[48be770] | 1 | #power_law model |
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| 2 | #conversion of PowerLawAbsModel.py |
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[b15849c] | 3 | #converted by Steve King, Dec 2015 |
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[48be770] | 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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[eb69cce] | 13 | I(q) = \text{scale} \cdot q^{-\text{power}} + \text{background} |
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[48be770] | 14 | |
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[841753c] | 15 | Note the minus sign in front of the exponent. The exponent *power* |
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[525f3a9] | 16 | should therefore be entered as a **positive** number for fitting. |
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[48be770] | 17 | |
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[841753c] | 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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[48be770] | 20 | combining this model with other models. |
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| 21 | |
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| 22 | |
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[eb69cce] | 23 | References |
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| 24 | ---------- |
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[48be770] | 25 | |
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| 26 | None. |
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[0507e09] | 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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[48be770] | 40 | """ |
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| 41 | |
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[2d81cfe] | 42 | import numpy as np |
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[2c74c11] | 43 | from numpy import inf, errstate |
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[48be770] | 44 | |
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[841753c] | 45 | name = "power_law" |
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[48be770] | 46 | title = "Simple power law with a flat background" |
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| 47 | |
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[841753c] | 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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[48be770] | 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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[525f3a9] | 56 | parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]] |
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[48be770] | 57 | |
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[525f3a9] | 58 | # NB: Scale and Background are implicit parameters on every model |
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[841753c] | 59 | def Iq(q, power): |
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| 60 | # pylint: disable=missing-docstring |
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[2c74c11] | 61 | with errstate(divide='ignore'): |
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[40a87fa] | 62 | result = q**-power |
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| 63 | return result |
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[eb69cce] | 64 | Iq.vectorized = True # Iq accepts an array of q values |
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[48be770] | 65 | |
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[404ebbd] | 66 | def random(): |
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[b297ba9] | 67 | """Return a random parameter set for the model.""" |
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[404ebbd] | 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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[40a87fa] | 75 | demo = dict(scale=1.0, power=4.0, background=0.0) |
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[48be770] | 76 | |
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[8fe0b9b] | 77 | tests = [ |
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[841753c] | 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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