1 | double form_volume(double a_side, double b_side, double c_side, |
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2 | double arim_thickness, double brim_thickness, double crim_thickness); |
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3 | double Iq(double q, double core_sld, double arim_sld, double brim_sld, double crim_sld, |
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4 | double solvent_sld, double a_side, double b_side, double c_side, |
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5 | double arim_thickness, double brim_thickness, double crim_thickness); |
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6 | double Iqxy(double qx, double qy, double core_sld, double arim_sld, double brim_sld, |
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7 | double crim_sld, double solvent_sld, double a_side, double b_side, |
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8 | double c_side, double arim_thickness, double brim_thickness, |
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9 | double crim_thickness, double theta, double phi, double psi); |
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10 | |
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11 | double form_volume(double a_side, double b_side, double c_side, |
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12 | double arim_thickness, double brim_thickness, double crim_thickness) |
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13 | { |
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14 | //return a_side * b_side * c_side; |
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15 | return a_side * b_side * c_side + |
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16 | 2.0 * arim_thickness * b_side * c_side + |
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17 | 2.0 * brim_thickness * a_side * c_side + |
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18 | 2.0 * crim_thickness * a_side * b_side; |
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19 | } |
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20 | |
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21 | double Iq(double q, |
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22 | double core_sld, |
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23 | double arim_sld, |
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24 | double brim_sld, |
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25 | double crim_sld, |
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26 | double solvent_sld, |
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27 | double a_side, |
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28 | double b_side, |
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29 | double c_side, |
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30 | double arim_thickness, |
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31 | double brim_thickness, |
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32 | double crim_thickness) |
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33 | { |
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34 | // Code converted from functions CSPPKernel and CSParallelepiped in libCylinder.c_scaled |
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35 | // Did not understand the code completely, it should be rechecked (Miguel Gonzalez) |
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36 | |
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37 | double t1, t2, t3, t4, tmp, answer; |
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38 | double mu = q * b_side; |
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39 | |
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40 | //calculate volume before rescaling (in original code, but not used) |
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41 | //double vol = form_volume(a_side, b_side, c_side, arim_thickness, brim_thickness, crim_thickness); |
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42 | //double vol = a_side * b_side * c_side + |
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43 | // 2.0 * arim_thickness * b_side * c_side + |
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44 | // 2.0 * brim_thickness * a_side * c_side + |
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45 | // 2.0 * crim_thickness * a_side * b_side; |
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46 | |
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47 | // Scale sides by B |
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48 | double a_scaled = a_side / b_side; |
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49 | double c_scaled = c_side / b_side; |
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50 | |
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51 | // DelRho values (note that drC is not used later) |
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52 | double dr0 = core_sld-solvent_sld; |
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53 | double drA = arim_sld-solvent_sld; |
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54 | double drB = brim_sld-solvent_sld; |
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55 | //double drC = crim_sld-solvent_sld; |
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56 | |
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57 | //Order of integration |
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58 | int nordi=76; |
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59 | int nordj=76; |
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60 | |
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61 | // outer integral (with nordi gauss points), integration limits = 0, 1 |
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62 | double summ = 0; //initialize integral |
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63 | |
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64 | for( int i=0; i<nordi; i++) { |
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65 | |
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66 | // inner integral (with nordj gauss points), integration limits = 0, 1 |
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67 | |
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68 | double summj = 0.0; |
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69 | double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); |
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70 | |
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71 | for(int j=0; j<nordj; j++) { |
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72 | |
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73 | double uu = 0.5 * ( Gauss76Z[j] + 1.0 ); |
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74 | double mudum = mu * sqrt(1.0-sigma*sigma); |
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75 | |
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76 | double Vin = a_side * b_side * c_side; |
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77 | //double Vot = (a_side * b_side * c_side + |
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78 | // 2.0 * arim_thickness * b_side * c_side + |
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79 | // 2.0 * a_side * brim_thickness * c_side + |
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80 | // 2.0 * a_side * b_side * crim_thickness); |
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81 | double V1 = (2.0 * arim_thickness * b_side * c_side); // incorrect V1 (aa*bb*cc+2*ta*bb*cc) |
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82 | double V2 = (2.0 * a_side * brim_thickness * c_side); // incorrect V2(aa*bb*cc+2*aa*tb*cc) |
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83 | |
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84 | // ta and tb correspond to the definitions in CSPPKernel, but they don't make sense to me (MG) |
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85 | // the a_scaled in the definition of tb was present in CSPPKernel in libCylinder.c, |
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86 | // while in cspkernel in csparallelepiped.cpp (used for the 2D), all the definitions |
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87 | // for ta, tb, tc use also A + 2*rim_thickness (but not scaled by B!!!) |
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88 | double ta = (a_scaled+2.0*arim_thickness)/b_side; |
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89 | double tb = (a_scaled+2.0*brim_thickness)/b_side; |
