invariant.py @ ad4053a

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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 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):
303	sigma = self.data.dy
304	else:
305	sigma = numpy.ones(len(self.data.x))
306
307	# Compute theory data f(x)
308	fx[idx] = self.data.y[idx]
309
310	# Linearize the data
311	if self.model is not None:
312	linearized_data = self.model.linearize_data(\
313	LoaderData1D(self.data.x[idx],
314	fx[idx],
315	dy = sigma[idx]))
316	else:
317	linearized_data = LoaderData1D(self.data.x[idx],
318	fx[idx],
319	dy = sigma[idx])
320
321	##power is given only for function = power_law
322	if power != None:
323	sigma2 = linearized_data.dy * linearized_data.dy
324	a = -(power)
325	b = (numpy.sum(linearized_data.y/sigma2) \
326	- a*numpy.sum(linearized_data.x/sigma2))/numpy.sum(1.0/sigma2)
327
328
329	deltas = linearized_data.x*a + \
330	numpy.ones(len(linearized_data.x))*b-linearized_data.y
331	residuals = numpy.sum(deltas*deltas/sigma2)
332
333	err = math.fabs(residuals) / numpy.sum(1.0/sigma2)
334	return [a, b], [0, math.sqrt(err)]
335	else:
336	A = numpy.vstack([ linearized_data.x/linearized_data.dy,
337	1.0/linearized_data.dy]).T
338	(p, residuals, rank, s) = numpy.linalg.lstsq(A,
339	linearized_data.y/linearized_data.dy)
340
341	# Get the covariance matrix, defined as inv_cov = a_transposed * a
342	err = numpy.zeros(2)
343	try:
344	inv_cov = numpy.dot(A.transpose(), A)
345	cov = numpy.linalg.pinv(inv_cov)
346	err_matrix = math.fabs(residuals) * cov
347	err = [math.sqrt(err_matrix[0][0]), math.sqrt(err_matrix[1][1])]
348	except:
349	err = [-1.0, -1.0]
350
351	return p, err
352
353
354	class InvariantCalculator(object):
355	"""
356	Compute invariant if data is given.
357	Can provide volume fraction and surface area if the user provides
358	Porod constant and contrast values.
359
360	:precondition: the user must send a data of type DataLoader.Data1D
361	the user provide background and scale values.
362
363	:note: Some computations depends on each others.
364	"""
365	def __init__(self, data, background=0, scale=1 ):
366	"""
367	Initialize variables.
368
369	:param data: data must be of type DataLoader.Data1D
370	:param background: Background value. The data will be corrected
371	before processing
372	:param scale: Scaling factor for I(q). The data will be corrected
373	before processing
374	"""
375	# Background and scale should be private data member if the only way to
376	# change them are by instantiating a new object.
377	self._background = background
378	self._scale = scale
379	# slit height for smeared data
380	self._smeared = None
381	# The data should be private
382	self._data = self._get_data(data)
383	# get the dxl if the data is smeared: This is done only once on init.
384	if self._data.dxl != None and self._data.dxl.all() >0:
385	# assumes constant dxl
386	self._smeared = self._data.dxl[0]
387
388	# Since there are multiple variants of Q*, you should force the
389	# user to use the get method and keep Q* a private data member
390	self._qstar = None
391
392	# You should keep the error on Q* so you can reuse it without
393	# recomputing the whole thing.
