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patpc.c
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patpc.c
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#define _GNU_SOURCE
#define TWOPI 2.0 * M_PI
#define CHOOSE_PMAX_AUTOMATICALLY 1001
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "count_lines_in_ASCII_file.h" // for count_lines_in_ASCII_file()
// check if we are allowed to use CFITSIO to read OGIP FITS event lists
#ifndef PATPC_NOCFITSIO
#include <fitsio.h>
#endif
// check if we are allowed to use GSL
#ifndef PATPC_NOGSL
#include <gsl/gsl_sort.h> // for gsl_sort()
#include <gsl/gsl_statistics.h>
#else
static int compare_phases( const void *obs11, const void *obs22 ) {
double *obs1= (double *)obs11;
double *obs2= (double *)obs22;
if ( obs1 < obs2 ) {
return -1;
}
return 1;
}
#endif
void print_usage_info( char **argv ) {
fprintf( stderr, "Usage:\n %s photon_arrival_times_sec.dat # Automatically select period search range\n or\n %s photon_arrival_times_sec.dat P(sec) # Test significance of a single priod\n or\n %s photon_arrival_times_sec.dat Pmax(sec) Pmin(sec) # Search a range of trial periods\n or\n %s photon_arrival_times_sec.dat Pmax(sec) Pmin(sec) phasestep # Set search step size\n", argv[0], argv[0], argv[0], argv[0] );
#ifndef PATPC_NOCFITSIO
fprintf( stderr, "You may also specify an event FITS file as the input:\n %s photon_arrival_times_sec.evt\n or\n %s photon_arrival_times_sec.svt Pmax(sec) Pmin(sec) phasestep\n", argv[0], argv[0] );
#endif
return;
}
void say_hello( char **argv ) {
fprintf( stderr,
"Hi, this is %s\nThe code will construct a power spectrum and the Hm statistic \n\
as a function of frequency from the input list of photon arrival times.\n\
The H-test was originally proposed by \n\
https://ui.adsabs.harvard.edu/abs/1989A&A...221..180D\n\
While writing the code I was mostly following \n\
https://ui.adsabs.harvard.edu/abs/2011ApJ...732...38K\n\
The probability is calculated following \n\
https://ui.adsabs.harvard.edu/abs/2010A&A...517L...9D\n\n",
argv[0] );
// Nice discussion of DFT and the Nyquist frequency
// https://ui.adsabs.harvard.edu/abs/2014MNRAS.445..437M/abstract
return;
}
int is_comment( char *str ) {
int i;
int is_empty= 1;
int n= strlen( str );
if ( n < 1 )
return 1;
for ( i= 0; i < n - 1; i++ ) {
if ( str[i] != 'E' && str[i] != 'e' && str[i] != ' ' && str[i] != '0' && str[i] != '1' && str[i] != '2' && str[i] != '3' && str[i] != '4' && str[i] != '5' && str[i] != '6' && str[i] != '7' && str[i] != '8' && str[i] != '9' && str[i] != '.' && str[i] != '\r' && str[i] != '\n' && str[i] != '\t' && str[i] != '+' && str[i] != '-' )
return 1;
if ( str[i] == '\t' )
str[i]= ' ';
if ( str[i] == '\r' )
str[i]= ' ';
if ( str[i] != ' ' )
is_empty= 0;
}
if ( is_empty == 1 )
return 1;
return 0;
}
// We use the fit by de Jager & Busching (2010)
// https://ui.adsabs.harvard.edu/abs/2010A&A...517L...9D
//
// The fit takes into account the maximization over the number of harmonics,
// but it does not take into account multiple trials with multiple trial frequencies!
