1 | double form_volume(double r_minor, double r_ratio, double length); |
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2 | double Iq(double q, double r_minor, double r_ratio, double length, |
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3 | double sld, double solvent_sld); |
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4 | double Iqxy(double qx, double qy, double r_minor, double r_ratio, double length, |
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5 | double sld, double solvent_sld, double theta, double phi, double psi); |
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6 | |
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7 | |
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8 | double _elliptical_cylinder_kernel(double q, double r_minor, double r_ratio, double theta); |
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9 | |
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10 | double _elliptical_cylinder_kernel(double q, double r_minor, double r_ratio, double theta) |
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11 | { |
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12 | // This is the function LAMBDA1^2 in Feigin's notation |
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13 | // q is the q-value for the calculation (1/A) |
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14 | // r_minor is the transformed radius"a" in Feigin's notation |
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15 | // r_ratio is the ratio (major radius)/(minor radius) of the Ellipsoid [=] --- |
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16 | // theta is the dummy variable of the integration |
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17 | |
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18 | double retval,arg; |
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19 | |
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20 | arg = q*r_minor*sqrt((1.0+r_ratio*r_ratio)/2+(1.0-r_ratio*r_ratio)*cos(theta)/2); |
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21 | if (arg == 0.0){ |
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22 | retval = 1.0; |
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23 | }else{ |
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24 | retval = 2.0*NR_BessJ1(arg)/arg; |
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25 | } |
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26 | return retval*retval ; |
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27 | } |
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28 | |
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29 | |
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30 | double form_volume(double r_minor, double r_ratio, double length) |
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31 | { |
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32 | return M_PI * r_minor * r_minor * r_ratio * length; |
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33 | } |
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34 | |
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35 | double Iq(double q, double r_minor, double r_ratio, double length, |
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36 | double sld, double solvent_sld) { |
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37 | |
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38 | const int nordi=76; //order of integration |
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39 | const int nordj=20; |
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40 | double va,vb; //upper and lower integration limits |
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41 | double summ,zi,yyy,answer; //running tally of integration |
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42 | double summj,vaj,vbj,zij,arg,si; //for the inner integration |
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43 | |
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44 | // orientational average limits |
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45 | va = 0.0; |
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46 | vb = 1.0; |
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47 | // inner integral limits |
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48 | vaj=0.0; |
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49 | vbj=M_PI; |
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50 | |
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51 | //initialize integral |
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52 | summ = 0.0; |
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53 | |
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54 | const double delrho = sld - solvent_sld; |
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55 | |
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56 | for(int i=0;i<nordi;i++) { |
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57 | //setup inner integral over the ellipsoidal cross-section |
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58 | summj=0; |
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59 | zi = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; //the "x" dummy |
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60 | arg = r_minor*sqrt(1.0-zi*zi); |
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61 | for(int j=0;j<nordj;j++) { |
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62 | //20 gauss points for the inner integral |
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63 | zij = ( Gauss20Z[j]*(vbj-vaj) + vaj + vbj )/2.0; //the "y" dummy |
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64 | yyy = Gauss20Wt[j] * _elliptical_cylinder_kernel(q, arg, r_ratio, zij); |
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65 | summj += yyy; |
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66 | } |
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67 | //now calculate the value of the inner integral |
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68 | answer = (vbj-vaj)/2.0*summj; |
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69 | //divide integral by Pi |
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70 | answer /= M_PI; |
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71 | |
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72 | //now calculate outer integral |
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73 | arg = q*length*zi/2.0; |
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74 | if (arg == 0.0){ |
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75 | si = 1.0; |
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76 | }else{ |
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77 | si = sin(arg) * sin(arg) / arg / arg; |
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78 | } |
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79 | yyy = Gauss76Wt[i] * answer * si; |
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80 | summ += yyy; |
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81 | } |
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82 | |
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83 | answer = (vb-va)/2.0*summ; |
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84 | // Multiply by contrast^2 |
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85 | answer *= delrho*delrho; |
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86 | |
