void
correctIQ (CXB sigbuf, IQ iq, BOOLEAN isTX, int subchan)
{
int i;
REAL doit;
if (IQdoit == 0) return;
if (subchan == 0) doit = iq->mu;
else doit = 0;
if(!isTX)
{
// if (subchan == 0) // removed so that sub rx's will get IQ correction
for (i = 0; i < CXBhave (sigbuf); i++)
{
iq->del[iq->index] = CXBdata(sigbuf,i);
iq->y[iq->index] = Cadd(iq->del[iq->index],Cmul(iq->w[0],Conjg(iq->del[iq->index])));
iq->y[iq->index] = Cadd(iq->y[iq->index],Cmul(iq->w[1],Conjg(iq->y[iq->index])));
iq->w[1] = Csub(iq->w[1], Cscl(Cmul(iq->y[iq->index],iq->y[iq->index]), doit)); // this is where the adaption happens
CXBdata(sigbuf,i)=iq->y[iq->index];
iq->index = (iq->index+iq->MASK)&iq->MASK;
}
//fprintf(stderr, "w1 real: %g, w1 imag: %g\n", iq->w[1].re, iq->w[1].im); fflush(stderr);
}
else
{
for (i = 0; i < CXBhave (sigbuf); i++)
{
CXBimag (sigbuf, i) += iq->phase * CXBreal (sigbuf, i);
CXBreal (sigbuf, i) *= iq->gain;
}
}
}
void hypser(fcomplex a, fcomplex b, fcomplex c, fcomplex z, fcomplex *series,
fcomplex *deriv)
{
void nrerror(char error_text[]);
int n;
fcomplex aa,bb,cc,fac,temp;
deriv->r=0.0;
deriv->i=0.0;
fac=Complex(1.0,0.0);
temp=fac;
aa=a;
bb=b;
cc=c;
for (n=1;n<=1000;n++) {
fac=Cmul(fac,Cmul(aa,Cdiv(bb,cc)));
deriv->r+=fac.r;
deriv->i+=fac.i;
fac=Cmul(fac,RCmul(1.0/n,z));
*series=Cadd(temp,fac);
if (series->r == temp.r && series->i == temp.i) return;
temp= *series;
aa=Cadd(aa,ONE);
bb=Cadd(bb,ONE);
cc=Cadd(cc,ONE);
}
nrerror("convergence failure in hypser");
}
void hypdrv(float s, float yy[], float dyyds[])
{
fcomplex z,y[3],dyds[3];
y[1]=Complex(yy[1],yy[2]);
y[2]=Complex(yy[3],yy[4]);
z=Cadd(z0,RCmul(s,dz));
dyds[1]=Cmul(y[2],dz);
dyds[2]=Cmul(Csub(Cmul(Cmul(aa,bb),y[1]),Cmul(Csub(cc,
Cmul(Cadd(Cadd(aa,bb),ONE),z)),y[2])),
Cdiv(dz,Cmul(z,Csub(ONE,z))));
dyyds[1]=dyds[1].r;
dyyds[2]=dyds[1].i;
dyyds[3]=dyds[2].r;
dyyds[4]=dyds[2].i;
}
void zroots(fcomplex a[], int m, fcomplex roots[], int polish)
{
void zroots(fcomplex a[], int m, fcomplex *x, int *its);
int i, its, j, jj;
fcomplex x, b, c, ad[MAXM];
for (j = 0; j <= m; j++) ad[j] = a[j];
for (j = m; j >= 1; j--) {
x Complex(0.0, 0.0);
laguer(ad, j, &x, &its);
if (fabs(x.i) <= 2.0*EPS*fabs(x.r)) x.i = 0.0;
roots[j] = x;
b = ad[j];
for (jj = j - 1; jj >= 0; jj--) {
c = ad[jj];
ad[jj] = b;
b = Cadd(Cmul(x, b), c);
}
}
if (polish)
for (j = 1; j <= m; j++)
laguer(a, m, &roots[j], &its);
for (j = 2; j <= m; j++) {
x = roots[j];
for (i = j - 1; i >= 1; i--) {
if (rootes.r <= x.r) break;
roots[i + 1] = roots[i];
}
roots[i + 1] = x;
}
}
/*We use the Cauchy Gourat theorem to compute the derivatives of the double(Mellin+Laplace) transform */
static dcomplex dermellin(dcomplex l, double sg, double r, int nummom)
{
dcomplex term, cv, mu;
int i;
double r0,sumr, sumi/*,x[NPOINTS_FUSAITAGL+1],w[NPOINTS_FUSAITAGL+1]*/;
double v;
double *x,*w;
x=malloc((NPOINTS_FUSAITAGL+1)*sizeof(double));
w=malloc((NPOINTS_FUSAITAGL+1)*sizeof(double));
sumr=0.0;
sumi=0.0;
gauleg(0, 2*M_PI, x, w,NPOINTS_FUSAITAGL);
v = 2*r/(sg*sg)-1.0;
cv = Complex(v,0.0);
mu = Csqrt(Cadd(Complex(v*v,0), RCmul(2.0,l)));
r0 = Creal(RCmul(0.5,Csub(mu,cv)));
if(r0>1.0) r0=0.25;
for (i=1;i<=NPOINTS_FUSAITAGL;i++)
{
term = RCmul(pow(r0,nummom), Cexp(Complex(0.0, nummom*x[i])));
sumr += w[i]*Creal(Cdiv(mellintransform(l, RCmul(r0, Cexp(Complex(0.0, x[i]))), sg, r), term));
sumi += w[i]*Cimag(Cdiv(mellintransform(l, RCmul(r0, Cexp(Complex(0.0, x[i]))), sg, r), term));
}
free(x);
free(w);
return Complex(exp(factln(nummom))*sumr/(2.0*M_PI),exp(factln(nummom))*sumi/(2.0*M_PI));
}
/*Use the Abate-Whitt for numerical inversion of the Laplace transform*/
static double SumAW(double expiry,
double sg, double r, double aa, int terms, int totterms, int nummoment)
{
int k;
double h=sg*sg*expiry/4.0;
double Eulero;
dcomplex term;
dcomplex sum;
double *sum_r;
sum_r = malloc((totterms-terms+2)*sizeof(double));
sum =Complex(0.0, 0.0);
Eulero = 0.0;
sum =RCmul(1.0/2.0,dermellin(Complex(aa/(2.0*h),0), sg, r,nummoment));
for (k=1;k<=totterms;k++)
{
term = RCmul(PNL_ALTERNATE(k) ,dermellin(Complex(aa/(2.0*h) , k*M_PI/h),sg, r,nummoment ));
sum = Cadd(term, sum);
if(terms<= k) sum_r[k-terms+1]= sum.r;
}
for (k=0;k<=totterms-terms;k++)
{
Eulero = Eulero + bico(totterms-terms,k) * pow( 2.0, -(totterms-terms) ) * sum_r[k+1];
