manipulations.py @ 552b3d5

ESS_GUIESS_GUI_DocsESS_GUI_batch_fittingESS_GUI_bumps_abstractionESS_GUI_iss1116ESS_GUI_iss879ESS_GUI_iss959ESS_GUI_openclESS_GUI_orderingESS_GUI_sync_sascalccostrafo411magnetic_scattrelease-4.1.1release-4.1.2release-4.2.2release_4.0.1ticket-1009ticket-1094-headlessticket-1242-2d-resolutionticket-1243ticket-1249ticket885unittest-saveload

Last change on this file since 552b3d5 was 729bcf6, checked in by Jae Cho <jhjcho@…>, 14 years ago
for circular and sectot average, calculate qvalues and dq values more accurately.
Property mode set to `100644`
File size: 40.9 KB

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1
2	#####################################################################
3	#This software was developed by the University of Tennessee as part of the
4	#Distributed Data Analysis of Neutron Scattering Experiments (DANSE)
5	#project funded by the US National Science Foundation.
6	#See the license text in license.txt
7	#copyright 2008, University of Tennessee
8	######################################################################
9
10	"""
11	Data manipulations for 2D data sets.
12	Using the meta data information, various types of averaging
13	are performed in Q-space
14	"""
15	#TODO: copy the meta data from the 2D object to the resulting 1D object
16	import math
17	import numpy
18
19	#from data_info import plottable_2D
20	from data_info import Data1D
21
22
23	def get_q(dx, dy, det_dist, wavelength):
24	"""
25	:param dx: x-distance from beam center [mm]
26	:param dy: y-distance from beam center [mm]
27
28	:return: q-value at the given position
29	"""
30	# Distance from beam center in the plane of detector
31	plane_dist = math.sqrt(dxdx + dydy)
32	# Half of the scattering angle
33	theta = 0.5 * math.atan(plane_dist/det_dist)
34	return (4.0 * math.pi/wavelength) * math.sin(theta)
35
36	def get_q_compo(dx, dy, det_dist, wavelength, compo=None):
37	"""
38	This reduces tiny error at very large q.
39	Implementation of this func is not started yet.<--ToDo
40	"""
41	if dy == 0:
42	if dx >= 0:
43	angle_xy = 0
44	else:
45	angle_xy = math.pi
46	else:
47	angle_xy = math.atan(dx/dy)
48
49	if compo == "x":
50	out = get_q(dx, dy, det_dist, wavelength) * math.cos(angle_xy)
51	elif compo == "y":
52	out = get_q(dx, dy, det_dist, wavelength) * math.sin(angle_xy)
53	else:
54	out = get_q(dx, dy, det_dist, wavelength)
55	return out
56
57	def flip_phi(phi):
58	"""
59	Correct phi to within the 0 <= to <= 2pi range
60
61	:return: phi in >=0 and <=2Pi
62	"""
63	Pi = math.pi
64	if phi < 0:
65	phi_out = phi + (2 * Pi)
66	elif phi > (2 * Pi):
67	phi_out = phi - (2 * Pi)
68	else:
69	phi_out = phi
70	return phi_out
71
72	def reader2D_converter(data2d=None):
73	"""
74	convert old 2d format opened by IhorReader or danse_reader
75	to new Data2D format
76
77	:param data2d: 2d array of Data2D object
78
79	:return: 1d arrays of Data2D object
80
81	"""
82	if data2d.data == None or data2d.x_bins == None or data2d.y_bins == None:
83	raise ValueError, "Can't convert this data: data=None..."
84
85	from DataLoader.data_info import Data2D
86
87	new_x = numpy.tile(data2d.x_bins, (len(data2d.y_bins), 1))
88	new_y = numpy.tile(data2d.y_bins, (len(data2d.x_bins), 1))
89	new_y = new_y.swapaxes(0, 1)
90
91	new_data = data2d.data.flatten()
92	qx_data = new_x.flatten()
93	qy_data = new_y.flatten()
94	q_data = numpy.sqrt(qx_dataqx_data + qy_dataqy_data)
95	if data2d.err_data == None or numpy.any(data2d.err_data <= 0):
96	new_err_data = numpy.sqrt(numpy.abs(new_data))
97	else:
98	new_err_data = data2d.err_data.flatten()
99	mask = numpy.ones(len(new_data), dtype=bool)
100
101	output = Data2D()
102	output = data2d
103	output.data = new_data
104	output.err_data = new_err_data
105	output.qx_data = qx_data
106	output.qy_data = qy_data
107	output.q_data = q_data
108	output.mask = mask
109
110	return output
111
112	class _Slab(object):
113	"""
114	Compute average I(Q) for a region of interest
115	"""
116	def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0,
117	y_max=0.0, bin_width=0.001):
118	# Minimum Qx value [A-1]
119	self.x_min = x_min
120	# Maximum Qx value [A-1]
121	self.x_max = x_max
122	# Minimum Qy value [A-1]
123	self.y_min = y_min
124	# Maximum Qy value [A-1]
125	self.y_max = y_max
126	# Bin width (step size) [A-1]
127	self.bin_width = bin_width
128	# If True, I(\|Q\|) will be return, otherwise,
129	# negative q-values are allowed
130	self.fold = False
131
132	def __call__(self, data2D):
133	return NotImplemented
134
135	def _avg(self, data2D, maj):
136	"""
