Source code for sasmodels.resolution2d

#This software was developed by the University of Tennessee as part of the
#Distributed Data Analysis of Neutron Scattering Experiments (DANSE)
#project funded by the US National Science Foundation.
#See the license text in license.txt
from __future__ import division

import numpy as np  # type: ignore
from numpy import pi, cos, sin, sqrt  # type: ignore

from . import resolution
from .resolution import Resolution

## Singular point
SIGMA_ZERO = 1.0e-010
## Limit of how many sigmas to be covered for the Gaussian smearing
# default: 2.5 to cover 98.7% of Gaussian
NSIGMA = 3.0
## Defaults
NR = {'xhigh':10, 'high':5, 'med':5, 'low':3}
NPHI = {'xhigh':20, 'high':12, 'med':6, 'low':4}

## Defaults
N_SLIT_PERP = {'xhigh':1000, 'high':500, 'med':200, 'low':50}
N_SLIT_PERP_DOC = ", ".join("%s=%d"%(name, value)
                            for value, name in
                            sorted((2*v+1, k) for k, v in N_SLIT_PERP.items()))

[docs]class Pinhole2D(Resolution): """ Gaussian Q smearing class for SAS 2d data """ def __init__(self, data=None, index=None, nsigma=NSIGMA, accuracy='Low', coords='polar'): """ Assumption: equally spaced bins in dq_r, dq_phi space. :param data: 2d data used to set the smearing parameters :param index: 1d array with len(data) to define the range of the calculation: elements are given as True or False :param nr: number of bins in dq_r-axis :param nphi: number of bins in dq_phi-axis :param coord: coordinates [string], 'polar' or 'cartesian' """ ## Accuracy: Higher stands for more sampling points in both directions ## of r and phi. ## number of bins in r axis for over-sampling = NR[accuracy.lower()] ## number of bins in phi axis for over-sampling self.nphi = NPHI[accuracy.lower()] ## maximum nsigmas self.nsigma = nsigma self.coords = coords self._init_data(data, index) def _init_data(self, data, index): """ Get qx_data, qy_data, dqx_data,dqy_data, and calculate phi_data=arctan(qx_data/qy_data) """ # TODO: maybe don't need to hold copy of qx,qy,dqx,dqy,data,index # just need q_calc and weights = data self.index = index if index is not None else slice(None) self.qx_data = data.qx_data[self.index] self.qy_data = data.qy_data[self.index] self.q_data = data.q_data[self.index] dqx = getattr(data, 'dqx_data', None) dqy = getattr(data, 'dqy_data', None) if dqx is not None and dqy is not None: # Here dqx and dqy mean dq_parr and dq_perp self.dqx_data = dqx[self.index] self.dqy_data = dqy[self.index] ## Remove singular points if exists self.dqx_data[self.dqx_data < SIGMA_ZERO] = SIGMA_ZERO self.dqy_data[self.dqy_data < SIGMA_ZERO] = SIGMA_ZERO qx_calc, qy_calc, weights = self._calc_res() self.q_calc = [qx_calc, qy_calc] self.q_calc_weights = weights else: # No resolution information self.dqx_data = self.dqy_data = None self.q_calc = [self.qx_data, self.qy_data] self.q_calc_weights = None #self.phi_data = np.arctan(self.qx_data / self.qy_data) def _calc_res(self): """ Over sampling of r_nbins times phi_nbins, calculate Gaussian weights, then find smeared intensity """ nr, nphi =, self.nphi # Total number of bins = # of bins nbins = nr * nphi # Number of bins in the dqr direction (polar coordinate of dqx and dqy) bin_size = self.nsigma / nr # in dq_r-direction times # of bins in dq_phi-direction # data length in the range of self.index nq = len(self.qx_data) # Mean values of dqr at each bins # starting from the half of bin size r = bin_size / 2.0 + np.arange(nr) * bin_size # mean values of qphi at each bines phi = np.arange(nphi) dphi = phi * 2.0 * pi / nphi dphi = dphi.repeat(nr) ## Transform to polar coordinate, # and set dphi at each data points ; 1d array dphi = dphi.repeat(nq) q_phi = self.qy_data / self.qx_data # Starting angle is different between polar # and cartesian coordinates. #if self.coords != 'polar': # dphi += np.arctan( q_phi * self.dqx_data/ \ # self.dqy_data).repeat(nbins).reshape(nq,\ # nbins).transpose().flatten() # The angle (phi) of the original q point q_phi = np.arctan(q_phi).repeat(nbins)\ .reshape([nq, nbins]).transpose().flatten() ## Find Gaussian weight for each dq bins: The weight depends only # on r-direction (The integration may not need) weight_res = (np.exp(-0.5 * (r - bin_size / 2.0)**2) - np.exp(-0.5 * (r + bin_size / 2.0)**2)) # No needs of normalization here. #weight_res /= np.sum(weight_res) weight_res = weight_res.repeat(nphi).reshape(nr, nphi) weight_res = weight_res.transpose().flatten() ## Set dr for all dq bins for averaging dr = r.repeat(nphi).reshape(nr, nphi).transpose().flatten() ## Set dqr for all data points dqx = np.outer(dr, self.dqx_data).flatten() dqy = np.outer(dr, self.dqy_data).flatten() qx = self.qx_data.repeat(nbins)\ .reshape(nq, nbins).transpose().flatten() qy = self.qy_data.repeat(nbins)\ .reshape(nq, nbins).transpose().flatten() # The polar needs rotation by -q_phi if self.coords == 'polar': q_r = sqrt(qx**2 + qy**2) qx_res = ((dqx*cos(dphi) + q_r) * cos(-q_phi) + dqy*sin(dphi) * sin(-q_phi)) qy_res = (-(dqx*cos(dphi) + q_r) * sin(-q_phi) + dqy*sin(dphi) * cos(-q_phi)) else: qx_res = qx + dqx*cos(dphi) qy_res = qy + dqy*sin(dphi) return qx_res, qy_res, weight_res
[docs] def apply(self, theory): if self.q_calc_weights is not None: # TODO: interpolate rather than recomputing all the different qx,qy # Resolution needs to be applied nq, nbins = len(self.qx_data), * self.nphi ## Reshape into 2d array to use np weighted averaging theory = np.reshape(theory, (nbins, nq)) ## Averaging with Gaussian weighting: normalization included. value = np.average(theory, axis=0, weights=self.q_calc_weights) ## Return the smeared values in the range of self.index return value else: return theory
[docs]class Slit2D(Resolution): """ Slit aperture with resolution function on an oriented sample. *q* points at which the data is measured. *qx_width* slit width in qx *qy_width* slit height in qy; current implementation requires a fixed qy_width for all q points. *q_calc* is the list of q points to calculate, or None if this should be estimated from the *q* and *qx_width*. *accuracy* determines the number of *qy* points to compute for each *q*. The values are stored in sasmodels.resolution2d.N_SLIT_PERP. The default values are: %s """ __doc__ = __doc__%N_SLIT_PERP_DOC def __init__(self, q, qx_width, qy_width=0., q_calc=None, accuracy='low'): # Remember what q and width was used even though we won't need them # after the weight matrix is constructed self.q, self.qx_width, self.qy_width = q, qx_width, qy_width # Allow independent resolution on each qx point even though it is not # needed in practice. Set qy_width to the maximum qy width. if np.isscalar(qx_width): qx_width = np.ones(len(q))*qx_width else: qx_width = np.asarray(qx_width) if not np.isscalar(qy_width): qy_width = np.max(qy_width) # Build grid of qx, qy points if q_calc is not None: qx_calc = np.sort(q_calc) else: qx_calc = resolution.pinhole_extend_q(q, qx_width, nsigma=3) qy_min, qy_max = np.log10(np.min(q)), np.log10(qy_width) qy_calc = np.logspace(qy_min, qy_max, N_SLIT_PERP[accuracy]) qy_calc = np.hstack((-qy_calc[::-1], 0, qy_calc)) self.q_calc = [v.flatten() for v in np.meshgrid(qx_calc, qy_calc)] self.qx_calc, self.qy_calc = qx_calc, qy_calc self.nx, self.ny = len(qx_calc), len(qy_calc) self.dy = 2*qy_width/self.ny # Build weight matrix for resolution integration if np.any(qx_width > 0): self.weights = resolution.pinhole_resolution( qx_calc, q, np.maximum(qx_width, resolution.MINIMUM_RESOLUTION)) elif len(qx_calc) == len(q) and np.all(qx_calc == q): self.weights = None else: raise ValueError("Slit2D fails with q_calc != q")
[docs] def apply(self, theory): Iq = np.trapz(theory.reshape(self.ny, self.nx), axis=0, x=self.qy_calc) if self.weights is not None: Iq = resolution.apply_resolution_matrix(self.weights, Iq) return Iq