| 1 | """ |
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| 2 | Data manipulations for 2D data sets. |
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| 3 | Using the meta data information, various types of averaging |
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| 4 | are performed in Q-space |
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| 5 | """ |
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| 6 | |
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| 7 | """ |
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| 8 | This software was developed by the University of Tennessee as part of the |
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| 9 | Distributed Data Analysis of Neutron Scattering Experiments (DANSE) |
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| 10 | project funded by the US National Science Foundation. |
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| 11 | |
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| 12 | See the license text in license.txt |
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| 13 | |
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| 14 | copyright 2008, University of Tennessee |
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| 15 | """ |
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| 16 | #TODO: copy the meta data from the 2D object to the resulting 1D object |
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| 17 | |
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| 18 | from data_info import plottable_2D, Data1D |
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| 19 | import math |
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| 20 | import numpy |
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| 21 | |
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| 22 | def get_q(dx, dy, det_dist, wavelength): |
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| 23 | """ |
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| 24 | @param dx: x-distance from beam center [mm] |
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| 25 | @param dy: y-distance from beam center [mm] |
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| 26 | @return: q-value at the given position |
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| 27 | """ |
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| 28 | # Distance from beam center in the plane of detector |
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| 29 | plane_dist = math.sqrt(dx*dx + dy*dy) |
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| 30 | # Half of the scattering angle |
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| 31 | theta = 0.5*math.atan(plane_dist/det_dist) |
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| 32 | return (4.0*math.pi/wavelength)*math.sin(theta) |
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| 33 | |
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| 34 | class _Slab(object): |
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| 35 | """ |
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| 36 | Compute average I(Q) for a region of interest |
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| 37 | """ |
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| 38 | def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0, bin_width=0.001): |
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| 39 | # Minimum Qx value [A-1] |
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| 40 | self.x_min = x_min |
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| 41 | # Maximum Qx value [A-1] |
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| 42 | self.x_max = x_max |
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| 43 | # Minimum Qy value [A-1] |
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| 44 | self.y_min = y_min |
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| 45 | # Maximum Qy value [A-1] |
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| 46 | self.y_max = y_max |
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| 47 | # Bin width (step size) [A-1] |
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| 48 | self.bin_width = bin_width |
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| 49 | # If True, I(|Q|) will be return, otherwise, negative q-values are allowed |
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| 50 | self.fold = False |
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| 51 | |
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| 52 | def __call__(self, data2D): return NotImplemented |
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| 53 | |
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| 54 | def _avg(self, data2D, maj): |
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| 55 | """ |
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| 56 | Compute average I(Q_maj) for a region of interest. |
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| 57 | The major axis is defined as the axis of Q_maj. |
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| 58 | The minor axis is the axis that we average over. |
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| 59 | |
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| 60 | @param data2D: Data2D object |
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| 61 | @param maj_min: min value on the major axis |
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| 62 | @return: Data1D object |
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| 63 | """ |
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| 64 | if len(data2D.detector) != 1: |
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| 65 | raise RuntimeError, "_Slab._avg: invalid number of detectors: %g" % len(data2D.detector) |
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| 66 | |
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| 67 | pixel_width_x = data2D.detector[0].pixel_size.x |
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| 68 | pixel_width_y = data2D.detector[0].pixel_size.y |
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| 69 | det_dist = data2D.detector[0].distance |
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| 70 | wavelength = data2D.source.wavelength |
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| 71 | center_x = data2D.detector[0].beam_center.x/pixel_width_x |
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| 72 | center_y = data2D.detector[0].beam_center.y/pixel_width_y |
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| 73 | |
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| 74 | # Build array of Q intervals |
