LALSimulation.c

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/*
 * Copyright (C) 2008 J. Creighton, T. Creighton
 *
 *  This program is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 *
 *  This program is distributed in the hope that it will be useful,
 *  but WITHOUT ANY WARRANTY; without even the implied warranty of
 *  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *  GNU General Public License for more details.
 *
 *  You should have received a copy of the GNU General Public License
 *  along with with program; see the file COPYING. If not, write to the
 *  Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
 *  MA  02110-1301  USA
 */
 
/*
 * ============================================================================
 *
 *                                  Preamble
 *
 * ============================================================================
 */
 
 
#include <math.h>
#include <gsl/gsl_sf_expint.h>
#include <lal/LALSimulation.h>
#include <lal/LALDetectors.h>
#include <lal/DetResponse.h>
#include <lal/Date.h>
#include <lal/Units.h>
#include <lal/TimeDelay.h>
#include <lal/SkyCoordinates.h>
#include <lal/TimeSeries.h>
#include <lal/TimeSeriesInterp.h>
#include <lal/FrequencySeries.h>
#include <lal/TimeFreqFFT.h>
#include <lal/Window.h>
#include "check_series_macros.h"
 
/*
 * ============================================================================
 *
 *                                 Utilities
 *
 * ============================================================================
 */
 
 
/*
 * Note:  this function will round really really large numbers "up" to 0.
 */
 
 
static unsigned long round_up_to_power_of_two(unsigned long x)
{
        unsigned n;
 
        x--;
        /* if x shares bits with x + 1, then x + 1 is not a power of 2 */
        for(n = 1; n && (x & (x + 1)); n *= 2)
                x |= x >> n;
 
        return x + 1;
}
 
 
/**
 * @brief Turn a detector prefix string into a LALDetector structure.
 * @details
 * The first two characters of the input string are used as the instrument
 * name, which allows channel names in the form `H1:LSC-STRAIN` to be used.
 * The return value is a pointer into the lalCachedDetectors array, so
 * modifications to the contents are global.  Make a copy of the structure if
 * you want to modify it safely.
 * @param[in] string The detector prefix string.
 * @returns
 * A cached LALDetector structure corresponding to the supplied prefix.
 * @retval NULL Unrecognized prefix string.
 */
const LALDetector *XLALDetectorPrefixToLALDetector(
        const char *string
)
{
        int i;
 
        for(i = 0; i < LAL_NUM_DETECTORS; i++)
                if(!strncmp(string, lalCachedDetectors[i].frDetector.prefix, 2))
                        return &lalCachedDetectors[i];
 
        XLALPrintError("%s(): error: can't identify instrument from string \"%s\"\n", __func__, string);
        XLAL_ERROR_NULL(XLAL_EDATA);
}
 
 
/*
 * ============================================================================
 *
 *                            Injection Machinery
 *
 * ============================================================================
 */
 
 
#if 0
REAL8TimeSeries * XLALSimQuasiPeriodicInjectionREAL8TimeSeries( REAL8TimeSeries *aplus, REAL8TimeSeries *across, REAL8TimeSeries *frequency, REAL8TimeSeries *phi, REAL8TimeSeries *psi, SkyPosition *position, LALDetector *detector, EphemerisData *ephemerides, LIGOTimeGPS *start, REAL8 deltaT, UINT4 length, COMPLEX16FrequencySeries *response )
{
        REAL8 slowDeltaT = 600.0; /* 10 minutes */
        UINT4 slowLength;
 
        /* sanity checks */
 
        /* SET UP LOOK-UP TABLES */
 
        /* construct time-dependent time-delay look-up table */
        /* uses ephemeris */
        /* sampled slowDeltaT */
        /* starts 8 min before injection start, ends 8 min after injection end */
        slowLength = floor(0.5 + (length*deltaT + 16.0)/slowDeltaT);
 
        /* construct time-dependent polarization response look-up table */
        /* sampled at slowDeltaT */
        /* starts 8 min before injection start, ends 8 min after injection end */
        fplus;
        fcross;
 
 
 
        /* apply time-dependent time-delay */
        /* apply time-dependent polarization response */
        /* apply frequency-dependent detector response */
        for ( j = 0; j < injection->length; ++j ) {
                REAL8 dt;
                REAL8 fpl;
                REAL8 fcr;
                REAL8 apl;
                REAL8 acr;
                REAL8 freq;
                REAL8 phase;
                REAL8 pol;
 
                /* interpolate to get dt, fpl, fcr */
 
                /* interpolate to get apl, acr, freq, phase, pol */
                /* but not at detector time: detector time plus dt */
 
                /* rotate fpl and fcr using pol */
 
                /* adjust apl, acr, and phase by detector response at freq */
 
                injection->data->data[j] = fpl*apl*cos(phase) + fcr*acr*sin(phase); /* or something like this */
 
        }
 
 
 
}
#endif
 
 
struct highfreq_kernel_data {
        double welch_factor;
        double T; /*armlen/(c*deltaT)*/
        double armcos;
};
 
 
/**
 * This kernel function incorporates beyond-long-wavelength effects.
 * The derivation of the formula is summarized in
 * Soichiro Morisaki, "Kernel function for injection of signals with short
 * wavelength", LIGO-T1800394.
 */
static void highfreq_kernel(double *cached_kernel, int kernel_length, double residual, void *data)
{
        struct highfreq_kernel_data *kernel_data = data;
        double welch_factor = kernel_data->welch_factor;
        double T = kernel_data->T;
        double armcos = kernel_data->armcos;
        double *stop = cached_kernel + kernel_length;
        int i;
 
        for(i = -(kernel_length - 1) / 2; cached_kernel < stop; i++) {
                double x = i + residual;
                double y = welch_factor * x;
                if(fabs(y) < 1.) {
                        double Si1 = gsl_sf_Si(LAL_PI * (x + T * armcos));
                        double Si2 = gsl_sf_Si(LAL_PI * (x + T));
                        double Si3 = gsl_sf_Si(LAL_PI * (x - T));
                        *cached_kernel++ = ((Si2 - Si1) / (T * (1. - armcos)) + (Si1 - Si3) / (T * (1. + armcos))) * (1. - y * y) / LAL_TWOPI;
                } else
                        *cached_kernel++ = 0.;
        }
};
 
 
/**
 * @brief Transforms the waveform polarizations into a detector strain
 * @details
 * This routine takes the plus and cross waveform polarizations, along
 * with the sky position, polarization angle, and detector structure,
 * and computes the external strain on the detector.
 *
 * The input time series should have their epochs set to the start of
 * those time series at the geocetre (for simplicity the epochs must be
 * the same, and they must have the same length and sample rates)
 *
 * @param[in] hplus Pointer to a REAL8TimeSeries containing the plus polarization waveform
 * @param[in] hcross Pointer to a REAL8TimeSeries containing the cross polarization waveform
 * @param[in] right_ascension The right ascension of the source in radians
 * @param[in] declination The declination of the source in radians
 * @param[in] psi The polarization angle giving the orientation of the wave co-ordinate system in radians
 * @param[in] detector Pointer to a LALDetector structure for the detector into which the injection is destined to be injected
 *
 * @returns
 * The strain time series as seen in the detector, with the epoch set to
 * the start of the time series at that detector.  The output time series
 * units are the same as the two input time series (which must both have
 * the same sample units).
 *
 * @retval NULL Failure
 *
 * @note
 * A 19-sample Welch-windowed sinc kernel is used for sub-sample
 * interpolation.  See XLALREAL8TimeSeriesInterpEval() for more
 * information, and consider the frequency response of this kernel when
 * using this function with injections whose frequency content approaches
 * the Nyquist frequency.
 * @n@n
 * The geometric delay and antenna response are only recalculated every 250
 * ms --- the Earth's rotation is modelled as discontinuous jumps occurring
 * at a rate of 4 Hz.  The Earth rotates at 7e-5 rad/s, therefore given a
 * radius of 6e6 m and c=3e8 m/s, the maximum geometric speed for points on
 * the surface is about 1.5 us/s.  Updating the detector response and
 * geometric delay every 250 ms means the antenna response is accurate to
 * about +/- 20 urad and the geometric delay to about +/- 300 ns (about
 * 0.01 sample at 32 kHz).  Because we use UTC (instead of UT1) sidereal
 * time is only accurate to +/- 900 ms, so assuming the Earth's orientation
 * to be fixed for 250 ms at a time is not the dominant source of Earth
 * orientation error in these calculations, but one should be aware of the
 * periodic nature of the updates if extreme phase stability is required.
 * @n@n
 * The output time series is padded to capture the interpolation kernel
 * structure resulting from possible sharp edges at the start or end of the
 * input time series data.  Neglecting the padding for the interpolation
 * kernel's impulse response, the output time series is, in general, not
 * the same duration as the input time series due to Doppler compression or
 * resulting from Earth rotation.
 */
REAL8TimeSeries *XLALSimDetectorStrainREAL8TimeSeries(
        const REAL8TimeSeries *hplus,
        const REAL8TimeSeries *hcross,
        REAL8 right_ascension,
        REAL8 declination,
        REAL8 psi,
        const LALDetector *detector
)
{
        /* mean arm length in samples */
        const double arm_length_samples = (detector->frDetector.xArmMidpoint + detector->frDetector.yArmMidpoint) / (LAL_C_SI * hplus->deltaT);
        /* kernel length in samples.  increase by 28 times the arm length
         * to accomodate the additional signal delay. */
        const int kernel_length = 67 + 48 * lround(2.0 * arm_length_samples);
        /* 0.25 s or 1 sample whichever is larger */
        const unsigned det_resp_interval = round(0.25 / hplus->deltaT) < 1 ? 1 : round(0.25 / hplus->deltaT);
        REAL8TimeSeries *xsignal = NULL;
        REAL8TimeSeries *ysignal = NULL;
        LALREAL8TimeSeriesInterp *xinterp = NULL;
        LALREAL8TimeSeriesInterp *yinterp = NULL;
        struct highfreq_kernel_data xdata;
        struct highfreq_kernel_data ydata;
        double fxplus = XLAL_REAL8_FAIL_NAN;
        double fxcross = XLAL_REAL8_FAIL_NAN;
        double fyplus = XLAL_REAL8_FAIL_NAN;
        double fycross = XLAL_REAL8_FAIL_NAN;
        double geometric_delay = XLAL_REAL8_FAIL_NAN;
        LIGOTimeGPS t;  /* a time */
        double dt;      /* an offset */
        char *name;
        REAL8TimeSeries *h = NULL;
        unsigned i;
 
        /* check input */
 
        LAL_CHECK_VALID_SERIES(hplus, NULL);
        LAL_CHECK_VALID_SERIES(hcross, NULL);
        LAL_CHECK_CONSISTENT_TIME_SERIES(hplus, hcross, NULL);
        /* test that the input's length can be treated as a signed valued
         * without overflow, and that adding the kernel length plus an
         * Earth diameter's worth of samples won't overflow */
        if((int) hplus->data->length < 0 || (int) (hplus->data->length + kernel_length + 2.0 * LAL_REARTH_SI / LAL_C_SI / hplus->deltaT) < 0) {
                XLALPrintError("%s(): error: input series too long\n", __func__);
                XLAL_ERROR_NULL(XLAL_EBADLEN);
        }
 
