Changes in / [d77eca8:630156b] in sasmodels


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29 edited

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  • explore/angular_pd.py

    r8267e0b r12eb36b  
    4747 
    4848def draw_mesh_new(ax, theta, dtheta, phi, dphi, flow, radius=10., dist='gauss'): 
    49     theta_center = radians(90-theta) 
     49    theta_center = radians(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=90-theta if use_new else theta, azim=phi) 
     139            ax.view_init(elev=theta, azim=phi) 
    140140        plt.gcf().canvas.draw() 
    141141 

  • sasmodels/kernel_header.c

    rb00a646 r1e7b0db0  
    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  
    161150#if 1 
    162151//think cos(theta) should be sin(theta) in new coords, RKH 11Jan2017 
    … …  
    177166#endif 
    178167 
    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 
    199168#define ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, cos_alpha, cos_mu, cos_nu) do { \ 
    200169    q = sqrt(qx*qx + qy*qy); \ 
    … …  
    211180    cos_nu = (-cos_phi*sin_psi*sin_theta + sin_phi*cos_psi)*qxhat + sin_psi*cos_theta*qyhat; \ 
    212181    } while (0) 
    213 #endif 

  • sasmodels/models/barbell.py

    r9802ab3 rfcb33e4  
    6868The 2D scattering intensity is calculated similar to the 2D cylinder model. 
    6969 
    70 .. figure:: img/cylinder_angle_definition.png 
     70.. figure:: img/cylinder_angle_definition.jpg 
    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, sin, cos, pi 
     89from numpy import inf 
    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, [-360, 360], "orientation", "Barbell axis to beam angle"], 
    111               ["phi",         "degrees",     60, [-360, 360], "orientation", "Rotation about beam"], 
     110              ["theta",       "degrees",     60, [-inf, inf], "orientation", "In plane angle"], 
     111              ["phi",         "degrees",     60, [-inf, inf], "orientation", "Out of plane angle"], 
    112112             ] 
    113113# pylint: enable=bad-whitespace, line-too-long 
    … …  
    125125            phi_pd=15, phi_pd_n=0, 
    126126           ) 
    127 q = 0.1 
    128 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    129 qx = q*cos(pi/6.0) 
    130 qy = q*sin(pi/6.0) 
    131 tests = [[{}, 0.075, 25.5691260532], 
    132         [{'theta':80., 'phi':10.}, (qx, qy), 3.04233067789], 
    133         ] 
    134 del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/bcc_paracrystal.c

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

  • sasmodels/models/bcc_paracrystal.py

    r69e1afc r925ad6e  
    7979be accurate. 
    8080 
    81 .. figure:: img/parallelepiped_angle_definition.png 
     81.. figure:: img/bcc_angle_definition.png 
    8282 
    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). 
     83    Orientation of the crystal with respect to the scattering plane. 
    8584 
    8685References 
    … …  
    10099""" 
    101100 
    102 from numpy import inf, pi 
     101from numpy import inf 
    103102 
    104103name = "bcc_paracrystal" 
    … …  
    123122              ["sld",         "1e-6/Ang^2",  4,    [-inf, inf], "sld",         "Particle scattering length density"], 
    124123              ["sld_solvent", "1e-6/Ang^2",  1,    [-inf, inf], "sld",         "Solvent scattering length density"], 
    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"] 
     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"] 
    128127             ] 
    129128# pylint: enable=bad-whitespace, line-too-long 
    … …  
    142141    psi_pd=15, psi_pd_n=0, 
    143142    ) 
    144 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    145 # add 2d test later 
    146 q =4.*pi/220. 
    147 tests = [ 
    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

    r9802ab3 rfcb33e4  
    7171The 2D scattering intensity is calculated similar to the 2D cylinder model. 
    7272 
    73 .. figure:: img/cylinder_angle_definition.png 
     73.. figure:: img/cylinder_angle_definition.jpg 
    7474 
    7575    Definition of the angles for oriented 2D cylinders. 
    … …  
    9191 
    9292""" 
    93 from numpy import inf, sin, cos, pi 
     93from numpy import inf 
    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, [-360, 360], "orientation", "cylinder axis to beam angle"], 
    132               ["phi",        "degrees", 60, [-360, 360], "orientation", "rotation about beam"], 
     131              ["theta",      "degrees", 60, [-inf, inf], "orientation", "inclination angle"], 
     132              ["phi",        "degrees", 60, [-inf, inf], "orientation", "deflection angle"], 
    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) 
    147 q = 0.1 
    148 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    149 qx = q*cos(pi/6.0) 
    150 qy = q*sin(pi/6.0) 
    151 tests = [[{}, 0.075, 26.0698570695], 
    152         [{'theta':80., 'phi':10.}, (qx, qy), 0.561811990502], 
    153         ] 
    154 del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/core_shell_bicelle.c

    rb260926 r592343f  
    3030 
    3131static double 
    32 bicelle_kernel(double q, 
     32bicelle_kernel(double qq, 
    3333              double rad, 
    3434              double radthick, 
    3535              double facthick, 
    36               double halflength, 
     36              double length, 
    3737              double rhoc, 
    3838              double rhoh, 
    … …  
    4242              double cos_alpha) 
    4343{ 
     44    double si1,si2,be1,be2; 
     45 
    4446    const double dr1 = rhoc-rhoh; 
    4547    const double dr2 = rhor-rhosolv; 
    4648    const double dr3 = rhoh-rhor; 
    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); 
     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; 
    5056 
    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); 
     57    be1 = sas_2J1x_x(besarg1); 
     58    be2 = sas_2J1x_x(besarg2); 
     59    si1 = sas_sinx_x(sinarg1); 
     60    si2 = sas_sinx_x(sinarg2); 
    5561 
    5662    const double t = vol1*dr1*si1*be1 + 
    … …  
    5864                     vol3*dr3*si2*be1; 
    5965 
    60     const double retval = t*t; 
     66    const double retval = t*t*sin_alpha; 
    6167 
    6268    return retval; 
    … …  
    6571 
    6672static double 
    67 bicelle_integration(double q, 
     73bicelle_integration(double qq, 
    6874                   double rad, 
    6975                   double radthick, 
    … …  
    7783    // set up the integration end points 
    7884    const double uplim = M_PI_4; 
    79     const double halflength = 0.5*length; 
     85    const double halfheight = 0.5*length; 
    8086 
    8187    double summ = 0.0; 
    … …  
    8490        double sin_alpha, cos_alpha; // slots to hold sincos function output 
    8591        SINCOS(alpha, sin_alpha, cos_alpha); 
    86         double yyy = Gauss76Wt[i] * bicelle_kernel(q, rad, radthick, facthick, 
    87                              halflength, rhoc, rhoh, rhor, rhosolv, 
     92        double yyy = Gauss76Wt[i] * bicelle_kernel(qq, rad, radthick, facthick, 
     93                             halfheight, rhoc, rhoh, rhor, rhosolv, 
    8894                             sin_alpha, cos_alpha); 
    89         summ += yyy*sin_alpha; 
     95        summ += yyy; 
    9096    } 
    9197 
    … …  
    113119    double answer = bicelle_kernel(q, radius, thick_rim, thick_face, 
    114120                           0.5*length, core_sld, face_sld, rim_sld, 
    115                            solvent_sld, sin_alpha, cos_alpha); 
    116     return 1.0e-4*answer; 
     121                           solvent_sld, sin_alpha, cos_alpha) / fabs(sin_alpha); 
     122 
     123    answer *= 1.0e-4; 
     124 
     125    return answer; 
    117126} 
    118127 

