/**
* \brief Provides an interface between code build from \ref lalinspiral_findchirp and
* various simulation packages for injecting chirps into data.
* \author Brown, D. A. and Creighton, T. D
*
* Injects the signals described
* in the linked list of \c SimInspiralTable structures \c events
* into the data \c chan. The response function \c resp should
* contain the response function to use when injecting the signals into the data.
*/
void
LALFindChirpInjectIMR (
LALStatus *status,
REAL4TimeSeries *chan,
SimInspiralTable *events,
SimRingdownTable *ringdownevents,
COMPLEX8FrequencySeries *resp,
INT4 injectSignalType
)
{
UINT4 k;
DetectorResponse detector;
SimInspiralTable *thisEvent = NULL;
SimRingdownTable *thisRingdownEvent = NULL;
PPNParamStruc ppnParams;
CoherentGW waveform, *wfm;
INT8 waveformStartTime;
REAL4TimeSeries signalvec;
COMPLEX8Vector *unity = NULL;
CHAR warnMsg[512];
#if 0
UINT4 n;
UINT4 i;
#endif
INITSTATUS(status);
ATTATCHSTATUSPTR( status );
ASSERT( chan, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( chan->data, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( chan->data->data, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( events, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( resp, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( resp->data, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
ASSERT( resp->data->data, status,
FINDCHIRPH_ENULL, FINDCHIRPH_MSGENULL );
/*
*
* set up structures and parameters needed
*
*/
/* fixed waveform injection parameters */
memset( &ppnParams, 0, sizeof(PPNParamStruc) );
ppnParams.deltaT = chan->deltaT;
ppnParams.lengthIn = 0;
ppnParams.ppn = NULL;
/*
*
* compute the transfer function from the given response function
*
*/
/* allocate memory and copy the parameters describing the freq series */
memset( &detector, 0, sizeof( DetectorResponse ) );
detector.transfer = (COMPLEX8FrequencySeries *)
LALCalloc( 1, sizeof(COMPLEX8FrequencySeries) );
if ( ! detector.transfer )
{
ABORT( status, FINDCHIRPH_EALOC, FINDCHIRPH_MSGEALOC );
}
memcpy( &(detector.transfer->epoch), &(resp->epoch),
sizeof(LIGOTimeGPS) );
detector.transfer->f0 = resp->f0;
detector.transfer->deltaF = resp->deltaF;
detector.site = (LALDetector *) LALMalloc( sizeof(LALDetector) );
/* set the detector site */
switch ( chan->name[0] )
{
case 'H':
*(detector.site) = lalCachedDetectors[LALDetectorIndexLHODIFF];
LALWarning( status, "computing waveform for Hanford." );
break;
case 'L':
*(detector.site) = lalCachedDetectors[LALDetectorIndexLLODIFF];
LALWarning( status, "computing waveform for Livingston." );
break;
case 'G':
*(detector.site) = lalCachedDetectors[LALDetectorIndexGEO600DIFF];
LALWarning( status, "computing waveform for GEO600." );
break;
case 'T':
*(detector.site) = lalCachedDetectors[LALDetectorIndexTAMA300DIFF];
LALWarning( status, "computing waveform for TAMA300." );
break;
case 'V':
*(detector.site) = lalCachedDetectors[LALDetectorIndexVIRGODIFF];
LALWarning( status, "computing waveform for Virgo." );
break;
default:
LALFree( detector.site );
detector.site = NULL;
LALWarning( status, "Unknown detector site, computing plus mode "
"waveform with no time delay" );
break;
}
/* set up units for the transfer function */
if (XLALUnitDivide( &(detector.transfer->sampleUnits),
&lalADCCountUnit, &lalStrainUnit ) == NULL) {
ABORTXLAL(status);
}
/* invert the response function to get the transfer function */
LALCCreateVector( status->statusPtr, &( detector.transfer->data ),
resp->data->length );
CHECKSTATUSPTR( status );
LALCCreateVector( status->statusPtr, &unity, resp->data->length );
CHECKSTATUSPTR( status );
for ( k = 0; k < resp->data->length; ++k )
{
unity->data[k] = 1.0;
}
LALCCVectorDivide( status->statusPtr, detector.transfer->data, unity,
resp->data );
CHECKSTATUSPTR( status );
LALCDestroyVector( status->statusPtr, &unity );
CHECKSTATUSPTR( status );
thisRingdownEvent = ringdownevents;
/*
*
* loop over the signals and inject them into the time series
*
*/
for ( thisEvent = events; thisEvent; thisEvent = thisEvent->next)
{
/*
*
* generate waveform and inject it into the data
*
*/
/* clear the waveform structure */
memset( &waveform, 0, sizeof(CoherentGW) );
LALGenerateInspiral(status->statusPtr, &waveform, thisEvent, &ppnParams);
CHECKSTATUSPTR( status );
/* add the ringdown */
wfm = XLALGenerateInspRing( &waveform, thisEvent, thisRingdownEvent,
injectSignalType );
if ( !wfm )
{
fprintf( stderr, "Failed to generate the waveform \n" );
if (xlalErrno == XLAL_EFAILED)
{
fprintf( stderr, "Too much merger\n");
XLALDestroyREAL4TimeSeries( chan );
xlalErrno = XLAL_SUCCESS;
return;
}
else exit ( 1 );
}
waveform = *wfm;
LALInfo( status, ppnParams.termDescription );
if ( thisEvent->geocent_end_time.gpsSeconds )
{
/* get the gps start time of the signal to inject */
waveformStartTime = XLALGPSToINT8NS( &(thisEvent->geocent_end_time) );
waveformStartTime -= (INT8) ( 1000000000.0 * ppnParams.tc );
}
else
{
LALInfo( status, "Waveform start time is zero: injecting waveform "
"into center of data segment" );
/* center the waveform in the data segment */
waveformStartTime = XLALGPSToINT8NS( &(chan->epoch) );
waveformStartTime += (INT8) ( 1000000000.0 *
((REAL8) (chan->data->length - ppnParams.length) / 2.0) * chan->deltaT
);
}
snprintf( warnMsg, sizeof(warnMsg)/sizeof(*warnMsg),
"Injected waveform timing:\n"
"thisEvent->geocent_end_time.gpsSeconds = %d\n"
"thisEvent->geocent_end_time.gpsNanoSeconds = %d\n"
"ppnParams.tc = %e\n"
"waveformStartTime = %" LAL_INT8_FORMAT "\n",
thisEvent->geocent_end_time.gpsSeconds,
thisEvent->geocent_end_time.gpsNanoSeconds,
ppnParams.tc,
waveformStartTime );
LALInfo( status, warnMsg );
/* clear the signal structure */
memset( &signalvec, 0, sizeof(REAL4TimeSeries) );
/* set the start times for injection */
XLALINT8NSToGPS( &(waveform.a->epoch), waveformStartTime );
memcpy( &(waveform.f->epoch), &(waveform.a->epoch),
sizeof(LIGOTimeGPS) );
memcpy( &(waveform.phi->epoch), &(waveform.a->epoch),
sizeof(LIGOTimeGPS) );
/* set the start time of the signal vector to the start time of the chan */
signalvec.epoch = chan->epoch;
/* set the parameters for the signal time series */
signalvec.deltaT = chan->deltaT;
if ( ( signalvec.f0 = chan->f0 ) != 0 )
{
ABORT( status, FINDCHIRPH_EHETR, FINDCHIRPH_MSGEHETR );
}
signalvec.sampleUnits = lalADCCountUnit;
/* simulate the detectors response to the inspiral */
LALSCreateVector( status->statusPtr, &(signalvec.data), chan->data->length );
CHECKSTATUSPTR( status );
LALSimulateCoherentGW( status->statusPtr,
&signalvec, &waveform, &detector );
CHECKSTATUSPTR( status );
/* *****************************************************************************/
#if 0
FILE *fp;
char fname[512];
UINT4 jj, kplus, kcross;
snprintf( fname, sizeof(fname) / sizeof(*fname),
"waveform-%d-%d-%s.txt",
thisEvent->geocent_end_time.gpsSeconds,
thisEvent->geocent_end_time.gpsNanoSeconds,
thisEvent->waveform );
fp = fopen( fname, "w" );
for( jj = 0, kplus = 0, kcross = 1; jj < waveform.phi->data->length;
++jj, kplus += 2, kcross +=2 )
{
fprintf(fp, "%d %e %e %le %e\n", jj,
waveform.a->data->data[kplus],
waveform.a->data->data[kcross],
waveform.phi->data->data[jj],
waveform.f->data->data[jj]);
}
fclose( fp );
#endif
/* ********************************************************************************/
#if 0
FILE *fp;
char fname[512];
UINT4 jj;
snprintf( fname, sizeof(fname) / sizeof(*fname),
"waveform-%d-%d-%s.txt",
thisEvent->geocent_end_time.gpsSeconds,
thisEvent->geocent_end_time.gpsNanoSeconds,
thisEvent->waveform );
fp = fopen( fname, "w" );
for( jj = 0; jj < signalvec.data->length; ++jj )
{
fprintf(fp, "%d %e %e \n", jj, signalvec.data->data[jj]);
}
fclose( fp );
#endif
/* ********************************************************************************/
/* inject the signal into the data channel */
LALSSInjectTimeSeries( status->statusPtr, chan, &signalvec );
CHECKSTATUSPTR( status );
/* allocate and go to next SimRingdownTable */
if( thisEvent->next )
thisRingdownEvent = thisRingdownEvent->next = (SimRingdownTable *)
calloc( 1, sizeof(SimRingdownTable) );
else
thisRingdownEvent->next = NULL;
/* destroy the signal */
LALSDestroyVector( status->statusPtr, &(signalvec.data) );
CHECKSTATUSPTR( status );
LALSDestroyVectorSequence( status->statusPtr, &(waveform.a->data) );
CHECKSTATUSPTR( status );
LALSDestroyVector( status->statusPtr, &(waveform.f->data) );
CHECKSTATUSPTR( status );
LALDDestroyVector( status->statusPtr, &(waveform.phi->data) );
CHECKSTATUSPTR( status );
if ( waveform.shift )
{
LALSDestroyVector( status->statusPtr, &(waveform.shift->data) );
CHECKSTATUSPTR( status );
}
LALFree( waveform.a );
LALFree( waveform.f );
LALFree( waveform.phi );
if ( waveform.shift )
{
LALFree( waveform.shift );
}
}
LALCDestroyVector( status->statusPtr, &( detector.transfer->data ) );
CHECKSTATUSPTR( status );
if ( detector.site ) LALFree( detector.site );
LALFree( detector.transfer );
DETATCHSTATUSPTR( status );
RETURN( status );
}
/**
* \author Creighton, T. D.
*
* \brief Computes a continuous waveform with frequency drift and Doppler
* modulation from a parabolic orbital trajectory.
*
* This function computes a quaiperiodic waveform using the spindown and
* orbital parameters in <tt>*params</tt>, storing the result in
* <tt>*output</tt>.
*
* In the <tt>*params</tt> structure, the routine uses all the "input"
* fields specified in \ref GenerateSpinOrbitCW_h, and sets all of the
* "output" fields. If <tt>params-\>f</tt>=\c NULL, no spindown
* modulation is performed. If <tt>params-\>oneMinusEcc</tt>\f$\neq0\f$, or if
* <tt>params-\>rPeriNorm</tt>\f$\times\f$<tt>params-\>angularSpeed</tt>\f$\geq1\f$
* (faster-than-light speed at periapsis), an error is returned.
*
* In the <tt>*output</tt> structure, the field <tt>output-\>h</tt> is
* ignored, but all other pointer fields must be set to \c NULL. The
* function will create and allocate space for <tt>output-\>a</tt>,
* <tt>output-\>f</tt>, and <tt>output-\>phi</tt> as necessary. The
* <tt>output-\>shift</tt> field will remain set to \c NULL.
*
* ### Algorithm ###
*
* For parabolic orbits, we combine \eqref{eq_spinorbit-tr},
* \eqref{eq_spinorbit-t}, and \eqref{eq_spinorbit-upsilon} to get \f$t_r\f$
* directly as a function of \f$E\f$:
* \f{equation}{
* \label{eq_cubic-e}
* t_r = t_p + \frac{r_p\sin i}{c} \left[ \cos\omega +
* \left(\frac{1}{v_p} + \cos\omega\right)E -
* \frac{\sin\omega}{4}E^2 + \frac{1}{12v_p}E^3\right] \;,
* \f}
* where \f$v_p=r_p\dot{\upsilon}_p\sin i/c\f$ is a normalized velocity at
* periapsis. Following the prescription for the general analytic
* solution to the real cubic equation, we substitute
* \f$E=x+3v_p\sin\omega\f$ to obtain:
* \f{equation}{
* \label{eq_cubic-x}
* x^3 + px = q \;,
* \f}
* where:
* \f{eqnarray}{
* \label{eq_cubic-p}
* p & = & 12 + 12v_p\cos\omega - 3v_p^2\sin^2\omega \;, \\
* \label{eq_cubic-q}
* q & = & 12v_p^2\sin\omega\cos\omega - 24v_p\sin\omega +
* 2v_p^3\sin^3\omega + 12\dot{\upsilon}_p(t_r-t_p) \;.
* \f}
* We note that \f$p>0\f$ is guaranteed as long as \f$v_p<1\f$, so the right-hand
* side of \eqref{eq_cubic-x} is monotonic in \f$x\f$ and has exactly one
* root. However, \f$p\rightarrow0\f$ in the limit \f$v_p\rightarrow1\f$ and
* \f$\omega=\pi\f$. This may cause some loss of precision in subsequent
* calculations. But \f$v_p\sim1\f$ means that our solution will be
* inaccurate anyway because we ignore significant relativistic effects.
*
* Since \f$p>0\f$, we can substitute \f$x=y\sqrt{3/4p}\f$ to obtain:
* \f{equation}{
* 4y^3 + 3y = \frac{q}{2}\left(\frac{3}{p}\right)^{3/2} \equiv C \;.
* \f}
* Using the triple-angle hyperbolic identity
* \f$\sinh(3\theta)=4\sinh^3\theta+3\sinh\theta\f$, we have
* \f$y=\sinh\left(\frac{1}{3}\sinh^{-1}C\right)\f$. The solution to the
* original cubic equation is then:
* \f{equation}{
* E = 3v_p\sin\omega + 2\sqrt{\frac{p}{3}}
* \sinh\left(\frac{1}{3}\sinh^{-1}C\right) \;.
* \f}
* To ease the calculation of \f$E\f$, we precompute the constant part
* \f$E_0=3v_p\sin\omega\f$ and the coefficient \f$\Delta E=2\sqrt{p/3}\f$.
* Similarly for \f$C\f$, we precompute a constant piece \f$C_0\f$ evaluated at
* the epoch of the output time series, and a stepsize coefficient
* \f$\Delta C=6(p/3)^{3/2}\dot{\upsilon}_p\Delta t\f$, where \f$\Delta t\f$ is
* the step size in the (output) time series in \f$t_r\f$. Thus at any
* timestep \f$i\f$, we obtain \f$C\f$ and hence \f$E\f$ via:
* \f{eqnarray}{
* C & = & C_0 + i\Delta C \;,\\
* E & = & E_0 + \Delta E\times\left\{\begin{array}{l@{\qquad}c}
* \sinh\left[\frac{1}{3}\ln\left(
* C + \sqrt{C^2+1} \right) \right]\;, & C\geq0 \;,\\ \\
* \sinh\left[-\frac{1}{3}\ln\left(
* -C + \sqrt{C^2+1} \right) \right]\;, & C\leq0 \;,\\
* \end{array}\right.
* \f}
* where we have explicitly written \f$\sinh^{-1}\f$ in terms of functions in
* \c math.h. Once \f$E\f$ is found, we can compute
* \f$t=E(12+E^2)/(12\dot{\upsilon}_p)\f$ (where again \f$1/12\dot{\upsilon}_p\f$
* can be precomputed), and hence \f$f\f$ and \f$\phi\f$ via
* \eqref{eq_taylorcw-freq} and \eqref{eq_taylorcw-phi}. The
* frequency \f$f\f$ must then be divided by the Doppler factor:
* \f[
* 1 + \frac{\dot{R}}{c} = 1 + \frac{v_p}{4+E^2}\left(
* 4\cos\omega - 2E\sin\omega \right)
* \f]
* (where once again \f$4\cos\omega\f$ and \f$2\sin\omega\f$ can be precomputed).
