[1325] | 1 | //#--------------------------------------------------------------------------- |
---|
| 2 | //# pks_maths.cc: Mathematical functions for Parkes single-dish data reduction |
---|
| 3 | //#--------------------------------------------------------------------------- |
---|
| 4 | //# Copyright (C) 1994-2006 |
---|
| 5 | //# Associated Universities, Inc. Washington DC, USA. |
---|
| 6 | //# |
---|
| 7 | //# This library is free software; you can redistribute it and/or modify it |
---|
| 8 | //# under the terms of the GNU Library General Public License as published by |
---|
| 9 | //# the Free Software Foundation; either version 2 of the License, or (at your |
---|
| 10 | //# option) any later version. |
---|
| 11 | //# |
---|
| 12 | //# This library is distributed in the hope that it will be useful, but WITHOUT |
---|
| 13 | //# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
---|
| 14 | //# FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library General Public |
---|
| 15 | //# License for more details. |
---|
| 16 | //# |
---|
| 17 | //# You should have received a copy of the GNU Library General Public License |
---|
| 18 | //# along with this library; if not, write to the Free Software Foundation, |
---|
| 19 | //# Inc., 675 Massachusetts Ave, Cambridge, MA 02139, USA. |
---|
| 20 | //# |
---|
| 21 | //# Correspondence concerning AIPS++ should be addressed as follows: |
---|
| 22 | //# Internet email: aips2-request@nrao.edu. |
---|
| 23 | //# Postal address: AIPS++ Project Office |
---|
| 24 | //# National Radio Astronomy Observatory |
---|
| 25 | //# 520 Edgemont Road |
---|
| 26 | //# Charlottesville, VA 22903-2475 USA |
---|
| 27 | //# |
---|
| 28 | //# Original: Mark Calabretta |
---|
| 29 | //# $Id: pks_maths.cc,v 1.5 2006/05/19 00:12:35 mcalabre Exp $ |
---|
| 30 | //---------------------------------------------------------------------------- |
---|
| 31 | |
---|
| 32 | // AIPS++ includes. |
---|
| 33 | #include <casa/aips.h> |
---|
| 34 | #include <casa/math.h> |
---|
| 35 | #include <casa/Arrays/ArrayMath.h> |
---|
| 36 | #include <casa/Arrays/Vector.h> |
---|
| 37 | #include <casa/BasicSL/Constants.h> |
---|
| 38 | #include <casa/Utilities/GenSort.h> |
---|
| 39 | |
---|
| 40 | // Parkes includes. |
---|
| 41 | #include <atnf/pks/pks_maths.h> |
---|
| 42 | |
---|
| 43 | |
---|
| 44 | //----------------------------------------------------------------------- nint |
---|
| 45 | |
---|
| 46 | // Nearest integral value; halfway cases are rounded to the integral value |
---|
| 47 | // larger in value. No check is made for integer overflow. |
---|
| 48 | |
---|
| 49 | Int nint(Double v) |
---|
| 50 | { |
---|
| 51 | return Int(floor(v + 0.5)); |
---|
| 52 | } |
---|
| 53 | |
---|
| 54 | //---------------------------------------------------------------------- anint |
---|
| 55 | |
---|
| 56 | // Nearest integral value; halfway cases are rounded to the integral value |
---|
| 57 | // larger in value. |
---|
| 58 | |
---|
| 59 | Double anint(Double v) |
---|
| 60 | { |
---|
| 61 | return floor(v + 0.5); |
---|
| 62 | } |
---|
| 63 | |
---|
| 64 | //---------------------------------------------------------------------- round |
---|
| 65 | |
---|
| 66 | // Round value v to the nearest integral multiple of precision p. |
---|
| 67 | |
---|
| 68 | Double round(Double v, Double p) |
---|
| 69 | { |
---|
| 70 | return p * floor(v/p + 0.5); |
---|
| 71 | } |
---|
| 72 | |
---|
| 73 | //--------------------------------------------------------------------- median |
---|
| 74 | |
---|
