Changeset af0e70c in sasmodels


Ignore:
Timestamp:
Apr 19, 2016 6:48:40 AM (9 years ago)
Author:
wojciech
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:
7c20ba0
Parents:
25b82a1
Message:

Removed old parameter data structure

Location:
sasmodels/models
Files:
2 edited

Legend:

Unmodified
Added
Removed

  • sasmodels/models/spherical_sld.c

    r1bf66d9 raf0e70c  
    22    int n_shells, 
    33    double radius_core, 
     4    double thick_inter0, 
    45    double thick_flat[], 
    56    double thick_inter[]) 
    … …  
    78    int i; 
    89    double r = radius_core; 
     10    r += thick_inter0; 
    911    for (i=0; i < n_shells; i++) { 
    1012        r += thick_inter[i]; 
    … …  
    1517 
    1618 
    17 static double sphere_sld_kernel(double dp[], double q) { 
    18   int n = dp[0]; 
    19   int i,j,k; 
    20  
    21   double scale = dp[1]; 
    22   double thick_inter_core = dp[2]; 
    23   double sld_core = dp[4]; 
    24   double sld_solv = dp[5]; 
    25   double background = dp[6]; 
    26   double npts = dp[57]; //number of sub_layers in each interface 
    27   double nsl=npts;//21.0; //nsl = Num_sub_layer:  must be ODD double number 
    28   int n_s; 
    29  
    30   double sld_i,sld_f,dz,bes,fun,f,vol,qr,r,contr,f2; 
    31   double sign,slope=0.0; 
    32   double pi; 
    33  
    34   double total_thick=0.0; 
    35  
    36   int fun_type[12]; 
    37   double sld[12]; 
    38   double thick_inter[12]; 
    39   double thick[12]; 
    40   double fun_coef[12]; 
    41  
    42   fun_type[0] = dp[3]; 
    43   fun_coef[0] = fabs(dp[58]); 
    44   for (i =1; i<=n; i++){ 
    45     sld[i] = dp[i+6]; 
    46     thick_inter[i]= dp[i+16]; 
    47     thick[i] = dp[i+26]; 
    48     fun_type[i] = dp[i+36]; 
    49     fun_coef[i] = fabs(dp[i+46]); 
    50     total_thick += thick[i]; 
    51     total_thick += thick_inter[i]; 
    52   } 
    53   sld[0] = sld_core; 
    54   sld[n+1] = sld_solv; 
    55   thick[0] = dp[59]; 
    56   thick[n+1] = total_thick/5.0; 
    57   thick_inter[0] = thick_inter_core; 
    58   thick_inter[n+1] = 0.0; 
    59   fun_coef[n+1] = 0.0; 
    60   pi = 4.0*atan(1.0); 
    61   f = 0.0; 
    62   r = 0.0; 
    63   vol = 0.0; 
    64   //vol_pre = 0.0; 
    65   //vol_sub = 0.0; 
    66   sld_f = sld_core; 
    67  
    68   //floor_nsl = floor(nsl/2.0); 
    69  
    70   dz = 0.0; 
    71   // iteration for # of shells + core + solvent 
    72   for (i=0;i<=n+1; i++){ 
    73     //iteration for N sub-layers 
    74     //if (fabs(thick[i]) <= 1e-24){ 
    75     //   continue; 
    76     //} 
    77     // iteration for flat and interface 
    78     for (j=0;j<2;j++){ 
    79       // iteration for sub_shells in the interface 
    80       // starts from #1 sub-layer 
    81       for (n_s=1;n_s<=nsl; n_s++){ 
    82         // for solvent, it doesn't have an interface 
    83         if (i==n+1 && j==1) 
    84           break; 
    85         // for flat layers 
    86         if (j==0){ 
    87           dz = thick[i]; 
    88           sld_i = sld[i]; 
    89           slope = 0.0; 
     19static double sphere_sld_kernel( 
     20    double q, 
     21    int n_shells, 
     22    int npts_inter, 
     23    double radius_core, 
     24    double sld_core, 
     25    double sld_solvent, 
     26    double func_inter_core, 
     27    double thick_inter_core, 
