void iauAtciq(double rc, double dc,
double pr, double pd, double px, double rv,
iauASTROM *astrom, double *ri, double *di)
/*
** - - - - - - - - -
** i a u A t c i q
** - - - - - - - - -
**
** Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
** star-independent astrometry parameters.
**
** Use of this function is appropriate when efficiency is important and
** where many star positions are to be transformed for one date. The
** star-independent parameters can be obtained by calling one of the
** functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
**
** If the parallax and proper motions are zero the iauAtciqz function
** can be used instead.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** rc,dc double ICRS RA,Dec at J2000.0 (radians)
** pr double RA proper motion (radians/year; Note 3)
** pd double Dec proper motion (radians/year)
** px double parallax (arcsec)
** rv double radial velocity (km/s, +ve if receding)
** astrom iauASTROM* star-independent astrometry parameters:
** pmt double PM time interval (SSB, Julian years)
** eb double[3] SSB to observer (vector, au)
** eh double[3] Sun to observer (unit vector)
** em double distance from Sun to observer (au)
** v double[3] barycentric observer velocity (vector, c)
** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
** bpn double[3][3] bias-precession-nutation matrix
** along double longitude + s' (radians)
** xpl double polar motion xp wrt local meridian (radians)
** ypl double polar motion yp wrt local meridian (radians)
** sphi double sine of geodetic latitude
** cphi double cosine of geodetic latitude
** diurab double magnitude of diurnal aberration vector
** eral double "local" Earth rotation angle (radians)
** refa double refraction constant A (radians)
** refb double refraction constant B (radians)
**
** Returned:
** ri,di double CIRS RA,Dec (radians)
**
** Notes:
**
** 1) All the vectors are with respect to BCRS axes.
**
** 2) Star data for an epoch other than J2000.0 (for example from the
** Hipparcos catalog, which has an epoch of J1991.25) will require a
** preliminary call to iauPmsafe before use.
**
** 3) The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
**
** Called:
** iauPmpx proper motion and parallax
** iauLdsun light deflection by the Sun
** iauAb stellar aberration
** iauRxp product of r-matrix and pv-vector
** iauC2s p-vector to spherical
** iauAnp normalize angle into range 0 to 2pi
**
** This revision: 2013 October 9
**
** SOFA release 2016-05-03
**
** Copyright (C) 2016 IAU SOFA Board. See notes at end.
*/
{
double pco[3], pnat[3], ppr[3], pi[3], w;
/* Proper motion and parallax, giving BCRS coordinate direction. */
iauPmpx(rc, dc, pr, pd, px, rv, astrom->pmt, astrom->eb, pco);
/* Light deflection by the Sun, giving BCRS natural direction. */
iauLdsun(pco, astrom->eh, astrom->em, pnat);
/* Aberration, giving GCRS proper direction. */
iauAb(pnat, astrom->v, astrom->em, astrom->bm1, ppr);
/* Bias-precession-nutation, giving CIRS proper direction. */
iauRxp(astrom->bpn, ppr, pi);
/* CIRS RA,Dec. */
iauC2s(pi, &w, di);
*ri = iauAnp(w);
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2016
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void iauAticqn(double ri, double di, iauASTROM *astrom,
int n, iauLDBODY b[], double *rc, double *dc)
/*
** - - - - - - - - -
** i a u A t i c q n
** - - - - - - - - -
**
** Quick CIRS to ICRS astrometric place transformation, given the star-
** independent astrometry parameters plus a list of light-deflecting
** bodies.
**
** Use of this function is appropriate when efficiency is important and
** where many star positions are all to be transformed for one date.
** The star-independent astrometry parameters can be obtained by
** calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
** or iauApcs[13].
*
* If the only light-deflecting body to be taken into account is the
* Sun, the iauAticq function can be used instead.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** ri,di double CIRS RA,Dec (radians)
