source: sasview/sansmodels/src/c_models/onion.cpp @ 6e10cff

/**
        This software was developed by the University of Tennessee as part of the
        Distributed Data Analysis of Neutron Scattering Experiments (DANSE)
        project funded by the US National Science Foundation.

        If you use DANSE applications to do scientific research that leads to
        publication, we ask that you acknowledge the use of the software with the
        following sentence:

        "This work benefited from DANSE software developed under NSF award DMR-0520547."

        copyright 2008, University of Tennessee
 */

/**
 * Scattering model classes
 * The classes use the IGOR library found in
 *   sansmodels/src/libigor
 *
 */

#include <math.h>
#include "parameters.hh"
#include <stdio.h>
#include <stdlib.h>
using namespace std;
#include "onion.h"

// Convenience parameter structure
typedef struct {
  int n_shells;
  double scale;
  double rad_core0;
  double sld_core0;
  double sld_solv;
  double background;
  double sld_out_shell1;
  double sld_out_shell2;
  double sld_out_shell3;
  double sld_out_shell4;
  double sld_out_shell5;
  double sld_out_shell6;
  double sld_out_shell7;
  double sld_out_shell8;
  double sld_out_shell9;
  double sld_out_shell10;
  double sld_in_shell1;
  double sld_in_shell2;
  double sld_in_shell3;
  double sld_in_shell4;
  double sld_in_shell5;
  double sld_in_shell6;
  double sld_in_shell7;
  double sld_in_shell8;
  double sld_in_shell9;
  double sld_in_shell10;

  double A_shell1;
  double A_shell2;
  double A_shell3;
  double A_shell4;
  double A_shell5;
  double A_shell6;
  double A_shell7;
  double A_shell8;
  double A_shell9;
  double A_shell10;

  double thick_shell1;
  double thick_shell2;
  double thick_shell3;
  double thick_shell4;
  double thick_shell5;
  double thick_shell6;
  double thick_shell7;
  double thick_shell8;
  double thick_shell9;
  double thick_shell10;

  int func_shell1;
  int func_shell2;
  int func_shell3;
  int func_shell4;
  int func_shell5;
  int func_shell6;
  int func_shell7;
  int func_shell8;
  int func_shell9;
  int func_shell10;
} OnionParameters;

// some details can be found in sld_cal.c
static double so_kernel(double dp[], double q) {
  int n = dp[0];
  double scale = dp[1];
  double rad_core0 = dp[2];
  double sld_core0 = dp[3];
  double sld_solv = dp[4];
  double background = dp[5];
  int i,j;
  double bes,fun,alpha,f,vol,vol_pre,vol_sub,qr,r,contr,f2;
  double sign;
  double pi;
  double r0 = 0.0;

  double *sld_out;
  double *slope;
  double *sld_in;
  double *thick;
  double *A;
  int *fun_type;

  sld_out = (double*)malloc((n+2)*sizeof(double));
  slope = (double*)malloc((n+2)*sizeof(double));
  sld_in = (double*)malloc((n+2)*sizeof(double));
  thick = (double*)malloc((n+2)*sizeof(double));
  A = (double*)malloc((n+2)*sizeof(double));
  fun_type = (int*)malloc((n+2)*sizeof(int));

  for (i =1; i<=n; i++){
    sld_out[i] = dp[i+5];
    sld_in[i] = dp[i+15];
    A[i] = dp[i+25];
    thick[i] = dp[i+35];
    fun_type[i] = dp[i+45];
  }
  sld_out[0] = sld_core0;
  sld_out[n+1] = sld_solv;
  sld_in[0] = sld_core0;
  sld_in[n+1] = sld_solv;
  thick[0] = rad_core0;
  thick[n+1] = 1e+10;
  A[0] = 0.0;
  A[n+1] = 0.0;
  fun_type[0] = 0;
  fun_type[n+1] = 0;


  pi = 4.0*atan(1.0);
  f = 0.0;
  r = 0.0;
  vol = 0.0;
  vol_pre = 0.0;
  vol_sub = 0.0;

