Changeset ba62072 in sasmodels


Ignore:
Timestamp:
May 16, 2017 9:43:24 AM (8 years ago)
Author:
GitHub <noreply@…>
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
3a45c2c, bb4b509
Parents:
630156b (diff), d77eca8 (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
git-author:
Paul Butler <butlerpd@…> (05/16/17 09:43:24)
git-committer:
GitHub <noreply@…> (05/16/17 09:43:24)
Message:

Merge pull request #37 from SasView?/ticket-890

Ticket 890: use new orientation definition for asymmetric shapes

Files:
8 added
8 deleted
29 edited

Legend:

Unmodified
Added
Removed

  • explore/angular_pd.py

    r12eb36b r8267e0b  
    4747 
    4848def draw_mesh_new(ax, theta, dtheta, phi, dphi, flow, radius=10., dist='gauss'): 
    49     theta_center = radians(theta) 
     49    theta_center = radians(90-theta) 
    5050    phi_center = radians(phi) 
    5151    flow_center = radians(flow) 
    … …  
    137137                              radius=11., dist=dist) 
    138138        if not axis.startswith('d'): 
    139             ax.view_init(elev=theta, azim=phi) 
     139            ax.view_init(elev=90-theta if use_new else theta, azim=phi) 
    140140        plt.gcf().canvas.draw() 
    141141 

  • sasmodels/kernel_header.c

    rdaeef4c rb00a646  
    148148inline double sas_sinx_x(double x) { return x==0 ? 1.0 : sin(x)/x; } 
    149149 
     150// To rotate from the canonical position to theta, phi, psi, first rotate by 
     151// psi about the major axis, oriented along z, which is a rotation in the 
     152// detector plane xy. Next rotate by theta about the y axis, aligning the major 
     153// axis in the xz plane. Finally, rotate by phi in the detector plane xy. 
     154// To compute the scattering, undo these rotations in reverse order: 
     155//     rotate in xy by -phi, rotate in xz by -theta, rotate in xy by -psi 
     156// The returned q is the length of the q vector and (xhat, yhat, zhat) is a unit 
     157// vector in the q direction. 
     158// To change between counterclockwise and clockwise rotation, change the 
     159// sign of phi and psi. 
     160 
    150161#if 1 
    151162//think cos(theta) should be sin(theta) in new coords, RKH 11Jan2017 
    … …  
    166177#endif 
    167178 
     179#if 1 
     180#define ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat) do { \ 
     181    q = sqrt(qx*qx + qy*qy); \ 
     182    const double qxhat = qx/q; \ 
     183    const double qyhat = qy/q; \ 
     184    double sin_theta, cos_theta; \ 
     185    double sin_phi, cos_phi; \ 
     186    double sin_psi, cos_psi; \ 
     187    SINCOS(theta*M_PI_180, sin_theta, cos_theta); \ 
     188    SINCOS(phi*M_PI_180, sin_phi, cos_phi); \ 
     189    SINCOS(psi*M_PI_180, sin_psi, cos_psi); \ 
     190    xhat = qxhat*(-sin_phi*sin_psi + cos_theta*cos_phi*cos_psi) \ 
     191         + qyhat*( cos_phi*sin_psi + cos_theta*sin_phi*cos_psi); \ 
     192    yhat = qxhat*(-sin_phi*cos_psi - cos_theta*cos_phi*sin_psi) \ 
     193         + qyhat*( cos_phi*cos_psi - cos_theta*sin_phi*sin_psi); \ 
     194    zhat = qxhat*(-sin_theta*cos_phi) \ 
     195         + qyhat*(-sin_theta*sin_phi); \ 
     196    } while (0) 
     197#else 
     198// SasView 3.x definition of orientation 
    168199#define ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_alpha, cos_mu, cos_nu) do { \ 
    169200    q = sqrt(qx*qx + qy*qy); \ 
    … …  
    180211    cos_nu = (-cos_phi*sin_psi*sin_theta + sin_phi*cos_psi)*qxhat + sin_psi*cos_theta*qyhat; \ 
    181212    } while (0) 
     213#endif 

  • sasmodels/models/barbell.py

    rfcb33e4 r9802ab3  
    6868The 2D scattering intensity is calculated similar to the 2D cylinder model. 
    6969 
    70 .. figure:: img/cylinder_angle_definition.jpg 
     70.. figure:: img/cylinder_angle_definition.png 
    7171 
    7272    Definition of the angles for oriented 2D barbells. 
    … …  
    8787* **Last Reviewed by:** Richard Heenan **Date:** January 4, 2017 
    8888""" 
    89 from numpy import inf 
     89from numpy import inf, sin, cos, pi 
    9090 
    9191name = "barbell" 
    … …  
    108108              ["radius",      "Ang",         20, [0, inf],    "volume",      "Cylindrical bar radius"], 
    109109              ["length",      "Ang",        400, [0, inf],    "volume",      "Cylinder bar length"], 
    110               ["theta",       "degrees",     60, [-inf, inf], "orientation", "In plane angle"], 
    111               ["phi",         "degrees",     60, [-inf, inf], "orientation", "Out of plane angle"], 
     110              ["theta",       "degrees",     60, [-360, 360], "orientation", "Barbell axis to beam angle"], 
     111              ["phi",         "degrees",     60, [-360, 360], "orientation", "Rotation about beam"], 
    112112             ] 
    113113# pylint: enable=bad-whitespace, line-too-long 
    … …  
    125125            phi_pd=15, phi_pd_n=0, 
    126126           ) 
     127q = 0.1 
     128# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     129qx = q*cos(pi/6.0) 
     130qy = q*sin(pi/6.0) 
     131tests = [[{}, 0.075, 25.5691260532], 
     132        [{'theta':80., 'phi':10.}, (qx, qy), 3.04233067789], 
     133        ] 
     134del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/bcc_paracrystal.c

    r4962519 r50beefe  
    9090    double theta, double phi, double psi) 
    9191{ 
    92     double q, cos_a1, cos_a2, cos_a3; 
    93     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_a3, cos_a2, cos_a1); 
     92    double q, zhat, yhat, xhat; 
     93    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    9494 
    95     const double a1 = +cos_a3 - cos_a1 + cos_a2; 
    96     const double a2 = +cos_a3 + cos_a1 - cos_a2; 
    97     const double a3 = -cos_a3 + cos_a1 + cos_a2; 
     95    const double a1 = +xhat - zhat + yhat; 
     96    const double a2 = +xhat + zhat - yhat; 
     97    const double a3 = -xhat + zhat + yhat; 
    9898 
    9999    const double qd = 0.5*q*dnn; 

  • sasmodels/models/bcc_paracrystal.py

    r925ad6e r69e1afc  
    7979be accurate. 
    8080 
    81 .. figure:: img/bcc_angle_definition.png 
     81.. figure:: img/parallelepiped_angle_definition.png 
    8282 
    83     Orientation of the crystal with respect to the scattering plane. 
     83    Orientation of the crystal with respect to the scattering plane, when  
     84    $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). 
    8485 
    8586References 
    … …  
    99100""" 
    100101 
    101 from numpy import inf 
     102from numpy import inf, pi 
    102103 
    103104name = "bcc_paracrystal" 
    … …  
    122123              ["sld",         "1e-6/Ang^2",  4,    [-inf, inf], "sld",         "Particle scattering length density"], 
    123124              ["sld_solvent", "1e-6/Ang^2",  1,    [-inf, inf], "sld",         "Solvent scattering length density"], 
    124               ["theta",       "degrees",    60,    [-inf, inf], "orientation", "In plane angle"], 
    125               ["phi",         "degrees",    60,    [-inf, inf], "orientation", "Out of plane angle"], 
    126               ["psi",         "degrees",    60,    [-inf, inf], "orientation", "Out of plane angle"] 
     125              ["theta",       "degrees",    60,    [-360, 360], "orientation", "c axis to beam angle"], 
     126              ["phi",         "degrees",    60,    [-360, 360], "orientation", "rotation about beam"], 
     127              ["psi",         "degrees",    60,    [-360, 360], "orientation", "rotation about c axis"] 
    127128             ] 
    128129# pylint: enable=bad-whitespace, line-too-long 
    … …  
    141142    psi_pd=15, psi_pd_n=0, 
    142143    ) 
     144# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     145# add 2d test later 
     146q =4.*pi/220. 
     147tests = [ 
     148    [{ }, 
     149     [0.001, q, 0.215268], [1.46601394721, 2.85851284174, 0.00866710287078]], 
     150    [{'theta':20.0,'phi':30,'psi':40.0},(-0.017,0.035),2082.20264399 ], 
     151    [{'theta':20.0,'phi':30,'psi':40.0},(-0.081,0.011),0.436323144781 ] 
     152    ] 

  • sasmodels/models/capped_cylinder.py

    rfcb33e4 r9802ab3  
    7171The 2D scattering intensity is calculated similar to the 2D cylinder model. 
    7272 
    73 .. figure:: img/cylinder_angle_definition.jpg 
     73.. figure:: img/cylinder_angle_definition.png 
    7474 
    7575    Definition of the angles for oriented 2D cylinders. 
    … …  
    9191 
    9292""" 
    93 from numpy import inf 
     93from numpy import inf, sin, cos, pi 
    9494 
    9595name = "capped_cylinder" 
    … …  
    129129              ["radius_cap", "Ang",     20, [0, inf],    "volume", "Cap radius"], 
    130130              ["length",     "Ang",    400, [0, inf],    "volume", "Cylinder length"], 
    131               ["theta",      "degrees", 60, [-inf, inf], "orientation", "inclination angle"], 
    132               ["phi",        "degrees", 60, [-inf, inf], "orientation", "deflection angle"], 
     131              ["theta",      "degrees", 60, [-360, 360], "orientation", "cylinder axis to beam angle"], 
     132              ["phi",        "degrees", 60, [-360, 360], "orientation", "rotation about beam"], 
    133133             ] 
    134134# pylint: enable=bad-whitespace, line-too-long 
    … …  
    145145            theta_pd=15, theta_pd_n=45, 
    146146            phi_pd=15, phi_pd_n=1) 
     147q = 0.1 
     148# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     149qx = q*cos(pi/6.0) 
     150qy = q*sin(pi/6.0) 
     151tests = [[{}, 0.075, 26.0698570695], 
     152        [{'theta':80., 'phi':10.}, (qx, qy), 0.561811990502], 
     153        ] 
     154del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/core_shell_bicelle.c