        /* generate name */
 
        name = XLALMalloc(strlen(detector->frDetector.prefix) + 11);
        if(!name)
                goto error;
        sprintf(name, "%s injection", detector->frDetector.prefix);
 
        /* allocate output time series.  the time series' duration is
         * adjusted to account for Doppler-induced dilation of the
         * waveform, and is padded to accomodate ringing of the
         * interpolation kernel.  the sign of dt follows from the
         * observation that time stamps in the output time series are
         * mapped to time stamps in the input time series by adding the
         * output of XLALTimeDelayFromEarthCenter(), so if that number is
         * larger at the start of the waveform than at the end then the
         * output time series must be longer than the input.  (the Earth's
         * rotation is not super-luminal so we don't have to account for
         * time reversals in the mapping) */
 
        /* time (at geocentre) of end of waveform */
        t = hplus->epoch;
        if(!XLALGPSAdd(&t, hplus->data->length * hplus->deltaT)) {
                XLALFree(name);
                goto error;
        }
        /* change in geometric delay from start to end */
        dt = XLALTimeDelayFromEarthCenter(detector->location, right_ascension, declination, &hplus->epoch) - XLALTimeDelayFromEarthCenter(detector->location, right_ascension, declination, &t);
        /* allocate, lengthen sequence to incorporate time delay caused by
         * beyond-long-wavelength effect */
        h = XLALCreateREAL8TimeSeries(name, &hplus->epoch, hplus->f0, hplus->deltaT, &hplus->sampleUnits, (int) hplus->data->length + kernel_length - 1 + ceil(dt / hplus->deltaT) + lround(4.0 * arm_length_samples));
        XLALFree(name);
        if(!h)
                goto error;
 
        /* shift the epoch so that the start of the input time series
         * passes through this detector at the time of the sample at offset
         * (kernel_length-1)/2   we assume the kernel is sufficiently short
         * that it doesn't matter whether we compute the geometric delay at
         * the start or middle of the kernel. */
 
        geometric_delay = XLALTimeDelayFromEarthCenter(detector->location, right_ascension, declination, &h->epoch);
        if(XLAL_IS_REAL8_FAIL_NAN(geometric_delay))
                goto error;
        if(!XLALGPSAdd(&h->epoch, geometric_delay - (kernel_length - 1) / 2 * h->deltaT))
                goto error;
 
        /* round epoch to an integer sample boundary so that
         * XLALSimAddInjectionREAL8TimeSeries() can use no-op code path.
         * note:  we assume a sample boundary occurs on the integer second.
         * if this isn't the case (e.g, time-shifted injections or some GEO
         * data) that's OK, but we might end up paying for a second
         * sub-sample time shift when adding the the time series into the
         * target data stream in XLALSimAddInjectionREAL8TimeSeries().
         * don't bother checking for errors, this is changing the timestamp
         * by less than 1 sample, if we're that close to overflowing it'll
         * be caught in the loop below. */
 
        dt = XLALGPSModf(&dt, &h->epoch);
        XLALGPSAdd(&h->epoch, round(dt / h->deltaT) * h->deltaT - dt);
 
        /* Compute signals at the times of samples in hplus in advance.
         * It reduces the computational cost for interpolation */
 
        xsignal = XLALCreateREAL8TimeSeries("xsignal", &hplus->epoch, hplus->f0, hplus->deltaT, &hplus->sampleUnits, (int) hplus->data->length);
        ysignal = XLALCreateREAL8TimeSeries("ysignal", &hplus->epoch, hplus->f0, hplus->deltaT, &hplus->sampleUnits, (int) hplus->data->length);
        for(i = 0; i < hplus->data->length; i++) {
                t = hplus->epoch;
                if(!XLALGPSAdd(&t, i * hplus->deltaT))
                        goto error;
                /* Compute detector's response. Here the geometric delay
                 * from geocenter is neglected since it is small compared
                 * to the rotational period of the Earth */
                if(!(i % det_resp_interval)) {
                        double armlen = XLAL_REAL8_FAIL_NAN;
                        double xcos = XLAL_REAL8_FAIL_NAN;
                        double ycos = XLAL_REAL8_FAIL_NAN;
                        XLALComputeDetAMResponseParts(&armlen, &xcos, &ycos, &fxplus, &fyplus, &fxcross, &fycross, detector, right_ascension, declination, psi, XLALGreenwichMeanSiderealTime(&t));
                }
                xsignal->data->data[i] = fxplus * hplus->data->data[i] + fxcross * hcross->data->data[i];
                ysignal->data->data[i] = fyplus * hplus->data->data[i] + fycross * hcross->data->data[i];
                if(XLAL_IS_REAL8_FAIL_NAN(xsignal->data->data[i]) || XLAL_IS_REAL8_FAIL_NAN(ysignal->data->data[i]))
                        goto error;
        }
 
        /* initialize interpolators. */
 
        /* use filtering interpolators.  see TimeSeriesInterp.c for
         * meaning of welch_factor */
        xdata.welch_factor = ydata.welch_factor = 1.0 / ((kernel_length - 1.) / 2. + 1.);
        xinterp = XLALREAL8TimeSeriesInterpCreate(xsignal, kernel_length, highfreq_kernel, &xdata);
        yinterp = XLALREAL8TimeSeriesInterpCreate(ysignal, kernel_length, highfreq_kernel, &ydata);
        if(!xinterp || !yinterp)
                goto error;
 
        /* compute output sample by sample */
        /* FIXME: Now xdata and ydata are not renewed until geometric delay
         * changes significantly. This can cause systematic errors. For
         * example, if the detector is on the North pole, xdata and ydata
         * are never renewed although armcos can be changing. */
 
        for(i = 0; i < h->data->length; i++) {
                /* time of sample in detector */
                t = h->epoch;
                if(!XLALGPSAdd(&t, i * h->deltaT))
                        goto error;
 
                /* geometric delay from geocentre and highfreq_kernel_data */
                if(!(i % det_resp_interval)) {
                        geometric_delay = -XLALTimeDelayFromEarthCenter(detector->location, right_ascension, declination, &t);
                        /* Compute highfreq_kernel_data */
                        double armlen = XLAL_REAL8_FAIL_NAN;
                        XLALComputeDetAMResponseParts(&armlen, &xdata.armcos, &ydata.armcos, &fxplus, &fyplus, &fxcross, &fycross, detector, right_ascension, declination, psi, XLALGreenwichMeanSiderealTime(&t));
                        armlen /= LAL_C_SI * h->deltaT;
                        xdata.T = armlen;
                        ydata.T = armlen;
                }
                if(XLAL_IS_REAL8_FAIL_NAN(geometric_delay))
                        goto error;
                if(XLAL_IS_REAL8_FAIL_NAN(xdata.T) || XLAL_IS_REAL8_FAIL_NAN(ydata.T) || XLAL_IS_REAL8_FAIL_NAN(xdata.armcos) || XLAL_IS_REAL8_FAIL_NAN(ydata.armcos))
                        goto error;
 
                /* time of sample at geocentre */
                if(!XLALGPSAdd(&t, geometric_delay))
                        goto error;
 
                /* evaluate linear combination of interpolators */
                h->data->data[i] = XLALREAL8TimeSeriesInterpEval(xinterp, &t, 0) + XLALREAL8TimeSeriesInterpEval(yinterp, &t, 0);
 
                if(XLAL_IS_REAL8_FAIL_NAN(h->data->data[i]))
                        goto error;
        }
 
        /* done */
        XLALREAL8TimeSeriesInterpDestroy(xinterp);
        XLALREAL8TimeSeriesInterpDestroy(yinterp);
        XLALDestroyREAL8TimeSeries(xsignal);
        XLALDestroyREAL8TimeSeries(ysignal);
        return h;
 
error:
        XLALREAL8TimeSeriesInterpDestroy(xinterp);
        XLALREAL8TimeSeriesInterpDestroy(yinterp);
        XLALDestroyREAL8TimeSeries(xsignal);
        XLALDestroyREAL8TimeSeries(ysignal);
        XLALDestroyREAL8TimeSeries(h);
        XLAL_ERROR_NULL(XLAL_EFUNC);
}
 
 
/**
 * @brief Adds a detector strain time series to detector data.
 * @details
 * Essentially a wrapper for XLALAddREAL8TimeSeries(), but performs
 * sub-sample re-interpolation to adjust the source time series epoch to
 * lie on an integer sample boundary in the target time series.  This
 * transformation is done in the frequency domain, so it is convenient to
 * allow a response function to be applied at the same time.  Passing NULL
 * for the response function turns this feature off (i.e., uses a unit
 * response).
 *
 * This function accepts source and target time series whose units are not
 * the same, and allows the two time series to be herterodyned (although it
 * currently requires them to have the same heterodyne frequency).
 *
 * @param[in,out] target Pointer to the time series into which the strain will
 * be added
 *
 * @param[in,out] h Pointer to the time series containing the detector strain
 * (the strain data is modified by this routine)
 *
 * @param[in] response Pointer to the response function transforming strain to
 * detector output units, or NULL for unit response.
 *
 * @retval 0 Success
 * @retval <0 Failure
 *
 * @attention
 * The source time series is modified in place by this function!
 */
int XLALSimAddInjectionREAL8TimeSeries(
        REAL8TimeSeries *target,
        REAL8TimeSeries *h,
        const COMPLEX16FrequencySeries *response
)
{
        /* 1 ns is about 10^-5 samples at 16384 Hz */
        const double noop_threshold = 1e-4;     /* samples */
        /* the source time series is padded with at least this many 0's at
         * the start and end before re-interpolation in an attempt to
         * suppress aperiodicity artifacts, and 1/2 this many samples is
         * clipped from the start and end afterwards */
        const unsigned aperiodicity_suppression_buffer = 32768;
        double start_sample_int;
        double start_sample_frac;
 
        /* check input */
 
        /* FIXME:  since we route the source time series through the
         * frequency domain, it might not be hard to adjust the heterodyne
         * frequency and sample rate to match the target time series
         * instead of making it an error if they don't match. */
 
        if(h->deltaT != target->deltaT || h->f0 != target->f0) {
                XLALPrintError("%s(): error: input sample rates or heterodyne frequencies do not match\n", __func__);
                XLAL_ERROR(XLAL_EINVAL);
        }
 
        /* compute the integer and fractional parts of the sample index in
         * the target time series on which the source time series begins.
         * modf() returns integer and fractional parts that have the same
         * sign, e.g. -3.9 --> -3 + -0.9.  we adjust these so that the
         * magnitude of the fractional part is not greater than 0.5, e.g.
         * -3.9 --> -4 + 0.1, so that we never do more than 1/2 a sample of
         * re-interpolation.  I don't know if really makes any difference,
         * though */
 
        start_sample_frac = modf(XLALGPSDiff(&h->epoch, &target->epoch) / target->deltaT, &start_sample_int);
        if(start_sample_frac < -0.5) {
                start_sample_frac += 1.0;
                start_sample_int -= 1.0;
        } else if(start_sample_frac > +0.5) {
                start_sample_frac -= 1.0;
                start_sample_int += 1.0;
        }
 