137	Compute average I(Q_maj) for a region of interest.
138	The major axis is defined as the axis of Q_maj.
139	The minor axis is the axis that we average over.
140
141	:param data2D: Data2D object
142	:param maj_min: min value on the major axis
143
144	:return: Data1D object
145	"""
146	if len(data2D.detector) != 1:
147	msg = "_Slab._avg: invalid number of "
148	msg += " detectors: %g" % len(data2D.detector)
149	raise RuntimeError, msg
150
151	# Get data
152	data = data2D.data[numpy.isfinite(data2D.data)]
153	q_data = data2D.q_data[numpy.isfinite(data2D.data)]
154	err_data = data2D.err_data[numpy.isfinite(data2D.data)]
155	qx_data = data2D.qx_data[numpy.isfinite(data2D.data)]
156	qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
157
158	# Build array of Q intervals
159	if maj == 'x':
160	if self.fold:
161	x_min = 0
162	else: x_min = self.x_min
163	nbins = int(math.ceil((self.x_max - x_min)/self.bin_width))
164	qbins = self.bin_width * numpy.arange(nbins) + x_min
165	elif maj == 'y':
166	if self.fold: y_min = 0
167	else: y_min = self.y_min
168	nbins = int(math.ceil((self.y_max - y_min)/self.bin_width))
169	qbins = self.bin_width * numpy.arange(nbins) + y_min
170	else:
171	raise RuntimeError, "_Slab._avg: unrecognized axis %s" % str(maj)
172
173	x = numpy.zeros(nbins)
174	y = numpy.zeros(nbins)
175	err_y = numpy.zeros(nbins)
176	y_counts = numpy.zeros(nbins)
177
178	# Average pixelsize in q space
179	for npts in range(len(data)):
180	# default frac
181	frac_x = 0
182	frac_y = 0
183	# get ROI
184	if self.x_min <= qx_data[npts] and self.x_max > qx_data[npts]:
185	frac_x = 1
186	if self.y_min <= qy_data[npts] and self.y_max > qy_data[npts]:
187	frac_y = 1
188	frac = frac_x * frac_y
189
190	if frac == 0:
191	continue
192	# binning: find axis of q
193	if maj == 'x':
194	q_value = qx_data[npts]
195	min = x_min
196	if maj == 'y':
197	q_value = qy_data[npts]
198	min = y_min
199	if self.fold and q_value < 0:
200	q_value = -q_value
201	# bin
202	i_q = int(math.ceil((q_value - min)/self.bin_width)) - 1
203
204	# skip outside of max bins
205	if i_q < 0 or i_q >= nbins:
206	continue
207
208	# give it full weight
209	#frac = 1
210
211	#TODO: find better definition of x[i_q] based on q_data
212	x[i_q] += frac * q_value#min + (i_q + 1) * self.bin_width / 2.0
213	y[i_q] += frac * data[npts]
214
215	if err_data == None or err_data[npts] == 0.0:
216	if data[npts] < 0: data[npts] = -data[npts]
217	err_y[i_q] += frac * frac * data[npts]
218	else:
219	err_y[i_q] += frac * frac * err_data[npts] * err_data[npts]
220	y_counts[i_q] += frac
221
222	# Average the sums
223	for n in range(nbins):
224	err_y[n] = math.sqrt(err_y[n])
225
226	err_y = err_y / y_counts
227	y = y / y_counts
228	x = x / y_counts
229	idx = (numpy.isfinite(y) & numpy.isfinite(x))
230
231	if not idx.any():
232	msg = "Average Error: No points inside ROI to average..."
233	raise ValueError, msg
234	#elif len(y[idx])!= nbins:
235	# msg = "empty bin(s) due to tight binning..."
236	# print "resulted",nbins- len(y[idx]), msg
237	return Data1D(x=x[idx], y=y[idx], dy=err_y[idx])
238
239	class SlabY(_Slab):
240	"""
241	Compute average I(Qy) for a region of interest
242	"""
243	def __call__(self, data2D):
244	"""
245	Compute average I(Qy) for a region of interest
246
247	:param data2D: Data2D object
248
249	:return: Data1D object
250	"""
251	return self._avg(data2D, 'y')
252
253	class SlabX(_Slab):
254	"""
255	Compute average I(Qx) for a region of interest
256	"""
257	def __call__(self, data2D):
258	"""
259	Compute average I(Qx) for a region of interest
260
261	:param data2D: Data2D object
262
263	:return: Data1D object
264
265	"""
266	return self._avg(data2D, 'x')
267
268	class Boxsum(object):
269	"""
