Changes in / [c63a7c8:ab60822] in sasmodels


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  • doc/conf.py

    r8ae8532 r30b60d2  
    211211#latex_preamble = '' 
    212212LATEX_PREAMBLE=r""" 
     213\newcommand{\lt}{<} 
     214\newcommand{\gt}{>} 
    213215\renewcommand{\AA}{\text{\r{A}}} % Allow \AA in math mode 
    214216\usepackage[utf8]{inputenc}      % Allow unicode symbols in text 

  • doc/guide/magnetism/magnetism.rst

    r990d8df r990d8df  
    1616 
    1717.. figure:: 
    18     mag_img/mag_vector.bmp 
     18    mag_img/mag_vector.png 
    1919 
    2020The magnetic scattering length density is then 
    … …  
    3636 
    3737.. figure:: 
    38     mag_img/M_angles_pic.bmp 
     38    mag_img/M_angles_pic.png 
    3939 
    4040If the angles of the $Q$ vector and the spin-axis $x'$ to the $x$ - axis are 

  • doc/guide/plugin.rst

    r870a2f4 r30b60d2  
    117117Models that do not conform to these requirements will *never* be incorporated 
    118118into the built-in library. 
    119  
    120 More complete documentation for the sasmodels package can be found at 
    121 `<http://www.sasview.org/sasmodels>`_. In particular, 
    122 `<http://www.sasview.org/sasmodels/api/generate.html#module-sasmodels.generate>`_ 
    123 describes the structure of a model. 
    124119 
    125120 
    … …  
    613608 
    614609    sas_gamma(x): 
    615         Gamma function $\text{sas_gamma}(x) = \Gamma(x)$. 
     610        Gamma function sas_gamma\ $(x) = \Gamma(x)$. 
    616611 
    617612        The standard math function, tgamma(x) is unstable for $x < 1$ 
    … …  
    623618    sas_erf(x), sas_erfc(x): 
    624619        Error function 
    625         $\text{sas_erf}(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,dt$ 
     620        sas_erf\ $(x) = \frac{2}{\sqrt\pi}\int_0^x e^{-t^2}\,dt$ 
    626621        and complementary error function 
    627         $\text{sas_erfc}(x) = \frac{2}{\sqrt\pi}\int_x^{\infty} e^{-t^2}\,dt$. 
     622        sas_erfc\ $(x) = \frac{2}{\sqrt\pi}\int_x^{\infty} e^{-t^2}\,dt$. 
    628623 
    629624        The standard math functions erf(x) and erfc(x) are slower and broken 
    … …  
    634629 
    635630    sas_J0(x): 
    636         Bessel function of the first kind $\text{sas_J0}(x)=J_0(x)$ where 
     631        Bessel function of the first kind sas_J0\ $(x)=J_0(x)$ where 
    637632        $J_0(x) = \frac{1}{\pi}\int_0^\pi \cos(x\sin(\tau))\,d\tau$. 
    638633 
    … …  
    643638 
    644639    sas_J1(x): 
    645         Bessel function of the first kind  $\text{sas_J1}(x)=J_1(x)$ where 
     640        Bessel function of the first kind  sas_J1\ $(x)=J_1(x)$ where 
    646641        $J_1(x) = \frac{1}{\pi}\int_0^\pi \cos(\tau - x\sin(\tau))\,d\tau$. 
    647642 
    … …  
    652647 
    653648    sas_JN(n, x): 
    654         Bessel function of the first kind and integer order $n$: 
    655         $\text{sas_JN}(n, x)=J_n(x)$ where 
     649        Bessel function of the first kind and integer order $n$, 
     650        sas_JN\ $(n, x) =J_n(x)$ where 
    656651        $J_n(x) = \frac{1}{\pi}\int_0^\pi \cos(n\tau - x\sin(\tau))\,d\tau$. 
    657         If $n$ = 0 or 1, it uses sas_J0(x) or sas_J1(x), respectively. 
     652        If $n$ = 0 or 1, it uses sas_J0($x$) or sas_J1($x$), respectively. 
    658653 
    659654        The standard math function jn(n, x) is not available on all platforms. 
    … …  
    663658 
    664659    sas_Si(x): 
    665         Sine integral $\text{Si}(x) = \int_0^x \tfrac{\sin t}{t}\,dt$. 
     660        Sine integral Si\ $(x) = \int_0^x \tfrac{\sin t}{t}\,dt$. 
    666661 
    667662        This function uses Taylor series for small and large arguments: 
    … …  
    688683    sas_3j1x_x(x): 
    689684        Spherical Bessel form 
    690         $\text{sph_j1c}(x) = 3 j_1(x)/x = 3 (\sin(x) - x \cos(x))/x^3$, 
     685        sph_j1c\ $(x) = 3 j_1(x)/x = 3 (\sin(x) - x \cos(x))/x^3$, 
    691686        with a limiting value of 1 at $x=0$, where $j_1(x)$ is the spherical 
    692687        Bessel function of the first kind and first order. 
    … …  
    699694 
    700695    sas_2J1x_x(x): 
    701         Bessel form $\text{sas_J1c}(x) = 2 J_1(x)/x$, with a limiting value 
     696        Bessel form sas_J1c\ $(x) = 2 J_1(x)/x$, with a limiting value 
    702697        of 1 at $x=0$, where $J_1(x)$ is the Bessel function of first kind 
    703698        and first order. 