  • sasmodels/models/core_shell_bicelle.py

    r9802ab3 r8afefae  
    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 For oriented bicelles the *theta*, and *phi* orientation parameters will appear when fitting 2D data,  
    66 see the :ref:`cylinder` model for further information. 
     65The *theta* and *phi* parameters are not used for the 1D output. 
    6766Our implementation of the scattering kernel and the 1D scattering intensity 
    6867use the c-library from NIST. 
    6968 
    70 .. figure:: img/cylinder_angle_definition.png 
     69.. figure:: img/cylinder_angle_definition.jpg 
    7170 
    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 $\theta  = \phi = 0$. 
     71    Definition of the angles for the oriented core shell bicelle tmodel. 
    7572 
    7673 
    … …  
    9188""" 
    9289 
    93 from numpy import inf, sin, cos, pi 
     90from numpy import inf, sin, cos 
    9491 
    9592name = "core_shell_bicelle" 
    … …  
    138135    ["sld_rim",        "1e-6/Ang^2", 4, [-inf, inf], "sld",         "Cylinder rim scattering length density"], 
    139136    ["sld_solvent",    "1e-6/Ang^2", 1, [-inf, inf], "sld",         "Solvent scattering length density"], 
    140     ["theta",          "degrees",   90, [-360, 360], "orientation", "cylinder axis to beam angle"], 
    141     ["phi",            "degrees",    0, [-360, 360], "orientation", "rotation about beam"] 
     137    ["theta",          "degrees",   90, [-inf, inf], "orientation", "In plane angle"], 
     138    ["phi",            "degrees",    0, [-inf, inf], "orientation", "Out of plane angle"], 
    142139    ] 
    143140 
    … …  
    158155            theta=90, 
    159156            phi=0) 
    160 q = 0.1 
    161 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    162 qx = q*cos(pi/6.0) 
    163 qy = q*sin(pi/6.0) 
    164 tests = [[{}, 0.05, 7.4883545957], 
    165         [{'theta':80., 'phi':10.}, (qx, qy), 2.81048892474 ] 
    166         ] 
    167 del qx, qy  # not necessary to delete, but cleaner 
    168157 
     158#qx, qy = 0.4 * cos(pi/2.0), 0.5 * sin(0) 

  • sasmodels/models/core_shell_bicelle_elliptical.c

    rdedcf34 r592343f  
     1double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length); 
     2double 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 
     14double 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 
    128// NOTE that "length" here is the full height of the core! 
    2 static double 
    3 form_volume(double r_minor, 
    4         double x_core, 
    5         double thick_rim, 
    6         double thick_face, 
    7         double length) 
     29double form_volume(double radius, double x_core, double thick_rim, double thick_face, double length) 
    830{ 
    9     return M_PI*(r_minor+thick_rim)*(r_minor*x_core+thick_rim)*(length+2.0*thick_face); 
     31    return M_PI*(radius+thick_rim)*(radius*x_core+thick_rim)*(length+2.0*thick_face); 
    1032} 
    1133 
    12 static double 
    13 Iq(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) 
     34double  
     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) 
    2345{ 
    2446    double si1,si2,be1,be2; 
    2547     // core_shell_bicelle_elliptical, RKH Dec 2016, based on elliptical_cylinder and core_shell_bicelle 
    26      // tested against limiting cases of cylinder, elliptical_cylinder, stacked_discs, and core_shell_bicelle 
     48     // tested against limiting cases of cylinder, elliptical_cylinder and core_shell_bicelle 
    2749     //    const double uplim = M_PI_4; 
    2850    const double halfheight = 0.5*length; 
    … …  
    3355    //const double vbj=M_PI; 
    3456 
    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); 
     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); 
    4466 
    4567    //initialize integral 
    … …  
    5274        const double sin_alpha = sqrt(1.0 - cos_alpha*cos_alpha); 
    5375        double inner_sum=0; 
    54         double sinarg1 = q*halfheight*cos_alpha; 
    55         double sinarg2 = q*(halfheight+thick_face)*cos_alpha; 
     76        double sinarg1 = qq*halfheight*cos_alpha; 
     77        double sinarg2 = qq*(halfheight+facthick)*cos_alpha; 
    5678        si1 = sas_sinx_x(sinarg1); 
    5779        si2 = sas_sinx_x(sinarg2); 
    … …  
    6082            //const double beta = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; 
    6183            const double beta = ( Gauss76Z[j] +1.0)*M_PI_2; 
    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; 
     84            const double rr = sqrt(rA - rB*cos(beta)); 
     85            double besarg1 = qq*rr*sin_alpha; 
     86            double besarg2 = qq*(rr+radthick)*sin_alpha; 
    6587            be1 = sas_2J1x_x(besarg1); 
    6688            be2 = sas_2J1x_x(besarg2); 
    … …  
    7698} 
    7799 
    78 static double 
     100double  
    79101Iqxy(double qx, double qy, 
    80           double r_minor, 
     102          double rad, 
    81103          double x_core, 
    82           double thick_rim, 
    83           double thick_face, 
     104          double radthick, 
     105          double facthick, 
    84106          double length, 
    85107          double rhoc, 
    … …  
    92114{ 
    93115       // THIS NEEDS TESTING 
    94     double q, xhat, yhat, zhat; 
    95     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
     116    double qq, cos_val, cos_mu, cos_nu; 
     117    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, qq, cos_val, cos_mu, cos_nu); 
    96118    const double dr1 = rhoc-rhoh; 
    97119    const double dr2 = rhor-rhosolv; 
    98120    const double dr3 = rhoh-rhor; 
    99     const double r_major = r_minor*x_core; 
     121    const double radius_major = rad*x_core; 
    100122    const double halfheight = 0.5*length; 
    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); 
     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); 
    104126 
    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 ); 
     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 ); 
    113135    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); 
    114137    return 1.0e-4 * Aq; 
    115138} 