    r592343f rb260926  
    3030 
    3131static double 
    32 bicelle_kernel(double qq, 
     32bicelle_kernel(double q, 
    3333              double rad, 
    3434              double radthick, 
    3535              double facthick, 
    36               double length, 
     36              double halflength, 
    3737              double rhoc, 
    3838              double rhoh, 
    … …  
    4242              double cos_alpha) 
    4343{ 
    44     double si1,si2,be1,be2; 
    45  
    4644    const double dr1 = rhoc-rhoh; 
    4745    const double dr2 = rhor-rhosolv; 
    4846    const double dr3 = rhoh-rhor; 
    49     const double vol1 = M_PI*rad*rad*(2.0*length); 
    50     const double vol2 = M_PI*(rad+radthick)*(rad+radthick)*2.0*(length+facthick); 
    51     const double vol3 = M_PI*rad*rad*2.0*(length+facthick); 
    52     double besarg1 = qq*rad*sin_alpha; 
    53     double besarg2 = qq*(rad+radthick)*sin_alpha; 
    54     double sinarg1 = qq*length*cos_alpha; 
    55     double sinarg2 = qq*(length+facthick)*cos_alpha; 
     47    const double vol1 = M_PI*square(rad)*2.0*(halflength); 
     48    const double vol2 = M_PI*square(rad+radthick)*2.0*(halflength+facthick); 
     49    const double vol3 = M_PI*square(rad)*2.0*(halflength+facthick); 
    5650 
    57     be1 = sas_2J1x_x(besarg1); 
    58     be2 = sas_2J1x_x(besarg2); 
    59     si1 = sas_sinx_x(sinarg1); 
    60     si2 = sas_sinx_x(sinarg2); 
     51    const double be1 = sas_2J1x_x(q*(rad)*sin_alpha); 
     52    const double be2 = sas_2J1x_x(q*(rad+radthick)*sin_alpha); 
     53    const double si1 = sas_sinx_x(q*(halflength)*cos_alpha); 
     54    const double si2 = sas_sinx_x(q*(halflength+facthick)*cos_alpha); 
    6155 
    6256    const double t = vol1*dr1*si1*be1 + 
    … …  
    6458                     vol3*dr3*si2*be1; 
    6559 
    66     const double retval = t*t*sin_alpha; 
     60    const double retval = t*t; 
    6761 
    6862    return retval; 
    … …  
    7165 
    7266static double 
    73 bicelle_integration(double qq, 
     67bicelle_integration(double q, 
    7468                   double rad, 
    7569                   double radthick, 
    … …  
    8377    // set up the integration end points 
    8478    const double uplim = M_PI_4; 
    85     const double halfheight = 0.5*length; 
     79    const double halflength = 0.5*length; 
    8680 
    8781    double summ = 0.0; 
    … …  
    9084        double sin_alpha, cos_alpha; // slots to hold sincos function output 
    9185        SINCOS(alpha, sin_alpha, cos_alpha); 
    92         double yyy = Gauss76Wt[i] * bicelle_kernel(qq, rad, radthick, facthick, 
    93                              halfheight, rhoc, rhoh, rhor, rhosolv, 
     86        double yyy = Gauss76Wt[i] * bicelle_kernel(q, rad, radthick, facthick, 
     87                             halflength, rhoc, rhoh, rhor, rhosolv, 
    9488                             sin_alpha, cos_alpha); 
    95         summ += yyy; 
     89        summ += yyy*sin_alpha; 
    9690    } 
    9791 
    … …  
    119113    double answer = bicelle_kernel(q, radius, thick_rim, thick_face, 
    120114                           0.5*length, core_sld, face_sld, rim_sld, 
    121                            solvent_sld, sin_alpha, cos_alpha) / fabs(sin_alpha); 
    122  
    123     answer *= 1.0e-4; 
    124  
    125     return answer; 
     115                           solvent_sld, sin_alpha, cos_alpha); 
     116    return 1.0e-4*answer; 
    126117} 
    127118 

  • sasmodels/models/core_shell_bicelle.py

    r3b9a526 r9802ab3  
    4747.. math:: 
    4848 
    49         \begin{align}     
     49    \begin{align}     
    5050    F(Q,\alpha) = &\bigg[  
    5151    (\rho_c - \rho_f) V_c \frac{2J_1(QRsin \alpha)}{QRsin\alpha}\frac{sin(QLcos\alpha/2)}{Q(L/2)cos\alpha} \\ 
    … …  
    6363cylinders is then given by integrating over all possible $\theta$ and $\phi$. 
    6464 
    65 The *theta* and *phi* parameters are not used for the 1D output. 
     65For oriented bicelles the *theta*, and *phi* orientation parameters will appear when fitting 2D data,  
     66see the :ref:`cylinder` model for further information. 
    6667Our implementation of the scattering kernel and the 1D scattering intensity 
    6768use the c-library from NIST. 
    6869 
    69 .. figure:: img/cylinder_angle_definition.jpg 
     70.. figure:: img/cylinder_angle_definition.png 
    7071 
    71     Definition of the angles for the oriented core shell bicelle tmodel. 
     72    Definition of the angles for the oriented core shell bicelle model, 
     73    note that the cylinder axis of the bicelle starts along the beam direction 
     74    when $\theta  = \phi = 0$. 
    7275 
    7376 
    … …  
    8891""" 
    8992 
    90 from numpy import inf, sin, cos 
     93from numpy import inf, sin, cos, pi 
    9194 
    9295name = "core_shell_bicelle" 
    … …  
    135138    ["sld_rim",        "1e-6/Ang^2", 4, [-inf, inf], "sld",         "Cylinder rim scattering length density"], 
    136139    ["sld_solvent",    "1e-6/Ang^2", 1, [-inf, inf], "sld",         "Solvent scattering length density"], 
    137     ["theta",          "degrees",   90, [-inf, inf], "orientation", "In plane angle"], 
    138     ["phi",            "degrees",    0, [-inf, inf], "orientation", "Out of plane angle"], 
     140    ["theta",          "degrees",   90, [-360, 360], "orientation", "cylinder axis to beam angle"], 
     141    ["phi",            "degrees",    0, [-360, 360], "orientation", "rotation about beam"] 
    139142    ] 
    140143 
    … …  
    155158            theta=90, 
    156159            phi=0) 
     160q = 0.1 
     161# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     162qx = q*cos(pi/6.0) 
     163qy = q*sin(pi/6.0) 
     164tests = [[{}, 0.05, 7.4883545957], 
     165        [{'theta':80., 'phi':10.}, (qx, qy), 2.81048892474 ] 
     166        ] 
     167del qx, qy  # not necessary to delete, but cleaner 
    157168 
    158 #qx, qy = 0.4 * cos(pi/2.0), 0.5 * sin(0) 

  • sasmodels/models/core_shell_bicelle_elliptical.c

    r592343f rdedcf34  
    1 double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length); 
    2 double Iq(double q, 
    3           double radius, 
    4           double x_core, 
    5           double thick_rim, 
    6           double thick_face, 
    7           double length, 
    8           double core_sld, 
    9           double face_sld, 
    10           double rim_sld, 
    11           double solvent_sld); 
    12  
    13  
    14 double Iqxy(double qx, double qy, 
    15           double radius, 
    16           double x_core, 
    17           double thick_rim, 
    18           double thick_face, 
    19           double length, 
    20           double core_sld, 
    21           double face_sld, 
    22           double rim_sld, 
    23           double solvent_sld, 
    24           double theta, 
    25           double phi, 
    26           double psi); 
    27  
    281// NOTE that "length" here is the full height of the core! 
    29 double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length) 
     2static double 
     3form_volume(double r_minor, 
     4        double x_core, 
     5        double thick_rim, 
     6        double thick_face, 
     7        double length) 
    308{ 
    31     return M_PI*(radius+thick_rim)*(radius*x_core+thick_rim)*(length+2.0*thick_face); 
     9    return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); 
    3210} 
    3311 
    34 double  
    35                 Iq(double qq, 
    36                    double rad, 
    37                    double x_core, 
    38                    double radthick, 
    39                    double facthick, 
    40                    double length, 
    41                    double rhoc, 
    42                    double rhoh, 
    43                    double rhor, 
    44                    double rhosolv) 
     12static double 
     13Iq(double q, 
     14        double r_minor, 
     15        double x_core, 
     16        double thick_rim, 
     17        double thick_face, 
     18        double length, 
     19        double rhoc, 
     20        double rhoh, 
     21        double rhor, 
     22        double rhosolv) 
    4523{ 
    4624    double si1,si2,be1,be2; 
    4725     // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle 
    48      // tested against limiting cases of cylinder, elliptical_cylinder and core_shell_bicelle 
     26     // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle 
    4927     //    const double uplim = M_PI_4; 
    5028    const double halfheight = 0.5*length; 
    … …  
    5533    //const double vbj=M_PI; 
    5634 
    57     const double radius_major = rad * x_core; 
    58     const double rA = 0.5*(square(radius_major) + square(rad)); 
    59     const double rB = 0.5*(square(radius_major) - square(rad)); 
    60     const double dr1 = (rhoc-rhoh)   *M_PI*rad*radius_major*(2.0*halfheight);; 
    61     const double dr2 = (rhor-rhosolv)*M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); 
    62     const double dr3 = (rhoh-rhor)   *M_PI*rad*radius_major*2.0*(halfheight+facthick); 
    63     //const double vol1 = M_PI*rad*radius_major*(2.0*halfheight); 
    64     //const double vol2 = M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); 
    65     //const double vol3 = M_PI*rad*radius_major*2.0*(halfheight+facthick); 
     35    const double r_major = r_minor * x_core; 
     36    const double r2A = 0.5*(square(r_major) + square(r_minor)); 
     37    const double r2B = 0.5*(square(r_major) - square(r_minor)); 
     38    const double dr1 = (rhoc-rhoh)   *M_PI*r_minor*r_major*(2.0*halfheight);; 
     39    const double dr2 = (rhor-rhosolv)*M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); 
     40    const double dr3 = (rhoh-rhor)   *M_PI*r_minor*r_major*2.0*(halfheight+thick_face); 
     41    //const double vol1 = M_PI*r_minor*r_major*(2.0*halfheight); 
     42    //const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); 
     43    //const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); 
    6644 
    6745    //initialize integral 
    … …  
    7452        const double sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha); 
    7553        double inner_sum=0; 
    76         double sinarg1 = qq*halfheight*cos_alpha; 
    77         double sinarg2 = qq*(halfheight+facthick)*cos_alpha; 
     54        double sinarg1 = q*halfheight*cos_alpha; 
     55        double sinarg2 = q*(halfheight+thick_face)*cos_alpha; 
    7856        si1 = sas_sinx_x(sinarg1); 
    7957        si2 = sas_sinx_x(sinarg2); 
    … …  
    8260            //const double beta = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; 
    8361            const double beta = ( Gauss76Z[j] +1.0)*M_PI_2; 
    84             const double rr = sqrt(rA - rB*cos(beta)); 
    85             double besarg1 = qq*rr*sin_alpha; 
    86             double besarg2 = qq*(rr+radthick)*sin_alpha; 
     62            const double rr = sqrt(r2A - r2B*cos(beta)); 
     63            double besarg1 = q*rr*sin_alpha; 
     64            double besarg2 = q*(rr+thick_rim)*sin_alpha; 
    8765            be1 = sas_2J1x_x(besarg1); 
    8866            be2 = sas_2J1x_x(besarg2); 
    … …  
    9876} 
    9977 
    100 double  
     78static double 
    10179Iqxy(double qx, double qy, 
    102           double rad, 
     80          double r_minor, 
    10381          double x_core, 
    104           double radthick, 
    105           double facthick, 
     82          double thick_rim, 
     83          double thick_face, 
    10684          double length, 
    10785          double rhoc, 
    … …  
    11492{ 
    11593       // THIS NEEDS TESTING 
    116     double qq, cos_val, cos_mu, cos_nu; 
    117     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, qq, cos_val, cos_mu, cos_nu); 
     94    double q, xhat, yhat, zhat; 
     95    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    11896    const double dr1 = rhoc-rhoh; 
    11997    const double dr2 = rhor-rhosolv; 
    12098    const double dr3 = rhoh-rhor; 
    121     const double radius_major = rad*x_core; 
     99    const double r_major = r_minor*x_core; 
    122100    const double halfheight = 0.5*length; 
    123     const double vol1 = M_PI*rad*radius_major*length; 
    124     const double vol2 = M_PI*(rad+radthick)*(radius_major+radthick)*2.0*(halfheight+facthick); 
    125     const double vol3 = M_PI*rad*radius_major*2.0*(halfheight+facthick); 
     101    const double vol1 = M_PI*r_minor*r_major*length; 
     102    const double vol2 = M_PI*(r_minor+thick_rim)*(r_major+thick_rim)*2.0*(halfheight+thick_face); 
     103    const double vol3 = M_PI*r_minor*r_major*2.0*(halfheight+thick_face); 
    126104 
    127     // Compute:  r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) 
    128     // Given:    radius_major = r_ratio * radius_minor   
    129     // ASSUME the sin_alpha is included in the separate integration over orientation of rod angle 
    130     const double r = rad*sqrt(square(x_core*cos_nu) + cos_mu*cos_mu); 
    131     const double be1 = sas_2J1x_x( qq*r ); 
    132     const double be2 = sas_2J1x_x( qq*(r + radthick ) ); 
    133     const double si1 = sas_sinx_x( qq*halfheight*cos_val ); 
    134     const double si2 = sas_sinx_x( qq*(halfheight + facthick)*cos_val ); 
     105    // Compute effective radius in rotated coordinates 
     106    const double r_hat = sqrt(square(r_major*xhat) + square(r_minor*yhat)); 
     107    const double rshell_hat = sqrt(square((r_major+thick_rim)*xhat) 
     108                                   + square((r_minor+thick_rim)*yhat)); 
     109    const double be1 = sas_2J1x_x( q*r_hat ); 
     110    const double be2 = sas_2J1x_x( q*rshell_hat ); 
     111    const double si1 = sas_sinx_x( q*halfheight*zhat ); 
     112    const double si2 = sas_sinx_x( q*(halfheight + thick_face)*zhat ); 
    135113    const double Aq = square( vol1*dr1*si1*be1 + vol2*dr2*si2*be2 +  vol3*dr3*si2*be1); 
    136     //const double vol = form_volume(radius_minor, r_ratio, length); 
    137114    return 1.0e-4 * Aq; 
    138115} 

