1 | real form_volume(real radius, real length); |
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2 | real Iq(real q, real sld, real solvent_sld, real radius, real length); |
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3 | real Iqxy(real qx, real qy, real sld, real solvent_sld, real radius, real length, real theta, real phi); |
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4 | |
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5 | real form_volume(real radius, real length) |
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6 | { |
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7 | return M_PI*radius*radius*length; |
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8 | } |
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9 | |
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10 | real Iq(real q, |
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11 | real sld, |
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12 | real solvent_sld, |
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13 | real radius, |
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14 | real length) |
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15 | { |
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16 | const real halflength = REAL(0.5)*length; |
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17 | real summ = REAL(0.0); |
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18 | // real lower=0, upper=M_PI_2; |
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19 | for (int i=0; i<76 ;i++) { |
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20 | // translate a point in [-1,1] to a point in [lower,upper] |
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21 | //const real zi = ( Gauss76Z[i]*(upper-lower) + upper + lower )/2.0; |
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22 | const real zi = REAL(0.5)*(Gauss76Z[i]*M_PI_2 + M_PI_2); |
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23 | summ += Gauss76Wt[i] * CylKernel(q, radius, halflength, zi); |
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24 | } |
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25 | // translate dx in [-1,1] to dx in [lower,upper] |
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26 | //const real form = (upper-lower)/2.0*summ; |
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27 | const real form = summ * M_PI_4; |
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28 | |
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29 | // Multiply by contrast^2, normalize by cylinder volume and convert to cm-1 |
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30 | // NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
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31 | // The additional volume factor is for polydisperse volume normalization. |
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32 | const real s = (sld - solvent_sld) * form_volume(radius, length); |
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33 | return REAL(1.0e-4) * form * s * s; |
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34 | } |
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35 | |
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36 | |
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37 | real Iqxy(real qx, real qy, |
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38 | real sld, |
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39 | real solvent_sld, |
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40 | real radius, |
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41 | real length, |
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42 | real theta, |
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43 | real phi) |
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44 | { |
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45 | real sn, cn; // slots to hold sincos function output |
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46 | |
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47 | // Compute angle alpha between q and the cylinder axis |
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48 | SINCOS(theta*M_PI_180, sn, cn); |
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49 | // # The following correction factor exists in sasview, but it can't be |
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50 | // # right, so we are leaving it out for now. |
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51 | // const real correction = fabs(cn)*M_PI_2; |
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52 | const real q = sqrt(qx*qx+qy*qy); |
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53 | const real cos_val = cn*cos(phi*M_PI_180)*(qx/q) + sn*(qy/q); |
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54 | const real alpha = acos(cos_val); |
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55 | |
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56 | // The following is CylKernel() / sin(alpha), but we are doing it in place |
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57 | // to avoid sin(alpha)/sin(alpha) for alpha = 0. It is also a teensy bit |
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58 | // faster since we don't mulitply and divide sin(alpha). |
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59 | SINCOS(alpha, sn, cn); |
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60 | const real besarg = q*radius*sn; |
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61 | const real siarg = REAL(0.5)*q*length*cn; |
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62 | // lim_{x->0} J1(x)/x = 1/2, lim_{x->0} sin(x)/x = 1 |
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63 | const real bj = (besarg == REAL(0.0) ? REAL(0.5) : J1(besarg)/besarg); |
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64 | const real si = (siarg == REAL(0.0) ? REAL(1.0) : sin(siarg)/siarg); |
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65 | const real form = REAL(4.0)*bj*bj*si*si; |
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66 | |
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67 | // Multiply by contrast^2, normalize by cylinder volume and convert to cm-1 |
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68 | // NOTE that for this (Fournet) definition of the integral, one must MULTIPLY by Vcyl |
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69 | // The additional volume factor is for polydisperse volume normalization. |
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70 | const real s = (sld - solvent_sld) * form_volume(radius, length); |
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71 | return REAL(1.0e-4) * form * s * s; // * correction; |
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72 | } |
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