270	Perform the sum of counts in a 2D region of interest.
271	"""
272	def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
273	# Minimum Qx value [A-1]
274	self.x_min = x_min
275	# Maximum Qx value [A-1]
276	self.x_max = x_max
277	# Minimum Qy value [A-1]
278	self.y_min = y_min
279	# Maximum Qy value [A-1]
280	self.y_max = y_max
281
282	def __call__(self, data2D):
283	"""
284	Perform the sum in the region of interest
285
286	:param data2D: Data2D object
287
288	:return: number of counts, error on number of counts
289
290	"""
291	y, err_y, y_counts = self._sum(data2D)
292
293	# Average the sums
294	counts = 0 if y_counts == 0 else y
295	error = 0 if y_counts == 0 else math.sqrt(err_y)
296
297	return counts, error
298
299	def _sum(self, data2D):
300	"""
301	Perform the sum in the region of interest
302
303	:param data2D: Data2D object
304
305	:return: number of counts,
306	error on number of counts, number of entries summed
307
308	"""
309	if len(data2D.detector) != 1:
310	msg = "Circular averaging: invalid number "
311	msg += "of detectors: %g" % len(data2D.detector)
312	raise RuntimeError, msg
313	# Get data
314	data = data2D.data[numpy.isfinite(data2D.data)]
315	q_data = data2D.q_data[numpy.isfinite(data2D.data)]
316	err_data = data2D.err_data[numpy.isfinite(data2D.data)]
317	qx_data = data2D.qx_data[numpy.isfinite(data2D.data)]
318	qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
319
320	y = 0.0
321	err_y = 0.0
322	y_counts = 0.0
323
324	# Average pixelsize in q space
325	for npts in range(len(data)):
326	# default frac
327	frac_x = 0
328	frac_y = 0
329
330	# get min and max at each points
331	qx = qx_data[npts]
332	qy = qy_data[npts]
333
334	# get the ROI
335	if self.x_min <= qx and self.x_max > qx:
336	frac_x = 1
337	if self.y_min <= qy and self.y_max > qy:
338	frac_y = 1
339	#Find the fraction along each directions
340	frac = frac_x * frac_y
341	if frac == 0:
342	continue
343	y += frac * data[npts]
344	if err_data == None or err_data[npts] == 0.0:
345	if data[npts] < 0:
346	data[npts] = -data[npts]
347	err_y += frac * frac * data[npts]
348	else:
349	err_y += frac * frac * err_data[npts] * err_data[npts]
350	y_counts += frac
351	return y, err_y, y_counts
352
353
354
355	class Boxavg(Boxsum):
356	"""
357	Perform the average of counts in a 2D region of interest.
358	"""
359	def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
360	super(Boxavg, self).__init__(x_min=x_min, x_max=x_max,
361	y_min=y_min, y_max=y_max)
362
363	def __call__(self, data2D):
364	"""
365	Perform the sum in the region of interest
366
367	:param data2D: Data2D object
368
369	:return: average counts, error on average counts
370
371	"""
372	y, err_y, y_counts = self._sum(data2D)
373
374	# Average the sums
375	counts = 0 if y_counts == 0 else y/y_counts
376	error = 0 if y_counts == 0 else math.sqrt(err_y)/y_counts
377
378	return counts, error
379
380	def get_pixel_fraction_square(x, xmin, xmax):
381	"""
382	Return the fraction of the length
383	from xmin to x.::
384
385
386	A B
387	+-----------+---------+
388	xmin x xmax
389
390	:param x: x-value
391	:param xmin: minimum x for the length considered
392	:param xmax: minimum x for the length considered
393
394	:return: (x-xmin)/(xmax-xmin) when xmin < x < xmax
395
396	"""
397	if x <= xmin:
398	return 0.0
399	if x > xmin and x < xmax:
400	return (x - xmin) / (xmax - xmin)
401	else:
402	return 1.0
403
404
405	class CircularAverage(object):
406	"""
407	Perform circular averaging on 2D data
408
409	The data returned is the distribution of counts
410	as a function of Q
411	"""
412	def __init__(self, r_min=0.0, r_max=0.0, bin_width=0.0005):
413	# Minimum radius included in the average [A-1]
414	self.r_min = r_min
415	# Maximum radius included in the average [A-1]
416	self.r_max = r_max
417	# Bin width (step size) [A-1]
418	self.bin_width = bin_width
419
420	def __call__(self, data2D):
421	"""
422	Perform circular averaging on the data
423
424	:param data2D: Data2D object
425
426	:return: Data1D object
427	"""
428	# Get data W/ finite values
429	data = data2D.data[numpy.isfinite(data2D.data)]
430	q_data = data2D.q_data[numpy.isfinite(data2D.data)]
431	qx_data = data2D.qx_data[numpy.isfinite(data2D.data)]
432	err_data = data2D.err_data[numpy.isfinite(data2D.data)]
433
434	dq_data = None
435
436	# Get the dq for resolution averaging
437	if data2D.dqx_data != None and data2D.dqy_data != None:
438	# The pinholes and det. pix contribution present
439	# in both direction of the 2D which must be subtracted when
440	# converting to 1D: dq_overlap should calculated ideally at
441	# q = 0. Note This method works on only pinhole geometry.
442	# Extrapolate dqx(r) and dqy(phi) at q = 0, and take an average.
443	z_max = max(data2D.q_data)
444	z_min = min(data2D.q_data)
445	x_max = data2D.dqx_data[data2D.q_data[z_max]]
446	x_min = data2D.dqx_data[data2D.q_data[z_min]]
447	y_max = data2D.dqy_data[data2D.q_data[z_max]]
448	y_min = data2D.dqy_data[data2D.q_data[z_min]]
449	# Find qdx at q = 0
450	dq_overlap_x = (x_min * z_max - x_max * z_min) / (z_max - z_min)
451	# when extrapolation goes wrong
452	if dq_overlap_x > min(data2D.dqx_data):
453	dq_overlap_x = min(data2D.dqx_data)
454	dq_overlap_x *= dq_overlap_x
455	# Find qdx at q = 0
456	dq_overlap_y = (y_min * z_max - y_max * z_min) / (z_max - z_min)
457	# when extrapolation goes wrong
458	if dq_overlap_y > min(data2D.dqy_data):
459	dq_overlap_y = min(data2D.dqy_data)
460	# get dq at q=0.