        /* perform sub-sample interpolation if needed */
 
        if(fabs(start_sample_frac) > noop_threshold || response) {
                COMPLEX16FrequencySeries *tilde_h;
                REAL8FFTPlan *plan;
                REAL8Window *window;
                unsigned i;
 
                /* extend the source time series by adding the
                 * "aperiodicity padding" to the start and end.  for
                 * efficiency's sake, make sure the new length is a power
                 * of two, and don't forget to adjust the start index in
                 * the target time series. */
 
                i = round_up_to_power_of_two(h->data->length + 2 * aperiodicity_suppression_buffer);
                if(i < h->data->length) {
                        /* integer overflow */
                        XLALPrintError("%s(): error: source time series too long\n", __func__);
                        XLAL_ERROR(XLAL_EBADLEN);
                }
                start_sample_int -= (i - h->data->length) / 2;
                if(!XLALResizeREAL8TimeSeries(h, -(int) (i - h->data->length) / 2, i))
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* transform source time series to frequency domain.  the
                 * FFT function populates the frequency series' metadata
                 * with the appropriate values. */
 
                tilde_h = XLALCreateCOMPLEX16FrequencySeries(NULL, &h->epoch, 0, 0, &lalDimensionlessUnit, h->data->length / 2 + 1);
                plan = XLALCreateForwardREAL8FFTPlan(h->data->length, 0);
                if(!tilde_h || !plan) {
                        XLALDestroyCOMPLEX16FrequencySeries(tilde_h);
                        XLALDestroyREAL8FFTPlan(plan);
                        XLAL_ERROR(XLAL_EFUNC);
                }
                i = XLALREAL8TimeFreqFFT(tilde_h, h, plan);
                XLALDestroyREAL8FFTPlan(plan);
                if(i) {
                        XLALDestroyCOMPLEX16FrequencySeries(tilde_h);
                        XLAL_ERROR(XLAL_EFUNC);
                }
 
                /* apply sub-sample time correction and optional response
                 * function */
 
                for(i = 0; i < tilde_h->data->length; i++) {
                        const double f = tilde_h->f0 + i * tilde_h->deltaF;
                        COMPLEX16 fac;
 
                        /* phase for sub-sample time correction */
 
                        fac = cexp(-I * LAL_TWOPI * f * start_sample_frac * target->deltaT);
 
                        /* divide the source by the response function.  if
                         * a frequency is required that lies outside the
                         * domain of definition of the response function,
                         * then the response is assumed equal to its value
                         * at the nearest edge of the domain of definition.
                         * within the domain of definition, frequencies are
                         * rounded to the nearest bin.  if the response
                         * function is zero in some bin, then the source
                         * data is zeroed in that bin (instead of dividing
                         * by 0).  */
 
                        /* FIXME:  should we use GSL to construct an
                         * interpolator for the modulus and phase as
                         * functions of frequency, and use that to evaluate
                         * the response?  instead of rounding to nearest
                         * bin? */
 
                        if(response) {
                                int j = floor((f - response->f0) / response->deltaF + 0.5);
                                if(j < 0)
                                        j = 0;
                                else if((unsigned) j > response->data->length - 1)
                                        j = response->data->length - 1;
                                if(response->data->data[j] == 0.0)
                                        fac = 0.0;
                                else
                                        fac /= response->data->data[j];
                        }
 
                        /* apply factor */
 
                        tilde_h->data->data[i] *= fac;
                }
 
                /* adjust DC and Nyquist components.  the DC component must
                 * always be real-valued.  because we have adjusted the
                 * source time series to have a length that is an even
                 * integer (we've made it a power of 2) the Nyquist
                 * component must also be real valued. */
 
                if(response) {
                        /* a response function has been provided.  zero the
                         * DC and Nyquist components */
                        if(tilde_h->f0 == 0.0)
                                tilde_h->data->data[0] = 0.0;
                        tilde_h->data->data[tilde_h->data->length - 1] = 0.0;
                } else {
                        /* no response has been provided.  set the phase of
                         * the DC component to 0, set the imaginary
                         * component of the Nyquist to 0 */
                        if(tilde_h->f0 == 0.0)
                                tilde_h->data->data[0] = cabs(tilde_h->data->data[0]);
                        tilde_h->data->data[tilde_h->data->length - 1] = creal(tilde_h->data->data[tilde_h->data->length - 1]);
                }
 
                /* return to time domain */
 
                plan = XLALCreateReverseREAL8FFTPlan(h->data->length, 0);
                if(!plan) {
                        XLALDestroyCOMPLEX16FrequencySeries(tilde_h);
                        XLAL_ERROR(XLAL_EFUNC);
                }
                i = XLALREAL8FreqTimeFFT(h, tilde_h, plan);
                XLALDestroyREAL8FFTPlan(plan);
                XLALDestroyCOMPLEX16FrequencySeries(tilde_h);
                if(i)
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* the deltaT can get "corrupted" by floating point
                 * round-off during its trip through the frequency domain.
                 * since this function starts by confirming that the sample
                 * rate of the source matches that of the target time
                 * series, we can use the target series' sample rate to
                 * reset the source's sample rate to its original value.
                 * but we do a check to make sure we're not masking a real
                 * bug */
 
                if(fabs(h->deltaT - target->deltaT) / target->deltaT > 1e-12) {
                        XLALPrintError("%s(): error: oops, internal sample rate mismatch\n", __func__);
                        XLAL_ERROR(XLAL_EERR);
                }
                h->deltaT = target->deltaT;
 
                /* set source epoch from target epoch and integer sample
                 * offset */
 
                h->epoch = target->epoch;
                XLALGPSAdd(&h->epoch, start_sample_int * target->deltaT);
 
                /* clip half of the "aperiodicity padding" from the start
                 * and end of the source time series in a continuing effort
                 * to suppress aperiodicity artifacts. */
 
                if(!XLALResizeREAL8TimeSeries(h, aperiodicity_suppression_buffer / 2, h->data->length - aperiodicity_suppression_buffer))
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* apply a Tukey window whose tapers lie within the
                 * remaining aperiodicity padding. leaving one sample of
                 * the aperiodicty padding untouched on each side of the
                 * original time series because the data might have been
                 * shifted into it */
 
                window = XLALCreateTukeyREAL8Window(h->data->length, (double) (aperiodicity_suppression_buffer - 2) / h->data->length);
                if(!window)
                        XLAL_ERROR(XLAL_EFUNC);
                for(i = 0; i < h->data->length; i++)
                        h->data->data[i] *= window->data->data[i];
                XLALDestroyREAL8Window(window);
        }
 
        /* add source time series to target time series */
 
        if(!XLALAddREAL8TimeSeries(target, h))
                XLAL_ERROR(XLAL_EFUNC);
 
        /* done */
 
        return 0;
}
 
 
/**
 * @brief Adds a detector strain time series to detector data.
 * @details
 * Essentially a wrapper for XLALAddREAL4TimeSeries(), but performs
 * sub-sample re-interpolation to adjust the source time series epoch to
 * lie on an integer sample boundary in the target time series.  This
 * transformation is done in the frequency domain, so it is convenient to
 * allow a response function to be applied at the same time.  Passing NULL
 * for the response function turns this feature off (i.e., uses a unit
 * response).
 *
 * This function accepts source and target time series whose units are not
 * the same, and allows the two time series to be herterodyned (although it
 * currently requires them to have the same heterodyne frequency).
 *
 * @param[in,out] target Pointer to the time series into which the strain will
 * be added
 *
 * @param[in,out] h Pointer to the time series containing the detector strain
 * (the strain data is modified by this routine)
 *
 * @param[in] response Pointer to the response function transforming strain to
 * detector output units, or NULL for unit response.
 *
 * @retval 0 Success
 * @retval <0 Failure
 *
 * @attention
 * The source time series is modified in place by this function!
 */
int XLALSimAddInjectionREAL4TimeSeries(
        REAL4TimeSeries *target,
        REAL4TimeSeries *h,
        const COMPLEX8FrequencySeries *response
)
{
        /* 1 ns is about 10^-5 samples at 16384 Hz */
        const double noop_threshold = 1e-4;     /* samples */
        /* the source time series is padded with at least this many 0's at
         * the start and end before re-interpolation in an attempt to
         * suppress aperiodicity artifacts, and 1/2 this many samples is
         * clipped from the start and end afterwards */
        const unsigned aperiodicity_suppression_buffer = 32768;
        double start_sample_int;
        double start_sample_frac;
 
        /* check input */
 
        /* FIXME:  since we route the source time series through the
         * frequency domain, it might not be hard to adjust the heterodyne
         * frequency and sample rate to match the target time series
         * instead of making it an error if they don't match. */
 
        if(h->deltaT != target->deltaT || h->f0 != target->f0) {
                XLALPrintError("%s(): error: input sample rates or heterodyne frequencies do not match\n", __func__);
                XLAL_ERROR(XLAL_EINVAL);
        }
 
        /* compute the integer and fractional parts of the sample index in
         * the target time series on which the source time series begins.
         * modf() returns integer and fractional parts that have the same
         * sign, e.g. -3.9 --> -3 + -0.9.  we adjust these so that the
         * magnitude of the fractional part is not greater than 0.5, e.g.
         * -3.9 --> -4 + 0.1, so that we never do more than 1/2 a sample of
         * re-interpolation.  I don't know if really makes any difference,
         * though */
 
        start_sample_frac = modf(XLALGPSDiff(&h->epoch, &target->epoch) / target->deltaT, &start_sample_int);
        if(start_sample_frac < -0.5) {
                start_sample_frac += 1.0;
                start_sample_int -= 1.0;
        } else if(start_sample_frac > +0.5) {
                start_sample_frac -= 1.0;
                start_sample_int += 1.0;
        }
 
        /* perform sub-sample interpolation if needed */
 
        if(fabs(start_sample_frac) > noop_threshold || response) {
                COMPLEX8FrequencySeries *tilde_h;
                REAL4FFTPlan *plan;
                REAL4Window *window;
                unsigned i;
 
                /* extend the source time series by adding the "aperiodicity
                 * padding" to the start and end.  for efficiency's sake, make sure
                 * the new length is a power of two, and don't forget to adjust the
                 * start index in the target time series. */
 
                i = round_up_to_power_of_two(h->data->length + 2 * aperiodicity_suppression_buffer);
                if(i < h->data->length) {
                        /* integer overflow */
                        XLALPrintError("%s(): error: source time series too long\n", __func__);
                        XLAL_ERROR(XLAL_EBADLEN);
                }
                start_sample_int -= (i - h->data->length) / 2;
                if(!XLALResizeREAL4TimeSeries(h, -(int) (i - h->data->length) / 2, i))
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* transform source time series to frequency domain.  the FFT
                 * function populates the frequency series' metadata with the
                 * appropriate values. */
 
                tilde_h = XLALCreateCOMPLEX8FrequencySeries(NULL, &h->epoch, 0, 0, &lalDimensionlessUnit, h->data->length / 2 + 1);
                plan = XLALCreateForwardREAL4FFTPlan(h->data->length, 0);
                if(!tilde_h || !plan) {
                        XLALDestroyCOMPLEX8FrequencySeries(tilde_h);
                        XLALDestroyREAL4FFTPlan(plan);
                        XLAL_ERROR(XLAL_EFUNC);
                }
                i = XLALREAL4TimeFreqFFT(tilde_h, h, plan);
                XLALDestroyREAL4FFTPlan(plan);
                if(i) {
                        XLALDestroyCOMPLEX8FrequencySeries(tilde_h);
                        XLAL_ERROR(XLAL_EFUNC);
                }
 
