invariant.py @ 3fc01c5

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Last change on this file since 3fc01c5 was 3fc01c5, checked in by Jae Cho <jhjcho@…>, 12 years ago
fixing pylint warnings
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1	#####################################################################
2	#This software was developed by the University of Tennessee as part of the
3	#Distributed Data Analysis of Neutron Scattering Experiments (DANSE)
4	#project funded by the US National Science Foundation.
5	#See the license text in license.txt
6	#copyright 2010, University of Tennessee
7	######################################################################
8
9	"""
10	This module implements invariant and its related computations.
11
12	:author: Gervaise B. Alina/UTK
13	:author: Mathieu Doucet/UTK
14	:author: Jae Cho/UTK
15
16	"""
17	import math
18	import numpy
19
20	from sans.dataloader.data_info import Data1D as LoaderData1D
21
22	# The minimum q-value to be used when extrapolating
23	Q_MINIMUM = 1e-5
24
25	# The maximum q-value to be used when extrapolating
26	Q_MAXIMUM = 10
27
28	# Number of steps in the extrapolation
29	INTEGRATION_NSTEPS = 1000
30
31	class Transform(object):
32	"""
33	Define interface that need to compute a function or an inverse
34	function given some x, y
35	"""
36
37	def linearize_data(self, data):
38	"""
39	Linearize data so that a linear fit can be performed.
40	Filter out the data that can't be transformed.
41
42	:param data: LoadData1D instance
43
44	"""
45	# Check that the vector lengths are equal
46	assert(len(data.x)==len(data.y))
47	if data.dy is not None:
48	assert(len(data.x)==len(data.dy))
49	dy = data.dy
50	else:
51	dy = numpy.ones(len(data.y))
52
53	# Transform the data
54	data_points = zip(data.x, data.y, dy)
55
56	output_points = [(self.linearize_q_value(p[0]),
57	math.log(p[1]),
58	p[2]/p[1]) for p in data_points if p[0]>0 and \
59	p[1]>0 and p[2]>0]
60
61	x_out, y_out, dy_out = zip(*output_points)
62
63	# Create Data1D object
64	x_out = numpy.asarray(x_out)
65	y_out = numpy.asarray(y_out)
66	dy_out = numpy.asarray(dy_out)
67	linear_data = LoaderData1D(x=x_out, y=y_out, dy=dy_out)
68
69	return linear_data
70
71	def get_allowed_bins(self, data):
72	"""
73	Goes through the data points and returns a list of boolean values
74	to indicate whether each points is allowed by the model or not.
75
76	:param data: Data1D object
77	"""
78	return [p[0]>0 and p[1]>0 and p[2]>0 for p in zip(data.x, data.y,
79	data.dy)]
80
81	def linearize_q_value(self, value):
82	"""
83	Transform the input q-value for linearization
84	"""
85	return NotImplemented
86
87	def extract_model_parameters(self, constant, slope, dconstant=0, dslope=0):
88	"""
89	set private member
90	"""
91	return NotImplemented
92
93	def evaluate_model(self, x):
94	"""
95	Returns an array f(x) values where f is the Transform function.
96	"""
97	return NotImplemented
98
99	def evaluate_model_errors(self, x):
100	"""
101	Returns an array of I(q) errors
102	"""
103	return NotImplemented
104
105	class Guinier(Transform):
106	"""
107	class of type Transform that performs operations related to guinier
108	function
109	"""
110	def __init__(self, scale=1, radius=60):
111	Transform.__init__(self)
112	self.scale = scale
113	self.radius = radius
114	## Uncertainty of scale parameter
115	self.dscale = 0
116	## Unvertainty of radius parameter
117	self.dradius = 0
118
119	def linearize_q_value(self, value):
120	"""
121	Transform the input q-value for linearization
122
123	:param value: q-value
124
125	:return: q*q
126	"""
127	return value * value
128
129	def extract_model_parameters(self, constant, slope, dconstant=0, dslope=0):
130	"""
131	assign new value to the scale and the radius
132	"""
133	self.scale = math.exp(constant)
134	self.radius = math.sqrt(-3 * slope)
135
136	# Errors
137	self.dscale = math.exp(constant)*dconstant
138	self.dradius = -3.0/2.0/math.sqrt(-3 * slope)*dslope
139
140	return [self.radius, self.scale], [self.dradius, self.dscale]
141
142	def evaluate_model(self, x):
143	"""
144	return F(x)= scale* e-((radiusx)*2/3)
145	"""
146	return self._guinier(x)
147
148	def evaluate_model_errors(self, x):
149	"""
150	Returns the error on I(q) for the given array of q-values
151
152	:param x: array of q-values
153	"""
154	p1 = numpy.array([self.dscale * math.exp(-((self.radius * q)**2/3)) \
155	for q in x])
156	p2 = numpy.array([self.scale * math.exp(-((self.radius * q)**2/3))\
157	* (-(q*2/3)) 2 * self.radius * self.dradius for q in x])
158	diq2 = p1p1 + p2p2
159	return numpy.array( [math.sqrt(err) for err in diq2] )
160
161	def _guinier(self, x):
162	"""
