int main( int argc, char *argv[] )
{
const UINT4 n = 65536;
const REAL4 dt = 1.0 / 16384.0;
static LALStatus status;
static REAL4TimeSeries x;
static COMPLEX8FrequencySeries X;
static REAL4TimeSeries y;
static REAL4FrequencySeries Y;
static COMPLEX8TimeSeries z;
static COMPLEX8FrequencySeries Z;
RealFFTPlan *fwdRealPlan = NULL;
RealFFTPlan *revRealPlan = NULL;
ComplexFFTPlan *fwdComplexPlan = NULL;
ComplexFFTPlan *revComplexPlan = NULL;
RandomParams *randpar = NULL;
AverageSpectrumParams avgSpecParams;
UINT4 srate[] = { 4096, 9000 };
UINT4 npts[] = { 262144, 1048576 };
REAL4 var[] = { 5, 16 };
UINT4 j, sr, np, vr;
/*CHAR fname[2048];*/
ParseOptions( argc, argv );
LALSCreateVector( &status, &x.data, n );
TestStatus( &status, CODES( 0 ), 1 );
LALCCreateVector( &status, &X.data, n / 2 + 1 );
TestStatus( &status, CODES( 0 ), 1 );
LALCCreateVector( &status, &z.data, n );
TestStatus( &status, CODES( 0 ), 1 );
LALCCreateVector( &status, &Z.data, n );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateForwardRealFFTPlan( &status, &fwdRealPlan, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateReverseRealFFTPlan( &status, &revRealPlan, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateForwardComplexFFTPlan( &status, &fwdComplexPlan, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateReverseComplexFFTPlan( &status, &revComplexPlan, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
randpar = XLALCreateRandomParams( 100 );
/*
*
* Try the real transform.
*
*/
x.f0 = 0;
x.deltaT = dt;
x.sampleUnits = lalMeterUnit;
snprintf( x.name, sizeof( x.name ), "x" );
XLALNormalDeviates( x.data, randpar );
for ( j = 0; j < n; ++j ) /* add a 60 Hz line */
{
REAL4 t = j * dt;
x.data->data[j] += 0.1 * cos( LAL_TWOPI * 60.0 * t );
}
LALSPrintTimeSeries( &x, "x.out" );
snprintf( X.name, sizeof( X.name ), "X" );
LALTimeFreqRealFFT( &status, &X, &x, fwdRealPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALCPrintFrequencySeries( &X, "X.out" );
LALFreqTimeRealFFT( &status, &x, &X, revRealPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALSPrintTimeSeries( &x, "xx.out" );
/*
*
* Try the average power spectum.
*
*/
avgSpecParams.method = useMean;
for ( np = 0; np < XLAL_NUM_ELEM(npts) ; ++np )
{
/* length of time series for 7 segments, overlapped by 1/2 segment */
UINT4 tsLength = npts[np] * 7 - 6 * npts[np] / 2;
LALCreateVector( &status, &y.data, tsLength );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateVector( &status, &Y.data, npts[np] / 2 + 1 );
TestStatus( &status, CODES( 0 ), 1 );
avgSpecParams.overlap = npts[np] / 2;
/* create the window */
avgSpecParams.window = XLALCreateHannREAL4Window(npts[np]);
avgSpecParams.plan = NULL;
LALCreateForwardRealFFTPlan( &status, &avgSpecParams.plan, npts[np], 0 );
TestStatus( &status, CODES( 0 ), 1 );
for ( sr = 0; sr < XLAL_NUM_ELEM(srate) ; ++sr )
{
/* set the sample rate of the time series */
y.deltaT = 1.0 / (REAL8) srate[sr];
for ( vr = 0; vr < XLAL_NUM_ELEM(var) ; ++vr )
{
REAL4 eps = 1e-6; /* very conservative fp precision */
REAL4 Sfk = 2.0 * var[vr] * var[vr] * y.deltaT;
REAL4 sfk = 0;
REAL4 lbn;
REAL4 sig;
REAL4 ssq;
REAL4 tol;
/* create the data */
XLALNormalDeviates( y.data, randpar );
ssq = 0;
for ( j = 0; j < y.data->length; ++j )
{
y.data->data[j] *= var[vr];
ssq += y.data->data[j] * y.data->data[j];
}
/* compute tolerance for comparison */
lbn = log( y.data->length ) / log( 2 );
sig = sqrt( 2.5 * lbn * eps * eps * ssq / y.data->length );
tol = 5 * sig;
/* compute the psd and find the average */
LALREAL4AverageSpectrum( &status, &Y, &y, &avgSpecParams );
TestStatus( &status, CODES( 0 ), 1 );
LALSMoment( &status, &sfk, Y.data, 1 );
TestStatus( &status, CODES( 0 ), 1 );
/* check the result */
if ( fabs(Sfk-sfk) > tol )
{
fprintf( stderr, "FAIL: PSD estimate appears incorrect\n");
fprintf( stderr, "expected %e, got %e ", Sfk, sfk );
fprintf( stderr, "(difference = %e, tolerance = %e)\n",
fabs(Sfk-sfk), tol );
exit(2);
}
}
}
/* destroy structures that need to be resized */
LALDestroyRealFFTPlan( &status, &avgSpecParams.plan );
TestStatus( &status, CODES( 0 ), 1 );
XLALDestroyREAL4Window( avgSpecParams.window );
LALDestroyVector( &status, &y.data );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyVector( &status, &Y.data );
TestStatus( &status, CODES( 0 ), 1 );
}
/*
*
* Try the complex transform.