| 75 | // Compute the weighted median value of an array. |
---|
| 76 | |
---|
| 77 | Float median(const Vector<Float> &v, const Vector<Float> &wgt) |
---|
| 78 | { |
---|
| 79 | uInt nElem = v.nelements(); |
---|
| 80 | if (nElem == 0) return 0.0f; |
---|
| 81 | |
---|
| 82 | // Generate the sort index. |
---|
| 83 | Vector<uInt> sortindex(nElem); |
---|
| 84 | GenSortIndirect<Float>::sort(sortindex, v); |
---|
| 85 | |
---|
| 86 | // Find the middle weight. |
---|
| 87 | Float wgt_2 = sum(wgt)/2.0f; |
---|
| 88 | |
---|
| 89 | // Find the corresponding vector element. |
---|
| 90 | Float weight = 0.0f; |
---|
| 91 | Float accwgt = 0.0f; |
---|
| 92 | uInt j1 = 0; |
---|
| 93 | uInt j2; |
---|
| 94 | for (j2 = 0; j2 < nElem; j2++) { |
---|
| 95 | weight = wgt(sortindex(j2)); |
---|
| 96 | if (weight == 0.0f) { |
---|
| 97 | // Ignore zero-weight data; |
---|
| 98 | continue; |
---|
| 99 | } |
---|
| 100 | |
---|
| 101 | // The accumulated weight. |
---|
| 102 | accwgt += weight; |
---|
| 103 | |
---|
| 104 | if (accwgt <= wgt_2) { |
---|
| 105 | // Keep looping. |
---|
| 106 | j1 = j2; |
---|
| 107 | } else { |
---|
| 108 | break; |
---|
| 109 | } |
---|
| 110 | } |
---|
| 111 | |
---|
| 112 | // Compute weighted median. |
---|
| 113 | Float v1 = v(sortindex(j1)); |
---|
| 114 | Float v2 = v(sortindex(j2)); |
---|
| 115 | |
---|
| 116 | // Compute pro-rata value from below. |
---|
| 117 | Float dw = wgt_2 - (accwgt - weight); |
---|
| 118 | v1 += (v2 - v1) * dw / weight; |
---|
| 119 | |
---|
| 120 | // Find next non-zero-weight value. |
---|
| 121 | for (j2++ ; j2 < nElem; j2++) { |
---|
| 122 | weight = wgt(sortindex(j2)); |
---|
| 123 | if (weight != 0.0f) { |
---|
| 124 | break; |
---|
| 125 | } |
---|
| 126 | } |
---|
| 127 | |
---|
| 128 | if (j2 < nElem) { |
---|
| 129 | // Compute pro-rata value from above. |
---|
| 130 | Float v3 = v(sortindex(j2)); |
---|
| 131 | |
---|
| 132 | v2 += (v3 - v2) * dw / weight; |
---|
| 133 | } |
---|
| 134 | |
---|
| 135 | return (v1 + v2)/2.0f; |
---|
| 136 | } |
---|
| 137 | |
---|
| 138 | //---------------------------------------------------------------- angularDist |
---|
| 139 | |
---|
| 140 | // Determine the angular distance between two directions (angles in radians). |
---|
| 141 | |
---|
| 142 | Double angularDist(Double lng0, Double lat0, Double lng, Double lat) |
---|
| 143 | { |
---|
| 144 | Double costheta = sin(lat0)*sin(lat) + cos(lat0)*cos(lat)*cos(lng0-lng); |
---|
| 145 | return acos(costheta); |
---|
| 146 | } |
---|
| 147 | |
---|
| 148 | //--------------------------------------------------------------------- distPA |
---|
| 149 | |
---|
| 150 | void distPA(Double lng0, Double lat0, Double lng, Double lat, Double &dist, |
---|
| 151 | Double &pa) |
---|
| 152 | |
---|
| 153 | // Determine the generalized position angle of the field point (lng,lat) from |
---|
| 154 | // the reference point (lng0,lat0) and the angular distance between them |
---|
| 155 | // (angles in radians). |
---|
| 156 | |
---|
| 157 | { |
---|
| 158 | // Euler angles which rotate the coordinate frame so that (lng0,lat0) is |
---|
| 159 | // at the pole of the new system, with the pole of the old system at zero |
---|
| 160 | // longitude in the new. |
---|
| 161 | Double phi0 = C::pi_2 + lng0; |
---|
| 162 | Double theta = C::pi_2 - lat0; |
---|
| 163 | Double phi = -C::pi_2; |
---|
| 164 | |
---|
| 165 | // Rotate the field point to the new system. |
---|
| 166 | Double alpha, beta; |
---|
| 167 | eulerx(lng, lat, phi0, theta, phi, alpha, beta); |
---|
| 168 | |
---|
| 169 | dist = C::pi_2 - beta; |
---|