163	Retrive the guinier function after apply an inverse guinier function
164	to x
165	Compute a F(x) = scale* e-((radiusx)*2/3).
166
167	:param x: a vector of q values
168	:param scale: the scale value
169	:param radius: the guinier radius value
170
171	:return: F(x)
172	"""
173	# transform the radius of coming from the inverse guinier function to a
174	# a radius of a guinier function
175	if self.radius <= 0:
176	msg = "Rg expected positive value, but got %s"%self.radius
177	raise ValueError(msg)
178	value = numpy.array([math.exp(-((self.radius * i)**2/3)) for i in x ])
179	return self.scale * value
180
181	class PowerLaw(Transform):
182	"""
183	class of type transform that perform operation related to power_law
184	function
185	"""
186	def __init__(self, scale=1, power=4):
187	Transform.__init__(self)
188	self.scale = scale
189	self.power = power
190
191	def linearize_q_value(self, value):
192	"""
193	Transform the input q-value for linearization
194
195	:param value: q-value
196
197	:return: log(q)
198	"""
199	return math.log(value)
200
201	def extract_model_parameters(self, constant, slope, dconstant=0, dslope=0):
202	"""
203	Assign new value to the scale and the power
204	"""
205	self.power = -slope
206	self.scale = math.exp(constant)
207
208	# Errors
209	self.dscale = math.exp(constant)*dconstant
210	self.dpower = -dslope
211
212	return [self.power, self.scale], [self.dpower, self.dscale]
213
214	def evaluate_model(self, x):
215	"""
216	given a scale and a radius transform x, y using a power_law
217	function
218	"""
219	return self._power_law(x)
220
221	def evaluate_model_errors(self, x):
222	"""
223	Returns the error on I(q) for the given array of q-values
224	:param x: array of q-values
225	"""
226	p1 = numpy.array([self.dscale * math.pow(q, -self.power) for q in x])
227	p2 = numpy.array([self.scale * self.power * math.pow(q, -self.power-1)\
228	* self.dpower for q in x])
229	diq2 = p1p1 + p2p2
230	return numpy.array( [math.sqrt(err) for err in diq2] )
231
232	def _power_law(self, x):
233	"""
234	F(x) = scale* (x)^(-power)
235	when power= 4. the model is porod
236	else power_law
237	The model has three parameters: ::
238	1. x: a vector of q values
239	2. power: power of the function
240	3. scale : scale factor value
241
242	:param x: array
243	:return: F(x)
244	"""
245	if self.power <= 0:
246	msg = "Power_law function expected positive power,"
247	msg += " but got %s"%self.power
248	raise ValueError(msg)
249	if self.scale <= 0:
250	msg = "scale expected positive value, but got %s"%self.scale
251	raise ValueError(msg)
252
253	value = numpy.array([ math.pow(i, -self.power) for i in x ])
254	return self.scale * value
255
256	class Extrapolator:
257	"""
258	Extrapolate I(q) distribution using a given model
259	"""
260	def __init__(self, data, model=None):
261	"""
262	Determine a and b given a linear equation y = ax + b
263
264	If a model is given, it will be used to linearize the data before
265	the extrapolation is performed. If None,
266	a simple linear fit will be done.