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| 75 | if maj=='x': |
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| 76 | nbins = int(math.ceil((self.x_max-self.x_min)/self.bin_width)) |
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| 77 | qbins = self.bin_width*numpy.arange(nbins)+self.x_min |
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| 78 | elif maj=='y': |
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| 79 | nbins = int(math.ceil((self.y_max-self.y_min)/self.bin_width)) |
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| 80 | qbins = self.bin_width*numpy.arange(nbins)+self.y_min |
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| 81 | else: |
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| 82 | raise RuntimeError, "_Slab._avg: unrecognized axis %s" % str(maj) |
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| 83 | |
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| 84 | x = numpy.zeros(nbins) |
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| 85 | y = numpy.zeros(nbins) |
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| 86 | err_y = numpy.zeros(nbins) |
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| 87 | y_counts = numpy.zeros(nbins) |
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| 88 | |
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| 89 | for i in range(numpy.size(data2D.data,1)): |
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| 90 | # Min and max x-value for the pixel |
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| 91 | minx = pixel_width_x*(i - center_x) |
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| 92 | maxx = pixel_width_x*(i+1.0 - center_x) |
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| 93 | |
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| 94 | qxmin = get_q(minx, 0.0, det_dist, wavelength) |
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| 95 | qxmax = get_q(maxx, 0.0, det_dist, wavelength) |
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| 96 | |
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| 97 | # Get the count fraction in x for that pixel |
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| 98 | frac_min = get_pixel_fraction_square(self.x_min, qxmin, qxmax) |
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| 99 | frac_max = get_pixel_fraction_square(self.x_max, qxmin, qxmax) |
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| 100 | frac_x = frac_max - frac_min |
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| 101 | |
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| 102 | if frac_x == 0: |
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| 103 | continue |
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| 104 | |
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| 105 | if maj=='x': |
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| 106 | dx = pixel_width_x*(i+0.5 - center_x) |
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| 107 | q_value = get_q(dx, 0.0, det_dist, wavelength) |
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| 108 | if self.fold==False and dx<0: |
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| 109 | q_value = -q_value |
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| 110 | i_q = int(math.ceil((q_value-self.x_min)/self.bin_width)) - 1 |
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| 111 | |
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| 112 | if i_q<0 or i_q>=nbins: |
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| 113 | continue |
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| 114 | |
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| 115 | for j in range(numpy.size(data2D.data,0)): |
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| 116 | # Min and max y-value for the pixel |
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| 117 | miny = pixel_width_y*(j - center_y) |
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| 118 | maxy = pixel_width_y*(j+1.0 - center_y) |
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| 119 | |
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| 120 | qymin = get_q(0.0, miny, det_dist, wavelength) |
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| 121 | qymax = get_q(0.0, maxy, det_dist, wavelength) |
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| 122 | |
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| 123 | # Get the count fraction in x for that pixel |
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| 124 | frac_min = get_pixel_fraction_square(self.y_min, qymin, qymax) |
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| 125 | frac_max = get_pixel_fraction_square(self.y_max, qymin, qymax) |
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| 126 | frac_y = frac_max - frac_min |
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| 127 | |
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| 128 | frac = frac_x * frac_y |
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| 129 | |
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| 130 | if frac == 0: |
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| 131 | continue |
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| 132 | |
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| 133 | if maj=='y': |
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| 134 | dy = pixel_width_y*(j+0.5 - center_y) |
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| 135 | q_value = get_q(0.0, dy, det_dist, wavelength) |
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| 136 | if self.fold==False and dy<0: |
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| 137 | q_value = -q_value |
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| 138 | i_q = int(math.ceil((q_value-self.y_min)/self.bin_width)) - 1 |
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| 139 | |
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| 140 | if i_q<0 or i_q>=nbins: |
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| 141 | continue |
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| 142 | |
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| 143 | x[i_q] = q_value |
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| 144 | y[i_q] += frac * data2D.data[j][i] |
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| 145 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
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| 146 | err_y[i_q] += frac * frac * math.fabs(data2D.data[j][i]) |
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| 147 | else: |