}
free(sum_r);
return exp(aa/2.0)*Eulero/h;
}
void
SDROMnoiseblanker (NB nb)
{
int i;
for (i = 0; i < CXBsize (nb->sigbuf); i++)
{
REAL cmag = Cmag (CXBdata (nb->sigbuf, i));
nb->average_sig = Cadd (Cscl (nb->average_sig, 0.75),
Cscl (CXBdata (nb->sigbuf, i), 0.25));
nb->average_mag = (REAL) (0.999 * (nb->average_mag) + 0.001 * cmag);
if (cmag > (nb->threshold * nb->average_mag))
CXBdata (nb->sigbuf, i) = nb->average_sig;
}
}
void
blms_adapt (BLMS blms)
{
int sigsize = CXBhave (blms->signal);
int sigidx = 0;
// fputs("Inside\n",stderr),fflush(stderr);
do {
int j;
memcpy (blms->delay_line, &blms->delay_line[128], sizeof (COMPLEX) * 128); // do overlap move
memcpy (&blms->delay_line[128], &CXBdata (blms->signal, sigidx), sizeof (COMPLEX) * 128); // copy in new data
fftwf_execute (blms->Xplan); // compute transform of input data
for (j = 0; j < 256; j++) {
blms->Yhat[j] = Cmul (blms->What[j], blms->Xhat[j]); // Filter new signal in freq. domain
blms->Xhat[j] = Conjg (blms->Xhat[j]); // take input data's complex conjugate
}
fftwf_execute (blms->Yplan); //compute output signal transform
for (j = 128; j < 256; j++)
blms->y[j] = Cscl (blms->y[j], BLKSCL);
memset (blms->y, 0, 128 * sizeof (COMPLEX));
for (j = 128; j < 256; j++)
blms->error[j] = Csub (blms->delay_line[j], blms->y[j]); // compute error signal
if (blms->filter_type)
memcpy (&CXBdata (blms->signal, sigidx), &blms->y[128], 128 * sizeof (COMPLEX)); // if noise filter, output y
else
memcpy (&CXBdata (blms->signal, sigidx), &blms->error[128], 128 * sizeof (COMPLEX)); // if notch filter, output error
fftwf_execute (blms->Errhatplan); // compute transform of the error signal
for (j = 0; j < 256; j++)
blms->Errhat[j] = Cmul (blms->Errhat[j], blms->Xhat[j]); // compute cross correlation transform
fftwf_execute (blms->UPDplan); // compute inverse transform of cross correlation transform
for (j = 0; j < 128; j++)
blms->update[j] = Cscl (blms->update[j], BLKSCL);
memset (&blms->update[128], 0, sizeof (COMPLEX) * 128); // zero the last block of the update, so we get
// filter coefficients only at front of buffer
fftwf_execute (blms->Wplan);
for (j = 0; j < 256; j++)
{
blms->What[j] = Cadd (Cscl (blms->What[j], blms->leak_rate), // leak the W away
Cscl (blms->Update[j], blms->adaptation_rate)); // update at adaptation rate
}
sigidx += 128; // move to next block in the signal buffer
} while (sigidx < sigsize); // done?
}
/**
* Complex Modified Bessel function of the first kind
* divided by exp(|Creal(z)|)
*
* @param z a complex number
* @param v a real number, the order of the Bessel function
*
*/
dcomplex pnl_complex_bessel_i_scaled( double v, dcomplex z )
{
int nz, ierr;
dcomplex cy;
int n = 1;
int kode = 2;
if (v >= 0)
{
pnl_zbesi(CADDR(z), &v, &kode, &n, CADDR(cy), &nz, &ierr);
DO_MTHERR("ive:");
}
else
{
dcomplex aux1, aux2;
aux1 = pnl_complex_bessel_i_scaled (-v, z);
aux2 = pnl_complex_bessel_k (-v, z);
aux2 = CRmul (aux2, M_2_PI * sin(M_PI * -v) * exp ( -fabs ( Creal(z) ) ));
cy = Cadd (aux1, aux2);
}
return cy;
}
/**
* Complex Bessel function of the second kind
* divided by exp(|Imag(z)|)
*
* @param z a complex number
* @param v a real number, the order of the Bessel function
*
*/
dcomplex pnl_complex_bessel_y_scaled( double v, dcomplex z )
{
int nz, ierr;
dcomplex cy, cwork;
int n = 1;
int kode = 2;
if (v >= 0)
{
pnl_zbesy(CADDR(z), &v, &kode, &n, CADDR(cy), &nz, CADDR(cwork), &ierr);
DO_MTHERR("yve:");
}
else
{
dcomplex aux1, aux2;
aux1 = pnl_complex_bessel_y_scaled (-v, z);
aux1 = CRmul (aux1, cos(M_PI * v));
aux2 = pnl_complex_bessel_j_scaled (-v, z);
aux2 = CRmul (aux2, sin(M_PI * -v));
cy = Cadd (aux1, aux2);
}
return cy;
}
/**
* Complex Bessel function of the first kind
*
* @param z a complex number
* @param v a real number, the order of the Bessel function
*
*/
dcomplex pnl_complex_bessel_j( double v, dcomplex z )
{
int nz, ierr;
dcomplex cy;
int n = 1;
int kode = 1;
if (v >= 0)
{
pnl_zbesj(CADDR(z), &v, &kode, &n, CADDR(cy), &nz, &ierr);
DO_MTHERR("jv:");
}
else
{
dcomplex aux1, aux2;
aux1 = pnl_complex_bessel_j (-v, z);
aux1 = CRmul (aux1, cos(M_PI * v));
aux2 = pnl_complex_bessel_y (-v, z);
aux2 = CRmul (aux2, sin(M_PI * v));
cy = Cadd (aux1, aux2);
}
return cy;
}
static int compute_price(double tt, double H, double K, double r_premia, double v0, double kappa, double theta, double sigma, double rho,