267
268	:param data: data containing x and y such as y = ax + b
269	:param model: optional Transform object
270	"""
271	self.data = data
272	self.model = model
273
274	# Set qmin as the lowest non-zero value
275	self.qmin = Q_MINIMUM
276	for q_value in self.data.x:
277	if q_value > 0:
278	self.qmin = q_value
279	break
280	self.qmax = max(self.data.x)
281
282	def fit(self, power=None, qmin=None, qmax=None):
283	"""
284	Fit data for y = ax + b return a and b
285
286	:param power: a fixed, otherwise None
287	:param qmin: Minimum Q-value
288	:param qmax: Maximum Q-value
289	"""
290	if qmin is None:
291	qmin = self.qmin
292	if qmax is None:
293	qmax = self.qmax
294
295	# Identify the bin range for the fit
296	idx = (self.data.x >= qmin) & (self.data.x <= qmax)
297
298	fx = numpy.zeros(len(self.data.x))
299
300	# Uncertainty
301	if type(self.data.dy)==numpy.ndarray and \
302	len(self.data.dy)==len(self.data.x) and \
303	numpy.all(self.data.dy>0):
304	sigma = self.data.dy
305	else:
306	sigma = numpy.ones(len(self.data.x))
307
308	# Compute theory data f(x)
309	fx[idx] = self.data.y[idx]
310
311	# Linearize the data
312	if self.model is not None:
313	linearized_data = self.model.linearize_data(\
314	LoaderData1D(self.data.x[idx],
315	fx[idx],
316	dy = sigma[idx]))
317	else:
318	linearized_data = LoaderData1D(self.data.x[idx],
319	fx[idx],
320	dy = sigma[idx])
321
322	##power is given only for function = power_law
323	if power != None:
324	sigma2 = linearized_data.dy * linearized_data.dy
325	a = -(power)
326	b = (numpy.sum(linearized_data.y/sigma2) \
327	- a*numpy.sum(linearized_data.x/sigma2))/numpy.sum(1.0/sigma2)
328
329
330	deltas = linearized_data.x*a + \
331	numpy.ones(len(linearized_data.x))*b-linearized_data.y
332	residuals = numpy.sum(deltas*deltas/sigma2)
333
334	err = math.fabs(residuals) / numpy.sum(1.0/sigma2)
335	return [a, b], [0, math.sqrt(err)]
336	else:
337	A = numpy.vstack([ linearized_data.x/linearized_data.dy,
338	1.0/linearized_data.dy]).T
339	(p, residuals, rank, s) = numpy.linalg.lstsq(A,
340	linearized_data.y/linearized_data.dy)
341
342	# Get the covariance matrix, defined as inv_cov = a_transposed * a
343	err = numpy.zeros(2)
344	try:
345	inv_cov = numpy.dot(A.transpose(), A)
346	cov = numpy.linalg.pinv(inv_cov)
347	err_matrix = math.fabs(residuals) * cov
348	err = [math.sqrt(err_matrix[0][0]), math.sqrt(err_matrix[1][1])]
349	except:
350	err = [-1.0, -1.0]
351
352	return p, err
353
354
355	class InvariantCalculator(object):
356	"""
357	Compute invariant if data is given.
358	Can provide volume fraction and surface area if the user provides
359	Porod constant and contrast values.
360
361	:precondition: the user must send a data of type DataLoader.Data1D
362	the user provide background and scale values.
363
364	:note: Some computations depends on each others.
365	"""
366	def __init__(self, data, background=0, scale=1 ):
367	"""
368	Initialize variables.
369
370	:param data: data must be of type DataLoader.Data1D
371	:param background: Background value. The data will be corrected
372	before processing
373	:param scale: Scaling factor for I(q). The data will be corrected
374	before processing
375	"""
376	# Background and scale should be private data member if the only way to
377	# change them are by instantiating a new object.
378	self._background = background
379	self._scale = scale
380	# slit height for smeared data
381	self._smeared = None
382	# The data should be private
383	self._data = self._get_data(data)
384	# get the dxl if the data is smeared: This is done only once on init.
385	if self._data.dxl != None and self._data.dxl.all() >0:
386	# assumes constant dxl
387	self._smeared = self._data.dxl[0]
388
389	# Since there are multiple variants of Q*, you should force the
390	# user to use the get method and keep Q* a private data member
391	self._qstar = None
392
393	# You should keep the error on Q* so you can reuse it without
394	# recomputing the whole thing.
