1 | // by jcho |
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2 | |
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3 | #include <math.h> |
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4 | |
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5 | #include "libfunc.h" |
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6 | |
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7 | #include <stdio.h> |
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8 | |
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9 | |
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10 | |
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11 | //used in Si func |
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12 | |
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13 | int factorial(int i) { |
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14 | |
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15 | int k, j; |
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16 | if (i<2){ |
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17 | return 1; |
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18 | } |
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19 | |
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20 | k=1; |
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21 | |
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22 | for(j=1;j<i;j++) { |
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23 | k=k*(j+1); |
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24 | } |
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25 | |
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26 | return k; |
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27 | |
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28 | } |
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29 | |
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30 | |
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31 | |
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32 | // Used in pearl nec model |
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33 | |
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34 | // Sine integral function: approximated within 1%!!! |
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35 | |
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36 | // integral of sin(x)/x up to namx term nmax=6 looks the best. |
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37 | |
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38 | double Si(double x) |
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39 | |
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40 | { |
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41 | int i; |
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42 | int nmax=6; |
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43 | double out; |
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44 | long double power; |
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45 | double pi = 4.0*atan(1.0); |
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46 | |
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47 | if (x >= pi*6.2/4.0){ |
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48 | double out_sin = 0.0; |
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49 | double out_cos = 0.0; |
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50 | out = pi/2.0; |
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51 | |
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52 | for (i=0; i<nmax-2; i+=1) { |
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53 | out_cos += pow(-1.0, i) * (double)factorial(2*i) / pow(x, 2*i+1); |
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54 | out_sin += pow(-1.0, i) * (double)factorial(2*i+1) / pow(x, 2*i+2); |
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55 | } |
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56 | |
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57 | out -= cos(x) * out_cos; |
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58 | out -= sin(x) * out_sin; |
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59 | return out; |
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60 | } |
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61 | |
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62 | out = 0.0; |
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63 | |
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64 | for (i=0; i<nmax; i+=1) { |
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65 | if (i==0) { |
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66 | out += x; |
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67 | continue; |
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68 | } |
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69 | |
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70 | power = pow(x,(2 * i + 1)); |
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71 | out += (double)pow(-1, i) * power / ((2.0 * (double)i + 1.0) * (double)factorial(2 * i + 1)); |
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72 | |
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73 | //printf ("Si=%g %g %d\n", x, out, i); |
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74 | } |
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75 | |
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76 | return out; |
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77 | } |
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78 | |
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79 | |
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80 | |
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81 | double sinc(double x) |
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82 | { |
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83 | if (x==0.0){ |
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84 | return 1.0; |
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85 | } |
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86 | return sin(x)/x; |
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87 | } |
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88 | |
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89 | //The code calculating magnetic sld below seems to be not used. |
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90 | //Keeping it in order to check if it is not breaking anything. |
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91 | // calculate magnetic sld and return total sld |
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92 | // bn : contrast (not just sld of the layer) |
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93 | // m0: max mag of M; mtheta: angle from x-z plane; |
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94 | // mphi: angle (anti-clock-wise)of x-z projection(M) from x axis |
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95 | // spinfraci: the fraction of UP among UP+Down (before sample) |
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96 | // spinfracf: the fraction of UP among UP+Down (after sample and before detector) |
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97 | // spintheta: angle (anti-clock-wise) between neutron spin(up) and x axis |
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98 | // Note: all angles are in degrees. |
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99 | // void cal_msld(polar_sld *p_sld, int isangle, double qx, double qy, double bn, |
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100 | // double m01, double mtheta1, double mphi1, |
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101 | // double spinfraci, double spinfracf, double spintheta) |
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102 | // { |
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103 | // //locals |
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104 | // double q_x = qx; |
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105 | // double q_y = qy; |
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106 | // double sld = bn; |
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107 | // int is_angle = isangle; |
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108 | // double pi = 4.0*atan(1.0); |
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109 | // double s_theta = spintheta * pi/180.0; |
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110 | // double m_max = m01; |
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111 | // double m_phi = mphi1; |
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112 | // double m_theta = mtheta1; |
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113 | // double in_spin = spinfraci; |
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114 | // double out_spin = spinfracf; |
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115 | // |