double L, int M, int Nt )
{
/*Variables*/
int j, n, k;
double r; /*continuous rate*/
double min_log_price, max_log_price;
double ds, dt; /*price and time discretization steps*/
double rho_hat; /*parameter after substitution*/
double q, factor, discount_factor; /*pde parameters*/
double treshold = 1e-9; /* when we assume probability to be zero and switch to a different equation*/
int k_d, k_u; /*n+1 vertice numbers, depending on [n][k]*/
double sigma_local, gamma; /*wh factors parameters*/
double beta_minus, beta_plus; /*wh-factors coefficients*/
double local_barrier; /*a barrier depending on [n][k], to check crossing on each step*/
//if (2.0 * kappa * theta < pow(sigma, 2))
// return 1; /*Novikov condition not satisfied, probability values could be incorrect*/
/*Body*/
r = log(1 + r_premia / 100);
/*building voltree*/
tree_v(tt, v0, kappa, theta, sigma, Nt);
/*spacial variable. Price space construction*/
min_log_price = L*log(0.5) - (rho / sigma)* V[Nt][Nt];
max_log_price = L*log(2);
ds = (max_log_price - min_log_price) / double(M);
for (j = 0; j < M; j++)
{
ba_log_prices[j] = min_log_price + j*ds;
ba_prices[j] = H*exp(ba_log_prices[j] + (rho / sigma)* V[0][0]);
}
dt = tt / double(Nt);
/*fft frequences we'll need in every vertice of a tree*/
fftfreq(M, ds);
rho_hat = sqrt(1.0 - pow(rho, 2.0));
q = 1.0 / dt + r;
factor = pow(q*dt, -1.0);
//discount_factor = exp(r*dt);
discount_factor = r - rho / sigma * kappa * theta;
/*filling F_next matrice by initial (in time T) conditions*/
for (j = 0; j < M; j++)
for (k = 0; k < Nt + 1; k++)
{
F_next[j][k] = Complex(G(H*exp(ba_log_prices[j] + (rho / sigma)* V[Nt][k]), K), 0);
}
/*here the main cycle starts - the backward induction procedure*/
for (n = Nt - 1; n >= 0; n--)
{
printf("Processing: %d of %d\n", n, Nt-1);
for (k = 0; k <= n; k++)
{
/*to calculate the binomial expectation we should use matrices from the tree method.
After (n,k) vertice one could either get to (n+1,k_u) or (n+1, k_d). The numbers k_u and k_d could be
read from f_up and f_down matrices, by the rule of addition, for example:
f_down[i][j] = -z;
Rd = V[i + 1][j - z]
f_up[i][j] = z;
Ru = V[i + 1][j + z];
*/
k_u = k + f_up[n][k];
k_d = k + f_down[n][k];
local_barrier = - (rho / sigma) * V[n][k];
/*initial conditions of a step*/
for (j = 0; j < M; j++)
{
//f_n_plus_1_k_u[j] = F[j][n+1][k_u];
//f_n_plus_1_k_d[j] = F[j][n+1][k_d];
f_n_plus_1_k_u[j] = F_next[j][k_u];
f_n_plus_1_k_d[j] = F_next[j][k_d];
}
/*applying indicator function*/
for (j = 0; j < M; j++)
{
if (ba_log_prices[j] < local_barrier)
{
f_n_plus_1_k_u[j].r = 0.0;
f_n_plus_1_k_u[j].i = 0.0;
f_n_plus_1_k_d[j].r = 0.0;
f_n_plus_1_k_d[j].i = 0.0;
}
}
if (V[n][k] >= treshold)
{
/*set up variance - dependent parameters for a given step*/
sigma_local = rho_hat * sqrt(V[n][k]);
gamma = r - 0.5 * V[n][k] - rho / sigma * kappa * (theta - V[n][k]); /*also local*/
/* beta_plus and beta_minus*/
/*beta_minus = -(gamma + sqrt(gamma^2 + 2 * sigma^2 * q)) / sigma^2
beta_plus = -(gamma - sqrt(gamma^2 + 2 * sigma^2 * q)) / sigma^2*/
beta_minus = -(gamma + sqrt(pow(gamma,2) + 2 * pow(sigma_local,2) * q)) / pow(sigma_local,2);
beta_plus = -(gamma - sqrt(pow(gamma,2) + 2 * pow(sigma_local,2) * q)) / pow(sigma_local,2);
for (j = 0; j < M; j++)
{
/* factor functions
phi_plus_array = ([beta_plus / (beta_plus - i * 2 * pi*xi) for xi in xi_space])
phi_minus_array = ([-beta_minus / (-beta_minus + i * 2 * pi*xi) for xi in xi_space]) */
phi_plus_array[j] = RCdiv(beta_plus, RCsub(beta_plus, RCmul((2.0 * PI * fftfreqs[j]), CI)));
phi_minus_array[j] = RCdiv(-beta_minus, RCadd(-beta_minus, RCmul((2.0 * PI * fftfreqs[j]), CI)));
}
/*factorization calculation*/
/*f_n_k_u = factor * fft.ifft(phi_minus_array * fft.fft(
indicator(original_prices_array, 0) * fft.ifft(phi_plus_array * fft.fft(f_n_plus_1_k_u))))*/
for (int j = 0; j < M; j++)
{
f_n_plus_1_k_u_re[j] = f_n_plus_1_k_u[j].r;
f_n_plus_1_k_u_im[j] = f_n_plus_1_k_u[j].i;
}
pnl_fft2(f_n_plus_1_k_u_re, f_n_plus_1_k_u_im, M);
for (j = 0; j < M; j++) {
/*putting complex and imaginary part together again*/
f_n_plus_1_k_u_fft_results[j] = Complex(f_n_plus_1_k_u_re[j], f_n_plus_1_k_u_im[j]);
/*multiplying by phi_plus*/