| 170 | pa = -alpha; |
---|
| 171 | if (pa < -C::pi) pa = pa + C::_2pi; |
---|
| 172 | } |
---|
| 173 | |
---|
| 174 | //--------------------------------------------------------------------- eulerx |
---|
| 175 | |
---|
| 176 | void eulerx(Double lng0, Double lat0, Double phi0, Double theta, Double phi, |
---|
| 177 | Double &lng1, Double &lat1) |
---|
| 178 | |
---|
| 179 | // Applies the Euler angle based transformation of spherical coordinates. |
---|
| 180 | // |
---|
| 181 | // phi0 Longitude of the ascending node in the old system, radians. The |
---|
| 182 | // ascending node is the point of intersection of the equators of |
---|
| 183 | // the two systems such that the equator of the new system crosses |
---|
| 184 | // from south to north as viewed in the old system. |
---|
| 185 | // |
---|
| 186 | // theta Angle between the poles of the two systems, radians. THETA is |
---|
| 187 | // positive for a positive rotation about the ascending node. |
---|
| 188 | // |
---|
| 189 | // phi Longitude of the ascending node in the new system, radians. |
---|
| 190 | |
---|
| 191 | { |
---|
| 192 | // Compute intermediaries. |
---|
| 193 | Double lng0p = lng0 - phi0; |
---|
| 194 | Double slng0p = sin(lng0p); |
---|
| 195 | Double clng0p = cos(lng0p); |
---|
| 196 | Double slat0 = sin(lat0); |
---|
| 197 | Double clat0 = cos(lat0); |
---|
| 198 | Double ctheta = cos(theta); |
---|
| 199 | Double stheta = sin(theta); |
---|
| 200 | |
---|
| 201 | Double x = clat0*clng0p; |
---|
| 202 | Double y = clat0*slng0p*ctheta + slat0*stheta; |
---|
| 203 | |
---|
| 204 | // Longitude in the new system. |
---|
| 205 | if (x != 0.0 || y != 0.0) { |
---|
| 206 | lng1 = phi + atan2(y, x); |
---|
| 207 | } else { |
---|
| 208 | // Longitude at the poles in the new system is consistent with that |
---|
| 209 | // specified in the old system. |
---|
| 210 | lng1 = phi + lng0p; |
---|
| 211 | } |
---|
| 212 | lng1 = fmod(lng1, C::_2pi); |
---|
| 213 | if (lng1 < 0.0) lng1 += C::_2pi; |
---|
| 214 | |
---|
| 215 | lat1 = asin(slat0*ctheta - clat0*stheta*slng0p); |
---|
| 216 | } |
---|
| 217 | |
---|
| 218 | //------------------------------------------------------------------------ sol |
---|
| 219 | |
---|
| 220 | // Low precision coordinates of the Sun (accurate to 1 arcmin between 1800 and |
---|
| 221 | // 2200) from http://aa.usno.navy.mil/faq/docs/SunApprox.html matches closely |
---|
| 222 | // that in the Astronomical Almanac. |
---|
| 223 | |
---|
| 224 | void sol(Double mjd, Double &elng, Double &ra, Double &dec) |
---|
| 225 | { |
---|
| 226 | Double d2r = C::pi/180.0; |
---|
| 227 | |
---|
| 228 | // Number of days since J2000.0. |
---|
| 229 | Double d = mjd - 51544.5; |
---|
| 230 | |
---|
| 231 | // Mean longitude and mean anomaly of the Sun (deg). |
---|
| 232 | Double L = 280.459 + 0.98564736*d; |
---|
| 233 | Double g = 357.529 + 0.98560028*d; |
---|
| 234 | |
---|
| 235 | // Apparent ecliptic longitude corrected for aberration (deg). |
---|
| 236 | g *= d2r; |
---|
| 237 | elng = L + 1.915*sin(g) + 0.020*sin(g+g); |
---|
| 238 | elng = fmod(elng, 360.0); |
---|
| 239 | if (elng < 0.0) elng += 360.0; |
---|
| 240 | |
---|
| 241 | // Obliquity of the ecliptic (deg). |
---|
| 242 | Double epsilon = 23.439 - 0.00000036*d; |
---|
| 243 | |
---|
| 244 | // Transform ecliptic to equatorial coordinates. |
---|
| 245 | elng *= d2r; |
---|
| 246 | epsilon *= d2r; |
---|
| 247 | ra = atan2(cos(epsilon)*sin(elng), cos(elng)); |
---|
| 248 | dec = asin(sin(epsilon)*sin(elng)); |
---|
| 249 | if (ra < 0.0) ra += C::_2pi; |
---|
| 250 | } |
---|