                /* apply sub-sample time correction and optional response function
                 * */
 
                for(i = 0; i < tilde_h->data->length; i++) {
                        const double f = tilde_h->f0 + i * tilde_h->deltaF;
                        COMPLEX8 fac;
 
                        /* phase for sub-sample time correction */
 
                        fac = cexp(-I * LAL_TWOPI * f * start_sample_frac * target->deltaT);
 
                        /* divide the source by the response function.  if a
                         * frequency is required that lies outside the domain of
                         * definition of the response function, then the response
                         * is assumed equal to its value at the nearest edge of the
                         * domain of definition.  within the domain of definition,
                         * frequencies are rounded to the nearest bin.  if the
                         * response function is zero in some bin, then the source
                         * data is zeroed in that bin (instead of dividing by 0).
                         * */
 
                        /* FIXME:  should we use GSL to construct an interpolator
                         * for the modulus and phase as functions of frequency, and
                         * use that to evaluate the response?  instead of rounding
                         * to nearest bin? */
 
                        if(response) {
                                int j = floor((f - response->f0) / response->deltaF + 0.5);
                                if(j < 0)
                                        j = 0;
                                else if((unsigned) j > response->data->length - 1)
                                        j = response->data->length - 1;
                                if(response->data->data[j] == 0.0)
                                        fac = 0.0;
                                else
                                        fac /= response->data->data[j];
                        }
 
                        /* apply factor */
 
                        tilde_h->data->data[i] *= fac;
                }
 
                /* adjust DC and Nyquist components.  the DC component must always
                 * be real-valued.  because we have adjusted the source time series
                 * to have a length that is an even integer (we've made it a power
                 * of 2) the Nyquist component must also be real valued. */
 
                if(response) {
                        /* a response function has been provided.  zero the DC and
                         * Nyquist components */
                        if(tilde_h->f0 == 0.0)
                                tilde_h->data->data[0] = 0.0;
                        tilde_h->data->data[tilde_h->data->length - 1] = 0.0;
                } else {
                        /* no response has been provided.  set the phase of the DC
                         * component to 0, set the imaginary component of the
                         * Nyquist to 0 */
                        if(tilde_h->f0 == 0.0)
                                tilde_h->data->data[0] = cabsf(tilde_h->data->data[0]);
                        tilde_h->data->data[tilde_h->data->length - 1] = crealf(tilde_h->data->data[tilde_h->data->length - 1]);
                }
 
                /* return to time domain */
 
                plan = XLALCreateReverseREAL4FFTPlan(h->data->length, 0);
                if(!plan) {
                        XLALDestroyCOMPLEX8FrequencySeries(tilde_h);
                        XLAL_ERROR(XLAL_EFUNC);
                }
                i = XLALREAL4FreqTimeFFT(h, tilde_h, plan);
                XLALDestroyREAL4FFTPlan(plan);
                XLALDestroyCOMPLEX8FrequencySeries(tilde_h);
                if(i)
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* the deltaT can get "corrupted" by floating point round-off
                 * during its trip through the frequency domain.  since this
                 * function starts by confirming that the sample rate of the source
                 * matches that of the target time series, we can use the target
                 * series' sample rate to reset the source's sample rate to its
                 * original value.  but we do a check to make sure we're not
                 * masking a real bug */
 
                if(fabs(h->deltaT - target->deltaT) / target->deltaT > 1e-12) {
                        XLALPrintError("%s(): error: oops, internal sample rate mismatch\n", __func__);
                        XLAL_ERROR(XLAL_EERR);
                }
                h->deltaT = target->deltaT;
 
                /* set source epoch from target epoch and integer sample offset */
 
                h->epoch = target->epoch;
                XLALGPSAdd(&h->epoch, start_sample_int * target->deltaT);
 
                /* clip half of the "aperiodicity padding" from the start and end
                 * of the source time series in a continuing effort to suppress
                 * aperiodicity artifacts. */
 
                if(!XLALResizeREAL4TimeSeries(h, aperiodicity_suppression_buffer / 2, h->data->length - aperiodicity_suppression_buffer))
                        XLAL_ERROR(XLAL_EFUNC);
 
                /* apply a Tukey window whose tapers lie within the remaining
                 * aperiodicity padding. leaving one sample of the aperiodicty
                 * padding untouched on each side of the original time series
                 * because the data might have been shifted into it */
 
                window = XLALCreateTukeyREAL4Window(h->data->length, (double) (aperiodicity_suppression_buffer - 2) / h->data->length);
                if(!window)
                        XLAL_ERROR(XLAL_EFUNC);
                for(i = 0; i < h->data->length; i++)
                        h->data->data[i] *= window->data->data[i];
                XLALDestroyREAL4Window(window);
        }
 
        /* add source time series to target time series */
 
        if(!XLALAddREAL4TimeSeries(target, h))
                XLAL_ERROR(XLAL_EFUNC);
 
        /* done */
 
        return 0;
}
 
 
 
 
/* Helper routine that computes a segment of strain data with a single
 * time delay and beam pattern applied to the whole segment.  The duration
 * of the segment must therefore be reasonably short or else the movement
 * of the earth will invalidate the use of a single time shift and beam
 * pattern for the entire segment. */
static int XLALSimComputeStrainSegmentREAL8TimeSeries(
        REAL8TimeSeries *segment,
        const REAL8TimeSeries *hplus,
        const REAL8TimeSeries *hcross,
        COMPLEX16FrequencySeries *work1,
        COMPLEX16FrequencySeries *work2,
        REAL8FFTPlan *fwdplan,
        REAL8FFTPlan *revplan,
        REAL8Window *window,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX16FrequencySeries *response
)
{
        LIGOTimeGPS t;
        double gmst;
        double xcos;
        double ycos;
        double fxplus;
        double fyplus;
        double fxcross;
        double fycross;
        double armlen;
        double deltaT;
        double offint;
        double offrac;
        int offset;
        int j;
        size_t k;
 
        /* this routine assumes the segment has a length of N points where N is
         * a power of two and that the workspace frequency series and the FFT
         * plans are compatible with the size N; these assumptions are not
         * checked: the calling routine must ensure that they are true */
 
        /* compute fplus, fcross, and time delay from earth's center at the
         * time corresponding to the middle of the segment */
 
        t = segment->epoch;
        XLALGPSAdd(&t, 0.5 * segment->data->length * segment->deltaT);
        gmst = XLALGreenwichMeanSiderealTime(&t);
        XLALComputeDetAMResponseParts(&armlen, &xcos, &ycos, &fxplus, &fyplus,
                &fxcross, &fycross, detector, ra, dec, psi, gmst);
        deltaT = XLALTimeDelayFromEarthCenter(detector->location, ra, dec, &t);
 
        /* add to the geometric delay the difference in time between the
         * beginning of the injection timeseries and the beginning of the
         * segment */
 
        deltaT += XLALGPSDiff(&hplus->epoch, &segment->epoch);
 
        /* compute the integer and fractional parts of the sample index in the
         * segment on which the hplus and hcross time series begins: modf()
         * returns integer and fractional parts that have the same sign, e.g.,
         * -3.9 --> -3 + -0.9, and we adjust these so that magnitude of the
         * fractional part is not greater than 0.5, e.g., -3.9 --> -4.0 + 0.1,
         * so that we never do more than 1/2 a sample of re-interpolation */
 
        offrac = modf(deltaT / segment->deltaT, &offint);
        if (offrac < -0.5) {
                offrac += 1.0;
                offint -= 1.0;
        } else if (offrac > 0.5) {
                offrac -= 1.0;
                offint += 1.0;
        }
        offset = offint;
 
        /* now compute the sub-sample time shift that must be applied to the
         * segment data */
 
        deltaT = offrac * segment->deltaT;
 
        /* window the date and put it in frequency domain */
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hplus->data->length + offset) {
                        segment->data->data[j] = window->data->data[j]
                                * hplus->data->data[j - offset];
                } else
                        segment->data->data[j] = 0.0;
 
        if (XLALREAL8TimeFreqFFT(work1, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hcross->data->length + offset) {
                        segment->data->data[j] = window->data->data[j]
                                * hcross->data->data[j - offset];
                } else
                        segment->data->data[j] = 0.0;
 
        if (XLALREAL8TimeFreqFFT(work2, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        /* apply sub-sample time shift in frequency domain */
 
        for (k = 0; k < work1->data->length; ++k) {
                double f = work1->f0 + k * work1->deltaF;
                double beta = f * armlen / LAL_C_SI;
                COMPLEX16 Tx, Ty; /* x- and y-arm transfer functions */
                COMPLEX16 gplus, gcross;
                COMPLEX16 fac;
                
                /* phase for sub-sample time correction */
                fac = cexp(-I * LAL_TWOPI * f * deltaT);
                if (response)
                        fac /= response->data->data[k];
 
                Tx = XLALComputeDetArmTransferFunction(beta, xcos);
                Ty = XLALComputeDetArmTransferFunction(beta, ycos);
                gplus = Tx * fxplus + Ty * fyplus;
                gcross = Tx * fxcross + Ty * fycross;
 
                work1->data->data[k] *= gplus;
                work1->data->data[k] += gcross * work2->data->data[k];
                work1->data->data[k] *= fac;
        }
 
        /* adjust DC and Nyquist components: the DC component must always be
         * real-valued; because the calling routine has made the time series
         * have an even length, the Nyquist component must also be real-valued;
         * also this routine makes the assumption that both the DC and the
         * Nyquist components are zero */
 
        work1->data->data[0] = cabs(work1->data->data[0]);
        work1->data->data[work1->data->length - 1] =
                creal(work1->data->data[work1->data->length - 1]);
        
        /* return data to time domain */
 
        if (XLALREAL8FreqTimeFFT(segment, work1, revplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        return 0;
}
 
/* Helper routine that computes a segment of strain data with a single
 * time delay and beam pattern applied to the whole segment.  The duration
 * of the segment must therefore be reasonably short or else the movement
 * of the earth will invalidate the use of a single time shift and beam
 * pattern for the entire segment. */
static int XLALSimComputeStrainSegmentREAL4TimeSeries(
        REAL4TimeSeries *segment,
        const REAL4TimeSeries *hplus,
        const REAL4TimeSeries *hcross,
        COMPLEX8FrequencySeries *work1,
        COMPLEX8FrequencySeries *work2,
        REAL4FFTPlan *fwdplan,
        REAL4FFTPlan *revplan,
        REAL4Window *window,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX8FrequencySeries *response
)
{
        LIGOTimeGPS t;
        double gmst;
        double xcos;
        double ycos;
        double fxplus;
        double fyplus;
        double fxcross;
        double fycross;
        double armlen;
        double deltaT;
        double offint;
        double offrac;
        int offset;
        int j;
        size_t k;
 
