void addtoavgenergy(t_complex *list, real *result, int size, int tsteps)
{
int i;
for (i = 0; i < size; i++)
{
result[i] += cabs2(list[i])/tsteps;
}
}
dmat *psd1d(const dmat *v, /**<[in] The data sequence*/
long nseg /**<[in] Number of overlapping segments*/
){
long nx;
long ncol;
if(v->nx==1){
nx=v->ny;
ncol=1;
}else{
nx=v->nx;
ncol=v->ny;
}
if(nseg<=1) nseg=1;
const int lseg2=nx/(nseg+1);
const int lseg=lseg2*2;
dmat *psd=dnew(lseg2+1, ncol);
cmat *hat=cnew(lseg, 1);
//cfft2plan(hat, -1);
for(long icol=0; icol<ncol; icol++){
double *ppsd=psd->p+icol*(lseg2+1);
for(int iseg=0; iseg<nseg; iseg++){
double* p=v->p+icol*nx+iseg*lseg2;
for(int ix=0; ix<lseg; ix++){
hat->p[ix]=p[ix]*W_J(ix, lseg2);
}
cfft2(hat, -1);
ppsd[0]+=cabs2(hat->p[0]);
for(int ix=1; ix<lseg2; ix++){
ppsd[ix]+=cabs2(hat->p[ix])+cabs2(hat->p[lseg-ix]);
}
ppsd[lseg2]+=cabs2(hat->p[lseg2]);
}
}
double sumwt=0;
for(int ix=0; ix<lseg; ix++){
sumwt+=pow(W_J(ix, lseg2), 2);
}
sumwt*=lseg*nseg;
dscale(psd, 1./sumwt);
cfree(hat);
return psd;
}
// HIGHPASS
pzkContainer * t2hp(pzkContainer * pzk, real w0) {
pzkContainer * f = createPzkContainer(pzk->nextPole, pzk->nextZero);
uint i;
complex tmp;
f->amp = pzk->amp * pow(w0,(real)pzk->no_wz);
f->no_wz = -pzk->no_wz;
for( i = 0; i < pzk->nextPole; i++ ) {
tmp.re = w0;
tmp.im = 0;
f->no_wz++;
if( cisreal(pzk->poles[i]) ) {
f->amp /= -pzk->poles[i].re;
tmp.re /= pzk->poles[i].re;
} else {
tmp = cdiv(tmp, pzk->poles[i]);
f->amp /= cabs2(pzk->poles[i]);
f->no_wz++;
}
addPole(f, tmp);
}
for( i = 0; i < pzk->nextZero; i++ ) {
tmp.re = w0;
tmp.im = 0;
f->no_wz--;
if( cisreal(pzk->zeros[i]) ) {
f->amp *= -pzk->zeros[i].re;
tmp.re /= pzk->zeros[i].re;
} else {
tmp = cdiv(tmp, pzk->zeros[i]);
f->amp *= cabs2(pzk->zeros[i]);
f->no_wz--;
}
addZero(f, tmp);
}
f->type = highpass;
return f;
}
int mandel(double complex z) {
int maxiter = 80;
double complex c = z;
for (int n = 0; n < maxiter; ++n) {
if (cabs2(z) > 4.0) {
return n;
}
z = z*z+c;
}
return maxiter;
}
static int mandel(double cre, double cim, int MAX_ITER)
{
const float Z_MAX2 = 4.0;
double zre = cre, zim = cim;
int iter;
for (iter = 0; iter < MAX_ITER; iter++) {
double z1re, z1im;
z1re = zre * zre - zim * zim;
z1im = 2 * zre * zim;
z1re += cre;
z1im += cim;
if (cabs2(z1re, z1im) > Z_MAX2) {
return iter + 1; /* outside set */
}
zre = z1re;
zim = z1im;
}
return 0; /* inside set */
}
int PSDCalculator::calculatePowerSpectrum(
double *input, int inputLen,
double *output, int outputLen,
bool removeMean, bool interpolateHoles,
bool average, int averageLen,
bool apodize, ApodizeFunction apodizeFxn, double gaussianSigma,
PSDType outputType, double inputSamplingFreq) {
if (outputLen != calculateOutputVectorLength(inputLen, average, averageLen)) {
KstDebug::self()->log(QObject::tr("in PSDCalculator::calculatePowerSpectrum: received output array with wrong length."), KstDebug::Error);
return -1;
}
if (outputLen != _prevOutputLen) {
delete[] _a;
delete[] _w;
_awLen = outputLen*2;
_prevOutputLen = outputLen;
_a = new double[_awLen];
_w = new double[_awLen];
updateWindowFxn(apodizeFxn, gaussianSigma);
}
if ( (_prevApodizeFxn != apodizeFxn) || (_prevGaussianSigma != gaussianSigma) ) {
updateWindowFxn(apodizeFxn, gaussianSigma);
}
int currentCopyLen, nsamples = 0;
int i_samp, i_subset, ioffset;
memset(output, 0, sizeof(double) * outputLen);
bool done = false;
for (i_subset = 0; !done; i_subset++) {
//
// overlapping average => i_subset*outputLen...