  • doc/guide/resolution.rst

    rf8a2baa r30b60d2  
    212212elliptical Gaussian distribution. The $A$ is a normalization factor. 
    213213 
    214 .. figure:: resolution_2d_rotation.gif 
     214.. figure:: resolution_2d_rotation.png 
    215215 
    216216    Coordinate axis rotation for 2D resolution calculation. 

  • doc/rst_prolog

    ra0fb06a r30b60d2  
    11.. Set up some substitutions to make life easier... 
    2 .. Remove |biggamma|, etc. when they are no longer needed. 
    32 
    4  
    5 .. |alpha| unicode:: U+03B1 
    6 .. |beta| unicode:: U+03B2 
    7 .. |gamma| unicode:: U+03B3 
    8 .. |delta| unicode:: U+03B4 
    9 .. |epsilon| unicode:: U+03B5 
    10 .. |zeta| unicode:: U+03B6 
    11 .. |eta| unicode:: U+03B7 
    12 .. |theta| unicode:: U+03B8 
    13 .. |iota| unicode:: U+03B9 
    14 .. |kappa| unicode:: U+03BA 
    15 .. |lambda| unicode:: U+03BB 
    16 .. |mu| unicode:: U+03BC 
    17 .. |nu| unicode:: U+03BD 
    18 .. |xi| unicode:: U+03BE 
    19 .. |omicron| unicode:: U+03BF 
    20 .. |pi| unicode:: U+03C0 
    21 .. |rho| unicode:: U+03C1 
    22 .. |sigma| unicode:: U+03C3 
    23 .. |tau| unicode:: U+03C4 
    24 .. |upsilon| unicode:: U+03C5 
    25 .. |phi| unicode:: U+03C6 
    26 .. |chi| unicode:: U+03C7 
    27 .. |psi| unicode:: U+03C8 
    28 .. |omega| unicode:: U+03C9 
    29  
    30  
    31 .. |biggamma| unicode:: U+0393 
    32 .. |bigdelta| unicode:: U+0394 
    33 .. |bigzeta| unicode:: U+039E 
    34 .. |bigpsi| unicode:: U+03A8 
    35 .. |bigphi| unicode:: U+03A6 
    36 .. |bigsigma| unicode:: U+03A3 
    37 .. |Gamma| unicode:: U+0393 
    38 .. |Delta| unicode:: U+0394 
    39 .. |Zeta| unicode:: U+039E 
    40 .. |Psi| unicode:: U+03A8 
    41  
    42  
    43 .. |drho| replace:: |Delta|\ |rho| 
    443.. |Ang| unicode:: U+212B 
    454.. |Ang^-1| replace:: |Ang|\ :sup:`-1` 
    … …  
    5716.. |cm^-3| replace:: cm\ :sup:`-3` 
    5817.. |sr^-1| replace:: sr\ :sup:`-1` 
    59 .. |P0| replace:: P\ :sub:`0`\ 
    60 .. |A2| replace:: A\ :sub:`2`\ 
    61  
    62  
    63 .. |equiv| unicode:: U+2261 
    64 .. |noteql| unicode:: U+2260 
    65 .. |TM| unicode:: U+2122 
    66  
    6718 
    6819.. |cdot| unicode:: U+00B7 