  • sasmodels/models/core_shell_bicelle_elliptical.py

    r9802ab3 r8afefae  
    7676bicelles is then given by integrating over all possible $\alpha$ and $\psi$. 
    7777 
    78 For oriented bicelles the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
     78For oriented bicellles the *theta*, *phi* and *psi* orientation parameters only appear when fitting 2D data,  
    7979see the :ref:`elliptical-cylinder` model for further information. 
    8080 
    8181 
    82 .. figure:: img/elliptical_cylinder_angle_definition.png 
     82.. figure:: img/elliptical_cylinder_angle_definition.jpg 
    8383 
    84     Definition of the angles for the oriented core_shell_bicelle_elliptical particles.    
    85  
     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. 
    8686 
    8787 
    … …  
    9999""" 
    100100 
    101 from numpy import inf, sin, cos, pi 
     101from numpy import inf, sin, cos 
    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",    90.0, [-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"] 
     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"], 
    131131    ] 
    132132 
    … …  
    150150            psi=0) 
    151151 
    152 q = 0.1 
    153 # april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! 
    154 qx = q*cos(pi/6.0) 
    155 qy = q*sin(pi/6.0) 
     152#qx, qy = 0.4 * cos(pi/2.0), 0.5 * sin(0) 
    156153 
    157154tests = [ 
    … …  
    162159    'sld_core':4.0, 'sld_face':7.0, 'sld_rim':1.0, 'sld_solvent':6.0, 'background':0.0}, 
    163160    0.015, 286.540286], 
    164 #    [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], 
    165         ] 
    166  
    167 del qx, qy  # not necessary to delete, but cleaner 
     161] 

  • sasmodels/models/core_shell_cylinder.py

    r9b79f29 r8e68ea0  
    7373""" 
    7474 
    75 from numpy import pi, inf, sin, cos 
     75from numpy import pi, inf 
    7676 
    7777name = "core_shell_cylinder" 
    … …  
    117117              ["length", "Ang", 400, [0, inf], "volume", 
    118118               "Cylinder length"], 
    119               ["theta", "degrees", 60, [-360, 360], "orientation", 
    120                "cylinder axis to beam angle"], 
    121               ["phi", "degrees",   60, [-360, 360], "orientation", 
    122                "rotation about beam"], 
     119              ["theta", "degrees", 60, [-inf, inf], "orientation", 
     120               "In plane angle"], 
     121              ["phi", "degrees", 60, [-inf, inf], "orientation", 
     122               "Out of plane angle"], 
    123123             ] 
    124124 
    … …  
    151151            theta_pd=15, theta_pd_n=45, 
    152152            phi_pd=15, phi_pd_n=1) 
    153 q = 0.1 
    154 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    155 qx = q*cos(pi/6.0) 
    156 qy = q*sin(pi/6.0) 
    157 tests = [[{}, 0.075, 10.8552692237], 
    158         [{}, (qx, qy), 0.444618752741 ], 
    159         ] 
    160 del qx, qy  # not necessary to delete, but cleaner 
     153 

  • sasmodels/models/core_shell_ellipsoid.py

    r9802ab3 r8e68ea0  
    7777   F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} 
    7878 
    79 For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
    80 see the :ref:`elliptical-cylinder` model for further information. 
    8179 
    8280References 
    … …  
    134132    ["sld_shell",     "1e-6/Ang^2", 1,   [-inf, inf], "sld",         "Shell scattering length density"], 
    135133    ["sld_solvent",   "1e-6/Ang^2", 6.3, [-inf, inf], "sld",         "Solvent scattering length density"], 
    136     ["theta",         "degrees",    0,   [-360, 360], "orientation", "elipsoid axis to beam angle"], 
    137     ["phi",           "degrees",    0,   [-360, 360], "orientation", "rotation about beam"], 
     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"], 
    138136    ] 
    139137# pylint: enable=bad-whitespace, line-too-long 

  • sasmodels/models/core_shell_parallelepiped.c

    r92dfe0c r1e7b0db0  
    134134    double psi) 
    135135{ 
    136     double q, zhat, yhat, xhat; 
    137     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
     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); 
    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*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); 
     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); 
    168168     
    169169 