f_n_plus_1_k_u_fft_results[j] = Cmul(phi_plus_array[j], f_n_plus_1_k_u_fft_results[j]);
/*extracting imaginary and complex parts to use in further fft*/
f_n_plus_1_k_u_fft_results_re[j] = f_n_plus_1_k_u_fft_results[j].r;
f_n_plus_1_k_u_fft_results_im[j] = f_n_plus_1_k_u_fft_results[j].i;
}
pnl_ifft2(f_n_plus_1_k_u_fft_results_re, f_n_plus_1_k_u_fft_results_im, M);
/*applying indicator function, after ifft*/
for (j = 0; j < M; j++)
{
if (ba_log_prices[j] < local_barrier)
{
f_n_plus_1_k_u_fft_results_re[j] = 0.0;
f_n_plus_1_k_u_fft_results_im[j] = 0.0;
}
}
/*performing second fft */
pnl_fft2(f_n_plus_1_k_u_fft_results_re, f_n_plus_1_k_u_fft_results_im, M);
for (j = 0; j < M; j++) {
/*putting complex and imaginary part together again*/
f_n_plus_1_k_u_fft_results[j] = Complex(f_n_plus_1_k_u_fft_results_re[j], f_n_plus_1_k_u_fft_results_im[j]);
/*multiplying by phi_minus*/
f_n_plus_1_k_u_fft_results[j] = Cmul(phi_minus_array[j], f_n_plus_1_k_u_fft_results[j]);
/*extracting imaginary and complex parts to use in further fft*/
f_n_plus_1_k_u_fft_results_re[j] = f_n_plus_1_k_u_fft_results[j].r;
f_n_plus_1_k_u_fft_results_im[j] = f_n_plus_1_k_u_fft_results[j].i;
}
/*the very last ifft*/
pnl_ifft2(f_n_plus_1_k_u_fft_results_re, f_n_plus_1_k_u_fft_results_im, M);
/*multiplying by factor*/
for (j = 0; j < M; j++) {
f_n_k_u[j].r = factor * f_n_plus_1_k_u_fft_results_re[j];
f_n_k_u[j].i = factor * f_n_plus_1_k_u_fft_results_im[j];
}
/*f_n_k_d = factor * fft.ifft(phi_minus_array * fft.fft(
indicator(original_prices_array, 0) * fft.ifft(phi_plus_array * fft.fft(f_n_plus_1_k_d))))*/
for (int j = 0; j < M; j++)
{
f_n_plus_1_k_d_re[j] = f_n_plus_1_k_d[j].r;
f_n_plus_1_k_d_im[j] = f_n_plus_1_k_d[j].i;
}
pnl_fft2(f_n_plus_1_k_d_re, f_n_plus_1_k_d_im, M);
for (j = 0; j < M; j++) {
/*putting complex and imaginary part together again*/
f_n_plus_1_k_d_fft_results[j] = Complex(f_n_plus_1_k_d_re[j], f_n_plus_1_k_d_im[j]);
/*multiplying by phi_plus*/
f_n_plus_1_k_d_fft_results[j] = Cmul(phi_plus_array[j], f_n_plus_1_k_d_fft_results[j]);
/*extracting imaginary and complex parts to use in further fft*/
f_n_plus_1_k_d_fft_results_re[j] = f_n_plus_1_k_d_fft_results[j].r;
f_n_plus_1_k_d_fft_results_im[j] = f_n_plus_1_k_d_fft_results[j].i;
}
pnl_ifft2(f_n_plus_1_k_d_fft_results_re, f_n_plus_1_k_d_fft_results_im, M);
/*applying indicator function, after ifft*/
for (j = 0; j < M; j++)
{
if (ba_log_prices[j] < local_barrier)
{
f_n_plus_1_k_d_fft_results_re[j] = 0.0;
f_n_plus_1_k_d_fft_results_im[j] = 0.0;
}
}
/*performing second fft */
pnl_fft2(f_n_plus_1_k_d_fft_results_re, f_n_plus_1_k_d_fft_results_im, M);
for (j = 0; j < M; j++) {
/*putting complex and imaginary part together again*/
f_n_plus_1_k_d_fft_results[j] = Complex(f_n_plus_1_k_d_fft_results_re[j], f_n_plus_1_k_d_fft_results_im[j]);
/*multiplying by phi_minus*/
f_n_plus_1_k_d_fft_results[j] = Cmul(phi_minus_array[j], f_n_plus_1_k_d_fft_results[j]);
/*extracting imaginary and complex parts to use in further fft*/
f_n_plus_1_k_d_fft_results_re[j] = f_n_plus_1_k_d_fft_results[j].r;
f_n_plus_1_k_d_fft_results_im[j] = f_n_plus_1_k_d_fft_results[j].i;
}
/*the very last ifft*/
pnl_ifft2(f_n_plus_1_k_d_fft_results_re, f_n_plus_1_k_d_fft_results_im, M);
/*multiplying by factor*/
for (j = 0; j < M; j++) {
f_n_k_d[j].r = factor * f_n_plus_1_k_d_fft_results_re[j];
f_n_k_d[j].i = factor * f_n_plus_1_k_d_fft_results_im[j];
}
}
else if (V[n][k] < treshold)
{
/*applying indicator function*/
for (j = 0; j < M; j++)
{
if (ba_log_prices[j] < local_barrier)
{
f_n_plus_1_k_u[j].r = 0.0;
f_n_plus_1_k_u[j].i = 0.0;
f_n_plus_1_k_d[j].r = 0.0;
f_n_plus_1_k_d[j].i = 0.0;
}
}
for (j = 0; j < M; j++)
{
//f_n_plus_1_k_u[j] = F[j][n + 1][k_u];
f_n_plus_1_k_u[j] = F_next[j][k_u];
f_n_k_u[j] = CRsub(f_n_plus_1_k_u[j], discount_factor * dt);
f_n_k_d[j] = f_n_k_u[j];
}
}
/*
f_n_k = pd_f[n, k] * f_n_k_d + pu_f[n, k] * f_n_k_u
*/
for (j = 0; j < M; j++)
{
f_n_k[j] = Cadd(RCmul(pd_f[n][k], f_n_k_d[j]), RCmul(pu_f[n][k], f_n_k_u[j]));
F_prev[j][k] = f_n_k[j];
}
}
for (j = 0; j < M; j++)
{
for (int state = 0; state < Nt; state++)
{
F_next[j][state] = F_prev[j][state];
F_prev[j][state] = Complex(0,0);
}
}
}
/*Preprocessing F before showing out*/
for (j = 0; j < M; j++)
{
if (ba_prices[j] <= H)
{
F_next[j][0].r = 0;
}
if (F_next[j][0].r < 0.)