395	self._qstar_err = 0
396
397	# Extrapolation parameters
398	self._low_extrapolation_npts = 4
399	self._low_extrapolation_function = Guinier()
400	self._low_extrapolation_power = None
401	self._low_extrapolation_power_fitted = None
402
403	self._high_extrapolation_npts = 4
404	self._high_extrapolation_function = PowerLaw()
405	self._high_extrapolation_power = None
406	self._high_extrapolation_power_fitted = None
407
408	# Extrapolation range
409	self._low_q_limit = Q_MINIMUM
410
411	def _get_data(self, data):
412	"""
413	:note: this function must be call before computing any type
414	of invariant
415
416	:return: new data = self._scale *data - self._background
417	"""
418	if not issubclass(data.__class__, LoaderData1D):
419	#Process only data that inherited from DataLoader.Data_info.Data1D
420	raise ValueError,"Data must be of type DataLoader.Data1D"
421	#from copy import deepcopy
422	new_data = (self._scale * data) - self._background
423
424	# Check that the vector lengths are equal
425	assert(len(new_data.x)==len(new_data.y))
426
427	# Verify that the errors are set correctly
428	if new_data.dy is None or len(new_data.x) != len(new_data.dy) or \
429	(min(new_data.dy)==0 and max(new_data.dy)==0):
430	new_data.dy = numpy.ones(len(new_data.x))
431	return new_data
432
433	def _fit(self, model, qmin=Q_MINIMUM, qmax=Q_MAXIMUM, power=None):
434	"""
435	fit data with function using
436	data = self._get_data()
437	fx = Functor(data , function)
438	y = data.y
439	slope, constant = linalg.lstsq(y,fx)
440
441	:param qmin: data first q value to consider during the fit
442	:param qmax: data last q value to consider during the fit
443	:param power : power value to consider for power-law
444	:param function: the function to use during the fit
445
446	:return a: the scale of the function
447	:return b: the other parameter of the function for guinier will be radius
448	for power_law will be the power value
449	"""
450	extrapolator = Extrapolator(data=self._data, model=model)
451	p, dp = extrapolator.fit(power=power, qmin=qmin, qmax=qmax)
452
453	return model.extract_model_parameters(constant=p[1], slope=p[0],
454	dconstant=dp[1], dslope=dp[0])
455
456	def _get_qstar(self, data):
457	"""
458	Compute invariant for pinhole data.
459	This invariant is given by: ::
460
461	q_star = x0*2 y0 dx0 +x12 y1 *dx1
462	+ ..+ xn*2 yn *dxn for non smeared data
463
464	q_star = dxl0 x0 y0 dx0 +dxl1 x1 y1 dx1
465	+ ..+ dlxn xn yn *dxn for smeared data
466
467	where n >= len(data.x)-1
468	dxl = slit height dQl
469	dxi = 1/2*(xi+1 - xi) + (xi - xi-1)
470	dx0 = (x1 - x0)/2
471	dxn = (xn - xn-1)/2
472
473	:param data: the data to use to compute invariant.
474
475	:return q_star: invariant value for pinhole data. q_star > 0
476	"""
477	if len(data.x) <= 1 or len(data.y) <= 1 or len(data.x)!= len(data.y):
478	msg = "Length x and y must be equal"
479	msg += " and greater than 1; got x=%s, y=%s"%(len(data.x),
480	len(data.y))
481	raise ValueError, msg
482	else:
483	# Take care of smeared data
484	if self._smeared is None:
485	gx = data.x * data.x
486	# assumes that len(x) == len(dxl).
