1 | //#--------------------------------------------------------------------------- |
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2 | //# pks_maths.cc: Mathematical functions for Parkes single-dish data reduction |
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3 | //#--------------------------------------------------------------------------- |
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4 | //# livedata - processing pipeline for single-dish, multibeam spectral data. |
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5 | //# Copyright (C) 2004-2009, Australia Telescope National Facility, CSIRO |
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6 | //# |
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7 | //# This file is part of livedata. |
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8 | //# |
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9 | //# livedata is free software: you can redistribute it and/or modify it under |
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10 | //# the terms of the GNU General Public License as published by the Free |
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11 | //# Software Foundation, either version 3 of the License, or (at your option) |
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12 | //# any later version. |
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13 | //# |
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14 | //# livedata is distributed in the hope that it will be useful, but WITHOUT |
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15 | //# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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16 | //# FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for |
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17 | //# more details. |
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18 | //# |
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19 | //# You should have received a copy of the GNU General Public License along |
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20 | //# with livedata. If not, see <http://www.gnu.org/licenses/>. |
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21 | //# |
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22 | //# Correspondence concerning livedata may be directed to: |
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23 | //# Internet email: mcalabre@atnf.csiro.au |
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24 | //# Postal address: Dr. Mark Calabretta |
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25 | //# Australia Telescope National Facility, CSIRO |
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26 | //# PO Box 76 |
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27 | //# Epping NSW 1710 |
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28 | //# AUSTRALIA |
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29 | //# |
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30 | //# http://www.atnf.csiro.au/computing/software/livedata.html |
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31 | //# $Id: pks_maths.cc,v 1.7 2009-09-29 07:45:02 cal103 Exp $ |
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32 | //#--------------------------------------------------------------------------- |
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33 | //# Original: 2004/07/16 Mark Calabretta |
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34 | //#--------------------------------------------------------------------------- |
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35 | |
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36 | // AIPS++ includes. |
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37 | #include <casa/aips.h> |
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38 | #include <casa/math.h> |
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39 | #include <casa/Arrays/ArrayMath.h> |
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40 | #include <casa/Arrays/Vector.h> |
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41 | #include <casa/BasicSL/Constants.h> |
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42 | #include <casa/Utilities/GenSort.h> |
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43 | |
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44 | // Parkes includes. |
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45 | #include <atnf/pks/pks_maths.h> |
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46 | |
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47 | |
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48 | //----------------------------------------------------------------------- nint |
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49 | |
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50 | // Nearest integral value; halfway cases are rounded to the integral value |
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51 | // larger in value. No check is made for integer overflow. |
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52 | |
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53 | Int nint(Double v) |
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54 | { |
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55 | return Int(floor(v + 0.5)); |
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56 | } |
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57 | |
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58 | //---------------------------------------------------------------------- anint |
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59 | |
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60 | // Nearest integral value; halfway cases are rounded to the integral value |
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61 | // larger in value. |
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62 | |
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63 | Double anint(Double v) |
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64 | { |
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65 | return floor(v + 0.5); |
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66 | } |
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67 | |
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68 | //---------------------------------------------------------------------- round |
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69 | |
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70 | // Round value v to the nearest integral multiple of precision p. |
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71 | |
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72 | Double round(Double v, Double p) |
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73 | { |
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74 | return p * floor(v/p + 0.5); |
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75 | } |
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76 | |
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77 | //--------------------------------------------------------------------- median |
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78 | |
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79 | // Compute the weighted median value of an array. |
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80 | |
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81 | Float median(const Vector<Float> &v, const Vector<Float> &wgt) |
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82 | { |
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83 | uInt nElem = v.nelements(); |
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84 | if (nElem == 0) return 0.0f; |
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85 | |
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86 | // Generate the sort index. |
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87 | Vector<uInt> sortindex(nElem); |
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88 | GenSortIndirect<Float>::sort(sortindex, v); |
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89 | |
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90 | // Find the middle weight. |
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91 | Float wgt_2 = sum(wgt)/2.0f; |
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92 | |
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93 | // Find the corresponding vector element. |
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94 | Float weight = 0.0f; |
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95 | Float accwgt = 0.0f; |
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96 | uInt j1 = 0; |
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97 | uInt j2; |
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98 | for (j2 = 0; j2 < nElem; j2++) { |
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99 | weight = wgt(sortindex(j2)); |
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100 | if (weight == 0.0f) { |
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101 | // Ignore zero-weight data; |
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102 | continue; |
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103 | } |
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104 | |
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105 | // The accumulated weight. |
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106 | accwgt += weight; |
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107 | |
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108 | if (accwgt <= wgt_2) { |
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109 | // Keep looping. |
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110 | j1 = j2; |
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111 | } else { |
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112 | break; |
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113 | } |
