.. pr_help.rst .. This is a port of the original SasView html help file to ReSTructured text .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. P(r) Inversion Perspective ========================== Description ----------- This tool calculates a real-space distance distribution function, *P(r)*, using the inversion approach (Moore, 1908). *P(r)* is set to be equal to an expansion of base functions of the type |bigphi|\_n(r) = 2.r.sin(|pi|\ .n.r/D_max) The coefficient of each base function in the expansion is found by performing a least square fit with the following fit function |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 where I\ :sub:`meas`\ (Q) is the measured scattering intensity and I\ :sub:`th`\ (Q) is the prediction from the Fourier transform of the *P(r)* expansion. The *Reg_term* term is a regularization term set to the second derivative d\ :sup:`2`\ *P(r)* / dr\ :sup:`2` integrated over *r*. It is used to produce a smooth *P(r)* output. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Using the perspective --------------------- The user must enter * *Number of terms*: the number of base functions in the P(r) expansion. * *Regularization constant*: a multiplicative constant to set the size of the regularization term. * *Maximum distance*: the maximum distance between any two points in the system. .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ Reference --------- P.B. Moore *J. Appl. Cryst.*, 13 (1980) 168-175 .. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ .. note:: This help document was last changed by Steve King, 01May2015