{
F_next[j][0].r = 0;
}
}
return OK;
}
void frenel(float x, float *s, float *c)
{
void nrerror(char error_text[]);
int k,n,odd;
float a,ax,fact,pix2,sign,sum,sumc,sums,term,test;
fcomplex b,cc,d,h,del,cs;
ax=fabs(x);
if (ax < sqrt(FPMIN)) {
*s=0.0;
*c=ax;
} else if (ax <= XMIN) {
sum=sums=0.0;
sumc=ax;
sign=1.0;
fact=PIBY2*ax*ax;
odd=TRUE;
term=ax;
n=3;
for (k=1;k<=MAXIT;k++) {
term *= fact/k;
sum += sign*term/n;
test=fabs(sum)*EPS;
if (odd) {
sign = -sign;
sums=sum;
sum=sumc;
} else {
sumc=sum;
sum=sums;
}
if (term < test) break;
odd=!odd;
n += 2;
}
if (k > MAXIT) nrerror("series failed in frenel");
*s=sums;
*c=sumc;
} else {
pix2=PI*ax*ax;
b=Complex(1.0,-pix2);
cc=Complex(1.0/FPMIN,0.0);
d=h=Cdiv(ONE,b);
n = -1;
for (k=2;k<=MAXIT;k++) {
n += 2;
a = -n*(n+1);
b=Cadd(b,Complex(4.0,0.0));
d=Cdiv(ONE,Cadd(RCmul(a,d),b));
cc=Cadd(b,Cdiv(Complex(a,0.0),cc));
del=Cmul(cc,d);
h=Cmul(h,del);
if (fabs(del.r-1.0)+fabs(del.i) < EPS) break;
}
if (k > MAXIT) nrerror("cf failed in frenel");
h=Cmul(Complex(ax,-ax),h);
cs=Cmul(Complex(0.5,0.5),
Csub(ONE,Cmul(Complex(cos(0.5*pix2),sin(0.5*pix2)),h)));
*c=cs.r;
*s=cs.i;
}
if (x < 0.0) {
*c = -(*c);
*s = -(*s);
}
}
int CarrMethod_VectStrike(PnlVect *K,
PnlVect * Price,
double S0,
double T,
double B,
double CallPut,
double r,
double divid,
double sigma,
void * Model,
dcomplex (*ln_phi)(dcomplex u,double t,void * model))
{
int n;
dcomplex dzeta,dzetaBS;
double alpha=0.75;
int Nlimit = 4*2048;//2048;
//>> Should be even => use of real_fft
//number of integral discretization steps
double mone;//0.010;
double Kstep=B*2/(Nlimit); // strike domain is (-B,B)
double h = M_2PI/(Nlimit*Kstep);
//double B = 0.5*(Nlimit)*Kstep; // strike domain is (-B,B)
double vn = 0;
dcomplex vn_minus_alpha_plus_uno = Complex(0,-(alpha+1));
dcomplex i_vn_plus_alpha = Complex(alpha,0);
dcomplex uno_plus_alpha_plus_ivn =Complex(1+alpha,vn);
PnlVectComplex * y = pnl_vect_complex_create(Nlimit);
// Should become output
pnl_vect_resize(K,Nlimit);
pnl_vect_resize(Price,Nlimit);
//delta
mone=1;
//printf("limit integration %7.4f \n",A);
for(n=0; n<Nlimit; n++)
{
dzeta = Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,vn*B));
dzetaBS = Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,vn*B));
dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS));
dzeta = Cdiv(dzeta,i_vn_plus_alpha);
dzeta = Cdiv(dzeta,uno_plus_alpha_plus_ivn);
//>> With Simson rules
pnl_vect_complex_set(y,n,RCmul(3+mone-((n==0)?1:0),Conj(dzeta)));
//>> Update value
vn += h;
vn_minus_alpha_plus_uno.r+=h;
i_vn_plus_alpha.i+=h;
uno_plus_alpha_plus_ivn.i+=h;
mone*=-1;
}
pnl_ifft_inplace(y);
for(n=0;n<Nlimit;n++)
{
LET(K,n)=exp(-B+n*Kstep+(r-divid)*T)*(S0);
pnl_cf_call_bs(S0,GET(K,n),T,r,divid,sigma,&LET(Price,n),&vn);
LET(Price,n)+=2./3* S0/(Kstep)*exp(alpha*(B-n*Kstep)-divid*T)*GET_REAL(y,n);
}
if (CallPut==2)
for(n=0;n<Nlimit;n++)
LET(Price,n)-=S0*exp(-divid*T)+GET(K,n)*exp(-r*T);
/*
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-5),GET(Price,Nlimit/2-5));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-4),GET(Price,Nlimit/2-4));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-3),GET(Price,Nlimit/2-3));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-2),GET(Price,Nlimit/2-2));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2-1),GET(Price,Nlimit/2-1));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+0),GET(Price,Nlimit/2+0));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+1),GET(Price,Nlimit/2+1));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+2),GET(Price,Nlimit/2+2));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+3),GET(Price,Nlimit/2+3));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+4),GET(Price,Nlimit/2+4));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+5),GET(Price,Nlimit/2+5));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+6),GET(Price,Nlimit/2+6));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+7),GET(Price,Nlimit/2+7));
printf("Price K= %7.4f P= %7.4f \n",GET(K,Nlimit/2+8),GET(Price,Nlimit/2+8));
pnl_vect_free(&K);
pnl_vect_free(&Price);
*/
return OK;
}
void estdop(char file[],int nDopLines, float *a, float *b,float *c)
{
#define MULTILOOK 100
complexFloat *signal, *signalNext, *dop;
float *x_vec, *y_vec,*phase;
int x,line,firstLine;
getRec *r;
float t1, t2, t3;
long double sum;
float lastPhase;
r=fillOutGetRec(file);
firstLine=(r->nLines-nDopLines)/2;
signal=(complexFloat *)MALLOC(sizeof(complexFloat)*r->nSamples);
signalNext=(complexFloat *)MALLOC(sizeof(complexFloat)*r->nSamples);
