Changes in / [1896dff:ae32bb8] in sasmodels


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  • sasmodels/sesans.py

    rb397165 r94d13f1  
    1414import numpy as np  # type: ignore 
    1515from numpy import pi, exp  # type: ignore 
    16 from scipy.special import jv as besselj 
    17 #import direct_model.DataMixin as model 
    18          
    19 def make_q(q_max, Rmax): 
    20     r""" 
    21     Return a $q$ vector suitable for SESANS covering from $2\pi/ (10 R_{\max})$ 
    22     to $q_max$. This is the integration range of the Hankel transform; bigger range and  
    23     more points makes a better numerical integration. 
    24     Smaller q_min will increase reliable spin echo length range.  
    25     Rmax is the "radius" of the largest expected object and can be set elsewhere. 
    26     q_max is determined by the acceptance angle of the SESANS instrument. 
     16from scipy.special import j0 
     17 
     18class SesansTransform(object): 
    2719    """ 
    28     from sas.sascalc.data_util.nxsunit import Converter 
     20    Spin-Echo SANS transform calculator.  Similar to a resolution function, 
     21    the SesansTransform object takes I(q) for the set of *q_calc* values and 
     22    produces a transformed dataset 
    2923 
    30     q_min = dq = 0.1 * 2*pi / Rmax 
    31     return np.arange(q_min, 
    32                      Converter(q_max[1])(q_max[0], 
    33                                          units="1/A"), 
    34                      dq) 
    35      
    36 def make_all_q(data): 
     24    *SElength* (A) is the set of spin-echo lengths in the measured data. 
     25 
     26    *zaccept* (1/A) is the maximum acceptance of scattering vector in the spin 
     27    echo encoding dimension (for ToF: Q of min(R) and max(lam)). 
     28 
     29    *Rmax* (A) is the maximum size sensitivity; larger radius requires more 
     30    computation time. 
    3731    """ 
    38     Return a $q$ vector suitable for calculating the total scattering cross section for 
    39     calculating the effect of finite acceptance angles on Time of Flight SESANS instruments. 
    40     If no acceptance is given, or unwanted (set "unwanted" flag in paramfile), no all_q vector is needed. 
    41     If the instrument has a rectangular acceptance, 2 all_q vectors are needed. 
    42     If the instrument has a circular acceptance, 1 all_q vector is needed 
    43      
    44     """ 
    45     if not data.has_no_finite_acceptance: 
    46         return [] 
    47     elif data.has_yz_acceptance(data): 
    48         # compute qx, qy 
    49         Qx, Qy = np.meshgrid(qx, qy) 
    50         return [Qx, Qy] 
    51     else: 
    52         # else only need q 
    53         # data.has_z_acceptance 
    54         return [q] 
     32    #: SElength from the data in the original data units; not used by transform 
     33    #: but the GUI uses it, so make sure that it is present. 
     34    q = None  # type: np.ndarray 
    5535 
    56 def transform(data, q_calc, Iq_calc, qmono, Iq_mono): 
    57     """ 
    58     Decides which transform type is to be used, based on the experiment data file contents (header) 
    59     (2016-03-19: currently controlled from parameters script) 
    60     nqmono is the number of q vectors to be used for the detector integration 
    61     """ 
    62     nqmono = len(qmono) 
    63     if nqmono == 0: 
    64         result = call_hankel(data, q_calc, Iq_calc) 
    65     elif nqmono == 1: 
    66         q = qmono[0] 
    67         result = call_HankelAccept(data, q_calc, Iq_calc, q, Iq_mono) 
    68     else: 
    69         Qx, Qy = [qmono[0], qmono[1]] 
    70         Qx = np.reshape(Qx, nqx, nqy) 
    71         Qy = np.reshape(Qy, nqx, nqy) 
    72         Iq_mono = np.reshape(Iq_mono, nqx, nqy) 
    73         qx = Qx[0, :] 
    74         qy = Qy[:, 0] 
    75         result = call_Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono) 
     36    #: q values to calculate when computing transform 
     37    q_calc = None  # type: np.ndarray 
    7638 
    77     return result 
     39    # transform arrays 
     40    _H = None  # type: np.ndarray 
     41    _H0 = None # type: np.ndarray 
    7842 
    79 def call_hankel(data, q_calc, Iq_calc): 
    80     return hankel((data.x, data.x_unit), 
    81                   (data.lam, data.lam_unit), 
    82                   (data.sample.thickness, 
    83                    data.sample.thickness_unit), 
    84                   q_calc, Iq_calc) 
    85    
    86 def call_HankelAccept(data, q_calc, Iq_calc, q_mono, Iq_mono): 
    87     return hankel(data.x, data.lam * 1e-9, 
    88                   data.sample.thickness / 10, 
    89                   q_calc, Iq_calc) 
    90                    
    91 def call_Cosine2D(data, q_calc, Iq_calc, qx, qy, Iq_mono): 
    92     return hankel(data.x, data.y, data.lam * 1e-9, 
    93                   data.sample.thickness / 10, 
    94                   q_calc, Iq_calc) 
    95                          
    96 def TotalScatter(model, parameters):  #Work in progress!! 
