| 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 | |
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| 35 | |
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| 36 | class Slabs: |
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| 37 | def __init__(self): |
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| 38 | pass |
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| 39 | |
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| 40 | |
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| 41 | class Boxsum(object): |
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| 42 | """ |
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| 43 | Perform the sum of counts in a 2D region of interest. |
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| 44 | """ |
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| 45 | def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0): |
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| 46 | # Minimum Qx value [A-1] |
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| 47 | self.x_min = x_min |
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| 48 | # Maximum Qx value [A-1] |
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| 49 | self.x_max = x_max |
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| 50 | # Minimum Qy value [A-1] |
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| 51 | self.y_min = y_min |
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| 52 | # Maximum Qy value [A-1] |
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| 53 | self.y_max = y_max |
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| 54 | |
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| 55 | def __call__(self, data2D): |
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| 56 | """ |
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| 57 | Perform the sum in the region of interest |
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| 58 | |
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| 59 | @param data2D: Data2D object |
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| 60 | @return: number of counts, error on number of counts |
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| 61 | """ |
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| 62 | y, err_y, y_counts = self._sum(data2D) |
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| 63 | |
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| 64 | # Average the sums |
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| 65 | counts = 0 if y_counts==0 else y |
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| 66 | error = 0 if y_counts==0 else math.sqrt(err_y) |
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| 67 | |
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| 68 | return counts, error |
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| 69 | |
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| 70 | def _sum(self, data2D): |
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| 71 | """ |
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| 72 | Perform the sum in the region of interest |
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| 73 | @param data2D: Data2D object |
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| 74 | @return: number of counts, error on number of counts, number of entries summed |
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| 75 | """ |
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| 76 | if len(data2D.detector) != 1: |
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| 77 | raise RuntimeError, "Circular averaging: invalid number of detectors: %g" % len(data2D.detector) |
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| 78 | |
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| 79 | pixel_width = data2D.detector[0].pixel_size.x |
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| 80 | det_dist = data2D.detector[0].distance |
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| 81 | wavelength = data2D.source.wavelength |
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| 82 | center_x = data2D.detector[0].beam_center.x/pixel_width |
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| 83 | center_y = data2D.detector[0].beam_center.y/pixel_width |
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| 84 | |
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| 85 | y = 0.0 |
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| 86 | err_y = 0.0 |
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| 87 | y_counts = 0.0 |
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| 88 | |
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| 89 | for i in range(len(data2D.data)): |
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| 90 | # Min and max x-value for the pixel |
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| 91 | minx = pixel_width*(i - center_x) |
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| 92 | maxx = pixel_width*(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 | for j in range(len(data2D.data)): |
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| 103 | # Min and max y-value for the pixel |
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| 104 | miny = pixel_width*(j - center_y) |
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| 105 | maxy = pixel_width*(j+1.0 - center_y) |
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| 106 | |
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| 107 | qymin = get_q(0.0, miny, det_dist, wavelength) |
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| 108 | qymax = get_q(0.0, maxy, det_dist, wavelength) |
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| 109 | |
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| 110 | # Get the count fraction in x for that pixel |
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| 111 | frac_min = get_pixel_fraction_square(self.y_min, qymin, qymax) |
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| 112 | frac_max = get_pixel_fraction_square(self.y_max, qymin, qymax) |
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| 113 | frac_y = frac_max - frac_min |
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| 114 | |
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| 115 | frac = frac_x * frac_y |
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| 116 | |
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| 117 | y += frac * data2D.data[j][i] |
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| 118 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
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| 119 | err_y += frac * frac * math.fabs(data2D.data[j][i]) |
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| 120 | else: |
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| 121 | err_y += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
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| 122 | y_counts += frac |
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| 123 | |
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| 124 | return y, err_y, y_counts |
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| 125 | # Average the sums |
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| 126 | counts = 0 if y_counts==0 else y/y_counts |
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| 127 | error = 0 if y_counts==0 else math.sqrt(err_y)/y_counts |
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| 128 | |
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| 129 | return counts, error |
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| 130 | |
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| 131 | class Boxavg(Boxsum): |
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| 132 | """ |
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| 133 | Perform the average of counts in a 2D region of interest. |
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| 134 | """ |
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| 135 | def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0): |
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| 136 | super(Boxavg, self).__init__(x_min=x_min, x_max=x_max, y_min=y_min, y_max=y_max) |
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| 137 | |