double compute_false_detection_probability_from_Hm( double Hm, int *upper_limit_flag ) {
double probability;
// indicate that the return value is an upper limit
( *upper_limit_flag )= 0;
if ( Hm > 70 ) {
( *upper_limit_flag )= 1;
}
probability= exp( -0.4 * Hm );
return probability;
}
void compute_DFT( double *time_sec, size_t N_obs, double f, double *DFT, int harmonic ) {
size_t i;
double ReF, ImF, C, S, angle, dN_obs, dharmonic;
dharmonic= (double)harmonic;
ReF= ImF= 0.0;
//for(i=0;i<N_obs;i++){
for ( i= N_obs; i--; ) {
angle= TWOPI * dharmonic * f * ( time_sec[i] - time_sec[0] );
// not sure if we should bother subtracting time_sec[0], but I'm afraid of large numbers
sincos( angle, &S, &C );
ReF+= C;
ImF+= S;
}
ReF= ReF / dharmonic;
ImF= ImF / dharmonic;
dN_obs= (double)N_obs;
( *DFT )= 2.0 / dN_obs * ( ReF * ReF + ImF * ImF );
return;
}
void write_binned_lightcurve_time( double *sorted_photon_arrival_times_sec, size_t N_obs, double bin_width_sec ) {
FILE *outputfile;
size_t photon_counter;
int counts= 0;
double time;
outputfile= fopen( "binned_lightcurve_time.dat", "w" );
if ( NULL == outputfile ) {
fprintf( stderr, "ERROR: cannot open 'binned_lightcurve_time.dat' for writing!\n" );
return;
}
time= sorted_photon_arrival_times_sec[0];
for ( photon_counter= 0; photon_counter < N_obs; photon_counter++ ) {
if ( sorted_photon_arrival_times_sec[photon_counter] < time + bin_width_sec ) {
// add count to the current bin
counts++;
} else {
// bin completed
fprintf( outputfile, "%lf %lf %lf\n", time + bin_width_sec / 2.0 - sorted_photon_arrival_times_sec[0], (double)counts / bin_width_sec, sqrt( (double)counts ) / bin_width_sec );
// but where to put this new count
while ( 1 == 1 ) {
time+= bin_width_sec;
if ( sorted_photon_arrival_times_sec[photon_counter] < time + bin_width_sec ) {
counts= 1;
break;
} else {
counts= 0; // empty bin
// do not write out empty bins
}
}
}
} // for( photon_counter=0; photon_counter<N_obs; photon_counter++)
fclose( outputfile );
fprintf( stderr, "The binned lightcurve (in count rate units) is written to 'binned_lightcurve_time.dat'\n" );
fprintf( stderr, "The time of the first photon arrival %lf sec is subtracted from the lightcurve time stamps.\n", sorted_photon_arrival_times_sec[0] );
return;
}
void write_phase_folded_and_binned_lightcurve( double *photon_arrival_times_sec, size_t N_obs, double f ) {
FILE *outputfile;
size_t photon_counter;
size_t bin_counter;
double photon_phase;
double *bin_phase;
size_t *N_photons_in_bin;
double bin_width;
size_t number_of_phase_bins= 10;
double T0_sec= 0.0;
bin_width= 1.0 / (double)number_of_phase_bins;
outputfile= fopen( "phase_folded_and_binned_lightcurve.dat", "w" );
if ( NULL == outputfile ) {
fprintf( stderr, "ERROR writing 'phase_folded_and_binned_lightcurve.dat'\n" );
return;
}
bin_phase= malloc( number_of_phase_bins * sizeof( double ) );
N_photons_in_bin= malloc( number_of_phase_bins * sizeof( size_t ) );
bin_phase[0]= bin_width / 2.0;
#ifdef PATPC_ENABLE_OPENMP
#ifdef _OPENMP
#pragma omp parallel for private( bin_counter, photon_counter, photon_phase )
#endif
#endif
for ( bin_counter= 0; bin_counter < number_of_phase_bins; bin_counter++ ) {
if ( bin_counter > 0 ) {
bin_phase[bin_counter]= bin_phase[0] + (double)bin_counter * bin_width;
}
N_photons_in_bin[bin_counter]= 0;
for ( photon_counter= 0; photon_counter < N_obs; photon_counter++ ) {
photon_phase= (double)( ( photon_arrival_times_sec[photon_counter] - T0_sec ) * f - (double)(int)( ( photon_arrival_times_sec[photon_counter] - T0_sec ) * f ) );
//fprintf(stderr,"photon phase %lf\n",photon_phase);
if ( bin_phase[bin_counter] - bin_width / 2.0 <= photon_phase && photon_phase < bin_phase[bin_counter] + bin_width / 2.0 ) {
N_photons_in_bin[bin_counter]++;
}
}
}
// Need to have a separate loop for data output to avoid conflict with paralelization
for ( bin_counter= 0; bin_counter < number_of_phase_bins; bin_counter++ ) {
fprintf( outputfile, "%.5lf %5ld\n", bin_phase[bin_counter], N_photons_in_bin[bin_counter] );
