/** 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 #include "parameters.hh" #include #include using namespace std; #include "triaxial_ellipsoid.h" extern "C" { #include "libCylinder.h" #include "libStructureFactor.h" } typedef struct { double scale; double semi_axisA; double semi_axisB; double semi_axisC; double sldEll; double sldSolv; double background; double axis_theta; double axis_phi; double axis_psi; } TriaxialEllipsoidParameters; static double triaxial_ellipsoid_kernel(TriaxialEllipsoidParameters *pars, double q, double cos_val, double cos_nu, double cos_mu) { double t,a,b,c; double kernel; a = pars->semi_axisA ; b = pars->semi_axisB ; c = pars->semi_axisC ; t = q * sqrt(a*a*cos_nu*cos_nu+b*b*cos_mu*cos_mu+c*c*cos_val*cos_val); if (t==0.0){ kernel = 1.0; }else{ kernel = 3.0*(sin(t)-t*cos(t))/(t*t*t); } return kernel*kernel; } /** * Function to evaluate 2D scattering function * @param pars: parameters of the triaxial ellipsoid * @param q: q-value * @param q_x: q_x / q * @param q_y: q_y / q * @return: function value */ static double triaxial_ellipsoid_analytical_2D_scaled(TriaxialEllipsoidParameters *pars, double q, double q_x, double q_y) { double cyl_x, cyl_y, ella_x, ella_y, ellb_x, ellb_y; //double q_z; double cos_nu, cos_mu; double vol, cos_val; double answer; double pi = 4.0*atan(1.0); //convert angle degree to radian double theta = pars->axis_theta * pi/180.0; double phi = pars->axis_phi * pi/180.0; double psi = pars->axis_psi * pi/180.0; // Cylinder orientation cyl_x = cos(theta) * cos(phi); cyl_y = sin(theta); //cyl_z = -cos(theta) * sin(phi); // q vector //q_z = 0.0; //dx = 1.0; //dy = 1.0; // Compute the angle btw vector q and the // axis of the cylinder cos_val = cyl_x*q_x + cyl_y*q_y;// + cyl_z*q_z; // The following test should always pass if (fabs(cos_val)>1.0) { printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n"); return 0; } // Note: cos(alpha) = 0 and 1 will get an // undefined value from CylKernel //alpha = acos( cos_val ); //ellipse orientation: // the elliptical corss section was transformed and projected // into the detector plane already through sin(alpha)and furthermore psi remains as same // on the detector plane. // So, all we need is to calculate the angle (nu) of the minor axis of the ellipse wrt // the wave vector q. //x- y- component of a-axis on the detector plane. ella_x = -cos(phi)*sin(psi) * sin(theta)+sin(phi)*cos(psi); ella_y = sin(psi)*cos(theta); //x- y- component of b-axis on the detector plane. ellb_x = -sin(theta)*cos(psi)*cos(phi)-sin(psi)*sin(phi); ellb_y = cos(theta)*cos(psi); // calculate the axis of the ellipse wrt q-coord. cos_nu = ella_x*q_x + ella_y*q_y; cos_mu = ellb_x*q_x + ellb_y*q_y; // The following test should always pass if (fabs(cos_val)>1.0) { //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); cos_val = 1.0; } if (fabs(cos_nu)>1.0) { //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); cos_nu = 1.0; } if (fabs(cos_mu)>1.0) { //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); cos_mu = 1.0; } // Call the IGOR library function to get the kernel answer = triaxial_ellipsoid_kernel(pars, q, cos_val, cos_nu, cos_mu); // Multiply by contrast^2 answer *= (pars->sldEll- pars->sldSolv)*(pars->sldEll- pars->sldSolv); //normalize by cylinder volume //NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl vol = 4.0* pi/3.0 * pars->semi_axisA * pars->semi_axisB * pars->semi_axisC; answer *= vol; //convert to [cm-1] answer *= 1.0e8; //Scale answer *= pars->scale; // add in the background answer += pars->background; return answer; } /** * Function to evaluate 2D scattering function * @param pars: parameters of the triaxial ellipsoid * @param q: q-value * @return: function value */ static double triaxial_ellipsoid_analytical_2DXY(TriaxialEllipsoidParameters *pars, double