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| 138 | def __call__(self, data2D): |
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| 139 | """ |
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| 140 | Perform the sum in the region of interest |
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| 141 | |
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| 142 | @param data2D: Data2D object |
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| 143 | @return: average counts, error on average counts |
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| 144 | """ |
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| 145 | y, err_y, y_counts = self._sum(data2D) |
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| 146 | |
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| 147 | # Average the sums |
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| 148 | counts = 0 if y_counts==0 else y/y_counts |
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| 149 | error = 0 if y_counts==0 else math.sqrt(err_y)/y_counts |
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| 150 | |
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| 151 | return counts, error |
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| 152 | |
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| 153 | def get_pixel_fraction_square(x, xmin, xmax): |
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| 154 | """ |
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| 155 | Return the fraction of the length |
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| 156 | from xmin to x. |
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| 157 | |
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| 158 | A B |
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| 159 | +-----------+---------+ |
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| 160 | xmin x xmax |
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| 161 | |
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| 162 | @param x: x-value |
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| 163 | @param xmin: minimum x for the length considered |
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| 164 | @param xmax: minimum x for the length considered |
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| 165 | @return: (x-xmin)/(xmax-xmin) when xmin < x < xmax |
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| 166 | |
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| 167 | """ |
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| 168 | if x<=xmin: |
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| 169 | return 0.0 |
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| 170 | if x>xmin and x<xmax: |
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| 171 | return (x-xmin)/(xmax-xmin) |
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| 172 | else: |
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| 173 | return 1.0 |
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| 174 | |
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| 175 | |
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| 176 | class CircularAverage(object): |
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| 177 | """ |
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| 178 | Perform circular averaging on 2D data |
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| 179 | |
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| 180 | The data returned is the distribution of counts |
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| 181 | as a function of Q |
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| 182 | """ |
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| 183 | def __init__(self, r_min=0.0, r_max=0.0, bin_width=0.001): |
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| 184 | # Minimum radius included in the average [A-1] |
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| 185 | self.r_min = r_min |
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| 186 | # Maximum radius included in the average [A-1] |
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| 187 | self.r_max = r_max |
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| 188 | # Bin width (step size) [A-1] |
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| 189 | self.bin_width = bin_width |
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| 190 | |
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| 191 | def __call__(self, data2D): |
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| 192 | """ |
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| 193 | Perform circular averaging on the data |
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| 194 | |
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| 195 | @param data2D: Data2D object |
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| 196 | @return: Data1D object |
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| 197 | """ |
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| 198 | if len(data2D.detector) != 1: |
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| 199 | raise RuntimeError, "Circular averaging: invalid number of detectors: %g" % len(data2D.detector) |
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| 200 | |
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| 201 | pixel_width = data2D.detector[0].pixel_size.x |
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| 202 | det_dist = data2D.detector[0].distance |
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| 203 | wavelength = data2D.source.wavelength |
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| 204 | center_x = data2D.detector[0].beam_center.x/pixel_width |
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| 205 | center_y = data2D.detector[0].beam_center.y/pixel_width |
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| 206 | |
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| 207 | # Find out the maximum Q range |
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| 208 | xwidth = numpy.size(data2D.data,1)*pixel_width |
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| 209 | dx_max = xwidth - data2D.detector[0].beam_center.x |
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| 210 | if xwidth-dx_max>dx_max: |
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| 211 | dx_max = xwidth-dx_max |
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| 212 | |
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| 213 | ywidth = numpy.size(data2D.data,0)*pixel_width |
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| 214 | dy_max = ywidth - data2D.detector[0].beam_center.y |
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| 215 | if ywidth-dy_max>dy_max: |
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| 216 | dy_max = ywidth-dy_max |
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| 217 | |
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| 218 | qmax = get_q(dx_max, dy_max, det_dist, wavelength) |
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| 219 | |
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| 220 | # Build array of Q intervals |
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| 221 | nbins = int(math.ceil((qmax-self.r_min)/self.bin_width)) |
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| 222 | qbins = self.bin_width*numpy.arange(nbins)+self.r_min |
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| 223 | |
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| 224 | x = numpy.zeros(nbins) |
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| 225 | y = numpy.zeros(nbins) |
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| 226 | err_y = numpy.zeros(nbins) |
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| 227 | y_counts = numpy.zeros(nbins) |
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| 228 | |
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| 229 | for i in range(len(data2D.data)): |
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| 230 | dx = pixel_width*(i+0.5 - center_x) |
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| 231 | |
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| 232 | # Min and max x-value for the pixel |
