Changeset 0391dae in sasview
 Timestamp:
 Sep 6, 2016 1:59:56 AM (5 years ago)
 Branches:
 master, ESS_GUI, ESS_GUI_Docs, ESS_GUI_batch_fitting, ESS_GUI_bumps_abstraction, ESS_GUI_iss1116, ESS_GUI_iss879, ESS_GUI_iss959, ESS_GUI_opencl, ESS_GUI_ordering, ESS_GUI_sync_sascalc, costrafo411, magnetic_scatt, release4.1.1, release4.1.2, release4.2.2, release_4.0.1, ticket1009, ticket1094headless, ticket12422dresolution, ticket1243, ticket1249, ticket885, unittestsaveload
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 fd196cb
 Parents:
 f9b0c81
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src/sas/sasgui/perspectives/pr/media/pr_help.rst
rb64b87c r0391dae 15 15 *P(r)* is set to be equal to an expansion of base functions of the type 16 16 17 bigphi\_n(r) = 2.r.sin(pi\ .n.r/D_max) 17 .. math:: 18 \Phi_{n(r)} = 2 r sin(\frac{\pi n r}{D_{max}}) 18 19 19 The coefficient of each base function in the expansion is found by performing 20 The coefficient of each base function in the expansion is found by performing 20 21 a least square fit with the following fit function 21 22 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 23 .. math:: 23 24 24 where I\ :sub:`meas`\ (Q) is the measured scattering intensity and 25 I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)* 26 expansion. 25 \chi^2=\frac{\sum_i (I_{meas}(Q_i)I_{th}(Q_i))^2}{error^2}+Reg\_term 26 27 27 28 The *Reg_term* term is a regularization term set to the second derivative 29 d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a 30 smooth *P(r)* output. 28 where $I_{meas}(Q_i)$ is the measured scattering intensity and $I_{th}(Q_i)$ is 29 the prediction from the Fourier transform of the *P(r)* expansion. 30 31 The $Reg\_term$ term is a regularization term set to the second derivative 32 $d^2P(r)/d^2r$ integrated over $r$. It is used to produce a smooth *P(r)* output. 31 33 32 34 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ … … 45 47 system. 46 48 49 P(r) inversion requires that the background be perfectly subtracted. This is 50 often difficult to do well and thus many data sets will include a background. 51 For those cases, the user should check the "estimate background" box and the 52 module will do its best to estimate it. 53 54 The P(r) module is constantly computing in the background what the optimum 55 *number of terms* should be as well as the optimum *regularization constant*. 56 These are constantly updated in the buttons next to the entry boxes on the GUI. 57 These are almost always close and unless the user has a good reason to choose 58 differently they should just click on the buttons to accept both. {D_max} must 59 still be set by the user. However, besides looking at the output, the user can 60 click the explore button which will bring up a graph of chi^2 vs Dmax over a 61 range around the current Dmax. The user can change the range and the number of 62 points to explore in that range. They can also choose to plot several other 63 parameters as a function of Dmax including: I0, Rg, Oscillation parameter, 64 background, positive fraction, and 1sigma positive fraction. 65 47 66 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 48 67 … … 55 74 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 56 75 57 .. note:: This help document was last changed by Steve King, 01May201576 .. note:: This help document was last modified by Paul Butler, 05 September, 2016
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