void iauC2txy(double tta, double ttb, double uta, double utb,
double x, double y, double xp, double yp,
double rc2t[3][3])
/*
** - - - - - - - - -
** i a u C 2 t x y
** - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1,
** the CIP coordinates and the polar motion. IAU 2000.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** x,y double Celestial Intermediate Pole (Note 2)
** xp,yp double coordinates of the pole (radians, Note 3)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 4)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any o
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The Celestial Intermediate Pole coordinates are the x,y
** components of the unit vector in the Geocentric Celestial
** Reference System.
**
** 3) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 4) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), ERA is the Earth
** Rotation Angle and RPOM is the polar motion matrix.
**
** 5) Although its name does not include "00", This function is in fact
** specific to the IAU 2000 models.
**
** Called:
** iauC2ixy celestial-to-intermediate matrix, given X,Y
** iauEra00 Earth rotation angle, IAU 2000
** iauSp00 the TIO locator s', IERS 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** This revision: 2009 April 1
**
** Original version 2012-03-01
**
** Copyright (C) 2013 Naoki Arita. See notes at end.
*/
{
double rc2i[3][3], era, sp, rpom[3][3];
/* Form the celestial-to-intermediate matrix for this TT. */
iauC2ixy(tta, ttb, x, y, rc2i);
/* Predict the Earth rotation angle for this UT1. */
era = iauEra00(uta, utb);
/* Estimate s'. */
sp = iauSp00(tta, ttb);
/* Form the polar motion matrix. */
iauPom00(xp, yp, sp, rpom);
/* Combine to form the celestial-to-terrestrial matrix. */
iauC2tcio(rc2i, era, rpom, rc2t);
return;
/*----------------------------------------------------------------------
**
** Celes is a wrapper of the SOFA Library for Ruby.
**
** This file is redistributed and relicensed in accordance with
** the SOFA Software License (http://www.iausofa.org/tandc.html).
**
** The original library is available from IAU Standards of
** Fundamental Astronomy (http://www.iausofa.org/).
**
**
**
**
**
** Copyright (C) 2013, Naoki Arita
** All rights reserved.
**
** Redistribution and use in source and binary forms, with or without
** modification, are permitted provided that the following conditions
** are met:
**
** 1 Redistributions of source code must retain the above copyright
** notice, this list of conditions and the following disclaimer.
**
** 2 Redistributions in binary form must reproduce the above copyright
** notice, this list of conditions and the following disclaimer in
** the documentation and/or other materials provided with the
** distribution.
**
** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
** the International Astronomical Union nor the names of its
** contributors may be used to endorse or promote products derived
** from this software without specific prior written permission.
**
** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
** POSSIBILITY OF SUCH DAMAGE.
**
**--------------------------------------------------------------------*/
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
size_t numRow,numVec;
mxArray *retMat;
double *retData;
double ITRS2TIRS[3][3];//Inverse polar motion matrix
double *xVec, TT1, TT2;
double xp=0;
double yp=0;//The polar motion coordinates
if(nrhs<3||nrhs>4){
mexErrMsgTxt("Wrong number of inputs");
}
if(nlhs>2) {
mexErrMsgTxt("Wrong number of outputs.");
}
numRow = mxGetM(prhs[0]);
numVec = mxGetN(prhs[0]);
if(!(numRow==3||numRow==6)) {
mexErrMsgTxt("The input vector has a bad dimensionality.");
}
checkRealDoubleArray(prhs[0]);
xVec=(double*)mxGetData(prhs[0]);
TT1=getDoubleFromMatlab(prhs[1]);
TT2=getDoubleFromMatlab(prhs[2]);
//If xpyp should be found using the function getEOP.
if(nrhs<4||mxIsEmpty(prhs[3])) {
mxArray *retVals[1];
double *xpyp;
mxArray *JulUTCMATLAB[2];
double JulUTC[2];
int retVal;
//Get the time in UTC to look up the parameters by going to TAI and
//then UTC.
