1 | /** |
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2 | * @file thgeomag.cxx |
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3 | */ |
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4 | |
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5 | /* Copyright (C) 2006 Martin Budaj |
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6 | * |
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7 | * based on GPL-licensed code by |
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8 | * Copyright (C) 2000 Edward A Williams <Ed_Williams@compuserve.com> |
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9 | * |
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10 | * -------------------------------------------------------------------- |
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11 | * This program is free software; you can redistribute it and/or modify |
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12 | * it under the terms of the GNU General Public License as published by |
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13 | * the Free Software Foundation; either version 2 of the License, or |
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14 | * any later version. |
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15 | * |
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16 | * This program is distributed in the hope that it will be useful, |
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17 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
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18 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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19 | * GNU General Public License for more details. |
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20 | * |
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21 | * You should have received a copy of the GNU General Public License |
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22 | * along with this program; if not, write to the Free Software |
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23 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
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24 | * -------------------------------------------------------------------- |
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25 | */ |
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26 | |
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27 | #include "thgeomag.h" |
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28 | |
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29 | #include <math.h> |
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30 | #include "thgeomagdata.h" |
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31 | |
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32 | #define max(a,b) (((a) > (b)) ? (a) : (b)) |
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33 | |
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34 | /*struct magfield_ { |
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35 | double X, Y, Z; |
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36 | }; |
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37 | magfield_ magfield;*/ |
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38 | |
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39 | #define nmax thgeomag_maxdeg |
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40 | #define nmaxl thgeomag_maxdeg |
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41 | |
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42 | #define pi 3.14159265358979 |
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43 | #define a 6378.137 |
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44 | #define b 6356.7523142 |
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45 | #define r_0 6371.2 |
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46 | |
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47 | double thgeomag(double lat, double lon, double h, double dat) { |
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48 | |
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49 | int n,m; |
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50 | |
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51 | static double P[nmax+1][nmax+1]; |
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52 | static double DP[nmax+1][nmax+1]; |
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53 | static double gnm[nmax+1][nmax+1]; |
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54 | static double hnm[nmax+1][nmax+1]; |
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55 | static double sm[nmax+1]; |
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56 | static double cm[nmax+1]; |
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57 | |
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58 | static double root[nmax+1]; |
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59 | static double roots[nmax+1][nmax+1][2]; |
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60 | |
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61 | |
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62 | double yearfrac,sr,r,theta,c,s,psi,fn,fn_0,B_r,B_theta,B_phi,X,Y; /* Z */ |
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63 | double sinpsi, cospsi, inv_s; |
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64 | |
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65 | static int been_here = 0; |
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66 | |
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67 | double sinlat = sin(lat); |
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68 | double coslat = cos(lat); |
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69 | |
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70 | h = h / 1000; |
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71 | |
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72 | /* convert to geocentric */ |
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73 | sr = sqrt(a*a*coslat*coslat + b*b*sinlat*sinlat); |
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74 | /* sr is effective radius */ |
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75 | theta = atan2(coslat * (h*sr + a*a), sinlat * (h*sr + b*b)); |
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76 | |
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77 | /* theta is geocentric co-latitude */ |
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78 | |
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79 | r = h*h + 2.0*h * sr + |
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80 | (a*a*a*a - ( a*a*a*a - b*b*b*b ) * sinlat*sinlat ) / |
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81 | (a*a - (a*a - b*b) * sinlat*sinlat ); |
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82 | |
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83 | r = sqrt(r); |
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84 | |
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85 | /* r is geocentric radial distance */ |
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86 | c = cos(theta); |
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87 | s = sin(theta); |
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88 | /* protect against zero divide at geographic poles */ |
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89 | inv_s = 1.0 / (s + (s == 0.)*1.0e-8); |
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90 | |
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91 | /*zero out arrays */ |
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92 | for ( n = 0; n <= nmax; n++ ) { |
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93 | for ( m = 0; m <= n; m++ ) { |
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94 | P[n][m] = 0; |
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95 | DP[n][m] = 0; |
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96 | } |
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97 | } |
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98 | |
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99 | /* diagonal elements */ |
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100 | P[0][0] = 1; |
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101 | P[1][1] = s; |
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102 | DP[0][0] = 0; |
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103 | DP[1][1] = c; |
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104 | P[1][0] = c ; |
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105 | DP[1][0] = -s; |
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106 | |
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107 | /* these values will not change for subsequent function calls */ |
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108 | if( !been_here ) { |
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109 | for ( n = 2; n <= nmax; n++ ) { |
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110 | root[n] = sqrt((2.0*n-1) / (2.0*n)); |