  • sasmodels/models/core_shell_parallelepiped.py

    r9b79f29 rcb0dc22  
    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 1D calculation does **NOT** actually calculate a c face rim despite the presence of 
    9 the parameter. Some other aspects of the 1D calculation may be wrong. 
     8the model does **NOT** actually calculate a c face rim despite the presence of 
     9the parameter. 
    1010 
    1111.. note:: 
    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. 
     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. 
    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] 
    5750 
    5851.. note:: 
    5952 
    60     Why does t_B not appear in the above equation? 
    6153    For the calculation of the form factor to be valid, the sides of the solid 
    62     MUST (perhaps not any more?) be chosen such that** $A < B < C$. 
     54    MUST be chosen such that** $A < B < C$. 
    6355    If this inequality is not satisfied, the model will not report an error, 
    6456    but the calculation will not be correct and thus the result wrong. 
    6557 
    6658FITTING NOTES 
    67 If the scale is set equal to the particle volume fraction, $\phi$, the returned 
     59If the scale is set equal to the particle volume fraction, |phi|, the returned 
    6860value is the scattered intensity per unit volume, $I(q) = \phi P(q)$. 
    6961However, **no interparticle interference effects are included in this 
    … …  
    8173NB: The 2nd virial coefficient of the core_shell_parallelepiped is calculated 
    8274based on the the averaged effective radius $(=\sqrt{(A+2t_A)(B+2t_B)/\pi})$ 
    83 and length $(C+2t_C)$ values, after appropriately 
    84 sorting the three dimensions to give an oblate or prolate particle, to give an  
    85 effective radius, for $S(Q)$ when $P(Q) * S(Q)$ is applied. 
     75and length $(C+2t_C)$ values, and used as the effective radius 
     76for $S(Q)$ when $P(Q) * S(Q)$ is applied. 
    8677 
    8778To provide easy access to the orientation of the parallelepiped, we define the 
    … …  
    9283*x*-axis of the detector. 
    9384 
    94 .. figure:: img/parallelepiped_angle_definition.png 
     85.. figure:: img/parallelepiped_angle_definition.jpg 
    9586 
    9687    Definition of the angles for oriented core-shell parallelepipeds. 
    9788 
    98 .. figure:: img/parallelepiped_angle_projection.png 
     89.. figure:: img/parallelepiped_angle_projection.jpg 
    9990 
    10091    Examples of the angles for oriented core-shell parallelepipeds against the 
    … …  
    121112 
    122113import numpy as np 
    123 from numpy import pi, inf, sqrt, cos, sin 
     114from numpy import pi, inf, sqrt 
    124115 
    125116name = "core_shell_parallelepiped" 
    … …  
    153144              ["thick_rim_c", "Ang", 10, [0, inf], "volume", 
    154145               "Thickness of C rim"], 
    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"], 
     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"], 
    161152             ] 
    162153 
    … …  
    195186            psi_pd=10, psi_pd_n=1) 
    196187 
    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 
    198 qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) 
     188qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5) 
    199189tests = [[{}, 0.2, 0.533149288477], 
    200190         [{}, [0.2], [0.533149288477]], 
    201          [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0853299803222], 
    202          [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0853299803222]], 
     191         [{'theta':10.0, 'phi':10.0}, (qx, qy), 0.032102135569], 
     192         [{'theta':10.0, 'phi':10.0}, [(qx, qy)], [0.032102135569]], 
    203193        ] 
    204194del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/cylinder.py

    r9802ab3 r3330bb4  
    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.png 
     63.. figure:: img/cylinder_angle_definition.jpg 
    6464 
    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. 
     65    Definition of the angles for oriented cylinders. 
    6966 
    70 .. figure:: img/cylinder_angle_projection.png 
    71  
    72     Examples for oriented cylinders. 
    73  
    74 The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data.  
    75 On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
    76 appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, which when $\theta = \phi = 0$ are parallel  
    77 to 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  
    79 situations, with very broad distributions, should still be approached with care.)  
     67The $\theta$ and $\phi$ parameters only appear in the model when fitting 2d data. 
    8068 
    8169Validation 
    … …  
    135123              ["length", "Ang", 400, [0, inf], "volume", 
    136124               "Cylinder length"], 
    137               ["theta", "degrees", 60, [-360, 360], "orientation", 
    138                "cylinder axis to beam angle"], 
    139               ["phi", "degrees",   60, [-360, 360], "orientation", 
    140                "rotation about beam"], 
     125              ["theta", "degrees", 60, [-inf, inf], "orientation", 
     126               "latitude"], 
     127              ["phi", "degrees", 60, [-inf, inf], "orientation", 
     128               "longitude"], 
    141129             ] 
    142130 
    … …  
    164152tests = [[{}, 0.2, 0.042761386790780453], 
    165153        [{}, [0.2], [0.042761386790780453]], 
    166 #  new coords 
     154#  new coords     
    167155        [{'theta':80.1534480601659, 'phi':10.1510817110481}, (qx, qy), 0.03514647218513852], 
    168156        [{'theta':80.1534480601659, 'phi':10.1510817110481}, [(qx, qy)], [0.03514647218513852]], 

  • sasmodels/models/ellipsoid.c

    r3b571ae r130d4c7  
    33double Iqxy(double qx, double qy, double sld, double sld_solvent, 
    44    double radius_polar, double radius_equatorial, double theta, double phi); 
     5 
     6static 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} 
    527 
    628double form_volume(double radius_polar, double radius_equatorial) 
    … …  
    1537    double radius_equatorial) 
    1638{ 
    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  
    2639    // translate a point in [-1,1] to a point in [0, 1] 
    27     // const double u = Gauss76Z[i]*(upper-lower)/2 + (upper+lower)/2; 
    2840    const double zm = 0.5; 
    2941    const double zb = 0.5; 
    3042    double total = 0.0; 
    3143    for (int i=0;i<76;i++) { 
    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; 
     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); 
    3647    } 
    3748    // translate dx in [-1,1] to dx in [lower,upper] 
    … …  
    5162    double q, sin_alpha, cos_alpha; 
    5263    ORIENT_SYMMETRIC(qx, qy, theta, phi, q, sin_alpha, 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); 
     64    const double form = _ellipsoid_kernel(q, radius_polar, radius_equatorial, cos_alpha); 
    5665    const double s = (sld - sld_solvent) * form_volume(radius_polar, radius_equatorial); 
    5766 
    58     return 1.0e-4 * square(f * s); 
     67    return 1.0e-4 * form * s * s; 
    5968} 
    6069 

