LALInferenceRemoveLines.c

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/*
 * LALInferenceRemoveLines.c: Line removal functions for LALInference
 *
 * Copyright (C) 2013 Michael Coughlin
 *
 * 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
*/
 
 
#include <stdio.h>
#include <stdlib.h>
 
#include <lal/LALStdio.h>
#include <lal/LALStdlib.h>
 
#include <lal/LALInspiral.h>
#include <lal/LALCache.h>
#include <lal/LALFrStream.h>
#include <lal/TimeFreqFFT.h>
#include <lal/LALDetectors.h>
#include <lal/AVFactories.h>
#include <lal/ResampleTimeSeries.h>
#include <lal/TimeSeries.h>
#include <lal/FrequencySeries.h>
#include <lal/Units.h>
#include <lal/Date.h>
#include <lal/StringInput.h>
#include <lal/VectorOps.h>
#include <lal/Random.h>
#include <lal/LALNoiseModels.h>
#include <lal/XLALError.h>
#include <lal/GenerateInspiral.h>
 
#include <lal/SeqFactories.h>
#include <lal/DetectorSite.h>
#include <lal/GenerateInspiral.h>
#include <lal/GeneratePPNInspiral.h>
#include <lal/SimulateCoherentGW.h>
#include <lal/LIGOMetadataTables.h>
#include <lal/LIGOMetadataUtils.h>
#include <lal/LIGOMetadataInspiralUtils.h>
#include <lal/LIGOMetadataRingdownUtils.h>
#include <lal/LALInspiralBank.h>
#include <lal/FindChirp.h>
#include <lal/LALInspiralBank.h>
#include <lal/GenerateInspiral.h>
#include <lal/NRWaveInject.h>
#include <lal/GenerateInspRing.h>
#include <math.h>
#include <lal/LALInspiral.h>
#include <lal/LALSimulation.h>
 
#include <lal/LALInference.h>
#include <lal/LALInferenceReadData.h>
#include <lal/LALInferenceLikelihood.h>
#include <lal/LALInferenceTemplate.h>
#include <LALInferenceRemoveLines.h>
 
#include <gsl/gsl_errno.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include <gsl/gsl_fft_complex.h>
#include <gsl/gsl_fft_halfcomplex.h>
#include <gsl/gsl_spline.h>
#include <gsl/gsl_statistics.h>
 
#define max(a,b) (((a)>(b))?(a):(b))
 
static void median_cleanup_REAL8( REAL8FrequencySeries *work, UINT4 n );
static double chisqr(int Dof, double Cv);
static double igf(double S, double Z);
 
int LALInferenceRemoveLinesChiSquared(
    REAL8FrequencySeries        *spectrum,
    const REAL8TimeSeries       *tseries,
    UINT4                        seglen,
    UINT4                        stride,
    const REAL8Window           *window,
    const REAL8FFTPlan          *plan,
    REAL8                       *pvalues
    )
{
  REAL8FrequencySeries *work; /* array of frequency series */
  REAL8 *bin; /* array of bin values */
  UINT4 reclen; /* length of entire data record */
  UINT4 numseg;
  UINT4 seg;
  UINT4 k,l;
 
  if ( ! spectrum || ! tseries || ! plan )
      XLAL_ERROR( XLAL_EFAULT );
  if ( ! spectrum->data || ! tseries->data )
      XLAL_ERROR( XLAL_EINVAL );
  if ( tseries->deltaT <= 0.0 )
      XLAL_ERROR( XLAL_EINVAL );
 
  reclen = tseries->data->length;
  numseg = 1 + (reclen - seglen)/stride;
 
  /* consistency check for lengths: make sure that the segments cover the
 *    * data record completely */
  if ( (numseg - 1)*stride + seglen != reclen )
    XLAL_ERROR( XLAL_EBADLEN );
  if ( spectrum->data->length != seglen/2 + 1 )
    XLAL_ERROR( XLAL_EBADLEN );
 
  /* create frequency series data workspaces */
  work = XLALCalloc( numseg, sizeof( *work ) );
  if ( ! work )
    XLAL_ERROR( XLAL_ENOMEM );
  for ( seg = 0; seg < numseg; ++seg )
  {
    work[seg].data = XLALCreateREAL8Vector( spectrum->data->length );
    if ( ! work[seg].data )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  for ( seg = 0; seg < numseg; ++seg )
  {
    REAL8Vector savevec; /* save the time series data vector */
    int code;
 