  for (i =0; i<= n+1; i++){
    if (thick[i] == 0.0){
      continue;
    }
    if (fun_type[i]== 0 ){
      slope[i] = 0.0;
      A[i] = 0.0;
    }
    vol_pre = vol;
    switch(fun_type[i]){
    case 2 :
      r0 = r;
      if (A[i] == 0.0){
        slope[i] = 0.0;
      }
      else{
        slope[i] = (sld_out[i]-sld_in[i])/(exp(A[i])-1.0);
      }
      for (j=0; j<2; j++){
        if ( i == 0 && j == 0){
          continue;
        }
        if (i == n+1 && j == 1){
          continue;
        }
        if ( j == 1){
          sign = 1.0;
          r += thick[i];
        }
        else{
          sign = -1.0;
        }
        qr = q * r;
        alpha = A[i] * r/thick[i];
        fun = 0.0;
        if(qr == 0.0){
          fun = sign * 1.0;
          bes = sign * 1.0;
        }
        else{
          if (fabs(A[i]) > 0.0 ){
            fun = 3.0 * ((alpha*alpha - qr * qr) * sin(qr) - 2.0 * alpha * qr * cos(qr))/ ((alpha * alpha + qr * qr) * (alpha * alpha + qr * qr) * qr);
            fun = fun - 3.0 * (alpha * sin(qr) - qr * cos(qr)) / ((alpha * alpha + qr * qr) * qr);
            fun = - sign *fun;
            bes = sign * 3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr);
          }
          else {
            fun = sign * 3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr);
            bes = sign * 3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr);
          }
        }
        contr = slope[i]*exp(A[i]*(r-r0)/thick[i]);

        vol = 4.0 * pi / 3.0 * r * r * r;
        //if (j == 1 && fabs(sld_in[i]-sld_solv) < 1e-04*fabs(sld_solv) && A[i]==0.0){
        //  vol_sub += (vol_pre - vol);
        //}
        f += vol * (contr * (fun) + (sld_in[i]-slope[i]) * bes);
      }
      break;
    default :
      if (fun_type[i]==0){
        slope[i] = 0.0;
      }
      else{
        slope[i]= (sld_out[i] -sld_in[i])/thick[i];
      }
      contr = sld_in[i]-slope[i]*r;
      for (j=0; j<2; j++){
        if ( i == 0 && j == 0){
          continue;
        }
        if (i == n+1 && j == 1){
          continue;
        }
        if ( j == 1){
          sign = 1.0;
          r += thick[i];
        }
        else{
          sign = -1.0;
        }

        qr = q * r;
        fun = 0.0;
        if(qr == 0.0){
          bes = sign * 1.0;
        }
        else{
          bes = sign *  3.0 * (sin(qr) - qr * cos(qr)) / (qr * qr * qr);
          if (fabs(slope[i]) > 0.0 ){
            fun = sign * 3.0 * r * (2.0*qr*sin(qr)-((qr*qr)-2.0)*cos(qr))/(qr * qr * qr * qr);
          }
        }
        vol = 4.0 * pi / 3.0 * r * r * r;
        //if (j == 1 && fabs(sld_in[i]-sld_solv) < 1e-04*fabs(sld_solv) && fun_type[i]==0){
        //  vol_sub += (vol_pre - vol);
        //}
        f += vol * (bes * contr + fun * slope[i]);
      }
      break;
    }

  }
  //vol += vol_sub;
  f2 = f * f / vol * 1.0e8;
  f2 *= scale;
  f2 += background;

  free(sld_out);
  free(slope);
  free(sld_in);
  free(thick);
  free(A);
  free(fun_type);

  return (f2);
}


OnionModel :: OnionModel() {
  n_shells = Parameter(1.0);
  scale = Parameter(1.0);
  rad_core0 = Parameter(200.0);
  sld_core0 = Parameter(1e-06);
  sld_solv = Parameter(6.4e-06);
  background = Parameter(0.0);

