[ee60aa7] | 1 | static double |
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| 2 | outer_radius(double fp_n_shells, double thickness[], double interface[]) |
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[3330bb4] | 3 | { |
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| 4 | int n_shells= (int)(fp_n_shells + 0.5); |
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| 5 | double r = 0.0; |
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| 6 | for (int i=0; i < n_shells; i++) { |
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| 7 | r += thickness[i] + interface[i]; |
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| 8 | } |
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[ee60aa7] | 9 | return r; |
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| 10 | } |
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| 11 | |
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| 12 | static double form_volume( |
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| 13 | double fp_n_shells, |
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| 14 | double thickness[], |
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| 15 | double interface[]) |
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| 16 | { |
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| 17 | return M_4PI_3*cube(outer_radius(fp_n_shells, thickness, interface)); |
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[3330bb4] | 18 | } |
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| 19 | |
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[d277229] | 20 | static double |
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[a34b811] | 21 | radius_effective(int mode, double fp_n_shells, double thickness[], double interface[]) |
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[d277229] | 22 | { |
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[ee60aa7] | 23 | // case 1: outer radius |
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| 24 | return outer_radius(fp_n_shells, thickness, interface); |
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[d277229] | 25 | } |
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| 26 | |
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[3330bb4] | 27 | static double blend(int shape, double nu, double z) |
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| 28 | { |
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| 29 | if (shape==0) { |
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| 30 | const double num = sas_erf(nu * M_SQRT1_2 * (2.0*z - 1.0)); |
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| 31 | const double denom = 2.0 * sas_erf(nu * M_SQRT1_2); |
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| 32 | return num/denom + 0.5; |
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| 33 | } else if (shape==1) { |
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| 34 | return pow(z, nu); |
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| 35 | } else if (shape==2) { |
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| 36 | return 1.0 - pow(1.0 - z, nu); |
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| 37 | } else if (shape==3) { |
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| 38 | return expm1(-nu*z)/expm1(-nu); |
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| 39 | } else if (shape==4) { |
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| 40 | return expm1(nu*z)/expm1(nu); |
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| 41 | } else { |
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| 42 | return NAN; |
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| 43 | } |
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| 44 | } |
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| 45 | |
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| 46 | static double f_linear(double q, double r, double contrast, double slope) |
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| 47 | { |
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| 48 | const double qr = q * r; |
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| 49 | const double qrsq = qr * qr; |
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| 50 | const double bes = sas_3j1x_x(qr); |
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| 51 | double sinqr, cosqr; |
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| 52 | SINCOS(qr, sinqr, cosqr); |
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| 53 | const double fun = 3.0*r*(2.0*qr*sinqr - (qrsq-2.0)*cosqr)/(qrsq*qrsq); |
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| 54 | const double vol = M_4PI_3 * cube(r); |
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| 55 | return vol*(bes*contrast + fun*slope); |
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| 56 | } |
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| 57 | |
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| 58 | static double Iq( |
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| 59 | double q, |
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| 60 | double fp_n_shells, |
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| 61 | double sld_solvent, |
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| 62 | double sld[], |
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| 63 | double thickness[], |
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| 64 | double interface[], |
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| 65 | double shape[], |
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| 66 | double nu[], |
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| 67 | double fp_n_steps) |
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| 68 | { |
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| 69 | // iteration for # of shells + core + solvent |
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| 70 | int n_shells = (int)(fp_n_shells + 0.5); |
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| 71 | int n_steps = (int)(fp_n_steps + 0.5); |
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| 72 | double f=0.0; |
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| 73 | double r=0.0; |
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| 74 | for (int shell=0; shell<n_shells; shell++){ |
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| 75 | const double sld_l = sld[shell]; |
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| 76 | |
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| 77 | // uniform shell; r=0 => r^3=0 => f=0, so works for core as well. |
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| 78 | f -= M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); |
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| 79 | r += thickness[shell]; |
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| 80 | f += M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); |
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| 81 | |
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| 82 | // iterate over sub_shells in the interface |
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| 83 | const double dr = interface[shell]/n_steps; |
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| 84 | const double delta = (shell==n_shells-1 ? sld_solvent : sld[shell+1]) - sld_l; |
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| 85 | const double nu_shell = fmax(fabs(nu[shell]), 1.e-14); |
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| 86 | const int shape_shell = (int)(shape[shell]); |
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| 87 | |
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| 88 | // if there is no interface the equations don't work |
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| 89 | if (dr == 0.) continue; |