| 251 | |
---|
| 252 | //------------------------------------------------------------------------ gst |
---|
| 253 | |
---|
| 254 | // Greenwich mean sidereal time, and low precision Greenwich apparent sidereal |
---|
| 255 | // time, both in radian, from http://aa.usno.navy.mil/faq/docs/GAST.html. UT1 |
---|
| 256 | // is given in MJD form. |
---|
| 257 | |
---|
| 258 | void gst(Double ut1, Double &gmst, Double &gast) |
---|
| 259 | { |
---|
| 260 | Double d2r = C::pi/180.0; |
---|
| 261 | |
---|
| 262 | Double d = ut1 - 51544.5; |
---|
| 263 | Double d0 = int(ut1) - 51544.5; |
---|
| 264 | Double h = 24.0*(d - d0); |
---|
| 265 | Double t = d / 35625.0; |
---|
| 266 | |
---|
| 267 | // GMST (hr). |
---|
| 268 | gmst = 6.697374558 + 0.06570982441908*d0 + 1.00273790935*h + 0.000026*t*t; |
---|
| 269 | gmst = fmod(gmst, 24.0); |
---|
| 270 | |
---|
| 271 | // Longitude of the ascending node of the Moon (deg). |
---|
| 272 | Double Omega = 125.04 - 0.052954*d; |
---|
| 273 | |
---|
| 274 | // Mean Longitude of the Sun (deg). |
---|
| 275 | Double L = 280.47 + 0.98565*d; |
---|
| 276 | |
---|
| 277 | // Obliquity of the ecliptic (deg). |
---|
| 278 | Double epsilon = 23.4393 - 0.0000004*d; |
---|
| 279 | |
---|
| 280 | // Approximate nutation in longitude (hr). |
---|
| 281 | Double dpsi = -0.000319*sin(Omega*d2r) - 0.000024*sin((L+L)*d2r); |
---|
| 282 | |
---|
| 283 | // Equation of the equinoxes (hr). |
---|
| 284 | Double eqeq = dpsi*cos(epsilon*d2r); |
---|
| 285 | |
---|
| 286 | // GAST (hr). |
---|
| 287 | gast = gmst + eqeq; |
---|
| 288 | gast = fmod(gast, 24.0); |
---|
| 289 | |
---|
| 290 | // Convert to radian. |
---|
| 291 | gmst *= C::pi/12.0; |
---|
| 292 | gast *= C::pi/12.0; |
---|
| 293 | } |
---|
| 294 | |
---|
| 295 | //----------------------------------------------------------------------- azel |
---|
| 296 | |
---|
| 297 | // Convert (ra,dec) to (az,el), from |
---|
| 298 | // http://aa.usno.navy.mil/faq/docs/Alt_Az.html. Position as a Cartesian |
---|
| 299 | // triplet in m, UT1 in MJD form, and all angles in radian. |
---|
| 300 | |
---|
| 301 | void azel(const Vector<Double> position, Double ut1, Double ra, Double dec, |
---|
| 302 | Double &az, Double &el) |
---|
| 303 | { |
---|
| 304 | // Get gocentric longitude and latitude (rad). |
---|
| 305 | Double x = position(0); |
---|
| 306 | Double y = position(1); |
---|
| 307 | Double z = position(2); |
---|
| 308 | Double r = sqrt(x*x + y*y + z*z); |
---|
| 309 | Double lng = atan2(y, x); |
---|
| 310 | Double lat = asin(z/r); |
---|
| 311 | |
---|
| 312 | // Get GAST (rad). |
---|
| 313 | Double gast, gmst; |
---|
| 314 | gst(ut1, gmst, gast); |
---|
| 315 | |
---|
| 316 | // Local hour angle (rad). |
---|
| 317 | Double ha = (gast + lng) - ra; |
---|
| 318 | |
---|
| 319 | // Azimuth and elevation (rad). |
---|
| 320 | az = atan2(cos(dec)*sin(ha), cos(dec)*sin(lat)*cos(ha) - sin(dec)*cos(lat)); |
---|
| 321 | if (az < 0.0) az += C::_2pi; |
---|
| 322 | el = asin(cos(dec)*cos(lat)*cos(ha) + sin(dec)*sin(lat)); |
---|
| 323 | } |
---|
| 324 | |
---|
| 325 | //---------------------------------------------------------------------- solel |
---|
| 326 | |
---|
| 327 | // Compute the Solar elevation using the above functions. |
---|
| 328 | |
---|
| 329 | Double solel(const Vector<Double> position, Double ut1) |
---|
| 330 | { |
---|
| 331 | Double az, dec, el, elng, gast, gmst, ra; |
---|
| 332 | sol(ut1, elng, ra, dec); |
---|
| 333 | gst(ut1, gmst, gast); |
---|
| 334 | azel(position, ut1, ra, dec, az, el); |
---|
| 335 | return el; |
---|
| 336 | } |
---|