  • sasmodels/generate.py

    r573ffab r30b60d2  
    210210 
    211211# Conversion from units defined in the parameter table for each model 
    212 # to units displayed in the sphinx documentation.  
     212# to units displayed in the sphinx documentation. 
    213213# This section associates the unit with the macro to use to produce the LaTex 
    214214# code.  The macro itself needs to be defined in sasmodels/doc/rst_prolog. 
    … …  
    216216# NOTE: there is an RST_PROLOG at the end of this file which is NOT 
    217217# used for the bundled documentation. Still as long as we are defining the macros 
    218 # in two places any new addition should define the macro in both places.  
     218# in two places any new addition should define the macro in both places. 
    219219RST_UNITS = { 
    220220    "Ang": "|Ang|", 
    … …  
    898898.. |cm^-3| replace:: cm\ :sup:`-3` 
    899899.. |sr^-1| replace:: sr\ :sup:`-1` 
    900 .. |P0| replace:: P\ :sub:`0`\ 
    901  
    902 .. |equiv| unicode:: U+2261 
    903 .. |noteql| unicode:: U+2260 
    904 .. |TM| unicode:: U+2122 
    905900 
    906901.. |cdot| unicode:: U+00B7 

  • sasmodels/models/binary_hard_sphere.py

    r8f04da4 r30b60d2  
    2323    :nowrap: 
    2424 
    25     \begin{align} 
     25    \begin{align*} 
    2626    x &= \frac{(\phi_2 / \phi)\alpha^3}{(1-(\phi_2/\phi) + (\phi_2/\phi) 
    2727    \alpha^3)} \\ 
    2828    \phi &= \phi_1 + \phi_2 = \text{total volume fraction} \\ 
    2929    \alpha &= R_1/R_2 = \text{size ratio} 
    30     \end{align} 
     30    \end{align*} 
    3131 
    3232The 2D scattering intensity is the same as 1D, regardless of the orientation of 

  • sasmodels/models/core_shell_bicelle.py

    ra151caa r30b60d2  
    4141 
    4242    I(Q,\alpha) = \frac{\text{scale}}{V_t} \cdot 
    43         F(Q,\alpha)^2.sin(\alpha) + \text{background} 
     43        F(Q,\alpha)^2 \cdot sin(\alpha) + \text{background} 
    4444 
    4545where 
    4646 
    4747.. math:: 
     48    :nowrap: 
    4849 
    49     \begin{align} 
     50    \begin{align*} 
    5051    F(Q,\alpha) = &\bigg[ 
    5152    (\rho_c - \rho_f) V_c \frac{2J_1(QRsin \alpha)}{QRsin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ 
    … …  
    5354    &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R+t_r)sin\alpha)}{Q(R+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} 
    5455    \bigg] 
    55     \end{align} 
     56    \end{align*} 
    5657 
    5758where $V_t$ is the total volume of the bicelle, $V_c$ the volume of the core, 