//
ioffset = i_subset * outputLen;
//
// only zero pad if we really have to.
// It is better to adjust the last chunk's overlap...
//
if (ioffset + _awLen*5/4 < inputLen) {
currentCopyLen = _awLen; // will copy a complete window.
} else if (_awLen<inputLen) { // count the last one from the end.
ioffset = inputLen-_awLen - 1;
currentCopyLen = _awLen; // will copy a complete window.
done = true;
} else {
currentCopyLen = inputLen - ioffset; // will copy a partial window.
memset(&_a[currentCopyLen], 0, sizeof(double)*(_awLen - currentCopyLen)); // zero the leftovers.
done = true;
}
double mean = 0.0;
if (removeMean) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
mean += input[i_samp + ioffset];
}
mean /= (double)currentCopyLen;
}
//
// apply the PSD options (removeMean, apodize, etc.)
// separate cases for speed- although this shouldn't really matter -
// the rdft should be the most time consuming step by far for any large data set...
//
if (removeMean && apodize && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = (kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen) - mean)*_w[i_samp];
}
} else if (removeMean && apodize) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = (input[i_samp + ioffset] - mean)*_w[i_samp];
}
} else if (removeMean && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen) - mean;
}
} else if (apodize && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen)*_w[i_samp];
}
} else if (removeMean) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset] - mean;
}
} else if (apodize) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset]*_w[i_samp];
}
} else if (interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen);
}
} else {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset];
}
}
nsamples += currentCopyLen;
//
// real discrete fourier transorm on _a.
//
rdft(_awLen, 1, _a);
output[0] += _a[0] * _a[0];
output[outputLen-1] += _a[1] * _a[1];
for (i_samp = 1; i_samp < outputLen - 1; i_samp++) {
output[i_samp] += cabs2(_a[i_samp * 2], _a[i_samp * 2 + 1]);
}
}
double frequencyStep = 2.0*(double)inputSamplingFreq/(double)nsamples;
double norm = 2.0/(double)nsamples*2.0/(double)nsamples;
switch (outputType) {
default:
case PSDAmplitudeSpectralDensity: // amplitude spectral density (default) [V/Hz^1/2]
norm /= frequencyStep;
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] = sqrt(output[i_samp]*norm);
}
break;
case PSDPowerSpectralDensity: // power spectral density [V^2/Hz]
norm /= frequencyStep;
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] *= norm;
}
break;
case PSDAmplitudeSpectrum: // amplitude spectrum [V]
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] = sqrt(output[i_samp]*norm);
}
break;
case PSDPowerSpectrum: // power spectrum [V^2]
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] *= norm;
}
break;
}
return 0;
}
// BANDSTOP
pzkContainer * t2bs(pzkContainer * pzk, real w0, real dw) {
uint nop, noz, i;
pzkContainer * f;
const real w02 = w0*w0;
complex tmp, beta, gamma, cw0, cdwp2;
cw0.re = w0;
cw0.im = 0;
cdwp2.re = dw / 2;
cdwp2.im = 0;
noz = 2*pzk->nextZero;
nop = 2*pzk->nextPole;
if( pzk->no_wz > 0 ) {
noz += pzk->no_wz;
}
if( pzk->no_wz < 0 ) {
nop -= pzk->no_wz;
}
f = createPzkContainer(nop, noz);
f->wz = w0;
f->no_wz = -pzk->no_wz;
f->amp = pzk->amp * pow(dw, (real)(pzk->no_wz));
gamma.re = 0;
gamma.im = 0;
if( pzk->no_wz > 0 ) {
for( i = 0; i < pzk->no_wz; i++ ) {
addZero(f, gamma);
}
}
if( pzk->no_wz < 0 ) {
for( i = 0; i < -pzk->no_wz; i++ ) {
addPole(f, gamma);
