1 | r""" |
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2 | This model fits the Porod function |
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3 | |
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4 | .. math:: I(q) = C/q^4 |
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5 | |
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6 | to the data directly without any need for linearisation (cf. Log I(q) vs Log q). |
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7 | |
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8 | Here $C = 2\pi (\Delta\rho)^2 S_v$ is the scale factor where $S_v$ is |
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9 | the specific surface area (ie, surface area / volume) of the sample, and |
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10 | $\Delta\rho$ is the contrast factor. |
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11 | |
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12 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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13 | where the q vector is defined as |
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14 | |
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15 | .. math:: q = \sqrt{q_x^2+q_y^2} |
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16 | |
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17 | References |
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18 | ---------- |
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19 | |
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20 | .. [#] G Porod. *Kolloid Zeit*. 124 (1951) 83 |
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21 | .. [#] L A Feigin, D I Svergun, G W Taylor. *Structure Analysis by Small-Angle X-ray and Neutron Scattering*. Springer. (1987) |
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22 | |
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23 | Source |
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24 | ------ |
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25 | |
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26 | `porod.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/porod.py>`_ |
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27 | |
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28 | Authorship and Verification |
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29 | ---------------------------- |
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30 | |
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31 | * **Author:** |
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32 | * **Last Modified by:** |
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33 | * **Last Reviewed by:** |
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34 | * **Source added by :** Steve King **Date:** March 25, 2019 |
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35 | """ |
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36 | |
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37 | import numpy as np |
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38 | from numpy import inf, errstate |
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39 | |
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40 | name = "porod" |
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41 | title = "Porod function" |
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42 | description = """\ |
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43 | I(q) = scale/q^4 + background |
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44 | """ |
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45 | |
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46 | category = "shape-independent" |
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47 | |
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48 | parameters = [] |
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49 | |
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50 | def Iq(q): |
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51 | """ |
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52 | @param q: Input q-value |
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53 | """ |
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54 | with errstate(divide='ignore'): |
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55 | return q**-4 |
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56 | |
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57 | Iq.vectorized = True # Iq accepts an array of q values |
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58 | |
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59 | def random(): |
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60 | """Return a random parameter set for the model.""" |
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61 | sld, solvent = np.random.uniform(-0.5, 12, size=2) |
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62 | radius = 10**np.random.uniform(1, 4.7) |
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63 | Vf = 10**np.random.uniform(-3, -1) |
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64 | scale = 1e-4 * Vf * 2*np.pi*(sld-solvent)**2/(3*radius) |
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65 | pars = dict( |
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66 | scale=scale, |
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67 | ) |
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68 | return pars |
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69 | |
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70 | demo = dict(scale=1.5, background=0.5) |
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71 | |
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72 | tests = [ |
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73 | [{'scale': 0.00001, 'background':0.01}, 0.04, 3.916250], |
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74 | [{}, 0.0, inf], |
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75 | ] |
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