*
* This routine does not account for relativistic timing variations, and
* issues warnings or errors based on the criterea of
* \eqref{eq_relativistic-orbit} in GenerateEllipticSpinOrbitCW().
* The routine will also warn if
* it seems likely that \c REAL8 precision may not be sufficient to
* track the orbit accurately. We estimate that numerical errors could
* cause the number of computed wave cycles to vary by
* \f[
* \Delta N \lesssim f_0 T\epsilon\left[
* \sim6+\ln\left(|C|+\sqrt{|C|^2+1}\right)\right] \;,
* \f]
* where \f$|C|\f$ is the maximum magnitude of the variable \f$C\f$ over the
* course of the computation, \f$f_0T\f$ is the approximate total number of
* wave cycles over the computation, and \f$\epsilon\approx2\times10^{-16}\f$
* is the fractional precision of \c REAL8 arithmetic. If this
* estimate exceeds 0.01 cycles, a warning is issued.
*/
void
LALGenerateParabolicSpinOrbitCW( LALStatus *stat,
PulsarCoherentGW *output,
SpinOrbitCWParamStruc *params )
{
UINT4 n, i; /* number of and index over samples */
UINT4 nSpin = 0, j; /* number of and index over spindown terms */
REAL8 t, dt, tPow; /* time, interval, and t raised to a power */
REAL8 phi0, f0, twopif0; /* initial phase, frequency, and 2*pi*f0 */
REAL8 f, fPrev; /* current and previous values of frequency */
REAL4 df = 0.0; /* maximum difference between f and fPrev */
REAL8 phi; /* current value of phase */
REAL8 vp; /* projected speed at periapsis */
REAL8 argument; /* argument of periapsis */
REAL8 fourCosOmega; /* four times the cosine of argument */
REAL8 twoSinOmega; /* two times the sine of argument */
REAL8 vpCosOmega; /* vp times cosine of argument */
REAL8 vpSinOmega; /* vp times sine of argument */
REAL8 vpSinOmega2; /* vpSinOmega squared */
REAL8 vDot6; /* 6 times angular speed at periapsis */
REAL8 oneBy12vDot; /* one over (12 times angular speed) */
REAL8 pBy3; /* constant sqrt(p/3) in cubic equation */
REAL8 p32; /* constant (p/3)^1.5 in cubic equation */
REAL8 c, c0, dc; /* C variable, offset, and step increment */
REAL8 e, e2, e0; /* E variable, E^2, and constant piece of E */
REAL8 de; /* coefficient of sinh() piece of E */
REAL8 tpOff; /* orbit epoch - time series epoch (s) */
REAL8 spinOff; /* spin epoch - orbit epoch (s) */
REAL8 *fSpin = NULL; /* pointer to Taylor coefficients */
REAL4 *fData; /* pointer to frequency data */
REAL8 *phiData; /* pointer to phase data */
INITSTATUS(stat);
ATTATCHSTATUSPTR( stat );
/* Make sure parameter and output structures exist. */
ASSERT( params, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
ASSERT( output, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
/* Make sure output fields don't exist. */
ASSERT( !( output->a ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->f ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->phi ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->shift ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
/* If Taylor coeficients are specified, make sure they exist. */
if ( params->f ) {
ASSERT( params->f->data, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
nSpin = params->f->length;
fSpin = params->f->data;
}
/* Set up some constants (to avoid repeated calculation or
dereferencing), and make sure they have acceptable values. */
vp = params->rPeriNorm*params->angularSpeed;
vDot6 = 6.0*params->angularSpeed;
n = params->length;
dt = params->deltaT;
f0 = fPrev = params->f0;
if ( params->oneMinusEcc != 0.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EECC,
GENERATESPINORBITCWH_MSGEECC );
}
if ( vp >= 1.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EFTL,
GENERATESPINORBITCWH_MSGEFTL );
}
if ( vp <= 0.0 || dt <= 0.0 || f0 <= 0.0 || vDot6 <= 0.0 ||
n == 0 ) {
ABORT( stat, GENERATESPINORBITCWH_ESGN,
GENERATESPINORBITCWH_MSGESGN );
}
#ifndef NDEBUG
if ( lalDebugLevel & LALWARNING ) {
if ( f0*n*dt*vp*vp > 0.5 )
LALWarning( stat, "Orbit may have significant relativistic"
" effects that are not included" );
}
#endif
/* Compute offset between time series epoch and periapsis, and
betweem periapsis and spindown reference epoch. */
tpOff = (REAL8)( params->orbitEpoch.gpsSeconds -
params->epoch.gpsSeconds );
tpOff += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->epoch.gpsNanoSeconds );
spinOff = (REAL8)( params->orbitEpoch.gpsSeconds -
params->spinEpoch.gpsSeconds );
spinOff += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->spinEpoch.gpsNanoSeconds );
/* Set up some other constants. */
twopif0 = f0*LAL_TWOPI;
phi0 = params->phi0;
argument = params->omega;
oneBy12vDot = 0.5/vDot6;
fourCosOmega = 4.0*cos( argument );
twoSinOmega = 2.0*sin( argument );
vpCosOmega = 0.25*vp*fourCosOmega;
vpSinOmega = 0.5*vp*twoSinOmega;
vpSinOmega2 = vpSinOmega*vpSinOmega;
pBy3 = sqrt( 4.0*( 1.0 + vpCosOmega ) - vpSinOmega2 );
p32 = 1.0/( pBy3*pBy3*pBy3 );
c0 = p32*( vpSinOmega*( 6.0*vpCosOmega - 12.0 + vpSinOmega2 ) -
tpOff*vDot6 );
dc = p32*vDot6*dt;
e0 = 3.0*vpSinOmega;
de = 2.0*pBy3;
/* Check whether REAL8 precision is good enough. */
#ifndef NDEBUG
if ( lalDebugLevel & LALWARNING ) {
REAL8 x = fabs( c0 + n*dc ); /* a temporary computation variable */
if ( x < fabs( c0 ) )
x = fabs( c0 );
x = 6.0 + log( x + sqrt( x*x + 1.0 ) );
if ( LAL_REAL8_EPS*f0*dt*n*x > 0.01 )
LALWarning( stat, "REAL8 arithmetic may not have sufficient"
" precision for this orbit" );
}
#endif
/* Allocate output structures. */
if ( ( output->a = (REAL4TimeVectorSeries *)
LALMalloc( sizeof(REAL4TimeVectorSeries) ) ) == NULL ) {
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->a, 0, sizeof(REAL4TimeVectorSeries) );
if ( ( output->f = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->f, 0, sizeof(REAL4TimeSeries) );
if ( ( output->phi = (REAL8TimeSeries *)
LALMalloc( sizeof(REAL8TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->phi, 0, sizeof(REAL8TimeSeries) );
/* Set output structure metadata fields. */
output->position = params->position;
output->psi = params->psi;
output->a->epoch = output->f->epoch = output->phi->epoch
= params->epoch;
output->a->deltaT = n*params->deltaT;
output->f->deltaT = output->phi->deltaT = params->deltaT;
output->a->sampleUnits = lalStrainUnit;
output->f->sampleUnits = lalHertzUnit;
output->phi->sampleUnits = lalDimensionlessUnit;
snprintf( output->a->name, LALNameLength, "CW amplitudes" );
snprintf( output->f->name, LALNameLength, "CW frequency" );
snprintf( output->phi->name, LALNameLength, "CW phase" );
/* Allocate phase and frequency arrays. */
LALSCreateVector( stat->statusPtr, &( output->f->data ), n );
BEGINFAIL( stat ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
LALDCreateVector( stat->statusPtr, &( output->phi->data ), n );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
/* Allocate and fill amplitude array. */
{
CreateVectorSequenceIn in; /* input to create output->a */
in.length = 2;
in.vectorLength = 2;
LALSCreateVectorSequence( stat->statusPtr, &(output->a->data), &in );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
TRY( LALDDestroyVector( stat->statusPtr, &( output->phi->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
output->a->data->data[0] = output->a->data->data[2] = params->aPlus;
output->a->data->data[1] = output->a->data->data[3] = params->aCross;
}
/* Fill frequency and phase arrays. */
fData = output->f->data->data;
phiData = output->phi->data->data;
for ( i = 0; i < n; i++ ) {
/* Compute emission time. */
c = c0 + dc*i;
if ( c > 0 )
e = e0 + de*sinh( log( c + sqrt( c*c + 1.0 ) )/3.0 );
else
e = e0 + de*sinh( -log( -c + sqrt( c*c + 1.0 ) )/3.0 );
e2 = e*e;
phi = t = tPow = oneBy12vDot*e*( 12.0 + e2 );
/* Compute source emission phase and frequency. */
f = 1.0;
for ( j = 0; j < nSpin; j++ ) {
f += fSpin[j]*tPow;
phi += fSpin[j]*( tPow*=t )/( j + 2.0 );
}
/* Appy frequency Doppler shift. */
f *= f0 / ( 1.0 + vp*( fourCosOmega - e*twoSinOmega )
/( 4.0 + e2 ) );
phi *= twopif0;
if ( fabs( f - fPrev ) > df )
df = fabs( f - fPrev );
*(fData++) = fPrev = f;
*(phiData++) = phi + phi0;
}
/* Set output field and return. */
params->dfdt = df*dt;
DETATCHSTATUSPTR( stat );
RETURN( stat );
}
void
LALREAL4AverageSpectrum (
LALStatus *status,
REAL4FrequencySeries *fSeries,
REAL4TimeSeries *tSeries,
AverageSpectrumParams *params
)
{
UINT4 i, j, k; /* seg, ts and freq counters */
UINT4 numSeg; /* number of segments in average */
UINT4 fLength; /* length of requested power spec */
UINT4 tLength; /* length of time series segments */
REAL4Vector *tSegment = NULL; /* dummy time series segment */
COMPLEX8Vector *fSegment = NULL; /* dummy freq series segment */
REAL4 *tSeriesPtr; /* pointer to the segment data */
REAL4 psdNorm = 0; /* factor to multiply windows data */
REAL4 fftRe, fftIm; /* real and imag parts of fft */
REAL4 *s; /* work space for computing mean */
REAL4 *psdSeg = NULL; /* storage for individual specta */
LALUnit unit;
/* RAT4 negRootTwo = { -1, 1 }; */
INITSTATUS(status);
XLAL_PRINT_DEPRECATION_WARNING("XLALREAL4AverageSpectrumWelch");
ATTATCHSTATUSPTR (status);
/* check the input and output data pointers are non-null */
ASSERT( fSeries, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( fSeries->data, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( fSeries->data->data, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( tSeries, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( tSeries->data, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( tSeries->data->data, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
/* check the contents of the parameter structure */
ASSERT( params, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( params->window, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( params->window->data, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
ASSERT( params->window->data->length > 0, status,
TIMEFREQFFTH_EZSEG, TIMEFREQFFTH_MSGEZSEG );
ASSERT( params->plan, status,
TIMEFREQFFTH_ENULL, TIMEFREQFFTH_MSGENULL );
if ( ! ( params->method == useUnity || params->method == useMean ||
params->method == useMedian ) )
{
ABORT( status, TIMEFREQFFTH_EUAVG, TIMEFREQFFTH_MSGEUAVG );
}
/* check that the window length and fft storage lengths agree */
fLength = fSeries->data->length;
tLength = params->window->data->length;
if ( fLength != tLength / 2 + 1 )
{
ABORT( status, TIMEFREQFFTH_EMISM, TIMEFREQFFTH_MSGEMISM );
}
/* compute the number of segs, check that the length and overlap are valid */
numSeg = (tSeries->data->length - params->overlap) / (tLength - params->overlap);
if ( (tSeries->data->length - params->overlap) % (tLength - params->overlap) )
{
ABORT( status, TIMEFREQFFTH_EMISM, TIMEFREQFFTH_MSGEMISM );
}
/* clear the output spectrum and the workspace frequency series */
memset( fSeries->data->data, 0, fLength * sizeof(REAL4) );
/* compute the parameters of the output frequency series data */
fSeries->epoch = tSeries->epoch;
fSeries->f0 = tSeries->f0;
fSeries->deltaF = 1.0 / ( (REAL8) tLength * tSeries->deltaT );
if ( XLALUnitMultiply( &unit, &(tSeries->sampleUnits), &(tSeries->sampleUnits) ) == NULL ) {
ABORTXLAL(status);
}
if ( XLALUnitMultiply( &(fSeries->sampleUnits), &unit, &lalSecondUnit ) == NULL ) {
ABORTXLAL(status);
}
/* if this is a unit spectrum, just set the conents to unity and return */
if ( params->method == useUnity )
{
for ( k = 0; k < fLength; ++k )
{
fSeries->data->data[k] = 1.0;
}
DETATCHSTATUSPTR( status );
RETURN( status );
}
/* create temporary storage for the dummy time domain segment */
LALCreateVector( status->statusPtr, &tSegment, tLength );
CHECKSTATUSPTR( status );
/* create temporary storage for the individual ffts */
LALCCreateVector( status->statusPtr, &fSegment, fLength );
CHECKSTATUSPTR( status );
if ( params->method == useMedian )
{
/* create enough storage for the indivdiual power spectra */
psdSeg = XLALCalloc( numSeg, fLength * sizeof(REAL4) );
}
/* compute each of the power spectra used in the average */
for ( i = 0, tSeriesPtr = tSeries->data->data; i < (UINT4) numSeg; ++i )
{
/* copy the time series data to the dummy segment */
memcpy( tSegment->data, tSeriesPtr, tLength * sizeof(REAL4) );
/* window the time series segment */
for ( j = 0; j < tLength; ++j )
{
tSegment->data[j] *= params->window->data->data[j];
}
/* compute the fft of the data segment */
LALForwardRealFFT( status->statusPtr, fSegment, tSegment, params->plan );
CHECKSTATUSPTR (status);
/* advance the segment data pointer to the start of the next segment */
tSeriesPtr += tLength - params->overlap;
/* compute the psd components */
if ( params->method == useMean )
{
/* we can get away with less storage */
for ( k = 0; k < fLength; ++k )
{
fftRe = crealf(fSegment->data[k]);
fftIm = cimagf(fSegment->data[k]);
fSeries->data->data[k] += fftRe * fftRe + fftIm * fftIm;
}
/* halve the DC and Nyquist components to be consistent with T010095 */
fSeries->data->data[0] /= 2;
fSeries->data->data[fLength - 1] /= 2;
}
else if ( params->method == useMedian )
{
/* we must store all the spectra */
for ( k = 0; k < fLength; ++k )
{
fftRe = crealf(fSegment->data[k]);
fftIm = cimagf(fSegment->data[k]);
psdSeg[i * fLength + k] = fftRe * fftRe + fftIm * fftIm;
}
/* halve the DC and Nyquist components to be consistent with T010095 */
psdSeg[i * fLength] /= 2;
psdSeg[i * fLength + fLength - 1] /= 2;
}
}
/* destroy the dummy time series segment and the fft scratch space */
LALDestroyVector( status->statusPtr, &tSegment );
CHECKSTATUSPTR( status );
LALCDestroyVector( status->statusPtr, &fSegment );
CHECKSTATUSPTR( status );
/* compute the desired average of the spectra */
if ( params->method == useMean )
{
/* normalization constant for the arithmentic mean */
psdNorm = ( 2.0 * tSeries->deltaT ) /
( (REAL4) numSeg * params->window->sumofsquares );
/* normalize the psd to it matches the conventions document */
for ( k = 0; k < fLength; ++k )
{
fSeries->data->data[k] *= psdNorm;
}
}
else if ( params->method == useMedian )
{
REAL8 bias;
/* determine the running median bias */
/* note: this is not the correct bias if the segments are overlapped */
if ( params->overlap )
{
LALWarning( status, "Overlapping segments with median method causes a biased spectrum." );
}
TRY( LALRngMedBias( status->statusPtr, &bias, numSeg ), status );
/* normalization constant for the median */
psdNorm = ( 2.0 * tSeries->deltaT ) /
( bias * params->window->sumofsquares );
/* allocate memory array for insert sort */
s = XLALMalloc( numSeg * sizeof(REAL4) );
if ( ! s )
{
ABORT( status, TIMEFREQFFTH_EMALLOC, TIMEFREQFFTH_MSGEMALLOC );
}
/* compute the median spectra and normalize to the conventions doc */
for ( k = 0; k < fLength; ++k )
{
fSeries->data->data[k] = psdNorm *
MedianSpec( psdSeg, s, k, fLength, numSeg );
}
/* free memory used for sort array */
XLALFree( s );
/* destroy the storage for the individual spectra */
XLALFree( psdSeg );
}
DETATCHSTATUSPTR( status );
RETURN( status );
}
/**
* \author Creighton, T. D.