     28    double nu_inter_core, 
     29    double sld_flat[], 
     30    double thick_flat[], 
     31    double func_inter[], 
     32    double thick_inter[], 
     33    double nu_inter[] ) { 
     34 
     35    int i,j,k; 
     36    int n_s; 
     37 
     38    double sld_i,sld_f,dz,bes,fun,f,vol,qr,r,contr,f2; 
     39    double sign,slope=0.0; 
     40    double pi; 
     41 
     42    double total_thick=0.0; 
     43 
     44    //TODO: This part can be further simplified 
     45    int fun_type[12]; 
     46    double sld[12]; 
     47    double thick_internal[12]; 
     48    double thick[12]; 
     49    double fun_coef[12]; 
     50 
     51    fun_type[0] = func_inter_core; 
     52    fun_coef[0] = fabs(nu_inter_core); 
     53    sld[0] = sld_core; 
     54    thick[0] = radius_core; 
     55    thick_internal[0] = thick_inter_core; 
     56 
     57    for (i =1; i<=n_shells; i++){ 
     58        sld[i] = sld_flat[i-1]; 
     59        thick_internal[i]= thick_inter[i-1]; 
     60        thick[i] = thick_flat[i-1]; 
     61        fun_type[i] = func_inter[i-1]; 
     62        fun_coef[i] = fabs(nu_inter[i-1]); 
     63        total_thick += thick[i]; 
     64        total_thick += thick_internal[i]; //doesn't account for core layer 
     65    } 
     66 
     67    sld[n_shells+1] = sld_solvent; 
     68    thick[n_shells+1] = total_thick/5.0; 
     69    thick_internal[n_shells+1] = 0.0; 
     70    fun_coef[n_shells+1] = 0.0; 
     71    fun_type[n_shells+1] = 0; 
     72 
     73    pi = 4.0*atan(1.0); 
     74    f = 0.0; 
     75    r = 0.0; 
     76    vol = 0.0; 
     77    sld_f = sld_core; 
     78 
     79    dz = 0.0; 
     80    // iteration for # of shells + core + solvent 
     81    for (i=0;i<=n_shells+1; i++){ 
     82        // iteration for flat and interface 
     83        for (j=0;j<2;j++){ 
     84            // iteration for sub_shells in the interface 
     85            // starts from #1 sub-layer 
     86            for (n_s=1;n_s<=npts_inter; n_s++){ 
     87                // for solvent, it doesn't have an interface 
     88                if (i==n_shells+1 && j==1) 
     89                    break; 
     90                // for flat layers 
     91                if (j==0){ 
     92                    dz = thick[i]; 
     93                    sld_i = sld[i]; 
     94                    slope = 0.0; 
     95                } 
     96                // for interfacial sub_shells 
     97                else{ 
     98                    dz = thick_internal[i]/npts_inter; 
     99                    // find sld_i at the outer boundary of sub-layer #n_s 
     100                    sld_i = intersldfunc(fun_type[i], npts_inter, n_s, 
     101                            fun_coef[i], sld[i], sld[i+1]); 
     102                    // calculate slope 
     103                    slope= (sld_i -sld_f)/dz; 
     104                } 
     105                contr = sld_f-slope*r; 
     106                // iteration for the left and right boundary of the shells 
     107                for (k=0; k<2; k++){ 
     108                    // At r=0, the contribution to I is zero, so skip it. 
     109                    if ( i == 0 && j == 0 && k == 0){ 
     110                        continue; 
     111                    } 
     112                    // On the top of slovent there is no interface; skip it. 