}
free( N_photons_in_bin );
free( bin_phase );
fclose( outputfile );
fprintf( stderr, "The phase-folded lightcurve is written to 'phase_folded_and_binned_lightcurve.dat'\n" );
return;
}
int main( int argc, char **argv ) {
FILE *logfile;
FILE *outputfile;
FILE *inputfile;
size_t photon_counter;
size_t number_of_photons;
double *photon_arrival_times_sec;
double average_countrate;
double *freq;
double *power;
double df;
double fmin, fmax, T;
// default values of paximum and minimum trial periods and the phase step
double pmax= CHOOSE_PMAX_AUTOMATICALLY;
double pmin= 9;
double phase_step= 0.1;
double Nyquist_frequency;
double input_value_double;
size_t frequency_counter;
size_t N_freq, N_freq_presumably_independent;
// https://ui.adsabs.harvard.edu/abs/2011ApJ...732...38K/abstract
double **Z2;
int m= 20;
int c= 4;
int harmonic_counter;
double *Hm;
double power_peak, Hm_peak;
double power_peak_frequency, Hm_peak_frequency;
double Hm_probability;
int upper_limit_flag;
double Hm_probability_corrected_for_number_of_trials;
char input_line_buffer[1024];
char output_line_buffer[1024];
// print out the welcome message
say_hello( argv );
// check command line input
if ( argc < 2 ) {
print_usage_info( argv );
return 1;
}
// check if the input file can be opened
inputfile= fopen( argv[1], "r" );
if ( NULL == inputfile ) {
fprintf( stderr, "ERROR: cannot open the input file '%s'\n", argv[1] );
return 1;
}
fclose( inputfile );
// parse the optional command line arguments: pmax, pmin, phase_step
if ( argc >= 3 ) {
input_value_double= atof( argv[2] );
if ( 0.0 < input_value_double && input_value_double < 1e10 ) {
pmax= input_value_double;
} else {
fprintf( stderr, "The input value %lf seems unreasnoable\n", input_value_double );
}
}
if ( argc >= 4 ) {
input_value_double= atof( argv[3] );
if ( 0.0 < input_value_double && input_value_double < 1e10 ) {
pmin= input_value_double;
} else {
fprintf( stderr, "The input value %lf seems unreasnoable\n", input_value_double );
}
} else {
// if no minimum period is given ->
// -> and we are not selecting the period automatically
if ( pmax != CHOOSE_PMAX_AUTOMATICALLY ) {
// -> we are in the signle-frequency mode
pmin= pmax;
}
}
// make sure pmax>pmin (the order is not confused)
if ( pmin > pmax ) {
input_value_double= pmax;
pmax= pmin;
pmin= input_value_double;
}
// step in phase should be 1,0 or smaller, 0.1 is a good starting point
if ( argc == 5 ) {
input_value_double= atof( argv[4] );
if ( 0.0 < input_value_double && input_value_double <= 1.0 ) {
phase_step= input_value_double;
} else {
fprintf( stderr, "The input value %lf seems unreasnoable\n", input_value_double );
}
}
number_of_photons= 0;
// read photon arrival times from an OGIP FITS file
#ifndef PATPC_NOCFITSIO
fitsfile *fptr;
int status, colnum_TIME;
int colnum_TIME_type;
long num_rows;
char *filename_with_events_extension; // /data/myfile.fits[EVENTS]
filename_with_events_extension= malloc( ( strlen( argv[1] ) + 8 + 1 ) * sizeof( char ) );
sprintf( filename_with_events_extension, "%s[EVENTS]", argv[1] );
// Try to open the input file as a FITS table
fprintf( stderr, "Trying to open '%s'\n", filename_with_events_extension );
status= 0;
fits_open_table( &fptr, filename_with_events_extension, READONLY, &status );
if ( status == 0 ) {
// if we managed to open the FITS file
fits_get_num_rows( fptr, &num_rows, &status );
if ( status == 0 ) {
fprintf( stderr, "The [EVENTS] extension of the FITS file '%s' contains %ld rows\n", argv[1], num_rows );
fits_get_colnum( fptr, CASEINSEN, "TIME", &colnum_TIME, &status );
if ( status == 0 ) {
fits_get_coltype( fptr, colnum_TIME, &colnum_TIME_type, NULL, NULL, &status );
if ( status == 0 ) {
fprintf( stderr, "Found TIME column of type %d\nFor reference:\n21 -- signed short, 'I'\n41 -- signed long,\n81 -- 64-bit long signed integer 'K'\n42 -- single precision float, 'E'\n82 -- double precision float, 'D'\naccording to https://heasarc.gsfc.nasa.gov/docs/software/fitsio/c/c_user/node20.html\n", colnum_TIME_type );