461	dq_overlap_y *= dq_overlap_y
462
463	dq_overlap = numpy.sqrt((dq_overlap_x + dq_overlap_y)/2.0)
464	# Final protection of dq
465	if dq_overlap < 0:
466	dq_overlap = y_min
467	dqx_data = data2D.dqx_data[numpy.isfinite(data2D.data)]
468	dqy_data = data2D.dqy_data[numpy.isfinite(data2D.data)] - dq_overlap
469	# def; dqx_data = dq_r dqy_data = dq_phi
470	# Convert dq 2D to 1D here
471	dqx = dqx_data * dqx_data
472	dqy = dqy_data * dqy_data
473	dq_data = numpy.add(dqx, dqy)
474	dq_data = numpy.sqrt(dq_data)
475
476	#q_data_max = numpy.max(q_data)
477	if len(data2D.q_data) == None:
478	msg = "Circular averaging: invalid q_data: %g" % data2D.q_data
479	raise RuntimeError, msg
480
481	# Build array of Q intervals
482	nbins = int(math.ceil((self.r_max - self.r_min) / self.bin_width))
483	qbins = self.bin_width * numpy.arange(nbins) + self.r_min
484
485	x = numpy.zeros(nbins)
486	y = numpy.zeros(nbins)
487	err_y = numpy.zeros(nbins)
488	err_x = numpy.zeros(nbins)
489	y_counts = numpy.zeros(nbins)
490
491	for npt in range(len(data)):
492	frac = 0
493
494	# q-value at the pixel (j,i)
495	q_value = q_data[npt]
496	data_n = data[npt]
497
498	## No need to calculate the frac when all data are within range
499	if self.r_min >= self.r_max:
500	raise ValueError, "Limit Error: min > max"
501
502	if self.r_min <= q_value and q_value <= self.r_max:
503	frac = 1
504	if frac == 0:
505	continue
506	i_q = int(math.floor((q_value - self.r_min) / self.bin_width))
507
508	# Take care of the edge case at phi = 2pi.
509	if i_q == nbins:
510	i_q = nbins -1
511	y[i_q] += frac * data_n
512	# Take dqs from data to get the q_average
513	x[i_q] += frac * q_value
514	if err_data == None or err_data[npt] == 0.0:
515	if data_n < 0:
516	data_n = -data_n
517	err_y[i_q] += frac * frac * data_n
518	else:
519	err_y[i_q] += frac * frac * err_data[npt] * err_data[npt]
520	if dq_data != None:
521	# To be consistent with dq calculation in 1d reduction,
522	# we need just the averages (not quadratures) because
523	# it should not depend on the number of the q points
524	# in the qr bins.
525	err_x[i_q] += frac * dq_data[npt]
526	else:
527	err_x = None
528	y_counts[i_q] += frac
529
530	# Average the sums
531	for n in range(nbins):
532	if err_y[n] < 0: err_y[n] = -err_y[n]
533	err_y[n] = math.sqrt(err_y[n])
534	#if err_x != None:
535	# err_x[n] = math.sqrt(err_x[n])
536
537	err_y = err_y / y_counts
538	err_y[err_y==0] = numpy.average(err_y)
539	y = y / y_counts
540	x = x / y_counts
541	idx = (numpy.isfinite(y)) & (numpy.isfinite(x))
542	if err_x != None:
543	d_x = err_x[idx] / y_counts[idx]
544	else:
545	d_x = None
546
547	if not idx.any():
548	msg = "Average Error: No points inside ROI to average..."
549	raise ValueError, msg
550
551	return Data1D(x=x[idx], y=y[idx], dy=err_y[idx], dx=d_x)
552
553
554	class Ring(object):
555	"""
556	Defines a ring on a 2D data set.
557	The ring is defined by r_min, r_max, and
558	the position of the center of the ring.
559
560	The data returned is the distribution of counts
561	around the ring as a function of phi.
562
563	Phi_min and phi_max should be defined between 0 and 2*pi
564	in anti-clockwise starting from the x- axis on the left-hand side
565	"""
566	#Todo: remove center.
567	def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0, nbins=20):
568	# Minimum radius
569	self.r_min = r_min
570	# Maximum radius
571	self.r_max = r_max
572	# Center of the ring in x
573	self.center_x = center_x
574	# Center of the ring in y
575	self.center_y = center_y
576	# Number of angular bins
577	self.nbins_phi = nbins
578
579	def __call__(self, data2D):
580	"""
581	Apply the ring to the data set.
582	Returns the angular distribution for a given q range
583
584	:param data2D: Data2D object
585
586	:return: Data1D object
587	"""
588	if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
589	raise RuntimeError, "Ring averaging only take plottable_2D objects"
590
591	Pi = math.pi
592
593	# Get data
594	data = data2D.data[numpy.isfinite(data2D.data)]
595	q_data = data2D.q_data[numpy.isfinite(data2D.data)]
596	err_data = data2D.err_data[numpy.isfinite(data2D.data)]
597	qx_data = data2D.qx_data[numpy.isfinite(data2D.data)]
598	qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
599
600	q_data_max = numpy.max(q_data)
601
602	# Set space for 1d outputs
603	phi_bins = numpy.zeros(self.nbins_phi)
604	phi_counts = numpy.zeros(self.nbins_phi)
605	phi_values = numpy.zeros(self.nbins_phi)
606	phi_err = numpy.zeros(self.nbins_phi)
607
608	for npt in range(len(data)):
609	frac = 0
610	# q-value at the point (npt)
611	q_value = q_data[npt]
612	data_n = data[npt]
613
614	# phi-value at the point (npt)
615	phi_value = math.atan2(qy_data[npt], qx_data[npt]) + Pi
616
617	if self.r_min <= q_value and q_value <= self.r_max:
618	frac = 1
619	if frac == 0:
620	continue
621	# binning
622	i_phi = int(math.floor((self.nbins_phi) * phi_value / (2 * Pi)))
623
624	# Take care of the edge case at phi = 2pi.