  • sasmodels/models/core_shell_bicelle_elliptical.py

    r3b9a526 r9802ab3  
    7676bicelles is then given by integrating over all possible $\alpha$ and $\psi$. 
    7777 
    78 For oriented bicellles the *theta*, *phi* and *psi* orientation parameters only appear when fitting 2D data,  
     78For oriented bicelles the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
    7979see the :ref:`elliptical-cylinder` model for further information. 
    8080 
    8181 
    82 .. figure:: img/elliptical_cylinder_angle_definition.jpg 
     82.. figure:: img/elliptical_cylinder_angle_definition.png 
    8383 
    84     Definition of the angles for the oriented core_shell_bicelle_elliptical model. 
    85     Note that *theta* and *phi* are currently defined differently to those for the core_shell_bicelle model. 
     84    Definition of the angles for the oriented core_shell_bicelle_elliptical particles.    
     85 
    8686 
    8787 
    … …  
    9999""" 
    100100 
    101 from numpy import inf, sin, cos 
     101from numpy import inf, sin, cos, pi 
    102102 
    103103name = "core_shell_bicelle_elliptical" 
    … …  
    119119    ["radius",         "Ang",       30, [0, inf],    "volume",      "Cylinder core radius"], 
    120120    ["x_core",        "None",       3,  [0, inf],    "volume",      "axial ratio of core, X = r_polar/r_equatorial"], 
    121     ["thick_rim",  "Ang",        8, [0, inf],    "volume",      "Rim shell thickness"], 
    122     ["thick_face", "Ang",       14, [0, inf],    "volume",      "Cylinder face thickness"], 
    123     ["length",         "Ang",      50, [0, inf],    "volume",      "Cylinder length"], 
     121    ["thick_rim",  "Ang",            8, [0, inf],    "volume",      "Rim shell thickness"], 
     122    ["thick_face", "Ang",           14, [0, inf],    "volume",      "Cylinder face thickness"], 
     123    ["length",         "Ang",       50, [0, inf],    "volume",      "Cylinder length"], 
    124124    ["sld_core",       "1e-6/Ang^2", 4, [-inf, inf], "sld",         "Cylinder core scattering length density"], 
    125125    ["sld_face",       "1e-6/Ang^2", 7, [-inf, inf], "sld",         "Cylinder face scattering length density"], 
    126126    ["sld_rim",        "1e-6/Ang^2", 1, [-inf, inf], "sld",         "Cylinder rim scattering length density"], 
    127127    ["sld_solvent",    "1e-6/Ang^2", 6, [-inf, inf], "sld",         "Solvent scattering length density"], 
    128     ["theta",          "degrees",   90, [-360, 360], "orientation", "In plane angle"], 
    129     ["phi",            "degrees",    0, [-360, 360], "orientation", "Out of plane angle"], 
    130     ["psi",            "degrees",    0, [-360, 360], "orientation", "Major axis angle relative to Q"], 
     128    ["theta",       "degrees",    90.0, [-360, 360], "orientation", "cylinder axis to beam angle"], 
     129    ["phi",         "degrees",    0,    [-360, 360], "orientation", "rotation about beam"], 
     130    ["psi",         "degrees",    0,    [-360, 360], "orientation", "rotation about cylinder axis"] 
    131131    ] 
    132132 
    … …  
    150150            psi=0) 
    151151 
    152 #qx, qy = 0.4 * cos(pi/2.0), 0.5 * sin(0) 
     152q = 0.1 
     153# april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! 
     154qx = q*cos(pi/6.0) 
     155qy = q*sin(pi/6.0) 
    153156 
    154157tests = [ 
    … …  
    159162    'sld_core':4.0, 'sld_face':7.0, 'sld_rim':1.0, 'sld_solvent':6.0, 'background':0.0}, 
    160163    0.015, 286.540286], 
    161 ] 
     164#    [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], 
     165        ] 
     166 
     167del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/core_shell_cylinder.py

    rfcb33e4 r9b79f29  
    7373""" 
    7474 
    75 from numpy import pi, inf 
     75from numpy import pi, inf, sin, cos 
    7676 
    7777name = "core_shell_cylinder" 
    … …  
    117117              ["length", "Ang", 400, [0, inf], "volume", 
    118118               "Cylinder length"], 
    119               ["theta", "degrees", 60, [-inf, inf], "orientation", 
    120                "In plane angle"], 
    121               ["phi", "degrees", 60, [-inf, inf], "orientation", 
    122                "Out of plane angle"], 
     119              ["theta", "degrees", 60, [-360, 360], "orientation", 
     120               "cylinder axis to beam angle"], 
     121              ["phi", "degrees",   60, [-360, 360], "orientation", 
     122               "rotation about beam"], 
    123123             ] 
    124124 
    … …  
    151151            theta_pd=15, theta_pd_n=45, 
    152152            phi_pd=15, phi_pd_n=1) 
    153  
     153q = 0.1 
     154# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     155qx = q*cos(pi/6.0) 
     156qy = q*sin(pi/6.0) 
     157tests = [[{}, 0.075, 10.8552692237], 
     158        [{}, (qx, qy), 0.444618752741 ], 
     159        ] 
     160del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/core_shell_ellipsoid.py

    rdaeef4c r9802ab3  
    7777   F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} 
    7878 
     79For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
     80see the :ref:`elliptical-cylinder` model for further information. 
    7981 
    8082References 
    … …  
    132134    ["sld_shell",     "1e-6/Ang^2", 1,   [-inf, inf], "sld",         "Shell scattering length density"], 
    133135    ["sld_solvent",   "1e-6/Ang^2", 6.3, [-inf, inf], "sld",         "Solvent scattering length density"], 
    134     ["theta",         "degrees",    0,   [-inf, inf], "orientation", "Oblate orientation wrt incoming beam"], 
    135     ["phi",           "degrees",    0,   [-inf, inf], "orientation", "Oblate orientation in the plane of the detector"], 
     136    ["theta",         "degrees",    0,   [-360, 360], "orientation", "elipsoid axis to beam angle"], 
     137    ["phi",           "degrees",    0,   [-360, 360], "orientation", "rotation about beam"], 
    136138    ] 
    137139# pylint: enable=bad-whitespace, line-too-long 

  • sasmodels/models/core_shell_parallelepiped.c

    r1e7b0db0 r92dfe0c  
    134134    double psi) 
    135135{ 
    136     double q, cos_val_a, cos_val_b, cos_val_c; 
    137     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_val_c, cos_val_b, cos_val_a); 
     136    double q, zhat, yhat, xhat; 
     137    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    138138 
    139139    // cspkernel in csparallelepiped recoded here 
    … …  
    160160    double tc = length_a + 2.0*thick_rim_c; 
    161161    //handle arg=0 separately, as sin(t)/t -> 1 as t->0 
    162     double siA = sas_sinx_x(0.5*q*length_a*cos_val_a); 
    163     double siB = sas_sinx_x(0.5*q*length_b*cos_val_b); 
    164     double siC = sas_sinx_x(0.5*q*length_c*cos_val_c); 
    165     double siAt = sas_sinx_x(0.5*q*ta*cos_val_a); 
    166     double siBt = sas_sinx_x(0.5*q*tb*cos_val_b); 
    167     double siCt = sas_sinx_x(0.5*q*tc*cos_val_c); 
     162    double siA = sas_sinx_x(0.5*q*length_a*xhat); 
     163    double siB = sas_sinx_x(0.5*q*length_b*yhat); 
     164    double siC = sas_sinx_x(0.5*q*length_c*zhat); 
     165    double siAt = sas_sinx_x(0.5*q*ta*xhat); 
     166    double siBt = sas_sinx_x(0.5*q*tb*yhat); 
     167    double siCt = sas_sinx_x(0.5*q*tc*zhat); 
    168168     
    169169 