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| 148 | err_y[i_q] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
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| 149 | y_counts[i_q] += frac |
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| 150 | |
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| 151 | # Average the sums |
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| 152 | for i in range(nbins): |
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| 153 | if y_counts[i]>0: |
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| 154 | err_y[i] = math.sqrt(err_y[i])/y_counts[i] |
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| 155 | y[i] = y[i]/y_counts[i] |
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| 156 | |
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| 157 | return Data1D(x=x, y=y, dy=err_y) |
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| 158 | |
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| 159 | class SlabY(_Slab): |
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| 160 | """ |
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| 161 | Compute average I(Qy) for a region of interest |
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| 162 | """ |
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| 163 | def __call__(self, data2D): |
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| 164 | """ |
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| 165 | Compute average I(Qy) for a region of interest |
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| 166 | |
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| 167 | @param data2D: Data2D object |
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| 168 | @return: Data1D object |
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| 169 | """ |
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| 170 | return self._avg(data2D, 'y') |
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| 171 | |
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| 172 | class SlabX(_Slab): |
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| 173 | """ |
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| 174 | Compute average I(Qx) for a region of interest |
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| 175 | """ |
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| 176 | def __call__(self, data2D): |
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| 177 | """ |
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| 178 | Compute average I(Qx) for a region of interest |
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| 179 | |
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| 180 | @param data2D: Data2D object |
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| 181 | @return: Data1D object |
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| 182 | """ |
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| 183 | return self._avg(data2D, 'x') |
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| 184 | |
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| 185 | class Boxsum(object): |
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| 186 | """ |
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| 187 | Perform the sum of counts in a 2D region of interest. |
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| 188 | """ |
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| 189 | def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0): |
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| 190 | # Minimum Qx value [A-1] |
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| 191 | self.x_min = x_min |
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| 192 | # Maximum Qx value [A-1] |
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| 193 | self.x_max = x_max |
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| 194 | # Minimum Qy value [A-1] |
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| 195 | self.y_min = y_min |
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| 196 | # Maximum Qy value [A-1] |
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| 197 | self.y_max = y_max |
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| 198 | |
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| 199 | def __call__(self, data2D): |
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| 200 | """ |
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| 201 | Perform the sum in the region of interest |
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| 202 | |
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| 203 | @param data2D: Data2D object |
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| 204 | @return: number of counts, error on number of counts |
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| 205 | """ |
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| 206 | y, err_y, y_counts = self._sum(data2D) |
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| 207 | |
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| 208 | # Average the sums |
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| 209 | counts = 0 if y_counts==0 else y |
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| 210 | error = 0 if y_counts==0 else math.sqrt(err_y) |
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| 211 | |
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| 212 | return counts, error |
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| 213 | |
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| 214 | def _sum(self, data2D): |
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| 215 | """ |
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| 216 | Perform the sum in the region of interest |
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| 217 | @param data2D: Data2D object |
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| 218 | @return: number of counts, error on number of counts, number of entries summed |
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| 219 | """ |
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| 220 | if len(data2D.detector) != 1: |
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| 221 | raise RuntimeError, "Circular averaging: invalid number of detectors: %g" % len(data2D.detector) |
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| 222 | |
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| 223 | pixel_width_x = data2D.detector[0].pixel_size.x |
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| 224 | pixel_width_y = data2D.detector[0].pixel_size.y |
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| 225 | det_dist = data2D.detector[0].distance |