  sld_out_shell1 = Parameter(1.0e-06);
  sld_out_shell2 = Parameter(1.0e-06);
  sld_out_shell3 = Parameter(1.0e-06);
  sld_out_shell4 = Parameter(1.0e-06);
  sld_out_shell5 = Parameter(1.0e-06);
  sld_out_shell6 = Parameter(1.0e-06);
  sld_out_shell7 = Parameter(1.0e-06);
  sld_out_shell8 = Parameter(1.0e-06);
  sld_out_shell9 = Parameter(1.0e-06);
  sld_out_shell10 = Parameter(1.0e-06);

  sld_in_shell1 = Parameter(2.3e-06);
  sld_in_shell2 = Parameter(2.6e-06);
  sld_in_shell3 = Parameter(2.9e-06);
  sld_in_shell4 = Parameter(3.2e-06);
  sld_in_shell5 = Parameter(3.5e-06);
  sld_in_shell6 = Parameter(3.8e-06);
  sld_in_shell7 = Parameter(4.1e-06);
  sld_in_shell8 = Parameter(4.4e-06);
  sld_in_shell9 = Parameter(4.7e-06);
  sld_in_shell10 = Parameter(5.0e-06);

  A_shell1 = Parameter(1.0);
  A_shell2 = Parameter(1.0);
  A_shell3 = Parameter(1.0);
  A_shell4 = Parameter(1.0);
  A_shell5 = Parameter(1.0);
  A_shell6 = Parameter(1.0);
  A_shell7 = Parameter(1.0);
  A_shell8 = Parameter(1.0);
  A_shell9 = Parameter(1.0);
  A_shell10 = Parameter(1.0);

  thick_shell1 = Parameter(50.0);
  thick_shell2 = Parameter(50.0);
  thick_shell3 = Parameter(50.0);
  thick_shell4 = Parameter(50.0);
  thick_shell5 = Parameter(50.0);
  thick_shell6 = Parameter(50.0);
  thick_shell7 = Parameter(50.0);
  thick_shell8 = Parameter(50.0);
  thick_shell9 = Parameter(50.0);
  thick_shell10 = Parameter(50.0);

  func_shell1 = Parameter(2);
  func_shell2 = Parameter(2);
  func_shell3 = Parameter(2);
  func_shell4 = Parameter(2);
  func_shell5 = Parameter(2);
  func_shell6 = Parameter(2);
  func_shell7 = Parameter(2);
  func_shell8 = Parameter(2);
  func_shell9 = Parameter(2);
  func_shell10 = Parameter(2);
}

/**
 * Function to evaluate 1D scattering function
 * The NIST IGOR library is used for the actual calculation.
 * @param q: q-value
 * @return: function value
 */
double OnionModel :: operator()(double q) {
  double dp[56];
  // Fill parameter array for IGOR library
  // Add the background after averaging
  dp[0] = n_shells();
  dp[1] = scale();
  dp[2] = rad_core0();
  dp[3] = sld_core0();
  dp[4] = sld_solv();
  dp[5] = 0.0;

  dp[6] = sld_out_shell1();
  dp[7] = sld_out_shell2();
  dp[8] = sld_out_shell3();
  dp[9] = sld_out_shell4();
  dp[10] = sld_out_shell5();
  dp[11] = sld_out_shell6();
  dp[12] = sld_out_shell7();
  dp[13] = sld_out_shell8();
  dp[14] = sld_out_shell9();
  dp[15] = sld_out_shell10();

  dp[16] = sld_in_shell1();
  dp[17] = sld_in_shell2();
  dp[18] = sld_in_shell3();
  dp[19] = sld_in_shell4();
  dp[20] = sld_in_shell5();
  dp[21] = sld_in_shell6();
  dp[22] = sld_in_shell7();
  dp[23] = sld_in_shell8();
  dp[24] = sld_in_shell9();
  dp[25] = sld_in_shell10();