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114 | } |
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115 | |
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116 | // Compute weighted median. |
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117 | Float v1 = v(sortindex(j1)); |
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118 | Float v2 = v(sortindex(j2)); |
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119 | |
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120 | // Compute pro-rata value from below. |
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121 | Float dw = wgt_2 - (accwgt - weight); |
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122 | v1 += (v2 - v1) * dw / weight; |
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123 | |
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124 | // Find next non-zero-weight value. |
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125 | for (j2++ ; j2 < nElem; j2++) { |
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126 | weight = wgt(sortindex(j2)); |
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127 | if (weight != 0.0f) { |
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128 | break; |
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129 | } |
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130 | } |
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131 | |
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132 | if (j2 < nElem) { |
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133 | // Compute pro-rata value from above. |
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134 | Float v3 = v(sortindex(j2)); |
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135 | |
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136 | v2 += (v3 - v2) * dw / weight; |
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137 | } |
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138 | |
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139 | return (v1 + v2)/2.0f; |
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140 | } |
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141 | |
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142 | //---------------------------------------------------------------- angularDist |
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143 | |
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144 | // Determine the angular distance between two directions (angles in radians). |
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145 | |
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146 | Double angularDist(Double lng0, Double lat0, Double lng, Double lat) |
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147 | { |
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148 | Double costheta = sin(lat0)*sin(lat) + cos(lat0)*cos(lat)*cos(lng0-lng); |
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149 | return acos(costheta); |
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150 | } |
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151 | |
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152 | //--------------------------------------------------------------------- distPA |
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153 | |
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154 | void distPA(Double lng0, Double lat0, Double lng, Double lat, Double &dist, |
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155 | Double &pa) |
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156 | |
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157 | // Determine the generalized position angle of the field point (lng,lat) from |
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158 | // the reference point (lng0,lat0) and the angular distance between them |
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159 | // (angles in radians). |
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160 | |
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161 | { |
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162 | // Euler angles which rotate the coordinate frame so that (lng0,lat0) is |
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163 | // at the pole of the new system, with the pole of the old system at zero |
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164 | // longitude in the new. |
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165 | Double phi0 = C::pi_2 + lng0; |
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166 | Double theta = C::pi_2 - lat0; |
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167 | Double phi = -C::pi_2; |
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168 | |
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169 | // Rotate the field point to the new system. |
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170 | Double alpha, beta; |
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171 | eulerx(lng, lat, phi0, theta, phi, alpha, beta); |
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172 | |
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173 | dist = C::pi_2 - beta; |
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174 | pa = -alpha; |
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175 | if (pa < -C::pi) pa = pa + C::_2pi; |
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176 | } |
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177 | |
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178 | //--------------------------------------------------------------------- eulerx |
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179 | |
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180 | void eulerx(Double lng0, Double lat0, Double phi0, Double theta, Double phi, |
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181 | Double &lng1, Double &lat1) |
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182 | |
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183 | // Applies the Euler angle based transformation of spherical coordinates. |
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184 | // |
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185 | // phi0 Longitude of the ascending node in the old system, radians. The |
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186 | // ascending node is the point of intersection of the equators of |
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187 | // the two systems such that the equator of the new system crosses |
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188 | // from south to north as viewed in the old system. |
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189 | // |
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190 | // theta Angle between the poles of the two systems, radians. THETA is |
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191 | // positive for a positive rotation about the ascending node. |
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192 | // |
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193 | // phi Longitude of the ascending node in the new system, radians. |
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194 | |
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195 | { |
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196 | // Compute intermediaries. |
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197 | Double lng0p = lng0 - phi0; |
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198 | Double slng0p = sin(lng0p); |
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199 | Double clng0p = cos(lng0p); |
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200 | Double slat0 = sin(lat0); |
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201 | Double clat0 = cos(lat0); |
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202 | Double ctheta = cos(theta); |
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203 | Double stheta = sin(theta); |
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204 | |
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205 | Double x = clat0*clng0p; |
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206 | Double y = clat0*slng0p*ctheta + slat0*stheta; |
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207 | |
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208 | // Longitude in the new system. |
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209 | if (x != 0.0 || y != 0.0) { |
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210 | lng1 = phi + atan2(y, x); |
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211 | } else { |
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212 | // Longitude at the poles in the new system is consistent with that |
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213 | // specified in the old system. |
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214 | lng1 = phi + lng0p; |
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215 | } |
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216 | lng1 = fmod(lng1, C::_2pi); |
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217 | if (lng1 < 0.0) lng1 += C::_2pi; |
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218 | |
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219 | lat1 = asin(slat0*ctheta - clat0*stheta*slng0p); |
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220 | } |
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221 | |
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222 | //------------------------------------------------------------------------ sol |
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223 | |
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224 | // Low precision coordinates of the Sun (accurate to 1 arcmin between 1800 and |
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225 | // 2200) from http://aa.usno.navy.mil/faq/docs/SunApprox.html matches closely |
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226 | // that in the Astronomical Almanac. |