394	self._qstar_err = 0
395
396	# Extrapolation parameters
397	self._low_extrapolation_npts = 4
398	self._low_extrapolation_function = Guinier()
399	self._low_extrapolation_power = None
400	self._low_extrapolation_power_fitted = None
401
402	self._high_extrapolation_npts = 4
403	self._high_extrapolation_function = PowerLaw()
404	self._high_extrapolation_power = None
405	self._high_extrapolation_power_fitted = None
406
407	# Extrapolation range
408	self._low_q_limit = Q_MINIMUM
409
410	def _get_data(self, data):
411	"""
412	:note: this function must be call before computing any type
413	of invariant
414
415	:return: new data = self._scale *data - self._background
416	"""
417	if not issubclass(data.__class__, LoaderData1D):
418	#Process only data that inherited from DataLoader.Data_info.Data1D
419	raise ValueError,"Data must be of type DataLoader.Data1D"
420	#from copy import deepcopy
421	new_data = (self._scale * data) - self._background
422
423	# Check that the vector lengths are equal
424	assert(len(new_data.x)==len(new_data.y))
425
426	# Verify that the errors are set correctly
427	if new_data.dy is None or len(new_data.x) != len(new_data.dy) or \
428	(min(new_data.dy)==0 and max(new_data.dy)==0):
429	new_data.dy = numpy.ones(len(new_data.x))
430	return new_data
431
432	def _fit(self, model, qmin=Q_MINIMUM, qmax=Q_MAXIMUM, power=None):
433	"""
434	fit data with function using
435	data = self._get_data()
436	fx = Functor(data , function)
437	y = data.y
438	slope, constant = linalg.lstsq(y,fx)
439
440	:param qmin: data first q value to consider during the fit
441	:param qmax: data last q value to consider during the fit
442	:param power : power value to consider for power-law
443	:param function: the function to use during the fit
444
445	:return a: the scale of the function
446	:return b: the other parameter of the function for guinier will be radius
447	for power_law will be the power value
448	"""
449	extrapolator = Extrapolator(data=self._data, model=model)
450	p, dp = extrapolator.fit(power=power, qmin=qmin, qmax=qmax)
451
452	return model.extract_model_parameters(constant=p[1], slope=p[0],
453	dconstant=dp[1], dslope=dp[0])
454
455	def _get_qstar(self, data):
456	"""
457	Compute invariant for pinhole data.
458	This invariant is given by: ::
459
460	q_star = x0*2 y0 dx0 +x12 y1 *dx1
461	+ ..+ xn*2 yn *dxn for non smeared data
462
463	q_star = dxl0 x0 y0 dx0 +dxl1 x1 y1 dx1
464	+ ..+ dlxn xn yn *dxn for smeared data
465
466	where n >= len(data.x)-1
467	dxl = slit height dQl
468	dxi = 1/2*(xi+1 - xi) + (xi - xi-1)
469	dx0 = (x1 - x0)/2
470	dxn = (xn - xn-1)/2
471
472	:param data: the data to use to compute invariant.
473
474	:return q_star: invariant value for pinhole data. q_star > 0
475	"""
476	if len(data.x) <= 1 or len(data.y) <= 1 or len(data.x)!= len(data.y):
477	msg = "Length x and y must be equal"
478	msg += " and greater than 1; got x=%s, y=%s"%(len(data.x),
479	len(data.y))
480	raise ValueError, msg
481	else:
482	# Take care of smeared data
483	if self._smeared is None:
484	gx = data.x * data.x
485	# assumes that len(x) == len(dxl).
486	else:
487	gx = data.dxl * data.x
488
489	n = len(data.x)- 1
490	#compute the first delta q
491	dx0 = (data.x[1] - data.x[0])/2
492	#compute the last delta q
493	dxn = (data.x[n] - data.x[n-1])/2
494	sum = 0
495	sum += gx[0] * data.y[0] * dx0
496	sum += gx[n] * data.y[n] * dxn
497
498	if len(data.x) == 2:
499	return sum
500	else:
501	#iterate between for element different
502	#from the first and the last
503	for i in xrange(1, n-1):
504	dxi = (data.x[i+1] - data.x[i-1])/2
505	sum += gx[i] * data.y[i] * dxi
506	return sum
507
508	def _get_qstar_uncertainty(self, data):
509	"""