  • sasmodels/models/core_shell_parallelepiped.py

    rcb0dc22 r9b79f29  
    66The thickness and the scattering length density of the shell or  
    77"rim" can be different on each (pair) of faces. However at this time 
    8 the model does **NOT** actually calculate a c face rim despite the presence of 
    9 the parameter. 
     8the 1D calculation does **NOT** actually calculate a c face rim despite the presence of 
     9the parameter. Some other aspects of the 1D calculation may be wrong. 
    1010 
    1111.. note:: 
    12    This model was originally ported from NIST IGOR macros. However,t is not 
    13    yet fully understood by the SasView developers and is currently review. 
     12   This model was originally ported from NIST IGOR macros. However, it is not 
     13   yet fully understood by the SasView developers and is currently under review. 
    1414 
    1515The form factor is normalized by the particle volume $V$ such that 
    … …  
    4848amplitudes of the core and shell, in the same manner as a core-shell model. 
    4949 
     50.. math:: 
     51 
     52    F_{a}(Q,\alpha,\beta)= 
     53    \left[\frac{\sin(\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha \sin\beta)}{\tfrac{1}{2}Q(L_A+2t_A)\sin\alpha\sin\beta} 
     54    - \frac{\sin(\tfrac{1}{2}QL_A\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_A\sin\alpha \sin\beta} \right] 
     55    \left[\frac{\sin(\tfrac{1}{2}QL_B\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_B\sin\alpha \sin\beta} \right] 
     56    \left[\frac{\sin(\tfrac{1}{2}QL_C\sin\alpha \sin\beta)}{\tfrac{1}{2}QL_C\sin\alpha \sin\beta} \right] 
    5057 
    5158.. note:: 
    5259 
     60    Why does t_B not appear in the above equation? 
    5361    For the calculation of the form factor to be valid, the sides of the solid 
    54     MUST be chosen such that** $A < B < C$. 
     62    MUST (perhaps not any more?) be chosen such that** $A < B < C$. 
    5563    If this inequality is not satisfied, the model will not report an error, 
    5664    but the calculation will not be correct and thus the result wrong. 
    5765 
    5866FITTING NOTES 
    59 If the scale is set equal to the particle volume fraction, |phi|, the returned 
     67If the scale is set equal to the particle volume fraction, $\phi$, the returned 
    6068value is the scattered intensity per unit volume, $I(q) = \phi P(q)$. 
    6169However, **no interparticle interference effects are included in this 
    … …  
    7381NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated 
    7482based on the the averaged effective radius $(=\sqrt{(A+2t_A)(B+2t_B)/\pi})$ 
    75 and length $(C+2t_C)$ values, and used as the effective radius 
    76 for $S(Q)$ when $P(Q) * S(Q)$ is applied. 
     83and length $(C+2t_C)$ values, after appropriately 
     84sorting the three dimensions to give an oblate or prolate particle, to give an  
     85effective radius, for $S(Q)$ when $P(Q) * S(Q)$ is applied. 
    7786 
    7887To provide easy access to the orientation of the parallelepiped, we define the 
    … …  
    8392*x*-axis of the detector. 
    8493 
    85 .. figure:: img/parallelepiped_angle_definition.jpg 
     94.. figure:: img/parallelepiped_angle_definition.png 
    8695 
    8796    Definition of the angles for oriented core-shell parallelepipeds. 
    8897 
    89 .. figure:: img/parallelepiped_angle_projection.jpg 
     98.. figure:: img/parallelepiped_angle_projection.png 
    9099 
    91100    Examples of the angles for oriented core-shell parallelepipeds against the 
    … …  
    112121 
    113122import numpy as np 
    114 from numpy import pi, inf, sqrt 
     123from numpy import pi, inf, sqrt, cos, sin 
    115124 
    116125name = "core_shell_parallelepiped" 
    … …  
    144153              ["thick_rim_c", "Ang", 10, [0, inf], "volume", 
    145154               "Thickness of C rim"], 
    146               ["theta", "degrees", 0, [-inf, inf], "orientation", 
    147                "In plane angle"], 
    148               ["phi", "degrees", 0, [-inf, inf], "orientation", 
    149                "Out of plane angle"], 
    150               ["psi", "degrees", 0, [-inf, inf], "orientation", 
    151                "Rotation angle around its own c axis against q plane"], 
     155              ["theta", "degrees", 0, [-360, 360], "orientation", 
     156               "c axis to beam angle"], 
     157              ["phi", "degrees", 0, [-360, 360], "orientation", 
     158               "rotation about beam"], 
     159              ["psi", "degrees", 0, [-360, 360], "orientation", 
     160               "rotation about c axis"], 
    152161             ] 
    153162 
    … …  
    186195            psi_pd=10, psi_pd_n=1) 
    187196 
    188 qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5) 
     197# rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models 
     198qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) 
    189199tests = [[{}, 0.2, 0.533149288477], 
    190200         [{}, [0.2], [0.533149288477]], 
    191          [{'theta':10.0, 'phi':10.0}, (qx, qy), 0.032102135569], 
    192          [{'theta':10.0, 'phi':10.0}, [(qx, qy)], [0.032102135569]], 
     201         [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0853299803222], 
     202         [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0853299803222]], 
    193203        ] 
    194204del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/cylinder.py

    r3330bb4 r9802ab3  
    3838 
    3939 
    40 Numerical integration is simplified by a change of variable to $u = cos(\alpha)$ with  
    41 $sin(\alpha)=\sqrt{1-u^2}$.  
     40Numerical integration is simplified by a change of variable to $u = cos(\alpha)$ with 
     41$sin(\alpha)=\sqrt{1-u^2}$. 
    4242 
    4343The output of the 1D scattering intensity function for randomly oriented 
    … …  
    6161.. _cylinder-angle-definition: 
    6262 
    63 .. figure:: img/cylinder_angle_definition.jpg 
     63.. figure:: img/cylinder_angle_definition.png 
    6464 
    65     Definition of the angles for oriented cylinders. 
     65    Definition of the $\theta$ and $\phi$ orientation angles for a cylinder relative  
     66    to the beam line coordinates, plus an indication of their orientation distributions  
     67    which are described as rotations about each of the perpendicular axes $\delta_1$ and $\delta_2$  
     68    in the frame of the cylinder itself, which when $\theta = \phi = 0$ are parallel to the $Y$ and $X$ axes. 
    6669 
    67 The $\theta$ and $\phi$ parameters only appear in the model when fitting 2d data. 
     70.. figure:: img/cylinder_angle_projection.png 
     71 
     72    Examples for oriented cylinders. 
     73 
     74The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data.  
     75On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
     76appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, which when $\theta = \phi = 0$ are parallel  
     77to the $Y$ and $X$ axes of the instrument respectively. Some experimentation may be required to understand the 2d patterns fully. 
     78(Earlier implementations had numerical integration issues in some circumstances when orientation distributions passed through 90 degrees, such  
     79situations, with very broad distributions, should still be approached with care.)  
    6880 
    6981Validation 
    … …  
    123135              ["length", "Ang", 400, [0, inf], "volume", 
    124136               "Cylinder length"], 
    125               ["theta", "degrees", 60, [-inf, inf], "orientation", 
    126                "latitude"], 
    127               ["phi", "degrees", 60, [-inf, inf], "orientation", 
    128                "longitude"], 
     137              ["theta", "degrees", 60, [-360, 360], "orientation", 
     138               "cylinder axis to beam angle"], 
     139              ["phi", "degrees",   60, [-360, 360], "orientation", 
     140               "rotation about beam"], 
    129141             ] 
    130142 
    … …  
    152164tests = [[{}, 0.2, 0.042761386790780453], 
    153165        [{}, [0.2], [0.042761386790780453]], 
    154 #  new coords     
     166#  new coords 
    155167        [{'theta':80.1534480601659, 'phi':10.1510817110481}, (qx, qy), 0.03514647218513852], 
    156168        [{'theta':80.1534480601659, 'phi':10.1510817110481}, [(qx, qy)], [0.03514647218513852]], 

  • sasmodels/models/ellipsoid.c

    r130d4c7 r3b571ae  
    33double Iqxy(double qx, double qy, double sld, double sld_solvent, 
    44    double radius_polar, double radius_equatorial, double theta, double phi); 
    5  
    6 static double 
    7 _ellipsoid_kernel(double q, double radius_polar, double radius_equatorial, double cos_alpha) 
    8 { 
    9     double ratio = radius_polar/radius_equatorial; 
    10     // Using ratio v = Rp/Re, we can expand the following to match the 
    11     // form given in Guinier (1955) 
    12     //     r = Re * sqrt(1 + cos^2(T) (v^2 - 1)) 
    13     //       = Re * sqrt( (1 - cos^2(T)) + v^2 cos^2(T) ) 
    14     //       = Re * sqrt( sin^2(T) + v^2 cos^2(T) ) 
    15     //       = sqrt( Re^2 sin^2(T) + Rp^2 cos^2(T) ) 
    16     // 
    17     // Instead of using pythagoras we could pass in sin and cos; this may be 
    18     // slightly better for 2D which has already computed it, but it introduces 
    19     // an extra sqrt and square for 1-D not required by the current form, so 
    20     // leave it as is. 
    21     const double r = radius_equatorial 
    22                      * sqrt(1.0 + cos_alpha*cos_alpha*(ratio*ratio - 1.0)); 
    23     const double f = sas_3j1x_x(q*r); 
    24  
    25     return f*f; 
    26 } 
    275 
    286double form_volume(double radius_polar, double radius_equatorial) 
    … …  
    3715    double radius_equatorial) 
    3816{ 
     17    // Using ratio v = Rp/Re, we can implement the form given in Guinier (1955) 
     18    //     i(h) = int_0^pi/2 Phi^2(h a sqrt(cos^2 + v^2 sin^2) cos dT 
     19    //          = int_0^pi/2 Phi^2(h a sqrt((1-sin^2) + v^2 sin^2) cos dT 
     20    //          = int_0^pi/2 Phi^2(h a sqrt(1 + sin^2(v^2-1)) cos dT 
     21    // u-substitution of 
     22    //     u = sin, du = cos dT 
     23    //     i(h) = int_0^1 Phi^2(h a sqrt(1 + u^2(v^2-1)) du 
     24    const double v_square_minus_one = square(radius_polar/radius_equatorial) - 1.0; 
     25 
    3926    // translate a point in [-1,1] to a point in [0, 1] 
     27    // const double u = Gauss76Z[i]*(upper-lower)/2 + (upper+lower)/2; 
    4028    const double zm = 0.5; 
    4129    const double zb = 0.5; 
    4230    double total = 0.0; 
    4331    for (int i=0;i<76;i++) { 
    44         //const double cos_alpha = (Gauss76Z[i]*(upper-lower) + upper + lower)/2; 
    45         const double cos_alpha = Gauss76Z[i]*zm + zb; 
    46         total += Gauss76Wt[i] * _ellipsoid_kernel(q, radius_polar, radius_equatorial, cos_alpha); 
     32        const double u = Gauss76Z[i]*zm + zb; 
     33        const double r = radius_equatorial*sqrt(1.0 + u*u*v_square_minus_one); 
     34        const double f = sas_3j1x_x(q*r); 
     35        total += Gauss76Wt[i] * f * f; 
    4736    } 
    4837    // translate dx in [-1,1] to dx in [lower,upper] 
    … …  
    6251    double q, sin_alpha, cos_alpha; 
    6352    ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, cos_alpha); 
    64     const double form = _ellipsoid_kernel(q, radius_polar, radius_equatorial, cos_alpha); 
     53    const double r = sqrt(square(radius_equatorial*sin_alpha) 
     54                          + square(radius_polar*cos_alpha)); 
     55    const double f = sas_3j1x_x(q*r); 
    6556    const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); 
    6657 
    67     return 1.0e-4 * form * s * s; 
     58    return 1.0e-4 * square(f * s); 
    6859} 
    6960 