*
* \brief Computes the response of a detector to a coherent gravitational wave.
*
* This function takes a quasiperiodic gravitational waveform given in
* <tt>*signal</tt>, and estimates the corresponding response of the
* detector whose position, orientation, and transfer function are
* specified in <tt>*detector</tt>. The result is stored in
* <tt>*output</tt>.
*
* The fields <tt>output-\>epoch</tt>, <tt>output->deltaT</tt>, and
* <tt>output-\>data</tt> must already be set, in order to specify the time
* period and sampling rate for which the response is required. If
* <tt>output-\>f0</tt> is nonzero, idealized heterodyning is performed (an
* amount \f$2\pi f_0(t-t_0)\f$ is subtracted from the phase before computing
* the sinusoid, where \f$t_0\f$ is the heterodyning epoch defined in
* \c detector). For the input signal, <tt>signal-\>h</tt> is ignored,
* and the signal is treated as zero at any time for which either
* <tt>signal-\>a</tt> or <tt>signal-\>phi</tt> is not defined.
*
* This routine will convert <tt>signal-\>position</tt> to equatorial
* coordinates, if necessary.
*
* ### Algorithm ###
*
* The routine first accounts for the time delay between the detector and
* the solar system barycentre, based on the detector position
* information stored in <tt>*detector</tt> and the propagation direction
* specified in <tt>*signal</tt>. Values of the propagation delay are
* precomuted at fixed intervals and stored in a table, with the
* intervals \f$\Delta T_\mathrm{delay}\f$ chosen such that the value
* interpolated from adjacent table entries will never differ from the
* true value by more than some timing error \f$\sigma_T\f$. This implies
* that:
* \f[
* \Delta T_\mathrm{delay} \leq \sqrt{
* \frac{8\sigma_T}{\max\{a/c\}} } \; ,
* \f]
* where \f$\max\{a/c\}=1.32\times10^{-10}\mathrm{s}^{-1}\f$ is the maximum
* acceleration of an Earth-based detector in the barycentric frame. The
* total propagation delay also includes Einstein and Shapiro delay, but
* these are more slowly varying and thus do not constrain the table
* spacing. At present, a 400s table spacing is hardwired into the code,
* implying \f$\sigma_T\approx3\mu\f$s, comparable to the stated accuracy of
* <tt>LALBarycenter()</tt>.
*
* Next, the polarization response functions of the detector
* \f$F_{+,\times}(\alpha,\delta)\f$ are computed for every 10 minutes of the
* signal's duration, using the position of the source in <tt>*signal</tt>,
* the detector information in <tt>*detector</tt>, and the function
* <tt>LALComputeDetAMResponseSeries()</tt>. Subsequently, the
* polarization functions are estimated for each output sample by
* interpolating these precomputed values. This guarantees that the
* interpolated value is accurate to \f$\sim0.1\%\f$.
*
* Next, the frequency response of the detector is estimated in the
* quasiperiodic limit as follows:
* <ul>
* <li> At each sample point in <tt>*output</tt>, the propagation delay is
* computed and added to the sample time, and the instantaneous
* amplitudes \f$A_1\f$, \f$A_2\f$, frequency \f$f\f$, phase \f$\phi\f$, and polarization
* shift \f$\Phi\f$ are found by interpolating the nearest values in
* <tt>signal-\>a</tt>, <tt>signal-\>f</tt>, <tt>signal-\>phi</tt>, and
* <tt>signal-\>shift</tt>, respectively. If <tt>signal-\>f</tt> is not
* defined at that point in time, then \f$f\f$ is estimated by differencing
* the two nearest values of \f$\phi\f$, as \f$f\approx\Delta\phi/2\pi\Delta
* t\f$. If <tt>signal-\>shift</tt> is not defined, then \f$\Phi\f$ is treated as
* zero.</li>
* <li> The complex transfer function of the detector the frequency \f$f\f$
* is found by interpolating <tt>detector-\>transfer</tt>. The amplitude of
* the transfer function is multiplied with \f$A_1\f$ and \f$A_2\f$, and the
* phase of the transfer function is added to \f$\phi\f$,</li>
* <li> The plus and cross contributions \f$o_+\f$, \f$o_\times\f$ to the
* detector output are computed as in \eqref{eq_quasiperiodic_hpluscross}
* of \ref PulsarSimulateCoherentGW_h, but
* using the response-adjusted amplitudes and phase.</li>
* <li> The final detector response \f$o\f$ is computed as
* \f$o=(o_+F_+)+(o_\times F_\times)\f$.</li>
* </ul>
*
* ### A note on interpolation: ###
*
* Much of the computational work in this routine involves interpolating
* various time series to find their values at specific output times.
* The algorithm is summarized below.
*
* Let \f$A_j = A( t_A + j\Delta t_A )\f$ be a sampled time series, which we
* want to resample at new (output) time intervals \f$t_k = t_0 + k\Delta
* t\f$. We first precompute the following quantities:
* \f{eqnarray}{
* t_\mathrm{off} & = & \frac{t_0-t_A}{\Delta t_A} \; , \\
* dt & = & \frac{\Delta t}{\Delta t_A} \; .
* \f}
* Then, for each output sample time \f$t_k\f$, we compute:
* \f{eqnarray}{
* t & = & t_\mathrm{off} + k \times dt \; , \\
* j & = & \lfloor t \rfloor \; , \\
* f & = & t - j \; ,
* \f}
* where \f$\lfloor x\rfloor\f$ is the "floor" function; i.e.\ the largest
* integer \f$\leq x\f$. The time series sampled at the new time is then:
* \f[
* A(t_k) = f \times A_{j+1} + (1-f) \times A_j \; .
* \f]
*
* ### Notes ###
*
* The major computational hit in this routine comes from computing the
* sine and cosine of the phase angle in
* \eqref{eq_quasiperiodic_hpluscross} of
* \ref PulsarSimulateCoherentGW_h. For better online performance, these can
* be replaced by other (approximate) trig functions. Presently the code
* uses the native \c libm functions by default, or the function
* <tt>sincosp()</tt> in \c libsunmath \e if this function is
* available \e and the constant \c ONLINE is defined.
* Differences at the level of 0.01 begin to appear only for phase
* arguments greater than \f$10^{14}\f$ or so (corresponding to over 500
* years between phase epoch and observation time for frequencies of
* around 1kHz).
*
* To activate this feature, be sure that <tt>sunmath.h</tt> and
* \c libsunmath are on your system, and add <tt>-DONLINE</tt> to the
* <tt>--with-extra-cppflags</tt> configuration argument. In future this
* flag may be used to turn on other efficient trig algorithms on other
* (non-Solaris) platforms.
*
*/
void
LALPulsarSimulateCoherentGW( LALStatus *stat,
REAL4TimeSeries *output,
PulsarCoherentGW *CWsignal,
PulsarDetectorResponse *detector )
{
INT4 i, n; /* index over output->data, and its final value */
INT4 nMax; /* used to store limits on index ranges */
INT4 fInit, fFinal; /* index range for which CWsignal->f is defined */
INT4 shiftInit, shiftFinal; /* ditto for CWsignal->shift */
UINT4 dtDelayBy2; /* delay table half-interval (s) */
UINT4 dtPolBy2; /* polarization table half-interval (s) */
REAL4 *outData; /* pointer to output data */
REAL8 delayMin, delayMax; /* min and max values of time delay */
SkyPosition source; /* source sky position */
BOOLEAN transfer; /* 1 if transfer function is specified */
BOOLEAN fFlag = 0; /* 1 if frequency left detector->transfer range */
BOOLEAN pFlag = 0; /* 1 if frequency was estimated from phase */
/* get delay table and polaristion tables half intervals if defined (>0) in
the PulsarCoherentGW structure otherwise default to 400s for dtDelatBy2 and 300s
for dtPolBy2 */
dtDelayBy2 = CWsignal->dtDelayBy2 > 0 ? CWsignal->dtDelayBy2 : 400;
dtPolBy2 = CWsignal->dtPolBy2 > 0 ? CWsignal->dtPolBy2 : 300;
/* The amplitude, frequency, phase, polarization shift, polarization
response, and propagation delay are stored in arrays that must be
interpolated. For a quantity x, we define a pointer xData to the
data array. At some time t measured in units of output->deltaT,
the interpolation point in xData is given by ( xOff + t*xDt ),
where xOff is an offset and xDt is a relative sampling rate. */
LALDetAMResponseSeries polResponse;
REAL8Vector *delay = NULL;
REAL4 *aData, *fData, *shiftData, *plusData, *crossData;
REAL8 *phiData, *delayData;
REAL8 aOff, fOff, phiOff, shiftOff, polOff, delayOff;
REAL8 aDt, fDt, phiDt, shiftDt, polDt, delayDt;
/* Frequencies in the detector transfer function are interpolated
similarly, except everything is normalized with respect to
detector->transfer->deltaF. */
REAL4Vector *aTransfer = NULL;
REAL4Vector *phiTransfer = NULL;
REAL4Vector *phiTemp = NULL;
REAL4 *aTransData = NULL, *phiTransData = NULL;
REAL8 f0 = 1.0;
REAL8 phiFac = 1.0, fFac = 1.0;
/* Heterodyning phase factor LAL_TWOPI*output->f0*output->deltaT,
and phase offset at the start of the series
LAL_TWOPI*output->f0*(time offset). */
REAL8 heteroFac, phi0;
/* Variables required by the TCENTRE() macro, above. */
REAL8 realIndex;
INT4 intIndex;
REAL8 indexFrac;
INITSTATUS(stat);
ATTATCHSTATUSPTR( stat );
/* Make sure parameter structures and their fields exist. */
ASSERT( CWsignal, stat, SIMULATECOHERENTGWH_ENUL,
SIMULATECOHERENTGWH_MSGENUL );
if ( !( CWsignal->a ) ) {
ABORT( stat, SIMULATECOHERENTGWH_ESIG,
SIMULATECOHERENTGWH_MSGESIG );
}
ASSERT( CWsignal->a->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( CWsignal->a->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
if ( !( CWsignal->phi ) ) {
ABORT( stat, SIMULATECOHERENTGWH_ESIG,
SIMULATECOHERENTGWH_MSGESIG );
}
ASSERT( CWsignal->phi->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( CWsignal->phi->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
if ( CWsignal->f ) {
ASSERT( CWsignal->f->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( CWsignal->f->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
}
if ( CWsignal->shift ) {
ASSERT( CWsignal->shift->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( CWsignal->shift->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
}
ASSERT( detector, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
if ( ( transfer = ( detector->transfer != NULL ) ) ) {
ASSERT( detector->transfer->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( detector->transfer->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
}
ASSERT( output, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( output->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
ASSERT( output->data->data, stat,
SIMULATECOHERENTGWH_ENUL, SIMULATECOHERENTGWH_MSGENUL );
/* Check dimensions of amplitude array. */
ASSERT( CWsignal->a->data->vectorLength == 2, stat,
SIMULATECOHERENTGWH_EDIM, SIMULATECOHERENTGWH_MSGEDIM );
/* Make sure we never divide by zero. */
ASSERT( CWsignal->a->deltaT != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
ASSERT( CWsignal->phi->deltaT != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
aDt = output->deltaT / CWsignal->a->deltaT;
phiDt = output->deltaT / CWsignal->phi->deltaT;
ASSERT( aDt != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
ASSERT( phiDt != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
if ( CWsignal->f ) {
ASSERT( CWsignal->f->deltaT != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
fDt = output->deltaT / CWsignal->f->deltaT;
ASSERT( fDt != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
} else
fDt = 0.0;
if ( CWsignal->shift ) {
ASSERT( CWsignal->shift->deltaT != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
shiftDt = output->deltaT / CWsignal->shift->deltaT;
ASSERT( shiftDt != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
} else
shiftDt = 0.0;
if ( transfer ) {
ASSERT( detector->transfer->deltaF != 0.0, stat,
SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
fFac = 1.0 / detector->transfer->deltaF;
phiFac = fFac / ( LAL_TWOPI*CWsignal->phi->deltaT );
f0 = detector->transfer->f0/detector->transfer->deltaF;
}
heteroFac = LAL_TWOPI*output->f0*output->deltaT;
phi0 = (REAL8)( output->epoch.gpsSeconds -
detector->heterodyneEpoch.gpsSeconds );
phi0 += 0.000000001*(REAL8)( output->epoch.gpsNanoSeconds -
detector->heterodyneEpoch.gpsNanoSeconds );
phi0 *= LAL_TWOPI*output->f0;
if ( phi0 > 1.0/LAL_REAL8_EPS ) {
LALWarning( stat, "REAL8 arithmetic is not sufficient to maintain"
" heterodyne phase to within a radian." );
}
/* Check units on input, and set units on output. */
{
ASSERT( XLALUnitCompare( &(CWsignal->f->sampleUnits), &lalHertzUnit ) == 0, stat, SIMULATECOHERENTGWH_EUNIT, SIMULATECOHERENTGWH_MSGEUNIT );
ASSERT( XLALUnitCompare( &(CWsignal->phi->sampleUnits), &lalDimensionlessUnit ) == 0, stat, SIMULATECOHERENTGWH_EUNIT, SIMULATECOHERENTGWH_MSGEUNIT );
if( CWsignal->shift ) {
ASSERT( XLALUnitCompare( &(CWsignal->shift->sampleUnits), &lalDimensionlessUnit ) == 0, stat, SIMULATECOHERENTGWH_EUNIT, SIMULATECOHERENTGWH_MSGEUNIT );
}
if ( transfer ) {
if ( XLALUnitMultiply( &(output->sampleUnits), &(CWsignal->a->sampleUnits), &(detector->transfer->sampleUnits) ) == NULL ) {
ABORT( stat, SIMULATECOHERENTGWH_EUNIT, SIMULATECOHERENTGWH_MSGEUNIT );
}
} else {
output->sampleUnits = CWsignal->a->sampleUnits;
}
snprintf( output->name, LALNameLength, "response to %s", CWsignal->a->name );
}
/* Define temporary variables to access the data of CWsignal->a,
CWsignal->f, and CWsignal->phi. */
aData = CWsignal->a->data->data;
INT4 aLen = CWsignal->a->data->length * CWsignal->a->data->vectorLength;
phiData = CWsignal->phi->data->data;
INT4 phiLen = CWsignal->phi->data->length;
outData = output->data->data;
INT4 fLen=0, shiftLen=0;
if ( CWsignal->f )
{
fData = CWsignal->f->data->data;
fLen = CWsignal->f->data->length;
}
else
{
fData = NULL;
}
if ( CWsignal->shift )
{
shiftData = CWsignal->shift->data->data;
shiftLen = CWsignal->shift->data->length;
}
else
{
shiftData = NULL;
}
/* Convert source position to equatorial coordinates, if
required. */
if ( detector->site ) {
source = CWsignal->position;
if ( source.system != COORDINATESYSTEM_EQUATORIAL ) {
ConvertSkyParams params; /* parameters for conversion */
EarthPosition location; /* location of detector */
params.gpsTime = &( output->epoch );
params.system = COORDINATESYSTEM_EQUATORIAL;
if ( source.system == COORDINATESYSTEM_HORIZON ) {
params.zenith = &( location.geodetic );
location.x = detector->site->location[0];
location.y = detector->site->location[1];
location.z = detector->site->location[2];
TRY( LALGeocentricToGeodetic( stat->statusPtr, &location ),
stat );
}
TRY( LALConvertSkyCoordinates( stat->statusPtr, &source,
&source, ¶ms ), stat );
}
}
/* Generate the table of propagation delays.
