source: sasmodels/sasmodels/resolution2d.py @ 40a87fa

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Last change on this file since 40a87fa was 40a87fa, checked in by Paul Kienzle <pkienzle@…>, 8 years ago

lint and latex cleanup

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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"""
7from __future__ import division
8
9import numpy as np  # type: ignore
10from numpy import pi, cos, sin, sqrt  # type: ignore
11
12from . import resolution
13from .resolution import Resolution
14
15## Singular point
16SIGMA_ZERO = 1.0e-010
17## Limit of how many sigmas to be covered for the Gaussian smearing
18# default: 2.5 to cover 98.7% of Gaussian
19NSIGMA = 3.0
20## Defaults
21NR = {'xhigh':10, 'high':5, 'med':5, 'low':3}
22NPHI = {'xhigh':20, 'high':12, 'med':6, 'low':4}
23
24## Defaults
25N_SLIT_PERP = {'xhigh':1000, 'high':500, 'med':200, 'low':50}
26N_SLIT_PERP_DOC = ", ".join("%s=%d"%(name, value)
27                            for value, name in
28                            sorted((2*v+1, k) for k, v in N_SLIT_PERP.items()))
29
30class Pinhole2D(Resolution):
31    """
32    Gaussian Q smearing class for SAS 2d data
33    """
34
35    def __init__(self, data=None, index=None,
36                 nsigma=NSIGMA, accuracy='Low', coords='polar'):
37        """
38        Assumption: equally spaced bins in dq_r, dq_phi space.
39
40        :param data: 2d data used to set the smearing parameters
41        :param index: 1d array with len(data) to define the range
42         of the calculation: elements are given as True or False
43        :param nr: number of bins in dq_r-axis
44        :param nphi: number of bins in dq_phi-axis
45        :param coord: coordinates [string], 'polar' or 'cartesian'
46        """
47        ## Accuracy: Higher stands for more sampling points in both directions
48        ## of r and phi.
49        ## number of bins in r axis for over-sampling
50        self.nr = NR[accuracy.lower()]
51        ## number of bins in phi axis for over-sampling
52        self.nphi = NPHI[accuracy.lower()]
53        ## maximum nsigmas
54        self.nsigma = nsigma
55        self.coords = coords
56        self._init_data(data, index)
57
58    def _init_data(self, data, index):
59        """
60        Get qx_data, qy_data, dqx_data,dqy_data,
61        and calculate phi_data=arctan(qx_data/qy_data)
62        """
63        # TODO: maybe don't need to hold copy of qx,qy,dqx,dqy,data,index
64        # just need q_calc and weights
65        self.data = data
66        self.index = index
67
68        self.qx_data = data.qx_data[index]
69        self.qy_data = data.qy_data[index]
70        self.q_data = data.q_data[index]
71
72        dqx = getattr(data, 'dqx_data', None)
73        dqy = getattr(data, 'dqy_data', None)
74        if dqx is not None and dqy is not None:
75            # Here dqx and dqy mean dq_parr and dq_perp
76            self.dqx_data = dqx[index]
77            self.dqy_data = dqy[index]
78            ## Remove singular points if exists
79            self.dqx_data[self.dqx_data < SIGMA_ZERO] = SIGMA_ZERO
80            self.dqy_data[self.dqy_data < SIGMA_ZERO] = SIGMA_ZERO
81            qx_calc, qy_calc, weights = self._calc_res()
82            self.q_calc = [qx_calc, qy_calc]
83            self.q_calc_weights = weights
84        else:
85            # No resolution information
86            self.dqx_data = self.dqy_data = None
87            self.q_calc = [self.qx_data, self.qy_data]
88            self.q_calc_weights = None
89
90        #self.phi_data = np.arctan(self.qx_data / self.qy_data)
91
92    def _calc_res(self):
93        """
94        Over sampling of r_nbins times phi_nbins, calculate Gaussian weights,
95        then find smeared intensity
96        """
97        nr, nphi = self.nr, self.nphi
98        # Total number of bins = # of bins
99        nbins = nr * nphi
100        # Number of bins in the dqr direction (polar coordinate of dqx and dqy)
101        bin_size = self.nsigma / nr
102        # in dq_r-direction times # of bins in dq_phi-direction
103        # data length in the range of self.index
104        nq = len(self.qx_data)
105
106        # Mean values of dqr at each bins
107        # starting from the half of bin size
108        r = bin_size / 2.0 + np.arange(nr) * bin_size
109        # mean values of qphi at each bines
110        phi = np.arange(nphi)
111        dphi = phi * 2.0 * pi / nphi
112        dphi = dphi.repeat(nr)
113
114        ## Transform to polar coordinate,
115        #  and set dphi at each data points ; 1d array
116        dphi = dphi.repeat(nq)
117        q_phi = self.qy_data / self.qx_data
118
119        # Starting angle is different between polar
120        #  and cartesian coordinates.
121        #if self.coords != 'polar':
122        #    dphi += np.arctan( q_phi * self.dqx_data/ \
123        #                  self.dqy_data).repeat(nbins).reshape(nq,\
124        #                                nbins).transpose().flatten()
125
126        # The angle (phi) of the original q point