  • sasmodels/models/ellipsoid.py

    r925ad6e r9b79f29  
    1818.. math:: 
    1919 
    20     F(q,\alpha) = \frac{3 \Delta \rho V (\sin[qr(R_p,R_e,\alpha)] 
    21                 - \cos[qr(R_p,R_e,\alpha)])} 
    22                 {[qr(R_p,R_e,\alpha)]^3} 
     20    F(q,\alpha) = \Delta \rho V \frac{3(\sin qr  - qr \cos qr)}{(qr)^3} 
    2321 
    24 and 
     22for 
    2523 
    2624.. math:: 
    2725 
    28     r(R_p,R_e,\alpha) = \left[ R_e^2 \sin^2 \alpha 
    29         + R_p^2 \cos^2 \alpha \right]^{1/2} 
     26    r = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2} 
    3027 
    3128 
    3229$\alpha$ is the angle between the axis of the ellipsoid and $\vec q$, 
    33 $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the polar radius along the 
    34 rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular 
    35 to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the 
    36 scattering length density difference between the scatterer and the solvent. 
     30$V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid, $R_p$ is the polar 
     31radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial 
     32radius perpendicular to the rotational axis of the ellipsoid and 
     33$\Delta \rho$ (contrast) is the scattering length density difference between 
     34the scatterer and the solvent. 
    3735 
    38 For randomly oriented particles: 
     36For randomly oriented particles use the orientational average, 
    3937 
    4038.. math:: 
    4139 
    42    F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} 
     40   \langle F^2(q) \rangle = \int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)\,d\alpha} 
    4341 
     42 
     43computed via substitution of $u=\sin(\alpha)$, $du=\cos(\alpha)\,d\alpha$ as 
     44 
     45.. math:: 
     46 
     47    \langle F^2(q) \rangle = \int_0^1{F^2(q, u)\,du} 
     48 
     49with 
     50 
     51.. math:: 
     52 
     53    r = R_e \left[ 1 + u^2\left(R_p^2/R_e^2 - 1\right)\right]^{1/2} 
    4454 
    4555To provide easy access to the orientation of the ellipsoid, we define 
    … …  
    4858:ref:`cylinder orientation figure <cylinder-angle-definition>`. 
    4959For the ellipsoid, $\theta$ is the angle between the rotational axis 
    50 and the $z$ -axis. 
     60and the $z$ -axis in the $xz$ plane followed by a rotation by $\phi$ 
     61in the $xy$ plane. 
    5162 
    5263NB: The 2nd virial coefficient of the solid ellipsoid is calculated based 
    … …  
    90101than 500. 
    91102 
     103Model was also tested against the triaxial ellipsoid model with equal major 
     104and minor equatorial radii.  It is also consistent with the cyclinder model 
     105with polar radius equal to length and equatorial radius equal to radius. 
     106 
    92107References 
    93108---------- 
    … …  
    96111*Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, 
    97112Plenum Press, New York, 1987. 
     113 
     114Authorship and Verification 
     115---------------------------- 
     116 
     117* **Author:** NIST IGOR/DANSE **Date:** pre 2010 
     118* **Converted to sasmodels by:** Helen Park **Date:** July 9, 2014 
     119* **Last Modified by:** Paul Kienzle **Date:** March 22, 2017 
    98120""" 
    99121 
    100 from numpy import inf 
     122from numpy import inf, sin, cos, pi 
    101123 
    102124name = "ellipsoid" 
    … …  
    129151              ["radius_equatorial", "Ang", 400, [0, inf], "volume", 
    130152               "Equatorial radius"], 
    131               ["theta", "degrees", 60, [-inf, inf], "orientation", 
    132                "In plane angle"], 
    133               ["phi", "degrees", 60, [-inf, inf], "orientation", 
    134                "Out of plane angle"], 
     153              ["theta", "degrees", 60, [-360, 360], "orientation", 
     154               "ellipsoid axis to beam angle"], 
     155              ["phi", "degrees", 60, [-360, 360], "orientation", 
     156               "rotation about beam"], 
    135157             ] 
    136158 
    … …  
    139161def ER(radius_polar, radius_equatorial): 
    140162    import numpy as np 
    141  
     163# see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449 
    142164    ee = np.empty_like(radius_polar) 
    143165    idx = radius_polar > radius_equatorial 
    … …  
    168190            theta_pd=15, theta_pd_n=45, 
    169191            phi_pd=15, phi_pd_n=1) 
     192q = 0.1 
     193# april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     194qx = q*cos(pi/6.0) 
     195qy = q*sin(pi/6.0) 
     196tests = [[{}, 0.05, 54.8525847025], 
     197        [{'theta':80., 'phi':10.}, (qx, qy), 1.74134670026 ], 
     198        ] 
     199del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/elliptical_cylinder.c

    r592343f r61104c8  
    6767     double theta, double phi, double psi) 
    6868{ 
    69     double q, cos_val, cos_mu, cos_nu; 
    70     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_val, cos_mu, cos_nu); 
     69    double q, xhat, yhat, zhat; 
     70    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    7171 
    7272    // Compute:  r = sqrt((radius_major*cos_nu)^2 + (radius_minor*cos_mu)^2) 
    7373    // Given:    radius_major = r_ratio * radius_minor 
    74     const double r = radius_minor*sqrt(square(r_ratio*cos_nu) + cos_mu*cos_mu); 
     74    const double r = radius_minor*sqrt(square(r_ratio*xhat) + square(yhat)); 
    7575    const double be = sas_2J1x_x(q*r); 
    76     const double si = sas_sinx_x(q*0.5*length*cos_val); 
     76    const double si = sas_sinx_x(q*zhat*0.5*length); 
    7777    const double Aq = be * si; 
    7878    const double delrho = sld - solvent_sld; 

  • sasmodels/models/elliptical_cylinder.py

    rfcb33e4 r9802ab3  
    5757define the axis of the cylinder using two angles $\theta$, $\phi$ and $\Psi$ 
    5858(see :ref:`cylinder orientation <cylinder-angle-definition>`). The angle 
    59 $\Psi$ is the rotational angle around its own long_c axis against the $q$ plane. 
    60 For example, $\Psi = 0$ when the $r_\text{minor}$ axis is parallel to the 
    61 $x$ axis of the detector. 
     59$\Psi$ is the rotational angle around its own long_c axis.  
    6260 
    6361All angle parameters are valid and given only for 2D calculation; ie, an 
    6462oriented system. 
    6563 
    66 .. figure:: img/elliptical_cylinder_angle_definition.jpg 
     64.. figure:: img/elliptical_cylinder_angle_definition.png 
    6765 
    68     Definition of angles for 2D 
     66    Definition of angles for oriented elliptical cylinder, where axis_ratio is drawn >1, 
     67    and angle $\Psi$ is now a rotation around the axis of the cylinder. 
    6968 
    70 .. figure:: img/cylinder_angle_projection.jpg 
     69.. figure:: img/elliptical_cylinder_angle_projection.png 
    7170 
    7271    Examples of the angles for oriented elliptical cylinders against the 
    73     detector plane. 
     72    detector plane, with $\Psi$ = 0. 
     73 
     74The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data.  
     75On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
     76appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, the $b$ and $a$ axes of the  
     77cylinder cross section. (When $\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the instrument.)  
     78The third orientation distribution, in $\psi$, is about the $c$ axis of the particle. Some experimentation may be required to  
     79understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation  
     80distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.)  
    7481 
    7582NB: The 2nd virial coefficient of the cylinder is calculated based on the 
    … …  
    108115""" 
    109116 
    110 from numpy import pi, inf, sqrt 
     117from numpy import pi, inf, sqrt, sin, cos 
    111118 
    112119name = "elliptical_cylinder" 
    … …  
    125132              ["sld",         "1e-6/Ang^2", 4.0,   [-inf, inf], "sld",         "Cylinder scattering length density"], 
    126133              ["sld_solvent", "1e-6/Ang^2", 1.0,   [-inf, inf], "sld",         "Solvent scattering length density"], 
    127               ["theta",       "degrees",    90.0,  [-360, 360], "orientation", "In plane angle"], 
    128               ["phi",         "degrees",    0,     [-360, 360], "orientation", "Out of plane angle"], 
    129               ["psi",         "degrees",    0,     [-360, 360], "orientation", "Major axis angle relative to Q"]] 
     134              ["theta",       "degrees",    90.0,  [-360, 360], "orientation", "cylinder axis to beam angle"], 
     135              ["phi",         "degrees",    0,     [-360, 360], "orientation", "rotation about beam"], 
     136              ["psi",         "degrees",    0,     [-360, 360], "orientation", "rotation about cylinder axis"]] 
    130137 
    131138# pylint: enable=bad-whitespace, line-too-long 
    … …  
    149156                           + (length + radius) * (length + pi * radius)) 
    150157    return 0.5 * (ddd) ** (1. / 3.) 
     158q = 0.1 
     159# april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! 
     160qx = q*cos(pi/6.0) 
     161qy = q*sin(pi/6.0) 
    151162 
    152163tests = [ 
    … …  
    158169      'sld_solvent':1.0, 'background':0.0}, 
    159170     0.001, 675.504402], 
     171#    [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], 
    160172] 

  • sasmodels/models/fcc_paracrystal.c

    r4962519 r50beefe  
    9090    double theta, double phi, double psi) 
    9191{ 
    92     double q, cos_a1, cos_a2, cos_a3; 
    93     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_a3, cos_a2, cos_a1); 
     92    double q, zhat, yhat, xhat; 
     93    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    9494 
    95     const double a1 = cos_a2 + cos_a3; 
    96     const double a2 = cos_a3 + cos_a1; 
    97     const double a3 = cos_a2 + cos_a1; 
     95    const double a1 = yhat + xhat; 
     96    const double a2 = xhat + zhat; 
     97    const double a3 = yhat + zhat; 
    9898    const double qd = 0.5*q*dnn; 
    9999    const double arg = 0.5*square(qd*d_factor)*(a1*a1 + a2*a2 + a3*a3); 

  • sasmodels/models/fcc_paracrystal.py

    r925ad6e r69e1afc  
    76762D model computation. 
    7777 
    78 .. figure:: img/bcc_angle_definition.png 
     78.. figure:: img/parallelepiped_angle_definition.png 
    7979 
    80     Orientation of the crystal with respect to the scattering plane. 
     80    Orientation of the crystal with respect to the scattering plane, when  
     81    $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). 
    8182 
    8283References 
    … …  
    9091""" 
    9192 
    92 from numpy import inf 
     93from numpy import inf, pi 
    9394 
    9495name = "fcc_paracrystal" 
    … …  
    110111              ["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Particle scattering length density"], 
    111112              ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], 
    112               ["theta", "degrees", 60, [-inf, inf], "orientation", "In plane angle"], 
    113               ["phi", "degrees", 60, [-inf, inf], "orientation", "Out of plane angle"], 
    114               ["psi", "degrees", 60, [-inf, inf], "orientation", "Out of plane angle"] 
     113              ["theta",       "degrees",    60,    [-360, 360], "orientation", "c axis to beam angle"], 
     114              ["phi",         "degrees",    60,    [-360, 360], "orientation", "rotation about beam"], 
     115              ["psi",         "degrees",    60,    [-360, 360], "orientation", "rotation about c axis"] 
    115116             ] 
    116117# pylint: enable=bad-whitespace, line-too-long 
    … …  
    128129            psi_pd=15, psi_pd_n=0, 
    129130           ) 
     131# april 10 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
     132q =4.*pi/220. 
     133tests = [ 
     134    [{ }, 
     135     [0.001, q, 0.215268], [0.275164706668, 5.7776842567, 0.00958167119232]], 
     136     [{}, (-0.047,-0.007), 238.103096286], 
     137     [{}, (0.053,0.063), 0.863609587796 ], 
     138] 

