[ec392464] | 1 | .. pr_help.rst |
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| 2 | |
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| 3 | .. This is a port of the original SasView html help file to ReSTructured text |
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| 4 | .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. |
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| 5 | |
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| 6 | .. |pi| unicode:: U+03C0 |
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[8a22b5b] | 7 | .. |bigphi| unicode:: U+03A6 |
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| 8 | .. |bigsigma| unicode:: U+03A3 |
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[ec392464] | 9 | .. |chi| unicode:: U+03C7 |
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| 10 | |
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| 11 | P(r) Inversion Perspective |
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| 12 | ========================== |
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| 13 | |
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[8a22b5b] | 14 | Description |
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| 15 | ----------- |
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[ec392464] | 16 | |
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[8a22b5b] | 17 | This tool calculates a real-space distance distribution function, *P(r)*, using |
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| 18 | the inversion approach (Moore, 1908). |
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| 19 | |
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| 20 | *P(r)* is set to be equal to an expansion of base functions of the type |
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| 21 | |
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| 22 | |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max) |
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[ec392464] | 23 | |
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| 24 | The coefficient of each base function in the expansion is found by performing |
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[8a22b5b] | 25 | a least square fit with the following fit function |
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| 26 | |
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| 27 | |chi|\ :sup:`2` = |bigsigma|\ :sub:`i` [ I\ :sub:`meas`\ (Q\ :sub:`i`\ ) - I\ :sub:`th`\ (Q\ :sub:`i`\ ) ] :sup:`2` / (Error) :sup:`2` + Reg_term |
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[ec392464] | 28 | |
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[8a22b5b] | 29 | where I\ :sub:`meas`\ (Q) is the measured scattering intensity and |
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| 30 | I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)* |
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| 31 | expansion. |
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[ec392464] | 32 | |
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[8a22b5b] | 33 | The *Reg_term* term is a regularization term set to the second derivative |
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| 34 | d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a |
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| 35 | smooth *P(r)* output. |
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[ec392464] | 36 | |
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[8a22b5b] | 37 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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[ec392464] | 38 | |
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[a9dc4eb] | 39 | Using the perspective |
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| 40 | --------------------- |
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[ec392464] | 41 | |
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[8a22b5b] | 42 | The user must enter |
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| 43 | |
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| 44 | * *Number of terms*: the number of base functions in the P(r) expansion. |
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[ec392464] | 45 | |
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[8a22b5b] | 46 | * *Regularization constant*: a multiplicative constant to set the size of |
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[ec392464] | 47 | the regularization term. |
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| 48 | |
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[8a22b5b] | 49 | * *Maximum distance*: the maximum distance between any two points in the |
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[ec392464] | 50 | system. |
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[8a22b5b] | 51 | |
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| 52 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 53 | |
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| 54 | Reference |
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| 55 | --------- |
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| 56 | |
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| 57 | P.B. Moore |
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| 58 | *J. Appl. Cryst.*, 13 (1980) 168-175 |
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| 59 | |
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| 60 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 61 | |
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[a9dc4eb] | 62 | .. note:: This help document was last changed by Steve King, 01May2015 |
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