1 | double form_volume(double a_side, double b_side, double c_side); |
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2 | double Iq(double q, double sld, double solvent_sld, double a_side, double b_side, double c_side); |
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3 | double Iqxy(double qx, double qy, double sld, double solvent_sld, |
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4 | double a_side, double b_side, double c_side, double theta, double phi, double psi); |
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5 | |
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6 | // From Igor library |
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7 | double _pkernel(double a, double b,double c, double ala, double alb, double alc); |
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8 | double _pkernel(double a, double b,double c, double ala, double alb, double alc){ |
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9 | double argA,argB,argC,tmp1,tmp2,tmp3; |
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10 | //handle arg=0 separately, as sin(t)/t -> 1 as t->0 |
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11 | argA = 0.5*a*ala; |
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12 | argB = 0.5*b*alb; |
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13 | argC = 0.5*c*alc; |
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14 | if(argA==0.0) { |
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15 | tmp1 = 1.0; |
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16 | } else { |
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17 | tmp1 = sin(argA)*sin(argA)/argA/argA; |
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18 | } |
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19 | if (argB==0.0) { |
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20 | tmp2 = 1.0; |
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21 | } else { |
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22 | tmp2 = sin(argB)*sin(argB)/argB/argB; |
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23 | } |
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24 | if (argC==0.0) { |
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25 | tmp3 = 1.0; |
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26 | } else { |
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27 | tmp3 = sin(argC)*sin(argC)/argC/argC; |
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28 | } |
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29 | return (tmp1*tmp2*tmp3); |
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30 | |
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31 | } |
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32 | |
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33 | |
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34 | double form_volume(double a_side, double b_side, double c_side) |
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35 | { |
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36 | return a_side * b_side * c_side; |
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37 | } |
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38 | |
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39 | |
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40 | double Iq(double q, |
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41 | double sld, |
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42 | double solvent_sld, |
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43 | double a_side, |
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44 | double b_side, |
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45 | double c_side) |
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46 | { |
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47 | double tmp1, tmp2; |
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48 | |
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49 | double mu = q * b_side; |
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50 | |
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51 | // Scale sides by B |
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52 | double a_scaled = a_side / b_side; |
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53 | double c_scaled = c_side / b_side; |
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54 | |
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55 | //Order of integration |
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56 | int nordi=76; |
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57 | int nordj=76; |
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58 | |
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59 | // outer integral (with nordi gauss points), integration limits = 0, 1 |
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60 | double summ = 0; //initialize integral |
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61 | |
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62 | for( int i=0; i<nordi; i++) { |
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63 | |
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64 | // inner integral (with nordj gauss points), integration limits = 0, 1 |
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65 | |
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66 | double summj = 0.0; |
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67 | double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); |
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68 | |
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69 | for(int j=0; j<nordj; j++) { |
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70 | |
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71 | double uu = 0.5 * ( Gauss76Z[j] + 1.0 ); |
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72 | double mudum = mu * sqrt(1.0-sigma*sigma); |
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73 | double arg1 = 0.5 * mudum * cos(0.5*M_PI*uu); |
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74 | double arg2 = 0.5 * mudum * a_scaled * sin(0.5*M_PI*uu); |
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75 | if(arg1==0.0) { |
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76 | tmp1 = 1.0; |
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77 | } else { |
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78 | tmp1 = sin(arg1)*sin(arg1)/arg1/arg1; |
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79 | } |
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80 | if (arg2==0.0) { |
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81 | tmp2 = 1.0; |
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82 | } else { |
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83 | tmp2 = sin(arg2)*sin(arg2)/arg2/arg2; |
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84 | } |
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85 | |
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86 | summj += Gauss76Wt[j] * tmp1 * tmp2; |
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87 | } |
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88 | |
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89 | // value of the inner integral |
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90 | double answer = 0.5 * summj; |
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91 | |
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92 | double arg = 0.5 * mu * c_scaled * sigma; |
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93 | if ( arg == 0.0 ) { |
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94 | answer *= 1.0; |
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95 | } else { |
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96 | answer *= sin(arg)*sin(arg)/arg/arg; |
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97 | } |
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98 | |
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99 | // sum of outer integral |
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100 | summ += Gauss76Wt[i] * answer; |
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101 | |
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102 | } |
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103 | |
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104 | const double vd = (sld-solvent_sld) * form_volume(a_side, b_side, c_side); |
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105 | |
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106 | // convert from [1e-12 A-1] to [cm-1] and 0.5 factor for outer integral |
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107 | return 1.0e-4 * 0.5 * vd * vd * summ; |
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108 | |
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109 | } |
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110 | |
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111 | |
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112 | double Iqxy(double qx, double qy, |
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113 | double sld, |
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114 | double solvent_sld, |
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115 | double a_side, |
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116 | double b_side, |
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117 | double c_side, |
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118 | double theta, |
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119 | double phi, |
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120 | double psi) |
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121 | { |
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122 | double q = sqrt(qx*qx+qy*qy); |
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123 | double qx_scaled = qx/q; |
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124 | double qy_scaled = qy/q; |
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125 | |
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126 | // Convert angles given in degrees to radians |
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127 | theta *= M_PI_180; |
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128 | phi *= M_PI_180; |
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129 | psi *= M_PI_180; |
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130 | |
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131 | // Parallelepiped c axis orientation |
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132 | double cparallel_x = cos(theta) * cos(phi); |
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133 | double cparallel_y = sin(theta); |
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134 | |
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135 | // Compute angle between q and parallelepiped axis |
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136 | double cos_val_c = cparallel_x*qx_scaled + cparallel_y*qy_scaled;// + cparallel_z*qz; |
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137 | |
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138 | // Parallelepiped a axis orientation |
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139 | double parallel_x = -cos(phi)*sin(psi) * sin(theta)+sin(phi)*cos(psi); |
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140 | double parallel_y = sin(psi)*cos(theta); |
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141 | double cos_val_a = parallel_x*qx_scaled + parallel_y*qy_scaled; |
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142 | |
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143 | // Parallelepiped b axis orientation |
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144 | double bparallel_x = -sin(theta)*cos(psi)*cos(phi)-sin(psi)*sin(phi); |
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145 | double bparallel_y = cos(theta)*cos(psi); |
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146 | double cos_val_b = bparallel_x*qx_scaled + bparallel_y*qy_scaled; |
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147 | |
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148 | // The following tests should always pass |
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149 | if (fabs(cos_val_c)>1.0) { |
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150 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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151 | cos_val_c = 1.0; |
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152 | } |
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153 | if (fabs(cos_val_a)>1.0) { |
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154 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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155 | cos_val_a = 1.0; |
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156 | } |
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157 | if (fabs(cos_val_b)>1.0) { |
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158 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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159 | cos_val_b = 1.0; |
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160 | } |
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161 | |
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162 | // Call the IGOR library function to get the kernel |
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163 | double form = _pkernel( q*a_side, q*b_side, q*c_side, cos_val_a, cos_val_b, cos_val_c); |
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164 | |
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165 | // Multiply by contrast^2 |
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166 | const double vd = (sld - solvent_sld) * form_volume(a_side, b_side, c_side); |
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167 | return 1.0e-4 * vd * vd * form; |
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168 | } |
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