        /* this routine assumes the segment has a length of N points where N is
         * a power of two and that the workspace frequency series and the FFT
         * plans are compatible with the size N; these assumptions are not
         * checked: the calling routine must ensure that they are true */
 
        /* compute fplus, fcross, and time delay from earth's center at the
         * time corresponding to the middle of the segment */
 
        t = segment->epoch;
        XLALGPSAdd(&t, 0.5 * segment->data->length * segment->deltaT);
        gmst = XLALGreenwichMeanSiderealTime(&t);
        XLALComputeDetAMResponseParts(&armlen, &xcos, &ycos, &fxplus, &fyplus,
                &fxcross, &fycross, detector, ra, dec, psi, gmst);
        deltaT = XLALTimeDelayFromEarthCenter(detector->location, ra, dec, &t);
 
        /* add to the geometric delay the difference in time between the
         * beginning of the injection timeseries and the beginning of the
         * segment */
 
        deltaT += XLALGPSDiff(&hplus->epoch, &segment->epoch);
 
        /* compute the integer and fractional parts of the sample index in the
         * segment on which the hplus and hcross time series begins: modf()
         * returns integer and fractional parts that have the same sign, e.g.,
         * -3.9 --> -3 + -0.9, and we adjust these so that magnitude of the
         * fractional part is not greater than 0.5, e.g., -3.9 --> -4.0 + 0.1,
         * so that we never do more than 1/2 a sample of re-interpolation */
 
        offrac = modf(deltaT / segment->deltaT, &offint);
        if (offrac < -0.5) {
                offrac += 1.0;
                offint -= 1.0;
        } else if (offrac > 0.5) {
                offrac -= 1.0;
                offint += 1.0;
        }
        offset = offint;
 
        /* now compute the sub-sample time shift that must be applied to the
         * segment data */
 
        deltaT = offrac * segment->deltaT;
 
        /* window the date and put it in frequency domain */
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hplus->data->length + offset) {
                        segment->data->data[j] = window->data->data[j]
                                * hplus->data->data[j - offset];
                } else
                        segment->data->data[j] = 0.0;
 
        if (XLALREAL4TimeFreqFFT(work1, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hcross->data->length + offset) {
                        segment->data->data[j] = window->data->data[j]
                                * hcross->data->data[j - offset];
                } else
                        segment->data->data[j] = 0.0;
 
        if (XLALREAL4TimeFreqFFT(work2, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        /* apply sub-sample time shift in frequency domain */
 
        for (k = 0; k < work1->data->length; ++k) {
                double f = work1->f0 + k * work1->deltaF;
                double beta = f * armlen / LAL_C_SI;
                COMPLEX16 Tx, Ty; /* x- and y-arm transfer functions */
                COMPLEX16 gplus, gcross;
                COMPLEX16 fac;
                
                /* phase for sub-sample time correction */
                fac = cexp(-I * LAL_TWOPI * f * deltaT);
                if (response)
                        fac /= response->data->data[k];
 
                Tx = XLALComputeDetArmTransferFunction(beta, xcos);
                Ty = XLALComputeDetArmTransferFunction(beta, ycos);
                gplus = Tx * fxplus + Ty * fyplus;
                gcross = Tx * fxcross + Ty * fycross;
 
                work1->data->data[k] *= gplus;
                work1->data->data[k] += gcross * work2->data->data[k];
                work1->data->data[k] *= fac;
        }
 
        /* adjust DC and Nyquist components: the DC component must always be
         * real-valued; because the calling routine has made the time series
         * have an even length, the Nyquist component must also be real-valued;
         * also this routine makes the assumption that both the DC and the
         * Nyquist components are zero */
 
        work1->data->data[0] = cabs(work1->data->data[0]);
        work1->data->data[work1->data->length - 1] =
                creal(work1->data->data[work1->data->length - 1]);
        
        /* return data to time domain */
 
        if (XLALREAL4FreqTimeFFT(segment, work1, revplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        return 0;
}
 
/**
 * @brief Computes strain for a detector and injects into target time series.
 * @details This routine takes care of the time-changing time delay from
 * the Earth's center and the time-changing antenna response pattern; it
 * also accounts for deviations from the long-wavelength limit at high
 * frequencies.  An optional calibration response function can be provided
 * if the output time series is not in strain units.
 * @param[in,out] target Time series to inject strain into.
 * @param[in] hplus Time series with plus-polarization gravitational waveform.
 * @param[in] hcross Time series with cross-polarization gravitational waveform.
 * @param[in] ra Right ascension of the source (radians).
 * @param[in] dec Declination of the source (radians).
 * @param[in] psi Polarization angle of the source (radians).
 * @param[in] detector Detector to use when computing strain.
 * @param[in] response Response function to use, or NULL if none.
 * @retval 0 Success.
 * @retval <0 Failure.
 */
int XLALSimInjectDetectorStrainREAL8TimeSeries(
        REAL8TimeSeries *target,
        const REAL8TimeSeries *hplus,
        const REAL8TimeSeries *hcross,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX16FrequencySeries *response
)
{
        const double nominal_segdur = 2.0; /* nominal segment duration = 2s */
        const double max_time_delay = 0.1; /* generous allowed time delay */
        const size_t strides_per_segment = 2; /* 2 strides in one segment */
        LIGOTimeGPS t0;
        LIGOTimeGPS t1;
        size_t length;          /* length in samples of interval t0 - t1 */
        size_t seglen;          /* length of segment in samples */
        size_t padlen;          /* padding at beginning and end of segment */
        size_t ovrlap;          /* overlapping data length */
        size_t stride;          /* stride of each step */
        size_t nsteps;          /* number of steps to take */
        REAL8TimeSeries *h = NULL; /* strain timeseries to inject into target */
        REAL8TimeSeries *segment = NULL;
        COMPLEX16FrequencySeries *work1 = NULL;
        COMPLEX16FrequencySeries *work2 = NULL;
        REAL8FFTPlan *fwdplan = NULL;
        REAL8FFTPlan *revplan = NULL;
        REAL8Window *window = NULL;
        size_t step;
        size_t j;
        int errnum = 0;
 
        /* check validity and compatibility of time series */
 
        LAL_CHECK_VALID_SERIES(target, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hplus, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hcross, XLAL_FAILURE);
        LAL_CHECK_CONSISTENT_TIME_SERIES(hplus, hcross, XLAL_FAILURE);
        if (response == NULL) {
                LAL_CHECK_COMPATIBLE_TIME_SERIES(target, hplus, XLAL_FAILURE);
        } else {
                /* units do no need to agree, but sample interval and
                 * start frequency do */
                if (fabs(target->deltaT - hplus->deltaT ) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_ETIME);
                if (fabs(target->f0 - hplus->f0) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_EFREQ);
        }
                        
 
        /* constants describing the data segmentation: the length of the
         * segment must be a power of two and the segment duration is at least
         * nominal_segdur */
 
        seglen = round_up_to_power_of_two(nominal_segdur / target->deltaT);
        stride = seglen / strides_per_segment;
        padlen = max_time_delay / target->deltaT;
        ovrlap = seglen;
        ovrlap -= 2 * padlen;
        ovrlap -= stride;
 
        /* determine start and end time: the start time is the later of the
         * start of the hplus/hcross time series and the target time series;
         * the end time is the earlier of the end of the hplus/hcross time
         * series and the target time series */
 
        t0 = hplus->epoch;
        t1 = target->epoch;
        XLALGPSAdd(&t0, hplus->data->length * hplus->deltaT);
        XLALGPSAdd(&t1, target->data->length * target->deltaT);
        t1 = XLALGPSCmp(&t1, &t0) < 0 ? t1 : t0;
        t0 = hplus->epoch;
        t0 = XLALGPSCmp(&t0, &target->epoch) > 0 ? t0 : target->epoch;
 
        /* add padding of 1 stride before and after these start and end times */
 
        XLALGPSAdd(&t0, -1.0 * stride * target->deltaT);
        XLALGPSAdd(&t1, stride * target->deltaT);
 
        /* determine if this is a disjoint set: if so, there is nothing to do */
 
        if (XLALGPSCmp(&t1, &t0) <= 0)
                return 0;
 
        /* create a segment that is seglen samples long */
 
        segment = XLALCreateREAL8TimeSeries(NULL, &t0, target->f0,
                target->deltaT, &target->sampleUnits, seglen);
        if (!segment) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a time series to hold the strain to inject into the target */
 
        length = XLALGPSDiff(&t1, &t0) / target->deltaT;
        h = XLALCreateREAL8TimeSeries(NULL, &t0, target->f0, target->deltaT,
                &target->sampleUnits, length);
        if (!h) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
        memset(h->data->data, 0, h->data->length * sizeof(*h->data->data));
 
        /* determine number of steps it takes to go from t0 to t1 */
 
        nsteps = ((length%stride) ? (1 + length/stride) : (length/stride));
 
 
        /* create frequency-domain workspace; note that the FFT function
         * populates the frequency series' metadata with the appropriate
         * values */
 
        work1 = XLALCreateCOMPLEX16FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        work2 = XLALCreateCOMPLEX16FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        if (!work1 || !work2) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create forward and reverse FFT plans */
 
        fwdplan = XLALCreateForwardREAL8FFTPlan(seglen, 0);
        revplan = XLALCreateReverseREAL8FFTPlan(seglen, 0);
        if (!fwdplan || !revplan) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a Tukey window with tapers entirely within the padding */
 
        window = XLALCreateTukeyREAL8Window(seglen, (double)padlen / seglen); 
 
 
        /* loop over steps, adding data from the current step to the strain */
 
        for (step = 0; step < nsteps; ++step) {
 
                int status;
                size_t offset;
 
                /* compute one segment of strain with time appropriate beam
                 * pattern functions and time delays from earth's center */
 
                status = XLALSimComputeStrainSegmentREAL8TimeSeries(segment,                            hplus, hcross, work1, work2, fwdplan, revplan, window,
                        ra, dec, psi, detector, response);
                if (status < 0) {
                        errnum = XLAL_EFUNC;
                        goto freereturn;
                }
 
                /* compute the offset of this segment relative to the strain series */
 
                offset = XLALGPSDiff(&segment->epoch, &h->epoch) / h->deltaT;
                for (j = padlen; j < seglen - padlen; ++j)
                        if ((j + offset) < h->data->length) {
                                if (step && j - padlen < ovrlap) {
                                        /* feather overlapping data */
                                        double x = (double)(j - padlen) / ovrlap;
                                        h->data->data[j + offset] = x * segment->data->data[j]
                                                + (1.0 - x) * h->data->data[j + offset];
                                } else /* no feathering of remaining data */
                                        h->data->data[j + offset] = segment->data->data[j];
                        }
 
                /* advance segment start time the next step */
 
                XLALGPSAdd(&segment->epoch, stride * segment->deltaT);
        }
 
        /* apply window to beginning and end of time series to reduce ringing */
 
        for (j = 0; j < stride - padlen; ++j)
                h->data->data[j] = h->data->data[h->data->length - 1 - j] = 0.0;
        for ( ; j < stride; ++j) {
                double fac = window->data->data[j - (stride - padlen)];
                h->data->data[j] *= fac;
                h->data->data[h->data->length - 1 - j] *= fac;
        }
        