510	Compute invariant uncertainty with with pinhole data.
511	This uncertainty is given as follow: ::
512
513	dq_star = math.sqrt[(x0*2(dy0)dx0)*2 +
514	(x1*2 (dy1)dx1)2 + ..+ (xn2 (dyn)dxn)*2 ]
515	where n >= len(data.x)-1
516	dxi = 1/2*(xi+1 - xi) + (xi - xi-1)
517	dx0 = (x1 - x0)/2
518	dxn = (xn - xn-1)/2
519	dyn: error on dy
520
521	:param data:
522	:note: if data doesn't contain dy assume dy= math.sqrt(data.y)
523	"""
524	if len(data.x) <= 1 or len(data.y) <= 1 or \
525	len(data.x) != len(data.y) or \
526	(data.dy is not None and (len(data.dy) != len(data.y))):
527	msg = "Length of data.x and data.y must be equal"
528	msg += " and greater than 1; got x=%s, y=%s"%(len(data.x),
529	len(data.y))
530	raise ValueError, msg
531	else:
532	#Create error for data without dy error
533	if data.dy is None:
534	dy = math.sqrt(y)
535	else:
536	dy = data.dy
537	# Take care of smeared data
538	if self._smeared is None:
539	gx = data.x * data.x
540	# assumes that len(x) == len(dxl).
541	else:
542	gx = data.dxl * data.x
543
544	n = len(data.x) - 1
545	#compute the first delta
546	dx0 = (data.x[1] - data.x[0])/2
547	#compute the last delta
548	dxn= (data.x[n] - data.x[n-1])/2
549	sum = 0
550	sum += (gx[0] * dy[0] * dx0)**2
551	sum += (gx[n] * dy[n] * dxn)**2
552	if len(data.x) == 2:
553	return math.sqrt(sum)
554	else:
555	#iterate between for element different
556	#from the first and the last
557	for i in xrange(1, n-1):
558	dxi = (data.x[i+1] - data.x[i-1])/2
559	sum += (gx[i] * dy[i] * dxi)**2
560	return math.sqrt(sum)
561
562	def _get_extrapolated_data(self, model, npts=INTEGRATION_NSTEPS,
563	q_start=Q_MINIMUM, q_end=Q_MAXIMUM):
564	"""
565	:return: extrapolate data create from data
566	"""
567	#create new Data1D to compute the invariant
568	q = numpy.linspace(start=q_start,
569	stop=q_end,
570	num=npts,
571	endpoint=True)
572	iq = model.evaluate_model(q)
573	diq = model.evaluate_model_errors(q)
574
575	result_data = LoaderData1D(x=q, y=iq, dy=diq)
576	if self._smeared != None:
577	result_data.dxl = self._smeared * numpy.ones(len(q))
578	return result_data
579
580	def get_data(self):
581	"""
582	:return: self._data
583	"""
584	return self._data
585
586	def get_extrapolation_power(self, range='high'):
587	"""
588	:return: the fitted power for power law function for a given
589	extrapolation range
590	"""
591	if range == 'low':
592	return self._low_extrapolation_power_fitted
593	return self._high_extrapolation_power_fitted
594
595	def get_qstar_low(self):
596	"""
597	Compute the invariant for extrapolated data at low q range.
598
599	Implementation:
600	data = self._get_extra_data_low()
601	return self._get_qstar()
602
603	:return q_star: the invariant for data extrapolated at low q.
604	"""
605	# Data boundaries for fitting
606	qmin = self._data.x[0]
607	qmax = self._data.x[self._low_extrapolation_npts - 1]
608
609	# Extrapolate the low-Q data
610	p, dp = self._fit(model=self._low_extrapolation_function,
611	qmin=qmin,
612	qmax=qmax,
613	power=self._low_extrapolation_power)
614	self._low_extrapolation_power_fitted = p[0]
615
616	# Distribution starting point
617	self._low_q_limit = Q_MINIMUM
618	if Q_MINIMUM >= qmin:
619	self._low_q_limit = qmin/10
620
621	data = self._get_extrapolated_data(\
622	model=self._low_extrapolation_function,
623	npts=INTEGRATION_NSTEPS,
624	q_start=self._low_q_limit, q_end=qmin)
625
626	# Systematic error
627	# If we have smearing, the shape of the I(q) distribution at low Q will
628	# may not be a Guinier or simple power law. The following is
629	# a conservative estimation for the systematic error.