     113                    if (i == n_shells+1 && k == 1){ 
     114                        continue; 
     115                    } 
     116                    // At the right side (outer) boundary 
     117                    if ( k == 1){ 
     118                        sign = 1.0; 
     119                        r += dz; 
     120                    } 
     121                    // At the left side (inner) boundary 
     122                    else{ 
     123                        sign = -1.0; 
     124                    } 
     125 
     126                    qr = q * r; 
     127                    fun = 0.0; 
     128 
     129                    if(qr == 0.0){ 
     130                        bes = sign * 1.0; 
     131                    } 
     132                    else{ 
     133                        // for flat sub-layer 
     134                        //TODO: Single precision calculation fails here 
     135                        bes = sign *  sph_j1c(qr); 
     136                        if (fabs(slope) > 0.0 ){ 
     137                            const double qrsq = qr*qr; 
     138                            double sinqr, cosqr; 
     139                            SINCOS(qr, sinqr, cosqr); 
     140                            fun = sign * 3.0 * r * 
     141                            (2.0*qr*sinqr - (qrsq-2.0)*cosqr)/(qrsq * qrsq); 
     142                            // In the onioon model Jae-He's formula is rederived 
     143                            // and gives following: 
     144                            //fun = 3.0 * sign * r * 
     145                            //(2.0*cosqr + qr*sinqr)/(qrsq*qrsq); 
     146                            //But this seems not to be working in this case... 
     147                        } 
     148                    } 
     149 
     150                    // update total volume 
     151                    vol = M_4PI_3 * cube(r); 
     152                    f += vol * (bes * contr + fun * slope); 
     153                } 
     154                sld_f = sld_i; 
     155                // no sub-layer iteration (n_s loop) for the flat layer 
     156                if (j==0) 
     157                    break; 
     158            } 
    90159        } 
    91         // for interfacial sub_shells 
    92         else{ 
    93           dz = thick_inter[i]/nsl; 
    94           // find sld_i at the outer boundary of sub-layer #n_s 
    95           sld_i = intersldfunc(fun_type[i],nsl, n_s, fun_coef[i], sld[i], sld[i+1]); 
    96           // calculate slope 
    97           slope= (sld_i -sld_f)/dz; 
    98         } 
    99         contr = sld_f-slope*r; 
    100         // iteration for the left and right boundary of the shells(or sub_shells) 
    101         for (k=0; k<2; k++){ 
    102           // At r=0, the contribution to I is zero, so skip it. 
    103           if ( i == 0 && j == 0 && k == 0){ 
    104             continue; 
    105           } 
    106           // On the top of slovent there is no interface; skip it. 
    107           if (i == n+1 && k == 1){ 
    108             continue; 
    109           } 
    110           // At the right side (outer) boundary 
    111           if ( k == 1){ 
    112             sign = 1.0; 
    113             r += dz; 
    114           } 
    115           // At the left side (inner) boundary 
    116           else{ 
    117             sign = -1.0; 
    118           } 
    119           qr = q * r; 
    120           fun = 0.0; 
    121  
    122           if(qr == 0.0){ 
    123             // sigular point 
    124             bes = sign * 1.0; 
    125           } 
    126           else{ 
    127             // for flat sub-layer 
    128             //TODO: Single precision calculation most likely fails here 
    129             //bes = sign *  3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr); 
    130             bes = sign *  sph_j1c(qr); 
    131             if (fabs(slope) > 0.0 ){ 
    132               //fun = sign * 3.0 * r * (2.0*qr*sin(qr)-((qr*qr)-2.0)*cos(qr))/(qr * qr * qr * qr); 
    133               fun = sign * r * sph_j1c(qr) + sign * 3.0 * sin(qr)/(qr * qr * q ) 
    134                 + sign * 6.0 * cos(qr)/(qr * qr * qr * q); 
    135             } 
    136           } 
    137  
    138           //Some initial optimization tries 
    139           /*bes = (qr == 0.0 ? sign * 1.0 : sign *  3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr)); 
    140           //TODO: Will have to chnage this function 
    141           if (qr!= 0.0 && fabs(slope) > 0.0 ){ 
    142             fun = sign * 3.0 * r * (2.0*qr*sin(qr)-((qr*qr)-2.0)*cos(qr))/(qr * qr * qr * qr); 
    143           }*/ 
    144  
    145           // update total volume 
    146           vol = 4.0 * pi / 3.0 * r * r * r; 
    147           // we won't do the following volume correction for now. 