dop=(complexFloat *)MALLOC(sizeof(complexFloat)*r->nSamples);
x_vec=(float *)MALLOC(sizeof(float)*r->nSamples);
y_vec=(float *)MALLOC(sizeof(float)*r->nSamples);
phase=(float *)MALLOC(sizeof(float)*r->nSamples);
for (x = 0; x<r->nSamples; x++)
dop[x] = Czero();
getSignalLine(r,firstLine,signalNext,0,r->nSamples);
for (line = firstLine+1; line < firstLine+nDopLines; line++)
{
complexFloat *ptr = signal; signal = signalNext; signalNext = ptr;
getSignalLine(r,line,signalNext,0,r->nSamples);
for (x = 0; x<r->nSamples; x++)
dop[x] = Cadd(dop[x],Cmul(signalNext[x],Cconj(signal[x])));
}
/*Multilook the phase data along range.*/
for (x=0;x<r->nSamples/MULTILOOK;x++)
{
int i;
double out_r=0.0,out_i=0.0;
for (i=0;i<MULTILOOK;i++)
{
out_r+=dop[x*MULTILOOK+i].real;
out_i+=dop[x*MULTILOOK+i].imag;
}
dop[x].real = out_r;
dop[x].imag = out_i;
}
/*Phase-unwrap the doppler values into the "phase" array.*/
lastPhase=0;
for (x=0;x<r->nSamples/MULTILOOK;x++)
{
float nextPhase=atan2(dop[x].imag, dop[x].real)*(1.0/(2.0*pi));
while ((nextPhase-lastPhase)<-0.5) nextPhase+=1.0;
while ((nextPhase-lastPhase)>0.5) nextPhase-=1.0;
phase[x]=nextPhase;
lastPhase=nextPhase;
}
sum = 0.0;
for (x = 0; x<r->nSamples/MULTILOOK; x++)
{
sum += phase[x];
x_vec[x] = x*MULTILOOK;
y_vec[x] = phase[x];
}
// Don't output this file for now since none of our other software uses it
// This file causes the windows uninstaller not to fully uninstall
// if (1) /*Output doppler vs. range*/
// {
// FILE *f=FOPEN("dop_vs_rng","w");
// for (x=0;x<r->nSamples/MULTILOOK;x++)
// fprintf(f,"%.0f\t%f\n",x_vec[x],y_vec[x]);
// fclose(f);
// }
sum = sum / (r->nSamples/MULTILOOK);
if (!quietflag) printf(" Constant Average : y = %f\n",(float)sum);
if (logflag) {
sprintf(logbuf," Constant Average : y = %f\n",(float)sum);
printLog(logbuf);
}
yaxb(x_vec, y_vec, r->nSamples/MULTILOOK, &t1, &t2);
if (!quietflag) printf(" Linear Regression : y = %f x + %f\n",t1,t2);
if (logflag) {
sprintf(logbuf," Linear Regression : y = %f x + %f\n",t1,t2);
printLog(logbuf);
}
yax2bxc(x_vec, y_vec, r->nSamples/MULTILOOK, &t1, &t2, &t3);
if (!quietflag) printf(" Quadratic Regression: y = %f x^2 + %f x + %f\n",t1,t2,t3);
if (logflag) {
sprintf(logbuf," Quadratic Regression: y = %f x^2 + %f x + %f\n",t1,t2,t3);
printLog(logbuf);
}
*a = t3; *b = t2; *c = t1;
free((void *)signal);
free((void *)signalNext);
free((void *)dop);
free((void *)x_vec);
free((void *)y_vec);
free((void *)phase);
freeGetRec(r);
return;
}
void cisi(float x, float *ci, float *si)
{
void nrerror(char error_text[]);
int i,k,odd;
float a,err,fact,sign,sum,sumc,sums,t,term;
fcomplex h,b,c,d,del;
t=fabs(x);
if (t == 0.0) {
*si=0.0;
*ci = -1.0/FPMIN;
return;
}
if (t > TMIN) {
b=Complex(1.0,t);
c=Complex(1.0/FPMIN,0.0);
d=h=Cdiv(ONE,b);
for (i=2;i<=MAXIT;i++) {
a = -(i-1)*(i-1);
b=Cadd(b,Complex(2.0,0.0));
d=Cdiv(ONE,Cadd(RCmul(a,d),b));
c=Cadd(b,Cdiv(Complex(a,0.0),c));
del=Cmul(c,d);
h=Cmul(h,del);
if (fabs(del.r-1.0)+fabs(del.i) < EPS) break;
}
if (i > MAXIT) nrerror("cf failed in cisi");
h=Cmul(Complex(cos(t),-sin(t)),h);
*ci = -h.r;
*si=PIBY2+h.i;
} else {
if (t < sqrt(FPMIN)) {
sumc=0.0;
sums=t;
} else {
sum=sums=sumc=0.0;
sign=fact=1.0;
odd=TRUE;
for (k=1;k<=MAXIT;k++) {
fact *= t/k;
term=fact/k;
sum += sign*term;
err=term/fabs(sum);
if (odd) {
sign = -sign;
sums=sum;
sum=sumc;
} else {
sumc=sum;
sum=sums;
}
if (err < EPS) break;
odd=!odd;
}
if (k > MAXIT) nrerror("maxits exceeded in cisi");
}
*si=sums;
*ci=sumc+log(t)+EULER;
}
if (x < 0.0) *si = -(*si);
}
DttSP_EXP void
Audio_Callback2 (float **input, float **output, unsigned int nframes)
{
unsigned int thread;
BOOLEAN b = reset_em;
BOOLEAN return_empty=FALSE;
unsigned int i;
for(thread=0;thread<threadno;thread++)
{
if (top[thread].susp) return_empty = TRUE;
}
if (return_empty)
{
for(thread=0;thread<threadno;thread++)
{
memset (output[2*thread], 0, nframes * sizeof (float));
memset (output[2*thread+1], 0, nframes * sizeof (float));
}
return;
}
if (b)
{
//fprintf(stderr, "reset_em!\n"); fflush(stderr);
//fprintf(stdout,"Audio_Callback2: reset_em = TRUE\n"), fflush(stdout);
reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++) {
memset (output[2*thread], 0, nframes * sizeof (float));
memset (output[2*thread+1], 0, nframes * sizeof (float));
}
return;
}
#if 0
if (diversity.flag) {
// Deal with the transmitter first
if ((ringb_float_read_space (top[1].jack.ring.o.l) >= nframes)
&& (ringb_float_read_space (top[1].jack.ring.o.r) >= nframes))
{
ringb_float_read (top[1].jack.ring.o.l, output[2], nframes);