}
}
for( i = 0; i < pzk->nextPole; i++ ) {
if( cisreal(pzk->poles[i]) ) {
beta.re = cdwp2.re / pzk->poles[i].re;
tmp.re = 1 - ( w02/(beta.re*beta.re) );
if( tmp.re >= 0 ) {
tmp.re = sqrt( tmp.re );
gamma.im = 0;
gamma.re = beta.re * (1 + tmp.re);
addPole(f, gamma);
gamma.re = beta.re * (1 - tmp.re);
addPole(f, gamma);
} else {
tmp.im = sqrt( -tmp.re );
tmp.re = 1;
gamma = cmul2( beta.re, tmp );
addPole(f, gamma);
}
f->amp /= -pzk->poles[i].re;
f->no_wz++;
}
else {
beta = cdiv(cdwp2, pzk->poles[i]);
tmp = cdiv(cw0, beta);
tmp = csqrt( csub2(1, cmlt(tmp, tmp)) );
gamma = cmlt(beta, cadd2(1, tmp));
addPole(f, gamma);
gamma = cmlt(beta, csub2(1, tmp));
addPole(f, gamma);
f->amp /= cabs2(pzk->poles[i]);
f->no_wz += 2;
}
}
for( i = 0; i < pzk->nextZero; i++ ) {
if( cisreal(pzk->zeros[i]) ) {
beta.re = cdwp2.re / pzk->zeros[i].re;
tmp.re = 1 - ( w02/(beta.re*beta.re) );
if( tmp.re >= 0 ) {
tmp.re = sqrt( tmp.re );
gamma.im = 0;
gamma.re = beta.re * (1 + tmp.re);
addZero(f, gamma);
gamma.re = beta.re * (1 - tmp.re);
addZero(f, gamma);
} else {
tmp.im = sqrt( -tmp.re );
tmp.re = 1;
gamma = cmul2( beta.re, tmp );
addZero(f, gamma);
}
f->amp *= -pzk->zeros[i].re;
f->no_wz--;
}
else {
beta = cdiv(cdwp2, pzk->zeros[i]);
tmp = cdiv(cw0, beta);
tmp = csqrt( csub2(1, cmlt(tmp, tmp)) );
gamma = cmlt(beta, cadd2(1, tmp));
addZero(f, gamma);
gamma = cmlt(beta, csub2(1, tmp));
addZero(f, gamma);
f->amp *= cabs2(pzk->zeros[i]);
f->no_wz -= 2;
}
}
return f;
}
double *bayestar_sky_map_toa_phoa_snr(
long *npix, /* Input: number of HEALPix pixels. */
double gmst, /* Greenwich mean sidereal time in radians. */
int nifos, /* Input: number of detectors. */
const float (**responses)[3], /* Pointers to detector responses. */
const double **locations, /* Pointers to locations of detectors in Cartesian geographic coordinates. */
const double *toas, /* Input: array of times of arrival with arbitrary relative offset. (Make toas[0] == 0.) */
const double *phoas, /* Input: array of phases of arrival with arbitrary relative offset. (Make phoas[0] == 0.) */
const double *snrs, /* Input: array of SNRs. */
const double *w_toas, /* Input: sum-of-squares weights, (1/TOA variance)^2. */
const double *w1s, /* Input: first moments of angular frequency. */
const double *w2s, /* Input: second moments of angular frequency. */
const double *horizons, /* Distances at which a source would produce an SNR of 1 in each detector. */
double min_distance,
double max_distance,
int prior_distance_power) /* Use a prior of (distance)^(prior_distance_power) */
{
long nside;
long maxpix;
long i;
double d1[nifos];
double *P;
gsl_permutation *pix_perm;
double complex exp_i_phoas[nifos];
/* Hold GSL return values for any thread that fails. */
int gsl_errno = GSL_SUCCESS;
/* Storage for old GSL error handler. */
gsl_error_handler_t *old_handler;
/* Maximum number of subdivisions for adaptive integration. */
static const size_t subdivision_limit = 64;
/* Subdivide radial integral where likelihood is this fraction of the maximum,
* will be used in solving the quadratic to find the breakpoints */
static const double eta = 0.01;
/* Use this many integration steps in 2*psi */
static const int ntwopsi = 16;
/* Number of integration steps in cos(inclination) */
static const int nu = 16;
/* Number of integration steps in arrival time */
static const int nt = 16;
/* Rescale distances so that furthest horizon distance is 1. */
{
double d1max;
memcpy(d1, horizons, sizeof(d1));
for (d1max = d1[0], i = 1; i < nifos; i ++)