  • sasmodels/models/ellipsoid.py

    r9b79f29 r925ad6e  
    1818.. math:: 
    1919 
    20     F(q,\alpha) = \Delta \rho V \frac{3(\sin qr  - qr \cos qr)}{(qr)^3} 
     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} 
    2123 
    22 for 
     24and 
    2325 
    2426.. math:: 
    2527 
    26     r = \left[ R_e^2 \sin^2 \alpha + R_p^2 \cos^2 \alpha \right]^{1/2} 
     28    r(R_p,R_e,\alpha) = \left[ R_e^2 \sin^2 \alpha 
     29        + R_p^2 \cos^2 \alpha \right]^{1/2} 
    2730 
    2831 
    2932$\alpha$ is the angle between the axis of the ellipsoid and $\vec q$, 
    30 $V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid, $R_p$ is the polar 
    31 radius along the rotational axis of the ellipsoid, $R_e$ is the equatorial 
    32 radius perpendicular to the rotational axis of the ellipsoid and 
    33 $\Delta \rho$ (contrast) is the scattering length density difference between 
    34 the scatterer and the solvent. 
     33$V = (4/3)\pi R_pR_e^2$ is the volume of the ellipsoid , $R_p$ is the polar radius along the 
     34rotational axis of the ellipsoid, $R_e$ is the equatorial radius perpendicular 
     35to the rotational axis of the ellipsoid and $\Delta \rho$ (contrast) is the 
     36scattering length density difference between the scatterer and the solvent. 
    3537 
    36 For randomly oriented particles use the orientational average, 
     38For randomly oriented particles: 
    3739 
    3840.. math:: 
    3941 
    40    \langle F^2(q) \rangle = \int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)\,d\alpha} 
     42   F^2(q)=\int_{0}^{\pi/2}{F^2(q,\alpha)\sin(\alpha)d\alpha} 
    4143 
    42  
    43 computed 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  
    49 with 
    50  
    51 .. math:: 
    52  
    53     r = R_e \left[ 1 + u^2\left(R_p^2/R_e^2 - 1\right)\right]^{1/2} 
    5444 
    5545To provide easy access to the orientation of the ellipsoid, we define 
    … …  
    5848:ref:`cylinder orientation figure <cylinder-angle-definition>`. 
    5949For the ellipsoid, $\theta$ is the angle between the rotational axis 
    60 and the $z$ -axis in the $xz$ plane followed by a rotation by $\phi$ 
    61 in the $xy$ plane. 
     50and the $z$ -axis. 
    6251 
    6352NB: The 2nd virial coefficient of the solid ellipsoid is calculated based 
    … …  
    10190than 500. 
    10291 
    103 Model was also tested against the triaxial ellipsoid model with equal major 
    104 and minor equatorial radii.  It is also consistent with the cyclinder model 
    105 with polar radius equal to length and equatorial radius equal to radius. 
    106  
    10792References 
    10893---------- 
    … …  
    11196*Structure Analysis by Small-Angle X-Ray and Neutron Scattering*, 
    11297Plenum Press, New York, 1987. 
    113  
    114 Authorship 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 
    12098""" 
    12199 
    122 from numpy import inf, sin, cos, pi 
     100from numpy import inf 
    123101 
    124102name = "ellipsoid" 
    … …  
    151129              ["radius_equatorial", "Ang", 400, [0, inf], "volume", 
    152130               "Equatorial radius"], 
    153               ["theta", "degrees", 60, [-360, 360], "orientation", 
    154                "ellipsoid axis to beam angle"], 
    155               ["phi", "degrees", 60, [-360, 360], "orientation", 
    156                "rotation about beam"], 
     131              ["theta", "degrees", 60, [-inf, inf], "orientation", 
     132               "In plane angle"], 
     133              ["phi", "degrees", 60, [-inf, inf], "orientation", 
     134               "Out of plane angle"], 
    157135             ] 
    158136 
    … …  
    161139def ER(radius_polar, radius_equatorial): 
    162140    import numpy as np 
    163 # see equation (26) in A.Isihara, J.Chem.Phys. 18(1950)1446-1449 
     141 
    164142    ee = np.empty_like(radius_polar) 
    165143    idx = radius_polar > radius_equatorial 
    … …  
    190168            theta_pd=15, theta_pd_n=45, 
    191169            phi_pd=15, phi_pd_n=1) 
    192 q = 0.1 
    193 # april 6 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    194 qx = q*cos(pi/6.0) 
    195 qy = q*sin(pi/6.0) 
    196 tests = [[{}, 0.05, 54.8525847025], 
    197         [{'theta':80., 'phi':10.}, (qx, qy), 1.74134670026 ], 
    198         ] 
    199 del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/elliptical_cylinder.c

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

  • sasmodels/models/elliptical_cylinder.py

    r9802ab3 rfcb33e4  
    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.  
     59$\Psi$ is the rotational angle around its own long_c axis against the $q$ plane. 
     60For example, $\Psi = 0$ when the $r_\text{minor}$ axis is parallel to the 
     61$x$ axis of the detector. 
    6062 
    6163All angle parameters are valid and given only for 2D calculation; ie, an 
    6264oriented system. 
    6365 
    64 .. figure:: img/elliptical_cylinder_angle_definition.png 
     66.. figure:: img/elliptical_cylinder_angle_definition.jpg 
    6567 
    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. 
     68    Definition of angles for 2D 
    6869 
    69 .. figure:: img/elliptical_cylinder_angle_projection.png 
     70.. figure:: img/cylinder_angle_projection.jpg 
    7071 
    7172    Examples of the angles for oriented elliptical cylinders against the 
    72     detector plane, with $\Psi$ = 0. 
    73  
    74 The $\theta$ and $\phi$ parameters to orient the cylinder only appear in the model when fitting 2d data.  
    75 On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
    76 appear. These are actually rotations about the axes $\delta_1$ and $\delta_2$ of the cylinder, the $b$ and $a$ axes of the  
    77 cylinder cross section. (When $\theta = \phi = 0$ these are parallel to the $Y$ and $X$ axes of the instrument.)  
    78 The third orientation distribution, in $\psi$, is about the $c$ axis of the particle. Some experimentation may be required to  
    79 understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation  
    80 distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.)  
     73    detector plane. 
    8174 
    8275NB: The 2nd virial coefficient of the cylinder is calculated based on the 
    … …  
    115108""" 
    116109 
    117 from numpy import pi, inf, sqrt, sin, cos 
     110from numpy import pi, inf, sqrt 
    118111 
    119112name = "elliptical_cylinder" 
    … …  
    132125              ["sld",         "1e-6/Ang^2", 4.0,   [-inf, inf], "sld",         "Cylinder scattering length density"], 
    133126              ["sld_solvent", "1e-6/Ang^2", 1.0,   [-inf, inf], "sld",         "Solvent scattering length density"], 
    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"]] 
     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"]] 
    137130 
    138131# pylint: enable=bad-whitespace, line-too-long 
    … …  
    156149                           + (length + radius) * (length + pi * radius)) 
    157150    return 0.5 * (ddd) ** (1. / 3.) 
    158 q = 0.1 
    159 # april 6 2017, rkh added a 2d unit test, NOT READY YET pull #890 branch assume correct! 
    160 qx = q*cos(pi/6.0) 
    161 qy = q*sin(pi/6.0) 
    162151 
    163152tests = [ 
    … …  
    169158      'sld_solvent':1.0, 'background':0.0}, 
    170159     0.001, 675.504402], 
    171 #    [{'theta':80., 'phi':10.}, (qx, qy), 7.88866563001 ], 
    172160] 