    97 #    Calls a model with existing model parameters already in place, then integrate the product of q and I(q) from 0 to (4*pi/lambda) 
    98     allq = np.linspace(0,4*pi/wavelength,1000) 
    99     allIq = 1 
    100     integral = allq*allIq 
    101      
     43    def __init__(self, z, SElength, zaccept, Rmax): 
     44        # type: (np.ndarray, float, float) -> None 
     45        #import logging; logging.info("creating SESANS transform") 
     46        self.q = z 
     47        self._set_hankel(SElength, zaccept, Rmax) 
    10248 
     49    def apply(self, Iq): 
     50        # tye: (np.ndarray) -> np.ndarray 
     51        G0 = np.dot(self._H0, Iq) 
     52        G = np.dot(self._H.T, Iq) 
     53        P = G - G0 
     54        return P 
    10355 
    104 def Cosine2D(wavelength, magfield, thickness, qy, qz, Iqy, Iqz, modelname): #Work in progress!! Needs to call model still 
    105 #============================================================================== 
    106 #     2D Cosine Transform if "wavelength" is a vector 
    107 #============================================================================== 
    108 #allq is the q-space needed to create the total scattering cross-section 
     56    def _set_hankel(self, SElength, zaccept, Rmax): 
     57        # type: (np.ndarray, float, float) -> None 
     58        # Force float32 arrays, otherwise run into memory problems on some machines 
     59        SElength = np.asarray(SElength, dtype='float32') 
    10960 
    110     Gprime = np.zeros_like(wavelength, 'd') 
    111     s = np.zeros_like(wavelength, 'd') 
    112     sd = np.zeros_like(wavelength, 'd') 
    113     Gprime = np.zeros_like(wavelength, 'd') 
    114     f = np.zeros_like(wavelength, 'd') 
    115     for i, wavelength_i in enumerate(wavelength): 
    116         z = magfield*wavelength_i 
    117         allq=np.linspace() #for calculating the Q-range of the  scattering power integral 
    118         allIq=np.linspace()  # This is the model applied to the allq q-space. Needs to refference the model somehow 
    119         alldq = (allq[1]-allq[0])*1e10 
    120         sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) 
    121         s[i]=1-exp(-sigma) 
    122         for j, Iqy_j, qy_j in enumerate(qy): 
    123             for k, Iqz_k, qz_k in enumerate(qz): 
    124                 Iq = np.sqrt(Iqy_j^2+Iqz_k^2) 
    125                 q = np.sqrt(qy_j^2 + qz_k^2) 
    126                 Gintegral = Iq*cos(z*Qz_k) 
    127                 Gprime[i] += Gintegral 
    128 #                sigma = wavelength^2*thickness/2/pi* allq[i]*allIq[i] 
    129 #                s[i] += 1-exp(Totalscatter(modelname)*thickness) 
    130 #                For now, work with standard 2-phase scatter 
     61        #Rmax = #value in text box somewhere in FitPage? 