if (d1[i] > d1max)
d1max = d1[i];
for (i = 0; i < nifos; i ++)
d1[i] /= d1max;
min_distance /= d1max;
max_distance /= d1max;
}
(void)w2s; /* FIXME: remove unused parameter */
for (i = 0; i < nifos; i ++)
exp_i_phoas[i] = exp_i(phoas[i]);
/* Evaluate posterior term only first. */
P = bayestar_sky_map_toa_adapt_resolution(&pix_perm, &maxpix, npix, gmst, nifos, locations, toas, w_toas, autoresolution_count_pix_toa_phoa_snr);
if (!P)
return NULL;
/* Determine the lateral HEALPix resolution. */
nside = npix2nside(*npix);
/* Zero all pixels that didn't meet the TDOA cut. */
for (i = maxpix; i < *npix; i ++)
{
long ipix = gsl_permutation_get(pix_perm, i);
P[ipix] = -INFINITY;
}
/* Use our own error handler while in parallel section to avoid concurrent
* calls to the GSL error handler, which if provided by the user may not
* be threadsafe. */
old_handler = gsl_set_error_handler(my_gsl_error);
/* Compute posterior factor for amplitude consistency. */
#pragma omp parallel for firstprivate(gsl_errno) lastprivate(gsl_errno)
for (i = 0; i < maxpix; i ++)
{
/* Cancel further computation if a GSL error condition has occurred.
*
* Note: if one thread sets gsl_errno, not necessarily all thread will
* get the updated value. That's OK, because most failure modes will
* cause GSL error conditions on all threads. If we cared to have any
* failure on any thread terminate all of the other threads as quickly
* as possible, then we would want to insert the following pragma here:
*
* #pragma omp flush(gsl_errno)
*
* and likewise before any point where we set gsl_errno.
*/
if (gsl_errno != GSL_SUCCESS)
goto skip;
{
long ipix = gsl_permutation_get(pix_perm, i);
double complex F[nifos];
double theta, phi;
int itwopsi, iu, it, iifo;
double accum = -INFINITY;
double complex exp_i_toaphoa[nifos];
double dtau[nifos], mean_dtau;
/* Prepare workspace for adaptive integrator. */
gsl_integration_workspace *workspace = gsl_integration_workspace_alloc(subdivision_limit);
/* If the workspace could not be allocated, then record the GSL
* error value for later reporting when we leave the parallel
* section. Then, skip to the next loop iteration. */
if (!workspace)
{
gsl_errno = GSL_ENOMEM;
goto skip;
}
/* Look up polar coordinates of this pixel */
pix2ang_ring(nside, ipix, &theta, &phi);
toa_errors(dtau, theta, phi, gmst, nifos, locations, toas);
for (iifo = 0; iifo < nifos; iifo ++)
exp_i_toaphoa[iifo] = exp_i_phoas[iifo] * exp_i(w1s[iifo] * dtau[iifo]);
/* Find mean arrival time error */
mean_dtau = gsl_stats_wmean(w_toas, 1, dtau, 1, nifos);
/* Look up antenna factors */
for (iifo = 0; iifo < nifos; iifo++)
{
XLALComputeDetAMResponse(
(double *)&F[iifo], /* Type-punned real part */
1 + (double *)&F[iifo], /* Type-punned imag part */
responses[iifo], phi, M_PI_2 - theta, 0, gmst);
F[iifo] *= d1[iifo];
}
/* Integrate over 2*psi */
for (itwopsi = 0; itwopsi < ntwopsi; itwopsi++)
{
const double twopsi = (2 * M_PI / ntwopsi) * itwopsi;
const double complex exp_i_twopsi = exp_i(twopsi);
/* Integrate over u from u=-1 to u=1. */
for (iu = -nu; iu <= nu; iu++)
{
const double u = (double)iu / nu;
const double u2 = gsl_pow_2(u);
double A = 0, B = 0;
double breakpoints[5];
int num_breakpoints = 0;
double log_offset = -INFINITY;
/* The log-likelihood is quadratic in the estimated and true
* values of the SNR, and in 1/r. It is of the form A/r^2 + B/r,
* where A depends only on the true values of the SNR and is
* strictly negative and B depends on both the true values and
* the estimates and is strictly positive.
