[c5b7d07] | 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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[deb7ee0] | 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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[c5b7d07] | 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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[deb7ee0] | 33 | |
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[c5b7d07] | 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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[deb7ee0] | 39 | |
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[c5b7d07] | 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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[deb7ee0] | 47 | double tmp1, tmp2; |
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[c5b7d07] | 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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[deb7ee0] | 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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[c5b7d07] | 60 | double summ = 0; //initialize integral |
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| 61 | |
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[deb7ee0] | 62 | for( int i=0; i<nordi; i++) { |
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[c5b7d07] | 63 | |
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[deb7ee0] | 64 | // inner integral (with nordj gauss points), integration limits = 0, 1 |
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[c5b7d07] | 65 | |
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| 66 | double summj = 0.0; |
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[deb7ee0] | 67 | double sigma = 0.5 * ( Gauss76Z[i] + 1.0 ); |
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[c5b7d07] | 68 | |
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[deb7ee0] | 69 | for(int j=0; j<nordj; j++) { |
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[c5b7d07] | 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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[deb7ee0] | 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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[c5b7d07] | 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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[deb7ee0] | 86 | summj += Gauss76Wt[j] * tmp1 * tmp2; |
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[c5b7d07] | 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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[deb7ee0] | 99 | // sum of outer integral |
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| 100 | summ += Gauss76Wt[i] * answer; |
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[c5b7d07] | 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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[deb7ee0] | 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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[c5b7d07] | 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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