    /* save the time series data vector */
    savevec = *tseries->data;
 
    /* set the data vector to be appropriate for the even segment */
    tseries->data->length  = seglen;
    tseries->data->data   += seg * stride;
 
    /* compute the modified periodogram for the even segment */
    code = XLALREAL8ModifiedPeriodogram( work + seg, tseries, window, plan );
 
    /* restore the time series data vector to its original state */
    *tseries->data = savevec;
 
    /* now check for failure of the XLAL routine */
    if ( code == XLAL_FAILURE )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  bin = XLALMalloc( numseg * sizeof( *bin ) );
  if ( ! bin )
  {
    median_cleanup_REAL8( work, numseg ); /* cleanup */
    XLAL_ERROR( XLAL_ENOMEM );
  }
 
  double meanVal = 0, normVal = 0;
 
  UINT4 numBins = 100;
  int binIndex;
  float Observed[numBins];
  float Expected[numBins];
  int min = 0; int max = 100;
  int count;
  float interval = (float)(max - min ) / numBins;
  double CriticalValue = 0.0;
  double XSqr, XSqrTerm;
  double bin_val, expected_val;
 
  for ( k = 0; k < spectrum->data->length; ++k ) {
      pvalues[k] = 0.0;
  }
 
 
  /* now loop over frequency bins and compute the median-mean */
  for ( k = 0; k < spectrum->data->length; ++k )
  {
    /* assign array of even segment values to bin array for this freq bin */
    for ( seg = 0; seg < numseg; ++seg ) {
      bin[seg] = work[seg].data->data[k];
      meanVal = meanVal + work[seg].data->data[k];
    }
 
    meanVal = meanVal / (double) numseg;
 
    for ( l = 0; l < numBins; ++l ) {
        Observed[l] = 0.0;
        Expected[l] = 0.0;
    }
 
    count = 0.0;
    for ( seg = 0; seg < numseg; ++seg ) {
      normVal = 2 * bin[seg] / meanVal;
      binIndex = (int)((normVal- min)/interval);
 
      Observed[binIndex] = Observed[binIndex] + 1;
      count = count + 1;
    }
 
    CriticalValue = 0.0;
 
    for ( l = 0; l < numBins; ++l ) {
 
      bin_val = l*interval + min;
      expected_val = count * chisqr(2,bin_val);
 
      Expected[l] = expected_val;
 
      XSqr = Observed[l] - Expected[l];
 
      XSqrTerm = (float) ((XSqr * XSqr) / Expected[l]);
 
      CriticalValue = CriticalValue + XSqrTerm;
 
    }
 
    pvalues[k] = 1.0/CriticalValue;
 
  }
 
  /* free the workspace data */
  XLALFree( bin );
  median_cleanup_REAL8( work, numseg );
 
  return 0;
}
 
static double chisqr(int Dof, double Cv)
{
    if(Cv < 0 || Dof < 1)
    {
        return 0.0;
    }
    double K = ((double)Dof) * 0.5;
    double X = Cv * 0.5;
    if(Dof == 2)
    {
        return exp(-1.0 * X);
    }
 
    double PValue = igf(K, X);
    if(isnan(PValue) || isinf(PValue))
    {
        return 1e-14;
    }
 
    PValue /= tgamma(K);
 
    return (1.0 - PValue);
}
 
static double igf(double S, double Z)
{
    if(Z < 0.0)
    {
        return 0.0;
    }
    double Sc = (1.0 / S);
    Sc *= pow(Z, S);
    Sc *= exp(-Z);
 
    double Sum = 1.0;
    double Nom = 1.0;
    double Denom = 1.0;
 
    for(int k = 0; k < 200; k++)
    {
        Nom *= Z;
        S++;
        Denom *= S;
        Sum += (Nom / Denom);
    }
 