*
* The middle breakpoint is at the maximum of the log-likelihood,
* occurring at 1/r=-B/2A. The lower and upper breakpoints occur
* when the likelihood becomes eta times its maximum value. This
* occurs when
*
* A/r^2 + B/r = log(eta) - B^2/4A.
*
*/
/* Perform arrival time integral */
double accum1 = -INFINITY;
for (it = -nt/2; it <= nt/2; it++)
{
const double t = mean_dtau + LAL_REARTH_SI / LAL_C_SI * it / nt;
double complex i0arg_complex = 0;
for (iifo = 0; iifo < nifos; iifo++)
{
const double complex tmp = F[iifo] * exp_i_twopsi;
/* FIXME: could use - sign here to avoid conj below, but
* this probably just sets our sign convention relative to
* detection pipeline */
double complex phase_rhotimesr = 0.5 * (1 + u2) * creal(tmp) + I * u * cimag(tmp);
const double abs_rhotimesr_2 = cabs2(phase_rhotimesr);
const double abs_rhotimesr = sqrt(abs_rhotimesr_2);
phase_rhotimesr /= abs_rhotimesr;
i0arg_complex += exp_i_toaphoa[iifo] * exp_i(-w1s[iifo] * t) * phase_rhotimesr * gsl_pow_2(snrs[iifo]);
}
const double i0arg = cabs(i0arg_complex);
accum1 = logaddexp(accum1, log(gsl_sf_bessel_I0_scaled(i0arg)) + i0arg - 0.5 * gsl_stats_wtss_m(w_toas, 1, dtau, 1, nifos, t));
}
/* Loop over detectors */
for (iifo = 0; iifo < nifos; iifo++)
{
const double complex tmp = F[iifo] * exp_i_twopsi;
/* FIXME: could use - sign here to avoid conj below, but
* this probably just sets our sign convention relative to
* detection pipeline */
double complex phase_rhotimesr = 0.5 * (1 + u2) * creal(tmp) + I * u * cimag(tmp);
const double abs_rhotimesr_2 = cabs2(phase_rhotimesr);
const double abs_rhotimesr = sqrt(abs_rhotimesr_2);
A += abs_rhotimesr_2;
B += abs_rhotimesr * snrs[iifo];
}
A *= -0.5;
{
const double middle_breakpoint = -2 * A / B;
const double lower_breakpoint = 1 / (1 / middle_breakpoint + sqrt(log(eta) / A));
const double upper_breakpoint = 1 / (1 / middle_breakpoint - sqrt(log(eta) / A));
breakpoints[num_breakpoints++] = min_distance;
if(lower_breakpoint > breakpoints[num_breakpoints-1] && lower_breakpoint < max_distance)
breakpoints[num_breakpoints++] = lower_breakpoint;
if(middle_breakpoint > breakpoints[num_breakpoints-1] && middle_breakpoint < max_distance)
breakpoints[num_breakpoints++] = middle_breakpoint;
if(upper_breakpoint > breakpoints[num_breakpoints-1] && upper_breakpoint < max_distance)
breakpoints[num_breakpoints++] = upper_breakpoint;
breakpoints[num_breakpoints++] = max_distance;
}
{
/*
* Set log_offset to the maximum of the logarithm of the
* radial integrand evaluated at all of the breakpoints. */
int ibreakpoint;
for (ibreakpoint = 0; ibreakpoint < num_breakpoints; ibreakpoint++)
{
const double new_log_offset = log_radial_integrand(
breakpoints[ibreakpoint], A, B, prior_distance_power);
if (new_log_offset < INFINITY && new_log_offset > log_offset)
log_offset = new_log_offset;
}
}
{
/* Perform adaptive integration. Stop when a relative
* accuracy of 0.05 has been reached. */
inner_integrand_params integrand_params = {A, B, log_offset, prior_distance_power};
const gsl_function func = {radial_integrand, &integrand_params};
double result, abserr;
int ret = gsl_integration_qagp(&func, &breakpoints[0], num_breakpoints, DBL_MIN, 0.05, subdivision_limit, workspace, &result, &abserr);
/* If the integrator failed, then record the GSL error
* value for later reporting when we leave the parallel
* section. Then, break out of the loop. */
if (ret != GSL_SUCCESS)
{
gsl_errno = ret;
gsl_integration_workspace_free(workspace);
goto skip;
}
/* Take the logarithm and put the log-normalization back in. */
result = log(result) + integrand_params.log_offset + accum1;
