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period.c
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period.c
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#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "utils.h"
#include "eventdft.h"
static double normconst, totaltime, lofreq, dfreq, maxharmsum;
static double **coss, **sins, **alph, **beta;
static fcomplex *amplitudes;
static long initialized=0, numevents;
static long long numfreqs;
void free_eventdft()
/* Free the static vectors used by the *_eventdft() routines */
{
if (initialized){
free(coss[0]);
free(coss);
free(sins[0]);
free(sins);
free(alph[0]);
free(alph);
free(beta[0]);
free(beta);
free(amplitudes);
initialized = 0;
}
}
void prep_eventdft(double *events, long numevts, int maxnumharmsum,
double lof, double df)
/* Prepare the static variables and vectors for efficient calculation
of DFT points based on events. The FT will begin at frequency
'lof' (Hz) and continue upwards in frquency by stepsize 'df'.
There are 'numevents' input events with times 'events' (s). Up to
'maxharmsum' harmonics will be summed. */
{
long ii, jj;
double delta, theta, temp, midtime, time;
if (initialized){
printf("Re-initializing eventdft variables and arrays...\n");
free_eventdft();
}
numevents = numevts;
maxharmsum = maxnumharmsum;
numfreqs = 0;
normconst = 1.0 / sqrt((double) numevents);
lofreq = lof;
dfreq = df;
coss = gen_dmatrix(maxharmsum, numevents);
sins = gen_dmatrix(maxharmsum, numevents);
alph = gen_dmatrix(maxharmsum, numevents);
beta = gen_dmatrix(maxharmsum, numevents);
amplitudes = gen_cvect(maxharmsum);
totaltime = events[numevents-1] - events[0];
midtime = 0.5 * totaltime;
for (ii = 0; ii < maxharmsum; ii++){
for (jj = 0; jj < numevents; jj++){
time = events[jj] - midtime;
temp = -TWOPI * (ii + 1) * time;
delta = temp * df;
theta = temp * lofreq;
temp = sin(0.5 * delta);
alph[ii][jj] = -2.0 * temp * temp;
beta[ii][jj] = sin(delta);
coss[ii][jj] = cos(theta);
sins[ii][jj] = sin(theta);
}
}
initialized = 1;
}
fcomplex *calc_eventdft_point(double *freq)
/* Calculate the next frequency of the event DFT. A pointer to the
vector of normalized Fourier amplitudes (of length maxharmsum) is
returned. '*freq' contains the frequency (Hz) that it corresponds
to (dundamental). prep_eventdft() must have been called to
initialize the calcs. */
{
long ii, jj;
double aa, bb, cc, ss, *aptr, *bptr, *cptr, *sptr;
dcomplex result={0.0, 0.0};
(*freq) = lofreq + numfreqs * dfreq;
for (ii = 0; ii < maxharmsum; ii++){
aptr = alph[ii];
bptr = beta[ii];
cptr = coss[ii];
sptr = sins[ii];
result.r = result.i = 0.0;
for (jj = 0; jj < numevents; jj++){
aa = aptr[jj];
bb = bptr[jj];
cc = cptr[jj];
ss = sptr[jj];
result.r += cc;
result.i += ss;
cptr[jj] = cc * aa - ss * bb + cc;
sptr[jj] = ss * aa + cc * bb + ss;
}
amplitudes[ii].r = result.r * normconst;
amplitudes[ii].i = result.i * normconst;
}
numfreqs++;
return amplitudes;
}
fcomplex *eventdft(double *events, long numevents,
double lof, double df, long numf)
/* Return a set of normalized Fourier amplitudes/ calculated using an
event DFT for a set of 'nn' events 'tt'. The returned array is
allocated. */
{
long ii;
double freq;
fcomplex *famp, *amps;
amps = gen_cvect(numf);
prep_eventdft(events, numevents, 1, lof, df);
for (ii = 0; ii < numf; ii++){
famp = calc_eventdft_point(&freq);
amps[ii].r = famp->r;
amps[ii].i = famp->i;
}
free_eventdft();
return amps;
}
float *periodogram(double *xx, double *tt, long nn,
double lof, double df, long numf)
/* Return the normalized Lomb-Scargle Periodogram powers of 'numf'
frequencies (Hz) from the lowest freq 'lof' upwards by stepsize
'df'. There are 'nn' input data points with amplitudes 'xx' and
times 'tt' (s). The returned power vector is dynamically
allocated. */
{
long ii, jj;
float *pows;
double avg, var, ivar, c, cc, cwtau;
double s, ss, sumc, sumcxx, sums, sumsh, sumsxx,swtau;
double wtau, ttavg, ttmax, ttmin;
double arg, wtemp, *xxnorm, *wi, *wpi, *wpr, *wr;
/* Set-up */
davg_dvar(xx, nn, &avg, &var);
if (var==0.0)
ivar = 0.5;
else
ivar = 0.5 / var;
wr = gen_dvect(nn);
wi = gen_dvect(nn);
wpr = gen_dvect(nn);
wpi = gen_dvect(nn);
xxnorm = gen_dvect(nn);
pows = gen_fvect(numf);
/* Scale the times around the midpt */
ttmax = ttmin = tt[0];
for (ii = 0; ii < nn; ii++){
if (tt[ii] > ttmax) ttmax = tt[ii];
if (tt[ii] < ttmin) ttmin = tt[ii];
}
ttavg = 0.5 * (ttmax + ttmin);
/* Generate the trig recurrence values */
c = cos(TWOPI * lof);
s = sin(TWOPI * lof);
for (ii = 0; ii < nn; ii++){
arg = TWOPI * ((tt[ii] - ttavg) * df);
wtemp = sin(0.5 * arg);
wpr[ii] = -2.0 * wtemp * wtemp;
wpi[ii] = sin(arg);
wtemp = TWOPI * ((tt[ii] - ttavg) * lof);
wr[ii] = cos(wtemp);
wi[ii] = sin(wtemp);
if (var==0.0)
xxnorm[ii] = 1.0;
else
xxnorm[ii] = xx[ii] - avg;
}
/* Calculate the periodogram */
for (ii = 0; ii < numf; ii++){
sumsh = sumc = 0.0;
for (jj=0; jj<nn; jj++){
c = wr[jj];
s = wi[jj];
sumsh += s * c;
sumc += (c - s) * (c + s);
}
wtau = 0.5 * atan2(2.0 * sumsh, sumc);
cwtau = cos(wtau);
swtau = sin(wtau);
sums = sumc = sumsxx = sumcxx = 0.0;
/* Step through the data points */
for (jj = 0; jj < nn; jj++){
c = wr[jj];
s = wi[jj];
ss = s * cwtau - c * swtau;
cc = c * cwtau + s * swtau;
sums += ss * ss;
sumc += cc * cc;
sumsxx += xxnorm[jj] * ss;
sumcxx += xxnorm[jj] * cc;
wr[jj] += c * wpr[jj] - s * wpi[jj];
wi[jj] += s * wpr[jj] + c * wpi[jj];
}
/* Set the current power */
pows[ii] = ivar * (sumcxx * sumcxx / sumc +
sumsxx * sumsxx / sums);
}
/* Free the temp arrays and return */
free(wr);
free(wi);
free(wpr);
free(wpi);
free(xxnorm);
return(pows);
}