ringb_float_read (top[1].jack.ring.o.r, output[3], nframes);
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// input: copy from port to ring
if ((ringb_float_write_space (top[1].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[1].jack.ring.i.r) >= nframes))
{
ringb_float_write (top[1].jack.ring.i.l, input[2], nframes);
ringb_float_write (top[1].jack.ring.i.r, input[3], nframes);
}
else
{
// rb pathology
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// if enough accumulated in ring, fire dsp
if ((ringb_float_read_space (top[1].jack.ring.i.l) >= top[1].hold.size.frames) &&
(ringb_float_read_space (top[1].jack.ring.i.r) >= top[1].hold.size.frames))
sem_post (&top[1].sync.buf.sem);
//
// Deal with the diversity channel next
//
if ((ringb_float_read_space (top[0].jack.ring.o.l) >= nframes)
&& (ringb_float_read_space (top[0].jack.ring.o.r) >= nframes))
{
/*ringb_float_read (top[thread].jack.auxr.o.l, output[l], nframes);
ringb_float_read (top[thread].jack.auxr.o.r, output[r], nframes);*/
ringb_float_read (top[0].jack.ring.o.l, output[2], nframes);
ringb_float_read (top[0].jack.ring.o.r, output[3], nframes);
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// Deal with the diversity/phased array channel next
// input: copy from port to ring
if ((ringb_float_write_space (top[0].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[0].jack.ring.i.r) >= nframes) &&
(ringb_float_write_space (top[2].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[2].jack.ring.i.r) >= nframes))
{
REAL *l0 = input[0];
REAL *r0 = input[1];
REAL *l2 = input[4];
REAL *r2 = input[5];
for (i=0;i<nframes;i++) {
COMPLEX A = Cmplx(l0[i],r0[i]);
COMPLEX B = Cmplx(l2[i],r2[i]);
A = Cscl(Cadd(A,Cmul(B,diversity.scalar)),diversity.gain);
ringb_float_write (top[0].jack.ring.i.l, &A.re, 1);
ringb_float_write (top[0].jack.ring.i.r, &A.im, 1);
}
/*ringb_float_write (top[thread].jack.auxr.i.l, input[l], nframes);
ringb_float_write (top[thread].jack.auxr.i.r, input[r], nframes);*/
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// if enough accumulated in ring, fire dsp
if ((ringb_float_read_space (top[0].jack.ring.i.l) >= top[0].hold.size.frames) &&
(ringb_float_read_space (top[0].jack.ring.i.r) >= top[0].hold.size.frames))
sem_post (&top[0].sync.buf.sem);
//
// Deal with 2nd receiver channel now
//
if ((ringb_float_read_space (top[2].jack.ring.o.l) >= nframes)
&& (ringb_float_read_space (top[2].jack.ring.o.r) >= nframes))
{
/*ringb_float_read (top[thread].jack.auxr.o.l, output[l], nframes);
ringb_float_read (top[thread].jack.auxr.o.r, output[r], nframes);*/
ringb_float_read (top[2].jack.ring.o.l, output[4], nframes);
ringb_float_read (top[2].jack.ring.o.r, output[5], nframes);
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// input: copy from port to ring
if ((ringb_float_write_space (top[2].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[2].jack.ring.i.r) >= nframes))
{
ringb_float_write (top[2].jack.ring.i.l, input[4], nframes);
ringb_float_write (top[2].jack.ring.i.r, input[5], nframes);
}
else
{
// rb pathology
for(thread=0;thread<threadno;thread++)
{
memset (output[thread], 0, nframes * sizeof (float));
memset (output[thread], 0, nframes * sizeof (float));
}
return;
}
// if enough accumulated in ring, fire dsp
if ((ringb_float_read_space (top[2].jack.ring.i.l) >= top[2].hold.size.frames) &&
(ringb_float_read_space (top[2].jack.ring.i.r) >= top[2].hold.size.frames))
sem_post (&top[2].sync.buf.sem);
} else
#endif
for(thread=0; thread<threadno; thread++)
{
int l=2*thread, r = 2*thread+1;
if ((ringb_float_read_space (top[thread].jack.ring.o.l) >= nframes)
&& (ringb_float_read_space (top[thread].jack.ring.o.r) >= nframes))
{
/*ringb_float_read (top[thread].jack.auxr.o.l, output[l], nframes);
ringb_float_read (top[thread].jack.auxr.o.r, output[r], nframes);*/
ringb_float_read (top[thread].jack.ring.o.l, output[l], nframes);
ringb_float_read (top[thread].jack.ring.o.r, output[r], nframes);
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[2*thread ], 0, nframes * sizeof (float));
memset (output[2*thread+1], 0, nframes * sizeof (float));
}
return;
}
// input: copy from port to ring
if ((ringb_float_write_space (top[thread].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[thread].jack.ring.i.r) >= nframes))
{
if (diversity.flag && (thread == 0)) {
if ((ringb_float_write_space (top[2].jack.ring.i.l) >= nframes)
&& (ringb_float_write_space (top[2].jack.ring.i.r) >= nframes))
{
REAL *l0 = input[0];
REAL *r0 = input[1];