  • sasmodels/models/hollow_cylinder.py

    raea2e2a r9b79f29  
    6060""" 
    6161 
    62 from numpy import pi, inf 
     62from numpy import pi, inf, sin, cos 
    6363 
    6464name = "hollow_cylinder" 
    … …  
    8282    ["sld",         "1/Ang^2",  6.3, [-inf, inf], "sld",         "Cylinder sld"], 
    8383    ["sld_solvent", "1/Ang^2",  1,   [-inf, inf], "sld",         "Solvent sld"], 
    84     ["theta",       "degrees", 90,   [-360, 360], "orientation", "Theta angle"], 
    85     ["phi",         "degrees",  0,   [-360, 360], "orientation", "Phi angle"], 
     84    ["theta",       "degrees", 90,   [-360, 360], "orientation", "Cylinder axis to beam angle"], 
     85    ["phi",         "degrees",  0,   [-360, 360], "orientation", "Rotation about beam"], 
    8686    ] 
    8787# pylint: enable=bad-whitespace, line-too-long 
    … …  
    129129            theta_pd=10, theta_pd_n=5, 
    130130           ) 
    131  
     131q = 0.1 
     132# april 6 2017, rkh added a 2d unit test, assume correct! 
     133qx = q*cos(pi/6.0) 
     134qy = q*sin(pi/6.0) 
    132135# Parameters for unit tests 
    133136tests = [ 
    134137    [{}, 0.00005, 1764.926], 
    135138    [{}, 'VR', 1.8], 
    136     [{}, 0.001, 1756.76] 
    137     ] 
     139    [{}, 0.001, 1756.76], 
     140    [{}, (qx, qy), 2.36885476192  ], 
     141        ] 
     142del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/parallelepiped.c

    r1e7b0db0 rd605080  
    6767    double psi) 
    6868{ 
    69     double q, cos_val_a, cos_val_b, cos_val_c; 
    70     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_val_c, cos_val_b, cos_val_a); 
     69    double q, xhat, yhat, zhat; 
     70    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    7171 
    72     const double siA = sas_sinx_x(0.5*q*length_a*cos_val_a); 
    73     const double siB = sas_sinx_x(0.5*q*length_b*cos_val_b); 
    74     const double siC = sas_sinx_x(0.5*q*length_c*cos_val_c); 
     72    const double siA = sas_sinx_x(0.5*length_a*q*xhat); 
     73    const double siB = sas_sinx_x(0.5*length_b*q*yhat); 
     74    const double siC = sas_sinx_x(0.5*length_c*q*zhat); 
    7575    const double V = form_volume(length_a, length_b, length_c); 
    7676    const double drho = (sld - solvent_sld); 

  • sasmodels/models/parallelepiped.py

    r3330bb4 r34a9e4e  
    99---------- 
    1010 
    11 | This model calculates the scattering from a rectangular parallelepiped 
    12 | (\:numref:`parallelepiped-image`\). 
    13 | If you need to apply polydispersity, see also :ref:`rectangular-prism`. 
     11 This model calculates the scattering from a rectangular parallelepiped 
     12 (\:numref:`parallelepiped-image`\). 
     13 If you need to apply polydispersity, see also :ref:`rectangular-prism`. 
    1414 
    1515.. _parallelepiped-image: 
    1616 
     17 
    1718.. figure:: img/parallelepiped_geometry.jpg 
    1819 
    … …  
    2122.. note:: 
    2223 
    23    The edge of the solid must satisfy the condition that $A < B < C$. 
    24    This requirement is not enforced in the model, so it is up to the 
    25    user to check this during the analysis. 
     24The three dimensions of the parallelepiped (strictly here a cuboid) may be given in  
     25$any$ size order. To avoid multiple fit solutions, especially 
     26with Monte-Carlo fit methods, it may be advisable to restrict their ranges. There may  
     27be a number of closely similar "best fits", so some trial and error, or fixing of some  
     28dimensions at expected values, may help. 
    2629 
    2730The 1D scattering intensity $I(q)$ is calculated as: 
    … …  
    6770    \mu &= qB 
    6871 
    69  
    7072The scattering intensity per unit volume is returned in units of |cm^-1|. 
    7173 
    7274NB: The 2nd virial coefficient of the parallelepiped is calculated based on 
    73 the averaged effective radius $(=\sqrt{A B / \pi})$ and 
     75the averaged effective radius, after appropriately sorting the three 
     76dimensions, to give an oblate or prolate particle, $(=\sqrt{AB/\pi})$ and 
    7477length $(= C)$ values, and used as the effective radius for 
    7578$S(q)$ when $P(q) \cdot S(q)$ is applied. 
    … …  
    102105.. _parallelepiped-orientation: 
    103106 
    104 .. figure:: img/parallelepiped_angle_definition.jpg 
    105  
    106     Definition of the angles for oriented parallelepipeds. 
    107  
    108 .. figure:: img/parallelepiped_angle_projection.jpg 
    109  
    110     Examples of the angles for oriented parallelepipeds against the 
     107.. figure:: img/parallelepiped_angle_definition.png 
     108 
     109    Definition of the angles for oriented parallelepiped, shown with $A<B<C$. 
     110 
     111.. figure:: img/parallelepiped_angle_projection.png 
     112 
     113    Examples of the angles for an oriented parallelepiped against the 
    111114    detector plane. 
    112115 
     116On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
     117appear. These are actually rotations about axes $\delta_1$ and $\delta_2$ of the parallelepiped, perpendicular to the $a$ x $c$ and $b$ x $c$ faces.  
     118(When $\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the instrument.) The third orientation distribution, in $\psi$, is  
     119about the $c$ axis of the particle, perpendicular to the $a$ x $b$ face. Some experimentation may be required to  
     120understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation  
     121distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.)  
     122 
     123     
    113124For a given orientation of the parallelepiped, the 2D form factor is 
    114125calculated as 
    … …  
    116127.. math:: 
    117128 
    118     P(q_x, q_y) = \left[\frac{\sin(qA\cos\alpha/2)}{(qA\cos\alpha/2)}\right]^2 
    119                   \left[\frac{\sin(qB\cos\beta/2)}{(qB\cos\beta/2)}\right]^2 
    120                   \left[\frac{\sin(qC\cos\gamma/2)}{(qC\cos\gamma/2)}\right]^2 
     129    P(q_x, q_y) = \left[\frac{\sin(\tfrac{1}{2}qA\cos\alpha)}{(\tfrac{1}{2}qA\cos\alpha)}\right]^2 
     130                  \left[\frac{\sin(\tfrac{1}{2}qB\cos\beta)}{(\tfrac{1}{2}qB\cos\beta)}\right]^2 
     131                  \left[\frac{\sin(\tfrac{1}{2}qC\cos\gamma)}{(\tfrac{1}{2}qC\cos\gamma)}\right]^2 
    121132 
    122133with 
    … …  
    154165angles. 
    155166 
    156 This model is based on form factor calculations implemented in a c-library 
    157 provided by the NIST Center for Neutron Research (Kline, 2006). 
    158167 
    159168References 
    … …  
    163172 
    164173R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 
     174 
     175Authorship and Verification 
     176---------------------------- 
     177 
     178* **Author:** This model is based on form factor calculations implemented 
     179    in a c-library provided by the NIST Center for Neutron Research (Kline, 2006). 
     180* **Last Modified by:**  Paul Kienzle **Date:** April 05, 2017 
     181* **Last Reviewed by:**  Richard Heenan **Date:** April 06, 2017 
     182 
    165183""" 
    166184 
    167185import numpy as np 
    168 from numpy import pi, inf, sqrt 
     186from numpy import pi, inf, sqrt, sin, cos 
    169187 
    170188name = "parallelepiped" 
    … …  
    180198            mu = q*B 
    181199        V: Volume of the rectangular parallelepiped 
    182         alpha: angle between the long axis of the  
     200        alpha: angle between the long axis of the 
    183201            parallelepiped and the q-vector for 1D 
    184202""" 
    … …  
    196214              ["length_c", "Ang", 400, [0, inf], "volume", 
    197215               "Larger side of the parallelepiped"], 
    198               ["theta", "degrees", 60, [-inf, inf], "orientation", 
    199                "In plane angle"], 
    200               ["phi", "degrees", 60, [-inf, inf], "orientation", 
    201                "Out of plane angle"], 
    202               ["psi", "degrees", 60, [-inf, inf], "orientation", 
    203                "Rotation angle around its own c axis against q plane"], 
     216              ["theta", "degrees", 60, [-360, 360], "orientation", 
     217               "c axis to beam angle"], 
     218              ["phi", "degrees", 60, [-360, 360], "orientation", 
     219               "rotation about beam"], 
     220              ["psi", "degrees", 60, [-360, 360], "orientation", 
     221               "rotation about c axis"], 
    204222             ] 
    205223 
    … …  
    208226def ER(length_a, length_b, length_c): 
    209227    """ 
    210         Return effective radius (ER) for P(q)*S(q) 
     228    Return effective radius (ER) for P(q)*S(q) 
    211229    """ 
    212  
     230    # now that axes can be in any size order, need to sort a,b,c where a~b and c is either much smaller 
     231    # or much larger 
     232    abc = np.vstack((length_a, length_b, length_c)) 
     233    abc = np.sort(abc, axis=0) 
     234    selector = (abc[1] - abc[0]) > (abc[2] - abc[1]) 
     235    length = np.where(selector, abc[0], abc[2]) 
    213236    # surface average radius (rough approximation) 
    214     surf_rad = sqrt(length_a * length_b / pi) 
    215  
    216     ddd = 0.75 * surf_rad * (2 * surf_rad * length_c + (length_c + surf_rad) * (length_c + pi * surf_rad)) 
     237    radius = np.sqrt(np.where(~selector, abc[0]*abc[1], abc[1]*abc[2]) / pi) 
     238 
     239    ddd = 0.75 * radius * (2*radius*length + (length + radius)*(length + pi*radius)) 
    217240    return 0.5 * (ddd) ** (1. / 3.) 
    218241 
    … …  
    230253            phi_pd=10, phi_pd_n=1, 
    231254            psi_pd=10, psi_pd_n=10) 
    232  
    233 qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5) 
     255# rkh 7/4/17 add random unit test for 2d, note make all params different, 2d values not tested against other codes or models 
     256qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) 
    234257tests = [[{}, 0.2, 0.17758004974], 
    235258         [{}, [0.2], [0.17758004974]], 
    236          [{'theta':10.0, 'phi':10.0}, (qx, qy), 0.00560296014], 
    237          [{'theta':10.0, 'phi':10.0}, [(qx, qy)], [0.00560296014]], 
     259         [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0089517140475], 
     260         [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0089517140475]], 
    238261        ] 
    239262del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/sc_paracrystal.c

    r4962519 r50beefe  
    111111          double psi) 
    112112{ 
    113     double q, cos_a1, cos_a2, cos_a3; 
    114     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_a3, cos_a2, cos_a1); 
     113    double q, zhat, yhat, xhat; 
     114    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    115115 
    116116    const double qd = q*dnn; 
    … …  
    118118    const double tanh_qd = tanh(arg); 
    119119    const double cosh_qd = cosh(arg); 
    120     const double Zq = tanh_qd/(1. - cos(qd*cos_a1)/cosh_qd) 
    121                     * tanh_qd/(1. - cos(qd*cos_a2)/cosh_qd) 
    122                     * tanh_qd/(1. - cos(qd*cos_a3)/cosh_qd); 
     120    const double Zq = tanh_qd/(1. - cos(qd*zhat)/cosh_qd) 
     121                    * tanh_qd/(1. - cos(qd*yhat)/cosh_qd) 
     122                    * tanh_qd/(1. - cos(qd*xhat)/cosh_qd); 
    123123 
    124124    const double Fq = sphere_form(q, radius, sphere_sld, solvent_sld)*Zq; 