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87 | const double vol = form_volume(r_minor, r_ratio, length); |
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88 | return answer*vol*vol*1e-4; |
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89 | } |
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90 | |
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91 | |
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92 | double Iqxy(double qx, double qy, double r_minor, double r_ratio, double length, |
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93 | double sld, double solvent_sld, double theta, double phi, double psi) { |
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94 | const double _theta = theta * M_PI / 180.0; |
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95 | const double _phi = phi * M_PI / 180.0; |
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96 | const double _psi = psi * M_PI / 180.0; |
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97 | const double q = sqrt(qx*qx+qy*qy); |
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98 | const double q_x = qx/q; |
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99 | const double q_y = qy/q; |
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100 | |
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101 | //Cylinder orientation |
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102 | double cyl_x = cos(_theta) * cos(_phi); |
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103 | double cyl_y = sin(_theta); |
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104 | |
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105 | //cyl_z = -cos(_theta) * sin(_phi); |
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106 | |
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107 | // q vector |
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108 | //q_z = 0; |
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109 | |
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110 | // Note: cos(alpha) = 0 and 1 will get an |
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111 | // undefined value from CylKernel |
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112 | //alpha = acos( cos_val ); |
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113 | |
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114 | //ellipse orientation: |
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115 | // the elliptical corss section was transformed and projected |
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116 | // into the detector plane already through sin(alpha)and furthermore psi remains as same |
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117 | // on the detector plane. |
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118 | // So, all we need is to calculate the angle (nu) of the minor axis of the ellipse wrt |
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119 | // the wave vector q. |
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120 | |
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121 | //x- y- component on the detector plane. |
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122 | const double ella_x = -cos(_phi)*sin(_psi) * sin(_theta)+sin(_phi)*cos(_psi); |
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123 | const double ella_y = sin(_psi)*cos(_theta); |
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124 | const double ellb_x = -sin(_theta)*cos(_psi)*cos(_phi)-sin(_psi)*sin(_phi); |
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125 | const double ellb_y = cos(_theta)*cos(_psi); |
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126 | |
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127 | // Compute the angle btw vector q and the |
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128 | // axis of the cylinder |
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129 | double cos_val = cyl_x*q_x + cyl_y*q_y;// + cyl_z*q_z; |
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130 | |
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131 | // calculate the axis of the ellipse wrt q-coord. |
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132 | double cos_nu = ella_x*q_x + ella_y*q_y; |
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133 | double cos_mu = ellb_x*q_x + ellb_y*q_y; |
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134 | |
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135 | // The following test should always pass |
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136 | if (fabs(cos_val)>1.0) { |
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137 | //printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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138 | cos_val = 1.0; |
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139 | } |
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140 | if (fabs(cos_nu)>1.0) { |
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141 | //printf("cyl_ana_2D: Unexpected error: cos(nu)>1\n"); |
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142 | cos_nu = 1.0; |
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143 | } |
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144 | if (fabs(cos_mu)>1.0) { |
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145 | //printf("cyl_ana_2D: Unexpected error: cos(nu)>1\n"); |
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146 | cos_mu = 1.0; |
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147 | } |
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148 | |
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149 | const double r_major = r_ratio * r_minor; |
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150 | const double qr = q*sqrt( r_major*r_major*cos_nu*cos_nu + r_minor*r_minor*cos_mu*cos_mu ); |
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151 | const double qL = q*length*cos_val/2.0; |
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152 | |
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153 | double Be; |
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154 | if (qr==0){ |
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155 | Be = 0.5; |
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156 | }else{ |
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157 | Be = NR_BessJ1(qr)/qr; |
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158 | } |
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159 | |
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160 | double Si; |
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161 | if (qL==0){ |
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162 | Si = 1.0; |
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163 | }else{ |
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164 | Si = sin(qL)/qL; |
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165 | } |
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166 | |
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167 | const double k = 2.0 * Be * Si; |
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168 | const double vol = form_volume(r_minor, r_ratio, length); |
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169 | return (sld - solvent_sld) * (sld - solvent_sld) * k * k *vol*vol*1.0e-4; |
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170 | } |
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