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| 233 | minx = pixel_width*(i - center_x) |
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| 234 | maxx = pixel_width*(i+1.0 - center_x) |
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| 235 | |
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| 236 | for j in range(len(data2D.data)): |
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| 237 | dy = pixel_width*(j+0.5 - center_y) |
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| 238 | |
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| 239 | q_value = get_q(dx, dy, det_dist, wavelength) |
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| 240 | |
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| 241 | # Min and max y-value for the pixel |
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| 242 | miny = pixel_width*(j - center_y) |
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| 243 | maxy = pixel_width*(j+1.0 - center_y) |
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| 244 | |
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| 245 | # Calculate the q-value for each corner |
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| 246 | # q_[x min or max][y min or max] |
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| 247 | q_00 = get_q(minx, miny, det_dist, wavelength) |
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| 248 | q_01 = get_q(minx, maxy, det_dist, wavelength) |
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| 249 | q_10 = get_q(maxx, miny, det_dist, wavelength) |
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| 250 | q_11 = get_q(maxx, maxy, det_dist, wavelength) |
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| 251 | |
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| 252 | # Look for intercept between each side of the pixel |
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| 253 | # and the constant-q ring for qmax |
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| 254 | frac_max = get_pixel_fraction(self.r_max, q_00, q_01, q_10, q_11) |
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| 255 | |
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| 256 | # Look for intercept between each side of the pixel |
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| 257 | # and the constant-q ring for qmin |
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| 258 | frac_min = get_pixel_fraction(self.r_min, q_00, q_01, q_10, q_11) |
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| 259 | |
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| 260 | # We are interested in the region between qmin and qmax |
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| 261 | # therefore the fraction of the surface of the pixel |
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| 262 | # that we will use to calculate the number of counts to |
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| 263 | # include is given by: |
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| 264 | frac = frac_max - frac_min |
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| 265 | |
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| 266 | i_q = int(math.ceil((q_value-self.r_min)/self.bin_width)) - 1 |
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| 267 | |
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| 268 | x[i_q] = q_value |
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| 269 | y[i_q] += frac * data2D.data[j][i] |
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| 270 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
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| 271 | err_y[i_q] += frac * frac * math.fabs(data2D.data[j][i]) |
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| 272 | else: |
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| 273 | err_y[i_q] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
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| 274 | y_counts[i_q] += frac |
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| 275 | |
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| 276 | # Average the sums |
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| 277 | for i in range(nbins): |
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| 278 | if y_counts[i]>0: |
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| 279 | err_y[i] = math.sqrt(err_y[i])/y_counts[i] |
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| 280 | y[i] = y[i]/y_counts[i] |
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| 281 | |
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| 282 | return Data1D(x=x, y=y, dy=err_y) |
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| 283 | |
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| 284 | |
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| 285 | class Ring(object): |
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| 286 | """ |
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| 287 | Defines a ring on a 2D data set. |
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| 288 | The ring is defined by r_min, r_max, and |
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| 289 | the position of the center of the ring. |
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| 290 | |
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| 291 | The data returned is the distribution of counts |
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| 292 | around the ring as a function of phi. |
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| 293 | |
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| 294 | """ |
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| 295 | |
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| 296 | def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0): |
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| 297 | # Minimum radius |
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| 298 | self.r_min = r_min |
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| 299 | # Maximum radius |
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| 300 | self.r_max = r_max |
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| 301 | # Center of the ring in x |
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| 302 | self.center_x = center_x |
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| 303 | # Center of the ring in y |
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| 304 | self.center_y = center_y |
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| 305 | # Number of angular bins |
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| 306 | self.nbins_phi = 20 |
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| 307 | |
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| 308 | def __call__(self, data2D): |
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| 309 | """ |
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| 310 | Apply the ring to the data set. |
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| 311 | Returns the angular distribution for a given q range |
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| 312 | |
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| 313 | @param data2D: Data2D object |
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| 314 | @return: Data1D object |
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| 315 | """ |
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| 316 | if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]: |
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| 317 | raise RuntimeError, "Ring averaging only take plottable_2D objects" |
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| 318 | |
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| 319 | data = data2D.data |
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| 320 | qmin = self.r_min |
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| 321 | qmax = self.r_max |
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| 322 | |
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| 323 | if len(data2D.detector) != 1: |
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| 324 | raise RuntimeError, "Ring averaging: invalid number of detectors: %g" % len(data2D.detector) |