retVal=iauTttai(TT1, TT2, &JulUTC[0], &JulUTC[1]);
if(retVal!=0) {
mexErrMsgTxt("An error occurred computing TAI.");
}
retVal=iauTaiutc(JulUTC[0], JulUTC[1], &JulUTC[0], &JulUTC[1]);
switch(retVal){
case 1:
mexWarnMsgTxt("Dubious Date entered.");
break;
case -1:
mexErrMsgTxt("Unacceptable date entered");
break;
default:
break;
}
JulUTCMATLAB[0]=doubleMat2Matlab(&JulUTC[0],1,1);
JulUTCMATLAB[1]=doubleMat2Matlab(&JulUTC[1],1,1);
//Get the Earth orientation parameters for the given date.
mexCallMATLAB(1,retVals,2,JulUTCMATLAB,"getEOP");
mxDestroyArray(JulUTCMATLAB[0]);
mxDestroyArray(JulUTCMATLAB[1]);
checkRealDoubleArray(retVals[0]);
if(mxGetM(retVals[0])!=2||mxGetN(retVals[0])!=1) {
mxDestroyArray(retVals[0]);
mexErrMsgTxt("Error using the getEOP function.");
return;
}
xpyp=(double*)mxGetData(retVals[0]);
xp=xpyp[0];
yp=xpyp[1];
//Free the returned array.
mxDestroyArray(retVals[0]);
}
//Get polar motion coordinates, if given.
if(nrhs>3&&!mxIsEmpty(prhs[3])) {
size_t dim1, dim2;
checkRealDoubleArray(prhs[3]);
dim1 = mxGetM(prhs[3]);
dim2 = mxGetN(prhs[3]);
if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) {
double *xpyp=(double*)mxGetData(prhs[3]);
xp=xpyp[0];
yp=xpyp[1];
} else {
mexErrMsgTxt("The polar motion coordinates have the wrong dimensionality.");
return;
}
}
//Get the rotation matrix from TIRS to ITRS.
{
double sp;
double TIRS2ITRS[3][3];//Polar motion matrix
//Get the Terrestrial Intermediate Origin (TIO) locator s' in
//radians
sp=iauSp00(TT1,TT2);
//Get the polar motion matrix
iauPom00(xp,yp,sp,TIRS2ITRS);
//The inverse polar motion matrix is given by the transpose of the
//polar motion matrix.
iauTr(TIRS2ITRS, ITRS2TIRS);
}
//Allocate space for the return vectors.
retMat=mxCreateDoubleMatrix(numRow,numVec,mxREAL);
retData=(double*)mxGetData(retMat);
{
size_t curVec;
for(curVec=0;curVec<numVec;curVec++) {
//Multiply the position vector with the rotation matrix.
iauRxp(ITRS2TIRS, xVec+numRow*curVec, retData+numRow*curVec);
//Multiply the velocity vector with the rotation matrix.
if(numRow>3) {
double *velITRS=xVec+numRow*curVec+3;//Velocity in ITRS
double *retDataVel=retData+numRow*curVec+3;//Velocity in ITRS
//Convert velocity from ITRS to TIRS.
iauRxp(ITRS2TIRS, velITRS, retDataVel);
}
}
}
plhs[0]=retMat;
if(nlhs>1) {
double *elPtr;
size_t i,j;
plhs[1]=mxCreateDoubleMatrix(3,3,mxREAL);
elPtr=(double*)mxGetData(plhs[1]);
for (i=0;i<3;i++) {
for(j=0;j<3;j++) {
elPtr[i+3*j]=ITRS2TIRS[i][j];
}
}
}
}
void mexFunction(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[]) {
size_t numRow,numVec;
mxArray *retMat;
double *xVec, *retData;
double TT1, TT2, UT11, UT12;
//The if-statements below should properly initialize all of the EOP.
//The following initializations to zero are to suppress warnings when
//compiling with -Wconditional-uninitialized.
double dX=0;
double dY=0;
double xp=0;
double yp=0;
double deltaT=0;
double LOD=0;
double ITRS2GCRS[3][3];
double TIRS2GCRS[3][3];
double invrPom[3][3];//Inverse polar motion matrix. TIRS=IPOM*ITRS.