487	else:
488	gx = data.dxl * data.x
489
490	n = len(data.x)- 1
491	#compute the first delta q
492	dx0 = (data.x[1] - data.x[0])/2
493	#compute the last delta q
494	dxn = (data.x[n] - data.x[n-1])/2
495	sum = 0
496	sum += gx[0] * data.y[0] * dx0
497	sum += gx[n] * data.y[n] * dxn
498
499	if len(data.x) == 2:
500	return sum
501	else:
502	#iterate between for element different
503	#from the first and the last
504	for i in xrange(1, n-1):
505	dxi = (data.x[i+1] - data.x[i-1])/2
506	sum += gx[i] * data.y[i] * dxi
507	return sum
508
509	def _get_qstar_uncertainty(self, data):
510	"""
511	Compute invariant uncertainty with with pinhole data.
512	This uncertainty is given as follow: ::
513
514	dq_star = math.sqrt[(x0*2(dy0)dx0)*2 +
515	(x1*2 (dy1)dx1)2 + ..+ (xn2 (dyn)dxn)*2 ]
516	where n >= len(data.x)-1
517	dxi = 1/2*(xi+1 - xi) + (xi - xi-1)
518	dx0 = (x1 - x0)/2
519	dxn = (xn - xn-1)/2
520	dyn: error on dy
521
522	:param data:
523	:note: if data doesn't contain dy assume dy= math.sqrt(data.y)
524	"""
525	if len(data.x) <= 1 or len(data.y) <= 1 or \
526	len(data.x) != len(data.y) or \
527	(data.dy is not None and (len(data.dy) != len(data.y))):
528	msg = "Length of data.x and data.y must be equal"
529	msg += " and greater than 1; got x=%s, y=%s"%(len(data.x),
530	len(data.y))
531	raise ValueError, msg
532	else:
533	#Create error for data without dy error
534	if data.dy is None:
535	dy = math.sqrt(data.y)
536	else:
537	dy = data.dy
538	# Take care of smeared data
539	if self._smeared is None:
540	gx = data.x * data.x
541	# assumes that len(x) == len(dxl).
542	else:
543	gx = data.dxl * data.x
544
545	n = len(data.x) - 1
546	#compute the first delta
547	dx0 = (data.x[1] - data.x[0])/2
548	#compute the last delta
549	dxn= (data.x[n] - data.x[n-1])/2
550	sum = 0
551	sum += (gx[0] * dy[0] * dx0)**2
552	sum += (gx[n] * dy[n] * dxn)**2
553	if len(data.x) == 2:
554	return math.sqrt(sum)
555	else:
556	#iterate between for element different
557	#from the first and the last
558	for i in xrange(1, n-1):
559	dxi = (data.x[i+1] - data.x[i-1])/2
560	sum += (gx[i] * dy[i] * dxi)**2
561	return math.sqrt(sum)
562
563	def _get_extrapolated_data(self, model, npts=INTEGRATION_NSTEPS,
564	q_start=Q_MINIMUM, q_end=Q_MAXIMUM):
565	"""
566	:return: extrapolate data create from data
567	"""
568	#create new Data1D to compute the invariant
569	q = numpy.linspace(start=q_start,
570	stop=q_end,
571	num=npts,
572	endpoint=True)
573	iq = model.evaluate_model(q)
574	diq = model.evaluate_model_errors(q)
575
576	result_data = LoaderData1D(x=q, y=iq, dy=diq)
577	if self._smeared != None:
578	result_data.dxl = self._smeared * numpy.ones(len(q))
579	return result_data
580
581	def get_data(self):
582	"""
583	:return: self._data
584	"""
585	return self._data
586
587	def get_extrapolation_power(self, range='high'):
588	"""
589	:return: the fitted power for power law function for a given
590	extrapolation range
591	"""
592	if range == 'low':
593	return self._low_extrapolation_power_fitted
594	return self._high_extrapolation_power_fitted
595
596	def get_qstar_low(self):
597	"""
598	Compute the invariant for extrapolated data at low q range.
599
600	Implementation:
601	data = self._get_extra_data_low()
602	return self._get_qstar()
603
604	:return q_star: the invariant for data extrapolated at low q.
605	"""
606	# Data boundaries for fitting
607	qmin = self._data.x[0]
608	qmax = self._data.x[self._low_extrapolation_npts - 1]
609
610	# Extrapolate the low-Q data
611	p, dp = self._fit(model=self._low_extrapolation_function,
612	qmin=qmin,
613	qmax=qmax,
614	power=self._low_extrapolation_power)
615	self._low_extrapolation_power_fitted = p[0]
616
617	# Distribution starting point
618	self._low_q_limit = Q_MINIMUM
619	if Q_MINIMUM >= qmin:
620	self._low_q_limit = qmin/10
621
622	data = self._get_extrapolated_data(\
623	model=self._low_extrapolation_function,
624	npts=INTEGRATION_NSTEPS,
625	q_start=self._low_q_limit, q_end=qmin)
626
627	# Systematic error
628	# If we have smearing, the shape of the I(q) distribution at low Q will
629	# may not be a Guinier or simple power law. The following is
630	# a conservative estimation for the systematic error.
