/************************************************************
* APPROX2(T,U) = (T * (1.410474 + U *. 5641896)) / (.75 + (U * (3. + U)))
************************************************************/
dcomplex cerf2(dcomplex t, dcomplex u)
{
dcomplex p, q, c;
p = dcmultr(u, 0.5641896);
p = dcaddr(p, 1.410474);
p = dcmult(t, p);
q = dcaddr(u, 3.0);
q = dcmult(u, q);
q = dcaddr(q, 0.75);
c = dcdiv(p, q);
return c;
}
/************************************************************
* APPROX1(T) = (T * .5641896) / (.5 + (T * T))
************************************************************/
dcomplex cerf1(dcomplex t)
{
dcomplex p, q, c;
p = dcmultr(t, 0.5641896);
q = dcmult(t,t);
q = dcaddr(q, 0.5);
c = dcdiv(p,q);
return c;
}
int dconvolve(const double *data, int ndata,
const double *syn, int nsyn,
double *conv)
{
int nextpow2();
void cfft();
int ncorr,n_max,i;
dcomplex *cdata,*csyn,*ccorr;
if (ndata <=0 || nsyn <=0) {
fprintf(stderr,"No data or syn is read in ...\n");
return -1;
}
ncorr = ndata+nsyn-1; // length of correlation time series
n_max = nextpow2(ncorr); // closest 2 power
// dynamic allocate array to avoid defining upper limit of the length
cdata = (dcomplex *) malloc(n_max * sizeof(dcomplex));
csyn = (dcomplex *) malloc(n_max * sizeof(dcomplex));
ccorr = (dcomplex *) malloc(n_max * sizeof(dcomplex));
// set complex data and syn array
for (i=0; i<ndata; i++) {cdata[i].re = data[i]; cdata[i].im = 0.;}
for (i=ndata; i<n_max; i++) cdata[i].re = cdata[i].im = 0.;
for (i=0; i<nsyn; i++) {csyn[i].re = syn[i]; csyn[i].im = 0.;}
for (i=nsyn; i<n_max; i++) csyn[i].re = csyn[i].im = 0.;
// fft both complex data and syn array
cfft(cdata,n_max,1);
cfft(csyn,n_max,1);
// in frequency domain, calculate the fft of correlation
for (i=0;i<n_max;i++) ccorr[i] = dcmult(cdata[i],csyn[i]);
// fft back to get the correlation time series
cfft(ccorr,n_max,-1);
for (i=0;i<ncorr;i++) conv[i] = ccorr[i].re/n_max;
free(cdata);
free(csyn);
free(ccorr);
return ncorr;
}
/************************************************************
* APPROX4(T,U) = (T * (36183.31 - U * (3321.99 - U * (1540.787 - U
* * (219.031 - U *(35.7668 - U *(1.320522 - U * .56419))))))
* / (32066.6 - U * (24322.8 - U * (9022.23 - U * (2186.18
* - U * (364.219 - U * (61.5704 - U * (1.84144 - U))))))))
************************************************************/
dcomplex cerf4(dcomplex t, dcomplex u)
{
dcomplex p, q, c;
double a[7] = {36183.31, 3321.99, 1540.787, 219.031, 35.7668,
1.320522, 0.56419};
double b[8] = {32066.6, 24322.8, 9022.23, 2186.18, 364.219,
61.5704, 1.84144, 1.0};
/* Polynomials are all in -U */
u = dcmultr(u, -1.0);
p = dcpoly(u, a, 6);
p = dcmult(t, p);
q = dcpoly(u, b, 7);
c = dcdiv(p, q);
return c;
}
/************************************************************
* Fast approximation to cerf(z) using the Humlicek w4
* algorithm
************************************************************/
void humlicek_w4(int n, double x[], double y, double *c_re, double *c_im)
{
int i;
double s, ax;
dcomplex t, u, c, cexpu;
if (y >= 15) {
/* All points are in region I */
for (i = 0; i < n; i++) {
t = dcsetri(y, -x[i]);
c = cerf1(t);
c_re[i] = c.re; c_im[i] = c.im;
}
} else if (y < 15 && y >= 5.5) {
/* Points are in region I or region II */
for (i = 0; i < n; i++) {
t = dcsetri(y, -x[i]);
s = fabs(x[i]) + y;
if (s >= 15) {
c = cerf1(t);
c_re[i] = c.re; c_im[i] = c.im;
} else {
u = dcmult(t, t);
c = cerf2(t, u);
c_re[i] = c.re; c_im[i] = c.im;
}
}
} else if (y < 5.5 && y >= 0.75) {
for (i = 0; i < n; i++) {
t = dcsetri(y, -x[i]);
s = fabs(x[i]) + y;
if (s >= 15) {
c = cerf1(t);
c_re[i] = c.re; c_im[i] = c.im;
} else if (s < 5.5) {
c = cerf3(t);
c_re[i] = c.re; c_im[i] = c.im;
} else {
u = dcmult(t, t);
c = cerf2(t, u);
c_re[i] = c.re; c_im[i] = c.im;
}
}
} else {
for (i = 0; i < n; i++) {
t = dcsetri(y, -x[i]);
ax = fabs(x[i]);
s = ax + y;
if (s >= 15) {
c = cerf1(t);
c_re[i] = c.re; c_im[i] = c.im;
} else if (s < 15.0 && s >= 5.5) {
u = dcmult(t, t);
c = cerf2(t, u);
c_re[i] = c.re; c_im[i] = c.im;
} else if (s < 5.5 && y >= (0.195 * ax - 0.176)) {
c = cerf3(t);
c_re[i] = c.re; c_im[i] = c.im;
} else {
u = dcmult(t, t);
c = cerf4(t,u);
cexpu = dcexp(u);
c = dcsub(cexpu, c);
c_re[i] = c.re; c_im[i] = c.im;
}
}
}
if (y == 0.0) {
for (i = 0; i < n; i++) {
c_re[i] = exp(-x[i]*x[i]);
}
}
}
int hilbert(int numsamp,const double *f,double *fhilb)
{
void cfft();
int find_length();
void detrend();
int i, j,npts_max;
double bpfilt;
dcomplex imag;
dcomplex *x;
if(numsamp<=0) {
fprintf(stderr,"%s\n","No data points read ....");
return (1);
}
npts_max = find_length(numsamp);
if (npts_max == 0) {
fprintf(stderr,"Too long input time series \n");
return (2);
}
x = (dcomplex *) malloc(npts_max * sizeof(dcomplex));
if ( x == NULL ) {
fprintf(stderr,"Incorrect allocation\n");
return (3);
}
imag.re = 0.; imag.im = 1.0;
for( i=0; i<numsamp; i++)
{
x[i].re = f[i];
x[i].im = 0.;
}
for(i=numsamp; i<npts_max; i++)
x[i].re = x[i].im = 0.;
cfft( x,npts_max,-1 );
for (i=1; i<=npts_max/2; ++i)
{
x[i] = dcmult(x[i],imag);
}
x[0].re = 0.;
x[0].im = 0.;
for( i=(npts_max/2)+1; i<npts_max; i++ )
x[i] = dconj(x[npts_max-i]);
cfft( x,npts_max,1 );
for( i=0; i<numsamp; i++)
fhilb[i] = x[i].re/npts_max;
detrend(fhilb, numsamp);
free(x);
return (0);
}
