[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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[b64b87c] | 6 | P(r) Calculation |
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| 7 | ================ |
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[ec392464] | 8 | |
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[8a22b5b] | 9 | Description |
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| 10 | ----------- |
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[ec392464] | 11 | |
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[1221196] | 12 | This tool calculates a real-space distance distribution function, *P(r)*, using |
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| 13 | the inversion approach (Moore, 1980). |
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[8a22b5b] | 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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[0391dae] | 17 | .. math:: |
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| 18 | \Phi_{n(r)} = 2 r sin(\frac{\pi n r}{D_{max}}) |
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[ec392464] | 19 | |
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[0391dae] | 20 | The coefficient of each base function in the expansion is found by performing |
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[8a22b5b] | 21 | a least square fit with the following fit function |
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| 22 | |
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[0391dae] | 23 | .. math:: |
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[ec392464] | 24 | |
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[0391dae] | 25 | \chi^2=\frac{\sum_i (I_{meas}(Q_i)-I_{th}(Q_i))^2}{error^2}+Reg\_term |
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[1221196] | 26 | |
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[ec392464] | 27 | |
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[0391dae] | 28 | where $I_{meas}(Q_i)$ is the measured scattering intensity and $I_{th}(Q_i)$ is |
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[1221196] | 29 | the prediction from the Fourier transform of the *P(r)* expansion. |
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[0391dae] | 30 | |
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[1221196] | 31 | The $Reg\_term$ term is a regularization term set to the second derivative |
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[0391dae] | 32 | $d^2P(r)/d^2r$ integrated over $r$. It is used to produce a smooth *P(r)* output. |
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[ec392464] | 33 | |
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[8a22b5b] | 34 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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[ec392464] | 35 | |
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[b64b87c] | 36 | Using P(r) inversion |
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| 37 | -------------------- |
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[ec392464] | 38 | |
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[8a22b5b] | 39 | The user must enter |
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| 40 | |
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| 41 | * *Number of terms*: the number of base functions in the P(r) expansion. |
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[1221196] | 42 | |
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[8a22b5b] | 43 | * *Regularization constant*: a multiplicative constant to set the size of |
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[ec392464] | 44 | the regularization term. |
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| 45 | |
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[8a22b5b] | 46 | * *Maximum distance*: the maximum distance between any two points in the |
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[ec392464] | 47 | system. |
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[8a22b5b] | 48 | |
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[0391dae] | 49 | P(r) inversion requires that the background be perfectly subtracted. This is |
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| 50 | often difficult to do well and thus many data sets will include a background. |
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| 51 | For those cases, the user should check the "estimate background" box and the |
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| 52 | module will do its best to estimate it. |
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| 53 | |
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| 54 | The P(r) module is constantly computing in the background what the optimum |
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| 55 | *number of terms* should be as well as the optimum *regularization constant*. |
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| 56 | These are constantly updated in the buttons next to the entry boxes on the GUI. |
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| 57 | These are almost always close and unless the user has a good reason to choose |
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| 58 | differently they should just click on the buttons to accept both. {D_max} must |
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| 59 | still be set by the user. However, besides looking at the output, the user can |
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| 60 | click the explore button which will bring up a graph of chi^2 vs Dmax over a |
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| 61 | range around the current Dmax. The user can change the range and the number of |
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| 62 | points to explore in that range. They can also choose to plot several other |
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| 63 | parameters as a function of Dmax including: I0, Rg, Oscillation parameter, |
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| 64 | background, positive fraction, and 1-sigma positive fraction. |
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| 65 | |
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[8a22b5b] | 66 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 67 | |
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| 68 | Reference |
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| 69 | --------- |
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| 70 | |
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| 71 | P.B. Moore |
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| 72 | *J. Appl. Cryst.*, 13 (1980) 168-175 |
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| 73 | |
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| 74 | .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ |
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| 75 | |
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[0391dae] | 76 | .. note:: This help document was last modified by Paul Butler, 05 September, 2016 |
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