1 | static double |
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2 | form_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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3 | { |
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4 | return length_a * (length_a*b2a_ratio) * (length_a*c2a_ratio); |
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5 | } |
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6 | |
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7 | static double |
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8 | radius_from_excluded_volume(double length_a, double b2a_ratio, double c2a_ratio) |
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9 | { |
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10 | double const r_equiv = sqrt(length_a*length_a*b2a_ratio/M_PI); |
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11 | double const length_c = c2a_ratio*length_a; |
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12 | return 0.5*cbrt(0.75*r_equiv*(2.0*r_equiv*length_c + (r_equiv + length_c)*(M_PI*r_equiv + length_c))); |
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13 | } |
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14 | |
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15 | static double |
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16 | radius_effective(int mode, double length_a, double b2a_ratio, double c2a_ratio) |
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17 | { |
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18 | switch (mode) { |
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19 | default: |
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20 | case 1: // equivalent cylinder excluded volume |
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21 | return radius_from_excluded_volume(length_a,b2a_ratio,c2a_ratio); |
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22 | case 2: // equivalent volume sphere |
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23 | return cbrt(cube(length_a)*b2a_ratio*c2a_ratio/M_4PI_3); |
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24 | case 3: // half length_a |
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25 | return 0.5 * length_a; |
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26 | case 4: // half length_b |
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27 | return 0.5 * length_a*b2a_ratio; |
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28 | case 5: // half length_c |
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29 | return 0.5 * length_a*c2a_ratio; |
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30 | case 6: // equivalent circular cross-section |
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31 | return length_a*sqrt(b2a_ratio/M_PI); |
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32 | case 7: // half ab diagonal |
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33 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio))); |
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34 | case 8: // half diagonal |
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35 | return 0.5*sqrt(square(length_a) * (1.0 + square(b2a_ratio) + square(c2a_ratio))); |
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36 | } |
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37 | } |
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38 | |
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39 | static double |
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40 | Iq(double q, |
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41 | double sld, |
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42 | double solvent_sld, |
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43 | double length_a, |
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44 | double b2a_ratio, |
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45 | double c2a_ratio) |
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46 | { |
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47 | const double length_b = length_a * b2a_ratio; |
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48 | const double length_c = length_a * c2a_ratio; |
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49 | const double a_half = 0.5 * length_a; |
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50 | const double b_half = 0.5 * length_b; |
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51 | const double c_half = 0.5 * length_c; |
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52 | |
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53 | //Integration limits to use in Gaussian quadrature |
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54 | const double v1a = 0.0; |
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55 | const double v1b = M_PI_2; //theta integration limits |
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56 | const double v2a = 0.0; |
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57 | const double v2b = M_PI_2; //phi integration limits |
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58 | |
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59 | double outer_sum = 0.0; |
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60 | for(int i=0; i<GAUSS_N; i++) { |
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61 | const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b ); |
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62 | double sin_theta, cos_theta; |
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63 | SINCOS(theta, sin_theta, cos_theta); |
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64 | |
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65 | const double termC = sas_sinx_x(q * c_half * cos_theta); |
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66 | |
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67 | double inner_sum = 0.0; |
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68 | for(int j=0; j<GAUSS_N; j++) { |
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69 | double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b ); |
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70 | double sin_phi, cos_phi; |
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71 | SINCOS(phi, sin_phi, cos_phi); |
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72 | |
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73 | // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0 |
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74 | const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi); |
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75 | const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi); |
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76 | const double AP = termA * termB * termC; |
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77 | inner_sum += GAUSS_W[j] * AP * AP; |
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78 | } |
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79 | inner_sum = 0.5 * (v2b-v2a) * inner_sum; |
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80 | outer_sum += GAUSS_W[i] * inner_sum * sin_theta; |
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81 | } |
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82 | |
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83 | double answer = 0.5*(v1b-v1a)*outer_sum; |
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84 | |
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85 | // Normalize by Pi (Eqn. 16). |
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86 | // The term (ABC)^2 does not appear because it was introduced before on |
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87 | // the definitions of termA, termB, termC. |
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88 | // The factor 2 appears because the theta integral has been defined between |
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89 | // 0 and pi/2, instead of 0 to pi. |
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90 | answer /= M_PI_2; //Form factor P(q) |
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91 | |
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92 | // Multiply by contrast^2 and volume^2 |
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93 | const double volume = length_a * length_b * length_c; |
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94 | answer *= square((sld-solvent_sld)*volume); |
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95 | |
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96 | // Convert from [1e-12 A-1] to [cm-1] |
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97 | answer *= 1.0e-4; |
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98 | |
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99 | return answer; |
