| 1 | double form_volume(double radius, |
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| 2 | double thickness); |
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| 3 | |
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| 4 | double Iq(double q, |
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| 5 | double radius, |
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| 6 | double thickness, |
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| 7 | double alpha, |
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| 8 | double beta, |
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| 9 | double sld_pringle, |
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| 10 | double sld_solvent); |
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| 11 | |
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| 12 | static |
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| 13 | double pringleC(double radius, |
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| 14 | double alpha, |
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| 15 | double beta, |
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| 16 | double q, |
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| 17 | double phi, |
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| 18 | double n) { |
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| 19 | |
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| 20 | double va, vb; |
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| 21 | double bessargs, cosarg, bessargcb; |
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| 22 | double r, retval, yyy; |
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| 23 | |
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| 24 | |
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| 25 | va = 0; |
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| 26 | vb = radius; |
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| 27 | |
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| 28 | // evaluate at Gauss points |
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| 29 | // remember to index from 0,size-1 |
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| 30 | |
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| 31 | double summ = 0.0; // initialize integral |
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| 32 | int ii = 0; |
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| 33 | do { |
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| 34 | // Using 76 Gauss points |
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| 35 | r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0; |
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| 36 | |
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| 37 | bessargs = q*r*sin(phi); |
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| 38 | cosarg = q*r*r*alpha*cos(phi); |
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| 39 | bessargcb = q*r*r*beta*cos(phi); |
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| 40 | |
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| 41 | yyy = Gauss76Wt[ii]*r*cos(cosarg) |
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| 42 | *sas_JN(n, bessargcb) |
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| 43 | *sas_JN(2*n, bessargs); |
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| 44 | summ += yyy; |
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| 45 | |
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| 46 | ii += 1; |
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| 47 | } while (ii < N_POINTS_76); // end of loop over quadrature points |
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| 48 | // |
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| 49 | // calculate value of integral to return |
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| 50 | |
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| 51 | retval = (vb - va) / 2.0 * summ; |
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| 52 | retval = retval / pow(r, 2.0); |
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| 53 | |
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| 54 | return retval; |
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| 55 | } |
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| 56 | |
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| 57 | static |
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| 58 | double pringleS(double radius, |
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| 59 | double alpha, |
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| 60 | double beta, |
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| 61 | double q, |
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| 62 | double phi, |
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| 63 | double n) { |
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| 64 | |
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| 65 | double va, vb, summ; |
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| 66 | double bessargs, sinarg, bessargcb; |
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| 67 | double r, retval, yyy; |
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| 68 | // set up the integration |
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| 69 | // end points and weights |
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| 70 | |
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| 71 | va = 0; |
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| 72 | vb = radius; |
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| 73 | |
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| 74 | // evaluate at Gauss points |
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| 75 | // remember to index from 0,size-1 |
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| 76 | |
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| 77 | summ = 0.0; // initialize integral |
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| 78 | int ii = 0; |
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| 79 | do { |
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| 80 | // Using 76 Gauss points |
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| 81 | r = (Gauss76Z[ii] * (vb - va) + vb + va) / 2.0; |
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| 82 | |
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| 83 | bessargs = q*r*sin(phi); |
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| 84 | sinarg = q*r*r*alpha*cos(phi); |
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| 85 | bessargcb = q*r*r*beta*cos(phi); |
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| 86 | |
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| 87 | yyy = Gauss76Wt[ii]*r*sin(sinarg) |
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| 88 | *sas_JN(n, bessargcb) |
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| 89 | *sas_JN(2*n, bessargs); |
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| 90 | summ += yyy; |
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| 91 | |
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| 92 | ii += 1; |
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| 93 | } while (ii < N_POINTS_76); |
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| 94 | |
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| 95 | // end of loop over quadrature points |
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| 96 | // |
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| 97 | // calculate value of integral to return |
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| 98 | |
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| 99 | retval = (vb-va)/2.0*summ; |
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| 100 | retval = retval/pow(r, 2.0); |
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| 101 | |
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| 102 | return retval; |
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| 103 | } |
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| 104 | |
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| 105 | static |
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| 106 | double _kernel(double thickness, |
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| 107 | double radius, |
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| 108 | double alpha, |
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| 109 | double beta, |
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| 110 | double q, |
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| 111 | double phi) { |
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| 112 | |
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| 113 | const double sincarg = q * thickness * cos(phi) / 2.0; |
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| 114 | const double sincterm = pow(sin(sincarg) / sincarg, 2.0); |
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| 115 | |
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| 116 | //calculate sum term from n = -3 to 3 |
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| 117 | double sumterm = 0.0; |
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| 118 | for (int nn = -3; nn <= 3; nn++) { |
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| 119 | double powc = pringleC(radius, alpha, beta, q, phi, nn); |
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| 120 | double pows = pringleS(radius, alpha, beta, q, phi, nn); |
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| 121 | sumterm += pow(powc, 2.0) + pow(pows, 2.0); |
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| 122 | } |
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| 123 | double retval = 4.0 * sin(phi) * sumterm * sincterm; |
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| 124 | |
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| 125 | return retval; |
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| 126 | |
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| 127 | } |
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| 128 | |
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| 129 | static double pringles_kernel(double q, |
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| 130 | double radius, |
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| 131 | double thickness, |
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| 132 | double alpha, |
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| 133 | double beta, |
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| 134 | double sld_pringle, |
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| 135 | double sld_solvent) |
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| 136 | { |
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| 137 | |
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| 138 | //upper and lower integration limits |
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| 139 | const double lolim = 0.0; |
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| 140 | const double uplim = M_PI / 2.0; |
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| 141 | |
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| 142 | double summ = 0.0; //initialize integral |
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| 143 | |
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| 144 | double delrho = sld_pringle - sld_solvent; //make contrast term |
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| 145 | |
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| 146 | for (int i = 0; i < N_POINTS_76; i++) { |
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| 147 | double phi = (Gauss76Z[i] * (uplim - lolim) + uplim + lolim) / 2.0; |
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| 148 | summ += Gauss76Wt[i] * _kernel(thickness, radius, alpha, beta, q, phi); |
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| 149 | } |
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| 150 | |
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| 151 | double answer = (uplim - lolim) / 2.0 * summ; |
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| 152 | answer *= delrho*delrho; |
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| 153 | |
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| 154 | return answer; |
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| 155 | } |
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| 156 | |
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| 157 | double form_volume(double radius, |
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| 158 | double thickness){ |
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| 159 | |
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| 160 | return 1.0; |
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| 161 | } |
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| 162 | |
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| 163 | double Iq(double q, |
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| 164 | double radius, |
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| 165 | double thickness, |
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| 166 | double alpha, |
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| 167 | double beta, |
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| 168 | double sld_pringle, |
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| 169 | double sld_solvent) |
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| 170 | { |
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| 171 | const double form = pringles_kernel(q, |
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| 172 | radius, |
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| 173 | thickness, |
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| 174 | alpha, |
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| 175 | beta, |
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| 176 | sld_pringle, |
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| 177 | sld_solvent); |
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| 178 | |
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| 179 | return 1.0e-4*form*M_PI*radius*radius*thickness; |
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| 180 | } |
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