double Omega[3];
if(nrhs<3||nrhs>7){
mexErrMsgTxt("Wrong number of inputs");
}
if(nlhs>2) {
mexErrMsgTxt("Wrong number of outputs.");
return;
}
checkRealDoubleArray(prhs[0]);
numRow = mxGetM(prhs[0]);
numVec = mxGetN(prhs[0]);
if(!(numRow==3||numRow==6)) {
mexErrMsgTxt("The input vector has a bad dimensionality.");
}
xVec=(double*)mxGetData(prhs[0]);
TT1=getDoubleFromMatlab(prhs[1]);
TT2=getDoubleFromMatlab(prhs[2]);
//If some values from the function getEOP will be needed.
if(nrhs<=6||mxIsEmpty(prhs[3])||mxIsEmpty(prhs[4])||mxIsEmpty(prhs[5])||mxIsEmpty(prhs[6])) {
mxArray *retVals[5];
double *xpyp, *dXdY;
mxArray *JulUTCMATLAB[2];
double JulUTC[2];
int retVal;
//Get the time in UTC to look up the parameters by going to TAI and
//then UTC.
retVal=iauTttai(TT1, TT2, &JulUTC[0], &JulUTC[1]);
if(retVal!=0) {
mexErrMsgTxt("An error occurred computing TAI.");
}
retVal=iauTaiutc(JulUTC[0], JulUTC[1], &JulUTC[0], &JulUTC[1]);
switch(retVal){
case 1:
mexWarnMsgTxt("Dubious Date entered.");
break;
case -1:
mexErrMsgTxt("Unacceptable date entered");
break;
default:
break;
}
JulUTCMATLAB[0]=doubleMat2Matlab(&JulUTC[0],1,1);
JulUTCMATLAB[1]=doubleMat2Matlab(&JulUTC[1],1,1);
//Get the Earth orientation parameters for the given date.
mexCallMATLAB(5,retVals,2,JulUTCMATLAB,"getEOP");
mxDestroyArray(JulUTCMATLAB[0]);
mxDestroyArray(JulUTCMATLAB[1]);
checkRealDoubleArray(retVals[0]);
checkRealDoubleArray(retVals[1]);
if(mxGetM(retVals[0])!=2||mxGetN(retVals[0])!=1||mxGetM(retVals[1])!=2||mxGetN(retVals[1])!=1) {
mxDestroyArray(retVals[0]);
mxDestroyArray(retVals[1]);
mxDestroyArray(retVals[2]);
mxDestroyArray(retVals[3]);
mxDestroyArray(retVals[4]);
mexErrMsgTxt("Error using the getEOP function.");
return;
}
xpyp=(double*)mxGetData(retVals[0]);
dXdY=(double*)mxGetData(retVals[1]);
xp=xpyp[0];
yp=xpyp[1];
dX=dXdY[0];
dY=dXdY[1];
//This is TT-UT1
deltaT=getDoubleFromMatlab(retVals[3]);
LOD=getDoubleFromMatlab(retVals[4]);
//Free the returned arrays.
mxDestroyArray(retVals[0]);
mxDestroyArray(retVals[1]);
mxDestroyArray(retVals[2]);
mxDestroyArray(retVals[3]);
mxDestroyArray(retVals[4]);
}
//If deltaT=TT-UT1 is given
if(nrhs>3&&!mxIsEmpty(prhs[3])) {
deltaT=getDoubleFromMatlab(prhs[3]);
}
//Obtain UT1 from terestrial time and deltaT.
iauTtut1(TT1, TT2, deltaT, &UT11, &UT12);
//If no values for the polar motion coordinates are given, then use
//zeros.
if(nrhs>4&&!mxIsEmpty(prhs[4])) {
size_t dim1, dim2;
checkRealDoubleArray(prhs[4]);
dim1 = mxGetM(prhs[4]);
dim2 = mxGetN(prhs[4]);
if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) {
double *xpyp=(double*)mxGetData(prhs[4]);
xp=xpyp[0];
yp=xpyp[1];
} else {
mexErrMsgTxt("The celestial pole offsets have the wrong dimensionality.");
return;
}
}
if(nrhs>5&&!mxIsEmpty(prhs[5])) {
size_t dim1, dim2;
checkRealDoubleArray(prhs[5]);
dim1 = mxGetM(prhs[5]);
dim2 = mxGetN(prhs[5]);
if((dim1==2&&dim2==1)||(dim1==1&&dim2==2)) {
double *dXdY=(double*)mxGetData(prhs[5]);
dX=dXdY[0];
dY=dXdY[1];
} else {
mexErrMsgTxt("The polar motion coordinates have the wrong dimensionality.");
return;
}
}
//If LOD is given
if(nrhs>6&&!mxIsEmpty(prhs[6])) {
LOD=getDoubleFromMatlab(prhs[6]);
}
//Compute the rotation matrix for going from ITRS to GCRS as well as
//the instantaneous vector angular momentum due to the Earth's rotation
//in TIRS coordinates.