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| 226 | wavelength = data2D.source.wavelength |
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| 227 | center_x = data2D.detector[0].beam_center.x/pixel_width_x |
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| 228 | center_y = data2D.detector[0].beam_center.y/pixel_width_y |
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| 229 | |
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| 230 | y = 0.0 |
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| 231 | err_y = 0.0 |
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| 232 | y_counts = 0.0 |
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| 233 | |
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| 234 | for i in range(numpy.size(data2D.data,1)): |
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| 235 | # Min and max x-value for the pixel |
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| 236 | minx = pixel_width_x*(i - center_x) |
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| 237 | maxx = pixel_width_x*(i+1.0 - center_x) |
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| 238 | |
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| 239 | qxmin = get_q(minx, 0.0, det_dist, wavelength) |
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| 240 | qxmax = get_q(maxx, 0.0, det_dist, wavelength) |
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| 241 | |
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| 242 | # Get the count fraction in x for that pixel |
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| 243 | frac_min = get_pixel_fraction_square(self.x_min, qxmin, qxmax) |
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| 244 | frac_max = get_pixel_fraction_square(self.x_max, qxmin, qxmax) |
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| 245 | frac_x = frac_max - frac_min |
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| 246 | |
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| 247 | for j in range(numpy.size(data2D.data,0)): |
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| 248 | # Min and max y-value for the pixel |
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| 249 | miny = pixel_width_y*(j - center_y) |
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| 250 | maxy = pixel_width_y*(j+1.0 - center_y) |
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| 251 | |
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| 252 | qymin = get_q(0.0, miny, det_dist, wavelength) |
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| 253 | qymax = get_q(0.0, maxy, det_dist, wavelength) |
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| 254 | |
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| 255 | # Get the count fraction in x for that pixel |
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| 256 | frac_min = get_pixel_fraction_square(self.y_min, qymin, qymax) |
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| 257 | frac_max = get_pixel_fraction_square(self.y_max, qymin, qymax) |
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| 258 | frac_y = frac_max - frac_min |
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| 259 | |
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| 260 | frac = frac_x * frac_y |
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| 261 | |
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| 262 | y += frac * data2D.data[j][i] |
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| 263 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
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| 264 | err_y += frac * frac * math.fabs(data2D.data[j][i]) |
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| 265 | else: |
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| 266 | err_y += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
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| 267 | y_counts += frac |
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| 268 | |
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| 269 | return y, err_y, y_counts |
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| 270 | |
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| 271 | class Boxavg(Boxsum): |
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| 272 | """ |
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| 273 | Perform the average of counts in a 2D region of interest. |
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| 274 | """ |
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| 275 | def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0): |
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| 276 | super(Boxavg, self).__init__(x_min=x_min, x_max=x_max, y_min=y_min, y_max=y_max) |
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| 277 | |
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| 278 | def __call__(self, data2D): |
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| 279 | """ |
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| 280 | Perform the sum in the region of interest |
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| 281 | |
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| 282 | @param data2D: Data2D object |
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| 283 | @return: average counts, error on average counts |
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| 284 | """ |
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| 285 | y, err_y, y_counts = self._sum(data2D) |
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| 286 | |
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| 287 | # Average the sums |
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| 288 | counts = 0 if y_counts==0 else y/y_counts |
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| 289 | error = 0 if y_counts==0 else math.sqrt(err_y)/y_counts |
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| 290 | |
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| 291 | return counts, error |
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| 292 | |
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| 293 | def get_pixel_fraction_square(x, xmin, xmax): |
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| 294 | """ |
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| 295 | Return the fraction of the length |
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| 296 | from xmin to x. |
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| 297 | |
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| 298 | A B |