 
        /* add computed strain to target time series */
 
        XLALAddREAL8TimeSeries(target, h);
 
freereturn:
 
        /* free all memory and return */
 
        XLALDestroyREAL8Window(window);
        XLALDestroyREAL8FFTPlan(revplan);
        XLALDestroyREAL8FFTPlan(fwdplan);
        XLALDestroyCOMPLEX16FrequencySeries(work2);
        XLALDestroyCOMPLEX16FrequencySeries(work1);
        XLALDestroyREAL8TimeSeries(h);
        XLALDestroyREAL8TimeSeries(segment);
 
        if (errnum)
                XLAL_ERROR(errnum);
        return 0;
}
 
/**
 * @brief Computes strain for a detector and injects into target time series.
 * @details This routine takes care of the time-changing time delay from
 * the Earth's center and the time-changing antenna response pattern; it
 * also accounts for deviations from the long-wavelength limit at high
 * frequencies.  An optional calibration response function can be provided
 * if the output time series is not in strain units.
 * @param[in,out] target Time series to inject strain into.
 * @param[in] hplus Time series with plus-polarization gravitational waveform.
 * @param[in] hcross Time series with cross-polarization gravitational waveform.
 * @param[in] ra Right ascension of the source (radians).
 * @param[in] dec Declination of the source (radians).
 * @param[in] psi Polarization angle of the source (radians).
 * @param[in] detector Detector to use when computing strain.
 * @param[in] response Response function to use, or NULL if none.
 * @retval 0 Success.
 * @retval <0 Failure.
 */
int XLALSimInjectDetectorStrainREAL4TimeSeries(
        REAL4TimeSeries *target,
        const REAL4TimeSeries *hplus,
        const REAL4TimeSeries *hcross,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX8FrequencySeries *response
)
{
        const double nominal_segdur = 2.0; /* nominal segment duration = 2s */
        const double max_time_delay = 0.1; /* generous allowed time delay */
        const size_t strides_per_segment = 2; /* 2 strides in one segment */
        LIGOTimeGPS t0;
        LIGOTimeGPS t1;
        size_t length;          /* length in samples of interval t0 - t1 */
        size_t seglen;          /* length of segment in samples */
        size_t padlen;          /* padding at beginning and end of segment */
        size_t ovrlap;          /* overlapping data length */
        size_t stride;          /* stride of each step */
        size_t nsteps;          /* number of steps to take */
        REAL4TimeSeries *h = NULL; /* strain timeseries to inject into target */
        REAL4TimeSeries *segment = NULL;
        COMPLEX8FrequencySeries *work1 = NULL;
        COMPLEX8FrequencySeries *work2 = NULL;
        REAL4FFTPlan *fwdplan = NULL;
        REAL4FFTPlan *revplan = NULL;
        REAL4Window *window = NULL;
        size_t step;
        size_t j;
        int errnum = 0;
 
        /* check validity and compatibility of time series */
 
        LAL_CHECK_VALID_SERIES(target, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hplus, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hcross, XLAL_FAILURE);
        LAL_CHECK_CONSISTENT_TIME_SERIES(hplus, hcross, XLAL_FAILURE);
        if (response == NULL) {
                LAL_CHECK_COMPATIBLE_TIME_SERIES(target, hplus, XLAL_FAILURE);
        } else {
                /* units do no need to agree, but sample interval and
                 * start frequency do */
                if (fabs(target->deltaT - hplus->deltaT ) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_ETIME);
                if (fabs(target->f0 - hplus->f0) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_EFREQ);
        }
                        
 
        /* constants describing the data segmentation: the length of the
         * segment must be a power of two and the segment duration is at least
         * nominal_segdur */
 
        seglen = round_up_to_power_of_two(nominal_segdur / target->deltaT);
        stride = seglen / strides_per_segment;
        padlen = max_time_delay / target->deltaT;
        ovrlap = seglen;
        ovrlap -= 2 * padlen;
        ovrlap -= stride;
 
        /* determine start and end time: the start time is the later of the
         * start of the hplus/hcross time series and the target time series;
         * the end time is the earlier of the end of the hplus/hcross time
         * series and the target time series */
 
        t0 = hplus->epoch;
        t1 = target->epoch;
        XLALGPSAdd(&t0, hplus->data->length * hplus->deltaT);
        XLALGPSAdd(&t1, target->data->length * target->deltaT);
        t1 = XLALGPSCmp(&t1, &t0) < 0 ? t1 : t0;
        t0 = hplus->epoch;
        t0 = XLALGPSCmp(&t0, &target->epoch) > 0 ? t0 : target->epoch;
 
        /* add padding of 1 stride before and after these start and end times */
 
        XLALGPSAdd(&t0, -1.0 * stride * target->deltaT);
        XLALGPSAdd(&t1, stride * target->deltaT);
 
        /* determine if this is a disjoint set: if so, there is nothing to do */
 
        if (XLALGPSCmp(&t1, &t0) <= 0)
                return 0;
 
        /* create a segment that is seglen samples long */
 
        segment = XLALCreateREAL4TimeSeries(NULL, &t0, target->f0,
                target->deltaT, &target->sampleUnits, seglen);
        if (!segment) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a time series to hold the strain to inject into the target */
 
        length = XLALGPSDiff(&t1, &t0) / target->deltaT;
        h = XLALCreateREAL4TimeSeries(NULL, &t0, target->f0, target->deltaT,
                &target->sampleUnits, length);
        if (!h) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
        memset(h->data->data, 0, h->data->length * sizeof(*h->data->data));
 
        /* determine number of steps it takes to go from t0 to t1 */
 
        nsteps = ((length%stride) ? (1 + length/stride) : (length/stride));
 
 
        /* create frequency-domain workspace; note that the FFT function
         * populates the frequency series' metadata with the appropriate
         * values */
 
        work1 = XLALCreateCOMPLEX8FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        work2 = XLALCreateCOMPLEX8FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        if (!work1 || !work2) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create forward and reverse FFT plans */
 
        fwdplan = XLALCreateForwardREAL4FFTPlan(seglen, 0);
        revplan = XLALCreateReverseREAL4FFTPlan(seglen, 0);
        if (!fwdplan || !revplan) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a Tukey window with tapers entirely within the padding */
 
        window = XLALCreateTukeyREAL4Window(seglen, (double)padlen / seglen); 
 
 
        /* loop over steps, adding data from the current step to the strain */
 
        for (step = 0; step < nsteps; ++step) {
 
                int status;
                size_t offset;
 
                /* compute one segment of strain with time appropriate beam
                 * pattern functions and time delays from earth's center */
 
                status = XLALSimComputeStrainSegmentREAL4TimeSeries(segment,                            hplus, hcross, work1, work2, fwdplan, revplan, window,
                        ra, dec, psi, detector, response);
                if (status < 0) {
                        errnum = XLAL_EFUNC;
                        goto freereturn;
                }
 
                /* compute the offset of this segment relative to the strain series */
 
                offset = XLALGPSDiff(&segment->epoch, &h->epoch) / h->deltaT;
                for (j = padlen; j < seglen - padlen; ++j)
                        if ((j + offset) < h->data->length) {
                                if (step && j - padlen < ovrlap) {
                                        /* feather overlapping data */
                                        double x = (double)(j - padlen) / ovrlap;
                                        h->data->data[j + offset] = x * segment->data->data[j]
                                                + (1.0 - x) * h->data->data[j + offset];
                                } else /* no feathering of remaining data */
                                        h->data->data[j + offset] = segment->data->data[j];
                        }
 
                /* advance segment start time the next step */
 
                XLALGPSAdd(&segment->epoch, stride * segment->deltaT);
        }
 
        /* apply window to beginning and end of time series to reduce ringing */
 
        for (j = 0; j < stride - padlen; ++j)
                h->data->data[j] = h->data->data[h->data->length - 1 - j] = 0.0;
        for ( ; j < stride; ++j) {
                double fac = window->data->data[j - (stride - padlen)];
                h->data->data[j] *= fac;
                h->data->data[h->data->length - 1 - j] *= fac;
        }
        
 
        /* add computed strain to target time series */
 
        XLALAddREAL4TimeSeries(target, h);
 
freereturn:
 
        /* free all memory and return */
 
        XLALDestroyREAL4Window(window);
        XLALDestroyREAL4FFTPlan(revplan);
        XLALDestroyREAL4FFTPlan(fwdplan);
        XLALDestroyCOMPLEX8FrequencySeries(work2);
        XLALDestroyCOMPLEX8FrequencySeries(work1);
        XLALDestroyREAL4TimeSeries(h);
        XLALDestroyREAL4TimeSeries(segment);
 
        if (errnum)
                XLAL_ERROR(errnum);
        return 0;
}
 
 
/*
 * The following routines are more computationally efficient but they
 * assume the long-wavelength limit is valid.
 */
 
 
/* Helper routine that computes a segment of strain data with a single
 * time delay and beam pattern applied to the whole segment.  The duration
 * of the segment must therefore be reasonably short or else the movement
 * of the earth will invalidate the use of a single time shift and beam
 * pattern for the entire segment. */
static int XLALSimComputeLWLStrainSegmentREAL8TimeSeries(
        REAL8TimeSeries *segment,
        const REAL8TimeSeries *hplus,
        const REAL8TimeSeries *hcross,
        COMPLEX16FrequencySeries *work,
        REAL8FFTPlan *fwdplan,
        REAL8FFTPlan *revplan,
        REAL8Window *window,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX16FrequencySeries *response
)
{
        LIGOTimeGPS t;
        double gmst;
        double fplus;
        double fcross;
        double deltaT;
        double offint;
        double offrac;
        int offset;
        int j;
        size_t k;
 
        /* this routine assumes the segment has a length of N points where N is
         * a power of two and that the workspace frequency series and the FFT
         * plans are compatible with the size N; these assumptions are not
         * checked: the calling routine must ensure that they are true */
 
        /* compute fplus, fcross, and time delay from earth's center at the
         * time corresponding to the middle of the segment */
 
        t = segment->epoch;
        XLALGPSAdd(&t, 0.5 * segment->data->length * segment->deltaT);
        gmst = XLALGreenwichMeanSiderealTime(&t);
        XLALComputeDetAMResponse(&fplus, &fcross,
                (const REAL4(*)[3])(uintptr_t)detector->response, ra, dec, psi, gmst);
        deltaT = XLALTimeDelayFromEarthCenter(detector->location, ra, dec, &t);
 
        /* add to the geometric delay the difference in time between the
         * beginning of the injection timeseries and the beginning of the
         * segment */
 
        deltaT += XLALGPSDiff(&hplus->epoch, &segment->epoch);
 
        /* compute the integer and fractional parts of the sample index in the
         * segment on which the hplus and hcross time series begins: modf()
         * returns integer and fractional parts that have the same sign, e.g.,
         * -3.9 --> -3 + -0.9, and we adjust these so that magnitude of the
         * fractional part is not greater than 0.5, e.g., -3.9 --> -4.0 + 0.1,
         * so that we never do more than 1/2 a sample of re-interpolation */
 
        offrac = modf(deltaT / segment->deltaT, &offint);
        if (offrac < -0.5) {
                offrac += 1.0;
                offint -= 1.0;
        } else if (offrac > 0.5) {
                offrac -= 1.0;
                offint += 1.0;
        }
        offset = offint;
 