  • sasmodels/models/core_shell_bicelle_elliptical.py

    r8f04da4 r30b60d2  
    4242 
    4343    I(Q,\alpha,\psi) = \frac{\text{scale}}{V_t} \cdot 
    44         F(Q,\alpha, \psi)^2.sin(\alpha) + \text{background} 
     44        F(Q,\alpha, \psi)^2 \cdot sin(\alpha) + \text{background} 
    4545 
    46 where a numerical integration of $F(Q,\alpha, \psi)^2.sin(\alpha)$ is carried out over \alpha and \psi for: 
     46where a numerical integration of $F(Q,\alpha, \psi)^2 \cdot sin(\alpha)$ is carried out over \alpha and \psi for: 
    4747 
    4848.. math:: 
     49    :nowrap: 
    4950 
    50         \begin{align} 
     51    \begin{align*} 
    5152    F(Q,\alpha,\psi) = &\bigg[ 
    5253    (\rho_c - \rho_f) V_c \frac{2J_1(QR'sin \alpha)}{QR'sin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ 
    … …  
    5455    &+(\rho_r - \rho_s) V_t \frac{2J_1(Q(R'+t_r)sin\alpha)}{Q(R'+t_r)sin\alpha}\frac{sin(Q(L/2+t_f)cos\alpha)}{Q(L/2+t_f)cos\alpha} 
    5556    \bigg] 
    56     \end{align} 
     57    \end{align*} 
    5758 
    5859where 

  • sasmodels/models/core_shell_ellipsoid.py

    r9f6823b r30b60d2  
    4444 
    4545.. math:: 
    46     \begin{align} 
     46    :nowrap: 
     47 
     48    \begin{align*} 
    4749    F(q,\alpha) = &f(q,radius\_equat\_core,radius\_equat\_core.x\_core,\alpha) \\ 
    4850    &+ f(q,radius\_equat\_core + thick\_shell,radius\_equat\_core.x\_core + thick\_shell.x\_polar\_shell,\alpha) 
    49     \end{align} 
     51    \end{align*} 
    5052 
    5153where 

  • sasmodels/models/fractal_core_shell.py

    r8f04da4 r8f04da4  
    3131$\rho_{solv}$ are the scattering length densities of the core, shell, and 
    3232solvent respectively, $r_c$ and $r_s$ are the radius of the core and the radius 
    33 of the whole particle respectively, $D_f$ is the fractal dimension, and |xi| the 
     33of the whole particle respectively, $D_f$ is the fractal dimension, and $\xi$ the 
    3434correlation length. 
    3535 

  • sasmodels/models/hollow_rectangular_prism.py

    r8f04da4 r30b60d2  
    3131  :nowrap: 
    3232 
    33   \begin{align} 
     33  \begin{align*} 
    3434  A_{P\Delta}(q) & =  A B C 
    3535    \left[\frac{\sin \bigl( q \frac{C}{2} \cos\theta \bigr)} 
    … …  
    4747    \left[ \frac{\sin \bigl[ q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi \bigr]} 
    4848    {q \bigl(\frac{B}{2}-\Delta\bigr) \sin\theta \cos\phi} \right] 
    49   \end{align} 
     49  \end{align*} 
    5050 
    5151where $A$, $B$ and $C$ are the external sides of the parallelepiped fulfilling 

  • sasmodels/models/multilayer_vesicle.py

    r870a2f4 r870a2f4  
    3333.. math:: 
    3434 
    35      r_i &= r_c + (i-1)(t_s + t_w) && \text{ solvent radius before shell } i \\ 
    36      R_i &= r_i + t_s && \text{ shell radius for shell } i 
     35     r_i &= r_c + (i-1)(t_s + t_w) \text{ solvent radius before shell } i \\ 
     36     R_i &= r_i + t_s \text{ shell radius for shell } i 
    3737 
    3838$\phi$ is the volume fraction of particles, $V(r)$ is the volume of a sphere 

  • sasmodels/models/parallelepiped.py

    r8f04da4 r30b60d2  
    2020   Parallelepiped with the corresponding definition of sides. 
    2121 
    22 .. note:: 
    23  
    24 The three dimensions of the parallelepiped (strictly here a cuboid) may be given in 
    25 $any$ size order. To avoid multiple fit solutions, especially 
    26 with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may 
    27 be a number of closely similar "best fits", so some trial and error, or fixing of some 
    28 dimensions at expected values, may help. 
     22The three dimensions of the parallelepiped (strictly here a cuboid) may be 
     23given in *any* size order. To avoid multiple fit solutions, especially 
     24with Monte-Carlo fit methods, it may be advisable to restrict their ranges. 
     25There may be a number of closely similar "best fits", so some trial and 
     26error, or fixing of some dimensions at expected values, may help. 
    2927 
    3028The 1D scattering intensity $I(q)$ is calculated as: 