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| 299 | +-----------+---------+ |
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| 300 | xmin x xmax |
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| 301 | |
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| 302 | @param x: x-value |
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| 303 | @param xmin: minimum x for the length considered |
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| 304 | @param xmax: minimum x for the length considered |
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| 305 | @return: (x-xmin)/(xmax-xmin) when xmin < x < xmax |
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| 306 | |
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| 307 | """ |
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| 308 | if x<=xmin: |
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| 309 | return 0.0 |
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| 310 | if x>xmin and x<xmax: |
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| 311 | return (x-xmin)/(xmax-xmin) |
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| 312 | else: |
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| 313 | return 1.0 |
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| 314 | |
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| 315 | |
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| 316 | class CircularAverage(object): |
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| 317 | """ |
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| 318 | Perform circular averaging on 2D data |
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| 319 | |
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| 320 | The data returned is the distribution of counts |
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| 321 | as a function of Q |
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| 322 | """ |
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| 323 | def __init__(self, r_min=0.0, r_max=0.0, bin_width=0.001): |
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| 324 | # Minimum radius included in the average [A-1] |
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| 325 | self.r_min = r_min |
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| 326 | # Maximum radius included in the average [A-1] |
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| 327 | self.r_max = r_max |
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| 328 | # Bin width (step size) [A-1] |
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| 329 | self.bin_width = bin_width |
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| 330 | |
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| 331 | def __call__(self, data2D): |
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| 332 | """ |
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| 333 | Perform circular averaging on the data |
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| 334 | |
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| 335 | @param data2D: Data2D object |
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| 336 | @return: Data1D object |
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| 337 | """ |
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| 338 | if len(data2D.detector) != 1: |
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| 339 | raise RuntimeError, "Circular averaging: invalid number of detectors: %g" % len(data2D.detector) |
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| 340 | |
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| 341 | pixel_width_x = data2D.detector[0].pixel_size.x |
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| 342 | pixel_width_y = data2D.detector[0].pixel_size.y |
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| 343 | det_dist = data2D.detector[0].distance |
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| 344 | wavelength = data2D.source.wavelength |
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| 345 | center_x = data2D.detector[0].beam_center.x/pixel_width_x |
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| 346 | center_y = data2D.detector[0].beam_center.y/pixel_width_y |
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| 347 | |
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| 348 | # Find out the maximum Q range |
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| 349 | xwidth = numpy.size(data2D.data,1)*pixel_width_x |
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| 350 | dx_max = xwidth - data2D.detector[0].beam_center.x |
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| 351 | if xwidth-dx_max>dx_max: |
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| 352 | dx_max = xwidth-dx_max |
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| 353 | |
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| 354 | ywidth = numpy.size(data2D.data,0)*pixel_width_y |
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| 355 | dy_max = ywidth - data2D.detector[0].beam_center.y |
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| 356 | if ywidth-dy_max>dy_max: |
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| 357 | dy_max = ywidth-dy_max |
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| 358 | |
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| 359 | qmax = get_q(dx_max, dy_max, det_dist, wavelength) |
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| 360 | |
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| 361 | # Build array of Q intervals |
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| 362 | nbins = int(math.ceil((qmax-self.r_min)/self.bin_width)) |
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| 363 | qbins = self.bin_width*numpy.arange(nbins)+self.r_min |
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| 364 | |
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| 365 | x = numpy.zeros(nbins) |
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| 366 | y = numpy.zeros(nbins) |
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| 367 | err_y = numpy.zeros(nbins) |
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| 368 | y_counts = numpy.zeros(nbins) |
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| 369 | |
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| 370 | for i in range(numpy.size(data2D.data,1)): |
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| 371 | dx = pixel_width_x*(i+0.5 - center_x) |
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| 372 | |
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| 373 | # Min and max x-value for the pixel |