    148           // substrate empty area of volume 
    149           //if (k == 1 && fabs(sld_in[i]-sld_solv) < 1e-04*fabs(sld_solv) && fun_type[i]==0){ 
    150           //  vol_sub += (vol_pre - vol); 
    151           //} 
    152           f += vol * (bes * contr + fun * slope); 
    153         } 
    154         // remember this sld as sld_f 
    155         sld_f = sld_i; 
    156         // no sub-layer iteration (n_s loop) for the flat layer 
    157         if (j==0) 
    158           break; 
    159       } 
    160     } 
    161   } 
    162   f2 = f * f / vol; 
    163  
    164   return (f2); 
     160    } 
     161    f2 = f * f / vol; 
     162    return (f2); 
    165163} 
    166164 
    … …  
    177175    double sld_core, 
    178176    double sld_solvent, 
     177    double func_inter0, 
     178    double thick_inter0, 
     179    double nu_inter0, 
    179180    double sld_flat[], 
    180181    double thick_flat[], 
    … …  
    186187    double intensity; 
    187188    //TODO: Remove this container at later stage. 
    188     double dp[60]; 
     189    /*double dp[60]; 
    189190    dp[0] = n_shells; 
    190191    //This is scale will also have to be removed at some stage 
    191192    dp[1] = 1.0; 
    192     dp[2] = thick_inter[0]; 
    193     dp[3] = func_inter[0]; 
     193    dp[2] = thick_inter0; 
     194    dp[3] = func_inter0; 
    194195    dp[4] = sld_core; 
    195196    dp[5] = sld_solvent; 
    196197    dp[6] = 0.0; 
    197     dp[7] = sld_flat[0]; 
    198     //TODO: Something is messed up with this data strcucture! 
    199     dp[17] = thick_inter[0]; 
    200     dp[27] = thick_flat[0]; 
    201     dp[37] = func_inter[0]; 
    202     dp[47] = nu_inter[0]; 
    203  
    204     for (int i=1; i<=n_shells; i++){ 
     198 
     199    for (int i=0; i<n_shells; i++){ 
    205200        dp[i+7] = sld_flat[i]; 
    206201        dp[i+17] = thick_inter[i]; 
    … …  
    211206 
    212207    dp[57] = npts_inter; 
    213     dp[58] = nu_inter[0]; 
     208    dp[58] = nu_inter0; 
    214209    dp[59] = radius_core; 
    215  
    216     intensity = 1.0e-4*sphere_sld_kernel(dp,q); 
     210    */ 
     211    intensity = sphere_sld_kernel(q, n_shells, npts_inter, radius_core, 
     212                sld_core, sld_solvent, func_inter0, thick_inter0, nu_inter0, 
     213                sld_flat, thick_flat, func_inter, thick_inter, nu_inter); 
     214    intensity *=1.0e-4; 
    217215    //printf("%10d\n",intensity); 
    218216    return intensity; 

  • sasmodels/models/spherical_sld.py

    r1448db7a raf0e70c  
    11r""" 
    2 This model calculates an empirical functional form for SAS data using SpericalSLD profile 
    3  
    4 Similarly to the OnionExpShellModel, this model provides the form factor, P(q), for a multi-shell sphere, 
    5 where the interface between the each neighboring shells can be described by one of a number of functions 
    6 including error, power-law, and exponential functions. This model is to calculate the scattering intensity 
    7 by building a continuous custom SLD profile against the radius of the particle. The SLD profile is composed 
    8 of a flat core, a flat solvent, a number (up to 9 ) flat shells, and the interfacial layers between 
    9 the adjacent flat shells (or core, and solvent) (see below). 
     2This model calculates an empirical functional form for SAS data using 
     3SpericalSLD profile 
     4 
     5Similarly to the OnionExpShellModel, this model provides the form factor, 
     6P(q), for a multi-shell sphere, where the interface between the each neighboring 
     7shells can be described by one of a number of functions including error, 
     8power-law, and exponential functions. 
     9This model is to calculate the scattering intensity by building a continuous 
     10custom SLD profile against the radius of the particle. 
     11The SLD profile is composed of a flat core, a flat solvent, a number (up to 9 ) 
     12flat shells, and the interfacial layers between the adjacent flat shells 
     13(or core, and solvent) (see below). 