631	err = qminqminmath.fabs((qmin-self._low_q_limit)*\
632	(data.y[0] - data.y[INTEGRATION_NSTEPS-1]))
633	return self._get_qstar(data), self._get_qstar_uncertainty(data)+err
634
635	def get_qstar_high(self):
636	"""
637	Compute the invariant for extrapolated data at high q range.
638
639	Implementation:
640	data = self._get_extra_data_high()
641	return self._get_qstar()
642
643	:return q_star: the invariant for data extrapolated at high q.
644	"""
645	# Data boundaries for fitting
646	x_len = len(self._data.x) - 1
647	qmin = self._data.x[x_len - (self._high_extrapolation_npts - 1)]
648	qmax = self._data.x[x_len]
649
650	# fit the data with a model to get the appropriate parameters
651	p, dp = self._fit(model=self._high_extrapolation_function,
652	qmin=qmin,
653	qmax=qmax,
654	power=self._high_extrapolation_power)
655	self._high_extrapolation_power_fitted = p[0]
656
657	#create new Data1D to compute the invariant
658	data = self._get_extrapolated_data(\
659	model=self._high_extrapolation_function,
660	npts=INTEGRATION_NSTEPS,
661	q_start=qmax, q_end=Q_MAXIMUM)
662
663	return self._get_qstar(data), self._get_qstar_uncertainty(data)
664
665	def get_extra_data_low(self, npts_in=None, q_start=None, npts=20):
666	"""
667	Returns the extrapolated data used for the loew-Q invariant calculation.
668	By default, the distribution will cover the data points used for the
669	extrapolation. The number of overlap points is a parameter (npts_in).
670	By default, the maximum q-value of the distribution will be
671	the minimum q-value used when extrapolating for the purpose of the
672	invariant calculation.
673
674	:param npts_in: number of data points for which
675	the extrapolated data overlap
676	:param q_start: is the minimum value to uses for extrapolated data
677	:param npts: the number of points in the extrapolated distribution
678
679	"""
680	# Get extrapolation range
681	if q_start is None:
682	q_start = self._low_q_limit
683
684	if npts_in is None:
685	npts_in = self._low_extrapolation_npts
686	q_end = self._data.x[max(0, npts_in-1)]
687
688	if q_start >= q_end:
689	return numpy.zeros(0), numpy.zeros(0)
690
691	return self._get_extrapolated_data(\
692	model=self._low_extrapolation_function,
693	npts=npts,
694	q_start=q_start, q_end=q_end)
695
696	def get_extra_data_high(self, npts_in=None, q_end=Q_MAXIMUM, npts=20):
697	"""
698	Returns the extrapolated data used for the high-Q invariant calculation.
699	By default, the distribution will cover the data points used for the
700	extrapolation. The number of overlap points is a parameter (npts_in).
701	By default, the maximum q-value of the distribution will be Q_MAXIMUM,
702	the maximum q-value used when extrapolating for the purpose of the
703	invariant calculation.
704
705	:param npts_in: number of data points for which the
706	extrapolated data overlap
707	:param q_end: is the maximum value to uses for extrapolated data
708	:param npts: the number of points in the extrapolated distribution
709	"""
710	# Get extrapolation range
711	if npts_in is None:
712	npts_in = self._high_extrapolation_npts
713	_npts = len(self._data.x)
714	q_start = self._data.x[min(_npts, _npts-npts_in)]
715
716	if q_start >= q_end:
717	return numpy.zeros(0), numpy.zeros(0)
718
719	return self._get_extrapolated_data(\
720	model=self._high_extrapolation_function,
721	npts=npts,
722	q_start=q_start, q_end=q_end)
723
724	def set_extrapolation(self, range, npts=4, function=None, power=None):
725	"""
726	Set the extrapolation parameters for the high or low Q-range.
727	Note that this does not turn extrapolation on or off.
728
729	:param range: a keyword set the type of extrapolation . type string
730	:param npts: the numbers of q points of data to consider
731	for extrapolation
732	:param function: a keyword to select the function to use
733	for extrapolation.