/* Accumulate result. */
accum = logaddexp(accum, result);
}
}
}
/* Discard workspace for adaptive integrator. */
gsl_integration_workspace_free(workspace);
/* Store log posterior. */
P[ipix] = accum;
}
skip: /* this statement intentionally left blank */;
}
/* Restore old error handler. */
gsl_set_error_handler(old_handler);
/* Free permutation. */
gsl_permutation_free(pix_perm);
/* Check if there was an error in any thread evaluating any pixel. If there
* was, raise the error and return. */
if (gsl_errno != GSL_SUCCESS)
{
free(P);
GSL_ERROR_NULL(gsl_strerror(gsl_errno), gsl_errno);
}
/* Exponentiate and normalize posterior. */
pix_perm = get_pixel_ranks(*npix, P);
if (!pix_perm)
{
free(P);
return NULL;
}
exp_normalize(*npix, P, pix_perm);
gsl_permutation_free(pix_perm);
return P;
}
double bayestar_log_posterior_toa_phoa_snr(
double ra,
double sin_dec,
double distance,
double u,
double twopsi,
double t,
double gmst, /* Greenwich mean sidereal time in radians. */
int nifos, /* Input: number of detectors. */
const float (**responses)[3], /* Pointers to detector responses. */
const double **locations, /* Pointers to locations of detectors in Cartesian geographic coordinates. */
const double *toas, /* Input: array of times of arrival with arbitrary relative offset. (Make toas[0] == 0.) */
const double *phoas, /* Input: array of times of arrival with arbitrary relative offset. (Make toas[0] == 0.) */
const double *snrs, /* Input: array of SNRs. */
const double *w_toas, /* Input: sum-of-squares weights, (1/TOA variance)^2. */
const double *w1s, /* Input: first moments of angular frequency. */
const double *w2s, /* Input: second moments of angular frequency. */
const double *horizons, /* Distances at which a source would produce an SNR of 1 in each detector. */
int prior_distance_power) /* Use a prior of (distance)^(prior_distance_power) */
{
int iifo;
const double dec = asin(sin_dec);
const double u2 = gsl_pow_2(u);
const double complex exp_i_twopsi = exp_i(twopsi);
(void)w2s; /* FIXME: remove unused parameter */
/* Compute time of arrival errors */
double dt[nifos];
toa_errors(dt, M_PI_2 - dec, ra, gmst, nifos, locations, toas);
{
double mean_dt = gsl_stats_wmean(w_toas, 1, dt, 1, nifos);
for (iifo = 0; iifo < nifos; iifo++)
dt[iifo] += t - mean_dt;
}
/* Rescale distances so that furthest horizon distance is 1. */
double d1[nifos];
{
const double d1max = gsl_stats_max(horizons, 1, nifos);
for (iifo = 0; iifo < nifos; iifo ++)
d1[iifo] = horizons[iifo] / d1max;
distance /= d1max;
}
double logp = 0;
double complex i0arg_complex = 0;
double A = 0;
double B = 0;
/* Loop over detectors */
for (iifo = 0; iifo < nifos; iifo++)
{
double complex F;
XLALComputeDetAMResponse(
(double *)&F, /* Type-punned real part */
1 + (double *)&F, /* Type-punned imag part */
responses[iifo], ra, dec, 0, gmst);
F *= d1[iifo];
const double complex tmp = F * exp_i_twopsi;
double complex phase_rhotimesr = 0.5 * (1 + u2) * creal(tmp) + I * u * cimag(tmp);
const double abs_rhotimesr_2 = cabs2(phase_rhotimesr);
const double abs_rhotimesr = sqrt(abs_rhotimesr_2);
phase_rhotimesr /= abs_rhotimesr;
i0arg_complex += exp_i(phoas[iifo] + w1s[iifo] * dt[iifo]) * phase_rhotimesr * gsl_pow_2(snrs[iifo]);
logp += -0.5 * w_toas[iifo] * gsl_pow_2(dt[iifo]);
A += abs_rhotimesr_2;
B += abs_rhotimesr * snrs[iifo];
}
A *= -0.5;
const double i0arg = cabs(i0arg_complex);
/* Should be equivalent to, but more accurate than:
logp += log(gsl_sf_bessel_I0(i0arg))
*/
logp += log(gsl_sf_bessel_I0_scaled(i0arg)) + i0arg;
logp += log_radial_integrand(distance, A, B, prior_distance_power);