number_of_photons= num_rows;
if ( number_of_photons < 50 ) {
if ( pmin != pmax ) {
fprintf( stderr, "ERROR: too few photons for period search: %ld\n", number_of_photons );
return 1;
}
}
if ( number_of_photons < 100 ) {
if ( pmin != pmax ) {
fprintf( stderr, "ERROR: too few photons - period search may be unreliable: %ld\n", number_of_photons );
}
}
fprintf( stderr, "The input table '%s' contains %ld rows\n", filename_with_events_extension, number_of_photons );
photon_arrival_times_sec= (double *)malloc( number_of_photons * sizeof( double ) );
fits_read_col( fptr, TDOUBLE, colnum_TIME, 1, 1, number_of_photons, NULL, photon_arrival_times_sec, NULL, &status );
fits_report_error( stderr, status );
} else {
fits_report_error( stderr, status );
fprintf( stderr, "ERROR: cannot get type of TIME column!\n" );
}
} else {
fits_report_error( stderr, status );
fprintf( stderr, "ERROR: TIME column not found!\n" );
}
} else {
fits_report_error( stderr, status );
fprintf( stderr, "ERROR: fits_get_num_rows() failed\n" );
}
fits_close_file( fptr, &status );
} else {
//fits_report_error(stderr, status);
fprintf( stderr, "Failed to open '%s' as FITS table\n", filename_with_events_extension );
}
//exit(1); // !!!
free( filename_with_events_extension );
#endif
// read photon arrival times from an ASCII file
if ( number_of_photons == 0 ) {
// only if the input was not a FITS file
number_of_photons= count_lines_in_ASCII_file( argv[1] );
if ( number_of_photons < 100 ) {
if ( pmin != pmax ) {
fprintf( stderr, "ERROR: too few photons for period search: %ld\n", number_of_photons );
return 1;
}
} else {
fprintf( stderr, "The input ASCII file '%s' contains %ld lines\n", argv[1], number_of_photons );
}
photon_arrival_times_sec= (double *)malloc( number_of_photons * sizeof( double ) );
inputfile= fopen( argv[1], "r" );
photon_counter= 0;
while ( NULL != fgets( input_line_buffer, 1024, inputfile ) ) {
input_line_buffer[1024 - 1]= '\0'; // just in case
if ( 1 == is_comment( input_line_buffer ) ) {
continue; // it's a comment, not a data string
}
if ( 1 != sscanf( input_line_buffer, "%lf", &photon_arrival_times_sec[photon_counter] ) ) {
continue; // something went wron g while parsing the input line
}
photon_counter++;
}
fclose( inputfile );
//
// Summarize the data import results
fprintf( stderr, "Got arrival times of %ld photons (expected %ld) from the input ASCII file\n", photon_counter, number_of_photons );
// Reset number_of_photons as the number of photons may differ from the number of lines in the input file (due to omments or empty lines)
number_of_photons= photon_counter;
}
// Test if one way or the other we have read some photons
if ( number_of_photons < 2 ) {
fprintf( stderr, "ERROR: the input file '%s' contains only %ld photon(s)\n", argv[1], number_of_photons );
return 1;
}
// sorting photon arrival times just for the sake of conviniently getting the observation time range
#ifndef PATPC_NOGSL
// use GSL sort if available, as it might be faster
gsl_sort( photon_arrival_times_sec, 1, number_of_photons );
#else
// use the silly qsort() if no GSL is available
qsort( photon_arrival_times_sec, number_of_photons, sizeof( double ), compare_phases );
#endif
T= photon_arrival_times_sec[number_of_photons - 1] - photon_arrival_times_sec[0];
if ( T <= 0.0 ) {
fprintf( stderr, "ERROR: T=%lg<=0.0\n", T );
return 1;
}
logfile= fopen( "patpc.log", "w" );
if ( NULL == logfile ) {
fprintf( stderr, "ERROR: cannot open log file 'patpc.log' for writing!\n" );
return 1;
}
fprintf( logfile, "Input file: %s\n\n", argv[1] );
average_countrate= (double)number_of_photons / T;
sprintf( output_line_buffer, "The average count rate (assuming a non-interrupted observation) is %lg cts/s\n", average_countrate );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
#ifndef PATPC_NOGSL
double maximum_difference_between_photon_arrival_times_sec;
double minimum_difference_between_photon_arrival_times_sec;
double median_difference_between_photon_arrival_times_sec;