dtDelayBy2 = (UINT4)( 38924.9/sqrt( output->f0 +
1.0/output->deltaT ) ); */
delayDt = output->deltaT/( 2.0*dtDelayBy2 );
nMax = (UINT4)( output->data->length*delayDt ) + 3;
TRY( LALDCreateVector( stat->statusPtr, &delay, nMax ), stat );
delayData = delay->data;
/* Compute delay from solar system barycentre. */
if ( detector->site && detector->ephemerides ) {
LIGOTimeGPS gpsTime; /* detector time when we compute delay */
EarthState state; /* Earth position info at that time */
BarycenterInput input; /* input structure to LALBarycenter() */
EmissionTime emit; /* output structure from LALBarycenter() */
/* Arrange nested pointers, and set initial values. */
gpsTime = input.tgps = output->epoch;
gpsTime.gpsSeconds -= dtDelayBy2;
input.tgps.gpsSeconds -= dtDelayBy2;
input.site = *(detector->site);
for ( i = 0; i < 3; i++ )
input.site.location[i] /= LAL_C_SI;
input.alpha = source.longitude;
input.delta = source.latitude;
input.dInv = 0.0;
delayMin = delayMax = 1.1*LAL_AU_SI/( LAL_C_SI*output->deltaT );
delayMax *= -1;
/* Compute table. */
for ( i = 0; i < nMax; i++ ) {
REAL8 tDelay; /* propagation time */
LALBarycenterEarth( stat->statusPtr, &state, &gpsTime,
detector->ephemerides );
BEGINFAIL( stat )
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
ENDFAIL( stat );
LALBarycenter( stat->statusPtr, &emit, &input, &state );
BEGINFAIL( stat )
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
ENDFAIL( stat );
delayData[i] = tDelay = emit.deltaT/output->deltaT;
if ( tDelay < delayMin )
delayMin = tDelay;
if ( tDelay > delayMax )
delayMax = tDelay;
gpsTime.gpsSeconds += 2*dtDelayBy2;
input.tgps.gpsSeconds += 2*dtDelayBy2;
}
}
/* No information from which to compute delays. */
else {
LALInfo( stat, "Detector site and ephemerides absent; simulating hplus with no"
" propagation delays" );
memset( delayData, 0, nMax*sizeof(REAL8) );
delayMin = delayMax = 0.0;
}
/* Generate the table of polarization response functions. */
polDt = output->deltaT/( 2.0*dtPolBy2 );
nMax = (UINT4)( output->data->length*polDt ) + 3;
memset( &polResponse, 0, sizeof( LALDetAMResponseSeries ) );
polResponse.pPlus = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) );
polResponse.pCross = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) );
polResponse.pScalar = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) );
if ( !polResponse.pPlus || !polResponse.pCross ||
!polResponse.pScalar ) {
if ( polResponse.pPlus )
LALFree( polResponse.pPlus );
if ( polResponse.pCross )
LALFree( polResponse.pCross );
if ( polResponse.pScalar )
LALFree( polResponse.pScalar );
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
ABORT( stat, SIMULATECOHERENTGWH_EMEM,
SIMULATECOHERENTGWH_MSGEMEM );
}
memset( polResponse.pPlus, 0, sizeof(REAL4TimeSeries) );
memset( polResponse.pCross, 0, sizeof(REAL4TimeSeries) );
memset( polResponse.pScalar, 0, sizeof(REAL4TimeSeries) );
LALSCreateVector( stat->statusPtr, &( polResponse.pPlus->data ),
nMax );
BEGINFAIL( stat ) {
LALFree( polResponse.pPlus );
LALFree( polResponse.pCross );
LALFree( polResponse.pScalar );
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
} ENDFAIL( stat );
LALSCreateVector( stat->statusPtr, &( polResponse.pCross->data ),
nMax );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pPlus->data ) ), stat );
LALFree( polResponse.pPlus );
LALFree( polResponse.pCross );
LALFree( polResponse.pScalar );
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
} ENDFAIL( stat );
LALSCreateVector( stat->statusPtr, &( polResponse.pScalar->data ),
nMax );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pPlus->data ) ), stat );
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pCross->data ) ), stat );
LALFree( polResponse.pPlus );
LALFree( polResponse.pCross );
LALFree( polResponse.pScalar );
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
} ENDFAIL( stat );
plusData = polResponse.pPlus->data->data;
crossData = polResponse.pCross->data->data;
INT4 plusLen = polResponse.pPlus->data->length;
INT4 crossLen = polResponse.pCross->data->length;
if ( plusLen != crossLen ) {
XLALPrintError ("plusLen = %d != crossLen = %d\n", plusLen, crossLen );
ABORT ( stat, SIMULATECOHERENTGWH_EBAD, SIMULATECOHERENTGWH_MSGEBAD );
}
if ( detector->site ) {
LALSource polSource; /* position and polarization angle */
LALDetAndSource input; /* response input structure */
LALTimeIntervalAndNSample params; /* response parameter structure */
/* Arrange nested pointers, and set initial values. */
polSource.equatorialCoords = source;
polSource.orientation = (REAL8)( CWsignal->psi );
input.pSource = &polSource;
input.pDetector = detector->site;
params.epoch = output->epoch;
params.epoch.gpsSeconds -= dtPolBy2;
params.deltaT = 2.0*dtPolBy2;
params.nSample = nMax;
/* Compute table of responses. */
LALComputeDetAMResponseSeries( stat->statusPtr, &polResponse,
&input, ¶ms );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pPlus->data ) ), stat );
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pCross->data ) ), stat );
TRY( LALSDestroyVector( stat->statusPtr,
&( polResponse.pScalar->data ) ), stat );
LALFree( polResponse.pPlus );
LALFree( polResponse.pCross );
LALFree( polResponse.pScalar );
TRY( LALDDestroyVector( stat->statusPtr, &delay ), stat );
} ENDFAIL( stat );
} else {
void
LALRingInjectSignals(
LALStatus *stat,
REAL4TimeSeries *series,
SimRingdownTable *injections,
COMPLEX8FrequencySeries *resp,
INT4 calType
)
{
UINT4 k;
INT4 injStartTime;
INT4 injStopTime;
DetectorResponse detector;
COMPLEX8Vector *unity = NULL;
CoherentGW waveform;
RingParamStruc ringParam;
REAL4TimeSeries signalvec;
SimRingdownTable *simRingdown=NULL;
LALDetector *tmpDetector=NULL /*,*nullDetector=NULL*/;
COMPLEX8FrequencySeries *transfer = NULL;
INITSTATUS(stat);
ATTATCHSTATUSPTR( stat );
/* set up start and end of injection zone TODO: fix this hardwired 10 */
injStartTime = series->epoch.gpsSeconds - 10;
injStopTime = series->epoch.gpsSeconds + 10 + (INT4)(series->data->length
* series->deltaT);
/*
*compute the transfer function
*/
/* allocate memory and copy the parameters describing the freq series */
memset( &detector, 0, sizeof( DetectorResponse ) );
transfer = (COMPLEX8FrequencySeries *)
LALCalloc( 1, sizeof(COMPLEX8FrequencySeries) );
if ( ! transfer )
{
ABORT( stat, GENERATERINGH_EMEM, GENERATERINGH_MSGEMEM );
}
memcpy( &(transfer->epoch), &(resp->epoch),
sizeof(LIGOTimeGPS) );
transfer->f0 = resp->f0;
transfer->deltaF = resp->deltaF;
tmpDetector = detector.site = (LALDetector *) LALMalloc( sizeof(LALDetector) );
/* set the detector site */
switch ( series->name[0] )
{
case 'H':
*(detector.site) = lalCachedDetectors[LALDetectorIndexLHODIFF];
LALWarning( stat, "computing waveform for Hanford." );
break;
case 'L':
*(detector.site) = lalCachedDetectors[LALDetectorIndexLLODIFF];
LALWarning( stat, "computing waveform for Livingston." );
break;
default:
LALFree( detector.site );
detector.site = NULL;
tmpDetector = NULL;
LALWarning( stat, "Unknown detector site, computing plus mode "
"waveform with no time delay" );
break;
}
/* set up units for the transfer function */
if (XLALUnitDivide( &(detector.transfer->sampleUnits),
&lalADCCountUnit, &lalStrainUnit ) == NULL) {
ABORTXLAL(stat);
}
/* invert the response function to get the transfer function */
LALCCreateVector( stat->statusPtr, &( transfer->data ),
resp->data->length );
CHECKSTATUSPTR( stat );
LALCCreateVector( stat->statusPtr, &unity, resp->data->length );
CHECKSTATUSPTR( stat );
for ( k = 0; k < resp->data->length; ++k )
{
unity->data[k] = 1.0;
}
LALCCVectorDivide( stat->statusPtr, transfer->data, unity,
resp->data );
CHECKSTATUSPTR( stat );
LALCDestroyVector( stat->statusPtr, &unity );
CHECKSTATUSPTR( stat );
/* Set up a time series to hold signal in ADC counts */
signalvec.deltaT = series->deltaT;
if ( ( signalvec.f0 = series->f0 ) != 0 )
{
ABORT( stat, GENERATERINGH_EMEM, GENERATERINGH_MSGEMEM );
}
signalvec.sampleUnits = lalADCCountUnit;
signalvec.data=NULL;
LALSCreateVector( stat->statusPtr, &(signalvec.data),
series->data->length );
CHECKSTATUSPTR( stat );
/* loop over list of waveforms and inject into data stream */
simRingdown = injections;
while ( simRingdown )
{
/* only do the work if the ring is in injection zone */
if( (injStartTime - simRingdown->geocent_start_time.gpsSeconds) *
(injStopTime - simRingdown->geocent_start_time.gpsSeconds) > 0 )
{
simRingdown = simRingdown->next;
continue;
}
/* set the ring params */
ringParam.deltaT = series->deltaT;
if( !( strcmp( simRingdown->coordinates, "HORIZON" ) ) )
{
ringParam.system = COORDINATESYSTEM_HORIZON;
}
else if ( !( strcmp( simRingdown->coordinates, "ZENITH" ) ) )
{
/* set coordinate system for completeness */
ringParam.system = COORDINATESYSTEM_EQUATORIAL;
detector.site = NULL;
}
else if ( !( strcmp( simRingdown->coordinates, "GEOGRAPHIC" ) ) )
{
ringParam.system = COORDINATESYSTEM_GEOGRAPHIC;
}
else if ( !( strcmp( simRingdown->coordinates, "EQUATORIAL" ) ) )
{
ringParam.system = COORDINATESYSTEM_EQUATORIAL;
}
else if ( !( strcmp( simRingdown->coordinates, "ECLIPTIC" ) ) )
{
ringParam.system = COORDINATESYSTEM_ECLIPTIC;
}
else if ( !( strcmp( simRingdown->coordinates, "GALACTIC" ) ) )
{
ringParam.system = COORDINATESYSTEM_GALACTIC;
}
else
ringParam.system = COORDINATESYSTEM_EQUATORIAL;
/* generate the ring */
memset( &waveform, 0, sizeof(CoherentGW) );
LALGenerateRing( stat->statusPtr, &waveform, series, simRingdown, &ringParam );
CHECKSTATUSPTR( stat );
/* print the waveform to a file */
if ( 0 )
{
FILE *fp;
char fname[512];
UINT4 jj, kplus, kcross;
snprintf( fname, sizeof(fname) / sizeof(*fname),
"waveform-%d-%d-%s.txt",
simRingdown->geocent_start_time.gpsSeconds,
simRingdown->geocent_start_time.gpsNanoSeconds,
simRingdown->waveform );
fp = fopen( fname, "w" );
for( jj = 0, kplus = 0, kcross = 1; jj < waveform.phi->data->length;
++jj, kplus += 2, kcross +=2 )
{
fprintf(fp, "%d %e %e %le %e\n", jj,
waveform.a->data->data[kplus],
waveform.a->data->data[kcross],
waveform.phi->data->data[jj],
waveform.f->data->data[jj]);
}
fclose( fp );
}
/* end */
#if 0
fprintf( stderr, "a->epoch->gpsSeconds = %d\na->epoch->gpsNanoSeconds = %d\n",
waveform.a->epoch.gpsSeconds, waveform.a->epoch.gpsNanoSeconds );
fprintf( stderr, "phi->epoch->gpsSeconds = %d\nphi->epoch->gpsNanoSeconds = %d\n",
waveform.phi->epoch.gpsSeconds, waveform.phi->epoch.gpsNanoSeconds );
fprintf( stderr, "f->epoch->gpsSeconds = %d\nf->epoch->gpsNanoSeconds = %d\n",
waveform.f->epoch.gpsSeconds, waveform.f->epoch.gpsNanoSeconds );
#endif
/* must set the epoch of signal since it's used by coherent GW */
signalvec.epoch = series->epoch;
memset( signalvec.data->data, 0, signalvec.data->length * sizeof(REAL4) );
/* decide which way to calibrate the data; defaul to old way */
if( calType )
detector.transfer=NULL;
else
detector.transfer=transfer;
/* convert this into an ADC signal */
LALSimulateCoherentGW( stat->statusPtr,
&signalvec, &waveform, &detector );
CHECKSTATUSPTR( stat );
/* print the waveform to a file */
if ( 0 )
{
FILE *fp;
char fname[512];
UINT4 jj;
snprintf( fname, sizeof(fname) / sizeof(*fname),
"signal-%d-%d-%s.txt",
simRingdown->geocent_start_time.gpsSeconds,
simRingdown->geocent_start_time.gpsNanoSeconds,
simRingdown->waveform );
fp = fopen( fname, "w" );
for( jj = 0; jj < signalvec.data->length; ++jj )
{
fprintf( fp, "%d %le\n", jj, signalvec.data->data[jj] );
}
fclose( fp );
}
/* end */
#if 0
fprintf( stderr, "series.epoch->gpsSeconds = %d\nseries.epoch->gpsNanoSeconds = %d\n",
series->epoch.gpsSeconds, series->epoch.gpsNanoSeconds );
fprintf( stderr, "signalvec->epoch->gpsSeconds = %d\nsignalvec->epoch->gpsNanoSeconds = %d\n",
signalvec.epoch.gpsSeconds, signalvec.epoch.gpsNanoSeconds );
#endif
/* if calibration using RespFilt */
if( calType == 1 )
XLALRespFilt(&signalvec, transfer);
/* inject the signal into the data channel */
LALSSInjectTimeSeries( stat->statusPtr, series, &signalvec );
CHECKSTATUSPTR( stat );
/* free memory in coherent GW structure. TODO: fix this */
LALSDestroyVectorSequence( stat->statusPtr, &( waveform.a->data ) );
CHECKSTATUSPTR( stat );
LALSDestroyVector( stat->statusPtr, &( waveform.f->data ) );
CHECKSTATUSPTR( stat );
LALDDestroyVector( stat->statusPtr, &( waveform.phi->data ) );
CHECKSTATUSPTR( stat );
LALFree( waveform.a ); waveform.a = NULL;
LALFree( waveform.f ); waveform.f = NULL;
LALFree( waveform.phi ); waveform.phi = NULL;
/* reset the detector site information in case it changed */
detector.site = tmpDetector;
/* move on to next one */
simRingdown = simRingdown->next;
}
/* destroy the signal */
LALSDestroyVector( stat->statusPtr, &(signalvec.data) );
CHECKSTATUSPTR( stat );
LALCDestroyVector( stat->statusPtr, &( transfer->data ) );
CHECKSTATUSPTR( stat );
if ( detector.site ) LALFree( detector.site );
LALFree( transfer );
DETATCHSTATUSPTR( stat );
RETURN( stat );
}
/* Define a function for parsing a string literal. */
static void
LALLiteralToString( LALStatus *stat,
CHAR *string,
const CHAR *literal,
UINT4 length )
{
CHAR c; /* Current character being considered. */
UINT4 n = 0; /* Counter of number of characters written. */
INITSTATUS(stat);
/* Find open quote. */
while ( ( c = *literal ) != '"' && c != '\n' && c != '\0' )
literal++;
if ( *literal != '"' ) {
LALWarning( stat, "No open quote found" );
RETURN( stat );
}
literal++;
/* Start parsing. */
while ( n < length - 1 ) {
/* End of literal, either implicit or explicit. */
if ( ( c = *(literal++) ) == '\0' || c == '\n' ) {
LALWarning( stat, "No close quote found" );
string[n] = '\0';
RETURN( stat );
} else if ( c == '"' ) {
string[n] = '\0';
RETURN( stat );
}
/* Escape sequence. */
else if ( c == '\\' ) {
/* Do not allow actual end-of-line or end-of-string to be
escaped. */
if ( ( c = *(literal++) ) == '\0' || c == '\n' ) {
LALWarning( stat, "No close quote found" );
string[n] = '\0';
RETURN( stat );
}
/* Other special escape characters. */
else if ( c == 'a' || c == 'A' )
string[n++] = '\a';
else if ( c == 'b' || c == 'B' )
string[n++] = '\b';
else if ( c == 'f' || c == 'F' )
string[n++] = '\f';
else if ( c == 'n' || c == 'N' )
string[n++] = '\n';
else if ( c == 'r' || c == 'R' )
string[n++] = '\r';
else if ( c == 't' || c == 'T' )
string[n++] = '\t';
else if ( c == 'v' || c == 'V' )
string[n++] = '\v';
/* Hexadecimal character code. */
else if ( c == 'x' || c == 'X' ) {
c = *(literal++); /* first digit */
if ( isxdigit( c ) ) {
UINT2 value;
if ( isdigit( c ) )
value = c - '0';
else
value = 10 + tolower( c ) - 'a';
c = *(literal++); /* second digit */
if ( isxdigit( c ) ) {
value *= 16;
if ( isdigit( c ) )
value += c - '0';
else
value += 10 + tolower( c ) - 'a';
} else /* no second digit */
literal--;
string[n++] = (CHAR)( value );
if ( value == 0 ) {
LALWarning( stat, "Found explicit end-of-string \\0" );