    return Sum * Sc;
}
 
static void median_cleanup_REAL8( REAL8FrequencySeries *work, UINT4 n )
{
  int saveErrno = xlalErrno;
  UINT4 i;
  for ( i = 0; i < n; ++i )
    if ( work[i].data )
      XLALDestroyREAL8Vector( work[i].data );
  XLALFree( work );
  xlalErrno = saveErrno;
  return;
}
 
int LALInferenceRemoveLinesKS(
    REAL8FrequencySeries        *spectrum,
    const REAL8TimeSeries       *tseries,
    UINT4                        seglen,
    UINT4                        stride,
    const REAL8Window           *window,
    const REAL8FFTPlan          *plan,
    REAL8                       *pvalues
    )
{
  REAL8FrequencySeries *work; /* array of frequency series */
  REAL8 *bin; /* array of bin values */
  UINT4 reclen; /* length of entire data record */
  UINT4 numseg;
  UINT4 seg;
  UINT4 k,l;
 
  if ( ! spectrum || ! tseries || ! plan )
      XLAL_ERROR( XLAL_EFAULT );
  if ( ! spectrum->data || ! tseries->data )
      XLAL_ERROR( XLAL_EINVAL );
  if ( tseries->deltaT <= 0.0 )
      XLAL_ERROR( XLAL_EINVAL );
 
  reclen = tseries->data->length;
  numseg = 1 + (reclen - seglen)/stride;
 
  /* consistency check for lengths: make sure that the segments cover the
 *  *  *    * data record completely */
  if ( (numseg - 1)*stride + seglen != reclen )
    XLAL_ERROR( XLAL_EBADLEN );
  if ( spectrum->data->length != seglen/2 + 1 )
    XLAL_ERROR( XLAL_EBADLEN );
  /* create frequency series data workspaces */
  work = XLALCalloc( numseg, sizeof( *work ) );
  if ( ! work )
    XLAL_ERROR( XLAL_ENOMEM );
  for ( seg = 0; seg < numseg; ++seg )
  {
    work[seg].data = XLALCreateREAL8Vector( spectrum->data->length );
    if ( ! work[seg].data )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  for ( seg = 0; seg < numseg; ++seg )
  {
    REAL8Vector savevec; /* save the time series data vector */
    int code;
 
    /* save the time series data vector */
    savevec = *tseries->data;
 
    /* set the data vector to be appropriate for the even segment */
    tseries->data->length  = seglen;
    tseries->data->data   += seg * stride;
 
    /* compute the modified periodogram for the even segment */
    code = XLALREAL8ModifiedPeriodogram( work + seg, tseries, window, plan );
 
    /* restore the time series data vector to its original state */
    *tseries->data = savevec;
 
    /* now check for failure of the XLAL routine */
    if ( code == XLAL_FAILURE )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  bin = XLALMalloc( numseg * sizeof( *bin ) );
  if ( ! bin )
  {
    median_cleanup_REAL8( work, numseg ); /* cleanup */
    XLAL_ERROR( XLAL_ENOMEM );
  }
 
  double meanVal = 0, normVal = 0;
 
  UINT4 numBins = 100;
  int binIndex;
  float Observed[numBins];
  float Expected[numBins];
  float ObservedCDF[numBins];
  float ExpectedCDF[numBins];
  int min = 0; int max = 100;
  int count;
  float interval = (float)(max - min ) / numBins;
  float ObservedSum, ExpectedSum;
  double KS, KSVal, nKSsquared;
  double bin_val, expected_val;
 
  for ( k = 0; k < spectrum->data->length; ++k ) {
      pvalues[k] = 0.0;
  }
 
  /* now loop over frequency bins and compute the median-mean */
  for ( k = 0; k < spectrum->data->length; ++k )
  {
    /* assign array of even segment values to bin array for this freq bin */
    for ( seg = 0; seg < numseg; ++seg ) {
      bin[seg] = work[seg].data->data[k];
      meanVal = meanVal + work[seg].data->data[k];
    }
 
    meanVal = meanVal / (double) numseg;
 
    for ( l = 0; l < numBins; ++l ) {
        Observed[l] = 0.0;
        Expected[l] = 0.0;
        ObservedCDF[l] = 0.0;
        ExpectedCDF[l] = 0.0;
    }
 
    count = 0.0;
    for ( seg = 0; seg < numseg; ++seg ) {
      normVal = 2 * bin[seg] / meanVal;
      binIndex = (int)((normVal- min)/interval);
 