double *differences_between_photon_arrival_times_sec;
differences_between_photon_arrival_times_sec= (double *)malloc( number_of_photons * sizeof( double ) );
for ( photon_counter= 1; photon_counter < number_of_photons; photon_counter++ ) {
differences_between_photon_arrival_times_sec[photon_counter - 1]= photon_arrival_times_sec[photon_counter] - photon_arrival_times_sec[photon_counter - 1];
//fprintf(stderr, "%lf-%lf=%lf\n", photon_arrival_times_sec[photon_counter], photon_arrival_times_sec[photon_counter-1], differences_between_photon_arrival_times_sec[photon_counter-1]);
}
gsl_sort( differences_between_photon_arrival_times_sec, 1, number_of_photons - 1 );
median_difference_between_photon_arrival_times_sec= gsl_stats_median_from_sorted_data( differences_between_photon_arrival_times_sec, 1, number_of_photons - 1 );
minimum_difference_between_photon_arrival_times_sec= gsl_stats_min( differences_between_photon_arrival_times_sec, 1, number_of_photons - 1 );
maximum_difference_between_photon_arrival_times_sec= gsl_stats_max( differences_between_photon_arrival_times_sec, 1, number_of_photons - 1 );
free( differences_between_photon_arrival_times_sec );
sprintf( output_line_buffer, "The minimum difference between photon arrival times is %lf sec (detector reponse time?)\n", minimum_difference_between_photon_arrival_times_sec );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "The median difference between photon arrival times is %lf sec, corresponding to the count rate of %lf cts/s\n", median_difference_between_photon_arrival_times_sec, 1.0 / median_difference_between_photon_arrival_times_sec );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "The maximum difference between photon arrival times is %lf sec (gap in coverage?)\n", maximum_difference_between_photon_arrival_times_sec );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
#endif
// automatically choose pmax value
if ( pmax == 1001 ) {
pmax= T / 10.0;
}
// Warn the user if the specified maximum trial period is too long
if ( pmax > T / 10.0 ) {
fprintf( stderr, "WARNING: the maximum trial period of %lf sec is %.2lf of the total duration of the observation!\n", pmax, pmax / T );
}
// we follow https://ui.adsabs.harvard.edu/abs/2014MNRAS.445..437M/abstract
Nyquist_frequency= (double)number_of_photons / 2.0 * (double)( number_of_photons - 1 ) / ( (double)number_of_photons * T );
// automatically choose pmin value
if ( pmin == 9 ) {
pmin= 1.0 / Nyquist_frequency;
}
// Warn the user if the specified minimum trial period is too short
if ( pmin < 1.0 / Nyquist_frequency ) {
fprintf( stderr, "NOTE: the minimum trial period of %lf sec is shorter than %lf sec corresponding to the estimated Nyquist frequency %lf Hz.\n It is unclear to the author how the estimated Nyquist frequency is related to a reasonable choice of the minimum trial period. The minimum trial period is likely more related to the time constant of the detector (minimum time difference between the recorded photons),\n", pmin, 1.0 / Nyquist_frequency, Nyquist_frequency );
}
fmin= 1.0 / pmax;
fmax= 1.0 / pmin;
// estimate the number of independent frequencies
df= 1.0 / T;
N_freq_presumably_independent= ( size_t )( ( fmax - fmin ) / df + 0.5 );
// We may be interested to test if there is any significant variability present at a given frequency
//if ( N_freq_presumably_independent < 10 ) {
if ( N_freq_presumably_independent == 0 ) {
N_freq_presumably_independent= 1;
}
if ( N_freq_presumably_independent < 0 ) {
fprintf( stderr, "ERROR: N_freq_presumably_independent=%ld\n", N_freq_presumably_independent );
return 1;
}
// count the number of trial frequencies
// we want the frequency step to be small to make sure the real peak does not fall between the two sample frquencies
df= phase_step / T;
N_freq= ( size_t )( ( fmax - fmin ) / df + 0.5 );
// If we are asked to explore a very narrow frequency range - do it
if( N_freq<10 ) {
N_freq= 10;
}
// old test
//if ( N_freq < 10 ) {
// fprintf( stderr, "ERROR: N_freq=%ld\n", N_freq );