RETURN( stat );
}
} else { /* no first digit */
LALWarning( stat, "Treating empty hex cde as explicit"
" end-of-string \\0" );
string[n] = '\0';
RETURN( stat );
}
}
/* Octal character code. */
else if ( c >= '0' && c < '8' ) {
UINT2 value = c - '0';
c = *(literal++); /* second digit */
if ( c >= '0' && c < '8' ) {
value *= 8;
value += c - '0';
c = *(literal++); /* third digit */
if ( c >= '0' && c < '8' ) {
value *= 8;
value += c - '0';
} else /* no third digit */
literal--;
} else /* no second digit */
literal--;
if ( value > 255 )
LALWarning( stat, "Ignoring octal character code >= '\\400'" );
else
string[n++] = (CHAR)( value );
if ( value == 0 ) {
LALWarning( stat, "Found explicit end-of-string \\0" );
RETURN( stat );
}
}
/* Other escaped character. */
else {
if ( c != '\\' && c != '?' && c != '\'' && c != '"' )
LALWarning( stat, "Dropping \\ from unrecognized escape"
" sequence" );
string[n++] = c;
}
}
/* Other character. */
else
string[n++] = c;
}
if ( *literal != '"' )
LALWarning( stat, "Reached maximum length before reading close"
" quote" );
string[n] = '\0';
RETURN( stat );
}
/** \see See \ref LALInspiralHybridHexagonalBank_c for documentation */
void
LALInspiralCreatePNCoarseBankHybridHexa(
LALStatus *status,
InspiralTemplateList **list,
INT4 *nlist,
InspiralCoarseBankIn coarseIn
)
{
INT4 i;
INT4 firstId = 0;
REAL4 A0, A3;
REAL4 piFl;
InspiralBankParams bankPars;
InspiralTemplate *tempPars;
InspiralMomentsEtc moments;
InspiralCell *cells = 0;
HexaGridParam gridParam;
CellEvolution cellEvolution;
CellList *cellList = NULL;
INITSTATUS(status);
ATTATCHSTATUSPTR( status );
ASSERT( coarseIn.mMin > 0., status,
LALINSPIRALBANKH_ESIZE, LALINSPIRALBANKH_MSGESIZE );
ASSERT( coarseIn.mMax > 0., status,
LALINSPIRALBANKH_ESIZE, LALINSPIRALBANKH_MSGESIZE );
ASSERT( coarseIn.MMax >= 2.*coarseIn.mMin, status,
LALINSPIRALBANKH_ESIZE, LALINSPIRALBANKH_MSGESIZE );
/* Set the elements of the metric and tempPars structures in */
/* conformity with the coarseIn structure */
if ( !(tempPars = (InspiralTemplate *)
LALCalloc( 1, sizeof(InspiralTemplate))))
{
LALFree(tempPars);
LALFree(cells);
ABORT( status, LALINSPIRALBANKH_EMEM, LALINSPIRALBANKH_MSGEMEM );
}
LALInspiralSetParams( status->statusPtr, tempPars, coarseIn );
CHECKSTATUSPTR( status );
/* Identify the boundary of search and parameters for the */
/* first lattice point */
LALInspiralSetSearchLimits( status->statusPtr, &bankPars, coarseIn );
CHECKSTATUSPTR( status );
tempPars->totalMass = coarseIn.MMax;
tempPars->eta = 0.25;
tempPars->ieta = 1.L;
tempPars->fLower = coarseIn.fLower;
tempPars->massChoice = m1Andm2;
tempPars->mass1 = coarseIn.mMin;
tempPars->mass2 = coarseIn.mMax;
LALInspiralParameterCalc( status->statusPtr, tempPars );
CHECKSTATUSPTR( status );
/* Get the moments of the PSD integrand and other parameters */
/* required in the computation of the metric once for all. */
LALGetInspiralMoments(
status->statusPtr,
&moments,
&coarseIn.shf,
tempPars );
CHECKSTATUSPTR( status );
/* Allocate memory for one cell */
cells = (InspiralCell*)
LALCalloc(1, sizeof(InspiralCell) );
/*define gridParam*/
gridParam.mm = coarseIn.mmCoarse;
gridParam.x0Min = bankPars.x0Min;
gridParam.x0Max = bankPars.x0Max;
gridParam.x1Min = bankPars.x1Min;
gridParam.x1Max = bankPars.x1Max;
gridParam.mMin = coarseIn.mMin;
gridParam.mMax = coarseIn.mMax;
gridParam.MMin = coarseIn.MMin;
gridParam.MMax = coarseIn.MMax;
gridParam.etaMin = coarseIn.etamin;
gridParam.space = coarseIn.space;
gridParam.massRange = coarseIn.massRange;
gridParam.gridSpacing = coarseIn.gridSpacing;
gridParam.fLower = coarseIn.fLower;
cellEvolution.nTemplate = 1;
cellEvolution.nTemplateMax = 1;
cellEvolution.fertile = 0;
/* initialise that first cell */
tempPars->massChoice = t03;
cells[0].t0 = tempPars->t0;
cells[0].t3 = tempPars->t3;
/* some aliases */
piFl = LAL_PI * tempPars->fLower;
A0 = 5. / pow(piFl, 8./3.) / 256.;
A3 = LAL_PI / pow(piFl, 5./3.)/8.;
/* Initialise the first template */
LALInitHexagonalBank(
status->statusPtr,
&cells, firstId,
&moments, tempPars,
&gridParam, &cellEvolution,
&cellList);
CHECKSTATUSPTR( status );
{
INT4 k, kk; /*some indexes*/
INT4 *new_list = NULL;
CellList *ptr = NULL;
INT4 length = 1; /* default size of the bank when we
start the bank generation. */
/* we re-allocate an array which size equals the
* template bank size. */
if (! (new_list = LALMalloc(length*sizeof(INT4))))
{
ABORT( status, LALINSPIRALBANKH_EMEM, LALINSPIRALBANKH_MSGEMEM );
}
/* while there are cells/template which can propagate, we carry on the loop.*/
while (cellEvolution.fertile)
{
length = LALListLength(cellList);
/*realloc some memory for the next template*/
if (! (new_list = LALRealloc(new_list, length*sizeof(INT4))))
{
ABORT( status, LALINSPIRALBANKH_EMEM, LALINSPIRALBANKH_MSGEMEM );
/* freeing memory here ? */
}
ptr = cellList;
/* we extract the ids which might change within the LALPopulateCell
* function. Indeed the bank might grow and then we will lost track
* of ids/bank size and so on. */
for ( k = 0; k < length; k++)
{
new_list[k] = ptr->id;
ptr = ptr->next;
}
/* look at all the template/ids in the current bank to search for fertile cells */
for (kk = 0; kk < length; kk++)
{
k = new_list[kk];
if ( cells[k].status == Fertile)
{
LALPopulateCell(status->statusPtr, &moments, &cells,
k, tempPars, &gridParam, &cellEvolution, &cellList);
CHECKSTATUSPTR( status );
/* now the bank might have grown, but we only look at the
* template created before this for loop, when we entered
* in the while loop
* */
}
}
}
LALFree(new_list);
}
#if 1
{
INT4 edge1=0, edge2=0;
gridParam.gridSpacing = Hexagonal;
i=0;
while (i<cellEvolution.nTemplate){
if (cells[i].position == Edge){
edge1 = i;
cells[i].position = In;
i=cellEvolution.nTemplate;
}
i++;
}
i=0;
while (i<cellEvolution.nTemplate){
if (cells[i].position == Edge){
edge2=i;
cells[i].position = In;
i=cellEvolution.nTemplate;
}
i++;
}
if (cells[edge1].t0 > cells[edge2].t0){
LALPopulateNarrowEdge(status->statusPtr, &moments, &cells,
edge1, tempPars, &gridParam, &cellEvolution, &cellList, 0);
CHECKSTATUSPTR( status );
LALPopulateNarrowEdge(status->statusPtr, &moments, &cells,
edge2, tempPars, &gridParam, &cellEvolution, &cellList, 1);
CHECKSTATUSPTR( status );
}
else
{
LALPopulateNarrowEdge(status->statusPtr, &moments, &cells,
edge1, tempPars, &gridParam, &cellEvolution, &cellList, 1);
CHECKSTATUSPTR( status );
LALPopulateNarrowEdge(status->statusPtr, &moments, &cells,
edge2, tempPars, &gridParam, &cellEvolution, &cellList, 0);
CHECKSTATUSPTR( status );
}
}
#endif
if (cellList != NULL)
ABORT(status, LALINSPIRALBANKH_EHEXAINIT,LALINSPIRALBANKH_MSGEHEXAINIT);
/* Here is the current number of template generated. Now, we need
* to clean some of them which might be redundant.
* */
*nlist = cellEvolution.nTemplate;
{
INT4 k ;
INT4 length;
length = cellEvolution.nTemplate;
for ( k = 0; k < length; k++)
{
REAL4 a;
REAL4 b;
REAL4 x0;
REAL4 tempA3;
SFindRootIn input;
INT4 valid;
PRIN prin;
tempA3 = pow(A3, -5./2.)/pow(0.25,-1.5);
tempPars->t0 = cells[k].t0;
tempPars->t3 = cells[k].t3;
/* if non physical parameter i.e below eta=0.25*/
if(cells[k].RectPosition[0] == Below )
{
INT4 above=0, below=0, in=0, out=0;
/*first, we define the line which is along the long semi-axis of the
* ambiguity function, defined by the angle theta and the position of
* the template.
* */
a = tan(cells[k].metric.theta);
b = cells[k].t3 - a * cells[k].t0;
/* and call a function to search for a solution along eta=1/4 */
input.function = LALSPAF;
input.xmin = cells[k].t3-1e-3;
input.xmax = 1000;
input.xacc = 1e-6;
prin.ct = a * A0 * tempA3;
prin.b = b;
LALSBisectionFindRoot(status->statusPtr,
&x0, &input, (void *)&prin);
CHECKSTATUSPTR( status );
tempPars->t3 = x0 + 1e-3; /* to be sure it is physical */
tempPars->t0 = (tempPars->t3 - b)/a;
if (tempPars->t0 > 0)
{
LALInspiralParameterCalc(status->statusPtr, tempPars);
CHECKSTATUSPTR( status );
}
else
{
LALWarning(status,"HybridHexagonal placement: nothing to be done since t0<=0\n");
}
cells[k].t0 = tempPars->t0;
cells[k].t3 = tempPars->t3;
/* update its position values */
valid = 1;
GetPositionRectangle(status->statusPtr, &cells, k, tempPars ,
&gridParam,
&cellEvolution,
&cellList,
&valid);
{
switch (cells[k].RectPosition[1]){
case In: in +=1; break;
case Below: below +=1; break;
case Above: above +=1; break;
case Out: out +=1; break;
case Edge: break;
}
switch (cells[k].RectPosition[2]){
case In: in +=1; break;
case Below: below +=1; break;
case Above: above +=1; break;
case Out: out +=1; break;
case Edge: break;
}
switch (cells[k].RectPosition[3]){
case In: in +=1; break;
case Below: below +=1; break;
case Above: above +=1; break;
case Out: out +=1; break;
case Edge: break;
}
switch (cells[k].RectPosition[4]){
case In: in +=1; break;
case Below: below +=1; break;
case Above: above +=1; break;
case Out: out +=1; break;
case Edge: break;
}
}
if (above == 2 && cells[k].position == In)
{
if (cells[k].child[0] >=0 )
{
cells[cells[k].child[0]].position = Out;
}
else
{
/* nothing to be done, the child is not valid anyway*/
}
}
else
{
}
}
else
{
}
}
}
for (i=0; i<cellEvolution.nTemplate; i++) {
if (cells[i].position == In ) {
*nlist = *nlist +1;
}
}
/* allocate appropriate memory and fill the output bank */
*list = (InspiralTemplateList*)
LALRealloc( *list, sizeof(InspiralTemplateList) * (*nlist+1) );
if ( ! *list )
{
LALFree( tempPars );
ABORT( status, LALINSPIRALBANKH_EMEM, LALINSPIRALBANKH_MSGEMEM );
}
memset( *list + *nlist, 0, sizeof(InspiralTemplateList) );
{
*nlist = 0 ;
for (i=0; i<cellEvolution.nTemplate; i++)
{
if ((cells[i].position == In) && (cells[i].t0 > 0))
{
tempPars->t0 = cells[i].t0;
tempPars->t3 = cells[i].t3;
tempPars->massChoice = t03;
tempPars->fLower = coarseIn.fLower;
LALInspiralParameterCalc( status->statusPtr, tempPars );
CHECKSTATUSPTR( status );
(*list)[*nlist].ID = *nlist;
(*list)[*nlist].params = *tempPars;
(*list)[*nlist].metric = cells[i].metric;
++(*nlist);
}
}
}
LALFree( cells );
LALFree( tempPars );
DETATCHSTATUSPTR( status );
RETURN ( status );
}
void
LALInspiralEccentricityForInjection(
LALStatus *status,
CoherentGW *waveform,
InspiralTemplate *params,
PPNParamStruc *ppnParams
)
{
INT4 count, i;
REAL8 p, phiC;
REAL4Vector a; /* pointers to generated amplitude data */
REAL4Vector ff; /* pointers to generated frequency data */
REAL8Vector phi; /* generated phase data */
CreateVectorSequenceIn in;
CHAR message[256];
InspiralInit paramsInit;
INITSTATUS(status);
ATTATCHSTATUSPTR(status);
/* Make sure parameter and waveform structures exist. */
ASSERT( params, status, LALINSPIRALH_ENULL, LALINSPIRALH_MSGENULL );
ASSERT(waveform, status, LALINSPIRALH_ENULL, LALINSPIRALH_MSGENULL);
ASSERT( !( waveform->a ), status, LALINSPIRALH_ENULL, LALINSPIRALH_MSGENULL );
ASSERT( !( waveform->f ), status, LALINSPIRALH_ENULL, LALINSPIRALH_MSGENULL );
ASSERT( !( waveform->phi ), status, LALINSPIRALH_ENULL, LALINSPIRALH_MSGENULL );
/* Compute some parameters*/
LALInspiralInit(status->statusPtr, params, ¶msInit);
CHECKSTATUSPTR(status);
if (paramsInit.nbins == 0){
DETATCHSTATUSPTR(status);
RETURN (status);
}
/* Now we can allocate memory and vector for coherentGW structure*/
ff.length = paramsInit.nbins;
a.length = 2* paramsInit.nbins;
phi.length = paramsInit.nbins;
ff.data = (REAL4 *) LALCalloc(paramsInit.nbins, sizeof(REAL4));
a.data = (REAL4 *) LALCalloc(2 * paramsInit.nbins, sizeof(REAL4));
phi.data= (REAL8 *) LALCalloc(paramsInit.nbins, sizeof(REAL8));
/* Check momory allocation is okay */
if (!(ff.data) || !(a.data) || !(phi.data))
{
if (ff.data) LALFree(ff.data);
if (a.data) LALFree(a.data);
if (phi.data) LALFree(phi.data);
ABORT( status, LALINSPIRALH_EMEM, LALINSPIRALH_MSGEMEM );
}
count = 0;
/* Call the engine function */
LALInspiralEccentricityEngine(status->statusPtr, NULL, NULL, &a, &ff, &phi, &count, params);
BEGINFAIL( status )
{
LALFree(ff.data);
LALFree(a.data);
LALFree(phi.data);
}
ENDFAIL( status );
p = phi.data[count-1];
params->fFinal = ff.data[count-1];
sprintf(message, "cycles = %f", p/(double)LAL_TWOPI);
LALInfo(status, message);
if ( (INT4)(p/LAL_TWOPI) < 2 ){
sprintf(message, "The waveform has only %f cycles; we don't keep waveform with less than 2 cycles.",
p/(double)LAL_TWOPI );
XLALPrintError("%s", message);
LALWarning(status, message);
}
/*wrap the phase vector*/
phiC = phi.data[count-1] ;
for (i = 0; i < count; i++)
{
phi.data[i] = phi.data[i] - phiC + ppnParams->phi;
}
/* Allocate the waveform structures. */
if ( ( waveform->a = (REAL4TimeVectorSeries *)
LALCalloc(1, sizeof(REAL4TimeVectorSeries) ) ) == NULL ) {
ABORT( status, LALINSPIRALH_EMEM,
LALINSPIRALH_MSGEMEM );
}
if ( ( waveform->f = (REAL4TimeSeries *)
LALCalloc(1, sizeof(REAL4TimeSeries) ) ) == NULL ) {
LALFree( waveform->a ); waveform->a = NULL;
ABORT( status, LALINSPIRALH_EMEM,
LALINSPIRALH_MSGEMEM );
}
if ( ( waveform->phi = (REAL8TimeSeries *)
LALCalloc(1, sizeof(REAL8TimeSeries) ) ) == NULL ) {
LALFree( waveform->a ); waveform->a = NULL;
LALFree( waveform->f ); waveform->f = NULL;
ABORT( status, LALINSPIRALH_EMEM,
LALINSPIRALH_MSGEMEM );
}
in.length = (UINT4)(count);
in.vectorLength = 2;
LALSCreateVectorSequence( status->statusPtr, &( waveform->a->data ), &in );
CHECKSTATUSPTR(status);
LALSCreateVector( status->statusPtr, &( waveform->f->data ), count);
CHECKSTATUSPTR(status);
LALDCreateVector( status->statusPtr, &( waveform->phi->data ), count );
CHECKSTATUSPTR(status);
memcpy(waveform->f->data->data , ff.data, count*(sizeof(REAL4)));
memcpy(waveform->a->data->data , a.data, 2*count*(sizeof(REAL4)));
memcpy(waveform->phi->data->data ,phi.data, count*(sizeof(REAL8)));
waveform->a->deltaT = waveform->f->deltaT = waveform->phi->deltaT
= ppnParams->deltaT;
waveform->a->sampleUnits = lalStrainUnit;
waveform->f->sampleUnits = lalHertzUnit;
waveform->phi->sampleUnits = lalDimensionlessUnit;
waveform->position = ppnParams->position;
waveform->psi = ppnParams->psi;
snprintf( waveform->a->name, LALNameLength, "T1 inspiral amplitude" );
snprintf( waveform->f->name, LALNameLength, "T1 inspiral frequency" );
snprintf( waveform->phi->name, LALNameLength, "T1 inspiral phase" );
/* --- fill some output ---*/
ppnParams->tc = (double)(count-1) / params->tSampling ;
ppnParams->length = count;
ppnParams->dfdt = ((REAL4)(waveform->f->data->data[count-1]
- waveform->f->data->data[count-2]))
* ppnParams->deltaT;
ppnParams->fStop = params->fFinal;
ppnParams->termCode = GENERATEPPNINSPIRALH_EFSTOP;
ppnParams->termDescription = GENERATEPPNINSPIRALH_MSGEFSTOP;
ppnParams->fStart = ppnParams->fStartIn;
/* --- free memory --- */
LALFree(ff.data);
LALFree(a.data);
LALFree(phi.data);
DETATCHSTATUSPTR(status);
RETURN (status);
}
/**
* Anand: 26 October 2006
* This function nudges the templates in the list to
* the (max-total-mass = constant) line.