return logp;
}
int PSDCalculator::calculatePowerSpectrum(
double *input, int inputLen,
double *output, int outputLen,
bool removeMean, bool interpolateHoles,
bool average, int averageLen,
bool apodize, ApodizeFunction apodizeFxn, double gaussianSigma,
PSDType outputType, double inputSamplingFreq) {
if (outputLen != calculateOutputVectorLength(inputLen, average, averageLen)) {
Kst::Debug::self()->log(i18n("in PSDCalculator::calculatePowerSpectrum: received output array with wrong length."), Kst::Debug::Error);
return -1;
}
if (outputLen != _prevOutputLen) {
delete[] _a;
delete[] _w;
_awLen = outputLen*2;
_prevOutputLen = outputLen;
_a = new double[_awLen];
_w = new double[_awLen];
updateWindowFxn(apodizeFxn, gaussianSigma);
}
if ( (_prevApodizeFxn != apodizeFxn) || (_prevGaussianSigma != gaussianSigma) ) {
updateWindowFxn(apodizeFxn, gaussianSigma);
}
int currentCopyLen, nsamples = 0;
int i_samp, i_subset, ioffset;
memset(output, 0, sizeof(double)*outputLen); // initialize output.
// Mingw build could be 10 times slower (Gaussian apod, mostly 0 then?)
//MeasureTime time_in_rfdt("rdft()");
bool done = false;
for (i_subset = 0; !done; i_subset++) {
ioffset = i_subset*outputLen; //overlapping average => i_subset*outputLen
// only zero pad if we really have to. It is better to adjust the last chunk's
// overlap.
if (ioffset + _awLen*5/4 < inputLen) {
currentCopyLen = _awLen; //will copy a complete window.
} else if (_awLen<inputLen) { // count the last one from the end.
ioffset = inputLen-_awLen - 1;
currentCopyLen = _awLen; //will copy a complete window.
done = true;
} else {
currentCopyLen = inputLen - ioffset; //will copy a partial window.
memset(&_a[currentCopyLen], 0, sizeof(double)*(_awLen - currentCopyLen)); //zero the leftovers.
done = true;
}
double mean = 0.0;
if (removeMean) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
mean += input[i_samp + ioffset];
}
mean /= (double)currentCopyLen;
}
// apply the PSD options (removeMean, apodize, etc.)
// separate cases for speed- although this shouldn't really matter- the rdft should be the most time consuming step by far for any large data set.
if (removeMean && apodize && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = (Kst::kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen) - mean)*_w[i_samp];
}
} else if (removeMean && apodize) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = (input[i_samp + ioffset] - mean)*_w[i_samp];
}
} else if (removeMean && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = Kst::kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen) - mean;
}
} else if (apodize && interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = Kst::kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen)*_w[i_samp];
}
} else if (removeMean) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset] - mean;
}
} else if (apodize) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset]*_w[i_samp];
}
} else if (interpolateHoles) {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = Kst::kstInterpolateNoHoles(input, inputLen, i_samp + ioffset, inputLen);
}
} else {
for (i_samp = 0; i_samp < currentCopyLen; i_samp++) {
_a[i_samp] = input[i_samp + ioffset];
}
}
nsamples += currentCopyLen;
#if !defined(__QNX__)
rdft(_awLen, 1, _a); //real discrete fourier transorm on _a.
#else
Q_ASSERT(0); // there is a linking problem when not compling with pch. . .
#endif
output[0] += _a[0] * _a[0];
output[outputLen-1] += _a[1] * _a[1];
for (i_samp = 1; i_samp < outputLen - 1; i_samp++) {
output[i_samp] += cabs2(_a[i_samp * 2], _a[i_samp * 2 + 1]);
}
}
// FIXME: NORMALIZATION.