     62        q_max = 2*pi / (SElength[1] - SElength[0]) 
     63        q_min = 0.1 * 2*pi / (np.size(SElength) * SElength[-1]) 
     64        q = np.arange(q_min, q_max, q_min, dtype='float32') 
     65        dq = q_min 
    13166 
     67        H0 = np.float32(dq/(2*pi)) * q 
    13268 
    133                 sd[i] += Iq 
    134         f[i] = 1-s[i]+sd[i] 
    135         P[i] = (1-sd[i]/f[i])+1/f[i]*Gprime[i] 
     69        repq = np.tile(q, (SElength.size, 1)).T 
     70        repSE = np.tile(SElength, (q.size, 1)) 
     71        H = np.float32(dq/(2*pi)) * j0(repSE*repq) * repq 
    13672 
    137  
    138  
    139  
    140 def HankelAccept(wavelength, magfield, thickness, q, Iq, theta, modelname): 
    141 #============================================================================== 
    142 #     HankelTransform with fixed circular acceptance angle (circular aperture) for Time of Flight SESANS 
    143 #============================================================================== 
    144 #acceptq is the q-space needed to create limited acceptance effect 
    145     SElength= wavelength*magfield 
    146     G = np.zeros_like(SElength, 'd') 
    147     threshold=2*pi*theta/wavelength 
    148     for i, SElength_i in enumerate(SElength): 
    149         allq=np.linspace() #for calculating the Q-range of the  scattering power integral 
    150         allIq=np.linspace()  # This is the model applied to the allq q-space. Needs to refference the model somehow 
    151         alldq = (allq[1]-allq[0])*1e10 
    152         sigma[i]=wavelength[i]^2*thickness/2/pi*np.sum(allIq*allq*alldq) 
    153         s[i]=1-exp(-sigma) 
    154  
    155         dq = (q[1]-q[0])*1e10 
    156         a = (x<threshold) 
    157         acceptq = a*q 
    158         acceptIq = a*Iq 
    159  
    160         G[i] = np.sum(besselj(0, acceptq*SElength_i)*acceptIq*acceptq*dq) 
    161  
    162 #        G[i]=np.sum(integral) 
    163  
    164     G *= dq*1e10*2*pi 
    165  
    166     P = exp(thickness*wavelength**2/(4*pi**2)*(G-G[0])) 
    167      
    168 def hankel(SElength, wavelength, thickness, q, Iq): 
    169     r""" 
    170     Compute the expected SESANS polarization for a given SANS pattern. 
    171  
    172     Uses the hankel transform followed by the exponential.  The values for *zz* 
    173     (or spin echo length, or delta), wavelength and sample thickness should 
    174     come from the dataset.  $q$ should be chosen such that the oscillations 
    175     in $I(q)$ are well sampled (e.g., $5 \cdot 2 \pi/d_{\max}$). 
    176  
    177     *SElength* [A] is the set of $z$ points at which to compute the 
    178     Hankel transform 
    179  
    180     *wavelength* [m]  is the wavelength of each individual point *zz* 
    181  
    182     *thickness* [cm] is the sample thickness. 
    183  
    184     *q* [A$^{-1}$] is the set of $q$ points at which the model has been 
    185     computed. These should be equally spaced. 
    186  
    187     *I* [cm$^{-1}$] is the value of the SANS model at *q* 
    188     """ 
    189  
    190     from sas.sascalc.data_util.nxsunit import Converter 
    191     wavelength = Converter(wavelength[1])(wavelength[0],"A") 
    192     thickness = Converter(thickness[1])(thickness[0],"A") 
    193     Iq = Converter("1/cm")(Iq,"1/A") # All models default to inverse centimeters 
    194     SElength = Converter(SElength[1])(SElength[0],"A") 
    195  
    196     G = np.zeros_like(SElength, 'd') 
    197 #============================================================================== 
    198 #     Hankel Transform method if "wavelength" is a scalar; mono-chromatic SESANS 
    199 #============================================================================== 
    200     for i, SElength_i in enumerate(SElength): 
    201         integral = besselj(0, q*SElength_i)*Iq*q 
    202         G[i] = np.sum(integral) 
    203     G0 = np.sum(Iq*q) 
    204  
    205     # [m^-1] step size in q, needed for integration 
    206     dq = (q[1]-q[0]) 
    207  
    208     # integration step, convert q into [m**-1] and 2 pi circle integration 
    209     G *= dq*2*pi 
    210     G0 = np.sum(Iq*q)*dq*2*np.pi 
    211  
    212     P = exp(thickness*wavelength**2/(4*pi**2)*(G-G0)) 
    213  
    214     return P 
     73        self.q_calc = q 
     74        self._H, self._H0 = H, H0 
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