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Last change
on this file since b768e92 was
7805458,
checked in by smk78, 9 years ago
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Removed unit substitutions as these now handled by rst_prolog
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File size:
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[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 | P(r) Inversion Perspective |
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| 7 | ========================== |
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| 8 | |
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[8a22b5b] | 9 | Description |
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| 10 | ----------- |
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[ec392464] | 11 | |
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[8a22b5b] | 12 | This tool calculates a real-space distance distribution function, *P(r)*, using |
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| 13 | the inversion approach (Moore, 1908). |
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| 14 | |
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| 15 | *P(r)* is set to be equal to an expansion of base functions of the type |
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| 16 | |
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| 17 | |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max) |
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[ec392464] | 18 | |
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| 19 | The coefficient of each base function in the expansion is found by performing |
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[8a22b5b] | 20 | a least square fit with the following fit function |
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| 21 | |
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| 22 | |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] | 23 | |
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[8a22b5b] | 24 | where I\ :sub:`meas`\ (Q) is the measured scattering intensity and |
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| 25 | I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)* |
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| 26 | expansion. |
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[ec392464] | 27 | |
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[8a22b5b] | 28 | The *Reg_term* term is a regularization term set to the second derivative |
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| 29 | d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a |
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| 30 | smooth *P(r)* output. |
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[ec392464] | 31 | |
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[8a22b5b] | 32 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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[ec392464] | 33 | |
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[a9dc4eb] | 34 | Using the perspective |
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| 35 | --------------------- |
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[ec392464] | 36 | |
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[8a22b5b] | 37 | The user must enter |
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| 38 | |
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| 39 | * *Number of terms*: the number of base functions in the P(r) expansion. |
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[ec392464] | 40 | |
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[8a22b5b] | 41 | * *Regularization constant*: a multiplicative constant to set the size of |
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[ec392464] | 42 | the regularization term. |
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| 43 | |
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[8a22b5b] | 44 | * *Maximum distance*: the maximum distance between any two points in the |
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[ec392464] | 45 | system. |
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[8a22b5b] | 46 | |
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| 47 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 48 | |
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| 49 | Reference |
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| 50 | --------- |
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| 51 | |
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| 52 | P.B. Moore |
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| 53 | *J. Appl. Cryst.*, 13 (1980) 168-175 |
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| 54 | |
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| 55 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 56 | |
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[a9dc4eb] | 57 | .. note:: This help document was last changed by Steve King, 01May2015 |
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