  • sasmodels/models/rpa.py

    r4f9e288 r30b60d2  
    3030    These case numbers are different from those in the NIST SANS package! 
    3131 
    32 The models are based on the papers by Akcasu et al. [#Akcasu]_ and by 
    33 Hammouda [#Hammouda]_ assuming the polymer follows Gaussian statistics such 
     32The models are based on the papers by Akcasu *et al.* and by 
     33Hammouda assuming the polymer follows Gaussian statistics such 
    3434that $R_g^2 = n b^2/6$ where $b$ is the statistical segment length and $n$ is 
    3535the number of statistical segment lengths. A nice tutorial on how these are 
    3636constructed and implemented can be found in chapters 28 and 39 of Boualem 
    37 Hammouda's 'SANS Toolbox'[#toolbox]_. 
     37Hammouda's 'SANS Toolbox'. 
    3838 
    3939In brief the macroscopic cross sections are derived from the general forms 
    … …  
    4949  are calculated with respect to component D).** So the scattering contrast 
    5050  for a C/D blend = [SLD(component C) - SLD(component D)]\ :sup:`2`. 
    51 * Depending on which case is being used, the number of fitting parameters can  
     51* Depending on which case is being used, the number of fitting parameters can 
    5252  vary. 
    5353 
    … …  
    5757      component are obtained from other methods and held fixed while The *scale* 
    5858      parameter should be held equal to unity. 
    59     * The variables are normally the segment lengths (b\ :sub:`a`, b\ :sub:`b`, 
    60       etc) and $\chi$ parameters (K\ :sub:`ab`, K\ :sub:`ac`, etc). 
    61  
     59    * The variables are normally the segment lengths ($b_a$, $b_b$, 
     60      etc.) and $\chi$ parameters ($K_{ab}$, $K_{ac}$, etc). 
    6261 
    6362References 
    6463---------- 
    6564 
    66 .. [#Akcasu] A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 
    67    4136. 
    68 .. [#Hammouda] B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. 
    69 .. [#toolbox] https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf 
     65A Z Akcasu, R Klein and B Hammouda, *Macromolecules*, 26 (1993) 4136. 
     66 
     67B. Hammouda, *Advances in Polymer Science* 106 (1993) 87. 
     68 
     69B. Hammouda, *SANS Toolbox* 
     70https://www.ncnr.nist.gov/staff/hammouda/the_sans_toolbox.pdf. 
    7071 
    7172Authorship and Verification 

  • sasmodels/models/star_polymer.py

    rd439007 r30b60d2  
    77emanating from a common central (in the case of this model) point.  It is 
    88derived as a special case of on the Benoit model for general branched 
    9 polymers\ [#CITBenoit]_ as also used by Richter ''et. al.''\ [#CITRichter]_ 
     9polymers\ [#CITBenoit]_ as also used by Richter *et al.*\ [#CITRichter]_ 
    1010 
    1111For a star with $f$ arms the scattering intensity $I(q)$ is calculated as 

  • sasmodels/models/surface_fractal.py

    r48462b0 r30b60d2  
    99 
    1010.. math:: 
     11    :nowrap: 
    1112 
     13    \begin{align*} 
    1214    I(q) &= \text{scale} \times P(q)S(q) + \text{background} \\ 
    1315    P(q) &= F(qR)^2 \\ 
    … …  
    1517    S(q) &= \Gamma(5-D_S)\xi^{\,5-D_S}\left[1+(q\xi)^2 \right]^{-(5-D_S)/2} 
    1618            \sin\left[-(5-D_S) \tan^{-1}(q\xi) \right] q^{-1} \\ 
    17     \text{scale} &= \text{scale_factor}\, N V^2(\rho_\text{particle} - \rho_\text{solvent})^2 \\ 
     19    \text{scale} &= \text{scale factor}\, N V^1(\rho_\text{particle} - \rho_\text{solvent})^2 \\ 
    1820    V &= \frac{4}{3}\pi R^3 
     21    \end{align*} 
    1922 
    2023where $R$ is the radius of the building block, $D_S$ is the **surface** fractal 
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