    1014 
    1115.. figure:: img/spherical_sld_profile.gif 
    … …  
    1317    Exemplary SLD profile 
    1418 
    15 Unlike the <onion> model (using an analytical integration), 
    16 the interfacial layers here are sub-divided and numerically integrated assuming each of the sub-layers are described 
    17 by a line function. The number of the sub-layer can be given by users by setting the integer values of npts_inter. 
    18 The form factor is normalized by the total volume of the sphere. 
     19Unlike the <onion> model (using an analytical integration), the interfacial 
     20layers here are sub-divided and numerically integrated assuming each of the 
     21sub-layers are described by a line function. 
     22The number of the sub-layer can be given by users by setting the integer values 
     23of npts_inter. The form factor is normalized by the total volume of the sphere. 
    1924 
    2025Definition 
    … …  
    2934    \sum_{\text{flat}_i=0}^N f_{\text{flat}_i} +f_\text{solvent} 
    3035 
    31 For a spherically symmetric particle with a particle density $\rho_x(r)$ the sld function can be defined as: 
     36For a spherically symmetric particle with a particle density $\rho_x(r)$ 
     37the sld function can be defined as: 
    3238 
    3339.. math:: 
    … …  
    3945 
    4046.. math:: 
    41     f_\text{core} = 4 \pi \int_{0}^{r_\text{core}} \rho_\text{core} \frac{\sin(qr)} {qr} r^2 dr = 
     47    f_\text{core} = 4 \pi \int_{0}^{r_\text{core}} \rho_\text{core} 
     48    \frac{\sin(qr)} {qr} r^2 dr = 
    4249    3 \rho_\text{core} V(r_\text{core}) 
    43     \Big[ \frac{\sin(qr_\text{core}) - qr_\text{core} \cos(qr_\text{core})} {qr_\text{core}^3} \Big] 
    44  
    45     f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr 
    46  
    47     f_{\text{shell}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{flat}_i } \frac{\sin(qr)} {qr} r^2 dr = 
    48     3 \rho_{ \text{flat}_i } V ( r_{ \text{inter}_i } + \Delta t_{ \text{inter}_i } ) 
    49     \Big[ \frac{\sin(qr_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) - q (r_{\text{inter}_i} + 
    50     \Delta t_{ \text{inter}_i }) \cos(q( r_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) ) } 
     50    \Big[ \frac{\sin(qr_\text{core}) - qr_\text{core} \cos(qr_\text{core})} 
     51    {qr_\text{core}^3} \Big] 
     52 
     53    f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } 
     54    \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr 
     55 
     56    f_{\text{shell}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } 
     57    \rho_{ \text{flat}_i } \frac{\sin(qr)} {qr} r^2 dr = 
     58    3 \rho_{ \text{flat}_i } V ( r_{ \text{inter}_i } + 
     59    \Delta t_{ \text{inter}_i } ) 
     60    \Big[ \frac{\sin(qr_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) 
     61    - q (r_{\text{inter}_i} + \Delta t_{ \text{inter}_i }) 
     62    \cos(q( r_{\text{inter}_i} + \Delta t_{ \text{inter}_i } ) ) } 
    5163    {q ( r_{\text{inter}_i} + \Delta t_{ \text{inter}_i } )^3 }  \Big] 
    5264    -3 \rho_{ \text{flat}_i } V(r_{ \text{inter}_i }) 
    53     \Big[ \frac{\sin(qr_{\text{inter}_i}) - qr_{\text{flat}_i} \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big] 
    54  
    55     f_\text{solvent} = 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent} \frac{\sin(qr)} {qr} r^2 dr = 
     65    \Big[ \frac{\sin(qr_{\text{inter}_i}) - qr_{\text{flat}_i} 
     66    \cos(qr_{\text{inter}_i}) } {qr_{\text{inter}_i}^3} \Big] 
     67 
     68    f_\text{solvent} = 4 \pi \int_{r_N}^{\infty} \rho_\text{solvent} 