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| 90 | |
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| 91 | double sld_in = sld_l; |
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| 92 | for (int step=1; step <= n_steps; step++) { |
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| 93 | // find sld_i at the outer boundary of sub-shell step |
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| 94 | //const double z = (double)step/(double)n_steps; |
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| 95 | const double z = (double)step/(double)n_steps; |
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| 96 | const double fraction = blend(shape_shell, nu_shell, z); |
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| 97 | const double sld_out = fraction*delta + sld_l; |
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| 98 | // calculate slope |
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| 99 | const double slope = (sld_out - sld_in)/dr; |
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| 100 | const double contrast = sld_in - slope*r; |
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| 101 | |
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| 102 | // iteration for the left and right boundary of the shells |
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| 103 | f -= f_linear(q, r, contrast, slope); |
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| 104 | r += dr; |
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| 105 | f += f_linear(q, r, contrast, slope); |
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| 106 | sld_in = sld_out; |
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| 107 | } |
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| 108 | } |
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| 109 | // add in solvent effect |
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| 110 | f -= M_4PI_3 * cube(r) * sld_solvent * sas_3j1x_x(q*r); |
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| 111 | |
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| 112 | const double f2 = f * f * 1.0e-4; |
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| 113 | return f2; |
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| 114 | } |
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| 115 | |
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[71b751d] | 116 | static void Fq( |
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| 117 | double q, |
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| 118 | double *F1, |
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| 119 | double *F2, |
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| 120 | double fp_n_shells, |
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| 121 | double sld_solvent, |
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| 122 | double sld[], |
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| 123 | double thickness[], |
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| 124 | double interface[], |
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| 125 | double shape[], |
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| 126 | double nu[], |
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| 127 | double fp_n_steps) |
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| 128 | { |
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| 129 | // iteration for # of shells + core + solvent |
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| 130 | int n_shells = (int)(fp_n_shells + 0.5); |
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| 131 | int n_steps = (int)(fp_n_steps + 0.5); |
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| 132 | double f=0.0; |
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| 133 | double r=0.0; |
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| 134 | for (int shell=0; shell<n_shells; shell++){ |
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| 135 | const double sld_l = sld[shell]; |
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| 136 | |
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| 137 | // uniform shell; r=0 => r^3=0 => f=0, so works for core as well. |
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| 138 | f -= M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); |
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| 139 | r += thickness[shell]; |
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| 140 | f += M_4PI_3 * cube(r) * sld_l * sas_3j1x_x(q*r); |
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| 141 | |
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| 142 | // iterate over sub_shells in the interface |
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| 143 | const double dr = interface[shell]/n_steps; |
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| 144 | const double delta = (shell==n_shells-1 ? sld_solvent : sld[shell+1]) - sld_l; |
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| 145 | const double nu_shell = fmax(fabs(nu[shell]), 1.e-14); |
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| 146 | const int shape_shell = (int)(shape[shell]); |
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| 147 | |
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| 148 | // if there is no interface the equations don't work |
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| 149 | if (dr == 0.) continue; |
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| 150 | |
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| 151 | double sld_in = sld_l; |
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| 152 | for (int step=1; step <= n_steps; step++) { |
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| 153 | // find sld_i at the outer boundary of sub-shell step |
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| 154 | //const double z = (double)step/(double)n_steps; |
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| 155 | const double z = (double)step/(double)n_steps; |
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| 156 | const double fraction = blend(shape_shell, nu_shell, z); |
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| 157 | const double sld_out = fraction*delta + sld_l; |
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| 158 | // calculate slope |
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| 159 | const double slope = (sld_out - sld_in)/dr; |
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| 160 | const double contrast = sld_in - slope*r; |
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| 161 | |
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| 162 | // iteration for the left and right boundary of the shells |
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| 163 | f -= f_linear(q, r, contrast, slope); |
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| 164 | r += dr; |
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| 165 | f += f_linear(q, r, contrast, slope); |
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| 166 | sld_in = sld_out; |
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| 167 | } |
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| 168 | } |
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| 169 | // add in solvent effect |
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| 170 | f -= M_4PI_3 * cube(r) * sld_solvent * sas_3j1x_x(q*r); |
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| 171 | |
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| 172 | *F1 = 1e-2*f; |
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| 173 | *F2 = 1e-4*f*f; |
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| 174 | } |
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