[339ce67] | 1 | /* |
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| 2 | * Scattering model for a Capped Cylinder |
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| 3 | */ |
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| 4 | #include "capcyl.h" |
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| 5 | #include <math.h> |
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| 6 | #include "GaussWeights.h" |
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| 7 | #include "libCylinder.h" |
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[890ac7f1] | 8 | #include <stdio.h> |
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[339ce67] | 9 | |
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| 10 | /** |
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| 11 | * Function to evaluate 1D scattering function |
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| 12 | * @param pars: parameters of the CappedCylinder |
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| 13 | * @param q: q-value |
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| 14 | * @return: function value |
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| 15 | */ |
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| 16 | double capcyl_analytical_1D(CapCylParameters *pars, double q) { |
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| 17 | double dp[7]; |
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| 18 | double result; |
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| 19 | |
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| 20 | dp[0] = pars->scale; |
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| 21 | dp[1] = pars->rad_cyl; |
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| 22 | dp[2] = pars->len_cyl; |
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| 23 | dp[3] = pars->rad_cap; |
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| 24 | dp[4] = pars->sld_capcyl; |
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| 25 | dp[5] = pars->sld_solv; |
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| 26 | dp[6] = pars->background; |
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| 27 | |
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| 28 | result = CappedCylinder(dp, q); |
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| 29 | // Make Sure it never goes to inf/nan. |
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| 30 | if ( result == INFINITY || result == NAN){ |
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| 31 | result = pars->background; |
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| 32 | } |
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| 33 | return result; |
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| 34 | } |
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| 35 | |
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| 36 | |
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| 37 | double capcyl2d_kernel(double dp[], double q, double alpha) { |
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[a24f530] | 38 | int j; |
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[339ce67] | 39 | double Pi; |
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| 40 | double scale,contr,bkg,sldc,slds; |
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| 41 | double len,rad,hDist,endRad; |
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| 42 | int nordj=76; |
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| 43 | double zi=alpha,yyy,answer; //running tally of integration |
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| 44 | double summj,vaj,vbj,zij; //for the inner integration |
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| 45 | double arg1,arg2,inner,be; |
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| 46 | |
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| 47 | |
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| 48 | scale = dp[0]; |
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| 49 | rad = dp[1]; |
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| 50 | len = dp[2]; |
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| 51 | endRad = dp[3]; |
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| 52 | sldc = dp[4]; |
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| 53 | slds = dp[5]; |
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| 54 | bkg = dp[6]; |
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| 55 | |
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| 56 | hDist = -1.0*sqrt(fabs(endRad*endRad-rad*rad)); //by definition for this model |
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| 57 | |
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| 58 | contr = sldc-slds; |
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| 59 | |
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| 60 | Pi = 4.0*atan(1.0); |
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| 61 | vaj = -1.0*hDist/endRad; |
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| 62 | vbj = 1.0; //endpoints of inner integral |
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| 63 | |
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| 64 | summj=0.0; |
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| 65 | |
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| 66 | for(j=0;j<nordj;j++) { |
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| 67 | //20 gauss points for the inner integral |
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| 68 | zij = ( Gauss76Z[j]*(vbj-vaj) + vaj + vbj )/2.0; //the "t" dummy |
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| 69 | yyy = Gauss76Wt[j] * ConvLens_kernel(dp,q,zij,zi); //uses the same Kernel as the Dumbbell, here L>0 |
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| 70 | summj += yyy; |
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| 71 | } |
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| 72 | //now calculate the value of the inner integral |
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| 73 | inner = (vbj-vaj)/2.0*summj; |
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| 74 | inner *= 4.0*Pi*endRad*endRad*endRad; |
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| 75 | |
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| 76 | //now calculate outer integrand |
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| 77 | arg1 = q*len/2.0*cos(zi); |
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| 78 | arg2 = q*rad*sin(zi); |
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| 79 | yyy = inner; |
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| 80 | |
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| 81 | if(arg2 == 0) { |
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| 82 | be = 0.5; |
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| 83 | } else { |
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| 84 | be = NR_BessJ1(arg2)/arg2; |
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| 85 | } |
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| 86 | |
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| 87 | if(arg1 == 0.0) { //limiting value of sinc(0) is 1; sinc is not defined in math.h |
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| 88 | yyy += Pi*rad*rad*len*2.0*be; |
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| 89 | } else { |
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| 90 | yyy += Pi*rad*rad*len*sin(arg1)/arg1*2.0*be; |
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| 91 | } |
