[d5b6a9d] | 1 | /** |
---|
| 2 | This software was developed by the University of Tennessee as part of the |
---|
| 3 | Distributed Data Analysis of Neutron Scattering Experiments (DANSE) |
---|
| 4 | project funded by the US National Science Foundation. |
---|
| 5 | |
---|
| 6 | If you use DANSE applications to do scientific research that leads to |
---|
| 7 | publication, we ask that you acknowledge the use of the software with the |
---|
| 8 | following sentence: |
---|
| 9 | |
---|
| 10 | "This work benefited from DANSE software developed under NSF award DMR-0520547." |
---|
| 11 | |
---|
| 12 | copyright 2008, University of Tennessee |
---|
| 13 | */ |
---|
| 14 | |
---|
| 15 | /** |
---|
| 16 | * Scattering model classes |
---|
| 17 | * The classes use the IGOR library found in |
---|
| 18 | * sansmodels/src/libigor |
---|
| 19 | * |
---|
| 20 | */ |
---|
| 21 | |
---|
| 22 | #include <math.h> |
---|
| 23 | #include "parameters.hh" |
---|
| 24 | #include <stdio.h> |
---|
| 25 | using namespace std; |
---|
[0ba3b08] | 26 | #include "fcc.h" |
---|
[d5b6a9d] | 27 | |
---|
| 28 | extern "C" { |
---|
[0ba3b08] | 29 | #include "libSphere.h" |
---|
| 30 | } |
---|
| 31 | |
---|
| 32 | // Convenience parameter structure |
---|
| 33 | typedef struct { |
---|
| 34 | double scale; |
---|
| 35 | double dnn; |
---|
| 36 | double d_factor; |
---|
| 37 | double radius; |
---|
| 38 | double sldSph; |
---|
| 39 | double sldSolv; |
---|
| 40 | double background; |
---|
| 41 | double theta; |
---|
| 42 | double phi; |
---|
| 43 | double psi; |
---|
| 44 | } FCParameters; |
---|
| 45 | |
---|
| 46 | /** |
---|
| 47 | * Function to evaluate 2D scattering function |
---|
| 48 | * @param pars: parameters of the FCCCrystalModel |
---|
| 49 | * @param q: q-value |
---|
| 50 | * @param q_x: q_x / q |
---|
| 51 | * @param q_y: q_y / q |
---|
| 52 | * @return: function value |
---|
| 53 | */ |
---|
| 54 | static double fc_analytical_2D_scaled(FCParameters *pars, double q, double q_x, double q_y) { |
---|
| 55 | double b3_x, b3_y, b3_z, b1_x, b1_y; |
---|
| 56 | double q_z; |
---|
| 57 | double alpha, cos_val_b3, cos_val_b2, cos_val_b1; |
---|
| 58 | double a1_dot_q, a2_dot_q,a3_dot_q; |
---|
| 59 | double answer; |
---|
| 60 | double Pi = 4.0*atan(1.0); |
---|
| 61 | double aa, Da, qDa_2, latticeScale, Zq, Fkq, Fkq_2; |
---|
| 62 | |
---|
| 63 | double dp[5]; |
---|
| 64 | //convert angle degree to radian |
---|
| 65 | double theta = pars->theta * Pi/180.0; |
---|
| 66 | double phi = pars->phi * Pi/180.0; |
---|
| 67 | double psi = pars->psi * Pi/180.0; |
---|
| 68 | dp[0] = 1.0; |
---|
| 69 | dp[1] = pars->radius; |
---|
| 70 | dp[2] = pars->sldSph; |
---|
| 71 | dp[3] = pars->sldSolv; |
---|
| 72 | dp[4] = 0.0; |
---|
| 73 | |
---|
| 74 | aa = pars->dnn; |
---|
| 75 | Da = pars->d_factor*aa; |
---|
| 76 | qDa_2 = pow(q*Da,2.0); |
---|
| 77 | //contrast = pars->sldSph - pars->sldSolv; |
---|
| 78 | |
---|
| 79 | latticeScale = 4.0*(4.0/3.0)*Pi*(dp[1]*dp[1]*dp[1])/pow(aa*sqrt(2.0),3.0); |
---|
| 80 | // q vector |
---|
| 81 | q_z = 0.0; // for SANS; assuming qz is negligible |
---|
| 82 | /// Angles here are respect to detector coordinate |
---|
| 83 | /// instead of against q coordinate in PRB 36(46), 3(6), 1754(3854) |
---|