  • sasmodels/models/fcc_paracrystal.c

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

    r69e1afc r925ad6e  
    76762D model computation. 
    7777 
    78 .. figure:: img/parallelepiped_angle_definition.png 
     78.. figure:: img/bcc_angle_definition.png 
    7979 
    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). 
     80    Orientation of the crystal with respect to the scattering plane. 
    8281 
    8382References 
    … …  
    9190""" 
    9291 
    93 from numpy import inf, pi 
     92from numpy import inf 
    9493 
    9594name = "fcc_paracrystal" 
    … …  
    111110              ["sld", "1e-6/Ang^2", 4, [-inf, inf], "sld", "Particle scattering length density"], 
    112111              ["sld_solvent", "1e-6/Ang^2", 1, [-inf, inf], "sld", "Solvent scattering length density"], 
    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"] 
     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"] 
    116115             ] 
    117116# pylint: enable=bad-whitespace, line-too-long 
    … …  
    129128            psi_pd=15, psi_pd_n=0, 
    130129           ) 
    131 # april 10 2017, rkh add unit tests, NOT compared with any other calc method, assume correct! 
    132 q =4.*pi/220. 
    133 tests = [ 
    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

    r9b79f29 raea2e2a  
    6060""" 
    6161 
    62 from numpy import pi, inf, sin, cos 
     62from numpy import pi, inf 
    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", "Cylinder axis to beam angle"], 
    85     ["phi",         "degrees",  0,   [-360, 360], "orientation", "Rotation about beam"], 
     84    ["theta",       "degrees", 90,   [-360, 360], "orientation", "Theta angle"], 
     85    ["phi",         "degrees",  0,   [-360, 360], "orientation", "Phi angle"], 
    8686    ] 
    8787# pylint: enable=bad-whitespace, line-too-long 
    … …  
    129129            theta_pd=10, theta_pd_n=5, 
    130130           ) 
    131 q = 0.1 
    132 # april 6 2017, rkh added a 2d unit test, assume correct! 
    133 qx = q*cos(pi/6.0) 
    134 qy = q*sin(pi/6.0) 
     131 
    135132# Parameters for unit tests 
    136133tests = [ 
    137134    [{}, 0.00005, 1764.926], 
    138135    [{}, 'VR', 1.8], 
    139     [{}, 0.001, 1756.76], 
    140     [{}, (qx, qy), 2.36885476192  ], 
    141         ] 
    142 del qx, qy  # not necessary to delete, but cleaner 
     136    [{}, 0.001, 1756.76] 
     137    ] 

  • sasmodels/models/parallelepiped.c

    rd605080 r1e7b0db0  
    6767    double psi) 
    6868{ 
    69     double q, xhat, yhat, zhat; 
    70     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
     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); 
    7171 
    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); 
     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); 
    7575    const double V = form_volume(length_a, length_b, length_c); 
    7676    const double drho = (sld - solvent_sld); 

  • sasmodels/models/parallelepiped.py

    r34a9e4e r3330bb4  
    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  
    1817.. figure:: img/parallelepiped_geometry.jpg 
    1918 
    … …  
    2221.. note:: 
    2322 
    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. 
     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. 
    2926 
    3027The 1D scattering intensity $I(q)$ is calculated as: 
    … …  
    7067    \mu &= qB 
    7168 
     69 
    7270The scattering intensity per unit volume is returned in units of |cm^-1|. 
    7371 
    7472NB: The 2nd virial coefficient of the parallelepiped is calculated based on 
    75 the averaged effective radius, after appropriately sorting the three 
    76 dimensions, to give an oblate or prolate particle, $(=\sqrt{AB/\pi})$ and 
     73the averaged effective radius $(=\sqrt{A B / \pi})$ and 
    7774length $(= C)$ values, and used as the effective radius for 
    7875$S(q)$ when $P(q) \cdot S(q)$ is applied. 
    … …  
    105102.. _parallelepiped-orientation: 
    106103 
    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 
     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 
    114111    detector plane. 
    115112 
    116 On introducing "Orientational Distribution" in the angles, "distribution of theta" and "distribution of phi" parameters will 
    117 appear. 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  
    119 about the $c$ axis of the particle, perpendicular to the $a$ x $b$ face. Some experimentation may be required to  
    120 understand the 2d patterns fully. (Earlier implementations had numerical integration issues in some circumstances when orientation  
    121 distributions passed through 90 degrees, such situations, with very broad distributions, should still be approached with care.)  
    122  
    123      
    124113For a given orientation of the parallelepiped, the 2D form factor is 
    125114calculated as 
    … …  
    127116.. math:: 
    128117 
    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 
     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 
    132121 
    133122with 
    … …  
    165154angles. 
    166155 
     156This model is based on form factor calculations implemented in a c-library 
     157provided by the NIST Center for Neutron Research (Kline, 2006). 
    167158 
    168159References 
    … …  
    172163 
    173164R Nayuk and K Huber, *Z. Phys. Chem.*, 226 (2012) 837-854 
    174  
    175 Authorship 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  
    183165""" 
    184166 
    185167import numpy as np 
    186 from numpy import pi, inf, sqrt, sin, cos 
     168from numpy import pi, inf, sqrt 
    187169 
    188170name = "parallelepiped" 
    … …  
    198180            mu = q*B 
    199181        V: Volume of the rectangular parallelepiped 
    200         alpha: angle between the long axis of the 
     182        alpha: angle between the long axis of the  
    201183            parallelepiped and the q-vector for 1D 
    202184""" 
    … …  
    214196              ["length_c", "Ang", 400, [0, inf], "volume", 
    215197               "Larger side of the parallelepiped"], 
    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"], 
     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"], 
    222204             ] 
    223205 
    … …  
    226208def ER(length_a, length_b, length_c): 
    227209    """ 
    228     Return effective radius (ER) for P(q)*S(q) 
     210        Return effective radius (ER) for P(q)*S(q) 
    229211    """ 
    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]) 
     212 
    236213    # surface average radius (rough approximation) 
    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)) 
     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)) 
    240217    return 0.5 * (ddd) ** (1. / 3.) 
    241218 
    … …  
    253230            phi_pd=10, phi_pd_n=1, 
    254231            psi_pd=10, psi_pd_n=10) 
    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 
    256 qx, qy = 0.2 * cos(pi/6.), 0.2 * sin(pi/6.) 
     232 
     233qx, qy = 0.2 * np.cos(2.5), 0.2 * np.sin(2.5) 
    257234tests = [[{}, 0.2, 0.17758004974], 
    258235         [{}, [0.2], [0.17758004974]], 
    259          [{'theta':10.0, 'phi':20.0}, (qx, qy), 0.0089517140475], 
    260          [{'theta':10.0, 'phi':20.0}, [(qx, qy)], [0.0089517140475]], 
     236         [{'theta':10.0, 'phi':10.0}, (qx, qy), 0.00560296014], 
     237         [{'theta':10.0, 'phi':10.0}, [(qx, qy)], [0.00560296014]], 
    261238        ] 
    262239del qx, qy  # not necessary to delete, but cleaner 

