source: sasview/DataLoader/manipulations.py @ 2fc9243

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

"""
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

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.fabs(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    
         +-----------+--------+
         0                    1     <--- pixel size
         
        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 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):
        """
           Perform sector averaging.
            
           @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, qy_data)
        # check for major sector
        if self.phi_min > self.phi_max:
            out_major = (self.phi_min <= phi_data) or (self.phi_max > phi_data)
        else:
            out_major = (self.phi_min <= phi_data) & (self.phi_max > 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) or (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]