        /* now compute the sub-sample time shift that must be applied to the
         * segment data */
 
        deltaT = offrac * segment->deltaT;
 
        /* compute the strain from hplus and hcross and populate the segment
         * with this windowed data; apply appropriate integer offset */
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hplus->data->length + offset)
                        segment->data->data[j] = window->data->data[j]
                                * ( fplus * hplus->data->data[j - offset]
                                + fcross * hcross->data->data[j - offset] );
                else
                        segment->data->data[j] = 0.0;
 
 
        /* put segment in frequency domain */
 
        if (XLALREAL8TimeFreqFFT(work, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        /* apply sub-sample time shift in frequency domain */
 
        for (k = 0; k < work->data->length; ++k) {
                double f = work->f0 + k * work->deltaF;
                COMPLEX16 fac;
                
                /* phase for sub-sample time correction */
                fac = cexp(-I * LAL_TWOPI * f * deltaT);
                if (response)
                        fac /= response->data->data[k];
 
                work->data->data[k] *= fac;
        }
 
        /* adjust DC and Nyquist components: the DC component must always be
         * real-valued; because the calling routine has made the time series
         * have an even length, the Nyquist component must also be real-valued;
         * also this routine makes the assumption that both the DC and the
         * Nyquist components are zero */
 
        work->data->data[0] = cabs(work->data->data[0]);
        work->data->data[work->data->length - 1] =
                creal(work->data->data[work->data->length - 1]);
        
        /* return data to time domain */
 
        if (XLALREAL8FreqTimeFFT(segment, work, revplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        return 0;
}
 
 
/* Helper routine that computes a segment of strain data with a single
 * time delay and beam pattern applied to the whole segment.  The duration
 * of the segment must therefore be reasonably short or else the movement
 * of the earth will invalidate the use of a single time shift and beam
 * pattern for the entire segment. */
static int XLALSimComputeLWLStrainSegmentREAL4TimeSeries(
        REAL4TimeSeries *segment,
        const REAL4TimeSeries *hplus,
        const REAL4TimeSeries *hcross,
        COMPLEX8FrequencySeries *work,
        REAL4FFTPlan *fwdplan,
        REAL4FFTPlan *revplan,
        REAL4Window *window,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX8FrequencySeries *response
)
{
        LIGOTimeGPS t;
        double gmst;
        double fplus;
        double fcross;
        double deltaT;
        double offint;
        double offrac;
        int offset;
        int j;
        size_t k;
 
        /* this routine assumes the segment has a length of N points where N is
         * a power of two and that the workspace frequency series and the FFT
         * plans are compatible with the size N; these assumptions are not
         * checked: the calling routine must ensure that they are true */
 
        /* compute fplus, fcross, and time delay from earth's center at the
         * time corresponding to the middle of the segment */
 
        t = segment->epoch;
        XLALGPSAdd(&t, 0.5 * segment->data->length * segment->deltaT);
        gmst = XLALGreenwichMeanSiderealTime(&t);
        XLALComputeDetAMResponse(&fplus, &fcross,
                (const REAL4(*)[3])(uintptr_t)detector->response, ra, dec, psi, gmst);
        deltaT = XLALTimeDelayFromEarthCenter(detector->location, ra, dec, &t);
 
        /* add to the geometric delay the difference in time between the
         * beginning of the injection timeseries and the beginning of the
         * segment */
 
        deltaT += XLALGPSDiff(&hplus->epoch, &segment->epoch);
 
        /* compute the integer and fractional parts of the sample index in the
         * segment on which the hplus and hcross time series begins: modf()
         * returns integer and fractional parts that have the same sign, e.g.,
         * -3.9 --> -3 + -0.9, and we adjust these so that magnitude of the
         * fractional part is not greater than 0.5, e.g., -3.9 --> -4.0 + 0.1,
         * so that we never do more than 1/2 a sample of re-interpolation */
 
        offrac = modf(deltaT / segment->deltaT, &offint);
        if (offrac < -0.5) {
                offrac += 1.0;
                offint -= 1.0;
        } else if (offrac > 0.5) {
                offrac -= 1.0;
                offint += 1.0;
        }
        offset = offint;
 
        /* now compute the sub-sample time shift that must be applied to the
         * segment data */
 
        deltaT = offrac * segment->deltaT;
 
        /* compute the strain from hplus and hcross and populate the segment
         * with this windowed data; apply appropriate integer offset */
 
        for (j = 0; j < (int)segment->data->length; ++j)
                if (j >= offset && j < (int)hplus->data->length + offset)
                        segment->data->data[j] = window->data->data[j]
                                * ( fplus * hplus->data->data[j - offset]
                                + fcross * hcross->data->data[j - offset] );
                else
                        segment->data->data[j] = 0.0;
 
 
        /* put segment in frequency domain */
 
        if (XLALREAL4TimeFreqFFT(work, segment, fwdplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        /* apply sub-sample time shift in frequency domain */
 
        for (k = 0; k < work->data->length; ++k) {
                double f = work->f0 + k * work->deltaF;
                COMPLEX8 fac;
                
                /* phase for sub-sample time correction */
                fac = cexp(-I * LAL_TWOPI * f * deltaT);
                if (response)
                        fac /= response->data->data[k];
 
                work->data->data[k] *= fac;
        }
 
        /* adjust DC and Nyquist components: the DC component must always be
         * real-valued; because the calling routine has made the time series
         * have an even length, the Nyquist component must also be real-valued;
         * also this routine makes the assumption that both the DC and the
         * Nyquist components are zero */
 
        work->data->data[0] = cabs(work->data->data[0]);
        work->data->data[work->data->length - 1] =
                creal(work->data->data[work->data->length - 1]);
        
        /* return data to time domain */
 
        if (XLALREAL4FreqTimeFFT(segment, work, revplan) < 0)
                XLAL_ERROR(XLAL_EFUNC);
 
        return 0;
}
 
 
/**
 * @brief Computes strain for a detector and injects into target time series.
 * @details This routine takes care of the time-changing time delay from
 * the Earth's center and the time-changing antenna response pattern; it
 * does NOT account for deviations from the long-wavelength limit at high
 * frequencies.  An optional calibration response function can be provided
 * if the output time series is not in strain units.
 * @param[in,out] target Time series to inject strain into.
 * @param[in] hplus Time series with plus-polarization gravitational waveform.
 * @param[in] hcross Time series with cross-polarization gravitational waveform.
 * @param[in] ra Right ascension of the source (radians).
 * @param[in] dec Declination of the source (radians).
 * @param[in] psi Polarization angle of the source (radians).
 * @param[in] detector Detector to use when computing strain.
 * @param[in] response Response function to use, or NULL if none.
 * @retval 0 Success.
 * @retval <0 Failure.
 * @warning This routine assumes the long-wavelength limit (LWL) is valid
 * when computing the detector strain; at high frequencies near the free
 * spectral range of an interferometric detector this approximation becomes
 * invalid.
 */
int XLALSimInjectLWLDetectorStrainREAL8TimeSeries(
        REAL8TimeSeries *target,
        const REAL8TimeSeries *hplus,
        const REAL8TimeSeries *hcross,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX16FrequencySeries *response
)
{
        const double nominal_segdur = 2.0; /* nominal segment duration = 2s */
        const double max_time_delay = 0.1; /* generous allowed time delay */
        const size_t strides_per_segment = 2; /* 2 strides in one segment */
        LIGOTimeGPS t0;
        LIGOTimeGPS t1;
        size_t length;          /* length in samples of interval t0 - t1 */
        size_t seglen;          /* length of segment in samples */
        size_t padlen;          /* padding at beginning and end of segment */
        size_t ovrlap;          /* overlapping data length */
        size_t stride;          /* stride of each step */
        size_t nsteps;          /* number of steps to take */
        REAL8TimeSeries *h = NULL; /* strain timeseries to inject into target */
        REAL8TimeSeries *segment = NULL;
        COMPLEX16FrequencySeries *work = NULL;
        REAL8FFTPlan *fwdplan = NULL;
        REAL8FFTPlan *revplan = NULL;
        REAL8Window *window = NULL;
        size_t step;
        size_t j;
        int errnum = 0;
 
        /* check validity and compatibility of time series */
 
        LAL_CHECK_VALID_SERIES(target, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hplus, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hcross, XLAL_FAILURE);
        LAL_CHECK_CONSISTENT_TIME_SERIES(hplus, hcross, XLAL_FAILURE);
        if (response == NULL) {
                LAL_CHECK_COMPATIBLE_TIME_SERIES(target, hplus, XLAL_FAILURE);
        } else {
                /* units do no need to agree, but sample interval and
                 * start frequency do */
                if (fabs(target->deltaT - hplus->deltaT ) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_ETIME);
                if (fabs(target->f0 - hplus->f0) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_EFREQ);
        }
                        
 
        /* constants describing the data segmentation: the length of the
         * segment must be a power of two and the segment duration is at least
         * nominal_segdur */
 
        seglen = round_up_to_power_of_two(nominal_segdur / target->deltaT);
        stride = seglen / strides_per_segment;
        padlen = max_time_delay / target->deltaT;
        ovrlap = seglen;
        ovrlap -= 2 * padlen;
        ovrlap -= stride;
 
        /* determine start and end time: the start time is the later of the
         * start of the hplus/hcross time series and the target time series;
         * the end time is the earlier of the end of the hplus/hcross time
         * series and the target time series */
 
        t0 = hplus->epoch;
        t1 = target->epoch;
        XLALGPSAdd(&t0, hplus->data->length * hplus->deltaT);
        XLALGPSAdd(&t1, target->data->length * target->deltaT);
        t1 = XLALGPSCmp(&t1, &t0) < 0 ? t1 : t0;
        t0 = hplus->epoch;
        t0 = XLALGPSCmp(&t0, &target->epoch) > 0 ? t0 : target->epoch;
 
        /* add padding of 1 stride before and after these start and end times */
 
        XLALGPSAdd(&t0, -1.0 * stride * target->deltaT);
        XLALGPSAdd(&t1, stride * target->deltaT);
 
        /* determine if this is a disjoint set: if so, there is nothing to do */
 
        if (XLALGPSCmp(&t1, &t0) <= 0)
                return 0;
 
        /* create a segment that is seglen samples long */
 
        segment = XLALCreateREAL8TimeSeries(NULL, &t0, target->f0,
                target->deltaT, &target->sampleUnits, seglen);
        if (!segment) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a time series to hold the strain to inject into the target */
 
        length = XLALGPSDiff(&t1, &t0) / target->deltaT;
        h = XLALCreateREAL8TimeSeries(NULL, &t0, target->f0, target->deltaT,
                &target->sampleUnits, length);
        if (!h) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
        memset(h->data->data, 0, h->data->length * sizeof(*h->data->data));
 
        /* determine number of steps it takes to go from t0 to t1 */
 
        nsteps = ((length%stride) ? (1 + length/stride) : (length/stride));
 
