1 | #power_law model |
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2 | #conversion of PowerLawAbsModel.py |
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3 | #converted by Steve King, Dec 2015 |
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4 | |
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5 | r""" |
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6 | This model calculates a simple power law with a flat background. |
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7 | |
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8 | Definition |
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9 | ---------- |
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10 | |
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11 | .. math:: |
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12 | |
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13 | I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background} |
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14 | |
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15 | Note the minus sign in front of the exponent. The exponent *power* |
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16 | should therefore be entered as a **positive** number for fitting. |
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17 | |
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18 | Also note that unlike many other models, *scale* in this model |
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19 | is NOT explicitly related to a volume fraction. Be careful if |
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20 | combining this model with other models. |
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21 | |
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22 | |
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23 | References |
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24 | ---------- |
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25 | |
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26 | None. |
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27 | |
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28 | Source |
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29 | ------ |
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30 | |
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31 | `power_law.py <https://github.com/SasView/sasmodels/blob/master/sasmodels/models/power_law.py>`_ |
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32 | |
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33 | Authorship and Verification |
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34 | ---------------------------- |
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35 | |
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36 | * **Author:** |
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37 | * **Last Modified by:** |
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38 | * **Last Reviewed by:** |
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39 | * **Source added by :** Steve King **Date:** March 25, 2019 |
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40 | """ |
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41 | |
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42 | import numpy as np |
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43 | from numpy import inf, errstate |
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44 | |
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45 | name = "power_law" |
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46 | title = "Simple power law with a flat background" |
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47 | |
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48 | description = """ |
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49 | Evaluates the function |
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50 | I(q) = scale * q^(-power) + background |
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51 | NB: enter power as a positive number! |
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52 | """ |
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53 | category = "shape-independent" |
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54 | |
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55 | # ["name", "units", default, [lower, upper], "type", "description"], |
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56 | parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]] |
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57 | |
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58 | # NB: Scale and Background are implicit parameters on every model |
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59 | def Iq(q, power): |
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60 | # pylint: disable=missing-docstring |
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61 | with errstate(divide='ignore'): |
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62 | result = q**-power |
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63 | return result |
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64 | Iq.vectorized = True # Iq accepts an array of q values |
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65 | |
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66 | def random(): |
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67 | """Return a random parameter set for the model.""" |
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68 | power = np.random.uniform(1, 6) |
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69 | pars = dict( |
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70 | scale=0.1**power*10**np.random.uniform(-4, 2), |
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71 | power=power, |
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72 | ) |
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73 | return pars |
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74 | |
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75 | demo = dict(scale=1.0, power=4.0, background=0.0) |
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76 | |
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77 | tests = [ |
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78 | [{'scale': 1.0, 'power': 4.0, 'background' : 0.0}, |
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79 | [0.0106939, 0.469418], [7.64644e+07, 20.5949]], |
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80 | ] |
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