  • sasmodels/models/sc_paracrystal.c

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

  • sasmodels/models/sc_paracrystal.py

    r69e1afc r3330bb4  
    8383model computation. 
    8484 
    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). 
     85.. figure:: img/sc_crystal_angle_definition.jpg 
    8986 
    9087Reference 
    … …  
    130127              ["sld",  "1e-6/Ang^2",         3.0, [0.0, inf],  "sld",         "Sphere scattering length density"], 
    131128              ["sld_solvent", "1e-6/Ang^2",  6.3, [0.0, inf],  "sld",         "Solvent scattering length density"], 
    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"] 
     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"], 
    135132             ] 
    136133# pylint: enable=bad-whitespace, line-too-long 
    … …  
    149146 
    150147tests = [ 
    151     # Accuracy tests based on content in test/utest_extra_models.py, 2d tests added April 10, 2017 
     148    # Accuracy tests based on content in test/utest_extra_models.py 
    152149    [{}, 0.001, 10.3048], 
    153150    [{}, 0.215268, 0.00814889], 
    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 ] 
     151    [{}, (0.414467), 0.001313289] 
    157152    ] 
    158153 

  • sasmodels/models/stacked_disks.py

    r9802ab3 rb7e8b94  
    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.png 
     79.. figure:: img/cylinder_angle_definition.jpg 
    8080 
    8181    Examples of the angles against the detector plane. 
    … …  
    103103""" 
    104104 
    105 from numpy import inf, sin, cos, pi 
     105from numpy import inf 
    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,   [-360, 360], "orientation", "Orientation of the stacked disk axis w/respect incoming beam"], 
    134     ["phi",         "degrees",     0,   [-360, 360], "orientation", "Rotation about beam"], 
     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"], 
    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 q = 0.1 
    155 # april 6 2017, rkh added a 2d unit test, assume correct! 
    156 qx = q*cos(pi/6.0) 
    157 qy = q*sin(pi/6.0) 
     154# but should not matter here as so far all the tests are 1D not 2D 
    158155tests = [ 
    159156# Accuracy tests based on content in test/utest_extra_models.py. 
    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 
     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 
    163158    [{'thick_core': 10.0, 
    164159      'thick_layer': 15.0, 
    … …  
    191186    [{'thick_core': 10.0, 
    192187      '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, 
    206188      'radius': 3000.0, 
    207189      'n_stacking': 5, 
    … …  
    246228      'background': 0.001, 
    247229     }, ([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 ], 
    261230 
    262231    [{'thick_core': 10.0, 

  • sasmodels/models/triaxial_ellipsoid.c

    r68dd6a9 r925ad6e  
    2020    double radius_polar) 
    2121{ 
    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; 
     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; 
    2726    double outer = 0.0; 
    2827    for (int i=0;i<76;i++) { 
    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)); 
     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; 
    3234 
    3335        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             // 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; 
     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 ; 
    4241        } 
    43         outer += Gauss76Wt[i] * inner;  // correcting for dx later 
     42        outer += Gauss76Wt[i] * 0.5 * inner; 
    4443    } 
    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); 
     44    // translate dx in [-1,1] to dx in [lower,upper] 
     45    const double fqsq = outer*zm; 
    4746    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); 
    4847    return 1.0e-4 * s * s * fqsq; 
    … …  
    5958    double psi) 
    6059{ 
    61     double q, xhat, yhat, zhat; 
    62     ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, xhat, yhat, zhat); 
     60    double q, calpha, cmu, cnu; 
     61    ORIENT_ASYMMETRIC(qx, qy, theta, phi, psi, q, calpha, cmu, cnu); 
    6362 
    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); 
     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); 
    6867    const double s = (sld - sld_solvent) * form_volume(radius_equat_minor, radius_equat_major, radius_polar); 
    6968 