     69    \frac{\sin(qr)} {qr} r^2 dr = 
    5670    3 \rho_\text{solvent} V(r_N) 
    5771    \Big[ \frac{\sin(qr_N) - qr_N \cos(qr_N)} {qr_N^3} \Big] 
    … …  
    6680.. math:: 
    6781    \rho_{{inter}_i} (r) = \begin{cases} 
    68     B \exp\Big( \frac {\pm A(r - r_{\text{flat}_i})} {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\ 
    69     B \Big( \frac {(r - r_{\text{flat}_i})} {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A = 0 \\ 
     82    B \exp\Big( \frac {\pm A(r - r_{\text{flat}_i})} 
     83    {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\ 
     84    B \Big( \frac {(r - r_{\text{flat}_i})} 
     85    {\Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A = 0 \\ 
    7086    \end{cases} 
    7187 
    … …  
    7490.. math:: 
    7591    \rho_{{inter}_i} (r) = \begin{cases} 
    76     \pm B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} \Big) ^A  +C  & \text{for} A \neq 0 \\ 
     92    \pm B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} 
     93    \Big) ^A  +C  & \text{for} A \neq 0 \\ 
    7794    \rho_{\text{flat}_{i+1}}  & \text{for} A = 0 \\ 
    7895    \end{cases} 
    … …  
    8299.. math:: 
    83100    \rho_{{inter}_i} (r) = \begin{cases} 
    84     B \text{erf} \Big( \frac { A(r - r_{\text{flat}_i})} {\sqrt{2} \Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\ 
    85     B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} \Big)  +C  & \text{for} A = 0 \\ 
     101    B \text{erf} \Big( \frac { A(r - r_{\text{flat}_i})} 
     102    {\sqrt{2} \Delta t_{ \text{inter}_i }} \Big) +C  & \text{for} A \neq 0 \\ 
     103    B \Big( \frac {(r - r_{\text{flat}_i} )} {\Delta t_{ \text{inter}_i }} 
     104    \Big)  +C  & \text{for} A = 0 \\ 
    86105    \end{cases} 
    87106 
    88 The functions are normalized so that they vary between 0 and 1, and they are constrained such that the SLD 
    89 is continuous at the boundaries of the interface as well as each sub-layers. Thus B and C are determined. 
    90  
    91 Once $\rho_{\text{inter}_i}$ is found at the boundary of the sub-layer of the interface, we can find its contribution 
    92 to the form factor $P(q)$ 
    93  
    94 .. math:: 
    95     f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr = 
     107The functions are normalized so that they vary between 0 and 1, and they are 
     108constrained such that the SLD is continuous at the boundaries of the interface 
     109as well as each sub-layers. Thus B and C are determined. 
     110 
     111Once $\rho_{\text{inter}_i}$ is found at the boundary of the sub-layer of the 
     112interface, we can find its contribution to the form factor $P(q)$ 
     113 
     114.. math:: 
     115    f_{\text{inter}_i} = 4 \pi \int_{\Delta t_{ \text{inter}_i } } 
     116    \rho_{ \text{inter}_i } \frac{\sin(qr)} {qr} r^2 dr = 
    96117    4 \pi \sum_{j=0}^{npts_{\text{inter}_i} -1 } 
    97     \int_{r_j}^{r_{j+1}} \rho_{ \text{inter}_i } (r_j) \frac{\sin(qr)} {qr} r^2 dr \approx 
     118    \int_{r_j}^{r_{j+1}} \rho_{ \text{inter}_i } (r_j) 
     119    \frac{\sin(qr)} {qr} r^2 dr \approx 
    98120 
    99121    4 \pi \sum_{j=0}^{npts_{\text{inter}_i} -1 } \Big[ 
    100     3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } ( r_{j} ) V ( r_{ \text{sublayer}_j } ) 
    101     \Big[ \frac {r_j^2 \beta_\text{out}^2 \sin(\beta_\text{out}) - (\beta_\text{out}^2-2) \cos(\beta_\text{out}) } 
     122    3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } 
     123    ( r_{j} ) V ( r_{ \text{sublayer}_j } ) 
     124    \Big[ \frac {r_j^2 \beta_\text{out}^2 \sin(\beta_\text{out}) 
