[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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| 27 | """ |
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| 28 | |
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[2d81cfe] | 29 | import numpy as np |
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[2c74c11] | 30 | from numpy import inf, errstate |
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[48be770] | 31 | |
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[841753c] | 32 | name = "power_law" |
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[48be770] | 33 | title = "Simple power law with a flat background" |
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| 34 | |
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[841753c] | 35 | description = """ |
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| 36 | Evaluates the function |
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| 37 | I(q) = scale * q^(-power) + background |
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| 38 | NB: enter power as a positive number! |
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| 39 | """ |
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[48be770] | 40 | category = "shape-independent" |
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| 41 | |
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| 42 | # ["name", "units", default, [lower, upper], "type", "description"], |
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[525f3a9] | 43 | parameters = [["power", "", 4.0, [-inf, inf], "", "Power law exponent"]] |
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[48be770] | 44 | |
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[525f3a9] | 45 | # NB: Scale and Background are implicit parameters on every model |
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[841753c] | 46 | def Iq(q, power): |
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| 47 | # pylint: disable=missing-docstring |
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[2c74c11] | 48 | with errstate(divide='ignore'): |
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[40a87fa] | 49 | result = q**-power |
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| 50 | return result |
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[eb69cce] | 51 | Iq.vectorized = True # Iq accepts an array of q values |
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[48be770] | 52 | |
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[404ebbd] | 53 | def random(): |
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| 54 | power = np.random.uniform(1, 6) |
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| 55 | pars = dict( |
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| 56 | scale=0.1**power*10**np.random.uniform(-4, 2), |
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| 57 | power=power, |
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| 58 | ) |
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| 59 | return pars |
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| 60 | |
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[40a87fa] | 61 | demo = dict(scale=1.0, power=4.0, background=0.0) |
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[48be770] | 62 | |
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[8fe0b9b] | 63 | tests = [ |
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[841753c] | 64 | [{'scale': 1.0, 'power': 4.0, 'background' : 0.0}, |
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| 65 | [0.0106939, 0.469418], [7.64644e+07, 20.5949]], |
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| 66 | ] |
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