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| 374 | minx = pixel_width_x*(i - center_x) |
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| 375 | maxx = pixel_width_x*(i+1.0 - center_x) |
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| 376 | |
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| 377 | for j in range(numpy.size(data2D.data,0)): |
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| 378 | dy = pixel_width_y*(j+0.5 - center_y) |
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| 379 | |
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| 380 | q_value = get_q(dx, dy, det_dist, wavelength) |
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| 381 | |
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| 382 | # Min and max y-value for the pixel |
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| 383 | miny = pixel_width_y*(j - center_y) |
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| 384 | maxy = pixel_width_y*(j+1.0 - center_y) |
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| 385 | |
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| 386 | # Calculate the q-value for each corner |
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| 387 | # q_[x min or max][y min or max] |
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| 388 | q_00 = get_q(minx, miny, det_dist, wavelength) |
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| 389 | q_01 = get_q(minx, maxy, det_dist, wavelength) |
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| 390 | q_10 = get_q(maxx, miny, det_dist, wavelength) |
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| 391 | q_11 = get_q(maxx, maxy, det_dist, wavelength) |
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| 392 | |
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| 393 | # Look for intercept between each side of the pixel |
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| 394 | # and the constant-q ring for qmax |
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| 395 | frac_max = get_pixel_fraction(self.r_max, q_00, q_01, q_10, q_11) |
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| 396 | |
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| 397 | # Look for intercept between each side of the pixel |
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| 398 | # and the constant-q ring for qmin |
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| 399 | frac_min = get_pixel_fraction(self.r_min, q_00, q_01, q_10, q_11) |
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| 400 | |
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| 401 | # We are interested in the region between qmin and qmax |
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| 402 | # therefore the fraction of the surface of the pixel |
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| 403 | # that we will use to calculate the number of counts to |
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| 404 | # include is given by: |
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| 405 | frac = frac_max - frac_min |
|---|
| 406 | |
|---|
| 407 | i_q = int(math.ceil((q_value-self.r_min)/self.bin_width)) - 1 |
|---|
| 408 | |
|---|
| 409 | x[i_q] = q_value |
|---|
| 410 | y[i_q] += frac * data2D.data[j][i] |
|---|
| 411 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
|---|
| 412 | err_y[i_q] += frac * frac * math.fabs(data2D.data[j][i]) |
|---|
| 413 | else: |
|---|
| 414 | err_y[i_q] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
|---|
| 415 | y_counts[i_q] += frac |
|---|
| 416 | |
|---|
| 417 | # Average the sums |
|---|
| 418 | for i in range(nbins): |
|---|
| 419 | if y_counts[i]>0: |
|---|
| 420 | err_y[i] = math.sqrt(err_y[i])/y_counts[i] |
|---|
| 421 | y[i] = y[i]/y_counts[i] |
|---|
| 422 | |
|---|
| 423 | return Data1D(x=x, y=y, dy=err_y) |
|---|
| 424 | |
|---|
| 425 | |
|---|
| 426 | class Ring(object): |
|---|
| 427 | """ |
|---|
| 428 | Defines a ring on a 2D data set. |
|---|
| 429 | The ring is defined by r_min, r_max, and |
|---|
| 430 | the position of the center of the ring. |
|---|
| 431 | |
|---|
| 432 | The data returned is the distribution of counts |
|---|
| 433 | around the ring as a function of phi. |
|---|
| 434 | |
|---|
| 435 | """ |
|---|
| 436 | |
|---|
| 437 | def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0): |
|---|
| 438 | # Minimum radius |
|---|
| 439 | self.r_min = r_min |
|---|
| 440 | # Maximum radius |
|---|
| 441 | self.r_max = r_max |
|---|
| 442 | # Center of the ring in x |
|---|
| 443 | self.center_x = center_x |
|---|
| 444 | # Center of the ring in y |
|---|
| 445 | self.center_y = center_y |
|---|
| 446 | # Number of angular bins |
|---|
| 447 | self.nbins_phi = 20 |
|---|
| 448 | |
|---|
| 449 | def __call__(self, data2D): |
|---|
| 450 | """ |
|---|
| 451 | Apply the ring to the data set. |
|---|
| 452 | Returns the angular distribution for a given q range |
|---|
| 453 | |
|---|
| 454 | @param data2D: Data2D object |
|---|
| 455 | @return: Data1D object |
|---|
| 456 | """ |
|---|
| 457 | if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]: |
|---|
| 458 | raise RuntimeError, "Ring averaging only take plottable_2D objects" |
|---|
| 459 | |
|---|
| 460 | data = data2D.data |
|---|
| 461 | qmin = self.r_min |
|---|
| 462 | qmax = self.r_max |
|---|
| 463 | |
|---|
| 464 | if len(data2D.detector) != 1: |
|---|
| 465 | raise RuntimeError, "Ring averaging: invalid number of detectors: %g" % len(data2D.detector) |
|---|
| 466 | pixel_width_x = data2D.detector[0].pixel_size.x |
|---|
| 467 | pixel_width_y = data2D.detector[0].pixel_size.y |
|---|
| 468 | det_dist = data2D.detector[0].distance |
|---|
| 469 | wavelength = data2D.source.wavelength |
|---|
| 470 | #center_x = self.center_x/pixel_width_x |
|---|
| 471 | #center_y = self.center_y/pixel_width_y |
|---|
| 472 | center_x = data2D.detector[0].beam_center.x/pixel_width_x |
|---|
| 473 | center_y = data2D.detector[0].beam_center.y/pixel_width_y |
|---|
| 474 | |
|---|
| 475 | |
|---|
| 476 | phi_bins = numpy.zeros(self.nbins_phi) |
|---|
| 477 | phi_counts = numpy.zeros(self.nbins_phi) |
|---|
| 478 | phi_values = numpy.zeros(self.nbins_phi) |
|---|
| 479 | phi_err = numpy.zeros(self.nbins_phi) |
|---|
| 480 | |
|---|
| 481 | for i in range(numpy.size(data,1)): |
|---|
| 482 | dx = pixel_width_x*(i+0.5 - center_x) |
|---|
| 483 | |
|---|
| 484 | # Min and max x-value for the pixel |
|---|
| 485 | minx = pixel_width_x*(i - center_x) |
|---|
| 486 | maxx = pixel_width_x*(i+1.0 - center_x) |
|---|
| 487 | |
|---|
| 488 | for j in range(numpy.size(data,0)): |
|---|
| 489 | dy = pixel_width_y*(j+0.5 - center_y) |