  • sasmodels/models/sc_paracrystal.py

    r3330bb4 r69e1afc  
    8383model computation. 
    8484 
    85 .. figure:: img/sc_crystal_angle_definition.jpg 
     85.. figure:: img/parallelepiped_angle_definition.png 
     86 
     87    Orientation of the crystal with respect to the scattering plane, when 
     88    $\theta = \phi = 0$ the $c$ axis is along the beam direction (the $z$ axis). 
    8689 
    8790Reference 
    … …  
    127130              ["sld",  "1e-6/Ang^2",         3.0, [0.0, inf],  "sld",         "Sphere scattering length density"], 
    128131              ["sld_solvent", "1e-6/Ang^2",  6.3, [0.0, inf],  "sld",         "Solvent scattering length density"], 
    129               ["theta",       "degrees",     0.0, [-inf, inf], "orientation", "Orientation of the a1 axis w/respect incoming beam"], 
    130               ["phi",         "degrees",     0.0, [-inf, inf], "orientation", "Orientation of the a2 in the plane of the detector"], 
    131               ["psi",         "degrees",     0.0, [-inf, inf], "orientation", "Orientation of the a3 in the plane of the detector"], 
     132              ["theta",       "degrees",    0,    [-360, 360], "orientation", "c axis to beam angle"], 
     133              ["phi",         "degrees",    0,    [-360, 360], "orientation", "rotation about beam"], 
     134              ["psi",         "degrees",    0,    [-360, 360], "orientation", "rotation about c axis"] 
    132135             ] 
    133136# pylint: enable=bad-whitespace, line-too-long 
    … …  
    146149 
    147150tests = [ 
    148     # Accuracy tests based on content in test/utest_extra_models.py 
     151    # Accuracy tests based on content in test/utest_extra_models.py, 2d tests added April 10, 2017 
    149152    [{}, 0.001, 10.3048], 
    150153    [{}, 0.215268, 0.00814889], 
    151     [{}, (0.414467), 0.001313289] 
     154    [{}, (0.414467), 0.001313289], 
     155    [{'theta':10.0,'phi':20,'psi':30.0},(0.045,-0.035),18.0397138402 ], 
     156    [{'theta':10.0,'phi':20,'psi':30.0},(0.023,0.045),0.0177333171285 ] 
    152157    ] 
    153158 

  • sasmodels/models/stacked_disks.py

    rc3ccaec r9802ab3  
    5858and $\sigma_d$ = the Gaussian standard deviation of the d-spacing (*sigma_d*). 
    5959Note that $D\cos(\alpha)$ is the component of $D$ parallel to $q$ and the last 
    60 term in the equation above is effectively a Debye-Waller factor term.  
     60term in the equation above is effectively a Debye-Waller factor term. 
    6161 
    6262.. note:: 
    … …  
    7777the axis of the cylinder using two angles $\theta$ and $\varphi$. 
    7878 
    79 .. figure:: img/cylinder_angle_definition.jpg 
     79.. figure:: img/cylinder_angle_definition.png 
    8080 
    8181    Examples of the angles against the detector plane. 
    … …  
    103103""" 
    104104 
    105 from numpy import inf 
     105from numpy import inf, sin, cos, pi 
    106106 
    107107name = "stacked_disks" 
    … …  
    131131    ["sld_layer",   "1e-6/Ang^2",  0.0, [-inf, inf], "sld",         "Layer scattering length density"], 
    132132    ["sld_solvent", "1e-6/Ang^2",  5.0, [-inf, inf], "sld",         "Solvent scattering length density"], 
    133     ["theta",       "degrees",     0,   [-inf, inf], "orientation", "Orientation of the stacked disk axis w/respect incoming beam"], 
    134     ["phi",         "degrees",     0,   [-inf, inf], "orientation", "Orientation of the stacked disk in the plane of the detector"], 
     133    ["theta",       "degrees",     0,   [-360, 360], "orientation", "Orientation of the stacked disk axis w/respect incoming beam"], 
     134    ["phi",         "degrees",     0,   [-360, 360], "orientation", "Rotation about beam"], 
    135135    ] 
    136136# pylint: enable=bad-whitespace, line-too-long 
    … …  
    152152# After redefinition of spherical coordinates - 
    153153# tests had in old coords theta=0, phi=0; new coords theta=90, phi=0 
    154 # but should not matter here as so far all the tests are 1D not 2D 
     154q = 0.1 
     155# april 6 2017, rkh added a 2d unit test, assume correct! 
     156qx = q*cos(pi/6.0) 
     157qy = q*sin(pi/6.0) 
    155158tests = [ 
    156159# Accuracy tests based on content in test/utest_extra_models.py. 
    157 # Added 2 tests with n_stacked = 5 using SasView 3.1.2 - PDB; for which alas q=0.001 values seem closer to n_stacked=1 not 5, changed assuming my 4.1 code OK, RKH 
     160# Added 2 tests with n_stacked = 5 using SasView 3.1.2 - PDB; 
     161# for which alas q=0.001 values seem closer to n_stacked=1 not 5, 
     162# changed assuming my 4.1 code OK, RKH 
    158163    [{'thick_core': 10.0, 
    159164      'thick_layer': 15.0, 
    … …  
    186191    [{'thick_core': 10.0, 
    187192      'thick_layer': 15.0, 
     193      'radius': 100.0, 
     194      'n_stacking': 5, 
     195      'sigma_d': 0.0, 
     196      'sld_core': 4.0, 
     197      'sld_layer': -0.4, 
     198      'solvent_sd': 5.0, 
     199      'theta': 90.0, 
     200      'phi': 20.0, 
     201      'scale': 0.01, 
     202      'background': 0.001}, 
     203      (qx, qy), 0.0491167089952  ], 
     204    [{'thick_core': 10.0, 
     205      'thick_layer': 15.0, 
    188206      'radius': 3000.0, 
    189207      'n_stacking': 5, 
    … …  
    228246      'background': 0.001, 
    229247     }, ([0.4, 0.5]), [0.00105074, 0.00121761]], 
     248    [{'thick_core': 10.0, 
     249      'thick_layer': 15.0, 
     250      'radius': 3000.0, 
     251      'n_stacking': 1.0, 
     252      'sigma_d': 0.0, 
     253      'sld_core': 4.0, 
     254      'sld_layer': -0.4, 
     255      'solvent_sd': 5.0, 
     256      'theta': 90.0, 
     257      'phi': 20.0, 
     258      'scale': 0.01, 
     259      'background': 0.001, 
     260     }, (qx, qy), 0.0341738733124 ], 
    230261 
    231262    [{'thick_core': 10.0, 

  • sasmodels/models/triaxial_ellipsoid.c

    r925ad6e r68dd6a9  
    2020    double radius_polar) 
    2121{ 
    22     double sn, cn; 
    23     // translate a point in [-1,1] to a point in [0, 1] 
    24     const double zm = 0.5; 
    25     const double zb = 0.5; 
     22    const double pa = square(radius_equat_minor/radius_equat_major) - 1.0; 
     23    const double pc = square(radius_polar/radius_equat_major) - 1.0; 
     24    // translate a point in [-1,1] to a point in [0, pi/2] 
     25    const double zm = M_PI_4; 
     26    const double zb = M_PI_4; 
    2627    double outer = 0.0; 
    2728    for (int i=0;i<76;i++) { 
    28         //const double cos_alpha = (Gauss76Z[i]*(upper-lower) + upper + lower)/2; 
    29         const double x = 0.5*(Gauss76Z[i] + 1.0); 
    30         SINCOS(M_PI_2*x, sn, cn); 
    31         const double acosx2 = radius_equat_minor*radius_equat_minor*cn*cn; 
    32         const double bsinx2 = radius_equat_major*radius_equat_major*sn*sn; 
    33         const double c2 = radius_polar*radius_polar; 
     29        //const double u = Gauss76Z[i]*(upper-lower)/2 + (upper + lower)/2; 
     30        const double phi = Gauss76Z[i]*zm + zb; 
     31        const double pa_sinsq_phi = pa*square(sin(phi)); 
    3432 
    3533        double inner = 0.0; 
     34        const double um = 0.5; 
     35        const double ub = 0.5; 
    3636        for (int j=0;j<76;j++) { 
    37             const double ysq = square(Gauss76Z[j]*zm + zb); 
    38             const double t = q*sqrt(acosx2 + bsinx2*(1.0-ysq) + c2*ysq); 
    39             const double fq = sas_3j1x_x(t); 
    40             inner += Gauss76Wt[j] * fq * fq ; 
     37            // translate a point in [-1,1] to a point in [0, 1] 
     38            const double usq = square(Gauss76Z[j]*um + ub); 
     39            const double r = radius_equat_major*sqrt(pa_sinsq_phi*(1.0-usq) + 1.0 + pc*usq); 
     40            const double fq = sas_3j1x_x(q*r); 
     41            inner += Gauss76Wt[j] * fq * fq; 
    4142        } 
    42         outer += Gauss76Wt[i] * 0.5 * inner; 
     43        outer += Gauss76Wt[i] * inner;  // correcting for dx later 
    4344    } 
    44     // translate dx in [-1,1] to dx in [lower,upper] 
    45     const double fqsq = outer*zm; 
     45    // translate integration ranges from [-1,1] to [lower,upper] and normalize by 4 pi 
     46    const double fqsq = outer/4.0;  // = outer*um*zm*8.0/(4.0*M_PI); 
    4647    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); 
    4748    return 1.0e-4 * s * s * fqsq; 
    … …  
    5859    double psi) 
    5960{ 
    60     double q, calpha, cmu, cnu; 
    61     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, calpha, cmu, cnu); 
     61    double q, xhat, yhat, zhat; 
     62    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
    6263 
    63     const double t = q*sqrt(radius_equat_minor*radius_equat_minor*cnu*cnu 
    64                           + radius_equat_major*radius_equat_major*cmu*cmu 
    65                           + radius_polar*radius_polar*calpha*calpha); 
    66     const double fq = sas_3j1x_x(t); 
     64    const double r = sqrt(square(radius_equat_minor*xhat) 
     65                          + square(radius_equat_major*yhat) 
     66                          + square(radius_polar*zhat)); 
     67    const double fq = sas_3j1x_x(q*r); 
    6768    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); 
    6869 