| 84 | // b3 axis orientation |
---|
| 85 | b3_x = sin(theta) * cos(phi);//negative sign here??? |
---|
| 86 | b3_y = sin(theta) * sin(phi); |
---|
| 87 | b3_z = cos(theta); |
---|
| 88 | cos_val_b3 = b3_x*q_x + b3_y*q_y + b3_z*q_z; |
---|
| 89 | alpha = acos(cos_val_b3); |
---|
| 90 | // b1 axis orientation |
---|
| 91 | b1_x = sin(psi); |
---|
| 92 | b1_y = cos(psi); |
---|
| 93 | cos_val_b1 = (b1_x*q_x + b1_y*q_y); |
---|
| 94 | // b2 axis orientation |
---|
| 95 | cos_val_b2 = sin(acos(cos_val_b1)); |
---|
| 96 | // alpha correction |
---|
| 97 | cos_val_b2 *= sin(alpha); |
---|
| 98 | cos_val_b1 *= sin(alpha); |
---|
| 99 | |
---|
| 100 | // Compute the angle btw vector q and the a3 axis |
---|
| 101 | a3_dot_q = 0.5*aa*q*(cos_val_b2+cos_val_b1); |
---|
| 102 | |
---|
| 103 | // a1 axis |
---|
| 104 | a1_dot_q = 0.5*aa*q*(cos_val_b2+cos_val_b3); |
---|
| 105 | |
---|
| 106 | // a2 axis |
---|
| 107 | a2_dot_q = 0.5*aa*q*(cos_val_b3+cos_val_b1); |
---|
| 108 | |
---|
| 109 | // The following test should always pass |
---|
| 110 | if (fabs(cos_val_b3)>1.0) { |
---|
| 111 | printf("fcc_ana_2D: Unexpected error: cos(alpha)>1\n"); |
---|
| 112 | return 0; |
---|
| 113 | } |
---|
| 114 | // Get Fkq and Fkq_2 |
---|
| 115 | Fkq = exp(-0.5*pow(Da/aa,2.0)*(a1_dot_q*a1_dot_q+a2_dot_q*a2_dot_q+a3_dot_q*a3_dot_q)); |
---|
| 116 | Fkq_2 = Fkq*Fkq; |
---|
| 117 | // Call Zq=Z1*Z2*Z3 |
---|
| 118 | Zq = (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a1_dot_q)+Fkq_2); |
---|
| 119 | Zq = Zq * (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a2_dot_q)+Fkq_2); |
---|
| 120 | Zq = Zq * (1.0-Fkq_2)/(1.0-2.0*Fkq*cos(a3_dot_q)+Fkq_2); |
---|
| 121 | |
---|
| 122 | // Use SphereForm directly from libigor |
---|
| 123 | answer = SphereForm(dp,q)*Zq; |
---|
| 124 | |
---|
| 125 | //consider scales |
---|
| 126 | answer *= latticeScale * pars->scale; |
---|
| 127 | |
---|
| 128 | // This FIXES a singualrity the kernel in libigor. |
---|
| 129 | if ( answer == INFINITY || answer == NAN){ |
---|
| 130 | answer = 0.0; |
---|
| 131 | } |
---|
| 132 | |
---|
| 133 | // add background |
---|
| 134 | answer += pars->background; |
---|
| 135 | |
---|
| 136 | return answer; |
---|
| 137 | } |
---|
| 138 | |
---|
| 139 | /** |
---|
| 140 | * Function to evaluate 2D scattering function |
---|
| 141 | * @param pars: parameters of the FCC_ParaCrystal |
---|
| 142 | * @param q: q-value |
---|
| 143 | * @return: function value |
---|
| 144 | */ |
---|
| 145 | static double fc_analytical_2DXY(FCParameters *pars, double qx, double qy){ |
---|
| 146 | double q; |
---|
| 147 | q = sqrt(qx*qx+qy*qy); |
---|
| 148 | return fc_analytical_2D_scaled(pars, q, qx/q, qy/q); |
---|
[d5b6a9d] | 149 | } |
---|
| 150 | |
---|
| 151 | FCCrystalModel :: FCCrystalModel() { |
---|
[0ba3b08] | 152 | scale = Parameter(1.0); |
---|
| 153 | dnn = Parameter(220.0); |
---|
| 154 | d_factor = Parameter(0.06); |
---|
| 155 | radius = Parameter(40.0, true); |
---|
| 156 | radius.set_min(0.0); |
---|
| 157 | sldSph = Parameter(3.0e-6); |
---|
| 158 | sldSolv = Parameter(6.3e-6); |
---|
| 159 | background = Parameter(0.0); |
---|
| 160 | theta = Parameter(0.0, true); |
---|
| 161 | phi = Parameter(0.0, true); |
---|
| 162 | psi = Parameter(0.0, true); |
---|
[d5b6a9d] | 163 | } |
---|