127        q_phi = np.arctan(q_phi).repeat(nbins)\
128            .reshape(nq, nbins).transpose().flatten()
129        ## Find Gaussian weight for each dq bins: The weight depends only
130        #  on r-direction (The integration may not need)
131        weight_res = (np.exp(-0.5 * (r - bin_size / 2.0)**2)  -
132                      np.exp(-0.5 * (r + bin_size / 2.0)**2))
133        # No needs of normalization here.
134        #weight_res /= np.sum(weight_res)
135        weight_res = weight_res.repeat(nphi).reshape(nr, nphi)
136        weight_res = weight_res.transpose().flatten()
137
138        ## Set dr for all dq bins for averaging
139        dr = r.repeat(nphi).reshape(nr, nphi).transpose().flatten()
140        ## Set dqr for all data points
141        dqx = np.outer(dr, self.dqx_data).flatten()
142        dqy = np.outer(dr, self.dqy_data).flatten()
143
144        qx = self.qx_data.repeat(nbins)\
145            .reshape(nq, nbins).transpose().flatten()
146        qy = self.qy_data.repeat(nbins)\
147            .reshape(nq, nbins).transpose().flatten()
148
149        # The polar needs rotation by -q_phi
150        if self.coords == 'polar':
151            q_r = sqrt(qx**2 + qy**2)
152            qx_res = ((dqx*cos(dphi) + q_r) * cos(-q_phi)
153                      + dqy*sin(dphi) * sin(-q_phi))
154            qy_res = (-(dqx*cos(dphi) + q_r) * sin(-q_phi)
155                      + dqy*sin(dphi) * cos(-q_phi))
156        else:
157            qx_res = qx + dqx*cos(dphi)
158            qy_res = qy + dqy*sin(dphi)
159
160
161        return qx_res, qy_res, weight_res
162
163    def apply(self, theory):
164        if self.q_calc_weights is not None:
165            # TODO: interpolate rather than recomputing all the different qx,qy
166            # Resolution needs to be applied
167            nq, nbins = len(self.qx_data), self.nr * self.nphi
168            ## Reshape into 2d array to use np weighted averaging
169            theory = np.reshape(theory, (nbins, nq))
170            ## Averaging with Gaussian weighting: normalization included.
171            value = np.average(theory, axis=0, weights=self.q_calc_weights)
172            ## Return the smeared values in the range of self.index
173            return value
174        else:
175            return theory
176
177
178class Slit2D(Resolution):
179    """
180    Slit aperture with resolution function on an oriented sample.
181
182    *q* points at which the data is measured.
183
184    *qx_width* slit width in qx
185
186    *qy_width* slit height in qy; current implementation requires a fixed
187    qy_width for all q points.
188
189    *q_calc* is the list of q points to calculate, or None if this
190    should be estimated from the *q* and *qx_width*.
191
192    *accuracy* determines the number of *qy* points to compute for each *q*.
193    The values are stored in sasmodels.resolution2d.N_SLIT_PERP.  The default
194    values are: %s
195    """
196    __doc__ = __doc__%N_SLIT_PERP_DOC
197    def __init__(self, q, qx_width, qy_width=0., q_calc=None, accuracy='low'):
198        # Remember what q and width was used even though we won't need them
199        # after the weight matrix is constructed
200        self.q, self.qx_width, self.qy_width = q, qx_width, qy_width
201
202        # Allow independent resolution on each qx point even though it is not
203        # needed in practice.  Set qy_width to the maximum qy width.
204        if np.isscalar(qx_width):
205            qx_width = np.ones(len(q))*qx_width
206        else:
207            qx_width = np.asarray(qx_width)
208        if not np.isscalar(qy_width):
209            qy_width = np.max(qy_width)
210
211        # Build grid of qx, qy points
212        if q_calc is not None:
213            qx_calc = np.sort(q_calc)
214        else:
215            qx_calc = resolution.pinhole_extend_q(q, qx_width, nsigma=3)
216        qy_min, qy_max = np.log10(np.min(q)), np.log10(qy_width)
217        qy_calc = np.logspace(qy_min, qy_max, N_SLIT_PERP[accuracy])
218        qy_calc = np.hstack((-qy_calc[::-1], 0, qy_calc))
219        self.q_calc = [v.flatten() for v in np.meshgrid(qx_calc, qy_calc)]
220        self.qx_calc, self.qy_calc = qx_calc, qy_calc
221        self.nx, self.ny = len(qx_calc), len(qy_calc)
222        self.dy = 2*qy_width/self.ny
223
224        # Build weight matrix for resolution integration
225        if np.any(qx_width > 0):
226            self.weights = resolution.pinhole_resolution(qx_calc, q,
227                    np.maximum(qx_width, resolution.MINIMUM_RESOLUTION))
228        elif len(qx_calc) == len(q) and np.all(qx_calc == q):
229            self.weights = None
230        else:
231            raise ValueError("Slit2D fails with q_calc != q")
232
233    def apply(self, theory):
234        Iq = np.trapz(theory.reshape(self.ny, self.nx), axis=0, x=self.qy_calc)
235        if self.weights is not None:
236            Iq = resolution.apply_resolution_matrix(self.weights, Iq)
237        return Iq
238
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