|---|
| 490 | |
|---|
| 491 | q_value = get_q(dx, dy, det_dist, wavelength) |
|---|
| 492 | |
|---|
| 493 | # Min and max y-value for the pixel |
|---|
| 494 | miny = pixel_width_y*(j - center_y) |
|---|
| 495 | maxy = pixel_width_y*(j+1.0 - center_y) |
|---|
| 496 | |
|---|
| 497 | # Calculate the q-value for each corner |
|---|
| 498 | # q_[x min or max][y min or max] |
|---|
| 499 | q_00 = get_q(minx, miny, det_dist, wavelength) |
|---|
| 500 | q_01 = get_q(minx, maxy, det_dist, wavelength) |
|---|
| 501 | q_10 = get_q(maxx, miny, det_dist, wavelength) |
|---|
| 502 | q_11 = get_q(maxx, maxy, det_dist, wavelength) |
|---|
| 503 | |
|---|
| 504 | # Look for intercept between each side of the pixel |
|---|
| 505 | # and the constant-q ring for qmax |
|---|
| 506 | frac_max = get_pixel_fraction(qmax, q_00, q_01, q_10, q_11) |
|---|
| 507 | |
|---|
| 508 | # Look for intercept between each side of the pixel |
|---|
| 509 | # and the constant-q ring for qmin |
|---|
| 510 | frac_min = get_pixel_fraction(qmin, q_00, q_01, q_10, q_11) |
|---|
| 511 | |
|---|
| 512 | # We are interested in the region between qmin and qmax |
|---|
| 513 | # therefore the fraction of the surface of the pixel |
|---|
| 514 | # that we will use to calculate the number of counts to |
|---|
| 515 | # include is given by: |
|---|
| 516 | |
|---|
| 517 | frac = frac_max - frac_min |
|---|
| 518 | |
|---|
| 519 | i_phi = int(math.ceil(self.nbins_phi*(math.atan2(dy, dx)+math.pi)/(2.0*math.pi))) - 1 |
|---|
| 520 | |
|---|
| 521 | phi_bins[i_phi] += frac * data[j][i] |
|---|
| 522 | |
|---|
| 523 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
|---|
| 524 | phi_err[i_phi] += frac * frac * math.fabs(data2D.data[j][i]) |
|---|
| 525 | else: |
|---|
| 526 | phi_err[i_phi] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
|---|
| 527 | phi_counts[i_phi] += frac |
|---|
| 528 | |
|---|
| 529 | for i in range(self.nbins_phi): |
|---|
| 530 | phi_bins[i] = phi_bins[i] / phi_counts[i] |
|---|
| 531 | phi_err[i] = math.sqrt(phi_err[i]) / phi_counts[i] |
|---|
| 532 | phi_values[i] = 2.0*math.pi/self.nbins_phi*(1.0*i + 0.5) |
|---|
| 533 | |
|---|
| 534 | return Data1D(x=phi_values, y=phi_bins, dy=phi_err) |
|---|
| 535 | |
|---|
| 536 | def get_pixel_fraction(qmax, q_00, q_01, q_10, q_11): |
|---|
| 537 | """ |
|---|
| 538 | Returns the fraction of the pixel defined by |
|---|
| 539 | the four corners (q_00, q_01, q_10, q_11) that |
|---|
| 540 | has q < qmax. |
|---|
| 541 | |
|---|
| 542 | q_01 q_11 |
|---|
| 543 | y=1 +--------------+ |
|---|
| 544 | | | |
|---|
| 545 | | | |
|---|
| 546 | | | |
|---|
| 547 | y=0 +--------------+ |
|---|
| 548 | q_00 q_01 |
|---|
| 549 | |
|---|
| 550 | x=0 x=1 |
|---|
| 551 | |
|---|
| 552 | """ |
|---|
| 553 | |
|---|
| 554 | # y side for x = minx |
|---|
| 555 | x_0 = get_intercept(qmax, q_00, q_01) |
|---|
| 556 | # y side for x = maxx |
|---|
| 557 | x_1 = get_intercept(qmax, q_10, q_11) |
|---|
| 558 | |
|---|
| 559 | # x side for y = miny |
|---|
| 560 | y_0 = get_intercept(qmax, q_00, q_10) |
|---|
| 561 | # x side for y = maxy |
|---|
| 562 | y_1 = get_intercept(qmax, q_01, q_11) |
|---|
| 563 | |
|---|
| 564 | # surface fraction for a 1x1 pixel |
|---|
| 565 | frac_max = 0 |
|---|
| 566 | |
|---|
| 567 | if x_0 and x_1: |
|---|
| 568 | frac_max = (x_0+x_1)/2.0 |
|---|
| 569 | |
|---|
| 570 | elif y_0 and y_1: |
|---|
| 571 | frac_max = (y_0+y_1)/2.0 |
|---|
| 572 | |
|---|
| 573 | elif x_0 and y_0: |
|---|
| 574 | if q_00 < q_10: |
|---|
| 575 | frac_max = x_0*y_0/2.0 |
|---|
| 576 | else: |
|---|
| 577 | frac_max = 1.0-x_0*y_0/2.0 |
|---|
| 578 | |
|---|
| 579 | elif x_0 and y_1: |
|---|
| 580 | if q_00 < q_10: |
|---|
| 581 | frac_max = x_0*y_1/2.0 |
|---|
| 582 | else: |
|---|
| 583 | frac_max = 1.0-x_0*y_1/2.0 |
|---|
| 584 | |
|---|
| 585 | elif x_1 and y_0: |
|---|
| 586 | if q_00 > q_10: |
|---|
| 587 | frac_max = x_1*y_0/2.0 |
|---|
| 588 | else: |
|---|
| 589 | frac_max = 1.0-x_1*y_0/2.0 |
|---|
| 590 | |
|---|
| 591 | elif x_1 and y_1: |
|---|
| 592 | if q_00 < q_10: |
|---|
| 593 | frac_max = 1.0 - (1.0-x_1)*(1.0-y_1)/2.0 |
|---|
| 594 | else: |
|---|
| 595 | frac_max = (1.0-x_1)*(1.0-y_1)/2.0 |
|---|
| 596 | |
|---|
| 597 | # If we make it here, there is no intercept between |
|---|
| 598 | # this pixel and the constant-q ring. We only need |
|---|
| 599 | # to know if we have to include it or exclude it. |
|---|
| 600 | elif (q_00+q_01+q_10+q_11)/4.0 < qmax: |
|---|
| 601 | frac_max = 1.0 |
|---|
| 602 | |
|---|
| 603 | return frac_max |
|---|
| 604 | |
|---|
| 605 | def get_intercept(q, q_0, q_1): |
|---|
| 606 | """ |
|---|
| 607 | Returns the fraction of the side at which the |
|---|
| 608 | q-value intercept the pixel, None otherwise. |
|---|
| 609 | The values returned is the fraction ON THE SIDE |
|---|
| 610 | OF THE LOWEST Q. |
|---|
| 611 | |
|---|
| 612 | |
|---|
| 613 | |
|---|
| 614 | A B |
|---|
| 615 | +-----------+--------+ |
|---|
| 616 | 0 1 <--- pixel size |
|---|
| 617 | |
|---|
| 618 | Q_0 -------- Q ----- Q_1 <--- equivalent Q range |
|---|
| 619 | |
|---|
| 620 | |
|---|
| 621 | if Q_1 > Q_0, A is returned |
|---|
| 622 | if Q_1 < Q_0, B is returned |
|---|
| 623 | |
|---|
| 624 | if Q is outside the range of [Q_0, Q_1], None is returned |
|---|
| 625 | |
|---|
| 626 | """ |
|---|
| 627 | if q_1 > q_0: |
|---|
| 628 | if (q > q_0 and q <= q_1): |
|---|
| 629 | return (q-q_0)/(q_1 - q_0) |
|---|
| 630 | else: |
|---|
| 631 | if (q > q_1 and q <= q_0): |
|---|
| 632 | return (q-q_1)/(q_0 - q_1) |
|---|
| 633 | return None |
|---|
| 634 | |
|---|
| 635 | |
|---|
| 636 | class _Sector: |
|---|
| 637 | """ |
|---|
| 638 | Defines a sector region on a 2D data set. |
|---|
| 639 | The sector is defined by r_min, r_max, phi_min, phi_max, |
|---|
| 640 | and the position of the center of the ring. |
|---|
| 641 | |
|---|
| 642 | Phi is defined between 0 and 2pi |
|---|
| 643 | """ |
|---|
| 644 | def __init__(self, r_min, r_max, phi_min, phi_max): |
|---|
| 645 | self.r_min = r_min |
|---|
| 646 | self.r_max = r_max |
|---|
| 647 | self.phi_min = phi_min |
|---|
| 648 | self.phi_max = phi_max |
|---|
| 649 | self.nbins = 20 |
|---|
| 650 | |
|---|
| 651 | def _agv(self, data2D, run='phi'): |
|---|
| 652 | """ |
|---|
| 653 | Perform sector averaging. |
|---|
| 654 | |
|---|
| 655 | @param data2D: Data2D object |
|---|
| 656 | @param run: define the varying parameter ('phi' or 'q') |
|---|
| 657 | @return: Data1D object |
|---|
| 658 | """ |
|---|
| 659 | if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]: |
|---|
| 660 | raise RuntimeError, "Ring averaging only take plottable_2D objects" |
|---|
| 661 | |