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100 | } |
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101 | |
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102 | static void |
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103 | Fq(double q, |
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104 | double *F1, |
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105 | double *F2, |
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106 | double sld, |
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107 | double solvent_sld, |
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108 | double length_a, |
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109 | double b2a_ratio, |
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110 | double c2a_ratio) |
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111 | { |
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112 | const double length_b = length_a * b2a_ratio; |
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113 | const double length_c = length_a * c2a_ratio; |
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114 | const double a_half = 0.5 * length_a; |
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115 | const double b_half = 0.5 * length_b; |
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116 | const double c_half = 0.5 * length_c; |
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117 | |
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118 | //Integration limits to use in Gaussian quadrature |
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119 | const double v1a = 0.0; |
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120 | const double v1b = M_PI_2; //theta integration limits |
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121 | const double v2a = 0.0; |
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122 | const double v2b = M_PI_2; //phi integration limits |
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123 | |
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124 | double outer_sum_F1 = 0.0; |
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125 | double outer_sum_F2 = 0.0; |
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126 | for(int i=0; i<GAUSS_N; i++) { |
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127 | const double theta = 0.5 * ( GAUSS_Z[i]*(v1b-v1a) + v1a + v1b ); |
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128 | double sin_theta, cos_theta; |
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129 | SINCOS(theta, sin_theta, cos_theta); |
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130 | |
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131 | const double termC = sas_sinx_x(q * c_half * cos_theta); |
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132 | |
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133 | double inner_sum_F1 = 0.0; |
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134 | double inner_sum_F2 = 0.0; |
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135 | for(int j=0; j<GAUSS_N; j++) { |
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136 | double phi = 0.5 * ( GAUSS_Z[j]*(v2b-v2a) + v2a + v2b ); |
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137 | double sin_phi, cos_phi; |
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138 | SINCOS(phi, sin_phi, cos_phi); |
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139 | |
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140 | // Amplitude AP from eqn. (12), rewritten to avoid round-off effects when arg=0 |
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141 | const double termA = sas_sinx_x(q * a_half * sin_theta * sin_phi); |
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142 | const double termB = sas_sinx_x(q * b_half * sin_theta * cos_phi); |
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143 | const double AP = termA * termB * termC; |
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144 | inner_sum_F1 += GAUSS_W[j] * AP; |
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145 | inner_sum_F2 += GAUSS_W[j] * AP * AP; |
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146 | } |
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147 | inner_sum_F1 = 0.5 * (v2b-v2a) * inner_sum_F1; |
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148 | inner_sum_F2 = 0.5 * (v2b-v2a) * inner_sum_F2; |
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149 | outer_sum_F1 += GAUSS_W[i] * inner_sum_F1 * sin_theta; |
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150 | outer_sum_F2 += GAUSS_W[i] * inner_sum_F2 * sin_theta; |
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151 | } |
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152 | |
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153 | outer_sum_F1 *= 0.5*(v1b-v1a); |
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154 | outer_sum_F2 *= 0.5*(v1b-v1a); |
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155 | |
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156 | // Normalize by Pi (Eqn. 16). |
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157 | // The term (ABC)^2 does not appear because it was introduced before on |
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158 | // the definitions of termA, termB, termC. |
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159 | // The factor 2 appears because the theta integral has been defined between |
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160 | // 0 and pi/2, instead of 0 to pi. |
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161 | outer_sum_F1 /= M_PI_2; |
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162 | outer_sum_F2 /= M_PI_2; |
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163 | |
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164 | // Multiply by contrast and volume |
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165 | const double s = (sld-solvent_sld) * (length_a * length_b * length_c); |
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166 | |
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167 | // Convert from [1e-12 A-1] to [cm-1] |
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168 | *F1 = 1e-2 * s * outer_sum_F1; |
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169 | *F2 = 1e-4 * s * s * outer_sum_F2; |
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170 | } |
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171 | |
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172 | |
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173 | static double |
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174 | Iqabc(double qa, double qb, double qc, |
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175 | double sld, |
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176 | double solvent_sld, |
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177 | double length_a, |
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178 | double b2a_ratio, |
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179 | double c2a_ratio) |
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180 | { |
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181 | const double length_b = length_a * b2a_ratio; |
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182 | const double length_c = length_a * c2a_ratio; |
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183 | const double a_half = 0.5 * length_a; |
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184 | const double b_half = 0.5 * length_b; |
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185 | const double c_half = 0.5 * length_c; |
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186 | |
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187 | // Amplitude AP from eqn. (13) |
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188 | const double termA = sas_sinx_x(qa * a_half); |
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189 | const double termB = sas_sinx_x(qb * b_half); |
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190 | const double termC = sas_sinx_x(qc * c_half); |
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191 | const double AP = termA * termB * termC; |
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192 | |
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193 | // Multiply by contrast and volume |
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194 | const double s = (sld-solvent_sld) * (length_a * length_b * length_c); |
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195 | |
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196 | // Convert from [1e-12 A-1] to [cm-1] |
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197 | return 1.0e-4 * square(s * AP); |
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198 | } |
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