*
*/
z.f0 = 0;
z.deltaT = dt;
z.sampleUnits = lalVoltUnit;
snprintf( z.name, sizeof( z.name ), "z" );
{ /* dirty hack */
REAL4Vector tmp;
tmp.length = 2 * z.data->length;
tmp.data = (REAL4 *)z.data->data;
XLALNormalDeviates( &tmp, randpar );
}
for ( j = 0; j < n; ++j ) /* add a 50 Hz line and a 500 Hz ringdown */
{
REAL4 t = j * dt;
z.data->data[j] += 0.2 * cos( LAL_TWOPI * 50.0 * t );
z.data->data[j] += I * exp( -t ) * sin( LAL_TWOPI * 500.0 * t );
}
LALCPrintTimeSeries( &z, "z.out" );
TestStatus( &status, CODES( 0 ), 1 );
snprintf( Z.name, sizeof( Z.name ), "Z" );
LALTimeFreqComplexFFT( &status, &Z, &z, fwdComplexPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALCPrintFrequencySeries( &Z, "Z.out" );
LALFreqTimeComplexFFT( &status, &z, &Z, revComplexPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALCPrintTimeSeries( &z, "zz.out" );
XLALDestroyRandomParams( randpar );
LALDestroyRealFFTPlan( &status, &fwdRealPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyRealFFTPlan( &status, &revRealPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyComplexFFTPlan( &status, &fwdComplexPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyComplexFFTPlan( &status, &revComplexPlan );
TestStatus( &status, CODES( 0 ), 1 );
LALCDestroyVector( &status, &Z.data );
TestStatus( &status, CODES( 0 ), 1 );
LALCDestroyVector( &status, &z.data );
TestStatus( &status, CODES( 0 ), 1 );
LALCDestroyVector( &status, &X.data );
TestStatus( &status, CODES( 0 ), 1 );
LALSDestroyVector( &status, &x.data );
TestStatus( &status, CODES( 0 ), 1 );
LALCheckMemoryLeaks();
return 0;
}
int main( int argc, char *argv[] )
{
static LALStatus status;
RealFFTPlan *fwd = NULL;
RealFFTPlan *rev = NULL;
REAL4Vector *dat = NULL;
REAL4Vector *rfft = NULL;
REAL4Vector *ans = NULL;
COMPLEX8Vector *dft = NULL;
COMPLEX8Vector *fft = NULL;
#if LAL_CUDA_ENABLED
/* The test itself should pass at 1e-4, but it might fail at
* some rare cases where accuracy is bad for some numbers. */
REAL8 eps = 3e-4;
#else
/* very conservative floating point precision */
REAL8 eps = 1e-6;
#endif
REAL8 lbn;
REAL8 ssq;
REAL8 var;
REAL8 tol;
UINT4 nmax;
UINT4 m;
UINT4 n;
UINT4 i;
UINT4 j;
UINT4 k;
UINT4 s = 0;
FILE *fp;
ParseOptions( argc, argv );
m = m_;
n = n_;
fp = verbose ? stdout : NULL ;
if ( n == 0 )
{
nmax = 65536;
}
else
{
nmax = n--;
}
while ( n < nmax )
{
if ( n < 128 )
{
++n;
}
else
{
n *= 2;
}
LALSCreateVector( &status, &dat, n );
TestStatus( &status, CODES( 0 ), 1 );
LALSCreateVector( &status, &rfft, n );
TestStatus( &status, CODES( 0 ), 1 );
LALSCreateVector( &status, &ans, n );
TestStatus( &status, CODES( 0 ), 1 );
LALCCreateVector( &status, &dft, n / 2 + 1 );
TestStatus( &status, CODES( 0 ), 1 );
LALCCreateVector( &status, &fft, n / 2 + 1 );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateForwardRealFFTPlan( &status, &fwd, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
LALCreateReverseRealFFTPlan( &status, &rev, n, 0 );
TestStatus( &status, CODES( 0 ), 1 );
/*
*
* Do m trials of random data.
*
*/
for ( i = 0; i < m; ++i )
{
srand( s++ ); /* seed the random number generator */
/*
*
* Create data and compute error tolerance.
*
* Reference: Kaneko and Liu,
* "Accumulation of round-off error in fast fourier tranforms"
* J. Asssoc. Comp. Mach, Vol 17 (No 4) 637-654, October 1970.
*
*/
srand( i ); /* seed the random number generator */
ssq = 0;
for ( j = 0; j < n; ++j )
{
dat->data[j] = 20.0 * rand() / (REAL4)( RAND_MAX + 1.0 ) - 10.0;
ssq += dat->data[j] * dat->data[j];
fp ? fprintf( fp, "%e\n", dat->data[j] ) : 0;
}
lbn = log( n ) / log( 2 );
var = 2.5 * lbn * eps * eps * ssq / n;
tol = 5 * sqrt( var ); /* up to 5 sigma excursions */
fp ? fprintf( fp, "\neps = %e \ntol = %e\n", eps, tol ) : 0;
/*
*
* Perform forward FFT and DFT (only if n < 100).