      Observed[binIndex] = Observed[binIndex] + 1;
      count = count + 1;
    }
 
    for ( l = 0; l < numBins; ++l ) {
 
      bin_val = l*interval + min;
      expected_val = count * chisqr(2,bin_val);
 
      Expected[l] = expected_val;
 
    }
 
    ObservedSum = 0.0;
    ExpectedSum = 0.0;
 
    for ( l = 0; l < numBins; ++l ) {
 
      if (l > 0) {
          ObservedCDF[l] = ObservedCDF[l-1] + Observed[l];
          ExpectedCDF[l] = ExpectedCDF[l-1] + Expected[l];
 
      }
      else {
          ObservedCDF[l] = Observed[l];
          ExpectedCDF[l] = Expected[l];
      }
 
      ObservedSum = ObservedSum + Observed[l];
      ExpectedSum = ExpectedSum + Expected[l];
 
    }
 
    KS = 0.0;
 
    for ( l = 0; l < numBins; ++l ) {
 
        ObservedCDF[l] = ObservedCDF[l]/ObservedSum;
        ExpectedCDF[l] = ExpectedCDF[l]/ExpectedSum;
 
        KSVal = ObservedCDF[l] - ExpectedCDF[l];
 
        if (KSVal < 0) {
            KSVal = -KSVal;
        }
 
        if (KSVal > KS) {
            KS = KSVal;
        }
 
    }
 
    nKSsquared = count * KS * KS;
    pvalues[k] = 2*exp(-(2.000071+.331/sqrt(count)+1.409/count)*nKSsquared);
 
  }
 
  /* free the workspace data */
  XLALFree( bin );
  median_cleanup_REAL8( work, numseg );
 
  return 0;
}
 
int LALInferenceAverageSpectrumBinFit(
    REAL8FrequencySeries        *spectrum,
    const REAL8TimeSeries       *tseries,
    UINT4                        seglen,
    UINT4                        stride,
    const REAL8Window           *window,
    const REAL8FFTPlan          *plan,
    char*                       filename,
    LIGOTimeGPS                 GPStime
    )
{
  REAL8FrequencySeries *work; /* array of frequency series */
  REAL8 *bin; /* array of bin values */
  UINT4 reclen; /* length of entire data record */
  UINT4 numseg;
  UINT4 seg;
  UINT4 k;
 
  double trigtime = GPStime.gpsSeconds+1e-9*GPStime.gpsNanoSeconds;
  double PSDtime;
  double *PSDtimes;
  int *PSDtimesIndex, segindex;
 
  if ( ! spectrum || ! tseries || ! plan )
      XLAL_ERROR( XLAL_EFAULT );
  if ( ! spectrum->data || ! tseries->data )
      XLAL_ERROR( XLAL_EINVAL );
  if ( tseries->deltaT <= 0.0 )
      XLAL_ERROR( XLAL_EINVAL );
 
  reclen = tseries->data->length;
  numseg = 1 + (reclen - seglen)/stride;
 
  /* consistency check for lengths: make sure that the segments cover the
 *    * data record completely */
  if ( (numseg - 1)*stride + seglen != reclen )
    XLAL_ERROR( XLAL_EBADLEN );
  if ( spectrum->data->length != seglen/2 + 1 )
    XLAL_ERROR( XLAL_EBADLEN );
 
  /* create frequency series data workspaces */
  work = XLALCalloc( numseg, sizeof( *work ) );
  if ( ! work )
    XLAL_ERROR( XLAL_ENOMEM );
  for ( seg = 0; seg < numseg; ++seg )
  {
    work[seg].data = XLALCreateREAL8Vector( spectrum->data->length );
    if ( ! work[seg].data )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  PSDtimes = XLALMalloc( (numseg-1) * sizeof( *PSDtimes ) );
  PSDtimesIndex = XLALMalloc( (numseg-1) * sizeof( *PSDtimesIndex ) );
 
  int count = 0;
 
  for ( seg = 0; seg < numseg; ++seg )
  {
    REAL8Vector savevec; /* save the time series data vector */
    int code;
 
    /* save the time series data vector */
    savevec = *tseries->data;
 