  dp[26] = A_shell1();
  dp[27] = A_shell2();
  dp[28] = A_shell3();
  dp[29] = A_shell4();
  dp[30] = A_shell5();
  dp[31] = A_shell6();
  dp[32] = A_shell7();
  dp[33] = A_shell8();
  dp[34] = A_shell9();
  dp[35] = A_shell10();

  dp[36] = thick_shell1();
  dp[37] = thick_shell2();
  dp[38] = thick_shell3();
  dp[39] = thick_shell4();
  dp[40] = thick_shell5();
  dp[41] = thick_shell6();
  dp[42] = thick_shell7();
  dp[43] = thick_shell8();
  dp[44] = thick_shell9();
  dp[45] = thick_shell10();

  dp[46] = func_shell1();
  dp[47] = func_shell2();
  dp[48] = func_shell3();
  dp[49] = func_shell4();
  dp[50] = func_shell5();
  dp[51] = func_shell6();
  dp[52] = func_shell7();
  dp[53] = func_shell8();
  dp[54] = func_shell9();
  dp[55] = func_shell10();


  // Get the dispersion points for the radius
  vector<WeightPoint> weights_rad;
  rad_core0.get_weights(weights_rad);

  // Get the dispersion points for the thick 1
  vector<WeightPoint> weights_s1;
  thick_shell1.get_weights(weights_s1);

  // Get the dispersion points for the thick 2
  vector<WeightPoint> weights_s2;
  thick_shell2.get_weights(weights_s2);

  // Get the dispersion points for the thick 3
  vector<WeightPoint> weights_s3;
  thick_shell3.get_weights(weights_s3);

  // Get the dispersion points for the thick 4
  vector<WeightPoint> weights_s4;
  thick_shell4.get_weights(weights_s4);

  // Get the dispersion points for the thick 5
  vector<WeightPoint> weights_s5;
  thick_shell5.get_weights(weights_s5);

  // Get the dispersion points for the thick 6
  vector<WeightPoint> weights_s6;
  thick_shell6.get_weights(weights_s6);

  // Get the dispersion points for the thick 7
  vector<WeightPoint> weights_s7;
  thick_shell7.get_weights(weights_s7);

  // Get the dispersion points for the thick 8
  vector<WeightPoint> weights_s8;
  thick_shell8.get_weights(weights_s8);
  // Get the dispersion points for the thick 9
  vector<WeightPoint> weights_s9;
  thick_shell9.get_weights(weights_s9);

  // Get the dispersion points for the thick 10
  vector<WeightPoint> weights_s10;
  thick_shell10.get_weights(weights_s10);


  // Perform the computation, with all weight points
  double sum = 0.0;
  double norm = 0.0;
  double vol = 0.0;