{
double x, y, s, era, sp;
double rpom[3][3], rc2i[3][3];
double GCRS2ITRS[3][3];
double omega;
//Get the X,Y coordinates of the Celestial Intermediate Pole (CIP) and
//the Celestial Intermediate Origin (CIO) locator s, using the IAU 2006
//precession and IAU 2000A nutation models.
iauXys06a(TT1, TT2, &x, &y, &s);
//Add the CIP offsets.
x += dX;
y += dY;
//Get the GCRS-to-CIRS matrix
iauC2ixys(x, y, s, rc2i);
//Find the Earth rotation angle for the given UT1 time.
era = iauEra00(UT11, UT12);
//Get the Terrestrial Intermediate Origin (TIO) locator s' in radians
sp=iauSp00(TT1,TT2);
//Get the polar motion matrix
iauPom00(xp,yp,sp,rpom);
//Combine the GCRS-to-CIRS matrix, the Earth rotation angle, and the
//polar motion matrix to get a transformation matrix to get the
//rotation matrix to go from GCRS to ITRS.
iauC2tcio(rc2i, era, rpom,GCRS2ITRS);
//To go from the ITRS to the GCRS, we need to use the inverse rotation
//matrix, which is just the transpose of the rotation matrix.
iauTr(GCRS2ITRS, ITRS2GCRS);
//Next, to be able to transform the velocity, the rotation of the Earth
//has to be taken into account. This requires first transforming from
//ITRS to TIRS coordinates, where the rotational axis is the z-axis.
//That transformation requires the inverse polar motion matrix, which,
//being a rotation matrix, is given by its transpose.
iauTr(rpom, invrPom);
//Then, one must transform from TIRS to GCRS, which can be done by
//taking the inverse of the rotation matrix from GCRS to ITRS computed
//using the identity matrix for polar motion (i.e. no polar motion
//means leaving it in the TIRS.
{
double rident[3][3]={{1,0,0},{0,1,0},{0,0,1}};
double GCRS2TIRS[3][3];
iauC2tcio(rc2i, era, rident,GCRS2TIRS);
iauTr(GCRS2TIRS, TIRS2GCRS);
}
//The angular velocity vector of the Earth in the TIRS in radians.
omega=getScalarMatlabClassConst("Constants","IERSMeanEarthRotationRate");
//Adjust for LOD
omega=omega*(1-LOD/86400.0);//86400.0 is the number of seconds in a TT day.
Omega[0]=0;
Omega[1]=0;
Omega[2]=omega;
}
//Allocate space for the return vectors.
retMat=mxCreateDoubleMatrix(numRow,numVec,mxREAL);
retData=(double*)mxGetData(retMat);
{
size_t curVec;
for(curVec=0;curVec<numVec;curVec++) {
//Multiply the position vector with the rotation matrix.
iauRxp(ITRS2GCRS, xVec+numRow*curVec, retData+numRow*curVec);
//If a velocity vector was given.
if(numRow>3) {
double posTIRS[3];
double velTIRS[3];
double *posITRS=xVec+numRow*curVec;
double *velITRS=xVec+numRow*curVec+3;//Velocity in GCRS
double *retDataVel=retData+numRow*curVec+3;
double rotVel[3];
//If a velocity was provided with the position, then first
//convert into the TIRS, then account for the rotation of
//the Earth, then rotate into the GCRS.