    PSDtime = tseries->epoch.gpsSeconds + 1e-9*tseries->epoch.gpsNanoSeconds + seg*tseries->deltaT*seglen;
    if ((PSDtime > trigtime - 0.5) & (PSDtime < trigtime + 0.5))
    {
    }
    else {
    PSDtimes[count] = PSDtime;
    PSDtimesIndex[count] = seg;
 
    count = count + 1;
    }
 
    /* set the data vector to be appropriate for the even segment */
    tseries->data->length  = seglen;
    tseries->data->data   += seg * stride;
 
    /* compute the modified periodogram for the even segment */
    code = XLALREAL8ModifiedPeriodogram( work + seg, tseries, window, plan );
 
    /* restore the time series data vector to its original state */
    *tseries->data = savevec;
 
    /* now check for failure of the XLAL routine */
    if ( code == XLAL_FAILURE )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  bin = XLALMalloc( (numseg) * sizeof( *bin ) );
 
  if ( ! bin )
  {
    median_cleanup_REAL8( work, numseg ); /* cleanup */
    XLAL_ERROR( XLAL_ENOMEM );
  }
 
  double SUMx = 0, SUMy = 0, SUMxy = 0, SUMxx = 0;
  double f, t, datavallog;
  double slope, y_intercept, y_estimate, y_estimate_log;
  double deltaF = work->deltaF;
 
  FILE *out;
 
  out = fopen(filename, "w");
 
  /* now loop over frequency bins and compute the median-mean */
  for ( k = 0; k < spectrum->data->length; ++k )
  {
    f = ((double) k) * deltaF;
 
    fprintf(out,"%e",f);
    /* assign array of even segment values to bin array for this freq bin */
    for ( seg = 0; seg < numseg; ++seg ) {
      bin[seg] = work[seg].data->data[k];
      fprintf(out," %e ",bin[seg]);
    }
    fprintf(out,"\n");
 
    count = 0; SUMx = 0, SUMy = 0, SUMxy = 0, SUMxx = 0;
    for ( seg = 0; seg < numseg-1; ++seg ) {
      segindex = PSDtimesIndex[seg];
 
      t = PSDtimes[segindex];
      datavallog = log10(bin[segindex]);
 
      SUMx = SUMx + t;
      SUMy = SUMy + datavallog;
      SUMxy = SUMxy + t*datavallog;
      SUMxx = SUMxx + t*t;
 
      count = count + 1;
 
    }
 
    slope = ( SUMx*SUMy - count*SUMxy ) / ( SUMx*SUMx - count*SUMxx );
    y_intercept = ( SUMy - slope*SUMx ) / count;
 
    y_estimate_log = slope*trigtime + y_intercept;
    y_estimate = pow(10.0,y_estimate_log);
 
    spectrum->data->data[k] = y_estimate;
 
  }
 
  fclose(out);
 
  /* set metadata */
  spectrum->epoch       = work->epoch;
  spectrum->f0          = work->f0;
  spectrum->deltaF      = work->deltaF;
  spectrum->sampleUnits = work->sampleUnits;
 
  /* free the workspace data */
  XLALFree( bin );
  median_cleanup_REAL8( work, numseg );
 
  return 0;
 
}
 
int LALInferenceRemoveLinesPowerLaw(
    REAL8FrequencySeries        *spectrum,
    const REAL8TimeSeries       *tseries,
    UINT4                        seglen,
    UINT4                        stride,
    const REAL8Window           *window,
    const REAL8FFTPlan          *plan,
    REAL8                       *pvalues
    )
{
  REAL8FrequencySeries *work; /* array of frequency series */
  REAL8 *bin; /* array of bin values */
  UINT4 reclen; /* length of entire data record */
  UINT4 numseg;
  UINT4 seg;
  UINT4 k,l;
 
  if ( ! spectrum || ! tseries || ! plan )
      XLAL_ERROR( XLAL_EFAULT );
  if ( ! spectrum->data || ! tseries->data )
      XLAL_ERROR( XLAL_EINVAL );
  if ( tseries->deltaT <= 0.0 )
      XLAL_ERROR( XLAL_EINVAL );
 
  reclen = tseries->data->length;
  numseg = 1 + (reclen - seglen)/stride;
 