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| 325 | pixel_width = data2D.detector[0].pixel_size.x |
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| 326 | det_dist = data2D.detector[0].distance |
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| 327 | wavelength = data2D.source.wavelength |
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| 328 | center_x = self.center_x/pixel_width |
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| 329 | center_y = self.center_y/pixel_width |
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| 330 | |
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| 331 | phi_bins = numpy.zeros(self.nbins_phi) |
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| 332 | phi_counts = numpy.zeros(self.nbins_phi) |
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| 333 | phi_values = numpy.zeros(self.nbins_phi) |
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| 334 | phi_err = numpy.zeros(self.nbins_phi) |
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| 335 | |
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| 336 | for i in range(len(data)): |
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| 337 | dx = pixel_width*(i+0.5 - center_x) |
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| 338 | |
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| 339 | # Min and max x-value for the pixel |
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| 340 | minx = pixel_width*(i - center_x) |
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| 341 | maxx = pixel_width*(i+1.0 - center_x) |
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| 342 | |
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| 343 | for j in range(len(data)): |
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| 344 | dy = pixel_width*(j+0.5 - center_y) |
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| 345 | |
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| 346 | q_value = get_q(dx, dy, det_dist, wavelength) |
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| 347 | |
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| 348 | # Min and max y-value for the pixel |
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| 349 | miny = pixel_width*(j - center_y) |
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| 350 | maxy = pixel_width*(j+1.0 - center_y) |
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| 351 | |
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| 352 | # Calculate the q-value for each corner |
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| 353 | # q_[x min or max][y min or max] |
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| 354 | q_00 = get_q(minx, miny, det_dist, wavelength) |
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| 355 | q_01 = get_q(minx, maxy, det_dist, wavelength) |
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| 356 | q_10 = get_q(maxx, miny, det_dist, wavelength) |
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| 357 | q_11 = get_q(maxx, maxy, det_dist, wavelength) |
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| 358 | |
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| 359 | # Look for intercept between each side of the pixel |
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| 360 | # and the constant-q ring for qmax |
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| 361 | frac_max = get_pixel_fraction(qmax, q_00, q_01, q_10, q_11) |
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| 362 | |
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| 363 | # Look for intercept between each side of the pixel |
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| 364 | # and the constant-q ring for qmin |
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| 365 | frac_min = get_pixel_fraction(qmin, q_00, q_01, q_10, q_11) |
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| 366 | |
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| 367 | # We are interested in the region between qmin and qmax |
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| 368 | # therefore the fraction of the surface of the pixel |
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| 369 | # that we will use to calculate the number of counts to |
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| 370 | # include is given by: |
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| 371 | |
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| 372 | frac = frac_max - frac_min |
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| 373 | |
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| 374 | i_phi = int(math.ceil(self.nbins_phi*(math.atan2(dy, dx)+math.pi)/(2.0*math.pi)) - 1) |
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| 375 | |
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| 376 | phi_bins[i_phi] += frac * data[j][i] |
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| 377 | |
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| 378 | if data2D.err_data == None or data2D.err_data[j][i]==0.0: |
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| 379 | phi_err[i_phi] += frac * frac * math.fabs(data2D.data[j][i]) |
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| 380 | else: |
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| 381 | phi_err[i_phi] += frac * frac * data2D.err_data[j][i] * data2D.err_data[j][i] |
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| 382 | phi_counts[i_phi] += frac |
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| 383 | |
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| 384 | for i in range(self.nbins_phi): |
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| 385 | phi_bins[i] = phi_bins[i] / phi_counts[i] |
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| 386 | phi_err[i] = math.sqrt(phi_err[i]) / phi_counts[i] |
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| 387 | phi_values[i] = 2.0*math.pi/self.nbins_phi*(1.0*i + 0.5) |
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| 388 | |
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| 389 | return Data1D(x=phi_values, y=phi_bins, dy=phi_err) |
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| 390 | |
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| 391 | def get_pixel_fraction(qmax, q_00, q_01, q_10, q_11): |
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| 392 | """ |
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| 393 | Returns the fraction of the pixel defined by |
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| 394 | the four corners (q_00, q_01, q_10, q_11) that |
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| 395 | has q < qmax. |
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| 396 | |
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| 397 | q_01 q_11 |
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| 398 | y=1 +--------------+ |
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| 399 | | | |
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| 400 | | | |
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| 401 | | | |
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| 402 | y=0 +--------------+ |
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| 403 | q_00 q_01 |
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| 404 | |
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| 405 | x=0 x=1 |
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| 406 | |
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| 407 | """ |
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| 408 | |
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| 409 | # y side for x = minx |
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| 410 | x_0 = get_intercept(qmax, q_00, q_01) |
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| 411 | # y side for x = maxx |
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| 412 | x_1 = get_intercept(qmax, q_10, q_11) |
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| 413 | |
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| 414 | # x side for y = miny |
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| 415 | y_0 = get_intercept(qmax, q_00, q_10) |
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| 416 | # x side for y = maxy |
