isfinite(data2D.data)]
        qx_data = data2D.qx_data[numpy.isfinite(data2D.data)] 
        qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
        
        #set space for 1d outputs
        x        = numpy.zeros(self.nbins)
        y        = numpy.zeros(self.nbins)
        y_err    = numpy.zeros(self.nbins)         
        y_counts = numpy.zeros(self.nbins)
                      
        # 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)
        
        q_data_max = numpy.max(q_data)
                      
        for n in range(len(data)):     
                frac = 0
                
                # 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])+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: 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)
                    # 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)
                
                if not is_in: frac = 0                                                        
                if frac == 0: continue
                
                # Check which type of averaging we need
                if run.lower()=='phi': 
                    i_bin    = int(math.floor((self.nbins)*(phi_value-self.phi_min)\
                                              /(self.phi_max-self.phi_min)))
                else:
                    i_bin = int(math.floor((self.nbins)*(q_value-self.r_min)/(self.r_max-self.r_min)))

                # 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] += frac * data_n

                if err_data == None or err_data[n] ==0.0:
                    if data_n<0: data_n= -data_n
                    y_err[i_bin] += frac * frac * data_n
                else:
                    y_err[i_bin] += frac * frac * err_data[n]*err_data[n]
                y_counts[i_bin] += frac
       
        # 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:
                x[i] = (self.r_max-self.r_min)/self.nbins*(1.0*i + 0.5)+self.r_min
                
        idx = (numpy.isfinite(y)& numpy.isfinite(y_err))
        
        if not idx.any(): 
            raise ValueError, "Average Error: No points inside sector of ROI to average..." 
        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])
                
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
        mask = data2D.mask
        q_data = numpy.sqrt(qx_data*qx_data+qy_data*qy_data)
        #q_data_max = numpy.max(q_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
        mask = data2D.mask
        
        # 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        
        phi_data = numpy.zeros(len(qx_data))

        # get phi from data
        phi_data = numpy.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

if __name__ == "__main__": 

    from loader import Loader
    

    d = Loader().load('test/MAR07232_rest.ASC')
    #d = Loader().load('test/MP_New.sans')

    
    r = SectorQ(r_min=.000001, r_max=.01, phi_min=0.0, phi_max=2*math.pi)
    o = r(d)
    
    s = Ring(r_min=.000001, r_max=.01) 
    p = s(d)
    
    for i in range(len(o.x)):
        print o.x[i], o.y[i], o.dy[i]