625	if i_phi == self.nbins_phi:
626	i_phi = self.nbins_phi - 1
627	phi_bins[i_phi] += frac * data[npt]
628
629	if err_data == None or err_data[npt] == 0.0:
630	if data_n < 0:
631	data_n = -data_n
632	phi_err[i_phi] += frac * frac * math.fabs(data_n)
633	else:
634	phi_err[i_phi] += frac * frac * err_data[npt] * err_data[npt]
635	phi_counts[i_phi] += frac
636
637	for i in range(self.nbins_phi):
638	phi_bins[i] = phi_bins[i] / phi_counts[i]
639	phi_err[i] = math.sqrt(phi_err[i]) / phi_counts[i]
640	phi_values[i] = 2.0 * math.pi / self.nbins_phi * (1.0 * i + 0.5)
641
642	idx = (numpy.isfinite(phi_bins))
643
644	if not idx.any():
645	msg = "Average Error: No points inside ROI to average..."
646	raise ValueError, msg
647	#elif len(phi_bins[idx])!= self.nbins_phi:
648	# print "resulted",self.nbins_phi- len(phi_bins[idx])
649	#,"empty bin(s) due to tight binning..."
650	return Data1D(x=phi_values[idx], y=phi_bins[idx], dy=phi_err[idx])
651
652	def get_pixel_fraction(qmax, q_00, q_01, q_10, q_11):
653	"""
654	Returns the fraction of the pixel defined by
655	the four corners (q_00, q_01, q_10, q_11) that
656	has q < qmax.::
657
658	q_01 q_11
659	y=1 +--------------+
660	\| \|
661	\| \|
662	\| \|
663	y=0 +--------------+
664	q_00 q_10
665
666	x=0 x=1
667
668	"""
669	# y side for x = minx
670	x_0 = get_intercept(qmax, q_00, q_01)
671	# y side for x = maxx
672	x_1 = get_intercept(qmax, q_10, q_11)
673
674	# x side for y = miny
675	y_0 = get_intercept(qmax, q_00, q_10)
676	# x side for y = maxy
677	y_1 = get_intercept(qmax, q_01, q_11)
678
679	# surface fraction for a 1x1 pixel
680	frac_max = 0
681
682	if x_0 and x_1:
683	frac_max = (x_0 + x_1) / 2.0
684	elif y_0 and y_1:
685	frac_max = (y_0 + y_1) / 2.0
686	elif x_0 and y_0:
687	if q_00 < q_10:
688	frac_max = x_0 * y_0 / 2.0
689	else:
690	frac_max = 1.0 - x_0 * y_0 / 2.0
691	elif x_0 and y_1:
692	if q_00 < q_10:
693	frac_max = x_0 * y_1 / 2.0
694	else:
695	frac_max = 1.0 - x_0 * y_1 / 2.0
696	elif x_1 and y_0:
697	if q_00 > q_10:
698	frac_max = x_1 * y_0 / 2.0
699	else:
700	frac_max = 1.0 - x_1 * y_0 / 2.0
701	elif x_1 and y_1:
702	if q_00 < q_10:
703	frac_max = 1.0 - (1.0 - x_1) * (1.0 - y_1) / 2.0
704	else:
705	frac_max = (1.0 - x_1) * (1.0 - y_1) / 2.0
706
707	# If we make it here, there is no intercept between
708	# this pixel and the constant-q ring. We only need
709	# to know if we have to include it or exclude it.
710	elif (q_00 + q_01 + q_10 + q_11)/4.0 < qmax:
711	frac_max = 1.0
712
713	return frac_max
714
715	def get_intercept(q, q_0, q_1):
716	"""
717	Returns the fraction of the side at which the
718	q-value intercept the pixel, None otherwise.
719	The values returned is the fraction ON THE SIDE
720	OF THE LOWEST Q. ::
721
722
723	A B
724	+-----------+--------+ <--- pixel size
725	0 1
726	Q_0 -------- Q ----- Q_1 <--- equivalent Q range
727	if Q_1 > Q_0, A is returned
728	if Q_1 < Q_0, B is returned
729	if Q is outside the range of [Q_0, Q_1], None is returned
730
731	"""
732	if q_1 > q_0:
733	if (q > q_0 and q <= q_1):
734	return (q - q_0)/(q_1 - q_0)
735	else:
736	if (q > q_1 and q <= q_0):
737	return (q - q_1)/(q_0 - q_1)
738	return None
739
740	class _Sector:
741	"""
742	Defines a sector region on a 2D data set.
743	The sector is defined by r_min, r_max, phi_min, phi_max,
744	and the position of the center of the ring
745	where phi_min and phi_max are defined by the right
746	and left lines wrt central line
747	and phi_max could be less than phi_min.