| 164 | |
---|
| 165 | /** |
---|
| 166 | * Function to evaluate 1D scattering function |
---|
| 167 | * The NIST IGOR library is used for the actual calculation. |
---|
| 168 | * @param q: q-value |
---|
| 169 | * @return: function value |
---|
| 170 | */ |
---|
| 171 | double FCCrystalModel :: operator()(double q) { |
---|
[0ba3b08] | 172 | double dp[7]; |
---|
| 173 | |
---|
| 174 | // Fill parameter array for IGOR library |
---|
| 175 | // Add the background after averaging |
---|
| 176 | dp[0] = scale(); |
---|
| 177 | dp[1] = dnn(); |
---|
| 178 | dp[2] = d_factor(); |
---|
| 179 | dp[3] = radius(); |
---|
| 180 | dp[4] = sldSph(); |
---|
| 181 | dp[5] = sldSolv(); |
---|
| 182 | dp[6] = 0.0; |
---|
| 183 | |
---|
| 184 | // Get the dispersion points for the radius |
---|
| 185 | vector<WeightPoint> weights_rad; |
---|
| 186 | radius.get_weights(weights_rad); |
---|
| 187 | |
---|
| 188 | // Perform the computation, with all weight points |
---|
| 189 | double sum = 0.0; |
---|
| 190 | double norm = 0.0; |
---|
| 191 | double vol = 0.0; |
---|
| 192 | double result; |
---|
| 193 | |
---|
| 194 | // Loop over radius weight points |
---|
| 195 | for(size_t i=0; i<weights_rad.size(); i++) { |
---|
| 196 | dp[3] = weights_rad[i].value; |
---|
| 197 | |
---|
| 198 | //Un-normalize SphereForm by volume |
---|
| 199 | result = FCC_ParaCrystal(dp, q) * pow(weights_rad[i].value,3); |
---|
| 200 | // This FIXES a singualrity the kernel in libigor. |
---|
| 201 | if ( result == INFINITY || result == NAN){ |
---|
| 202 | result = 0.0; |
---|
| 203 | } |
---|
| 204 | sum += weights_rad[i].weight |
---|
| 205 | * result; |
---|
| 206 | //Find average volume |
---|
| 207 | vol += weights_rad[i].weight |
---|
| 208 | * pow(weights_rad[i].value,3); |
---|
| 209 | |
---|
| 210 | norm += weights_rad[i].weight; |
---|
| 211 | } |
---|
| 212 | |
---|
| 213 | if (vol != 0.0 && norm != 0.0) { |
---|
| 214 | //Re-normalize by avg volume |
---|
| 215 | sum = sum/(vol/norm);} |
---|
| 216 | return sum/norm + background(); |
---|
[d5b6a9d] | 217 | } |
---|
| 218 | |
---|
| 219 | /** |
---|
| 220 | * Function to evaluate 2D scattering function |
---|
| 221 | * @param q_x: value of Q along x |
---|
| 222 | * @param q_y: value of Q along y |
---|
| 223 | * @return: function value |
---|
| 224 | */ |
---|
| 225 | double FCCrystalModel :: operator()(double qx, double qy) { |
---|
[0ba3b08] | 226 | FCParameters dp; |
---|
| 227 | dp.scale = scale(); |
---|
| 228 | dp.dnn = dnn(); |
---|
| 229 | dp.d_factor = d_factor(); |
---|
| 230 | dp.radius = radius(); |
---|
| 231 | dp.sldSph = sldSph(); |
---|
| 232 | dp.sldSolv = sldSolv(); |
---|
| 233 | dp.background = 0.0; |
---|
| 234 | dp.theta = theta(); |
---|
| 235 | dp.phi = phi(); |
---|
| 236 | dp.psi = psi(); |
---|
| 237 | |
---|
| 238 | // Get the dispersion points for the radius |
---|
| 239 | vector<WeightPoint> weights_rad; |
---|
| 240 | radius.get_weights(weights_rad); |
---|
| 241 | |
---|
| 242 | // Get angular averaging for theta |
---|
| 243 | vector<WeightPoint> weights_theta; |
---|
| 244 | theta.get_weights(weights_theta); |
---|
| 245 | |
---|
| 246 | // Get angular averaging for phi |
---|
| 247 | vector<WeightPoint> weights_phi; |
---|
| 248 | phi.get_weights(weights_phi); |