|---|
| 662 | data = data2D.data |
|---|
| 663 | qmin = self.r_min |
|---|
| 664 | qmax = self.r_max |
|---|
| 665 | |
|---|
| 666 | if len(data2D.detector) != 1: |
|---|
| 667 | raise RuntimeError, "Ring averaging: invalid number of detectors: %g" % len(data2D.detector) |
|---|
| 668 | pixel_width_x = data2D.detector[0].pixel_size.x |
|---|
| 669 | pixel_width_y = data2D.detector[0].pixel_size.y |
|---|
| 670 | det_dist = data2D.detector[0].distance |
|---|
| 671 | wavelength = data2D.source.wavelength |
|---|
| 672 | center_x = data2D.detector[0].beam_center.x/pixel_width_x |
|---|
| 673 | center_y = data2D.detector[0].beam_center.y/pixel_width_y |
|---|
| 674 | |
|---|
| 675 | y = numpy.zeros(self.nbins) |
|---|
| 676 | y_counts = numpy.zeros(self.nbins) |
|---|
| 677 | x = numpy.zeros(self.nbins) |
|---|
| 678 | y_err = numpy.zeros(self.nbins) |
|---|
| 679 | |
|---|
| 680 | for i in range(numpy.size(data,1)): |
|---|
| 681 | dx = pixel_width_x*(i+0.5 - center_x) |
|---|
| 682 | |
|---|
| 683 | # Min and max x-value for the pixel |
|---|
| 684 | minx = pixel_width_x*(i - center_x) |
|---|
| 685 | maxx = pixel_width_x*(i+1.0 - center_x) |
|---|
| 686 | |
|---|
| 687 | for j in range(numpy.size(data,0)): |
|---|
| 688 | dy = pixel_width_y*(j+0.5 - center_y) |
|---|
| 689 | |
|---|
| 690 | q_value = get_q(dx, dy, det_dist, wavelength) |
|---|
| 691 | |
|---|
| 692 | # Min and max y-value for the pixel |
|---|
| 693 | miny = pixel_width_y*(j - center_y) |
|---|
| 694 | maxy = pixel_width_y*(j+1.0 - center_y) |
|---|
| 695 | |
|---|
| 696 | # Calculate the q-value for each corner |
|---|
| 697 | # q_[x min or max][y min or max] |
|---|
| 698 | q_00 = get_q(minx, miny, det_dist, wavelength) |
|---|
| 699 | q_01 = get_q(minx, maxy, det_dist, wavelength) |
|---|
| 700 | q_10 = get_q(maxx, miny, det_dist, wavelength) |
|---|
| 701 | q_11 = get_q(maxx, maxy, det_dist, wavelength) |
|---|
| 702 | |
|---|
| 703 | # Look for intercept between each side of the pixel |
|---|
| 704 | # and the constant-q ring for qmax |
|---|
| 705 | frac_max = get_pixel_fraction(qmax, q_00, q_01, q_10, q_11) |
|---|
| 706 | |
|---|
| 707 | # Look for intercept between each side of the pixel |
|---|
| 708 | # and the constant-q ring for qmin |
|---|
| 709 | frac_min = get_pixel_fraction(qmin, q_00, q_01, q_10, q_11) |
|---|
| 710 | |
|---|
| 711 | # We are interested in the region between qmin and qmax |
|---|
| 712 | # therefore the fraction of the surface of the pixel |
|---|
| 713 | # that we will use to calculate the number of counts to |
|---|
| 714 | # include is given by: |
|---|
| 715 | |
|---|
| 716 | frac = frac_max - frac_min |
|---|
| 717 | |
|---|
| 718 | # Compute phi and check whether it's within the limits |
|---|
| 719 | phi_value = math.atan2(dy, dx)+math.pi |
|---|
| 720 | if phi_value<self.phi_min or phi_value>self.phi_max: |
|---|
| 721 | continue |
|---|
| 722 | |
|---|
| 723 | # Check which type of averaging we need |
|---|
| 724 | if run.lower()=='phi': |
|---|
| 725 | i_bin = int(math.ceil(self.nbins*(phi_value-self.phi_min)/(self.phi_max-self.phi_min))) - 1 |
|---|
| 726 | else: |
|---|
| 727 | # If we don't need this pixel, skip the rest of the work |
|---|
| 728 | #TODO: an improvement here would be to compute the average |
|---|
| 729 | # Q for the pixel from the part that is covered by |
|---|
| 730 | # the ring defined by q_min/q_max rather than the complete |
|---|
| 731 | # pixel |
|---|
| 732 | if q_value<self.r_min or q_value>self.r_max: |
|---|
| 733 | continue |
|---|
| 734 | i_bin = int(math.ceil(self.nbins*(q_value-self.r_min)/(self.r_max-self.r_min))) - 1 |
|---|
| 735 | |
|---|
| 736 | try: |
|---|
| 737 | y[i_bin] += frac * data[j][i] |
|---|
| 738 | except: |
|---|
| 739 | import sys |
|---|
| 740 | print sys.exc_value |
|---|
| 741 | print i_bin, frac |
|---|
| 742 | |
|---|
| 743 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
|---|
| 744 | y_err[i_bin] += frac * frac * math.fabs(data2D.data[j][i]) |
|---|
| 745 | else: |
|---|
| 746 | y_err[i_bin] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
|---|
| 747 | y_counts[i_bin] += frac |
|---|
| 748 | |
|---|
| 749 | for i in range(self.nbins): |
|---|
| 750 | y[i] = y[i] / y_counts[i] |
|---|
| 751 | y_err[i] = math.sqrt(y_err[i]) / y_counts[i] |
|---|
| 752 | # Check which type of averaging we need |
|---|
| 753 | if run.lower()=='phi': |
|---|
| 754 | x[i] = (self.phi_max-self.phi_min)/self.nbins*(1.0*i + 0.5)+self.phi_min |
|---|
| 755 | else: |
|---|
| 756 | x[i] = (self.r_max-self.r_min)/self.nbins*(1.0*i + 0.5)+self.r_min |
|---|
| 757 | |
|---|
| 758 | return Data1D(x=x, y=y, dy=y_err) |
|---|
| 759 | |
|---|
| 760 | |
|---|
| 761 | class SectorPhi(_Sector): |
|---|
| 762 | """ |
|---|
| 763 | Sector average as a function of phi. |
|---|
| 764 | I(phi) is return and the data is averaged over Q. |
|---|
| 765 | |
|---|
| 766 | A sector is defined by r_min, r_max, phi_min, phi_max. |
|---|
| 767 | The number of bin in phi also has to be defined. |
|---|
| 768 | """ |
|---|
| 769 | def __call__(self, data2D): |
|---|
| 770 | """ |
|---|
| 771 | Perform sector average and return I(phi). |
|---|
| 772 | |
|---|
| 773 | @param data2D: Data2D object |
|---|
| 774 | @return: Data1D object |
|---|
| 775 | """ |
|---|
| 776 | return self._agv(data2D, 'phi') |
|---|
| 777 | |
|---|
| 778 | class SectorQ(_Sector): |
|---|
| 779 | """ |
|---|
| 780 | Sector average as a function of Q. |
|---|
| 781 | I(Q) is return and the data is averaged over phi. |
|---|
| 782 | |
|---|
| 783 | A sector is defined by r_min, r_max, phi_min, phi_max. |
|---|
| 784 | The number of bin in Q also has to be defined. |
|---|
| 785 | """ |
|---|
| 786 | def __call__(self, data2D): |
|---|
| 787 | """ |
|---|
| 788 | Perform sector average and return I(Q). |
|---|
| 789 | |
|---|
| 790 | @param data2D: Data2D object |
|---|
| 791 | @return: Data1D object |
|---|
| 792 | """ |
|---|
| 793 | return self._agv(data2D, 'q') |
|---|
| 794 | |
|---|
| 795 | if __name__ == "__main__": |
|---|
| 796 | |
|---|
| 797 | from loader import Loader |
|---|
| 798 | |
|---|
| 799 | |
|---|
| 800 | d = Loader().load('test/MAR07232_rest.ASC') |
|---|
| 801 | #d = Loader().load('test/MP_New.sans') |
|---|
| 802 | |
|---|
| 803 | |
|---|
| 804 | r = SectorQ(r_min=.005, r_max=.01, phi_min=0.0, phi_max=math.pi/2.0) |
|---|
| 805 | o = r(d) |
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| 806 | |
|---|
| 807 | s = Ring(r_min=.005, r_max=.01) |
|---|
| 808 | p = s(d) |
|---|
| 809 | |
|---|
| 810 | for i in range(len(o.x)): |
|---|
| 811 | print o.x[i], o.y[i], o.dy[i] |
|---|
| 812 | |
|---|
| 813 | |
|---|
| 814 | |
|---|