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116 | // double m_perp = 0.0; |
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117 | // double m_perp_z = 0.0; |
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118 | // double m_perp_y = 0.0; |
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119 | // double m_perp_x = 0.0; |
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120 | // double m_sigma_x = 0.0; |
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121 | // double m_sigma_z = 0.0; |
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122 | // double m_sigma_y = 0.0; |
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123 | // //double b_m = 0.0; |
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124 | // double q_angle = 0.0; |
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125 | // double mx = 0.0; |
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126 | // double my = 0.0; |
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127 | // double mz = 0.0; |
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128 | // double uu = sld; |
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129 | // double dd = sld; |
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130 | // double re_ud = 0.0; |
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131 | // double im_ud = 0.0; |
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132 | // double re_du = 0.0; |
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133 | // double im_du = 0.0; |
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134 | // const double norm=outspin; |
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135 | |
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136 | |
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137 | // The norm is needed to make sure that the scattering cross sections are |
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138 | //correctly weighted, such that the sum of spin-resolved measurements adds up to |
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139 | // the unpolarised or half-polarised scattering cross section. No intensity weighting |
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140 | // needed on the incoming polariser side (assuming that a user), has normalised |
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141 | // to the incoming flux with polariser in for SANSPOl and unpolarised beam, respectively. |
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142 | |
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143 | //if (out_spin < 0.5){norm=1-out_spin;} |
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144 | //else{norm=out_spin;} |
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145 | |
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146 | // //No mag means no further calculation |
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147 | // if (isangle>0) { |
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148 | // if (m_max < 1.0e-32){ |
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149 | // uu = sqrt(in_spin * out_spin/ norm) * uu ; |
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150 | // dd = sqrt((1.0 - in_spin) * (1.0 - out_spin)/ norm) * dd ; |
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151 | // } |
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152 | // } |
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153 | // else if (fabs(m_max)< 1.0e-32 && fabs(m_phi)< 1.0e-32 && fabs(m_theta)< 1.0e-32){ |
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154 | // uu = sqrt(in_spin * out_spin/ norm) * uu; |
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155 | // dd = sqrt((1.0 - in_spin) * (1.0 - out_spin)/ norm) * dd; |
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156 | // } else { |
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157 | // |
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158 | // //These are needed because of the precision of inputs |
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159 | // if (in_spin < 0.0) in_spin = 0.0; |
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160 | // if (in_spin > 1.0) in_spin = 1.0; |
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161 | // if (out_spin < 0.0) out_spin = 0.0; |
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162 | // if (out_spin > 1.0) out_spin = 1.0; |
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163 | // |
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164 | // if (q_x == 0.0) q_angle = pi / 2.0; |
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165 | // else q_angle = atan(q_y/q_x); |
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166 | // if (q_y < 0.0 && q_x < 0.0) q_angle -= pi; |
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167 | // else if (q_y > 0.0 && q_x < 0.0) q_angle += pi; |
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168 | // |
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169 | // q_angle = pi/2.0 - q_angle; |
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170 | // if (q_angle > pi) q_angle -= 2.0 * pi; |
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171 | // else if (q_angle < -pi) q_angle += 2.0 * pi; |
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172 | // |
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173 | // if (fabs(q_x) < 1.0e-16 && fabs(q_y) < 1.0e-16){ |
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174 | // m_perp = 0.0; |
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175 | // } |
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176 | // else { |
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177 | // m_perp = m_max; |
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178 | // } |
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179 | // if (is_angle > 0){ |
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180 | // m_phi *= pi/180.0; |
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181 | // m_theta *= pi/180.0; |
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182 | // mx = m_perp * cos(m_theta) * cos(m_phi); |
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183 | // my = m_perp * sin(m_theta); |
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184 | // mz = -(m_perp * cos(m_theta) * sin(m_phi)); |
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185 | // } |
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186 | // else{ |
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187 | // mx = m_perp; |
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188 | // my = m_phi; |
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189 | // mz = m_theta; |
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190 | // } |
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191 | // //ToDo: simplify these steps |
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192 | // // m_perp1 -m_perp2 |
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193 | // m_perp_x = (mx) * cos(q_angle); |
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194 | // m_perp_x -= (my) * sin(q_angle); |
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195 | // m_perp_y = m_perp_x; |
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196 | // m_perp_x *= cos(-q_angle); |
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197 | // m_perp_y *= sin(-q_angle); |
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198 | // m_perp_z = mz; |
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199 | // |
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200 | // m_sigma_x = (m_perp_x * cos(-s_theta) - m_perp_y * sin(-s_theta)); |
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201 | // m_sigma_y = (m_perp_x * sin(-s_theta) + m_perp_y * cos(-s_theta)); |
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202 | // m_sigma_z = (m_perp_z); |
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203 | // |
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204 | // //Find b |
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205 | // uu += m_sigma_x; |
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206 | // dd -= m_sigma_x; |
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207 | // re_ud = m_sigma_y; |
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208 | // re_du = m_sigma_y; |
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209 | // im_ud = m_sigma_z; |
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210 | // im_du = -m_sigma_z; |
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211 | // |
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212 | // uu = sqrt((in_spin) * (out_spin)/ norm) * uu; |
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213 | // dd = sqrt((1.0 - in_spin) * (1.0 - out_spin)/ norm) * dd; |
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214 | // |