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| 92 | yyy *= yyy; //sin(zi); |
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| 93 | answer = yyy; |
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| 94 | |
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| 95 | |
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| 96 | answer /= Pi*rad*rad*len + 2.0*Pi*(2.0*endRad*endRad*endRad/3.0+endRad*endRad*hDist-hDist*hDist*hDist/3.0); //divide by volume |
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| 97 | answer *= 1.0e8; //convert to cm^-1 |
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| 98 | answer *= contr*contr; |
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| 99 | answer *= scale; |
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| 100 | answer += bkg; |
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| 101 | |
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| 102 | return answer; |
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| 103 | } |
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| 104 | |
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| 105 | |
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| 106 | /** |
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| 107 | * Function to evaluate 2D scattering function |
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| 108 | * @param pars: parameters of the BarBell |
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| 109 | * @param q: q-value |
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| 110 | * @return: function value |
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| 111 | */ |
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| 112 | double capcyl_analytical_2DXY(CapCylParameters *pars, double qx, double qy){ |
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| 113 | double q; |
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| 114 | q = sqrt(qx*qx+qy*qy); |
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| 115 | return capcyl_analytical_2D_scaled(pars, q, qx/q, qy/q); |
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| 116 | } |
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| 117 | |
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| 118 | double capcyl_analytical_2D(CapCylParameters *pars, double q, double phi) { |
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| 119 | return capcyl_analytical_2D_scaled(pars, q, cos(phi), sin(phi)); |
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| 120 | } |
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| 121 | |
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| 122 | /** |
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| 123 | * Function to evaluate 2D scattering function |
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| 124 | * @param pars: parameters of the BarBell |
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| 125 | * @param q: q-value |
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| 126 | * @param q_x: q_x / q |
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| 127 | * @param q_y: q_y / q |
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| 128 | * @return: function value |
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| 129 | */ |
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| 130 | double capcyl_analytical_2D_scaled(CapCylParameters *pars, double q, double q_x, double q_y) { |
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| 131 | double cyl_x, cyl_y, cyl_z; |
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| 132 | double q_z; |
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[a24f530] | 133 | double alpha, cos_val; |
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[339ce67] | 134 | double answer; |
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| 135 | double dp[7]; |
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[890ac7f1] | 136 | //convert angle degree to radian |
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| 137 | double pi = 4.0*atan(1.0); |
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| 138 | double theta = pars->theta * pi/180.0; |
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| 139 | double phi = pars->phi * pi/180.0; |
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[339ce67] | 140 | |
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| 141 | dp[0] = pars->scale; |
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| 142 | dp[1] = pars->rad_cyl; |
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| 143 | dp[2] = pars->len_cyl; |
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| 144 | dp[3] = pars->rad_cap; |
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| 145 | dp[4] = pars->sld_capcyl; |
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| 146 | dp[5] = pars->sld_solv; |
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| 147 | dp[6] = pars->background; |
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| 148 | |
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| 149 | |
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| 150 | //double Pi = 4.0*atan(1.0); |
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| 151 | // Cylinder orientation |
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[4628e31] | 152 | cyl_x = sin(theta) * cos(phi); |
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| 153 | cyl_y = sin(theta) * sin(phi); |
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| 154 | cyl_z = cos(theta); |
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[339ce67] | 155 | |
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| 156 | // q vector |
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| 157 | q_z = 0; |
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| 158 | |
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| 159 | // Compute the angle btw vector q and the |
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| 160 | // axis of the cylinder |
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| 161 | cos_val = cyl_x*q_x + cyl_y*q_y + cyl_z*q_z; |
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| 162 | |
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| 163 | // The following test should always pass |
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| 164 | if (fabs(cos_val)>1.0) { |
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| 165 | printf("cyl_ana_2D: Unexpected error: cos(alpha)>1\n"); |
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| 166 | return 0; |
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| 167 | } |
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| 168 | |
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| 169 | // Note: cos(alpha) = 0 and 1 will get an |
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| 170 | // undefined value from CylKernel |
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| 171 | alpha = acos( cos_val ); |
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| 172 | |
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| 173 | // Call the IGOR library function to get the kernel |
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| 174 | answer = capcyl2d_kernel(dp, q, alpha)/sin(alpha); |
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| 175 | |
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| 176 | |
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| 177 | return answer; |
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| 178 | |
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| 179 | } |
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