734	of type string.
735	:param power: an power to apply power_low function
736
737	"""
738	range = range.lower()
739	if range not in ['high', 'low']:
740	raise ValueError, "Extrapolation range should be 'high' or 'low'"
741	function = function.lower()
742	if function not in ['power_law', 'guinier']:
743	msg = "Extrapolation function should be 'guinier' or 'power_law'"
744	raise ValueError, msg
745
746	if range == 'high':
747	if function != 'power_law':
748	msg = "Extrapolation only allows a power law at high Q"
749	raise ValueError, msg
750	self._high_extrapolation_npts = npts
751	self._high_extrapolation_power = power
752	self._high_extrapolation_power_fitted = power
753	else:
754	if function == 'power_law':
755	self._low_extrapolation_function = PowerLaw()
756	else:
757	self._low_extrapolation_function = Guinier()
758	self._low_extrapolation_npts = npts
759	self._low_extrapolation_power = power
760	self._low_extrapolation_power_fitted = power
761
762	def get_qstar(self, extrapolation=None):
763	"""
764	Compute the invariant of the local copy of data.
765
766	:param extrapolation: string to apply optional extrapolation
767
768	:return q_star: invariant of the data within data's q range
769
770	:warning: When using setting data to Data1D ,
771	the user is responsible of
772	checking that the scale and the background are
773	properly apply to the data
774
775	"""
776	self._qstar = self._get_qstar(self._data)
777	self._qstar_err = self._get_qstar_uncertainty(self._data)
778
779	if extrapolation is None:
780	return self._qstar
781
782	# Compute invariant plus invariant of extrapolated data
783	extrapolation = extrapolation.lower()
784	if extrapolation == "low":
785	qs_low, dqs_low = self.get_qstar_low()
786	qs_hi, dqs_hi = 0, 0
787
788	elif extrapolation == "high":
789	qs_low, dqs_low = 0, 0
790	qs_hi, dqs_hi = self.get_qstar_high()
791
792	elif extrapolation == "both":
793	qs_low, dqs_low = self.get_qstar_low()
794	qs_hi, dqs_hi = self.get_qstar_high()
795
796	self._qstar += qs_low + qs_hi
797	self._qstar_err = math.sqrt(self._qstar_err*self._qstar_err \
798	+ dqs_lowdqs_low + dqs_hidqs_hi)
799
800	return self._qstar
801
802	def get_surface(self, contrast, porod_const, extrapolation=None):
803	"""
804	Compute the specific surface from the data.
805
806	Implementation::
807
808	V = self.get_volume_fraction(contrast, extrapolation)
809
810	Compute the surface given by:
811	surface = (2pi V(1- V)*porod_const)/ q_star
812
813	:param contrast: contrast value to compute the volume
814	:param porod_const: Porod constant to compute the surface
815	:param extrapolation: string to apply optional extrapolation
816
817	:return: specific surface
818	"""
819	# Compute the volume
820	volume = self.get_volume_fraction(contrast, extrapolation)
821	return 2 * math.pi * volume (1 - volume) \
822	float(porod_const)/self._qstar
823
824	def get_volume_fraction(self, contrast, extrapolation=None):
825	"""
826	Compute volume fraction is deduced as follow: ::
827
828	q_star = 2(picontrast)*2 volume( 1- volume)
829	for k = 10^(-8)q_star/(2(pi\|contrast\|)*2)
830	we get 2 values of volume:
831	with 1 - 4 * k >= 0
832	volume1 = (1- sqrt(1- 4*k))/2
833	volume2 = (1+ sqrt(1- 4*k))/2
834
835	q_star: the invariant value included extrapolation is applied
836	unit 1/A^(3)*1/cm
837	q_star = self.get_qstar()
838
839	the result returned will be 0 <= volume <= 1
840
841	:param contrast: contrast value provides by the user of type float.