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90 | |
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91 | double arg1 = (0.5*mudum*a_scaled) * sin(0.5*M_PI*uu); |
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92 | double arg2 = (0.5*mudum) * cos(0.5*M_PI*uu); |
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93 | double arg3= (0.5*mudum*ta) * sin(0.5*M_PI*uu); |
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94 | double arg4= (0.5*mudum*tb) * cos(0.5*M_PI*uu); |
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95 | |
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96 | if(arg1==0.0){ |
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97 | t1 = 1.0; |
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98 | } else { |
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99 | t1 = (sin(arg1)/arg1); //defn for CSPP model sin(arg1)/arg1 test: (sin(arg1)/arg1)*(sin(arg1)/arg1) |
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100 | } |
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101 | if(arg2==0.0){ |
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102 | t2 = 1.0; |
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103 | } else { |
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104 | t2 = (sin(arg2)/arg2); //defn for CSPP model sin(arg2)/arg2 test: (sin(arg2)/arg2)*(sin(arg2)/arg2) |
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105 | } |
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106 | if(arg3==0.0){ |
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107 | t3 = 1.0; |
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108 | } else { |
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109 | t3 = sin(arg3)/arg3; |
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110 | } |
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111 | if(arg4==0.0){ |
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112 | t4 = 1.0; |
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113 | } else { |
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114 | t4 = sin(arg4)/arg4; |
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115 | } |
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116 | |
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117 | // Expression in libCylinder.c (neither drC nor Vot are used) |
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118 | tmp =( dr0*t1*t2*Vin + drA*(t3-t1)*t2*V1+ drB*t1*(t4-t2)*V2 )*( dr0*t1*t2*Vin + drA*(t3-t1)*t2*V1+ drB*t1*(t4-t2)*V2 ); // correct FF : square of sum of phase factors |
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119 | |
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120 | // To note also that in csparallelepiped.cpp, there is a function called |
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121 | // cspkernel, which seems to make more sense and has the following comment: |
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122 | // This expression is different from NIST/IGOR package (I strongly believe the IGOR is wrong!!!). 10/15/2010. |
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123 | // tmp =( dr0*tmp1*tmp2*tmp3*Vin + drA*(tmpt1-tmp1)*tmp2*tmp3*V1+ drB*tmp1*(tmpt2-tmp2)*tmp3*V2 + drC*tmp1*tmp2*(tmpt3-tmp3)*V3)* |
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124 | // ( dr0*tmp1*tmp2*tmp3*Vin + drA*(tmpt1-tmp1)*tmp2*tmp3*V1+ drB*tmp1*(tmpt2-tmp2)*tmp3*V2 + drC*tmp1*tmp2*(tmpt3-tmp3)*V3); // correct FF : square of sum of phase factors |
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125 | // This is the function called by csparallelepiped_analytical_2D_scaled, |
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126 | // while CSParallelepipedModel calls CSParallelepiped in libCylinder.c |
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127 | |
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128 | summj += Gauss76Wt[j] * tmp; |
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129 | |
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130 | } |
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131 | |
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132 | // value of the inner integral |
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133 | answer = 0.5 * summj; |
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134 | |
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135 | // finish the outer integral |
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136 | double arg = 0.5 * mu* c_scaled *sigma; |
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137 | if ( arg == 0.0 ) { |
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138 | answer *= 1.0; |
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139 | } else { |
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140 | answer *= sin(arg)*sin(arg)/arg/arg; |
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141 | } |
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142 | |
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143 | // now sum up the outer integral |
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144 | summ += Gauss76Wt[i] * answer; |
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145 | |
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146 | } |
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147 | |
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148 | answer = 0.5 * summ; |
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149 | |
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150 | //convert from [1e-12 A-1] to [cm-1] |
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151 | answer *= 1.0e-4; |
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152 | |
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153 | return answer; |
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154 | } |
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155 | |
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156 | double Iqxy(double qx, double qy, |
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157 | double core_sld, |
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158 | double arim_sld, |
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159 | double brim_sld, |
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160 | double crim_sld, |
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161 | double solvent_sld, |
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162 | double a_side, |
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163 | double b_side, |
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164 | double c_side, |
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165 | double arim_thickness, |
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166 | double brim_thickness, |
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167 | double crim_thickness, |
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168 | double theta, |
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169 | double phi, |
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170 | double psi) |
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171 | { |
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172 | double tmp1, tmp2, tmp3, tmpt1, tmpt2, tmpt3; |
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173 | |
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174 | double q = sqrt(qx*qx+qy*qy); |
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175 | double qx_scaled = qx/q; |
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176 | double qy_scaled = qy/q; |
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177 | |
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178 | // Convert angles given in degrees to radians |
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179 | theta *= M_PI_180; |
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180 | phi *= M_PI_180; |
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181 | psi *= M_PI_180; |
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182 | |
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183 | // Parallelepiped c axis orientation |
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184 | double cparallel_x = cos(theta) * cos(phi); |
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185 | double cparallel_y = sin(theta); |
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186 | |
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187 | // Compute angle between q and parallelepiped axis |
