# SasView/sasmodels

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 r""" For information about polarised and magnetic scattering, see the :ref:magnetism documentation. Definition ---------- The 1D scattering intensity is calculated in the following way (Guinier, 1955) .. math:: I(q) = \frac{\text{scale}}{V} \cdot \left[ 3V(\Delta\rho) \cdot \frac{\sin(qr) - qr\cos(qr))}{(qr)^3} \right]^2 + \text{background} where *scale* is a volume fraction, $V$ is the volume of the scatterer, $r$ is the radius of the sphere and *background* is the background level. *sld* and *sld_solvent* are the scattering length densities (SLDs) of the scatterer and the solvent respectively, whose difference is $\Delta\rho$. Note that if your data is in absolute scale, the *scale* should represent the volume fraction (which is unitless) if you have a good fit. If not, it should represent the volume fraction times a factor (by which your data might need to be rescaled). The 2D scattering intensity is the same as above, regardless of the orientation of $\vec q$. Validation ---------- Validation of our code was done by comparing the output of the 1D model to the output of the software provided by the NIST (Kline, 2006). References ---------- A Guinier and G. Fournet, *Small-Angle Scattering of X-Rays*, John Wiley and Sons, New York, (1955) * **Last Reviewed by:** S King and P Parker **Date:** 2013/09/09 and 2014/01/06 """ import numpy as np from numpy import inf name = "sphere" title = "Spheres with uniform scattering length density" description = """\ P(q)=(scale/V)*[3V(sld-sld_solvent)*(sin(qr)-qr cos(qr)) /(qr)^3]^2 + background r: radius of sphere V: The volume of the scatter sld: the SLD of the sphere sld_solvent: the SLD of the solvent """ category = "shape:sphere" # ["name", "units", default, [lower, upper], "type","description"], parameters = [["sld", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Layer scattering length density"], ["sld_solvent", "1e-6/Ang^2", 6, [-inf, inf], "sld", "Solvent scattering length density"], ["radius", "Ang", 50, [0, inf], "volume", "Sphere radius"], ] source = ["lib/sas_3j1x_x.c", "lib/sphere_form.c"] # No volume normalization despite having a volume parameter # This should perhaps be volume normalized? form_volume = """ return sphere_volume(radius); """ Iq = """ return sphere_form(q, radius, sld, sld_solvent); """ def ER(radius): """ Return equivalent radius (ER) """ return radius # VR defaults to 1.0 def random(): radius = 10**np.random.uniform(1.3, 4) pars = dict( radius=radius, ) return pars tests = [ [{}, 0.2, 0.726362], [{"scale": 1., "background": 0., "sld": 6., "sld_solvent": 1., "radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, 0.2, 0.228843], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "ER", 120.], [{"radius": 120., "radius_pd": 0.2, "radius_pd_n":45}, "VR", 1.], ]