748
749	Phi is defined between 0 and 2*pi in anti-clockwise
750	starting from the x- axis on the left-hand side
751	"""
752	def __init__(self, r_min, r_max, phi_min=0, phi_max=2*math.pi, nbins=20):
753	self.r_min = r_min
754	self.r_max = r_max
755	self.phi_min = phi_min
756	self.phi_max = phi_max
757	self.nbins = nbins
758
759
760	def _agv(self, data2D, run='phi'):
761	"""
762	Perform sector averaging.
763
764	:param data2D: Data2D object
765	:param run: define the varying parameter ('phi' , 'q' , or 'q2')
766
767	:return: Data1D object
768	"""
769	if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
770	raise RuntimeError, "Ring averaging only take plottable_2D objects"
771	Pi = math.pi
772
773	# Get the all data & info
774	data = data2D.data[numpy.isfinite(data2D.data)]
775	q_data = data2D.q_data[numpy.isfinite(data2D.data)]
776	err_data = data2D.err_data[numpy.isfinite(data2D.data)]
777	qx_data = data2D.qx_data[numpy.isfinite(data2D.data)]
778	qy_data = data2D.qy_data[numpy.isfinite(data2D.data)]
779	dq_data = None
780
781	# Get the dq for resolution averaging
782	if data2D.dqx_data != None and data2D.dqy_data != None:
783	# The pinholes and det. pix contribution present
784	# in both direction of the 2D which must be subtracted when
785	# converting to 1D: dq_overlap should calculated ideally at
786	# q = 0.
787	# Extrapolate dqy(perp) at q = 0
788	z_max = max(data2D.q_data)
789	z_min = min(data2D.q_data)
790	x_max = data2D.dqx_data[data2D.q_data[z_max]]
791	x_min = data2D.dqx_data[data2D.q_data[z_min]]
792	y_max = data2D.dqy_data[data2D.q_data[z_max]]
793	y_min = data2D.dqy_data[data2D.q_data[z_min]]
794	# Find qdx at q = 0
795	dq_overlap_x = (x_min * z_max - x_max * z_min) / (z_max - z_min)
796	# when extrapolation goes wrong
797	if dq_overlap_x > min(data2D.dqx_data):
798	dq_overlap_x = min(data2D.dqx_data)
799	dq_overlap_x *= dq_overlap_x
800	# Find qdx at q = 0
801	dq_overlap_y = (y_min * z_max - y_max * z_min) / (z_max - z_min)
802	# when extrapolation goes wrong
803	if dq_overlap_y > min(data2D.dqy_data):
804	dq_overlap_y = min(data2D.dqy_data)
805	# get dq at q=0.
806	dq_overlap_y *= dq_overlap_y
807
808	dq_overlap = numpy.sqrt((dq_overlap_x + dq_overlap_y) / 2.0)
809	if dq_overlap < 0:
810	dq_overlap = y_min
811	dqx_data = data2D.dqx_data[numpy.isfinite(data2D.data)]
812	dqy_data = data2D.dqy_data[numpy.isfinite(data2D.data)] - dq_overlap
813	# def; dqx_data = dq_r dqy_data = dq_phi
814	# Convert dq 2D to 1D here
815	dqx = dqx_data * dqx_data
816	dqy = dqy_data * dqy_data
817	dq_data = numpy.add(dqx, dqy)
818	dq_data = numpy.sqrt(dq_data)
819
820	#set space for 1d outputs
821	x = numpy.zeros(self.nbins)
822	y = numpy.zeros(self.nbins)
823	y_err = numpy.zeros(self.nbins)
824	x_err = numpy.zeros(self.nbins)
825	y_counts = numpy.zeros(self.nbins)
826
827	# Get the min and max into the region: 0 <= phi < 2Pi
828	phi_min = flip_phi(self.phi_min)
829	phi_max = flip_phi(self.phi_max)
830
831	q_data_max = numpy.max(q_data)
832
833	for n in range(len(data)):
834	frac = 0
835
836	# q-value at the pixel (j,i)
837	q_value = q_data[n]
838	data_n = data[n]
839
840	# Is pixel within range?
841	is_in = False
842
843	# phi-value of the pixel (j,i)
844	phi_value = math.atan2(qy_data[n], qx_data[n]) + Pi
845
846	## No need to calculate the frac when all data are within range
847	if self.r_min <= q_value and q_value <= self.r_max:
848	frac = 1
849	if frac == 0:
850	continue
851	#In case of two ROIs (symmetric major and minor regions)(for 'q2')
852	if run.lower()=='q2':
853	## For minor sector wing
854	# Calculate the minor wing phis
855	phi_min_minor = flip_phi(phi_min - Pi)
856	phi_max_minor = flip_phi(phi_max - Pi)
857	# Check if phis of the minor ring is within 0 to 2pi
858	if phi_min_minor > phi_max_minor:
859	is_in = (phi_value > phi_min_minor or \
860	phi_value < phi_max_minor)
861	else:
862	is_in = (phi_value > phi_min_minor and \
863	phi_value < phi_max_minor)
864
865	#For all cases(i.e.,for 'q', 'q2', and 'phi')
866	#Find pixels within ROI
867	if phi_min > phi_max:
868	is_in = is_in or (phi_value > phi_min or \
869	phi_value < phi_max)
870	else:
871	is_in = is_in or (phi_value >= phi_min and \
872	phi_value < phi_max)
873
874	if not is_in:
875	frac = 0
876	if frac == 0:
877	continue
878	# Check which type of averaging we need
879	if run.lower() == 'phi':
880	temp_x = (self.nbins) * (phi_value - self.phi_min)
881	temp_y = (self.phi_max - self.phi_min)
882	i_bin = int(math.floor(temp_x / temp_y))
883	else:
884	temp_x = (self.nbins) * (q_value - self.r_min)
885	temp_y = (self.r_max - self.r_min)
886	i_bin = int(math.floor(temp_x / temp_y))
887
888	# Take care of the edge case at phi = 2pi.