630	err = qminqminmath.fabs((qmin-self._low_q_limit)*\
631	(data.y[0] - data.y[INTEGRATION_NSTEPS-1]))
632	return self._get_qstar(data), self._get_qstar_uncertainty(data)+err
633
634	def get_qstar_high(self):
635	"""
636	Compute the invariant for extrapolated data at high q range.
637
638	Implementation:
639	data = self._get_extra_data_high()
640	return self._get_qstar()
641
642	:return q_star: the invariant for data extrapolated at high q.
643	"""
644	# Data boundaries for fitting
645	x_len = len(self._data.x) - 1
646	qmin = self._data.x[x_len - (self._high_extrapolation_npts - 1)]
647	qmax = self._data.x[x_len]
648
649	# fit the data with a model to get the appropriate parameters
650	p, dp = self._fit(model=self._high_extrapolation_function,
651	qmin=qmin,
652	qmax=qmax,
653	power=self._high_extrapolation_power)
654	self._high_extrapolation_power_fitted = p[0]
655
656	#create new Data1D to compute the invariant
657	data = self._get_extrapolated_data(\
658	model=self._high_extrapolation_function,
659	npts=INTEGRATION_NSTEPS,
660	q_start=qmax, q_end=Q_MAXIMUM)
661
662	return self._get_qstar(data), self._get_qstar_uncertainty(data)
663
664	def get_extra_data_low(self, npts_in=None, q_start=None, npts=20):
665	"""
666	Returns the extrapolated data used for the loew-Q invariant calculation.
667	By default, the distribution will cover the data points used for the
668	extrapolation. The number of overlap points is a parameter (npts_in).
669	By default, the maximum q-value of the distribution will be
670	the minimum q-value used when extrapolating for the purpose of the
671	invariant calculation.
672
673	:param npts_in: number of data points for which
674	the extrapolated data overlap
675	:param q_start: is the minimum value to uses for extrapolated data
676	:param npts: the number of points in the extrapolated distribution
677
678	"""
679	# Get extrapolation range
680	if q_start is None:
681	q_start = self._low_q_limit
682
683	if npts_in is None:
684	npts_in = self._low_extrapolation_npts
685	q_end = self._data.x[max(0, npts_in-1)]
686
687	if q_start >= q_end:
688	return numpy.zeros(0), numpy.zeros(0)
689
690	return self._get_extrapolated_data(\
691	model=self._low_extrapolation_function,
692	npts=npts,
693	q_start=q_start, q_end=q_end)
694
695	def get_extra_data_high(self, npts_in=None, q_end=Q_MAXIMUM, npts=20):
696	"""
697	Returns the extrapolated data used for the high-Q invariant calculation.
698	By default, the distribution will cover the data points used for the
699	extrapolation. The number of overlap points is a parameter (npts_in).
700	By default, the maximum q-value of the distribution will be Q_MAXIMUM,
701	the maximum q-value used when extrapolating for the purpose of the
702	invariant calculation.
703
704	:param npts_in: number of data points for which the
705	extrapolated data overlap
706	:param q_end: is the maximum value to uses for extrapolated data
707	:param npts: the number of points in the extrapolated distribution
708	"""
709	# Get extrapolation range
710	if npts_in is None:
711	npts_in = self._high_extrapolation_npts
712	_npts = len(self._data.x)
713	q_start = self._data.x[min(_npts, _npts-npts_in)]
714
715	if q_start >= q_end:
716	return numpy.zeros(0), numpy.zeros(0)
717
718	return self._get_extrapolated_data(\
719	model=self._high_extrapolation_function,
720	npts=npts,
721	q_start=q_start, q_end=q_end)
722
723	def set_extrapolation(self, range, npts=4, function=None, power=None):
724	"""
725	Set the extrapolation parameters for the high or low Q-range.
726	Note that this does not turn extrapolation on or off.
727
728	:param range: a keyword set the type of extrapolation . type string
729	:param npts: the numbers of q points of data to consider
730	for extrapolation
731	:param function: a keyword to select the function to use
732	for extrapolation.
733	of type string.