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111 | } |
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112 | |
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113 | for ( m = 0; m <= nmax; m++ ) { |
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114 | double mm = m*m; |
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115 | for ( n = max(m + 1, 2); n <= nmax; n++ ) { |
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116 | roots[m][n][0] = sqrt((n-1)*(n-1) - mm); |
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117 | roots[m][n][1] = 1.0 / sqrt( n*n - mm); |
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118 | } |
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119 | } |
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120 | been_here = 1; |
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121 | } |
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122 | |
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123 | for ( n=2; n <= nmax; n++ ) { |
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124 | /* double root = sqrt((2.0*n-1) / (2.0*n)); */ |
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125 | P[n][n] = P[n-1][n-1] * s * root[n]; |
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126 | DP[n][n] = (DP[n-1][n-1] * s + P[n-1][n-1] * c) * root[n]; |
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127 | } |
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128 | |
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129 | /* lower triangle */ |
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130 | for ( m = 0; m <= nmax; m++ ) { |
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131 | /* double mm = m*m; */ |
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132 | for ( n = max(m + 1, 2); n <= nmax; n++ ) { |
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133 | /* double root1 = sqrt((n-1)*(n-1) - mm); */ |
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134 | /* double root2 = 1.0 / sqrt( n*n - mm); */ |
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135 | P[n][m] = (P[n-1][m] * c * (2.0*n-1) - |
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136 | P[n-2][m] * roots[m][n][0]) * roots[m][n][1]; |
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137 | DP[n][m] = ((DP[n-1][m] * c - P[n-1][m] * s) * |
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138 | (2.0*n-1) - DP[n-2][m] * roots[m][n][0]) * roots[m][n][1]; |
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139 | } |
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140 | } |
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141 | |
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142 | /* compute gnm, hnm at dat */ |
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143 | |
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144 | int mindex = (int)((dat - thgeomag_minyear) / thgeomag_step); |
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145 | if (mindex < 0) mindex = 0; |
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146 | if (mindex > thgeomag_maxmindex) mindex = thgeomag_maxmindex; |
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147 | yearfrac = dat - thgeomag_step*mindex - thgeomag_minyear; |
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148 | |
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149 | for (n=1;n<=nmaxl;n++) { |
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150 | for (m = 0;m<=nmaxl;m++) { |
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151 | if (mindex == thgeomag_maxmindex) { |
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152 | gnm[n][m] = thgeomag_GNM[mindex][n][m] + yearfrac * thgeomag_GNMD[n][m]; |
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153 | hnm[n][m] = thgeomag_HNM[mindex][n][m] + yearfrac * thgeomag_HNMD[n][m]; |
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154 | } else { |
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155 | gnm[n][m] = thgeomag_GNM[mindex][n][m] + yearfrac / thgeomag_step * (thgeomag_GNM[mindex+1][n][m] - thgeomag_GNM[mindex][n][m]); |
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156 | hnm[n][m] = thgeomag_HNM[mindex][n][m] + yearfrac / thgeomag_step * (thgeomag_HNM[mindex+1][n][m] - thgeomag_HNM[mindex][n][m]); |
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157 | } |
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158 | } |
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159 | } |
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160 | |
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161 | /* compute sm (sin(m lon) and cm (cos(m lon)) */ |
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162 | for (m = 0;m<=nmaxl;m++) { |
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163 | sm[m] = sin(m * lon); |
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164 | cm[m] = cos(m * lon); |
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165 | } |
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166 | |
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167 | /* compute B fields */ |
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168 | B_r = 0.0; |
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169 | B_theta = 0.0; |
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170 | B_phi = 0.0; |
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171 | fn_0 = r_0/r; |
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172 | fn = fn_0 * fn_0; |
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173 | |
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174 | for ( n = 1; n <= nmaxl; n++ ) { |
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175 | double c1_n=0; |
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176 | double c2_n=0; |
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177 | double c3_n=0; |
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178 | for ( m = 0; m <= n; m++ ) { |
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179 | double tmp = (gnm[n][m] * cm[m] + hnm[n][m] * sm[m]); |
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180 | c1_n += tmp * P[n][m]; |
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181 | c2_n += tmp * DP[n][m]; |
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182 | c3_n += m * (gnm[n][m] * sm[m] - hnm[n][m] * cm[m]) * P[n][m]; |
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183 | } |
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184 | /* fn=pow(r_0/r,n+2.0); */ |
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185 | fn *= fn_0; |
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186 | B_r += (n + 1) * c1_n * fn; |
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187 | B_theta -= c2_n * fn; |
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188 | B_phi += c3_n * fn * inv_s; |
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189 | } |
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190 | |
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191 | |
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192 | |
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193 | /* Find geodetic field components: */ |
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194 | psi = theta - (pi / 2.0 - lat); |
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195 | sinpsi = sin(psi); |
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196 | cospsi = cos(psi); |
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197 | X = -B_theta * cospsi - B_r * sinpsi; |
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198 | Y = B_phi; |
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199 | /* Z = B_theta * sinpsi - B_r * cospsi; */ |
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200 | |
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201 | /* field[0]=B_r; |
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202 | field[1]=B_theta; |
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203 | field[2]=B_phi; |
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204 | field[3]=X; |
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205 | field[4]=Y; |
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206 | field[5]=Z;*/ /* output fields */ |
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207 | /* find variation in radians */ |
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208 | /* return zero variation at magnetic pole X=Y=0. */ |
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209 | /* E is positive */ |
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210 | |
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211 | /* magfield.X = X; |
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212 | magfield.Y = Y; |
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213 | magfield.Z = Z; */ |
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214 | |
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215 | return (X != 0. || Y != 0.) ? atan2(Y, X) : (double) 0.; |
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216 | } |
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217 | |
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