889	if i_bin == self.nbins:
890	i_bin = self.nbins - 1
891
892	## Get the total y
893	y[i_bin] += frac * data_n
894	x[i_bin] += frac * q_value
895	if err_data[n] == None or err_data[n] == 0.0:
896	if data_n < 0:
897	data_n = -data_n
898	y_err[i_bin] += frac * frac * data_n
899	else:
900	y_err[i_bin] += frac * frac * err_data[n] * err_data[n]
901
902	if dq_data != None:
903	# To be consistent with dq calculation in 1d reduction,
904	# we need just the averages (not quadratures) because
905	# it should not depend on the number of the q points
906	# in the qr bins.
907	x_err[i_bin] += frac * dq_data[n]
908	else:
909	x_err = None
910	y_counts[i_bin] += frac
911
912	# Organize the results
913	for i in range(self.nbins):
914	y[i] = y[i] / y_counts[i]
915	y_err[i] = math.sqrt(y_err[i]) / y_counts[i]
916
917	# The type of averaging: phi,q2, or q
918	# Calculate x[i]should be at the center of the bin
919	if run.lower()=='phi':
920	x[i] = (self.phi_max - self.phi_min) / self.nbins * \
921	(1.0 * i + 0.5) + self.phi_min
922	else:
923	# We take the center of ring area, not radius.
924	# This is more accurate than taking the radial center of ring.
925	#delta_r = (self.r_max - self.r_min) / self.nbins
926	#r_inner = self.r_min + delta_r * i
927	#r_outer = r_inner + delta_r
928	#x[i] = math.sqrt((r_inner * r_inner + r_outer * r_outer) / 2)
929	x[i] = x[i] / y_counts[i]
930	y_err[y_err==0] = numpy.average(y_err)
931	idx = (numpy.isfinite(y) & numpy.isfinite(y_err))
932	if x_err != None:
933	d_x = x_err[idx] / y_counts[idx]
934	else:
935	d_x = None
936	if not idx.any():
937	msg = "Average Error: No points inside sector of ROI to average..."
938	raise ValueError, msg
939	#elif len(y[idx])!= self.nbins:
940	# print "resulted",self.nbins- len(y[idx]),
941	#"empty bin(s) due to tight binning..."
942	return Data1D(x=x[idx], y=y[idx], dy=y_err[idx], dx=d_x)
943
944	class SectorPhi(_Sector):
945	"""
946	Sector average as a function of phi.
947	I(phi) is return and the data is averaged over Q.
948
949	A sector is defined by r_min, r_max, phi_min, phi_max.
950	The number of bin in phi also has to be defined.
951	"""
952	def __call__(self, data2D):
953	"""
954	Perform sector average and return I(phi).
955
956	:param data2D: Data2D object
957	:return: Data1D object
958	"""
959
960	return self._agv(data2D, 'phi')
961
962	class SectorQ(_Sector):
963	"""
964	Sector average as a function of Q for both symatric wings.
965	I(Q) is return and the data is averaged over phi.
966
967	A sector is defined by r_min, r_max, phi_min, phi_max.
968	r_min, r_max, phi_min, phi_max >0.
969	The number of bin in Q also has to be defined.
970	"""
971	def __call__(self, data2D):
972	"""
973	Perform sector average and return I(Q).
974
975	:param data2D: Data2D object
976
977	:return: Data1D object
978	"""
979	return self._agv(data2D, 'q2')
980
981	class Ringcut(object):
982	"""
983	Defines a ring on a 2D data set.
984	The ring is defined by r_min, r_max, and
985	the position of the center of the ring.
986
987	The data returned is the region inside the ring
988
989	Phi_min and phi_max should be defined between 0 and 2*pi
990	in anti-clockwise starting from the x- axis on the left-hand side
991	"""
992	def __init__(self, r_min=0, r_max=0, center_x=0, center_y=0 ):
993	# Minimum radius
994	self.r_min = r_min
995	# Maximum radius
996	self.r_max = r_max
997	# Center of the ring in x
998	self.center_x = center_x
999	# Center of the ring in y
1000	self.center_y = center_y
1001
1002
1003	def __call__(self, data2D):
1004	"""
1005	Apply the ring to the data set.
1006	Returns the angular distribution for a given q range
1007
1008	:param data2D: Data2D object
1009
1010	:return: index array in the range
1011	"""
1012	if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
1013	raise RuntimeError, "Ring cut only take plottable_2D objects"
1014
1015	# Get data
1016	qx_data = data2D.qx_data
1017	qy_data = data2D.qy_data
1018	mask = data2D.mask
1019	q_data = numpy.sqrt(qx_data * qx_data + qy_data * qy_data)
1020	#q_data_max = numpy.max(q_data)
1021
1022	# check whether or not the data point is inside ROI
1023	out = (self.r_min <= q_data) & (self.r_max >= q_data)
1024
1025	return (out)
1026
1027
1028	class Boxcut(object):
1029	"""