     125    - (\beta_\text{out}^2-2) \cos(\beta_\text{out}) } 
    102126    {\beta_\text{out}^4 } \Big] 
    103127 
    104     - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } ( r_{j} ) V ( r_{ \text{sublayer}_j-1 } ) 
    105     \Big[ \frac {r_{j-1}^2 \sin(\beta_\text{in}) - (\beta_\text{in}^2-2) \cos(\beta_\text{in}) } 
     128    - 3 ( \rho_{ \text{inter}_i } ( r_{j+1} ) - \rho_{ \text{inter}_i } 
     129    ( r_{j} ) V ( r_{ \text{sublayer}_j-1 } ) 
     130    \Big[ \frac {r_{j-1}^2 \sin(\beta_\text{in}) 
     131    - (\beta_\text{in}^2-2) \cos(\beta_\text{in}) } 
    106132    {\beta_\text{in}^4 } \Big] 
    107133 
    … …  
    120146    V(a) = \frac {4\pi}{3}a^3 
    121147 
    122     a_\text{in} ~ \frac{r_j}{r_{j+1} -r_j} \text{, } a_\text{out} ~ \frac{r_{j+1}}{r_{j+1} -r_j} 
     148    a_\text{in} ~ \frac{r_j}{r_{j+1} -r_j} \text{, } a_\text{out} 
     149    ~ \frac{r_{j+1}}{r_{j+1} -r_j} 
    123150 
    124151    \beta_\text{in} = qr_j \text{, } \beta_\text{out} = qr_{j+1} 
    125152 
    126153 
    127 We assume the $\rho_{\text{inter}_i} (r)$ can be approximately linear within a sub-layer $j$ 
     154We assume the $\rho_{\text{inter}_i} (r)$ can be approximately linear 
     155within a sub-layer $j$ 
    128156 
    129157Finally form factor can be calculated by 
    … …  
    131159.. math:: 
    132160 
    133     P(q) = \frac{[f]^2} {V_\text{particle}} \text{where} V_\text{particle} = V(r_{\text{shell}_N}) 
     161    P(q) = \frac{[f]^2} {V_\text{particle}} \text{where} V_\text{particle} 
     162    = V(r_{\text{shell}_N}) 
    134163 
    135164For 2D data the scattering intensity is calculated in the same way as 1D, 
    … …  
    150179 
    151180.. note:: 
    152     The outer most radius is used as the effective radius for S(Q) when $P(Q) * S(Q)$ is applied. 
     181    The outer most radius is used as the effective radius for S(Q) 
     182    when $P(Q) * S(Q)$ is applied. 
    153183 
    154184References 
    155185---------- 
    156 L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, New York, (1987) 
     186L A Feigin and D I Svergun, Structure Analysis by Small-Angle X-Ray 
     187and Neutron Scattering, Plenum Press, New York, (1987) 
    157188 
    158189""" 
    … …  
    170201# pylint: disable=bad-whitespace, line-too-long 
    171202#            ["name", "units", default, [lower, upper], "type", "description"], 
    172 parameters = [["n_shells",                "",               1,      [0, 9],         "", "number of shells"], 
    173               ["npts_inter",       "",               35,     [0, 35],        "", "number of points in each sublayer Must be odd number"], 
    174               ["radius_core",      "Ang",            50.0,   [0, inf],       "", "intern layer thickness"], 
    175               ["sld_core",         "1e-6/Ang^2",     2.07,   [-inf, inf],    "", "sld function flat"], 
    176               ["sld_solvent",      "1e-6/Ang^2",     1.0,    [-inf, inf],    "", "sld function solvent"], 
     203parameters = [["n_shells",          "",               1,      [0, 9],         "volume", "number of shells"], 
     204              ["npts_inter",        "",               35,     [0, inf],        "", "number of points in each sublayer Must be odd number"], 
     205              ["radius_core",       "Ang",            50.0,   [0, inf],       "volume", "intern layer thickness"], 
     206              ["sld_core",          "1e-6/Ang^2",     2.07,   [-inf, inf],    "", "sld function flat"], 
     207              ["sld_solvent",       "1e-6/Ang^2",     1.0,    [-inf, inf],    "", "sld function solvent"], 