734	:param power: an power to apply power_low function
735
736	"""
737	range = range.lower()
738	if range not in ['high', 'low']:
739	raise ValueError, "Extrapolation range should be 'high' or 'low'"
740	function = function.lower()
741	if function not in ['power_law', 'guinier']:
742	msg = "Extrapolation function should be 'guinier' or 'power_law'"
743	raise ValueError, msg
744
745	if range == 'high':
746	if function != 'power_law':
747	msg = "Extrapolation only allows a power law at high Q"
748	raise ValueError, msg
749	self._high_extrapolation_npts = npts
750	self._high_extrapolation_power = power
751	self._high_extrapolation_power_fitted = power
752	else:
753	if function == 'power_law':
754	self._low_extrapolation_function = PowerLaw()
755	else:
756	self._low_extrapolation_function = Guinier()
757	self._low_extrapolation_npts = npts
758	self._low_extrapolation_power = power
759	self._low_extrapolation_power_fitted = power
760
761	def get_qstar(self, extrapolation=None):
762	"""
763	Compute the invariant of the local copy of data.
764
765	:param extrapolation: string to apply optional extrapolation
766
767	:return q_star: invariant of the data within data's q range
768
769	:warning: When using setting data to Data1D ,
770	the user is responsible of
771	checking that the scale and the background are
772	properly apply to the data
773
774	"""
775	self._qstar = self._get_qstar(self._data)
776	self._qstar_err = self._get_qstar_uncertainty(self._data)
777
778	if extrapolation is None:
779	return self._qstar
780
781	# Compute invariant plus invariant of extrapolated data
782	extrapolation = extrapolation.lower()
783	if extrapolation == "low":
784	qs_low, dqs_low = self.get_qstar_low()
785	qs_hi, dqs_hi = 0, 0
786
787	elif extrapolation == "high":
788	qs_low, dqs_low = 0, 0
789	qs_hi, dqs_hi = self.get_qstar_high()
790
791	elif extrapolation == "both":
792	qs_low, dqs_low = self.get_qstar_low()
793	qs_hi, dqs_hi = self.get_qstar_high()
794
795	self._qstar += qs_low + qs_hi
796	self._qstar_err = math.sqrt(self._qstar_err*self._qstar_err \
797	+ dqs_lowdqs_low + dqs_hidqs_hi)
798
799	return self._qstar
800
801	def get_surface(self, contrast, porod_const, extrapolation=None):
802	"""
803	Compute the specific surface from the data.
804
805	Implementation::
806
807	V = self.get_volume_fraction(contrast, extrapolation)
808
809	Compute the surface given by:
810	surface = (2pi V(1- V)*porod_const)/ q_star
811
812	:param contrast: contrast value to compute the volume
813	:param porod_const: Porod constant to compute the surface
814	:param extrapolation: string to apply optional extrapolation
815
816	:return: specific surface
817	"""
818	# Compute the volume
819	volume = self.get_volume_fraction(contrast, extrapolation)
820	return 2 * math.pi * volume (1 - volume) \
821	float(porod_const)/self._qstar
822
823	def get_volume_fraction(self, contrast, extrapolation=None):
824	"""
825	Compute volume fraction is deduced as follow: ::
826
827	q_star = 2(picontrast)*2 volume( 1- volume)
828	for k = 10^(-8)q_star/(2(pi\|contrast\|)*2)
829	we get 2 values of volume:
830	with 1 - 4 * k >= 0
831	volume1 = (1- sqrt(1- 4*k))/2
832	volume2 = (1+ sqrt(1- 4*k))/2
833
834	q_star: the invariant value included extrapolation is applied
835	unit 1/A^(3)*1/cm
836	q_star = self.get_qstar()
837
838	the result returned will be 0 <= volume <= 1
839
840	:param contrast: contrast value provides by the user of type float.