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| 417 | y_1 = get_intercept(qmax, q_01, q_11) |
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| 418 | |
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| 419 | # surface fraction for a 1x1 pixel |
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| 420 | frac_max = 0 |
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| 421 | |
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| 422 | if x_0 and x_1: |
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| 423 | frac_max = (x_0+x_1)/2.0 |
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| 424 | |
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| 425 | elif y_0 and y_1: |
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| 426 | frac_max = (y_0+y_1)/2.0 |
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| 427 | |
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| 428 | elif x_0 and y_0: |
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| 429 | if q_00 < q_10: |
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| 430 | frac_max = x_0*y_0/2.0 |
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| 431 | else: |
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| 432 | frac_max = 1.0-x_0*y_0/2.0 |
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| 433 | |
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| 434 | elif x_0 and y_1: |
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| 435 | if q_00 < q_10: |
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| 436 | frac_max = x_0*y_1/2.0 |
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| 437 | else: |
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| 438 | frac_max = 1.0-x_0*y_1/2.0 |
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| 439 | |
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| 440 | elif x_1 and y_0: |
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| 441 | if q_00 > q_10: |
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| 442 | frac_max = x_1*y_0/2.0 |
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| 443 | else: |
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| 444 | frac_max = 1.0-x_1*y_0/2.0 |
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| 445 | |
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| 446 | elif x_1 and y_1: |
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| 447 | if q_00 < q_10: |
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| 448 | frac_max = 1.0 - (1.0-x_1)*(1.0-y_1)/2.0 |
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| 449 | else: |
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| 450 | frac_max = (1.0-x_1)*(1.0-y_1)/2.0 |
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| 451 | |
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| 452 | # If we make it here, there is no intercept between |
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| 453 | # this pixel and the constant-q ring. We only need |
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| 454 | # to know if we have to include it or exclude it. |
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| 455 | elif (q_00+q_01+q_10+q_11)/4.0 < qmax: |
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| 456 | frac_max = 1.0 |
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| 457 | |
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| 458 | return frac_max |
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| 459 | |
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| 460 | def get_intercept(q, q_0, q_1): |
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| 461 | """ |
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| 462 | Returns the fraction of the side at which the |
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| 463 | q-value intercept the pixel, None otherwise. |
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| 464 | The values returned is the fraction ON THE SIDE |
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| 465 | OF THE LOWEST Q. |
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| 466 | |
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| 467 | |
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| 468 | |
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| 469 | A B |
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| 470 | +-----------+--------+ |
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| 471 | 0 1 <--- pixel size |
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| 472 | |
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| 473 | Q_0 -------- Q ----- Q_1 <--- equivalent Q range |
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| 474 | |
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| 475 | |
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| 476 | if Q_1 > Q_0, A is returned |
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| 477 | if Q_1 < Q_0, B is returned |
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| 478 | |
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| 479 | if Q is outside the range of [Q_0, Q_1], None is returned |
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| 480 | |
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| 481 | """ |
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| 482 | if q_1 > q_0: |
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| 483 | if (q > q_0 and q <= q_1): |
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| 484 | return (q-q_0)/(q_1 - q_0) |
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| 485 | else: |
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| 486 | if (q > q_1 and q <= q_0): |
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| 487 | return (q-q_1)/(q_0 - q_1) |
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| 488 | return None |
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| 489 | |
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| 490 | |
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| 491 | class Sector: |
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| 492 | """ |
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| 493 | Defines a sector region on a 2D data set. |
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| 494 | The sector is defined by r_min, r_max, phi_min, phi_max, |
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| 495 | and the position of the center of the ring. |
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| 496 | """ |
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| 497 | pass |
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| 498 | |
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| 499 | if __name__ == "__main__": |
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| 500 | |
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| 501 | from loader import Loader |
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| 502 | |
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| 503 | |
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| 504 | d = Loader().load('test/MAR07232_rest.ASC') |
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| 505 | #d = Loader().load('test/MP_New.sans') |
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| 506 | |
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| 507 | |
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| 508 | #r = Boxsum(x_min=.2, x_max=.4, y_min=0.2, y_max=0.4) |
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| 509 | r = Boxsum(x_min=.01, x_max=.015, y_min=0.01, y_max=0.015) |
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| 510 | o = r(d) |
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| 511 | print o |
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| 512 | |
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| 513 | r = Boxavg(x_min=.01, x_max=.015, y_min=0.01, y_max=0.015) |
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| 514 | o = r(d) |
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| 515 | print o |
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| 516 | |
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| 517 | |
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| 518 | |
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