842	contrast unit is 1/A^(2)= 10^(16)cm^(2)
843	:param extrapolation: string to apply optional extrapolation
844
845	:return: volume fraction
846
847	:note: volume fraction must have no unit
848	"""
849	if contrast <= 0:
850	raise ValueError, "The contrast parameter must be greater than zero"
851
852	# Make sure Q star is up to date
853	self.get_qstar(extrapolation)
854
855	if self._qstar <= 0:
856	msg = "Invalid invariant: Invariant Q* must be greater than zero"
857	raise RuntimeError, msg
858
859	# Compute intermediate constant
860	k = 1.e-8 * self._qstar/(2 * (math.pi * math.fabs(float(contrast)))**2)
861	# Check discriminant value
862	discrim = 1 - 4 * k
863
864	# Compute volume fraction
865	if discrim < 0:
866	msg = "Could not compute the volume fraction: negative discriminant"
867	raise RuntimeError, msg
868	elif discrim == 0:
869	return 1/2
870	else:
871	volume1 = 0.5 * (1 - math.sqrt(discrim))
872	volume2 = 0.5 * (1 + math.sqrt(discrim))
873
874	if 0 <= volume1 and volume1 <= 1:
875	return volume1
876	elif 0 <= volume2 and volume2 <= 1:
877	return volume2
878	msg = "Could not compute the volume fraction: inconsistent results"
879	raise RuntimeError, msg
880
881	def get_qstar_with_error(self, extrapolation=None):
882	"""
883	Compute the invariant uncertainty.
884	This uncertainty computation depends on whether or not the data is
885	smeared.
886
887	:param extrapolation: string to apply optional extrapolation
888
889	:return: invariant, the invariant uncertainty
890	"""
891	self.get_qstar(extrapolation)
892	return self._qstar, self._qstar_err
893
894	def get_volume_fraction_with_error(self, contrast, extrapolation=None):
895	"""
896	Compute uncertainty on volume value as well as the volume fraction
897	This uncertainty is given by the following equation: ::
898
899	dV = 0.5 * (4k dq_star) /(2* math.sqrt(1-k* q_star))
900
901	for k = 10^(-8)q_star/(2(pi\|contrast\|)*2)
902
903	q_star: the invariant value including extrapolated value if existing
904	dq_star: the invariant uncertainty
905	dV: the volume uncertainty
906
907	The uncertainty will be set to -1 if it can't be computed.
908
909	:param contrast: contrast value
910	:param extrapolation: string to apply optional extrapolation
911
912	:return: V, dV = volume fraction, error on volume fraction
913	"""
914	volume = self.get_volume_fraction(contrast, extrapolation)
915
916	# Compute error
917	k = 1.e-8 * self._qstar /(2 * (math.pi* math.fabs(float(contrast)))**2)
918	# Check value inside the sqrt function
919	value = 1 - k * self._qstar
920	if (value) <= 0:
921	uncertainty = -1
922	# Compute uncertainty
923	uncertainty = math.fabs((0.5 * 4 * k * \
924	self._qstar_err)/(2 * math.sqrt(1 - k * self._qstar)))
925
926	return volume, uncertainty
927
928	def get_surface_with_error(self, contrast, porod_const, extrapolation=None):
929	"""
930	Compute uncertainty of the surface value as well as the surface value.
931	The uncertainty is given as follow: ::
932
933	dS = porod_const 2pi[( dV -2VdV)/q_star
934	+ dq_star(v-v**2)
935
936	q_star: the invariant value
937	dq_star: the invariant uncertainty
938	V: the volume fraction value
939	dV: the volume uncertainty
940
941	:param contrast: contrast value
942	:param porod_const: porod constant value
943	:param extrapolation: string to apply optional extrapolation
944
945	:return S, dS: the surface, with its uncertainty
946	"""
947	# We get the volume fraction, with error
948	# get_volume_fraction_with_error calls get_volume_fraction
949	# get_volume_fraction calls get_qstar
950	# which computes Qstar and dQstar
951	v, dv = self.get_volume_fraction_with_error(contrast, extrapolation)
952
953	s = self.get_surface(contrast=contrast, porod_const=porod_const,
954	extrapolation=extrapolation)
955	ds = porod_const * 2 * math.pi * (( dv - 2 * v * dv)/ self._qstar\
956	+ self._qstar_err * ( v - v**2))
957
958	return s, ds

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source: sasview/sansinvariant/src/sans/invariant/invariant.py @ 3fc01c5

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