* This is done only for those templates whose total
* mass exceeds the desired max-total-mass value. The
* templates are nudged along the metric eigen direction
* until they lie on the said line.
*/
void
LALNudgeTemplatesToConstantTotalMassLine(
LALStatus *status,
InspiralTemplateList **list,
INT4 nlist,
InspiralCoarseBankIn coarseIn
)
{
InspiralTemplate *tempPars=NULL;
InspiralMetric *metric=NULL;
InspiralMomentsEtc moments;
INITSTATUS(status);
ATTATCHSTATUSPTR( status );
/* If there are no templates, return now */
if ( nlist <= 0 )
{
LALWarning( status, "number of templates is <= 0 ! " );
DETATCHSTATUSPTR(status);
RETURN (status);
}
/* Allocate memory (only required to calculate noise moments) */
tempPars = (InspiralTemplate *)
LALCalloc( 1, sizeof(InspiralTemplate) );
metric = (InspiralMetric *)
LALCalloc( 1, sizeof(InspiralMetric) );
/* Init the tempPars */
LALInspiralSetParams( status->statusPtr, tempPars, coarseIn );
CHECKSTATUSPTR( status );
tempPars->totalMass = coarseIn.MMax;
tempPars->eta = 0.25;
tempPars->ieta = 1.L;
tempPars->fLower = coarseIn.fLower;
tempPars->massChoice = totalMassAndEta;
LALInspiralParameterCalc( status->statusPtr, tempPars );
CHECKSTATUSPTR( status );
/* Get the moments of the PSD required in the computation of the metric */
LALGetInspiralMoments( status->statusPtr, &moments, &coarseIn.shf, tempPars );
CHECKSTATUSPTR( status );
/* Loop over template list and nudge the templates if required */
{
INT4 i;
REAL4 P, Q, M, C, ms; /*, t0, t3;*/
M = coarseIn.MMax*LAL_MTSUN_SI;
P = (5./256.)*pow( (LAL_PI*coarseIn.fLower), -8./3. ) ;
Q = (LAL_PI/8.)*pow( (LAL_PI*coarseIn.fLower), -5./3. ) ;
for (i=0; i < nlist; i++)
{
/* If the totalMass of this template exceeds max-total-mass
* then nudge along the metric eigen-direction.
*/
if ( (*list)[i].params.totalMass > coarseIn.MMax )
{
ms = tan( LAL_PI/2. + (*list)[i].metric.theta );
C = (*list)[i].params.t3 - ms*((*list)[i].params.t0);
/* Calculate the new co-ordinates in tau0-tau3 space */
(*list)[i].params.t3 = C / ( 1. - (ms*P/(M*Q)) );
(*list)[i].params.t0 = P*(*list)[i].params.t3/(M*Q);
/* Calculate the other parameters */
LALInspiralParameterCalc( status->statusPtr, &(*list)[i].params );
CHECKSTATUSPTR( status );
/* Check that the new point has not gone down below the
* equal mass line. If it has, set it to m1=m2=coarseIn.MMax/2.0
*/
if ( (*list)[i].params.eta > 0.25L )
{
InputMasses originalMassChoice = (*list)[i].params.massChoice;
(*list)[i].params.totalMass = coarseIn.MMax ;
(*list)[i].params.eta = 0.25L;
(*list)[i].params.massChoice = totalMassAndEta;
LALInspiralParameterCalc( status->statusPtr, &(*list)[i].params );
CHECKSTATUSPTR( status );
/* Reset the massChoice to whatever it was */
(*list)[i].params.massChoice = originalMassChoice;
}
/* Recalculate the metric at this new point */
LALInspiralComputeMetric( status->statusPtr, &((*list)[i].metric),
&((*list)[i].params), &moments );
CHECKSTATUSPTR( status );
}
}/* Loop over templates */
}
/* Clean up */
LALFree( tempPars );
LALFree( metric );
/* Normal exit */
DETATCHSTATUSPTR(status);
RETURN (status);
}
/**
* \author Creighton, T. D.
*
* \brief Computes a continuous waveform with frequency drift and Doppler
* modulation from a hyperbolic orbital trajectory.
*
* This function computes a quaiperiodic waveform using the spindown and
* orbital parameters in <tt>*params</tt>, storing the result in
* <tt>*output</tt>.
*
* In the <tt>*params</tt> structure, the routine uses all the "input"
* fields specified in \ref GenerateSpinOrbitCW_h, and sets all of the
* "output" fields. If <tt>params-\>f</tt>=\c NULL, no spindown
* modulation is performed. If <tt>params-\>oneMinusEcc</tt>\f$\not<0\f$ (a
* non-hyperbolic orbit), or if
* <tt>params-\>rPeriNorm</tt>\f$\times\f$<tt>params-\>angularSpeed</tt>\f$\geq1\f$
* (faster-than-light speed at periapsis), an error is returned.
*
* In the <tt>*output</tt> structure, the field <tt>output-\>h</tt> is
* ignored, but all other pointer fields must be set to \c NULL. The
* function will create and allocate space for <tt>output-\>a</tt>,
* <tt>output-\>f</tt>, and <tt>output-\>phi</tt> as necessary. The
* <tt>output-\>shift</tt> field will remain set to \c NULL.
*
* ### Algorithm ###
*
* For hyperbolic orbits, we combine \eqref{eq_spinorbit-tr},
* \eqref{eq_spinorbit-t}, and \eqref{eq_spinorbit-upsilon} to get \f$t_r\f$
* directly as a function of \f$E\f$:
* \f{eqnarray}{
* \label{eq_tr-e3}
* t_r = t_p & + & \left(\frac{r_p \sin i}{c}\right)\sin\omega\\
* & + & \frac{1}{n} \left( -E +
* \left[v_p(e-1)\cos\omega + e\right]\sinh E
* - \left[v_p\sqrt{\frac{e-1}{e+1}}\sin\omega\right]
* [\cosh E - 1]\right) \;,
* \f}
* where \f$v_p=r_p\dot{\upsilon}_p\sin i/c\f$ is a normalized velocity at
* periapsis and \f$n=\dot{\upsilon}_p\sqrt{(1-e)^3/(1+e)}\f$ is a normalized
* angular speed for the orbit (the hyperbolic analogue of the mean
* angular speed for closed orbits). For simplicity we write this as:
* \f{equation}{
* \label{eq_tr-e4}
* t_r = T_p + \frac{1}{n}\left( E + A\sinh E + B[\cosh E - 1] \right) \;,
* \f}
*
* \figure{inject_hanomaly,eps,0.23,Function to be inverted to find eccentric anomaly}
*
* where \f$T_p\f$ is the \e observed time of periapsis passage. Thus
* the key numerical procedure in this routine is to invert the
* expression \f$x=E+A\sinh E+B(\cosh E - 1)\f$ to get \f$E(x)\f$. This function
* is sketched to the right (solid line), along with an approximation
* used for making an initial guess (dotted line), as described later.
*
* We note that \f$A^2-B^2<1\f$, although it approaches 1 when
* \f$e\rightarrow1\f$, or when \f$v_p\rightarrow1\f$ and either \f$e=0\f$ or
* \f$\omega=\pi\f$. Except in this limit, Newton-Raphson methods will
* converge rapidly for any initial guess. In this limit, though, the
* slope \f$dx/dE\f$ approaches zero at \f$E=0\f$, and an initial guess or
* iteration landing near this point will send the next iteration off to
* unacceptably large or small values. A hybrid root-finding strategy is
* used to deal with this, and with the exponential behaviour of \f$x\f$ at
* large \f$E\f$.
*
* First, we compute \f$x=x_{\pm1}\f$ at \f$E=\pm1\f$. If the desired \f$x\f$ lies
* in this range, we use a straightforward Newton-Raphson root finder,
* with the constraint that all guesses of \f$E\f$ are restricted to the
* domain \f$[-1,1]\f$. This guarantees that the scheme will eventually find
* itself on a uniformly-convergent trajectory.
*
* Second, for \f$E\f$ outside of this range, \f$x\f$ is dominated by the
* exponential terms: \f$x\approx\frac{1}{2}(A+B)\exp(E)\f$ for \f$E\gg1\f$, and
* \f$x\approx-\frac{1}{2}(A-B)\exp(-E)\f$ for \f$E\ll-1\f$. We therefore do an
* \e approximate Newton-Raphson iteration on the function \f$\ln|x|\f$,
* where the approximation is that we take \f$d\ln|x|/d|E|\approx1\f$. This
* involves computing an extra logarithm inside the loop, but gives very
* rapid convergence to high precision, since \f$\ln|x|\f$ is very nearly
* linear in these regions.
*
* At the start of the algorithm, we use an initial guess of
* \f$E=-\ln[-2(x-x_{-1})/(A-B)-\exp(1)]\f$ for \f$x<x_{-1}\f$, \f$E=x/x_{-1}\f$ for
* \f$x_{-1}\leq x\leq0\f$, \f$E=x/x_{+1}\f$ for \f$0\leq x\leq x_{+1}\f$, or
* \f$E=\ln[2(x-x_{+1})/(A+B)-\exp(1)]\f$ for \f$x>x_{+1}\f$. We refine this
* guess until we get agreement to within 0.01 parts in part in
* \f$N_\mathrm{cyc}\f$ (where \f$N_\mathrm{cyc}\f$ is the larger of the number
* of wave cycles in a time \f$2\pi/n\f$, or the number of wave cycles in the
* entire waveform being generated), or one part in \f$10^{15}\f$ (an order
* of magnitude off the best precision possible with \c REAL8
* numbers). The latter case indicates that \c REAL8 precision may
* fail to give accurate phasing, and one should consider modeling the
* orbit as a set of Taylor frequency coefficients \'{a} la
* <tt>LALGenerateTaylorCW()</tt>. On subsequent timesteps, we use the
* previous timestep as an initial guess, which is good so long as the
* timesteps are much smaller than \f$1/n\f$.
*
* Once a value of \f$E\f$ is found for a given timestep in the output
* series, we compute the system time \f$t\f$ via \eqref{eq_spinorbit-t},
* and use it to determine the wave phase and (non-Doppler-shifted)
* frequency via \eqref{eq_taylorcw-freq}
* and \eqref{eq_taylorcw-phi}. The Doppler shift on the frequency is
* then computed using \eqref{eq_spinorbit-upsilon}
* and \eqref{eq_orbit-rdot}. We use \f$\upsilon\f$ as an intermediate in
* the Doppler shift calculations, since expressing \f$\dot{R}\f$ directly in
* terms of \f$E\f$ results in expression of the form \f$(e-1)/(e\cosh E-1)\f$,
* which are difficult to simplify and face precision losses when
* \f$E\sim0\f$ and \f$e\rightarrow1\f$. By contrast, solving for \f$\upsilon\f$ is
* numerically stable provided that the system <tt>atan2()</tt> function is
* well-designed.
*
* This routine does not account for relativistic timing variations, and
* issues warnings or errors based on the criterea of
* \eqref{eq_relativistic-orbit} in \ref LALGenerateEllipticSpinOrbitCW().