1030	Find a rectangular 2D region of interest.
1031	"""
1032	def __init__(self, x_min=0.0, x_max=0.0, y_min=0.0, y_max=0.0):
1033	# Minimum Qx value [A-1]
1034	self.x_min = x_min
1035	# Maximum Qx value [A-1]
1036	self.x_max = x_max
1037	# Minimum Qy value [A-1]
1038	self.y_min = y_min
1039	# Maximum Qy value [A-1]
1040	self.y_max = y_max
1041
1042	def __call__(self, data2D):
1043	"""
1044	Find a rectangular 2D region of interest.
1045
1046	:param data2D: Data2D object
1047	:return: mask, 1d array (len = len(data))
1048	with Trues where the data points are inside ROI, otherwise False
1049	"""
1050	mask = self._find(data2D)
1051
1052	return mask
1053
1054	def _find(self, data2D):
1055	"""
1056	Find a rectangular 2D region of interest.
1057
1058	:param data2D: Data2D object
1059
1060	:return: out, 1d array (length = len(data))
1061	with Trues where the data points are inside ROI, otherwise Falses
1062	"""
1063	if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
1064	raise RuntimeError, "Boxcut take only plottable_2D objects"
1065	# Get qx_ and qy_data
1066	qx_data = data2D.qx_data
1067	qy_data = data2D.qy_data
1068	mask = data2D.mask
1069
1070	# check whether or not the data point is inside ROI
1071	outx = (self.x_min <= qx_data) & (self.x_max > qx_data)
1072	outy = (self.y_min <= qy_data) & (self.y_max > qy_data)
1073
1074	return (outx & outy)
1075
1076	class Sectorcut(object):
1077	"""
1078	Defines a sector (major + minor) region on a 2D data set.
1079	The sector is defined by phi_min, phi_max,
1080	where phi_min and phi_max are defined by the right
1081	and left lines wrt central line.
1082
1083	Phi_min and phi_max are given in units of radian
1084	and (phi_max-phi_min) should not be larger than pi
1085	"""
1086	def __init__(self, phi_min=0, phi_max=math.pi):
1087	self.phi_min = phi_min
1088	self.phi_max = phi_max
1089
1090	def __call__(self, data2D):
1091	"""
1092	Find a rectangular 2D region of interest.
1093
1094	:param data2D: Data2D object
1095
1096	:return: mask, 1d array (len = len(data))
1097
1098	with Trues where the data points are inside ROI, otherwise False
1099	"""
1100	mask = self._find(data2D)
1101
1102	return mask
1103
1104	def _find(self, data2D):
1105	"""
1106	Find a rectangular 2D region of interest.
1107
1108	:param data2D: Data2D object
1109
1110	:return: out, 1d array (length = len(data))
1111
1112	with Trues where the data points are inside ROI, otherwise Falses
1113	"""
1114	if data2D.__class__.__name__ not in ["Data2D", "plottable_2D"]:
1115	raise RuntimeError, "Sectorcut take only plottable_2D objects"
1116	Pi = math.pi
1117	# Get data
1118	qx_data = data2D.qx_data
1119	qy_data = data2D.qy_data
1120	phi_data = numpy.zeros(len(qx_data))
1121
1122	# get phi from data
1123	phi_data = numpy.arctan2(qy_data, qx_data)
1124
1125	# Get the min and max into the region: -pi <= phi < Pi
1126	phi_min_major = flip_phi(self.phi_min + Pi) - Pi
1127	phi_max_major = flip_phi(self.phi_max + Pi) - Pi
1128	# check for major sector
1129	if phi_min_major > phi_max_major:
1130	out_major = (phi_min_major <= phi_data) + (phi_max_major > phi_data)
1131	else:
1132	out_major = (phi_min_major <= phi_data) & (phi_max_major > phi_data)
1133
1134	# minor sector
1135	# Get the min and max into the region: -pi <= phi < Pi
1136	phi_min_minor = flip_phi(self.phi_min) - Pi
1137	phi_max_minor = flip_phi(self.phi_max) - Pi
1138
1139	# check for minor sector
1140	if phi_min_minor > phi_max_minor:
1141	out_minor = (phi_min_minor <= phi_data) + \
1142	(phi_max_minor >= phi_data)
1143	else:
1144	out_minor = (phi_min_minor <= phi_data) & \
1145	(phi_max_minor >= phi_data)
1146	out = out_major + out_minor
1147
1148	return out
1149
1150	if __name__ == "__main__":
1151
1152	from loader import Loader
1153
1154
1155	d = Loader().load('test/MAR07232_rest.ASC')
1156	#d = Loader().load('test/MP_New.sans')
1157
1158
1159	r = SectorQ(r_min=.000001, r_max=.01, phi_min=0.0, phi_max=2*math.pi)
1160	o = r(d)
1161
1162	s = Ring(r_min=.000001, r_max=.01)
1163	p = s(d)
1164
1165	for i in range(len(o.x)):
1166	print o.x[i], o.y[i], o.dy[i]
1167
1168
1169

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SasView

source: sasview/DataLoader/manipulations.py @ 552b3d5

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