  /* consistency check for lengths: make sure that the segments cover the
 *  *    * data record completely */
  if ( (numseg - 1)*stride + seglen != reclen )
    XLAL_ERROR( XLAL_EBADLEN );
  if ( spectrum->data->length != seglen/2 + 1 )
    XLAL_ERROR( XLAL_EBADLEN );
 
  /* create frequency series data workspaces */
  work = XLALCalloc( numseg, sizeof( *work ) );
  if ( ! work )
    XLAL_ERROR( XLAL_ENOMEM );
  for ( seg = 0; seg < numseg; ++seg )
  {
    work[seg].data = XLALCreateREAL8Vector( spectrum->data->length );
    if ( ! work[seg].data )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  for ( seg = 0; seg < numseg; ++seg )
  {
    REAL8Vector savevec; /* save the time series data vector */
    int code;
 
    /* save the time series data vector */
    savevec = *tseries->data;
 
    /* set the data vector to be appropriate for the even segment */
    tseries->data->length  = seglen;
    tseries->data->data   += seg * stride;
 
    /* compute the modified periodogram for the even segment */
    code = XLALREAL8ModifiedPeriodogram( work + seg, tseries, window, plan );
 
    /* restore the time series data vector to its original state */
    *tseries->data = savevec;
 
    /* now check for failure of the XLAL routine */
    if ( code == XLAL_FAILURE )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  bin = XLALMalloc( numseg * sizeof( *bin ) );
  if ( ! bin )
  {
    median_cleanup_REAL8( work, numseg ); /* cleanup */
    XLAL_ERROR( XLAL_ENOMEM );
  }
 
  int count;
  double SUMx = 0, SUMy = 0, SUMxy = 0, SUMxx = 0;
  double res, slope, y_intercept, y_estimate_log;
 
  double f, dataval, flog, datavallog;
 
  double deltaF = spectrum->deltaF;
 
  for ( k = 0; k < spectrum->data->length; ++k ) {
      pvalues[k] = 0.0;
  }
 
  UINT4 numBands = 4;
  float frequencyBands[4];
  frequencyBands[0] = 0, frequencyBands[1] = 10, frequencyBands[2] = 100, frequencyBands[3] = 2048;
 
  for ( l = 0; l < numBands-1; ++l)
  {
 
    count = 0, SUMx = 0, SUMy = 0, SUMxy = 0, SUMxx = 0;
    /* now loop over frequency bins and compute the median-mean */
    for ( k = 0; k < spectrum->data->length; ++k )
    {
 
      f = ((double) k) * deltaF;
      dataval = spectrum->data->data[k];
      flog = log10(f);
      datavallog = log10(dataval);
 
      if ((f>=frequencyBands[l]) & (f<=frequencyBands[l+1])) {
 
      SUMx = SUMx + flog;
      SUMy = SUMy + datavallog;
      SUMxy = SUMxy + flog*datavallog;
      SUMxx = SUMxx + flog*flog;
 
      count = count + 1;
 
      }
    }
 
    slope = ( SUMx*SUMy - count*SUMxy ) / ( SUMx*SUMx - count*SUMxx );
    y_intercept = ( SUMy - slope*SUMx ) / count;
 
    for (k=0; k<spectrum->data->length; ++k) {
 
      f = ((double) k) * deltaF;
      dataval = spectrum->data->data[k];
      flog = log10(f);
      datavallog = log10(dataval);
 
      if ((f>=frequencyBands[l]) & (f<=frequencyBands[l+1])) {
 
      y_estimate_log = slope*flog + y_intercept;
 
      res = fabs(datavallog - y_estimate_log);
      pvalues[k] = 1.0/res;
      }
    }
  }
 