** astrom iauASTROM* star-independent astrometry parameters:
** pmt double PM time interval (SSB, Julian years)
** eb double[3] SSB to observer (vector, au)
** eh double[3] Sun to observer (unit vector)
** em double distance from Sun to observer (au)
** v double[3] barycentric observer velocity (vector, c)
** bm1 double sqrt(1-|v|^2): reciprocal of Lorenz factor
** bpn double[3][3] bias-precession-nutation matrix
** along double longitude + s' (radians)
** xpl double polar motion xp wrt local meridian (radians)
** ypl double polar motion yp wrt local meridian (radians)
** sphi double sine of geodetic latitude
** cphi double cosine of geodetic latitude
** diurab double magnitude of diurnal aberration vector
** eral double "local" Earth rotation angle (radians)
** refa double refraction constant A (radians)
** refb double refraction constant B (radians)
** n int number of bodies (Note 3)
** b iauLDBODY[n] data for each of the n bodies (Notes 3,4):
** bm double mass of the body (solar masses, Note 5)
** dl double deflection limiter (Note 6)
** pv [2][3] barycentric PV of the body (au, au/day)
**
** Returned:
** rc,dc double ICRS astrometric RA,Dec (radians)
**
** Notes:
**
** 1) Iterative techniques are used for the aberration and light
** deflection corrections so that the functions iauAticqn and
** iauAtciqn are accurate inverses; even at the edge of the Sun's
** disk the discrepancy is only about 1 nanoarcsecond.
**
** 2) If the only light-deflecting body to be taken into account is the
** Sun, the iauAticq function can be used instead.
**
** 3) The struct b contains n entries, one for each body to be
** considered. If n = 0, no gravitational light deflection will be
** applied, not even for the Sun.
**
** 4) The struct b should include an entry for the Sun as well as for
** any planet or other body to be taken into account. The entries
** should be in the order in which the light passes the body.
**
** 5) In the entry in the b struct for body i, the mass parameter
** b[i].bm can, as required, be adjusted in order to allow for such
** effects as quadrupole field.
**
** 6) The deflection limiter parameter b[i].dl is phi^2/2, where phi is
** the angular separation (in radians) between star and body at
** which limiting is applied. As phi shrinks below the chosen
** threshold, the deflection is artificially reduced, reaching zero
** for phi = 0. Example values suitable for a terrestrial
** observer, together with masses, are as follows:
**
** body i b[i].bm b[i].dl
**
** Sun 1.0 6e-6
** Jupiter 0.00095435 3e-9
** Saturn 0.00028574 3e-10
**
** 7) For efficiency, validation of the contents of the b array is
** omitted. The supplied masses must be greater than zero, the
** position and velocity vectors must be right, and the deflection
** limiter greater than zero.
**
** Called:
** iauS2c spherical coordinates to unit vector
** iauTrxp product of transpose of r-matrix and p-vector
** iauZp zero p-vector
** iauAb stellar aberration
** iauLdn light deflection by n bodies
** iauC2s p-vector to spherical
** iauAnp normalize angle into range +/- pi
**
** This revision: 2013 October 9
**
** SOFA release 2015-02-09
**
** Copyright (C) 2015 IAU SOFA Board. See notes at end.
*/
{
int j, i;
double pi[3], ppr[3], pnat[3], pco[3], w, d[3], before[3], r2, r,
after[3];
/* CIRS RA,Dec to Cartesian. */
iauS2c(ri, di, pi);
/* Bias-precession-nutation, giving GCRS proper direction. */
iauTrxp(astrom->bpn, pi, ppr);
/* Aberration, giving GCRS natural direction. */
iauZp(d);
for (j = 0; j < 2; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = ppr[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
iauAb(before, astrom->v, astrom->em, astrom->bm1, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = ppr[i] - d[i];
pnat[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pnat[i] /= r;
}
}
/* Light deflection, giving BCRS coordinate direction. */
iauZp(d);
for (j = 0; j < 5; j++) {
r2 = 0.0;
for (i = 0; i < 3; i++) {
w = pnat[i] - d[i];
before[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
before[i] /= r;
}
iauLdn(n, b, astrom->eb, before, after);
r2 = 0.0;
for (i = 0; i < 3; i++) {
d[i] = after[i] - before[i];
w = pnat[i] - d[i];
pco[i] = w;
r2 += w*w;
}
r = sqrt(r2);
for (i = 0; i < 3; i++) {
pco[i] /= r;
}
}
/* ICRS astrometric RA,Dec. */
iauC2s(pco, &w, dc);
*rc = iauAnp(w);