     208              ["func_inter0",       "",               0,      [0, 4],         "", "Erf:0, RPower:1, LPower:2, RExp:3, LExp:4"], 
     209              ["thick_inter0",      "Ang",            50.0,   [0, inf],       "volume", "intern layer thickness for core layer"], 
     210              ["nu_inter0",         "",               2.5,    [-inf, inf],    "", "steepness parameter for core layer"], 
    177211              ["sld_flat[n_shells]",      "1e-6/Ang^2",     4.06,   [-inf, inf],    "", "sld function flat"], 
    178               ["thick_flat[n_shells]",    "Ang",            100.0,  [0, inf],       "", "flat layer_thickness"], 
     212              ["thick_flat[n_shells]",    "Ang",            100.0,  [0, inf],       "volume", "flat layer_thickness"], 
    179213              ["func_inter[n_shells]",    "",               0,      [0, 4],         "", "Erf:0, RPower:1, LPower:2, RExp:3, LExp:4"], 
    180               ["thick_inter[n_shells]",   "Ang",            50.0,   [0, inf],       "", "intern layer thickness"], 
     214              ["thick_inter[n_shells]",   "Ang",            50.0,   [0, inf],       "volume", "intern layer thickness"], 
    181215              ["nu_inter[n_shells]",      "",               2.5,    [-inf, inf],    "", "steepness parameter"], 
    182216              ] 
    … …  
    184218source = ["lib/librefl.c",  "lib/sph_j1c.c", "spherical_sld.c"] 
    185219 
     220profile_axes = ['Radius (A)', 'SLD (1e-6/A^2)'] 
    186221def profile(n_shells, radius_core,  sld_core,  sld_solvent, sld_flat, 
    187222            thick_flat, func_inter, thick_inter, nu_inter, npts_inter): 
    … …  
    256291 
    257292demo = { 
    258     "n_shells":4, 
    259     "npts_inter":35.0, 
    260     "radius_core":50.0, 
    261     "sld_core":2.07, 
     293    "n_shells": 4, 
     294    "npts_inter": 35.0, 
     295    "radius_core": 50.0, 
     296    "sld_core": 2.07, 
    262297    "sld_solvent": 1.0, 
    263     "sld_flat":[4.0,3.5,4.0,3.5,4.0], 
    264     "thick_flat":[100.0,100.0,100.0,100.0,100.0], 
    265     "func_inter":[0,0,0,0,0], 
    266     "thick_inter":[50.0,50.0,50.0,50.0,50.0], 
    267     "nu_inter":[2.5,2.5,2.5,2.5,2.5] 
     298    "thick_inter0": 50.0, 
     299    "func_inter0": 0, 
     300    "nu_inter0": 2.5, 
     301    "sld_flat":[4.0,3.5,4.0,3.5], 
     302    "thick_flat":[100.0,100.0,100.0,100.0], 
     303    "func_inter":[0,0,0,0], 
     304    "thick_inter":[50.0,50.0,50.0,50.0], 
     305    "nu_inter":[2.5,2.5,2.5,2.5], 
    268306    } 
    269307 
    … …  
    271309tests = [ 
    272310    # Accuracy tests based on content in test/utest_extra_models.py 
    273     [{'npts_iter':35, 
    274         'sld_solv':1, 
    275         'radius_core':50.0, 
    276         'sld_core':2.07, 
    277         'func_inter2':0.0, 
    278         'thick_inter2':50, 
    279         'nu_inter2':2.5, 
    280         'sld_flat2':4, 
    281         'thick_flat2':100, 
    282         'func_inter1':0.0, 
    283         'thick_inter1':50, 
    284         'nu_inter1':2.5, 
    285         'background': 0.0, 
     311    [{"n_shells":4, 
     312        'npts_inter':35, 
     313        "radius_core":50.0, 
     314        "sld_core":2.07, 
     315        "sld_solvent": 1.0, 
     316        "sld_flat":[4.0,3.5,4.0,3.5], 
     317        "thick_flat":[100.0,100.0,100.0,100.0], 
     318        "func_inter":[0,0,0,0], 
     319        "thick_inter":[50.0,50.0,50.0,50.0], 
     320        "nu_inter":[2.5,2.5,2.5,2.5] 
    286321    }, 0.001, 0.001], 
    287322] 
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