*/
void
LALGenerateHyperbolicSpinOrbitCW( LALStatus *stat,
PulsarCoherentGW *output,
SpinOrbitCWParamStruc *params )
{
UINT4 n, i; /* number of and index over samples */
UINT4 nSpin = 0, j; /* number of and index over spindown terms */
REAL8 t, dt, tPow; /* time, interval, and t raised to a power */
REAL8 phi0, f0, twopif0; /* initial phase, frequency, and 2*pi*f0 */
REAL8 f, fPrev; /* current and previous values of frequency */
REAL4 df = 0.0; /* maximum difference between f and fPrev */
REAL8 phi; /* current value of phase */
REAL8 vDotAvg; /* nomalized orbital angular speed */
REAL8 vp; /* projected speed at periapsis */
REAL8 upsilon, argument; /* true anomaly, and argument of periapsis */
REAL8 eCosOmega; /* eccentricity * cosine of argument */
REAL8 tPeriObs; /* time of observed periapsis */
REAL8 spinOff; /* spin epoch - orbit epoch */
REAL8 x; /* observed ``mean anomaly'' */
REAL8 xPlus, xMinus; /* limits where exponentials dominate */
REAL8 dx, dxMax; /* current and target errors in x */
REAL8 a, b; /* constants in equation for x */
REAL8 ecc; /* orbital eccentricity */
REAL8 eccMinusOne, eccPlusOne; /* ecc - 1 and ecc + 1 */
REAL8 e; /* hyperbolic anomaly */
REAL8 sinhe, coshe; /* sinh of e, and cosh of e minus 1 */
REAL8 *fSpin = NULL; /* pointer to Taylor coefficients */
REAL4 *fData; /* pointer to frequency data */
REAL8 *phiData; /* pointer to phase data */
INITSTATUS(stat);
ATTATCHSTATUSPTR( stat );
/* Make sure parameter and output structures exist. */
ASSERT( params, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
ASSERT( output, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
/* Make sure output fields don't exist. */
ASSERT( !( output->a ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->f ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->phi ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->shift ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
/* If Taylor coeficients are specified, make sure they exist. */
if ( params->f ) {
ASSERT( params->f->data, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
nSpin = params->f->length;
fSpin = params->f->data;
}
/* Set up some constants (to avoid repeated calculation or
dereferencing), and make sure they have acceptable values. */
eccMinusOne = -params->oneMinusEcc;
ecc = 1.0 + eccMinusOne;
eccPlusOne = 2.0 + eccMinusOne;
if ( eccMinusOne <= 0.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EECC,
GENERATESPINORBITCWH_MSGEECC );
}
vp = params->rPeriNorm*params->angularSpeed;
vDotAvg = params->angularSpeed
*sqrt( eccMinusOne*eccMinusOne*eccMinusOne/eccPlusOne );
n = params->length;
dt = params->deltaT;
f0 = fPrev = params->f0;
if ( vp >= 1.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EFTL,
GENERATESPINORBITCWH_MSGEFTL );
}
if ( vp <= 0.0 || dt <= 0.0 || f0 <= 0.0 || vDotAvg <= 0.0 ||
n == 0 ) {
ABORT( stat, GENERATESPINORBITCWH_ESGN,
GENERATESPINORBITCWH_MSGESGN );
}
/* Set up some other constants. */
twopif0 = f0*LAL_TWOPI;
phi0 = params->phi0;
argument = params->omega;
a = vp*eccMinusOne*cos( argument ) + ecc;
b = -vp*sqrt( eccMinusOne/eccPlusOne )*sin( argument );
eCosOmega = ecc*cos( argument );
if ( n*dt*vDotAvg > LAL_TWOPI )
dxMax = 0.01/( f0*n*dt );
else
dxMax = 0.01/( f0*LAL_TWOPI/vDotAvg );
if ( dxMax < 1.0e-15 ) {
dxMax = 1.0e-15;
#ifndef NDEBUG
LALWarning( stat, "REAL8 arithmetic may not have sufficient"
" precision for this orbit" );
#endif
}
#ifndef NDEBUG
if ( lalDebugLevel & LALWARNING ) {
REAL8 tau = n*dt;
if ( tau > LAL_TWOPI/vDotAvg )
tau = LAL_TWOPI/vDotAvg;
if ( f0*tau*vp*vp*ecc/eccPlusOne > 0.25 )
LALWarning( stat, "Orbit may have significant relativistic"
" effects that are not included" );
}
#endif
/* Compute offset between time series epoch and observed periapsis,
and betweem true periapsis and spindown reference epoch. */
tPeriObs = (REAL8)( params->orbitEpoch.gpsSeconds -
params->epoch.gpsSeconds );
tPeriObs += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->epoch.gpsNanoSeconds );
tPeriObs += params->rPeriNorm*sin( params->omega );
spinOff = (REAL8)( params->orbitEpoch.gpsSeconds -
params->spinEpoch.gpsSeconds );
spinOff += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->spinEpoch.gpsNanoSeconds );
/* Determine bounds of hybrid root-finding algorithm, and initial
guess for e. */
xMinus = 1.0 + a*sinh( -1.0 ) + b*cosh( -1.0 ) - b;
xPlus = -1.0 + a*sinh( 1.0 ) + b*cosh( 1.0 ) - b;
x = -vDotAvg*tPeriObs;
if ( x < xMinus )
e = -log( -2.0*( x - xMinus )/( a - b ) - exp( 1.0 ) );
else if ( x <= 0 )
e = x/xMinus;
else if ( x <= xPlus )
e = x/xPlus;
else
e = log( 2.0*( x - xPlus )/( a + b ) - exp( 1.0 ) );
sinhe = sinh( e );
coshe = cosh( e ) - 1.0;
/* Allocate output structures. */
if ( ( output->a = (REAL4TimeVectorSeries *)
LALMalloc( sizeof(REAL4TimeVectorSeries) ) ) == NULL ) {
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->a, 0, sizeof(REAL4TimeVectorSeries) );
if ( ( output->f = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->f, 0, sizeof(REAL4TimeSeries) );
if ( ( output->phi = (REAL8TimeSeries *)
LALMalloc( sizeof(REAL8TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->phi, 0, sizeof(REAL8TimeSeries) );
/* Set output structure metadata fields. */
output->position = params->position;
output->psi = params->psi;
output->a->epoch = output->f->epoch = output->phi->epoch
= params->epoch;
output->a->deltaT = n*params->deltaT;
output->f->deltaT = output->phi->deltaT = params->deltaT;
output->a->sampleUnits = lalStrainUnit;
output->f->sampleUnits = lalHertzUnit;
output->phi->sampleUnits = lalDimensionlessUnit;
snprintf( output->a->name, LALNameLength, "CW amplitudes" );
snprintf( output->f->name, LALNameLength, "CW frequency" );
snprintf( output->phi->name, LALNameLength, "CW phase" );
/* Allocate phase and frequency arrays. */
LALSCreateVector( stat->statusPtr, &( output->f->data ), n );
BEGINFAIL( stat ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
LALDCreateVector( stat->statusPtr, &( output->phi->data ), n );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
/* Allocate and fill amplitude array. */
{
CreateVectorSequenceIn in; /* input to create output->a */
in.length = 2;
in.vectorLength = 2;
LALSCreateVectorSequence( stat->statusPtr, &(output->a->data), &in );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
TRY( LALDDestroyVector( stat->statusPtr, &( output->phi->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
output->a->data->data[0] = output->a->data->data[2] = params->aPlus;
output->a->data->data[1] = output->a->data->data[3] = params->aCross;
}
/* Fill frequency and phase arrays. */
fData = output->f->data->data;
phiData = output->phi->data->data;
for ( i = 0; i < n; i++ ) {
x = vDotAvg*( i*dt - tPeriObs );
/* Use approximate Newton-Raphson method on ln|x| if |x| > 1. */
if ( x < xMinus ) {
x = log( -x );
while ( fabs( dx = log( e - a*sinhe - b*coshe ) - x ) > dxMax ) {
e += dx;
sinhe = sinh( e );
coshe = cosh( e ) - 1.0;
}
}
else if ( x > xPlus ) {
x = log( x );
while ( fabs( dx = log( -e + a*sinhe + b*coshe ) - x ) > dxMax ) {
e -= dx;
sinhe = sinh( e );
coshe = cosh( e ) - 1.0;
}
}
/* Use ordinary Newton-Raphson method on x if |x| <= 1. */
else {
while ( fabs( dx = -e + a*sinhe + b*coshe - x ) > dxMax ) {
e -= dx/( -1.0 + a*coshe + a + b*sinhe );
if ( e < -1.0 )
e = -1.0;
else if ( e > 1.0 )
e = 1.0;
sinhe = sinh( e );
coshe = cosh( e ) - 1.0;
}
}
/* Compute source emission time, phase, and frequency. */
phi = t = tPow =
( ecc*sinhe - e )/vDotAvg + spinOff;
f = 1.0;
for ( j = 0; j < nSpin; j++ ) {
f += fSpin[j]*tPow;
phi += fSpin[j]*( tPow*=t )/( j + 2.0 );
}
/* Appy frequency Doppler shift. */
upsilon = 2.0*atan2( sqrt( eccPlusOne*coshe ),
sqrt( eccMinusOne*( coshe + 2.0 ) ) );
f *= f0 / ( 1.0 + vp*( cos( argument + upsilon ) + eCosOmega )
/eccPlusOne );
phi *= twopif0;
if ( fabs( f - fPrev ) > df )
df = fabs( f - fPrev );
*(fData++) = fPrev = f;
*(phiData++) = phi + phi0;
}
/* Set output field and return. */
params->dfdt = df*dt;
DETATCHSTATUSPTR( stat );
RETURN( stat );
}
/** UNDOCUMENTED */
void
LALUpdateCalibration(
LALStatus *status,
CalibrationFunctions *output,
CalibrationFunctions *input,
CalibrationUpdateParams *params
)
{
const REAL4 tiny = 1e-6;
COMPLEX8Vector *save;
COMPLEX8 *R;
COMPLEX8 *C;
COMPLEX8 *R0;
COMPLEX8 *C0;
COMPLEX8 a;
COMPLEX8 ab;
REAL8 epoch;
REAL8 first_cal;
REAL8 duration;
REAL4 dt;
REAL4 i_r4;
UINT4 n;
UINT4 i;
UINT4 length = 0;
CHAR warnMsg[512];
INITSTATUS(status);
ATTATCHSTATUSPTR( status );
/* check input */
ASSERT( input, status, CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->sensingFunction, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->responseFunction, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->sensingFunction->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->responseFunction->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->sensingFunction->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( input->responseFunction->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
n = input->sensingFunction->data->length;
ASSERT( (int)n > 0, status, CALIBRATIONH_ESIZE, CALIBRATIONH_MSGESIZE );
ASSERT( input->responseFunction->data->length == n, status,
CALIBRATIONH_ESZMM, CALIBRATIONH_MSGESZMM );
/* check output */
ASSERT( output, status, CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->sensingFunction, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->responseFunction, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->sensingFunction->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->responseFunction->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->sensingFunction->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->responseFunction->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( output->sensingFunction->data->length == n, status,
CALIBRATIONH_ESZMM, CALIBRATIONH_MSGESZMM );
ASSERT( output->responseFunction->data->length == n, status,
CALIBRATIONH_ESZMM, CALIBRATIONH_MSGESZMM );
/* check params */
ASSERT( params, status, CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->sensingFactor, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->openLoopFactor, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->sensingFactor->deltaT, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->sensingFactor->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->openLoopFactor->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->sensingFactor->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->openLoopFactor->data->data, status,
CALIBRATIONH_ENULL, CALIBRATIONH_MSGENULL );
ASSERT( params->openLoopFactor->data->length ==
params->sensingFactor->data->length, status,
CALIBRATIONH_ESZMM, CALIBRATIONH_MSGESZMM );
R0 = input->responseFunction->data->data;
C0 = input->sensingFunction->data->data;
R = output->responseFunction->data->data;
C = output->sensingFunction->data->data;
save = output->responseFunction->data;
output->responseFunction = input->responseFunction;
output->responseFunction->data = save;
output->responseFunction->epoch = params->epoch;
save = output->sensingFunction->data;
output->sensingFunction = input->sensingFunction;
output->sensingFunction->data = save;
output->sensingFunction->epoch = params->epoch;
/* locate correct values of a and ab */
epoch = XLALGPSGetREAL8(&(params->epoch));
first_cal = XLALGPSGetREAL8(&(params->sensingFactor->epoch));
duration = XLALGPSGetREAL8(&(params->duration));
dt = epoch - first_cal;
/* find the first point at or before the requested time */
if ( (i_r4 = floor( dt / params->sensingFactor->deltaT ) ) < 0 )
{
ABORT( status, CALIBRATIONH_ETIME, CALIBRATIONH_MSGETIME );
}
else
{
i = (UINT4) i_r4;
}
/* compute the sum of the calibration factors */
a = ab = 0;
length = 0;
do
{
COMPLEX8 this_a;
COMPLEX8 this_ab;
if ( i > params->sensingFactor->data->length - 1 )
{
ABORT( status, CALIBRATIONH_ETIME, CALIBRATIONH_MSGETIME );
}
this_a = params->sensingFactor->data->data[i];
this_ab = params->openLoopFactor->data->data[i];
/* JC: I CHANGED THE LOGIC HERE TO WHAT I THOUGHT IT SHOULD BE! */
if ( ( fabs( creal(this_a) ) < tiny && fabs( cimag(this_a) ) < tiny ) ||
( fabs( creal(this_ab) ) < tiny && fabs( cimag(this_ab) ) < tiny ) )
{
/* this is a hack for the broken S2 calibration frame data */
if ( (params->epoch.gpsSeconds >= CAL_S2START) &&
(params->epoch.gpsSeconds < CAL_S2END ) )
{
/* if the zero is during S2 print a warning... */
snprintf( warnMsg, XLAL_NUM_ELEM(warnMsg),
"Zero calibration factors found during S2 at GPS %10.9f",
first_cal + (REAL8) i * params->sensingFactor->deltaT );
LALWarning( status, warnMsg );
}
else
{
/* ...or abort if we are outside S2 */
snprintf( warnMsg, XLAL_NUM_ELEM(warnMsg),
"Zero calibration factor found at GPS %10.9f",
first_cal + (REAL8) i * params->sensingFactor->deltaT );
LALWarning( status, warnMsg );
ABORT( status, CALIBRATIONH_EZERO, CALIBRATIONH_MSGEZERO );
}
}
else
{
/* increment the count of factors if we are adding a non-zero value */
++length;
}
/* add this value to the sum */
a += this_a;
ab += this_ab;
/* increment the calibration factor index */
++i;
}
while ( (first_cal + (REAL8) i * params->sensingFactor->deltaT) <
(epoch + duration) );
/* if all the calibration factors are zero the abort */
if ( ! length ||
(fabs( creal(a) ) < tiny && fabs( cimag(a) ) < tiny) ||
(fabs( creal(ab) ) < tiny && fabs( cimag(ab) ) < tiny) )
{
snprintf( warnMsg, XLAL_NUM_ELEM(warnMsg),
"Got %d calibration samples\nalpha and/or beta are zero:\n"
"Re a = %e\tIm a = %e\nRe ab = %e\tIm ab = %e",
length, creal(a), cimag(a), creal(ab), cimag(ab) );
LALWarning( status, warnMsg );
ABORT( status, CALIBRATIONH_EZERO, CALIBRATIONH_MSGEZERO );
}
/* compute the mean of the calibration factors from the sum */
a /= length;
ab /= length;
/* return the used values of alpha and alphabeta */
params->alpha = a;
params->alphabeta = ab;
snprintf( warnMsg, XLAL_NUM_ELEM(warnMsg),
"Got %d calibration samples\n"
"Re a = %e\tIm a = %e\nRe ab = %e\tIm ab = %e",
length, creal(a), cimag(a), creal(ab), cimag(ab) );
LALInfo( status, warnMsg );
for ( i = 0; i < n; ++i )
{
C[i] = a * C0[i];
R[i] = (ab * (C0[i] * R0[i] - 1.0) + 1.0) / C[i];
}
DETATCHSTATUSPTR( status );
RETURN( status );
}
/**
* \author Creighton, T. D.
*
* \brief Computes a continuous waveform with frequency drift and Doppler
* modulation from an elliptical orbital trajectory.
*
* This function computes a quaiperiodic waveform using the spindown and
* orbital parameters in <tt>*params</tt>, storing the result in
* <tt>*output</tt>.
*
* In the <tt>*params</tt> structure, the routine uses all the "input"
* fields specified in \ref GenerateSpinOrbitCW_h, and sets all of the
* "output" fields. If <tt>params-\>f</tt>=\c NULL, no spindown
* modulation is performed. If <tt>params-\>oneMinusEcc</tt>\f$\notin(0,1]\f$
* (an open orbit), or if
* <tt>params-\>rPeriNorm</tt>\f$\times\f$<tt>params-\>angularSpeed</tt>\f$\geq1\f$
* (faster-than-light speed at periapsis), an error is returned.
*
* In the <tt>*output</tt> structure, the field <tt>output-\>h</tt> is
* ignored, but all other pointer fields must be set to \c NULL. The
* function will create and allocate space for <tt>output-\>a</tt>,
* <tt>output-\>f</tt>, and <tt>output-\>phi</tt> as necessary. The
* <tt>output-\>shift</tt> field will remain set to \c NULL.
*
* ### Algorithm ###
*
* For elliptical orbits, we combine \eqref{eq_spinorbit-tr},
* \eqref{eq_spinorbit-t}, and \eqref{eq_spinorbit-upsilon} to get \f$t_r\f$
* directly as a function of the eccentric anomaly \f$E\f$:
* \f{eqnarray}{
* \label{eq_tr-e1}
* t_r = t_p & + & \left(\frac{r_p \sin i}{c}\right)\sin\omega\\
* & + & \left(\frac{P}{2\pi}\right) \left( E +
* \left[v_p(1-e)\cos\omega - e\right]\sin E
* + \left[v_p\sqrt{\frac{1-e}{1+e}}\sin\omega\right]
* [\cos E - 1]\right) \;,
* \f}
* where \f$v_p=r_p\dot{\upsilon}_p\sin i/c\f$ is a normalized velocity at
* periapsis and \f$P=2\pi\sqrt{(1+e)/(1-e)^3}/\dot{\upsilon}_p\f$ is the
* period of the orbit. For simplicity we write this as:
* \f{equation}{
* \label{eq_tr-e2}
* t_r = T_p + \frac{1}{n}\left( E + A\sin E + B[\cos E - 1] \right) \;,
* \f}
*
* \figure{inject_eanomaly,eps,0.23,Function to be inverted to find eccentric anomaly}
*
* where \f$T_p\f$ is the \e observed time of periapsis passage and
* \f$n=2\pi/P\f$ is the mean angular speed around the orbit. Thus the key
* numerical procedure in this routine is to invert the expression
* \f$x=E+A\sin E+B(\cos E - 1)\f$ to get \f$E(x)\f$. We note that
* \f$E(x+2n\pi)=E(x)+2n\pi\f$, so we only need to solve this expression in
* the interval \f$[0,2\pi)\f$, sketched to the right.