*
*/
LALForwardRealFFT( &status, fft, dat, fwd );
TestStatus( &status, CODES( 0 ), 1 );
LALREAL4VectorFFT( &status, rfft, dat, fwd );
TestStatus( &status, CODES( 0 ), 1 );
LALREAL4VectorFFT( &status, ans, rfft, rev );
TestStatus( &status, CODES( 0 ), 1 );
fp ? fprintf( fp, "rfft()\t\trfft(rfft())\trfft(rfft())\n\n" ) : 0;
for ( j = 0; j < n; ++j )
{
fp ? fprintf( fp, "%e\t%e\t%e\n",
rfft->data[j], ans->data[j], ans->data[j] / n ) : 0;
}
if ( n < 128 )
{
LALForwardRealDFT( &status, dft, dat );
TestStatus( &status, CODES( 0 ), 1 );
/*
*
* Check accuracy of FFT vs DFT.
*
*/
fp ? fprintf( fp, "\nfftre\t\tfftim\t\t" ) : 0;
fp ? fprintf( fp, "dtfre\t\tdftim\n" ) : 0;
for ( k = 0; k <= n / 2; ++k )
{
REAL8 fftre = creal(fft->data[k]);
REAL8 fftim = cimag(fft->data[k]);
REAL8 dftre = creal(dft->data[k]);
REAL8 dftim = cimag(dft->data[k]);
REAL8 errre = fabs( dftre - fftre );
REAL8 errim = fabs( dftim - fftim );
REAL8 avere = fabs( dftre + fftre ) / 2 + eps;
REAL8 aveim = fabs( dftim + fftim ) / 2 + eps;
REAL8 ferre = errre / avere;
REAL8 ferim = errim / aveim;
fp ? fprintf( fp, "%e\t%e\t", fftre, fftim ) : 0;
fp ? fprintf( fp, "%e\t%e\n", dftre, dftim ) : 0;
/* fp ? fprintf( fp, "%e\t%e\t", errre, errim ) : 0; */
/* fp ? fprintf( fp, "%e\t%e\n", ferre, ferim ) : 0; */
if ( ferre > eps && errre > tol )
{
fputs( "FAIL: Incorrect result from forward transform\n", stderr );
fprintf( stderr, "\tdifference = %e\n", errre );
fprintf( stderr, "\ttolerance = %e\n", tol );
fprintf( stderr, "\tfrac error = %e\n", ferre );
fprintf( stderr, "\tprecision = %e\n", eps );
return 1;
}
if ( ferim > eps && errim > tol )
{
fputs( "FAIL: Incorrect result from forward transform\n", stderr );
fprintf( stderr, "\tdifference = %e\n", errim );
fprintf( stderr, "\ttolerance = %e\n", tol );
fprintf( stderr, "\tfrac error = %e\n", ferim );
fprintf( stderr, "\tprecision = %e\n", eps );
return 1;
}
}
}
/*
*
* Perform reverse FFT and check accuracy vs original data.
*
*/
LALReverseRealFFT( &status, ans, fft, rev );
TestStatus( &status, CODES( 0 ), 1 );
fp ? fprintf( fp, "\ndat->data[j]\tans->data[j] / n\n" ) : 0;
for ( j = 0; j < n; ++j )
{
REAL8 err = fabs( dat->data[j] - ans->data[j] / n );
REAL8 ave = fabs( dat->data[j] + ans->data[j] / n ) / 2 + eps;
REAL8 fer = err / ave;
fp ? fprintf( fp, "%e\t%e\n", dat->data[j], ans->data[j] / n ) : 0;
/* fp ? fprintf( fp, "%e\t%e\n", err, fer ) : 0; */
if ( fer > eps && err > tol )
{
fputs( "FAIL: Incorrect result after reverse transform\n", stderr );
fprintf( stderr, "\tdifference = %e\n", err );
fprintf( stderr, "\ttolerance = %e\n", tol );
fprintf( stderr, "\tfrac error = %e\n", fer );
fprintf( stderr, "\tprecision = %e\n", eps );
return 1;
}
}
}
LALSDestroyVector( &status, &dat );
TestStatus( &status, CODES( 0 ), 1 );
LALSDestroyVector( &status, &rfft );
TestStatus( &status, CODES( 0 ), 1 );
LALSDestroyVector( &status, &ans );
TestStatus( &status, CODES( 0 ), 1 );
LALCDestroyVector( &status, &dft );
TestStatus( &status, CODES( 0 ), 1 );
LALCDestroyVector( &status, &fft );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyRealFFTPlan( &status, &fwd );
TestStatus( &status, CODES( 0 ), 1 );
LALDestroyRealFFTPlan( &status, &rev );
TestStatus( &status, CODES( 0 ), 1 );
}
LALCheckMemoryLeaks();
return 0;
}