/* This normalization doesn't give the same results as the original KstPSD.
double frequencyStep = .5*(double)inputSamplingFreq/(double)(outputLen-1);
//normalization factors which were left out earlier for speed.
// - 2.0 for the negative frequencies which were neglected by the rdft //FIXME: double check.
// - /(_awLen*_awLen) for the constant Wss from numerical recipes in C. (ensure that the window function agrees with this.)
// - /i_subset to average the powers in all the subsets.
double norm = 2.0/(double)_awLen/(double)_awLen/(double)i_subset;
*/
// original normalization
double frequencyStep = 2.0*(double)inputSamplingFreq/(double)nsamples; //OLD value for frequencyStep.
double norm = 2.0/(double)nsamples*2.0/(double)nsamples; //OLD value for norm.
switch (outputType) {
default:
case PSDAmplitudeSpectralDensity: // amplitude spectral density (default) [V/Hz^1/2]
norm /= frequencyStep;
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] = sqrt(output[i_samp]*norm);
}
break;
case PSDPowerSpectralDensity: // power spectral density [V^2/Hz]
norm /= frequencyStep;
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] *= norm;
}
break;
case PSDAmplitudeSpectrum: // amplitude spectrum [V]
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] = sqrt(output[i_samp]*norm);
}
break;
case PSDPowerSpectrum: // power spectrum [V^2]
for (i_samp = 0; i_samp < outputLen; i_samp++) {
output[i_samp] *= norm;
}
break;
}
return 0;
}
void KstPSDGenerator::updateNow() {
int i_subset, i_samp;
int n_subsets;
int v_len;
int copyLen;
QValueVector<double> psd, f;
double mean;
double nf;
bool done;
adjustLengths();
v_len = _inputVector->size();
n_subsets = v_len/_PSDLen+1;
if (v_len%_PSDLen==0) n_subsets--;
// always update when asked
_last_n_new = _inputVector->size();
for (i_samp = 0; i_samp < _PSDLen; i_samp++) {
(*_powerVector)[i_samp] = 0;
(*_frequencyVector)[i_samp] = i_samp*0.5*_Freq/( _PSDLen-1 );
}
_frequencyVectorStep = 0.5*_Freq/(_PSDLen - 1);
nf = 0;
done = false;
for (i_subset = 0; !done; i_subset++) {
// copy each chunk into a[] and find mean
if (i_subset*_PSDLen + _ALen < v_len) {
copyLen = _ALen;
} else {
copyLen = v_len - i_subset*_PSDLen;
done = true;
}
mean = 0;
for (i_samp = 0; i_samp < copyLen; i_samp++) {
mean += (
_a[i_samp] =
_inputVector->at(i_samp + i_subset*_PSDLen)
);
}
if (copyLen > 1) {
mean /= (double)copyLen;
}
if (apodize()) {
GenW(copyLen);
}
// remove mean and apodize
if (removeMean() && apodize()) {
for (i_samp=0; i_samp<copyLen; i_samp++) {
_a[i_samp]= (_a[i_samp]-mean)*_w[i_samp];
}
} else if (removeMean()) {
for (i_samp=0; i_samp<copyLen; i_samp++) {
_a[i_samp] -= mean;
}
} else if (apodize()) {
for (i_samp=0; i_samp<copyLen; i_samp++) {
_a[i_samp] *= _w[i_samp];
}
}
nf += copyLen;
for (;i_samp < _ALen; i_samp++) {
_a[i_samp] = 0.0;
}
// fft a
rdft(_ALen, 1, _a);
(*_powerVector)[0] += _a[0]*_a[0];
(*_powerVector)[_PSDLen-1] += _a[1]*_a[1];
for (i_samp=1; i_samp<_PSDLen-1; i_samp++) {
(*_powerVector)[i_samp]+= cabs2(_a[i_samp*2], _a[i_samp*2+1]);
}
}
_last_f0 = 0;
_last_n_subsets = n_subsets;
_last_n_new = 0;
nf = 1.0/(double(_Freq)*double(nf/2.0));
for ( i_samp = 0; i_samp<_PSDLen; i_samp++ ) {
(*_powerVector)[i_samp] = sqrt((*_powerVector)[i_samp]*nf);
}
if (_Freq <= 0.0) {
_Freq = 1.0;
}
}