841	contrast unit is 1/A^(2)= 10^(16)cm^(2)
842	:param extrapolation: string to apply optional extrapolation
843
844	:return: volume fraction
845
846	:note: volume fraction must have no unit
847	"""
848	if contrast <= 0:
849	raise ValueError, "The contrast parameter must be greater than zero"
850
851	# Make sure Q star is up to date
852	self.get_qstar(extrapolation)
853
854	if self._qstar <= 0:
855	msg = "Invalid invariant: Invariant Q* must be greater than zero"
856	raise RuntimeError, msg
857
858	# Compute intermediate constant
859	k = 1.e-8 * self._qstar/(2 * (math.pi * math.fabs(float(contrast)))**2)
860	# Check discriminant value
861	discrim = 1 - 4 * k
862
863	# Compute volume fraction
864	if discrim < 0:
865	msg = "Could not compute the volume fraction: negative discriminant"
866	raise RuntimeError, msg
867	elif discrim == 0:
868	return 1/2
869	else:
870	volume1 = 0.5 * (1 - math.sqrt(discrim))
871	volume2 = 0.5 * (1 + math.sqrt(discrim))
872
873	if 0 <= volume1 and volume1 <= 1:
874	return volume1
875	elif 0 <= volume2 and volume2 <= 1:
876	return volume2
877	msg = "Could not compute the volume fraction: inconsistent results"
878	raise RuntimeError, msg
879
880	def get_qstar_with_error(self, extrapolation=None):
881	"""
882	Compute the invariant uncertainty.
883	This uncertainty computation depends on whether or not the data is
884	smeared.
885
886	:param extrapolation: string to apply optional extrapolation
887
888	:return: invariant, the invariant uncertainty
889	"""
890	self.get_qstar(extrapolation)
891	return self._qstar, self._qstar_err
892
893	def get_volume_fraction_with_error(self, contrast, extrapolation=None):
894	"""
895	Compute uncertainty on volume value as well as the volume fraction
896	This uncertainty is given by the following equation: ::
897
898	dV = 0.5 * (4k dq_star) /(2* math.sqrt(1-k* q_star))
899
900	for k = 10^(-8)q_star/(2(pi\|contrast\|)*2)
901
902	q_star: the invariant value including extrapolated value if existing
903	dq_star: the invariant uncertainty
904	dV: the volume uncertainty
905
906	The uncertainty will be set to -1 if it can't be computed.
907
908	:param contrast: contrast value
909	:param extrapolation: string to apply optional extrapolation
910
911	:return: V, dV = volume fraction, error on volume fraction
912	"""
913	volume = self.get_volume_fraction(contrast, extrapolation)
914
915	# Compute error
916	k = 1.e-8 * self._qstar /(2 * (math.pi* math.fabs(float(contrast)))**2)
917	# Check value inside the sqrt function
918	value = 1 - k * self._qstar
919	if (value) <= 0:
920	uncertainty = -1
921	# Compute uncertainty
922	uncertainty = math.fabs((0.5 * 4 * k * \
923	self._qstar_err)/(2 * math.sqrt(1 - k * self._qstar)))
924
925	return volume, uncertainty
926
927	def get_surface_with_error(self, contrast, porod_const, extrapolation=None):
928	"""
929	Compute uncertainty of the surface value as well as the surface value.
930	The uncertainty is given as follow: ::
931
932	dS = porod_const 2pi[( dV -2VdV)/q_star
933	+ dq_star(v-v**2)
934
935	q_star: the invariant value
936	dq_star: the invariant uncertainty
937	V: the volume fraction value
938	dV: the volume uncertainty
939
940	:param contrast: contrast value
941	:param porod_const: porod constant value
942	:param extrapolation: string to apply optional extrapolation
943
944	:return S, dS: the surface, with its uncertainty
945	"""
946	# We get the volume fraction, with error
947	# get_volume_fraction_with_error calls get_volume_fraction
948	# get_volume_fraction calls get_qstar
949	# which computes Qstar and dQstar
950	v, dv = self.get_volume_fraction_with_error(contrast, extrapolation)
951
952	s = self.get_surface(contrast=contrast, porod_const=porod_const,
953	extrapolation=extrapolation)
954	ds = porod_const * 2 * math.pi * (( dv - 2 * v * dv)/ self._qstar\
955	+ self._qstar_err * ( v - v**2))
956
957	return s, ds

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SasView

source: sasview/sansinvariant/invariant.py @ ad4053a

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