  // Loop over radius weight points
  for(size_t i=0; i<weights_rad.size(); i++) {
    dp[2] = weights_rad[i].value;
    // Loop over radius weight points
    for(size_t j=0; j<weights_s1.size(); j++) {
      dp[36] = weights_s1[j].value;
      // Loop over radius weight points
      for(size_t k=0; k<weights_s2.size(); k++) {
        dp[37] = weights_s2[k].value;
        // Loop over radius weight points
        for(size_t l=0; l<weights_s3.size(); l++) {
          dp[38] = weights_s3[l].value;
          // Loop over radius weight points
          for(size_t m=0; m<weights_s4.size(); m++) {
            dp[39] = weights_s4[m].value;
            for(size_t n=0; n<weights_s5.size(); n++) {
              dp[40] = weights_s5[n].value;
              for(size_t o=0; o<weights_s6.size(); o++) {
                dp[41] = weights_s6[o].value;
                for(size_t p=0; p<weights_s7.size(); p++) {
                  dp[42] = weights_s7[p].value;
                  for(size_t t=0; t<weights_s8.size(); t++) {
                    dp[43] = weights_s8[t].value;
                    for(size_t r=0; r<weights_s9.size(); r++) {
                      dp[44] = weights_s9[r].value;
                      for(size_t s=0; s<weights_s10.size(); s++) {
                        dp[45] = weights_s10[s].value;
                        //Un-normalize Shells by volume
                        sum += weights_rad[i].weight*weights_s1[j].weight*weights_s2[k].weight*weights_s3[l].weight*weights_s4[m].weight
                            *weights_s5[n].weight*weights_s6[o].weight*weights_s7[p].weight*weights_s8[t].weight
                            *weights_s9[r].weight*weights_s10[s].weight
                            * so_kernel(dp,q) * pow((weights_rad[i].value+weights_s1[j].value+weights_s2[k].value+weights_s3[l].value+weights_s4[m].value
                                +weights_s5[n].value+weights_s6[o].value+weights_s7[p].value+weights_s8[t].value
                                +weights_s9[r].value+weights_s10[s].value),3.0);
                        //Find average volume
                        vol += weights_rad[i].weight*weights_s1[j].weight*weights_s2[k].weight*weights_s3[l].weight*weights_s4[m].weight
                            *weights_s5[n].weight*weights_s6[o].weight*weights_s7[p].weight*weights_s8[t].weight
                            *weights_s9[r].weight*weights_s10[s].weight
                            * pow((weights_rad[i].value+weights_s1[j].value+weights_s2[k].value+weights_s3[l].value+weights_s4[m].value
                                +weights_s5[n].value+weights_s6[o].value+weights_s7[p].value+weights_s8[t].value
                                +weights_s9[r].value+weights_s10[s].value),3.0);
                        norm += weights_rad[i].weight*weights_s1[j].weight*weights_s2[k].weight*weights_s3[l].weight*weights_s4[m].weight
                            *weights_s5[n].weight*weights_s6[o].weight*weights_s7[p].weight*weights_s8[t].weight
                            *weights_s9[r].weight*weights_s10[s].weight;
                      }
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }

  if (vol != 0.0 && norm != 0.0) {
    //Re-normalize by avg volume
    sum = sum/(vol/norm);}

  return sum/norm + background();
}

/**
 * Function to evaluate 2D scattering function
 * @param q_x: value of Q along x
 * @param q_y: value of Q along y
 * @return: function value
 */
double OnionModel :: operator()(double qx, double qy) {
  double q = sqrt(qx*qx + qy*qy);
  return (*this).operator()(q);
}

/**
 * Function to evaluate 2D scattering function
 * @param pars: parameters of the sphere
 * @param q: q-value
 * @param phi: angle phi
 * @return: function value
 */
double OnionModel :: evaluate_rphi(double q, double phi) {
  return (*this).operator()(q);
}

/**
 * Function to calculate effective radius
 * @return: effective radius value
 */
double OnionModel :: calculate_ER() {
  OnionParameters dp;
  dp.rad_core0 = rad_core0();
  dp.thick_shell1 = thick_shell1();
  dp.thick_shell2 = thick_shell2();
  dp.thick_shell3 = thick_shell3();
  dp.thick_shell4 = thick_shell4();
  dp.thick_shell5 = thick_shell5();
  dp.thick_shell6 = thick_shell6();
  dp.thick_shell7 = thick_shell7();
  dp.thick_shell8 = thick_shell8();
  dp.thick_shell9 = thick_shell9();
  dp.thick_shell10 = thick_shell10();

  double rad_out = 0.0;
  // Perform the computation, with all weight points
  double sum = 0.0;
  double norm = 0.0;

  // Get the dispersion points for the radius
  vector<WeightPoint> weights_rad;
  rad_core0.get_weights(weights_rad);

  // Get the dispersion points for the thick 1
  vector<WeightPoint> weights_s1;
  thick_shell1.get_weights(weights_s1);

  // Get the dispersion points for the thick 2
  vector<WeightPoint> weights_s2;
  thick_shell2.get_weights(weights_s2);

  // Get the dispersion points for the thick 3
  vector<WeightPoint> weights_s3;
  thick_shell3.get_weights(weights_s3);

  // Get the dispersion points for the thick 4
  vector<WeightPoint> weights_s4;
  thick_shell4.get_weights(weights_s4);
  // Get the dispersion points for the thick 5
  vector<WeightPoint> weights_s5;
  thick_shell5.get_weights(weights_s5);