// return 1;
//}
// Special single-frequency case
if( pmin == pmax ) {
N_freq=1;
}
// update the estimated number of independent frequencies following the shaman ritual of Schwarzenberg-Czerny (2003), Sec. 5.3
// https://ui.adsabs.harvard.edu/abs/2003ASPC..292..383S/abstract
if ( N_freq_presumably_independent > N_freq ) {
N_freq_presumably_independent= N_freq;
}
if ( N_freq_presumably_independent > number_of_photons ) {
N_freq_presumably_independent= number_of_photons;
}
sprintf( output_line_buffer, "\nSearch parameters:\n" );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Pmax = %lf sec (%lf Hz)\n", pmax, fmin );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Pmin = %lf sec (%lf Hz)\n", pmin, fmax );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Phase step = %lf (%lf Hz)\n", phase_step, df );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "\nDerived parameters:\n" );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Number of frequency steps = %ld\n", N_freq );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Estimated number of independent frequencies = %ld\n", N_freq_presumably_independent );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Nyquist frequency = %lf Hz (%lf sec)\n", Nyquist_frequency, 1.0 / Nyquist_frequency );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Duration of observations = %lf sec\n", T );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
freq= malloc( N_freq * sizeof( double ) );
power= malloc( N_freq * sizeof( double ) );
Hm= malloc( N_freq * sizeof( double ) );
Z2= (double **)malloc( N_freq * sizeof( double * ) );
// had to move malloc out of the parallell section
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
Z2[frequency_counter]= malloc( m * sizeof( double ) );
}
fprintf( stderr, "Running the period search...\n" );
// Main loop in frequency
#ifdef _OPENMP
#pragma omp parallel for private( frequency_counter, harmonic_counter )
#endif
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
freq[frequency_counter]= fmin + frequency_counter * df;
// compute Z2m values
for ( harmonic_counter= 0; harmonic_counter < m; harmonic_counter++ ) {
compute_DFT( photon_arrival_times_sec, number_of_photons, freq[frequency_counter], &Z2[frequency_counter][harmonic_counter], harmonic_counter + 1 );
if ( harmonic_counter == 0 ) {
// save simple power value too
power[frequency_counter]= Z2[frequency_counter][0];
} else {
Z2[frequency_counter][harmonic_counter]= Z2[frequency_counter][harmonic_counter - 1] + Z2[frequency_counter][harmonic_counter];
}
}
// compute Hm
Hm[frequency_counter]= Z2[frequency_counter][0] - c * ( 0 + 1 - 1 );
for ( harmonic_counter= 1; harmonic_counter < m; harmonic_counter++ ) {
if ( Hm[frequency_counter] < Z2[frequency_counter][harmonic_counter] - c * ( harmonic_counter + 1 - 1 ) ) {
Hm[frequency_counter]= Z2[frequency_counter][harmonic_counter] - c * ( harmonic_counter + 1 - 1 );
}
}
}
// find the power and Hm peaks
power_peak_frequency= freq[0];
power_peak= power[0];
Hm_peak_frequency= freq[0];
Hm_peak= Hm[0];
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
if ( power_peak < power[frequency_counter] ) {
power_peak= power[frequency_counter];
power_peak_frequency= freq[frequency_counter];
}
if ( Hm_peak < Hm[frequency_counter] ) {
Hm_peak= Hm[frequency_counter];
Hm_peak_frequency= freq[frequency_counter];
}
}
sprintf( output_line_buffer, "\nResults:\n" );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "The peak power is at period %7.3lf sec (%.7lf Hz) %lf\n", 1.0 / power_peak_frequency, power_peak_frequency, power_peak );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
// Rayleigh resolution criterion gives the minimum accuracy attainable by simple counting of cycles,
// see e.g. https://ui.adsabs.harvard.edu/abs/2003ASPC..292..383S/abstract
sprintf( output_line_buffer, "Rayleigh resolution +/-%7.3lf sec (%.7lf Hz)\n", 1.0 * ( 1.0 / power_peak_frequency * 1.0 / power_peak_frequency ) / T, 1.0 / T );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