//Convert velocity from ITRS to TIRS.
iauRxp(invrPom, velITRS, velTIRS);
//Convert position from ITRS to TIRS
iauRxp(invrPom, posITRS, posTIRS);
//Evaluate the cross product for the angular velocity due
//to the Earth's rotation.
iauPxp(Omega, posTIRS, rotVel);
//Add the instantaneous velocity due to rotation.
iauPpp(velTIRS, rotVel, retDataVel);
//Rotate from TIRS to GCRS
iauRxp(TIRS2GCRS, retDataVel, retDataVel);
}
}
}
plhs[0]=retMat;
if(nlhs>1) {
double *elPtr;
size_t i,j;
plhs[1]=mxCreateDoubleMatrix(3,3,mxREAL);
elPtr=(double*)mxGetData(plhs[1]);
for (i=0;i<3;i++) {
for(j=0;j<3;j++) {
elPtr[i+3*j]=ITRS2GCRS[i][j];
}
}
}
}
void iauC2t00b(double tta, double ttb, double uta, double utb,
double xp, double yp, double rc2t[3][3])
/*
** - - - - - - - - - -
** i a u C 2 t 0 0 b
** - - - - - - - - - -
**
** Form the celestial to terrestrial matrix given the date, the UT1 and
** the polar motion, using the IAU 2000B nutation model.
**
** This function is part of the International Astronomical Union's
** SOFA (Standards Of Fundamental Astronomy) software collection.
**
** Status: support function.
**
** Given:
** tta,ttb double TT as a 2-part Julian Date (Note 1)
** uta,utb double UT1 as a 2-part Julian Date (Note 1)
** xp,yp double coordinates of the pole (radians, Note 2)
**
** Returned:
** rc2t double[3][3] celestial-to-terrestrial matrix (Note 3)
**
** Notes:
**
** 1) The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
** apportioned in any convenient way between the arguments uta and
** utb. For example, JD(UT1)=2450123.7 could be expressed in any of
** these ways, among others:
**
** uta utb
**
** 2450123.7 0.0 (JD method)
** 2451545.0 -1421.3 (J2000 method)
** 2400000.5 50123.2 (MJD method)
** 2450123.5 0.2 (date & time method)
**
** The JD method is the most natural and convenient to use in
** cases where the loss of several decimal digits of resolution is
** acceptable. The J2000 and MJD methods are good compromises
** between resolution and convenience. In the case of uta,utb, the
** date & time method is best matched to the Earth rotation angle
** algorithm used: maximum precision is delivered when the uta
** argument is for 0hrs UT1 on the day in question and the utb
** argument lies in the range 0 to 1, or vice versa.
**
** 2) The arguments xp and yp are the coordinates (in radians) of the
** Celestial Intermediate Pole with respect to the International
** Terrestrial Reference System (see IERS Conventions 2003),
** measured along the meridians to 0 and 90 deg west respectively.
**
** 3) The matrix rc2t transforms from celestial to terrestrial
** coordinates:
**
** [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
**
** = rc2t * [CRS]
**
** where [CRS] is a vector in the Geocentric Celestial Reference
** System and [TRS] is a vector in the International Terrestrial
** Reference System (see IERS Conventions 2003), RC2I is the
** celestial-to-intermediate matrix, ERA is the Earth rotation
** angle and RPOM is the polar motion matrix.
**
** 4) The present function is faster, but slightly less accurate (about
** 1 mas), than the iauC2t00a function.
**
** Called:
** iauC2i00b celestial-to-intermediate matrix, IAU 2000B
** iauEra00 Earth rotation angle, IAU 2000
** iauPom00 polar motion matrix
** iauC2tcio form CIO-based celestial-to-terrestrial matrix
**
** Reference:
**
** McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
** IERS Technical Note No. 32, BKG (2004)
**
** This revision: 2009 April 1
**
** SOFA release 2012-03-01
**
** Copyright (C) 2012 IAU SOFA Board. See notes at end.
*/
{
double rc2i[3][3], era, rpom[3][3];
/* Form the celestial-to-intermediate matrix for this TT (IAU 2000B). */
iauC2i00b(tta, ttb, rc2i);
/* Predict the Earth rotation angle for this UT1. */
era = iauEra00(uta, utb);
/* Form the polar motion matrix (neglecting s'). */
iauPom00(xp, yp, 0.0, rpom);
/* Combine to form the celestial-to-terrestrial matrix. */
iauC2tcio(rc2i, era, rpom, rc2t);
return;
/*----------------------------------------------------------------------
**
** Copyright (C) 2012
** 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
**
**--------------------------------------------------------------------*/
}