  • sasmodels/models/triaxial_ellipsoid.py

    r3330bb4 r34a9e4e  
    22# Note: model title and parameter table are inserted automatically 
    33r""" 
    4 All three axes are of different lengths with $R_a \leq R_b \leq R_c$ 
    5 **Users should maintain this inequality for all calculations**. 
     4Definition 
     5---------- 
     6 
     7.. figure:: img/triaxial_ellipsoid_geometry.jpg 
     8 
     9    Ellipsoid with $R_a$ as *radius_equat_minor*, $R_b$ as *radius_equat_major* 
     10    and $R_c$ as *radius_polar*. 
     11 
     12Given an ellipsoid 
    613 
    714.. math:: 
    815 
    9     P(q) = \text{scale} V \left< F^2(q) \right> + \text{background} 
     16    \frac{X^2}{R_a^2} + \frac{Y^2}{R_b^2} + \frac{Z^2}{R_c^2} = 1 
    1017 
    11 where the volume $V = 4/3 \pi R_a R_b R_c$, and the averaging 
    12 $\left<\ldots\right>$ is applied over all orientations for 1D. 
    13  
    14 .. figure:: img/triaxial_ellipsoid_geometry.jpg 
    15  
    16     Ellipsoid schematic. 
    17  
    18 Definition 
    19 ---------- 
    20  
    21 The form factor calculated is 
     18the scattering for randomly oriented particles is defined by the average over 
     19all orientations $\Omega$ of: 
    2220 
    2321.. math:: 
    2422 
    25     P(q) = \frac{\text{scale}}{V}\int_0^1\int_0^1 
    26         \Phi^2(qR_a^2\cos^2( \pi x/2) + qR_b^2\sin^2(\pi y/2)(1-y^2) + R_c^2y^2) 
    27         dx dy 
     23    P(q) = \text{scale}(\Delta\rho)^2\frac{V}{4 \pi}\int_\Omega\Phi^2(qr)\,d\Omega 
     24           + \text{background} 
    2825 
    2926where 
    … …  
    3128.. math:: 
    3229 
    33     \Phi(u) = 3 u^{-3} (\sin u - u \cos u) 
     30    \Phi(qr) &= 3 j_1(qr)/qr = 3 (\sin qr - qr \cos qr)/(qr)^3 \\ 
     31    r^2 &= R_a^2e^2 + R_b^2f^2 + R_c^2g^2 \\ 
     32    V &= \tfrac{4}{3} \pi R_a R_b R_c 
    3433 
     34The $e$, $f$ and $g$ terms are the projections of the orientation vector on $X$, 
     35$Y$ and $Z$ respectively.  Keeping the orientation fixed at the canonical 
     36axes, we can integrate over the incident direction using polar angle 
     37$-\pi/2 \le \gamma \le \pi/2$ and equatorial angle $0 \le \phi \le 2\pi$ 
     38(as defined in ref [1]), 
     39 
     40 .. math:: 
     41 
     42     \langle\Phi^2\rangle = \int_0^{2\pi} \int_{-\pi/2}^{\pi/2} \Phi^2(qr) 
     43                                                \cos \gamma\,d\gamma d\phi 
     44 
     45with $e = \cos\gamma \sin\phi$, $f = \cos\gamma \cos\phi$ and $g = \sin\gamma$. 
     46A little algebra yields 
     47 
     48.. math:: 
     49 
     50    r^2 = b^2(p_a \sin^2 \phi \cos^2 \gamma + 1 + p_c \sin^2 \gamma) 
     51 
     52for 
     53 
     54.. math:: 
     55 
     56    p_a = \frac{a^2}{b^2} - 1 \text{ and } p_c = \frac{c^2}{b^2} - 1 
     57 
     58Due to symmetry, the ranges can be restricted to a single quadrant 
     59$0 \le \gamma \le \pi/2$ and $0 \le \phi \le \pi/2$, scaling the resulting 
     60integral by 8. The computation is done using the substitution $u = \sin\gamma$, 
     61$du = \cos\gamma\,d\gamma$, giving 
     62 
     63.. math:: 
     64 
     65    \langle\Phi^2\rangle &= 8 \int_0^{\pi/2} \int_0^1 \Phi^2(qr) du d\phi \\ 
     66    r^2 &= b^2(p_a \sin^2(\phi)(1 - u^2) + 1 + p_c u^2) 
     67 
     68Though for convenience we describe the three radii of the ellipsoid as equatorial 
     69and polar, they may be given in $any$ size order. To avoid multiple solutions, especially 
     70with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical 
     71small angle diffraction situations there may be a number of closely similar "best fits", 
     72so some trial and error, or fixing of some radii at expected values, may help. 
     73     
    3574To provide easy access to the orientation of the triaxial ellipsoid, 
    3675we define the axis of the cylinder using the angles $\theta$, $\phi$ 
    37 and $\psi$. These angles are defined on 
    38 :numref:`triaxial-ellipsoid-angles` . 
    39 The angle $\psi$ is the rotational angle around its own $c$ axis 
    40 against the $q$ plane. For example, $\psi = 0$ when the 
    41 $a$ axis is parallel to the $x$ axis of the detector. 
     76and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that 
     77angle $\phi$ is now NOT the same as in the equations above. 
     78 
     79.. figure:: img/elliptical_cylinder_angle_definition.png 
     80 
     81    Definition of angles for oriented triaxial ellipsoid, where radii are for illustration here  
     82    $a < b << c$ and angle $\Psi$ is a rotation around the axis of the particle. 
     83 
     84For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
     85see the :ref:`elliptical-cylinder` model for further information. 
    4286 
    4387.. _triaxial-ellipsoid-angles: 
    4488 
    45 .. figure:: img/triaxial_ellipsoid_angle_projection.jpg 
     89.. figure:: img/triaxial_ellipsoid_angle_projection.png 
    4690 
    47     The angles for oriented ellipsoid. 
     91    Some examples for an oriented triaxial ellipsoid. 
    4892 
    4993The radius-of-gyration for this system is  $R_g^2 = (R_a R_b R_c)^2/5$. 
    5094 
    51 The contrast is defined as SLD(ellipsoid) - SLD(solvent).  In the 
     95The contrast $\Delta\rho$ is defined as SLD(ellipsoid) - SLD(solvent).  In the 
    5296parameters, $R_a$ is the minor equatorial radius, $R_b$ is the major 
    5397equatorial radius, and $R_c$ is the polar radius of the ellipsoid. 
    5498 
    5599NB: The 2nd virial coefficient of the triaxial solid ellipsoid is 
    56 calculated based on the polar radius $R_p = R_c$ and equatorial 
    57 radius $R_e = \sqrt{R_a R_b}$, and used as the effective radius for 
     100calculated after sorting the three radii to give the most appropriate 
     101prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial 
     102radius,  $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for 
    58103$S(q)$ when $P(q) \cdot S(q)$ is applied. 
    59104 
    … …  
    69114---------- 
    70115 
    71 L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray 
    72 and Neutron Scattering*, Plenum, New York, 1987. 
     116[1] Finnigan, J.A., Jacobs, D.J., 1971. 
     117*Light scattering by ellipsoidal particles in solution*, 
     118J. Phys. D: Appl. Phys. 4, 72-77. doi:10.1088/0022-3727/4/1/310 
     119 
     120Authorship and Verification 
     121---------------------------- 
     122 
     123* **Author:** NIST IGOR/DANSE **Date:** pre 2010 
     124* **Last Modified by:** Paul Kienzle (improved calculation) **Date:** April 4, 2017 
     125* **Last Reviewed by:** Paul Kienzle & Richard Heenan **Date:**  April 4, 2017 
    73126""" 
    74127 
    75 from numpy import inf 
     128from numpy import inf, sin, cos, pi 
    76129 
    77130name = "triaxial_ellipsoid" 
    78131title = "Ellipsoid of uniform scattering length density with three independent axes." 
    79132 
    80 description = """\ 
    81 Note: During fitting ensure that the inequality ra<rb<rc is not 
    82         violated. Otherwise the calculation will 
    83         not be correct. 
     133description = """ 
     134   Triaxial ellipsoid - see main documentation. 
    84135""" 
    85136category = "shape:ellipsoid" 
    … …  
    91142               "Solvent scattering length density"], 
    92143              ["radius_equat_minor", "Ang", 20, [0, inf], "volume", 
    93                "Minor equatorial radius"], 
     144               "Minor equatorial radius, Ra"], 
    94145              ["radius_equat_major", "Ang", 400, [0, inf], "volume", 
    95                "Major equatorial radius"], 
     146               "Major equatorial radius, Rb"], 
    96147              ["radius_polar", "Ang", 10, [0, inf], "volume", 
    97                "Polar radius"], 
    98               ["theta", "degrees", 60, [-inf, inf], "orientation", 
    99                "In plane angle"], 
    100               ["phi", "degrees", 60, [-inf, inf], "orientation", 
    101                "Out of plane angle"], 
    102               ["psi", "degrees", 60, [-inf, inf], "orientation", 
    103                "Out of plane angle"], 
     148               "Polar radius, Rc"], 
     149              ["theta", "degrees", 60, [-360, 360], "orientation", 
     150               "polar axis to beam angle"], 
     151              ["phi", "degrees", 60, [-360, 360], "orientation", 
     152               "rotation about beam"], 
     153              ["psi", "degrees", 60, [-360, 360], "orientation", 
     154               "rotation about polar axis"], 
    104155             ] 
    105156 
    … …  
    108159def ER(radius_equat_minor, radius_equat_major, radius_polar): 
    109160    """ 
    110         Returns the effective radius used in the S*P calculation 
     161    Returns the effective radius used in the S*P calculation 
    111162    """ 
    112163    import numpy as np 
    113164    from .ellipsoid import ER as ellipsoid_ER 
    114     return ellipsoid_ER(radius_polar, np.sqrt(radius_equat_minor * radius_equat_major)) 
     165 
     166    # now that radii can be in any size order, radii need sorting a,b,c 
     167    # where a~b and c is either much smaller or much larger 
     168    radii = np.vstack((radius_equat_major, radius_equat_minor, radius_polar)) 
     169    radii = np.sort(radii, axis=0) 
     170    selector = (radii[1] - radii[0]) > (radii[2] - radii[1]) 
     171    polar = np.where(selector, radii[0], radii[2]) 
     172    equatorial = np.sqrt(np.where(~selector, radii[0]*radii[1], radii[1]*radii[2])) 
     173    return ellipsoid_ER(polar, equatorial) 
    115174 
    116175demo = dict(scale=1, background=0, 
    … …  
    124183            phi_pd=15, phi_pd_n=1, 
    125184            psi_pd=15, psi_pd_n=1) 
     185 
     186q = 0.1 
     187# april 6 2017, rkh add unit tests 
     188#     NOT compared with any other calc method, assume correct! 
     189# check 2d test after pull #890 
     190qx = q*cos(pi/6.0) 
     191qy = q*sin(pi/6.0) 
     192tests = [[{}, 0.05, 24.8839548033], 
     193        [{'theta':80., 'phi':10.}, (qx, qy), 166.712060266 ], 
     194        ] 
     195del qx, qy  # not necessary to delete, but cleaner 
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