---|
| 249 | |
---|
| 250 | // Get angular averaging for psi |
---|
| 251 | vector<WeightPoint> weights_psi; |
---|
| 252 | psi.get_weights(weights_psi); |
---|
| 253 | |
---|
| 254 | // Perform the computation, with all weight points |
---|
| 255 | double sum = 0.0; |
---|
| 256 | double norm = 0.0; |
---|
| 257 | double norm_vol = 0.0; |
---|
| 258 | double vol = 0.0; |
---|
| 259 | double pi = 4.0*atan(1.0); |
---|
| 260 | // Loop over radius weight points |
---|
| 261 | for(size_t i=0; i<weights_rad.size(); i++) { |
---|
| 262 | dp.radius = weights_rad[i].value; |
---|
| 263 | // Average over theta distribution |
---|
| 264 | for(size_t j=0; j< weights_theta.size(); j++) { |
---|
| 265 | dp.theta = weights_theta[j].value; |
---|
| 266 | // Average over phi distribution |
---|
| 267 | for(size_t k=0; k< weights_phi.size(); k++) { |
---|
| 268 | dp.phi = weights_phi[k].value; |
---|
| 269 | // Average over phi distribution |
---|
| 270 | for(size_t l=0; l< weights_psi.size(); l++) { |
---|
| 271 | dp.psi = weights_psi[l].value; |
---|
| 272 | //Un-normalize SphereForm by volume |
---|
| 273 | double _ptvalue = weights_rad[i].weight |
---|
| 274 | * weights_theta[j].weight |
---|
| 275 | * weights_phi[k].weight |
---|
| 276 | * weights_psi[l].weight |
---|
| 277 | * fc_analytical_2DXY(&dp, qx, qy); |
---|
| 278 | //* pow(weights_rad[i].value,3.0); |
---|
| 279 | // Consider when there is infinte or nan. |
---|
| 280 | if ( _ptvalue == INFINITY || _ptvalue == NAN){ |
---|
| 281 | _ptvalue = 0.0; |
---|
| 282 | } |
---|
| 283 | if (weights_theta.size()>1) { |
---|
| 284 | _ptvalue *= fabs(sin(weights_theta[j].value*pi/180.0)); |
---|
| 285 | } |
---|
| 286 | sum += _ptvalue; |
---|
| 287 | // This model dose not need the volume of spheres correction!!! |
---|
| 288 | norm += weights_rad[i].weight |
---|
| 289 | * weights_theta[j].weight |
---|
| 290 | * weights_phi[k].weight |
---|
| 291 | * weights_psi[l].weight; |
---|
| 292 | } |
---|
| 293 | } |
---|
| 294 | } |
---|
| 295 | } |
---|
| 296 | // Averaging in theta needs an extra normalization |
---|
| 297 | // factor to account for the sin(theta) term in the |
---|
| 298 | // integration (see documentation). |
---|
| 299 | if (weights_theta.size()>1) norm = norm / asin(1.0); |
---|
| 300 | |
---|
| 301 | if (vol != 0.0 && norm_vol != 0.0) { |
---|
| 302 | //Re-normalize by avg volume |
---|
| 303 | sum = sum/(vol/norm_vol);} |
---|
| 304 | |
---|
| 305 | return sum/norm + background(); |
---|
[d5b6a9d] | 306 | } |
---|
| 307 | |
---|
| 308 | /** |
---|
| 309 | * Function to evaluate 2D scattering function |
---|
| 310 | * @param pars: parameters of the FCCCrystal |
---|
| 311 | * @param q: q-value |
---|
| 312 | * @param phi: angle phi |
---|
| 313 | * @return: function value |
---|
| 314 | */ |
---|
| 315 | double FCCrystalModel :: evaluate_rphi(double q, double phi) { |
---|
[0ba3b08] | 316 | return (*this).operator()(q); |
---|
[d5b6a9d] | 317 | } |
---|
| 318 | |
---|
| 319 | /** |
---|
| 320 | * Function to calculate effective radius |
---|
| 321 | * @return: effective radius value |
---|
| 322 | */ |
---|
| 323 | double FCCrystalModel :: calculate_ER() { |
---|
[0ba3b08] | 324 | //NOT implemented yet!!! |
---|
| 325 | return 0.0; |
---|
[d5b6a9d] | 326 | } |
---|