  • sasmodels/models/triaxial_ellipsoid.py

    r34a9e4e r3330bb4  
    22# Note: model title and parameter table are inserted automatically 
    33r""" 
     4All three axes are of different lengths with $R_a \leq R_b \leq R_c$ 
     5**Users should maintain this inequality for all calculations**. 
     6 
     7.. math:: 
     8 
     9    P(q) = \text{scale} V \left< F^2(q) \right> + \text{background} 
     10 
     11where 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 
    418Definition 
    519---------- 
    620 
    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  
    12 Given an ellipsoid 
     21The form factor calculated is 
    1322 
    1423.. math:: 
    1524 
    16     \frac{X^2}{R_a^2} + \frac{Y^2}{R_b^2} + \frac{Z^2}{R_c^2} = 1 
    17  
    18 the scattering for randomly oriented particles is defined by the average over 
    19 all orientations $\Omega$ of: 
    20  
    21 .. math:: 
    22  
    23     P(q) = \text{scale}(\Delta\rho)^2\frac{V}{4 \pi}\int_\Omega\Phi^2(qr)\,d\Omega 
    24            + \text{background} 
     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 
    2528 
    2629where 
    … …  
    2831.. math:: 
    2932 
    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 
     33    \Phi(u) = 3 u^{-3} (\sin u - u \cos u) 
    3334 
    34 The $e$, $f$ and $g$ terms are the projections of the orientation vector on $X$, 
    35 $Y$ and $Z$ respectively.  Keeping the orientation fixed at the canonical 
    36 axes, 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  
    45 with $e = \cos\gamma \sin\phi$, $f = \cos\gamma \cos\phi$ and $g = \sin\gamma$. 
    46 A 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  
    52 for 
    53  
    54 .. math:: 
    55  
    56     p_a = \frac{a^2}{b^2} - 1 \text{ and } p_c = \frac{c^2}{b^2} - 1 
    57  
    58 Due 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 
    60 integral 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  
    68 Though for convenience we describe the three radii of the ellipsoid as equatorial 
    69 and polar, they may be given in $any$ size order. To avoid multiple solutions, especially 
    70 with Monte-Carlo fit methods, it may be advisable to restrict their ranges. For typical 
    71 small angle diffraction situations there may be a number of closely similar "best fits", 
    72 so some trial and error, or fixing of some radii at expected values, may help. 
    73      
    7435To provide easy access to the orientation of the triaxial ellipsoid, 
    7536we define the axis of the cylinder using the angles $\theta$, $\phi$ 
    76 and $\psi$. These angles are defined analogously to the elliptical_cylinder below, note that 
    77 angle $\phi$ 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  
    84 For oriented ellipsoids the *theta*, *phi* and *psi* orientation parameters will appear when fitting 2D data,  
    85 see the :ref:`elliptical-cylinder` model for further information. 
     37and $\psi$. These angles are defined on 
     38:numref:`triaxial-ellipsoid-angles` . 
     39The angle $\psi$ is the rotational angle around its own $c$ axis 
     40against the $q$ plane. For example, $\psi = 0$ when the 
     41$a$ axis is parallel to the $x$ axis of the detector. 
    8642 
    8743.. _triaxial-ellipsoid-angles: 
    8844 
    89 .. figure:: img/triaxial_ellipsoid_angle_projection.png 
     45.. figure:: img/triaxial_ellipsoid_angle_projection.jpg 
    9046 
    91     Some examples for an oriented triaxial ellipsoid. 
     47    The angles for oriented ellipsoid. 
    9248 
    9349The radius-of-gyration for this system is  $R_g^2 = (R_a R_b R_c)^2/5$. 
    9450 
    95 The contrast $\Delta\rho$ is defined as SLD(ellipsoid) - SLD(solvent).  In the 
     51The contrast is defined as SLD(ellipsoid) - SLD(solvent).  In the 
    9652parameters, $R_a$ is the minor equatorial radius, $R_b$ is the major 
    9753equatorial radius, and $R_c$ is the polar radius of the ellipsoid. 
    9854 
    9955NB: The 2nd virial coefficient of the triaxial solid ellipsoid is 
    100 calculated after sorting the three radii to give the most appropriate 
    101 prolate or oblate form, from the new polar radius $R_p = R_c$ and effective equatorial 
    102 radius,  $R_e = \sqrt{R_a R_b}$, to then be used as the effective radius for 
     56calculated based on the polar radius $R_p = R_c$ and equatorial 
     57radius $R_e = \sqrt{R_a R_b}$, and used as the effective radius for 
    10358$S(q)$ when $P(q) \cdot S(q)$ is applied. 
    10459 
    … …  
    11469---------- 
    11570 
    116 [1] Finnigan, J.A., Jacobs, D.J., 1971. 
    117 *Light scattering by ellipsoidal particles in solution*, 
    118 J. Phys. D: Appl. Phys. 4, 72-77. doi:10.1088/0022-3727/4/1/310 
    119  
    120 Authorship 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 
     71L A Feigin and D I Svergun, *Structure Analysis by Small-Angle X-Ray 
     72and Neutron Scattering*, Plenum, New York, 1987. 
    12673""" 
    12774 
    128 from numpy import inf, sin, cos, pi 
     75from numpy import inf 
    12976 
    13077name = "triaxial_ellipsoid" 
    13178title = "Ellipsoid of uniform scattering length density with three independent axes." 
    13279 
    133 description = """ 
    134    Triaxial ellipsoid - see main documentation. 
     80description = """\ 
     81Note: During fitting ensure that the inequality ra<rb<rc is not 
     82        violated. Otherwise the calculation will 
     83        not be correct. 
    13584""" 
    13685category = "shape:ellipsoid" 
    … …  
    14291               "Solvent scattering length density"], 
    14392              ["radius_equat_minor", "Ang", 20, [0, inf], "volume", 
    144                "Minor equatorial radius, Ra"], 
     93               "Minor equatorial radius"], 
    14594              ["radius_equat_major", "Ang", 400, [0, inf], "volume", 
    146                "Major equatorial radius, Rb"], 
     95               "Major equatorial radius"], 
    14796              ["radius_polar", "Ang", 10, [0, inf], "volume", 
    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"], 
     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"], 
    155104             ] 
    156105 
    … …  
    159108def ER(radius_equat_minor, radius_equat_major, radius_polar): 
    160109    """ 
    161     Returns the effective radius used in the S*P calculation 
     110        Returns the effective radius used in the S*P calculation 
    162111    """ 
    163112    import numpy as np 
    164113    from .ellipsoid import ER as ellipsoid_ER 
    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) 
     114    return ellipsoid_ER(radius_polar, np.sqrt(radius_equat_minor * radius_equat_major)) 
    174115 
    175116demo = dict(scale=1, background=0, 
    … …  
    183124            phi_pd=15, phi_pd_n=1, 
    184125            psi_pd=15, psi_pd_n=1) 
    185  
    186 q = 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 
    190 qx = q*cos(pi/6.0) 
    191 qy = q*sin(pi/6.0) 
    192 tests = [[{}, 0.05, 24.8839548033], 
    193         [{'theta':80., 'phi':10.}, (qx, qy), 166.712060266 ], 
    194         ] 
    195 del qx, qy  # not necessary to delete, but cleaner 
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