*
* We further note that \f$A^2+B^2<1\f$, although it approaches 1 when
* \f$e\rightarrow1\f$, or when \f$v_p\rightarrow1\f$ and either \f$e=0\f$ or
* \f$\omega=\pi\f$. Except in this limit, Newton-Raphson methods will
* converge rapidly for any initial guess. In this limit, though, the
* slope \f$dx/dE\f$ approaches zero at the point of inflection, and an
* initial guess or iteration landing near this point will send the next
* iteration off to unacceptably large or small values. However, by
* restricting all initial guesses and iterations to the domain
* \f$E\in[0,2\pi)\f$, one will always end up on a trajectory branch that
* will converge uniformly. This should converge faster than the more
* generically robust technique of bisection. (Note: the danger with Newton's method
* has been found to be unstable for certain binary orbital parameters. So if
* Newton's method fails to converge, a bisection algorithm is employed.)
*
* In this algorithm, we start the computation with an arbitrary initial
* guess of \f$E=0\f$, and refine it until the we get agreement to within
* 0.01 parts in part in \f$N_\mathrm{cyc}\f$ (where \f$N_\mathrm{cyc}\f$ is the
* larger of the number of wave cycles in an orbital period, or the
* number of wave cycles in the entire waveform being generated), or one
* part in \f$10^{15}\f$ (an order of magnitude off the best precision
* possible with \c REAL8 numbers). The latter case indicates that
* \c REAL8 precision may fail to give accurate phasing, and one
* should consider modeling the orbit as a set of Taylor frequency
* coefficients \'{a} la <tt>LALGenerateTaylorCW()</tt>. On subsequent
* timesteps, we use the previous timestep as an initial guess, which is
* good so long as the timesteps are much smaller than an orbital period.
* This sequence of guesses will have to readjust itself once every orbit
* (as \f$E\f$ jumps from \f$2\pi\f$ down to 0), but this is relatively
* infrequent; we don't bother trying to smooth this out because the
* additional tests would probably slow down the algorithm overall.
*
* Once a value of \f$E\f$ is found for a given timestep in the output
* series, we compute the system time \f$t\f$ via \eqref{eq_spinorbit-t},
* and use it to determine the wave phase and (non-Doppler-shifted)
* frequency via \eqref{eq_taylorcw-freq}
* and \eqref{eq_taylorcw-phi}. The Doppler shift on the frequency is
* then computed using \eqref{eq_spinorbit-upsilon}
* and \eqref{eq_orbit-rdot}. We use \f$\upsilon\f$ as an intermediate in
* the Doppler shift calculations, since expressing \f$\dot{R}\f$ directly in
* terms of \f$E\f$ results in expression of the form \f$(1-e)/(1-e\cos E)\f$,
* which are difficult to simplify and face precision losses when
* \f$E\sim0\f$ and \f$e\rightarrow1\f$. By contrast, solving for \f$\upsilon\f$ is
* numerically stable provided that the system <tt>atan2()</tt> function is
* well-designed.
*
* The routine does not account for variations in special relativistic or
* gravitational time dilation due to the elliptical orbit, nor does it
* deal with other gravitational effects such as Shapiro delay. To a
* very rough approximation, the amount of phase error induced by
* gravitational redshift goes something like \f$\Delta\phi\sim
* fT(v/c)^2\Delta(r_p/r)\f$, where \f$f\f$ is the typical wave frequency, \f$T\f$
* is either the length of data or the orbital period (whichever is
* \e smaller), \f$v\f$ is the \e true (unprojected) speed at
* periapsis, and \f$\Delta(r_p/r)\f$ is the total range swept out by the
* quantity \f$r_p/r\f$ over the course of the observation. Other
* relativistic effects such as special relativistic time dilation are
* comparable in magnitude. We make a crude estimate of when this is
* significant by noting that \f$v/c\gtrsim v_p\f$ but
* \f$\Delta(r_p/r)\lesssim 2e/(1+e)\f$; we take these approximations as
* equalities and require that \f$\Delta\phi\lesssim\pi\f$, giving:
* \f{equation}{
* \label{eq_relativistic-orbit}
* f_0Tv_p^2\frac{4e}{1+e}\lesssim1 \;.
* \f}
* When this critereon is violated, a warning is generated. Furthermore,
* as noted earlier, when \f$v_p\geq1\f$ the routine will return an error, as
* faster-than-light speeds can cause the emission and reception times to
* be non-monotonic functions of one another.
*/
void
LALGenerateEllipticSpinOrbitCW( LALStatus *stat,
PulsarCoherentGW *output,
SpinOrbitCWParamStruc *params )
{
UINT4 n, i; /* number of and index over samples */
UINT4 nSpin = 0, j; /* number of and index over spindown terms */
REAL8 t, dt, tPow; /* time, interval, and t raised to a power */
REAL8 phi0, f0, twopif0; /* initial phase, frequency, and 2*pi*f0 */
REAL8 f, fPrev; /* current and previous values of frequency */
REAL4 df = 0.0; /* maximum difference between f and fPrev */
REAL8 phi; /* current value of phase */
REAL8 p, vDotAvg; /* orbital period, and 2*pi/(period) */
REAL8 vp; /* projected speed at periapsis */
REAL8 upsilon, argument; /* true anomaly, and argument of periapsis */
REAL8 eCosOmega; /* eccentricity * cosine of argument */
REAL8 tPeriObs; /* time of observed periapsis */
REAL8 spinOff; /* spin epoch - orbit epoch */
REAL8 x; /* observed mean anomaly */
REAL8 dx, dxMax; /* current and target errors in x */
REAL8 a, b; /* constants in equation for x */
REAL8 ecc; /* orbital eccentricity */
REAL8 oneMinusEcc, onePlusEcc; /* 1 - ecc and 1 + ecc */
REAL8 e = 0.0; /* eccentric anomaly */
REAL8 de = 0.0; /* eccentric anomaly step */
REAL8 sine = 0.0, cose = 0.0; /* sine of e, and cosine of e minus 1 */
REAL8 *fSpin = NULL; /* pointer to Taylor coefficients */
REAL4 *fData; /* pointer to frequency data */
REAL8 *phiData; /* pointer to phase data */
INITSTATUS(stat);
ATTATCHSTATUSPTR( stat );
/* Make sure parameter and output structures exist. */
ASSERT( params, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
ASSERT( output, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
/* Make sure output fields don't exist. */
ASSERT( !( output->a ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->f ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->phi ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
ASSERT( !( output->shift ), stat, GENERATESPINORBITCWH_EOUT,
GENERATESPINORBITCWH_MSGEOUT );
/* If Taylor coeficients are specified, make sure they exist. */
if ( params->f ) {
ASSERT( params->f->data, stat, GENERATESPINORBITCWH_ENUL,
GENERATESPINORBITCWH_MSGENUL );
nSpin = params->f->length;
fSpin = params->f->data;
}
/* Set up some constants (to avoid repeated calculation or
dereferencing), and make sure they have acceptable values. */
oneMinusEcc = params->oneMinusEcc;
ecc = 1.0 - oneMinusEcc;
onePlusEcc = 1.0 + ecc;
if ( ecc < 0.0 || oneMinusEcc <= 0.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EECC,
GENERATESPINORBITCWH_MSGEECC );
}
vp = params->rPeriNorm*params->angularSpeed;
n = params->length;
dt = params->deltaT;
f0 = fPrev = params->f0;
vDotAvg = params->angularSpeed
*sqrt( oneMinusEcc*oneMinusEcc*oneMinusEcc/onePlusEcc );
if ( vp >= 1.0 ) {
ABORT( stat, GENERATESPINORBITCWH_EFTL,
GENERATESPINORBITCWH_MSGEFTL );
}
if ( vp <= 0.0 || dt <= 0.0 || f0 <= 0.0 || vDotAvg <= 0.0 ||
n == 0 ) {
ABORT( stat, GENERATESPINORBITCWH_ESGN,
GENERATESPINORBITCWH_MSGESGN );
}
/* Set up some other constants. */
twopif0 = f0*LAL_TWOPI;
phi0 = params->phi0;
argument = params->omega;
p = LAL_TWOPI/vDotAvg;
a = vp*oneMinusEcc*cos( argument ) + oneMinusEcc - 1.0;
b = vp*sqrt( oneMinusEcc/( onePlusEcc ) )*sin( argument );
eCosOmega = ecc*cos( argument );
if ( n*dt > p )
dxMax = 0.01/( f0*n*dt );
else
dxMax = 0.01/( f0*p );
if ( dxMax < 1.0e-15 ) {
dxMax = 1.0e-15;
#ifndef NDEBUG
LALWarning( stat, "REAL8 arithmetic may not have sufficient"
" precision for this orbit" );
#endif
}
#ifndef NDEBUG
if ( lalDebugLevel & LALWARNING ) {
REAL8 tau = n*dt;
if ( tau > p )
tau = p;
if ( f0*tau*vp*vp*ecc/onePlusEcc > 0.25 )
LALWarning( stat, "Orbit may have significant relativistic"
" effects that are not included" );
}
#endif
/* Compute offset between time series epoch and observed periapsis,
and betweem true periapsis and spindown reference epoch. */
tPeriObs = (REAL8)( params->orbitEpoch.gpsSeconds -
params->epoch.gpsSeconds );
tPeriObs += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->epoch.gpsNanoSeconds );
tPeriObs += params->rPeriNorm*sin( params->omega );
spinOff = (REAL8)( params->orbitEpoch.gpsSeconds -
params->spinEpoch.gpsSeconds );
spinOff += 1.0e-9 * (REAL8)( params->orbitEpoch.gpsNanoSeconds -
params->spinEpoch.gpsNanoSeconds );
/* Allocate output structures. */
if ( ( output->a = (REAL4TimeVectorSeries *)
LALMalloc( sizeof(REAL4TimeVectorSeries) ) ) == NULL ) {
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->a, 0, sizeof(REAL4TimeVectorSeries) );
if ( ( output->f = (REAL4TimeSeries *)
LALMalloc( sizeof(REAL4TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->f, 0, sizeof(REAL4TimeSeries) );
if ( ( output->phi = (REAL8TimeSeries *)
LALMalloc( sizeof(REAL8TimeSeries) ) ) == NULL ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
ABORT( stat, GENERATESPINORBITCWH_EMEM,
GENERATESPINORBITCWH_MSGEMEM );
}
memset( output->phi, 0, sizeof(REAL8TimeSeries) );
/* Set output structure metadata fields. */
output->position = params->position;
output->psi = params->psi;
output->a->epoch = output->f->epoch = output->phi->epoch
= params->epoch;
output->a->deltaT = n*params->deltaT;
output->f->deltaT = output->phi->deltaT = params->deltaT;
output->a->sampleUnits = lalStrainUnit;
output->f->sampleUnits = lalHertzUnit;
output->phi->sampleUnits = lalDimensionlessUnit;
snprintf( output->a->name, LALNameLength, "CW amplitudes" );
snprintf( output->f->name, LALNameLength, "CW frequency" );
snprintf( output->phi->name, LALNameLength, "CW phase" );
/* Allocate phase and frequency arrays. */
LALSCreateVector( stat->statusPtr, &( output->f->data ), n );
BEGINFAIL( stat ) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
LALDCreateVector( stat->statusPtr, &( output->phi->data ), n );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
/* Allocate and fill amplitude array. */
{
CreateVectorSequenceIn in; /* input to create output->a */
in.length = 2;
in.vectorLength = 2;
LALSCreateVectorSequence( stat->statusPtr, &(output->a->data), &in );
BEGINFAIL( stat ) {
TRY( LALSDestroyVector( stat->statusPtr, &( output->f->data ) ),
stat );
TRY( LALDDestroyVector( stat->statusPtr, &( output->phi->data ) ),
stat );
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
} ENDFAIL( stat );
output->a->data->data[0] = output->a->data->data[2] = params->aPlus;
output->a->data->data[1] = output->a->data->data[3] = params->aCross;
}
/* Fill frequency and phase arrays. */
fData = output->f->data->data;
phiData = output->phi->data->data;
for ( i = 0; i < n; i++ ) {
INT4 nOrb; /* number of orbits since the specified orbit epoch */
/* First, find x in the range [0,2*pi]. */
x = vDotAvg*( i*dt - tPeriObs );
nOrb = (INT4)( x/LAL_TWOPI );
if ( x < 0.0 )
nOrb -= 1;
x -= LAL_TWOPI*nOrb;
/* Newton-Raphson iteration to find E(x). Maximum of 100 iterations. */
INT4 maxiter = 100, iter = 0;
while ( iter<maxiter && fabs( dx = e + a*sine + b*cose - x ) > dxMax ) {
iter++;
//Make a check on the step-size so we don't step too far
de = dx/( 1.0 + a*cose + a - b*sine );
if ( de > LAL_PI )
de = LAL_PI;
else if ( de < -LAL_PI )
de = -LAL_PI;
e -= de;
if ( e < 0.0 )
e = 0.0;
else if ( e > LAL_TWOPI )
e = LAL_TWOPI;
sine = sin( e );
cose = cos( e ) - 1.0;
}
/* Bisection algorithm from GSL if Newton's method (above) fails to converge. */
if (iter==maxiter && fabs( dx = e + a*sine + b*cose - x ) > dxMax ) {
//Initialize solver
const gsl_root_fsolver_type *T = gsl_root_fsolver_bisection;
gsl_root_fsolver *s = gsl_root_fsolver_alloc(T);
REAL8 e_lo = 0.0, e_hi = LAL_TWOPI;
gsl_function F;
struct E_solver_params pars = {a, b, x};
F.function = &gsl_E_solver;
F.params = &pars;
if (gsl_root_fsolver_set(s, &F, e_lo, e_hi) != 0) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
ABORT( stat, -1, "GSL failed to set initial points" );
}
INT4 keepgoing = 1;
INT4 success = 0;
INT4 root_status = keepgoing;
e = 0.0;
iter = 0;
while (root_status==keepgoing && iter<maxiter) {
iter++;
root_status = gsl_root_fsolver_iterate(s);
if (root_status!=keepgoing && root_status!=success) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
ABORT( stat, -1, "gsl_root_fsolver_iterate() failed" );
}
e = gsl_root_fsolver_root(s);
sine = sin(e);
cose = cos(e) - 1.0;
if (fabs( dx = e + a*sine + b*cose - x ) > dxMax) root_status = keepgoing;
else root_status = success;
}
if (root_status!=success) {
LALFree( output->a ); output->a = NULL;
LALFree( output->f ); output->f = NULL;
LALFree( output->phi ); output->phi = NULL;
gsl_root_fsolver_free(s);
ABORT( stat, -1, "Could not converge using bisection algorithm" );
}
gsl_root_fsolver_free(s);
}
/* Compute source emission time, phase, and frequency. */
phi = t = tPow =
( e + LAL_TWOPI*nOrb - ecc*sine )/vDotAvg + spinOff;
f = 1.0;
for ( j = 0; j < nSpin; j++ ) {
f += fSpin[j]*tPow;
phi += fSpin[j]*( tPow*=t )/( j + 2.0 );
}
/* Appy frequency Doppler shift. */
upsilon = 2.0 * atan2 ( sqrt(onePlusEcc/oneMinusEcc) * sin(0.5*e), cos(0.5*e) );
f *= f0 / ( 1.0 + vp*( cos( argument + upsilon ) + eCosOmega ) /onePlusEcc );
phi *= twopif0;
if ( (i > 0) && (fabs( f - fPrev ) > df) )
df = fabs( f - fPrev );
*(fData++) = fPrev = f;
*(phiData++) = phi + phi0;
} /* for i < n */
/* Set output field and return. */
params->dfdt = df*dt;
DETATCHSTATUSPTR( stat );
RETURN( stat );
}