qx, double qy) { double q; q = sqrt(qx*qx+qy*qy); return triaxial_ellipsoid_analytical_2D_scaled(pars, q, qx/q, qy/q); } TriaxialEllipsoidModel :: TriaxialEllipsoidModel() { scale = Parameter(1.0); semi_axisA = Parameter(35.0, true); semi_axisA.set_min(0.0); semi_axisB = Parameter(100.0, true); semi_axisB.set_min(0.0); semi_axisC = Parameter(400.0, true); semi_axisC.set_min(0.0); sldEll = Parameter(1.0e-6); sldSolv = Parameter(6.3e-6); background = Parameter(0.0); axis_theta = Parameter(57.325, true); axis_phi = Parameter(57.325, true); axis_psi = Parameter(0.0, true); } /** * Function to evaluate 1D scattering function * The NIST IGOR library is used for the actual calculation. * @param q: q-value * @return: function value */ double TriaxialEllipsoidModel :: operator()(double q) { double dp[7]; // Fill parameter array for IGOR library // Add the background after averaging dp[0] = scale(); dp[1] = semi_axisA(); dp[2] = semi_axisB(); dp[3] = semi_axisC(); dp[4] = sldEll(); dp[5] = sldSolv(); dp[6] = 0.0; // Get the dispersion points for the semi axis A vector weights_semi_axisA; semi_axisA.get_weights(weights_semi_axisA); // Get the dispersion points for the semi axis B vector weights_semi_axisB; semi_axisB.get_weights(weights_semi_axisB); // Get the dispersion points for the semi axis C vector weights_semi_axisC; semi_axisC.get_weights(weights_semi_axisC); // Perform the computation, with all weight points double sum = 0.0; double norm = 0.0; double vol = 0.0; // Loop over semi axis A weight points for(int i=0; i< (int)weights_semi_axisA.size(); i++) { dp[1] = weights_semi_axisA[i].value; // Loop over semi axis B weight points for(int j=0; j< (int)weights_semi_axisB.size(); j++) { dp[2] = weights_semi_axisB[j].value; // Loop over semi axis C weight points for(int k=0; k< (int)weights_semi_axisC.size(); k++) { dp[3] = weights_semi_axisC[k].value; //Un-normalize by volume sum += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight* TriaxialEllipsoid(dp, q) * weights_semi_axisA[i].value*weights_semi_axisB[j].value*weights_semi_axisC[k].value; //Find average volume vol += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight * weights_semi_axisA[i].value*weights_semi_axisB[j].value*weights_semi_axisC[k].value; norm += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].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 TriaxialEllipsoidModel :: operator()(double qx, double qy) { TriaxialEllipsoidParameters dp; // Fill parameter array dp.scale = scale(); dp.semi_axisA = semi_axisA(); dp.semi_axisB = semi_axisB(); dp.semi_axisC = semi_axisC(); dp.sldEll = sldEll(); dp.sldSolv = sldSolv(); dp.background = 0.0; dp.axis_theta = axis_theta(); dp.axis_phi = axis_phi(); dp.axis_psi = axis_psi(); // Get the dispersion points for the semi_axis A vector weights_semi_axisA; semi_axisA.get_weights(weights_semi_axisA); // Get the dispersion points for the semi_axis B vector weights_semi_axisB; semi_axisB.get_weights(weights_semi_axisB); // Get the dispersion points for the semi_axis C vector weights_semi_axisC; semi_axisC.get_weights(weights_semi_axisC); // Get angular averaging for theta vector weights_theta; axis_theta.get_weights(weights_theta); // Get angular averaging for phi vector weights_phi; axis_phi.get_weights(weights_phi); // Get angular averaging for psi vector weights_psi; axis_psi.get_weights(weights_psi); // Perform the computation, with all weight points double sum = 0.0; double norm = 0.0; double norm_vol = 0.0; double vol = 0.0; double pi = 4.0*atan(1.0); // Loop over semi axis A weight points for(int i=0; i< (int)weights_semi_axisA.size(); i++) { dp.semi_axisA = weights_semi_axisA[i].value; // Loop over semi axis B weight points for(int j=0; j< (int)weights_semi_axisB.size(); j++) { dp.semi_axisB = weights_semi_axisB[j].value; // Loop