 
  /* free the workspace data */
  XLALFree( bin );
  median_cleanup_REAL8( work, numseg );
 
  return 0;
}
 
int LALInferenceXCorrBands(
    REAL8FrequencySeries        *spectrum,
    const REAL8TimeSeries       *tseries,
    UINT4                        seglen,
    UINT4                        stride,
    const REAL8Window           *window,
    const REAL8FFTPlan          *plan,
    REAL8                       *pvalues,
    char*                       filename
    )
{
  REAL8FrequencySeries *work; /* array of frequency series */
  REAL8 *bin; /* array of bin values */
  UINT4 reclen; /* length of entire data record */
  UINT4 numseg;
  UINT4 seg;
  UINT4 k,l;
 
  if ( ! spectrum || ! tseries || ! plan )
      XLAL_ERROR( XLAL_EFAULT );
  if ( ! spectrum->data || ! tseries->data )
      XLAL_ERROR( XLAL_EINVAL );
  if ( tseries->deltaT <= 0.0 )
      XLAL_ERROR( XLAL_EINVAL );
 
  reclen = tseries->data->length;
  numseg = 1 + (reclen - seglen)/stride;
 
  /* consistency check for lengths: make sure that the segments cover the
 *  *  *  *    * data record completely */
  if ( (numseg - 1)*stride + seglen != reclen )
    XLAL_ERROR( XLAL_EBADLEN );
  if ( spectrum->data->length != seglen/2 + 1 )
    XLAL_ERROR( XLAL_EBADLEN );
 
  /* create frequency series data workspaces */
  work = XLALCalloc( numseg, sizeof( *work ) );
  if ( ! work )
    XLAL_ERROR( XLAL_ENOMEM );
  for ( seg = 0; seg < numseg; ++seg )
  {
    work[seg].data = XLALCreateREAL8Vector( spectrum->data->length );
    if ( ! work[seg].data )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  for ( seg = 0; seg < numseg; ++seg )
  {
    REAL8Vector savevec; /* save the time series data vector */
    int code;
 
    /* save the time series data vector */
    savevec = *tseries->data;
 
    /* set the data vector to be appropriate for the even segment */
    tseries->data->length  = seglen;
    tseries->data->data   += seg * stride;
 
    /* compute the modified periodogram for the even segment */
    code = XLALREAL8ModifiedPeriodogram( work + seg, tseries, window, plan );
 
    /* restore the time series data vector to its original state */
    *tseries->data = savevec;
 
    /* now check for failure of the XLAL routine */
    if ( code == XLAL_FAILURE )
    {
      median_cleanup_REAL8( work, numseg ); /* cleanup */
      XLAL_ERROR( XLAL_EFUNC );
    }
  }
 
  /* create array to hold a particular frequency bin data */
  bin = XLALMalloc( numseg * sizeof( *bin ) );
  if ( ! bin )
  {
    median_cleanup_REAL8( work, numseg ); /* cleanup */
    XLAL_ERROR( XLAL_ENOMEM );
  }
 
  double mx,my,sx,sy,sxy,denom,r;
 
  for ( k = 0; k < spectrum->data->length; ++k ) {
      pvalues[k] = 0.0;
  }
 
  FILE *out;
 
  out = fopen(filename, "w");
 
  for ( k = 0; k < spectrum->data->length; ++k )
  {
    fprintf(out,"%e",((double) k) * work->deltaF);
 
    /* now loop over frequency bins and compute the median-mean */
    for ( l = 0; l < spectrum->data->length; ++l )
    {
 
      /* Calculate the mean of the two series x[], y[] */
      mx = 0;
      my = 0;
      for ( seg = 0; seg < numseg; ++seg ) {
        mx += work[seg].data->data[k];
        my += work[seg].data->data[l];
      }
      mx /= numseg;
      my /= numseg;
 
      /* Calculate the denominator */
      sx = 0;
      sy = 0;
      for ( seg = 0; seg < numseg; ++seg ) {
        sx += (work[seg].data->data[k] - mx) * (work[seg].data->data[k] - mx);
        sy += (work[seg].data->data[l] - my) * (work[seg].data->data[l] - my);
      }
      denom = sqrt(sx*sy);
 
      sxy = 0;
      for ( seg = 0; seg < numseg; ++seg ) {
         sxy += (work[seg].data->data[k] - mx) * (work[seg].data->data[l] - my);
      }
      r = fabs(sxy / denom);
 
      fprintf(out," %e ",r);
 
    }
 
    fprintf(out,"\n");
 
  }
 
  fclose(out);
 
  /* free the workspace data */
  XLALFree( bin );
  median_cleanup_REAL8( work, numseg );
 
  return 0;
}