 
        /* create frequency-domain workspace; note that the FFT function
         * populates the frequency series' metadata with the appropriate
         * values */
 
        work = XLALCreateCOMPLEX16FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        if (!work) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create forward and reverse FFT plans */
 
        fwdplan = XLALCreateForwardREAL8FFTPlan(seglen, 0);
        revplan = XLALCreateReverseREAL8FFTPlan(seglen, 0);
        if (!fwdplan || !revplan) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a Tukey window with tapers entirely within the padding */
 
        window = XLALCreateTukeyREAL8Window(seglen, (double)padlen / seglen); 
 
 
        /* loop over steps, adding data from the current step to the strain */
 
        for (step = 0; step < nsteps; ++step) {
 
                int status;
                size_t offset;
 
                /* compute one segment of strain with time appropriate beam
                 * pattern functions and time delays from earth's center */
 
                status = XLALSimComputeLWLStrainSegmentREAL8TimeSeries(segment,
                        hplus, hcross, work, fwdplan, revplan, window, ra, dec,
                        psi, detector, response);
                if (status < 0) {
                        errnum = XLAL_EFUNC;
                        goto freereturn;
                }
 
                /* compute the offset of this segment relative to the strain series */
 
                offset = XLALGPSDiff(&segment->epoch, &h->epoch) / h->deltaT;
                for (j = padlen; j < seglen - padlen; ++j)
                        if ((j + offset) < h->data->length) {
                                if (step && j - padlen < ovrlap) {
                                        /* feather overlapping data */
                                        double x = (double)(j - padlen) / ovrlap;
                                        h->data->data[j + offset] = x * segment->data->data[j]
                                                + (1.0 - x) * h->data->data[j + offset];
                                } else /* no feathering of remaining data */
                                        h->data->data[j + offset] = segment->data->data[j];
                        }
 
                /* advance segment start time the next step */
 
                XLALGPSAdd(&segment->epoch, stride * segment->deltaT);
        }
 
        /* apply window to beginning and end of time series to reduce ringing */
 
        for (j = 0; j < stride - padlen; ++j)
                h->data->data[j] = h->data->data[h->data->length - 1 - j] = 0.0;
        for ( ; j < stride; ++j) {
                double fac = window->data->data[j - (stride - padlen)];
                h->data->data[j] *= fac;
                h->data->data[h->data->length - 1 - j] *= fac;
        }
        
 
        /* add computed strain to target time series */
 
        XLALAddREAL8TimeSeries(target, h);
 
freereturn:
 
        /* free all memory and return */
 
        XLALDestroyREAL8Window(window);
        XLALDestroyREAL8FFTPlan(revplan);
        XLALDestroyREAL8FFTPlan(fwdplan);
        XLALDestroyCOMPLEX16FrequencySeries(work);
        XLALDestroyREAL8TimeSeries(h);
        XLALDestroyREAL8TimeSeries(segment);
 
        if (errnum)
                XLAL_ERROR(errnum);
        return 0;
}
 
 
/**
 * @brief Computes strain for a detector and injects into target time series.
 * @details This routine takes care of the time-changing time delay from
 * the Earth's center and the time-changing antenna response pattern; it
 * does NOT account for deviations from the long-wavelength limit at high
 * frequencies.  An optional calibration response function can be provided
 * if the output time series is not in strain units.
 * @param[in,out] target Time series to inject strain into.
 * @param[in] hplus Time series with plus-polarization gravitational waveform.
 * @param[in] hcross Time series with cross-polarization gravitational waveform.
 * @param[in] ra Right ascension of the source (radians).
 * @param[in] dec Declination of the source (radians).
 * @param[in] psi Polarization angle of the source (radians).
 * @param[in] detector Detector to use when computing strain.
 * @param[in] response Response function to use, or NULL if none.
 * @retval 0 Success.
 * @retval <0 Failure.
 * @warning This routine assumes the long-wavelength limit (LWL) is valid
 * when computing the detector strain; at high frequencies near the free
 * spectral range of an interferometric detector this approximation becomes
 * invalid.
 */
int XLALSimInjectLWLDetectorStrainREAL4TimeSeries(
        REAL4TimeSeries *target,
        const REAL4TimeSeries *hplus,
        const REAL4TimeSeries *hcross,
        double ra,
        double dec,
        double psi,
        LALDetector *detector,
        const COMPLEX8FrequencySeries *response
)
{
        const double nominal_segdur = 2.0; /* nominal segment duration = 2s */
        const double max_time_delay = 0.1; /* generous allowed time delay */
        const size_t strides_per_segment = 2; /* 2 strides in one segment */
        LIGOTimeGPS t0;
        LIGOTimeGPS t1;
        size_t length;          /* length in samples of interval t0 - t1 */
        size_t seglen;          /* length of segment in samples */
        size_t padlen;          /* padding at beginning and end of segment */
        size_t ovrlap;          /* overlapping data length */
        size_t stride;          /* stride of each step */
        size_t nsteps;          /* number of steps to take */
        REAL4TimeSeries *h = NULL; /* strain timeseries to inject into target */
        REAL4TimeSeries *segment = NULL;
        COMPLEX8FrequencySeries *work = NULL;
        REAL4FFTPlan *fwdplan = NULL;
        REAL4FFTPlan *revplan = NULL;
        REAL4Window *window = NULL;
        size_t step;
        size_t j;
        int errnum = 0;
 
        /* check validity and compatibility of time series */
 
        LAL_CHECK_VALID_SERIES(target, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hplus, XLAL_FAILURE);
        LAL_CHECK_VALID_SERIES(hcross, XLAL_FAILURE);
        LAL_CHECK_CONSISTENT_TIME_SERIES(hplus, hcross, XLAL_FAILURE);
        if (response == NULL) {
                LAL_CHECK_COMPATIBLE_TIME_SERIES(target, hplus, XLAL_FAILURE);
        } else {
                /* units do no need to agree, but sample interval and
                 * start frequency do */
                if (fabs(target->deltaT - hplus->deltaT ) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_ETIME);
                if (fabs(target->f0 - hplus->f0) > LAL_REAL8_EPS)
                        XLAL_ERROR(XLAL_EFREQ);
        }
                        
 
        /* constants describing the data segmentation: the length of the
         * segment must be a power of two and the segment duration is at least
         * nominal_segdur */
 
        seglen = round_up_to_power_of_two(nominal_segdur / target->deltaT);
        stride = seglen / strides_per_segment;
        padlen = max_time_delay / target->deltaT;
        ovrlap = seglen;
        ovrlap -= 2 * padlen;
        ovrlap -= stride;
 
        /* determine start and end time: the start time is the later of the
         * start of the hplus/hcross time series and the target time series;
         * the end time is the earlier of the end of the hplus/hcross time
         * series and the target time series */
 
        t0 = hplus->epoch;
        t1 = target->epoch;
        XLALGPSAdd(&t0, hplus->data->length * hplus->deltaT);
        XLALGPSAdd(&t1, target->data->length * target->deltaT);
        t1 = XLALGPSCmp(&t1, &t0) < 0 ? t1 : t0;
        t0 = hplus->epoch;
        t0 = XLALGPSCmp(&t0, &target->epoch) > 0 ? t0 : target->epoch;
 
        /* add padding of 1 stride before and after these start and end times */
 
        XLALGPSAdd(&t0, -1.0 * stride * target->deltaT);
        XLALGPSAdd(&t1, stride * target->deltaT);
 
        /* determine if this is a disjoint set: if so, there is nothing to do */
 
        if (XLALGPSCmp(&t1, &t0) <= 0)
                return 0;
 
        /* create a segment that is seglen samples long */
 
        segment = XLALCreateREAL4TimeSeries(NULL, &t0, target->f0,
                target->deltaT, &target->sampleUnits, seglen);
        if (!segment) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a time series to hold the strain to inject into the target */
 
        length = XLALGPSDiff(&t1, &t0) / target->deltaT;
        h = XLALCreateREAL4TimeSeries(NULL, &t0, target->f0, target->deltaT,
                &target->sampleUnits, length);
        if (!h) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
        memset(h->data->data, 0, h->data->length * sizeof(*h->data->data));
 
        /* determine number of steps it takes to go from t0 to t1 */
 
        nsteps = ((length%stride) ? (1 + length/stride) : (length/stride));
 
 
        /* create frequency-domain workspace; note that the FFT function
         * populates the frequency series' metadata with the appropriate
         * values */
 
        work = XLALCreateCOMPLEX8FrequencySeries(NULL, &t0, 0, 0,
                &lalDimensionlessUnit, seglen / 2 + 1);
        if (!work) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create forward and reverse FFT plans */
 
        fwdplan = XLALCreateForwardREAL4FFTPlan(seglen, 0);
        revplan = XLALCreateReverseREAL4FFTPlan(seglen, 0);
        if (!fwdplan || !revplan) {
                errnum = XLAL_EFUNC;
                goto freereturn;
        }
 
        /* create a Tukey window with tapers entirely within the padding */
 
        window = XLALCreateTukeyREAL4Window(seglen, (double)padlen / seglen); 
 
 
        /* loop over steps, adding data from the current step to the strain */
 
        for (step = 0; step < nsteps; ++step) {
 
                int status;
                size_t offset;
 
                /* compute one segment of strain with time appropriate beam
                 * pattern functions and time delays from earth's center */
 
                status = XLALSimComputeLWLStrainSegmentREAL4TimeSeries(segment,
                        hplus, hcross, work, fwdplan, revplan, window, ra, dec,
                        psi, detector, response);
                if (status < 0) {
                        errnum = XLAL_EFUNC;
                        goto freereturn;
                }
 
                /* compute the offset of this segment relative to the strain series */
 
                offset = XLALGPSDiff(&segment->epoch, &h->epoch) / h->deltaT;
                for (j = padlen; j < seglen - padlen; ++j)
                        if ((j + offset) < h->data->length) {
                                if (step && j - padlen < ovrlap) {
                                        /* feather overlapping data */
                                        double x = (double)(j - padlen) / ovrlap;
                                        h->data->data[j + offset] = x * segment->data->data[j]
                                                + (1.0 - x) * h->data->data[j + offset];
                                } else /* no feathering of remaining data */
                                        h->data->data[j + offset] = segment->data->data[j];
                        }
 
                /* advance segment start time the next step */
 
                XLALGPSAdd(&segment->epoch, stride * segment->deltaT);
        }
 
        /* apply window to beginning and end of time series to reduce ringing */
 
        for (j = 0; j < stride - padlen; ++j)
                h->data->data[j] = h->data->data[h->data->length - 1 - j] = 0.0;
        for ( ; j < stride; ++j) {
                double fac = window->data->data[j - (stride - padlen)];
                h->data->data[j] *= fac;
                h->data->data[h->data->length - 1 - j] *= fac;
        }
        
 
        /* add computed strain to target time series */
 
        XLALAddREAL4TimeSeries(target, h);
 
freereturn:
 
        /* free all memory and return */
 
        XLALDestroyREAL4Window(window);
        XLALDestroyREAL4FFTPlan(revplan);
        XLALDestroyREAL4FFTPlan(fwdplan);
        XLALDestroyCOMPLEX8FrequencySeries(work);
        XLALDestroyREAL4TimeSeries(h);
        XLALDestroyREAL4TimeSeries(segment);
 
        if (errnum)
                XLAL_ERROR(errnum);
        return 0;
}