over semi axis C weight points for(int k=0; k < (int)weights_semi_axisC.size(); k++) { dp.semi_axisC = weights_semi_axisC[k].value; // Average over theta distribution for(int l=0; l< (int)weights_theta.size(); l++) { dp.axis_theta = weights_theta[l].value; // Average over phi distribution for(int m=0; m <(int)weights_phi.size(); m++) { dp.axis_phi = weights_phi[m].value; // Average over psi distribution for(int n=0; n <(int)weights_psi.size(); n++) { dp.axis_psi = weights_psi[n].value; //Un-normalize by volume double _ptvalue = weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight * weights_theta[l].weight * weights_phi[m].weight * weights_psi[n].weight * triaxial_ellipsoid_analytical_2DXY(&dp, qx, qy) * weights_semi_axisA[i].value*weights_semi_axisB[j].value*weights_semi_axisC[k].value; if (weights_theta.size()>1) { _ptvalue *= fabs(cos(weights_theta[k].value*pi/180.0)); } sum += _ptvalue; //Find average volume vol += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight * weights_semi_axisA[i].value*weights_semi_axisB[j].value*weights_semi_axisC[k].value; //Find norm for volume norm_vol += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight; norm += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight * weights_theta[l].weight * weights_phi[m].weight * weights_psi[n].weight; } } } } } } // Averaging in theta needs an extra normalization // factor to account for the sin(theta) term in the // integration (see documentation). if (weights_theta.size()>1) norm = norm / asin(1.0); if (vol != 0.0 && norm_vol != 0.0) { //Re-normalize by avg volume sum = sum/(vol/norm_vol);} return sum/norm + background(); } /** * Function to evaluate 2D scattering function * @param pars: parameters of the triaxial ellipsoid * @param q: q-value * @param phi: angle phi * @return: function value */ double TriaxialEllipsoidModel :: evaluate_rphi(double q, double phi) { double qx = q*cos(phi); double qy = q*sin(phi); return (*this).operator()(qx, qy); } /** * Function to calculate effective radius * @return: effective radius value */ double TriaxialEllipsoidModel :: calculate_ER() { TriaxialEllipsoidParameters dp; dp.semi_axisA = semi_axisA(); dp.semi_axisB = semi_axisB(); //polar axis C dp.semi_axisC = semi_axisC(); double rad_out = 0.0; //Surface average radius at the equat. cross section. double suf_rad = sqrt(dp.semi_axisA * dp.semi_axisB); // Perform the computation, with all weight points double sum = 0.0; double norm = 0.0; // Get the dispersion points for the semi_axis A vector weights_semi_axisA; semi_axisA.get_weights(weights_semi_axisA); // Get the dispersion points for the semi_axis B vector weights_semi_axisB; semi_axisB.get_weights(weights_semi_axisB); // Get the dispersion points for the semi_axis C vector weights_semi_axisC; semi_axisC.get_weights(weights_semi_axisC); // Loop over semi axis A weight points for(int i=0; i< (int)weights_semi_axisA.size(); i++) { dp.semi_axisA = weights_semi_axisA[i].value; // Loop over semi axis B weight points for(int j=0; j< (int)weights_semi_axisB.size(); j++) { dp.semi_axisB = weights_semi_axisB[j].value; // Loop over semi axis C weight points for(int k=0; k < (int)weights_semi_axisC.size(); k++) { dp.semi_axisC = weights_semi_axisC[k].value; //Calculate surface averaged radius suf_rad = sqrt(dp.semi_axisA * dp.semi_axisB); //Sum sum += weights_semi_axisA[i].weight * weights_semi_axisB[j].weight * weights_semi_axisC[k].weight * DiamEllip(dp.semi_axisC, suf_rad)/2.0; //Norm norm += weights_semi_axisA[i].weight* weights_semi_axisB[j].weight * weights_semi_axisC[k].weight; } } } if (norm != 0){ //return the averaged value rad_out = sum/norm;} else{ //return normal value rad_out = DiamEllip(dp.semi_axisC, suf_rad)/2.0;} return rad_out; } double TriaxialEllipsoidModel :: calculate_VR() { return 1.0; }