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215 | // re_ud = sqrt(in_spin * (1.0 - out_spin)/ norm) * re_ud; |
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216 | // im_ud = sqrt(in_spin * (1.0 - out_spin)/ norm) * im_ud; |
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217 | // re_du = sqrt((1.0 - in_spin) * out_spin/ norm) * re_du; |
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218 | // im_du = sqrt((1.0 - in_spin) * out_spin/ norm) * im_du; |
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219 | // } |
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220 | // p_sld->uu = uu; |
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221 | // p_sld->dd = dd; |
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222 | // p_sld->re_ud = re_ud; |
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223 | // p_sld->im_ud = im_ud; |
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224 | // p_sld->re_du = re_du; |
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225 | // p_sld->im_du = im_du; |
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226 | // } |
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227 | |
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228 | |
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229 | /** Modifications below by kieranrcampbell@gmail.com |
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230 | Institut Laue-Langevin, July 2012 |
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231 | **/ |
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232 | |
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233 | /** |
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234 | Wojtek's comment Mar 22 2016: The remaing code can mostly likely be deleated |
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235 | Keeping it in order to check if it is not breaking anything |
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236 | **/ |
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237 | |
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238 | /* |
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239 | #define ITMAX 100 |
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240 | #define EPS 3.0e-7 |
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241 | #define FPMIN 1.0e-30 |
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242 | |
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243 | void gser(float *gamser, float a, float x, float *gln) { |
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244 | int n; |
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245 | float sum,del,ap; |
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246 | |
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247 | *gln = lgamma(a); |
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248 | if(x <= 0.0) { |
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249 | if (x < 0.0) printf("Error: x less than 0 in routine gser"); |
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250 | *gamser = 0.0; |
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251 | return; |
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252 | } else { |
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253 | ap = a; |
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254 | del = sum = 1.0/a; |
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255 | |
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256 | for(n=1;n<=ITMAX;n++) { |
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257 | ++ap; |
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258 | del *= x/ap; |
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259 | sum += del; |
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260 | if(fabs(del) < fabs(sum)*EPS) { |
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261 | *gamser = sum * exp(-x + a * log(x) - (*gln)); |
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262 | return; |
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263 | } |
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264 | } |
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265 | printf("a too large, ITMAX too small in routine gser"); |
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266 | return; |
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267 | |
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268 | } |
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269 | |
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270 | } |
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271 | */ |
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272 | /** |
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273 | Implements the incomplete gamma function Q(a,x) evaluated by its continued fraction |
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274 | representation |
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275 | **/ |
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276 | /* |
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277 | void gcf(float *gammcf, float a, float x, float *gln) { |
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278 | int i; |
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279 | float an,b,c,d,del,h; |
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280 | |
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281 | *gln = lgamma(a); |
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282 | b = x+1.0-a; |
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283 | c = 1.0/FPMIN; |
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284 | d = 1.0/b; |
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285 | h=d; |
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286 | for (i=1;i <= ITMAX; i++) { |
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287 | an = -i*(i-a); |
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288 | b += 2.0; |
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289 | d = an*d + b; |
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290 | if (fabs(d) < FPMIN) d = FPMIN; |
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291 | c = b+an/c; |
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292 | if (fabs(c) < FPMIN) c = FPMIN; |
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293 | d = 1.0/d; |
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294 | del = d*c; |
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295 | h += del; |
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296 | if (fabs(del-1.0) < EPS) break; |
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297 | } |
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298 | if (i > ITMAX) printf("a too large, ITMAX too small in gcf"); |
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299 | *gammcf = exp(-x+a*log(x)-(*gln))*h; |
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300 | return; |
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301 | } |
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302 | */ |
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303 | /** |
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304 | Represents incomplete error function, P(a,x) |
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305 | **/ |
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306 | /* |
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307 | float gammp(float a, float x) { |
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308 | float gamser,gammcf,gln; |
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309 | if(x < 0.0 || a <= 0.0) printf("Invalid arguments in routine gammp"); |
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310 | if (x < (a+1.0)) { |
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311 | gser(&gamser,a,x,&gln); |
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312 | return gamser; |
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313 | } else { |
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314 | gcf(&gammcf,a,x,&gln); |
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315 | return 1.0 - gammcf; |
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316 | } |
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317 | } |
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318 | */ |
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319 | /** |
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320 | Implementation of the error function, erf(x) |
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321 | **/ |
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322 | /* |
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323 | float erff(float x) { |
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324 | return x < 0.0 ? -gammp(0.5,x*x) : gammp(0.5,x*x); |
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325 | } |
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326 | */ |
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