//
sprintf( output_line_buffer, "The peak Hm is at period %7.3lf sec (%.7lf Hz) %lf\n", 1.0 / Hm_peak_frequency, Hm_peak_frequency, Hm_peak );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
// Rayleigh resolution criterion gives the minimum accuracy attainable by simple counting of cycles,
// see e.g. https://ui.adsabs.harvard.edu/abs/2003ASPC..292..383S/abstract
sprintf( output_line_buffer, "Rayleigh resolution +/-%7.3lf sec (%.7lf Hz)\n", 1.0 * ( 1.0 / Hm_peak_frequency * 1.0 / Hm_peak_frequency ) / T, 1.0 / T );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
Hm_probability= compute_false_detection_probability_from_Hm( Hm_peak, &upper_limit_flag );
// Bandwidth/Multitrial correction
Hm_probability_corrected_for_number_of_trials= (double)N_freq_presumably_independent * Hm_probability;
// for a discussion of period uncertainty and the meaning of phase step see also
// https://ui.adsabs.harvard.edu/abs/2018MNRAS.481.3083F/abstract
if ( upper_limit_flag == 0 ) {
sprintf( output_line_buffer, "Estimated single-trial probability of obtaining the above Hm value by chance is %lg\n", Hm_probability );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Same probability corrected for the number of trials (%6ld independent frequencies) %lg\n", N_freq_presumably_independent, Hm_probability_corrected_for_number_of_trials );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
} else {
sprintf( output_line_buffer, "Estimated single-trial probability of obtaining the above Hm value by chance is <%lg\n", Hm_probability );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
sprintf( output_line_buffer, "Probability corrected for the number of trials (%6ld independent frequencies) <%lg\n", N_freq_presumably_independent, Hm_probability_corrected_for_number_of_trials );
fputs( output_line_buffer, logfile );
fputs( output_line_buffer, stderr );
}
// free-up the memory
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
free( Z2[frequency_counter] );
}
free( Z2 );
// write-out the results
fprintf( stderr, "\nWriting the output files\n" );
fclose( logfile );
fprintf( stderr, "\nThe logs are saved to 'patpc.log'\n" );
// write power spectrum
outputfile= fopen( "power.dat", "w" );
if ( NULL == outputfile ) {
fprintf( stderr, "ERROR opening file 'power.dat' for writing!\n" );
return 1;
}
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
fprintf( outputfile, "%lf %lf\n", freq[frequency_counter], power[frequency_counter] );
}
fclose( outputfile );
fprintf( stderr, "The power spectrum is written to 'power.dat'\n" );
// write Hm as a function of frequency
outputfile= fopen( "Hm.dat", "w" );
if ( NULL == outputfile ) {
fprintf( stderr, "ERROR opening file 'Hm.dat' for writing!\n" );
return 1;
}
for ( frequency_counter= 0; frequency_counter < N_freq; frequency_counter++ ) {
fprintf( outputfile, "%lf %lf\n", freq[frequency_counter], Hm[frequency_counter] );
}
fclose( outputfile );
fprintf( stderr, "The Hm(frequency) is written to 'Hm.dat'\n" );
free( Hm );
free( power );
free( freq );
fprintf( stderr, "Making a phase plot corresponding to the Hm periodogram peak at %lf Hz\n", Hm_peak_frequency );
write_phase_folded_and_binned_lightcurve( photon_arrival_times_sec, number_of_photons, Hm_peak_frequency );
#ifndef PATPC_NOGSL
write_binned_lightcurve_time( photon_arrival_times_sec, number_of_photons, 25 * median_difference_between_photon_arrival_times_sec );
#else
write_binned_lightcurve_time( photon_arrival_times_sec, number_of_photons, 25 * average_countrate );
#endif
free( photon_arrival_times_sec );
// Try to run Gnuplot to make plots
if ( 0 == system( "gnuplot plot_everything.gnuplot" ) ) {
fprintf( stderr, "Making Hm periodogram, power spectrum and phase plots with GNUplot\n" );
fprintf( stderr, "To change the plots, edit 'plot_everything.gnuplot' and run 'gnuplot plot_everything.gnuplot'\n" );
} else {
fprintf( stderr, "ERROR making plots with GNUplot\n" );
}
// we are done
return 0;
}