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 | //retval = 2.0*J1(arg)/arg; |
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22 | retval = sas_J1c(arg); |
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23 | return retval*retval ; |
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24 | } |
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25 | |
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26 | |
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27 | double form_volume(double r_minor, double r_ratio, double length) |
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28 | { |
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29 | return M_PI * r_minor * r_minor * r_ratio * length; |
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30 | } |
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31 | |
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32 | double Iq(double q, double r_minor, double r_ratio, double length, |
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33 | double sld, double solvent_sld) { |
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34 | |
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35 | const int nordi=76; //order of integration |
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36 | const int nordj=20; |
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37 | double va,vb; //upper and lower integration limits |
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38 | double summ,zi,yyy,answer; //running tally of integration |
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39 | double summj,vaj,vbj,zij,arg,si; //for the inner integration |
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40 | |
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41 | // orientational average limits |
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42 | va = 0.0; |
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43 | vb = 1.0; |
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44 | // inner integral limits |
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45 | vaj=0.0; |
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46 | vbj=M_PI; |
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47 | |
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48 | //initialize integral |
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49 | summ = 0.0; |
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50 | |
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51 | const double delrho = sld - solvent_sld; |
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52 | |
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53 | for(int i=0;i<nordi;i++) { |
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54 | //setup inner integral over the ellipsoidal cross-section |
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55 | summj=0; |
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56 | zi = ( Gauss76Z[i]*(vb-va) + va + vb )/2.0; //the "x" dummy |
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57 | arg = r_minor*sqrt(1.0-zi*zi); |
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58 | for(int j=0;j<nordj;j++) { |
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59 | //20 gauss points for the inner integral |
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60 | zij = ( Gauss20Z[j]*(vbj-vaj) + vaj + vbj )/2.0; //the "y" dummy |
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61 | yyy = Gauss20Wt[j] * _elliptical_cylinder_kernel(q, arg, r_ratio, zij); |
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62 | summj += yyy; |
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63 | } |
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64 | //now calculate the value of the inner integral |
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65 | answer = (vbj-vaj)/2.0*summj; |
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66 | |
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67 | //now calculate outer integral |
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68 | arg = q*length*zi/2.0; |
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69 | si = square(sinc(arg)); |
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70 | yyy = Gauss76Wt[i] * answer * si; |
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71 | summ += yyy; |
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72 | } |
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73 | |
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74 | //divide integral by Pi |
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75 | answer = (vb-va)/2.0*summ/M_PI; |
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76 | // Multiply by contrast^2 |
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77 | answer *= delrho*delrho; |
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78 | |
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79 | const double vol = form_volume(r_minor, r_ratio, length); |
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80 | return answer*vol*vol*1.0e-4; |
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81 | } |
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82 | |
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83 | |
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84 | double Iqxy(double qx, double qy, double r_minor, double r_ratio, double length, |
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85 | double sld, double solvent_sld, double theta, double phi, double psi) { |
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86 | const double _theta = theta * M_PI / 180.0; |
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87 | const double _phi = phi * M_PI / 180.0; |
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88 | const double _psi = psi * M_PI / 180.0; |
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89 | const double q = sqrt(qx*qx+qy*qy); |
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90 | const double q_x = qx/q; |
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91 | const double q_y = qy/q; |
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92 | |
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93 | //Cylinder orientation |
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94 | double cyl_x = cos(_theta) * cos(_phi); |
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95 | double cyl_y = sin(_theta); |
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96 | |
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97 | //cyl_z = -cos(_theta) * sin(_phi); |
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98 | |
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99 | // q vector |
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100 | //q_z = 0; |
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101 | |
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102 | // Note: cos(alpha) = 0 and 1 will get an |
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103 | // undefined value from CylKernel |
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104 | //alpha = acos( cos_val ); |
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105 | |
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106 | //ellipse orientation: |
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107 | // the elliptical corss section was transformed and projected |
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108 | // into the detector plane already through sin(alpha)and furthermore psi remains as same |
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109 | // on the detector plane. |
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110 | // So, all we need is to calculate the angle (nu) of the minor axis of the ellipse wrt |
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111 | // the wave vector q. |
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112 | |
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113 | //x- y- component on the detector plane. |
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114 | const double ella_x = -cos(_phi)*sin(_psi) * sin(_theta)+sin(_phi)*cos(_psi); |
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115 | const double ella_y = sin(_psi)*cos(_theta); |
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116 | const double ellb_x = -sin(_theta)*cos(_psi)*cos(_phi)-sin(_psi)*sin(_phi); |
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117 | const double ellb_y = cos(_theta)*cos(_psi); |
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118 | |
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119 | // Compute the angle btw vector q and the |
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120 | // axis of the cylinder |
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121 | double cos_val = cyl_x*q_x + cyl_y*q_y;// + cyl_z*q_z; |
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122 | |
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123 | // calculate the axis of the ellipse wrt q-coord. |
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124 | double cos_nu = ella_x*q_x + ella_y*q_y; |
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125 | double cos_mu = ellb_x*q_x + ellb_y*q_y; |
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126 | |
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127 | // The following test should always pass |
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128 | if (fabs(cos_val)>1.0) { |
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129 | //printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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130 | cos_val = 1.0; |
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131 | } |
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132 | if (fabs(cos_nu)>1.0) { |
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133 | //printf("cyl_ana_2D: Unexpected error: cos(nu)>1\n"); |
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134 | cos_nu = 1.0; |
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135 | } |
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136 | if (fabs(cos_mu)>1.0) { |
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137 | //printf("cyl_ana_2D: Unexpected error: cos(nu)>1\n"); |
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138 | cos_mu = 1.0; |
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139 | } |
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140 | |
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141 | const double r_major = r_ratio * r_minor; |
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142 | 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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143 | const double qL = q*length*cos_val/2.0; |
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144 | |
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145 | double Be; |
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146 | if (qr==0){ |
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147 | Be = 0.5; |
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148 | }else{ |
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149 | //Be = NR_BessJ1(qr)/qr; |
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150 | Be = 0.5*sas_J1c(qr); |
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151 | } |
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152 | |
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153 | double Si; |
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154 | if (qL==0){ |
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155 | Si = 1.0; |
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156 | }else{ |
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157 | Si = sin(qL)/qL; |
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158 | } |
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159 | |
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160 | const double k = 2.0 * Be * Si; |
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161 | const double vol = form_volume(r_minor, r_ratio, length); |
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162 | return (sld - solvent_sld) * (sld - solvent_sld) * k * k *vol*vol*1.0e-4; |
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163 | } |
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