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188 | double cos_val_c = cparallel_x*qx_scaled + cparallel_y*qy_scaled;// + cparallel_z*qz; |
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189 | |
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190 | // Parallelepiped a axis orientation |
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191 | double parallel_x = -cos(phi)*sin(psi) * sin(theta)+sin(phi)*cos(psi); |
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192 | double parallel_y = sin(psi)*cos(theta); |
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193 | double cos_val_a = parallel_x*qx_scaled + parallel_y*qy_scaled; |
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194 | |
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195 | // Parallelepiped b axis orientation |
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196 | double bparallel_x = -sin(theta)*cos(psi)*cos(phi)-sin(psi)*sin(phi); |
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197 | double bparallel_y = cos(theta)*cos(psi); |
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198 | double cos_val_b = bparallel_x*qx_scaled + bparallel_y*qy_scaled; |
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199 | |
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200 | // The following tests should always pass |
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201 | if (fabs(cos_val_c)>1.0) { |
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202 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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203 | cos_val_c = 1.0; |
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204 | } |
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205 | if (fabs(cos_val_a)>1.0) { |
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206 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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207 | cos_val_a = 1.0; |
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208 | } |
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209 | if (fabs(cos_val_b)>1.0) { |
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210 | //printf("parallel_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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211 | cos_val_b = 1.0; |
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212 | } |
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213 | |
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214 | // cspkernel in csparallelepiped recoded here |
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215 | double dr0 = core_sld-solvent_sld; |
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216 | double drA = arim_sld-solvent_sld; |
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217 | double drB = brim_sld-solvent_sld; |
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218 | double drC = crim_sld-solvent_sld; |
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219 | double Vin = a_side * b_side * c_side; |
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220 | // As for the 1D case, Vot is not used |
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221 | //double Vot = (a_side * b_side * c_side + |
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222 | // 2.0 * arim_thickness * b_side * c_side + |
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223 | // 2.0 * a_side * brim_thickness * c_side + |
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224 | // 2.0 * a_side * b_side * crim_thickness); |
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225 | double V1 = (2.0 * arim_thickness * b_side * c_side); // incorrect V1 (aa*bb*cc+2*ta*bb*cc) |
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226 | double V2 = (2.0 * a_side * brim_thickness * c_side); // incorrect V2(aa*bb*cc+2*aa*tb*cc) |
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227 | double V3 = (2.0 * a_side * b_side * crim_thickness); |
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228 | // The definitions of ta, tb, tc are not the same as in the 1D case because there is no |
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229 | // the scaling by B. The use of a_side for the 3 of them seems clearly a mistake to me, |
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230 | // but for the moment I let it like this until understanding better the code. |
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231 | double ta = a_side + 2.0*arim_thickness; |
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232 | double tb = a_side + 2.0*brim_thickness; |
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233 | double tc = a_side + 2.0*crim_thickness; |
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234 | //handle arg=0 separately, as sin(t)/t -> 1 as t->0 |
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235 | double argA = 0.5*q*a_side*cos_val_a; |
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236 | double argB = 0.5*q*b_side*cos_val_b; |
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237 | double argC = 0.5*q*c_side*cos_val_c; |
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238 | double argtA = 0.5*q*ta*cos_val_a; |
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239 | double argtB = 0.5*q*tb*cos_val_b; |
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240 | double argtC = 0.5*q*tc*cos_val_c; |
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241 | |
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242 | if(argA==0.0) { |
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243 | tmp1 = 1.0; |
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244 | } else { |
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245 | tmp1 = sin(argA)/argA; |
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246 | } |
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247 | if (argB==0.0) { |
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248 | tmp2 = 1.0; |
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249 | } else { |
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250 | tmp2 = sin(argB)/argB; |
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251 | } |
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252 | if (argC==0.0) { |
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253 | tmp3 = 1.0; |
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254 | } else { |
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255 | tmp3 = sin(argC)/argC; |
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256 | } |
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257 | if(argtA==0.0) { |
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258 | tmpt1 = 1.0; |
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259 | } else { |
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260 | tmpt1 = sin(argtA)/argtA; |
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261 | } |
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262 | if (argtB==0.0) { |
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263 | tmpt2 = 1.0; |
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264 | } else { |
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265 | tmpt2 = sin(argtB)/argtB; |
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266 | } |
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267 | if (argtC==0.0) { |
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268 | tmpt3 = 1.0; |
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269 | } else { |
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270 | tmpt3 = sin(argtC)*sin(argtC)/argtC/argtC; |
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271 | } |
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272 | |
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273 | // f uses Vin, V1, V2, and V3 and it seems to have more sense than the value computed |
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274 | // in the 1D code, but should be checked! |
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275 | double f = ( dr0*tmp1*tmp2*tmp3*Vin + drA*(tmpt1-tmp1)*tmp2*tmp3*V1 + |
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276 | drB*tmp1*(tmpt2-tmp2)*tmp3*V2 + drC*tmp1*tmp2*(tmpt3-tmp3)*V3); |
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277 | |
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278 | return 1.0e-4 * f * f; |
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279 | } |
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