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227 | |
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228 | void sol(Double mjd, Double &elng, Double &ra, Double &dec) |
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229 | { |
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230 | Double d2r = C::pi/180.0; |
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231 | |
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232 | // Number of days since J2000.0. |
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233 | Double d = mjd - 51544.5; |
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234 | |
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235 | // Mean longitude and mean anomaly of the Sun (deg). |
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236 | Double L = 280.459 + 0.98564736*d; |
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237 | Double g = 357.529 + 0.98560028*d; |
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238 | |
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239 | // Apparent ecliptic longitude corrected for aberration (deg). |
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240 | g *= d2r; |
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241 | elng = L + 1.915*sin(g) + 0.020*sin(g+g); |
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242 | elng = fmod(elng, 360.0); |
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243 | if (elng < 0.0) elng += 360.0; |
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244 | |
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245 | // Obliquity of the ecliptic (deg). |
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246 | Double epsilon = 23.439 - 0.00000036*d; |
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247 | |
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248 | // Transform ecliptic to equatorial coordinates. |
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249 | elng *= d2r; |
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250 | epsilon *= d2r; |
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251 | ra = atan2(cos(epsilon)*sin(elng), cos(elng)); |
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252 | dec = asin(sin(epsilon)*sin(elng)); |
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253 | if (ra < 0.0) ra += C::_2pi; |
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254 | } |
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255 | |
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256 | //------------------------------------------------------------------------ gst |
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257 | |
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258 | // Greenwich mean sidereal time, and low precision Greenwich apparent sidereal |
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259 | // time, both in radian, from http://aa.usno.navy.mil/faq/docs/GAST.html. UT1 |
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260 | // is given in MJD form. |
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261 | |
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262 | void gst(Double ut1, Double &gmst, Double &gast) |
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263 | { |
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264 | Double d2r = C::pi/180.0; |
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265 | |
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266 | Double d = ut1 - 51544.5; |
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267 | Double d0 = int(ut1) - 51544.5; |
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268 | Double h = 24.0*(d - d0); |
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269 | Double t = d / 35625.0; |
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270 | |
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271 | // GMST (hr). |
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272 | gmst = 6.697374558 + 0.06570982441908*d0 + 1.00273790935*h + 0.000026*t*t; |
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273 | gmst = fmod(gmst, 24.0); |
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274 | |
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275 | // Longitude of the ascending node of the Moon (deg). |
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276 | Double Omega = 125.04 - 0.052954*d; |
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277 | |
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278 | // Mean Longitude of the Sun (deg). |
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279 | Double L = 280.47 + 0.98565*d; |
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280 | |
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281 | // Obliquity of the ecliptic (deg). |
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282 | Double epsilon = 23.4393 - 0.0000004*d; |
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283 | |
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284 | // Approximate nutation in longitude (hr). |
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285 | Double dpsi = -0.000319*sin(Omega*d2r) - 0.000024*sin((L+L)*d2r); |
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286 | |
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287 | // Equation of the equinoxes (hr). |
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288 | Double eqeq = dpsi*cos(epsilon*d2r); |
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289 | |
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290 | // GAST (hr). |
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291 | gast = gmst + eqeq; |
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292 | gast = fmod(gast, 24.0); |
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293 | |
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294 | // Convert to radian. |
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295 | gmst *= C::pi/12.0; |
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296 | gast *= C::pi/12.0; |
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297 | } |
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298 | |
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299 | //----------------------------------------------------------------------- azel |
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300 | |
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301 | // Convert (ra,dec) to (az,el). Position as a Cartesian triplet in m, UT1 in |
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302 | // MJD form, and all angles in radian. |
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303 | |
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304 | void azel(const Vector<Double> position, Double ut1, Double ra, Double dec, |
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305 | Double &az, Double &el) |
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306 | { |
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307 | // Get geocentric longitude and latitude (rad). |
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308 | Double x = position(0); |
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309 | Double y = position(1); |
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310 | Double z = position(2); |
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311 | Double r = sqrt(x*x + y*y + z*z); |
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312 | Double lng = atan2(y, x); |
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313 | Double lat = asin(z/r); |
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314 | |
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315 | // Get GAST (rad). |
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316 | Double gast, gmst; |
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317 | gst(ut1, gmst, gast); |
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318 | |
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319 | // Local hour angle (rad). |
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320 | Double ha = (gast + lng) - ra; |
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321 | |
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322 | // Azimuth and elevation (rad). |
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323 | az = atan2(-cos(dec)*sin(ha), |
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324 | sin(dec)*cos(lat) - cos(dec)*sin(lat)*cos(ha)); |
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325 | el = asin(sin(dec)*sin(lat) + cos(dec)*cos(lat)*cos(ha)); |
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326 | |
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327 | if (az < 0.0) az += C::_2pi; |
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328 | } |
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329 | |
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330 | //---------------------------------------------------------------------- solel |
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331 | |
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332 | // Compute the Solar elevation using the above functions. |
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333 | |
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334 | Double solel(const Vector<Double> position, Double ut1) |
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335 | { |
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336 | Double az, dec, el, elng, gast, gmst, ra; |
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337 | sol(ut1, elng, ra, dec); |
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338 | gst(ut1, gmst, gast); |
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339 | azel(position, ut1, ra, dec, az, el); |
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340 | return el; |
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341 | } |
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