  // Get the dispersion points for the thick 6
  vector<WeightPoint> weights_s6;
  thick_shell6.get_weights(weights_s6);

  // Get the dispersion points for the thick 7
  vector<WeightPoint> weights_s7;
  thick_shell7.get_weights(weights_s7);

  // Get the dispersion points for the thick 8
  vector<WeightPoint> weights_s8;
  thick_shell8.get_weights(weights_s8);
  // Get the dispersion points for the thick 9
  vector<WeightPoint> weights_s9;
  thick_shell9.get_weights(weights_s9);

  // Get the dispersion points for the thick 10
  vector<WeightPoint> weights_s10;
  thick_shell10.get_weights(weights_s10);


  // Loop over radius weight points
  for(size_t i=0; i<weights_rad.size(); i++) {
    dp.rad_core0 = weights_rad[i].value;
    // Loop over radius weight points
    for(size_t j=0; j<weights_s1.size(); j++) {
      dp.thick_shell1 = weights_s1[j].value;
      // Loop over radius weight points
      for(size_t k=0; k<weights_s2.size(); k++) {
        dp.thick_shell2 = weights_s2[k].value;
        // Loop over radius weight points
        for(size_t l=0; l<weights_s3.size(); l++) {
          dp.thick_shell3 = weights_s3[l].value;
          // Loop over radius weight points
          for(size_t m=0; m<weights_s4.size(); m++) {
            dp.thick_shell4 = weights_s4[m].value;
            // Loop over radius weight points
            for(size_t n=0; j<weights_s5.size(); n++) {
              dp.thick_shell5 = weights_s5[n].value;
              // Loop over radius weight points
              for(size_t o=0; k<weights_s6.size(); o++) {
                dp.thick_shell6 = weights_s6[o].value;
                // Loop over radius weight points
                for(size_t p=0; l<weights_s7.size(); p++) {
                  dp.thick_shell7 = weights_s7[p].value;
                  // Loop over radius weight points
                  for(size_t t=0; m<weights_s8.size(); t++) {
                    dp.thick_shell8 = weights_s8[t].value;
                    // Loop over radius weight points
                    for(size_t r=0; l<weights_s9.size(); r++) {
                      dp.thick_shell8 = weights_s9[r].value;
                      // Loop over radius weight points
                      for(size_t s=0; m<weights_s10.size(); s++) {
                        dp.thick_shell10 = weights_s10[s].value;
                        //Un-normalize FourShell by volume
                        sum += weights_rad[i].weight*weights_s1[j].weight*weights_s2[k].weight*weights_s3[l].weight*weights_s4[m].weight
                            *weights_s5[n].weight*weights_s6[o].weight*weights_s7[p].weight*weights_s8[t].weight
                            *weights_s9[r].weight*weights_s10[s].weight
                            * (dp.rad_core0+dp.thick_shell1+dp.thick_shell2+dp.thick_shell3+dp.thick_shell4+dp.thick_shell5
                                +dp.thick_shell6+dp.thick_shell7+dp.thick_shell8+dp.thick_shell9+dp.thick_shell10);
                        norm += weights_rad[i].weight*weights_s1[j].weight*weights_s2[k].weight*weights_s3[l].weight
                            *weights_s4[m].weight*weights_s5[n].weight*weights_s6[o].weight*weights_s7[p].weight
                            *weights_s8[t].weight*weights_s9[r].weight*weights_s10[s].weight;
                      }
                    }
                  }
                }
              }
            }
          }
        }
      }
    }
  }

  if (norm != 0){
    //return the averaged value
    rad_out =  sum/norm;}
  else{
    //return normal value
    rad_out = dp.rad_core0+dp.thick_shell1+dp.thick_shell2+dp.thick_shell3+dp.thick_shell4
        +dp.thick_shell5+dp.thick_shell6+dp.thick_shell7+dp.thick_shell8+dp.thick_shell9+dp.thick_shell10;}
  return rad_out;
}