/* Finished. */
/*----------------------------------------------------------------------
**
** Copyright (C) 2015
** Standards Of Fundamental Astronomy Board
** of the International Astronomical Union.
**
** =====================
** SOFA Software License
** =====================
**
** NOTICE TO USER:
**
** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
** CONDITIONS WHICH APPLY TO ITS USE.
**
** 1. The Software is owned by the IAU SOFA Board ("SOFA").
**
** 2. Permission is granted to anyone to use the SOFA software for any
** purpose, including commercial applications, free of charge and
** without payment of royalties, subject to the conditions and
** restrictions listed below.
**
** 3. You (the user) may copy and distribute SOFA source code to others,
** and use and adapt its code and algorithms in your own software,
** on a world-wide, royalty-free basis. That portion of your
** distribution that does not consist of intact and unchanged copies
** of SOFA source code files is a "derived work" that must comply
** with the following requirements:
**
** a) Your work shall be marked or carry a statement that it
** (i) uses routines and computations derived by you from
** software provided by SOFA under license to you; and
** (ii) does not itself constitute software provided by and/or
** endorsed by SOFA.
**
** b) The source code of your derived work must contain descriptions
** of how the derived work is based upon, contains and/or differs
** from the original SOFA software.
**
** c) The names of all routines in your derived work shall not
** include the prefix "iau" or "sofa" or trivial modifications
** thereof such as changes of case.
**
** d) The origin of the SOFA components of your derived work must
** not be misrepresented; you must not claim that you wrote the
** original software, nor file a patent application for SOFA
** software or algorithms embedded in the SOFA software.
**
** e) These requirements must be reproduced intact in any source
** distribution and shall apply to anyone to whom you have
** granted a further right to modify the source code of your
** derived work.
**
** Note that, as originally distributed, the SOFA software is
** intended to be a definitive implementation of the IAU standards,
** and consequently third-party modifications are discouraged. All
** variations, no matter how minor, must be explicitly marked as
** such, as explained above.
**
** 4. You shall not cause the SOFA software to be brought into
** disrepute, either by misuse, or use for inappropriate tasks, or
** by inappropriate modification.
**
** 5. The SOFA software is provided "as is" and SOFA makes no warranty
** as to its use or performance. SOFA does not and cannot warrant
** the performance or results which the user may obtain by using the
** SOFA software. SOFA makes no warranties, express or implied, as
** to non-infringement of third party rights, merchantability, or
** fitness for any particular purpose. In no event will SOFA be
** liable to the user for any consequential, incidental, or special
** damages, including any lost profits or lost savings, even if a
** SOFA representative has been advised of such damages, or for any
** claim by any third party.
**
** 6. The provision of any version of the SOFA software under the terms
** and conditions specified herein does not imply that future
** versions will also be made available under the same terms and
** conditions.
*
** In any published work or commercial product which uses the SOFA
** software directly, acknowledgement (see www.iausofa.org) is
** appreciated.
**
** Correspondence concerning SOFA software should be addressed as
** follows:
**
** By email: [email protected]
** By post: IAU SOFA Center
** HM Nautical Almanac Office
** UK Hydrographic Office
** Admiralty Way, Taunton
** Somerset, TA1 2DN
** United Kingdom
**
**--------------------------------------------------------------------*/
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
double *vOrig;
double *obsVel;
mxArray *retMATLAB;
double c, *retVec;
size_t numVec;
if(nrhs<2||nrhs>3) {
mexErrMsgTxt("Incorrect number of inputs.");
return;
}
if(nlhs>1) {
mexErrMsgTxt("Wrong number of outputs.");
return;
}
numVec=mxGetN(prhs[0]);
if(numVec!=mxGetN(prhs[1])||mxGetM(prhs[0])!=3||mxGetM(prhs[1])!=3) {
mexErrMsgTxt("The input vectors have the wrong dimensionality.");
return;
}
checkRealDoubleArray(prhs[0]);
vOrig=(double*)mxGetData(prhs[0]);
checkRealDoubleArray(prhs[1]);
obsVel=(double*)mxGetData(prhs[1]);
c=getScalarMatlabClassConst("Constants","speedOfLight");
//Allocate space for the return values.
retMATLAB=mxCreateDoubleMatrix(3,numVec,mxREAL);
retVec=(double*)mxGetData(retMATLAB);
//If the third parameter is provided, then use the algorithm from the IAU.
if(nrhs>2) {
double AU, *sunDist;
size_t curVec;
//Needed to convert units.
AU=getScalarMatlabClassConst("Constants","AstronomialUnit");
//If the dimensionality is wrong.
if(!((mxGetM(prhs[2])==1&&mxGetN(prhs[2])==numVec)||(mxGetM(prhs[2])==numVec&&mxGetN(prhs[2])==1))) {
mxDestroyArray(retMATLAB);
mexErrMsgTxt("The input vectors have the wrong dimensionality.");
return;
}
checkRealDoubleArray(prhs[0]);
sunDist=(double*)mxGetData(prhs[2]);
for(curVec=0;curVec<numVec;curVec++) {
double vecMag,unitVec[3];
double v[3];
double s;
double bm1;
//Get a unit direction vector and magnitude.
iauPn(vOrig+3*curVec, &vecMag, unitVec);
//Convert the velocity to units of the speed of light.
v[0]=obsVel[3*curVec]/c;
v[1]=obsVel[3*curVec+1]/c;
v[2]=obsVel[3*curVec+2]/c;
//The distance to the sun in AU.
s=sunDist[curVec]/AU;
//The reciprocal of the Lorentz factor.
bm1=sqrt(1-(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]));
//Perform the correction with the IAU's function.
iauAb(unitVec, v, s, bm1,retVec+3*curVec);
//Set the magnitude back to what it was.
retVec[3*curVec]*=vecMag;
retVec[3*curVec+1]*=vecMag;
retVec[3*curVec+2]*=vecMag;
}
} else {
//If the distance to the sun is not given, then just perform a normal
//special relativistic correction.
size_t curVec;
for(curVec=0;curVec<numVec;curVec++) {
double vecMag,lightVec[3];
//Get a unit direction vector and magnitude.
iauPn(vOrig+3*curVec, &vecMag, lightVec);
//The light is in direction lightVec with speed c
lightVec[0]*=c;
lightVec[1]*=c;
lightVec[2]*=c;
//The light travels at speed c with true direction uPosition.
//Add the velocity vector of the observer to that of light.
relVecAddC(c,obsVel+3*curVec,lightVec,retVec+3*curVec);
//Because one vector had a magnitude of c, the returned vector
//must have the same magnitude. Restore the previous magnitude.
retVec[3*curVec]*=vecMag/c;
retVec[3*curVec+1]*=vecMag/c;
retVec[3*curVec+2]*=vecMag/c;
}
}
//Set the return value.
plhs[0]=retMATLAB;
}
