Changeset 32c160a in sasmodels for sasmodels/models/cylinder_clone.c


Ignore:
Timestamp:
Aug 24, 2014 10:55:08 PM (10 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, costrafo411, magnetic_model, release_v0.94, release_v0.95, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
13d86bc
Parents:
1f21edf
Message:

support ER/VR python kernels; move metadata to python

File:
1 edited

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  • sasmodels/models/cylinder_clone.c

    r1f21edf r32c160a  
    1 /* PARAMETERS 
    2 { 
    3 name: "CylinderModel", 
    4 title: "Cylinder with uniform scattering length density", 
    5 include: [ "lib/J1.c", "lib/gauss76.c", "lib/cylkernel.c"], 
    6 parameters: [ 
    7    // [ "name", "units", default, [lower, upper], "type", "description" ], 
    8    [ "sldCyl", "1e-6/Ang^2", 4e-6, [-Infinity,Infinity], "", 
    9      "Cylinder scattering length density" ], 
    10    [ "sldSolv", "1e-6/Ang^2", 1e-6, [-Infinity,Infinity], "", 
    11      "Solvent scattering length density" ], 
    12    [ "radius", "Ang",  20, [0, Infinity], "volume", 
    13      "Cylinder radius" ], 
    14    [ "length", "Ang",  400, [0, Infinity], "volume", 
    15      "Cylinder length" ], 
    16    [ "cyl_theta", "degrees", 60, [-Infinity, Infinity], "orientation", 
    17      "In plane angle" ], 
    18    [ "cyl_phi", "degrees", 60, [-Infinity, Infinity], "orientation", 
    19      "Out of plane angle" ], 
    20 ], 
    21 description: "f(q)= 2*(sldCyl - sldSolv)*V*sin(qLcos(alpha/2))/[qLcos(alpha/2)]*J1(qRsin(alpha/2))/[qRsin(alpha)]", 
    22 } 
    23 PARAMETERS END 
    24  
    25 DOCUMENTATION 
    26 .. _CylinderModel: 
    27  
    28 CylinderModel 
    29 ============= 
    30  
    31 This model provides the form factor for a right circular cylinder with uniform 
    32 scattering length density. The form factor is normalized by the particle volume. 
    33  
    34 For information about polarised and magnetic scattering, click here_. 
    35  
    36 Definition 
    37 ---------- 
    38  
    39 The output of the 2D scattering intensity function for oriented cylinders is 
    40 given by (Guinier, 1955) 
    41  
    42 .. math:: 
    43  
    44     P(q,\alpha) = \frac{\text{scale}}{V}f^2(q) + \text{bkg} 
    45  
    46 where 
    47  
    48 .. math:: 
    49  
    50     f(q) = 2 (\Delta \rho) V 
    51            \frac{\sin (q L/2 \cos \alpha)}{q L/2 \cos \alpha} 
    52            \frac{J_1 (q r \sin \alpha)}{q r \sin \alpha} 
    53  
    54 and $\alpha$ is the angle between the axis of the cylinder and $\vec q$, $V$ 
    55 is the volume of the cylinder, $L$ is the length of the cylinder, $r$ is the 
    56 radius of the cylinder, and $d\rho$ (contrast) is the scattering length density 
    57 difference between the scatterer and the solvent. $J_1$ is the first order 
    58 Bessel function. 
    59  
    60 To provide easy access to the orientation of the cylinder, we define the 
    61 axis of the cylinder using two angles $\theta$ and $\phi$. Those angles 
    62 are defined in Figure :num:`figure #CylinderModel-orientation`. 
    63  
    64 .. _CylinderModel-orientation: 
    65  
    66 .. figure:: img/image061.JPG 
    67  
    68     Definition of the angles for oriented cylinders. 
    69  
    70 .. figure:: img/image062.JPG 
    71  
    72     Examples of the angles for oriented pp against the detector plane. 
    73  
    74 NB: The 2nd virial coefficient of the cylinder is calculated based on the 
    75 radius and length values, and used as the effective radius for $S(Q)$ 
    76 when $P(Q) \cdot S(Q)$ is applied. 
    77  
    78 The returned value is scaled to units of |cm^-1| and the parameters of 
    79 the CylinderModel are the following: 
    80  
    81 %(parameters)s 
    82  
    83 The output of the 1D scattering intensity function for randomly oriented 
    84 cylinders is then given by 
    85  
    86 .. math:: 
    87  
    88     P(q) = \frac{\text{scale}}{V} 
    89         \int_0^{\pi/2} f^2(q,\alpha) \sin \alpha d\alpha + \text{background} 
    90  
    91 The *theta* and *phi* parameters are not used for the 1D output. Our 
    92 implementation of the scattering kernel and the 1D scattering intensity 
    93 use the c-library from NIST. 
    94  
    95 Validation of the CylinderModel 
    96 ------------------------------- 
    97  
    98 Validation of our code was done by comparing the output of the 1D model 
    99 to the output of the software provided by the NIST (Kline, 2006). 
    100 Figure :num:`figure #CylinderModel-compare` shows a comparison of 
    101 the 1D output of our model and the output of the NIST software. 
    102  
    103 .. _CylinderModel-compare: 
    104  
    105 .. figure:: img/image065.JPG 
    106  
    107     Comparison of the SasView scattering intensity for a cylinder with the 
    108     output of the NIST SANS analysis software. 
    109     The parameters were set to: *Scale* = 1.0, *Radius* = 20 |Ang|, 
    110     *Length* = 400 |Ang|, *Contrast* = 3e-6 |Ang^-2|, and 
    111     *Background* = 0.01 |cm^-1|. 
    112  
    113 In general, averaging over a distribution of orientations is done by 
    114 evaluating the following 
    115  
    116 .. math:: 
    117  
    118     P(q) = \int_0^{\pi/2} d\phi 
    119         \int_0^\pi p(\theta, \phi) P_0(q,\alpha) \sin \theta d\theta 
    120  
    121  
    122 where $p(\theta,\phi)$ is the probability distribution for the orientation 
    123 and $P_0(q,\alpha)$ is the scattering intensity for the fully oriented 
    124 system. Since we have no other software to compare the implementation of 
    125 the intensity for fully oriented cylinders, we can compare the result of 
    126 averaging our 2D output using a uniform distribution $p(\theta, \phi) = 1.0$. 
    127 Figure :num:`figure #CylinderModel-crosscheck` shows the result of 
    128 such a cross-check. 
    129  
    130 .. _CylinderModel-crosscheck: 
    131  
    132 .. figure:: img/image066.JPG 
    133  
    134     Comparison of the intensity for uniformly distributed cylinders 
    135     calculated from our 2D model and the intensity from the NIST SANS 
    136     analysis software. 
    137     The parameters used were: *Scale* = 1.0, *Radius* = 20 |Ang|, 
    138     *Length* = 400 |Ang|, *Contrast* = 3e-6 |Ang^-2|, and 
    139     *Background* = 0.0 |cm^-1|. 
    140  
    141 DOCUMENTATION END 
    142 */ 
    1431real form_volume(real radius, real length); 
    1442real Iq(real q, real sld, real solvent_sld, real radius, real length); 
    1453real Iqxy(real qx, real qy, real sld, real solvent_sld, real radius, real length, real theta, real phi); 
    146  
    1474 
    1485real form_volume(real radius, real length) 
    … …  
    17330    return REAL(1.0e8) * form * s * s; 
    17431} 
    175  
    17632 
    17733real Iqxy(real qx, real qy, 
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