REAL *l2 = input[4];
REAL *r2 = input[5];
for (i=0;i<nframes;i++) {
COMPLEX A = Cmplx(l0[i],r0[i]);
COMPLEX B = Cmplx(l2[i],r2[i]);
A = Cscl(Cadd(A,Cmul(B,diversity.scalar)),diversity.gain);
ringb_float_write (top[0].jack.ring.i.l, &A.re, 1);
ringb_float_write (top[0].jack.ring.i.r, &A.im, 1);
}
/*ringb_float_write (top[thread].jack.auxr.i.l, input[l], nframes);
ringb_float_write (top[thread].jack.auxr.i.r, input[r], nframes);*/
} else {
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[2*thread ], 0, nframes * sizeof (float));
memset (output[2*thread+1], 0, nframes * sizeof (float));
}
return;
}
} else {
ringb_float_write (top[thread].jack.ring.i.l, input[l], nframes);
ringb_float_write (top[thread].jack.ring.i.r, input[r], nframes);
/*ringb_float_write (top[thread].jack.auxr.i.l, input[l], nframes);
ringb_float_write (top[thread].jack.auxr.i.r, input[r], nframes);*/
}
}
else
{
// rb pathology
//reset_system_audio(nframes);
for(thread=0;thread<threadno;thread++)
{
memset (output[2*thread ], 0, nframes * sizeof (float));
memset (output[2*thread+1], 0, nframes * sizeof (float));
}
return;
}
// if enough accumulated in ring, fire dsp
if ((ringb_float_read_space (top[thread].jack.ring.i.l) >= top[thread].hold.size.frames) &&
(ringb_float_read_space (top[thread].jack.ring.i.r) >= top[thread].hold.size.frames))
sem_post (&top[thread].sync.buf.sem);
}
}
DttSP_EXP void
PolyPhaseFIR (ResSt resst)
/******************************************************************************
* CALLING PARAMETERS:
* Name Use Description
* ____ ___ ___________
* *input pointer to input COMPLEX data array
* *output pointer to output COMPLEX data array
* RealFIR filter pointer to filter coefficients array
* *filterMemoryBuff pointer to buffer used as filter memory. Initialized
* all data to 0 before 1st call. length is calculated
* from numFiltTaps
* filterMemoryBuffLength length of filterMemoryBuff
* inputArrayLength length of input array :note that "output" may differ
* in length
* numFiltTaps number of filter taps in array "filtcoeff": <filterMemoryBuffLength
* indexfiltMemBuf index to where next input sample is to be stored in
* "filterMemoryBuff",initalized 0 to before first call
* interpFactor interpolation factor: output rate = input rate *
* "interpFactor" / "deciFactor".
* filterPhaseNum filter phase number (index), initialized to 0 before
* first call
* deciFactor decimation factor:
* output rate = (input rate * "interpFactor"/"deciFactor")
* numOutputSamples number of output samples placed in array "output"
*
* CALLED BY:
*
* RETURN VALUE:
* Name Description
* ____ ___________
* none
*
* DESCRIPTION: This function is used to change the sampling rate of the data.
* The input is first upsampled to a multiple of the desired
* sampling rate and then down sampled to the desired sampling rate.
*
* Ex. If we desire a 7200 Hz sampling rate for a signal that has
* been sampled at 8000 Hz the signal can first be upsampled
* by a factor of 9 which brings it up to 72000 Hz and then
* down sampled by a factor of 10 which results in a sampling
* rate of 7200 Hz.
*
* NOTES:
* Also, the "*filterMemoryBuff" MUST be 2^N REALs long. This
* routine uses circular addressing on this buffer assuming that
* it is 2^N REALs in length.
*
******************************************************************************/
{
/******************************************************************************
* LOCAL VARIABLE DECLARATIONS
*******************************************************************************
* Type Name Description
* ____ ____ ___________ */
int i, j, k, jj; /* counter variables */
COMPLEX *outptr;
resst->numOutputSamples = 0;
for (i = 0; i < resst->inputArrayLength; i++)
{
/*
* save data in circular buffer
*/
resst->filterMemoryBuff[resst->indexfiltMemBuf] = resst->input[i];
j = resst->indexfiltMemBuf;
jj = j;
/*
* circular addressing
*/
resst->indexfiltMemBuf = (resst->indexfiltMemBuf + 1) & resst->MASK;
/*
* loop through each filter phase: interpolate then decimate
*/
while (resst->filterPhaseNum < resst->interpFactor)
{
j = jj;
/* output[*numOutputSamples] = 0.0; */
outptr = resst->output + resst->numOutputSamples;
*outptr = cxzero;
/*
* perform convolution
*/
for (k = resst->filterPhaseNum; k < resst->numFiltTaps;
k += resst->interpFactor)
{
/* output[*numOutputSamples] += filtcoeff[k]*filterMemoryBuff[j]; */
//*outptr += resst->filtcoeff[k]* resst->filterMemoryBuff[j];
*outptr =
Cadd (*outptr,
Cscl (resst->filterMemoryBuff[j],
FIRtap (resst->filter, k)));
/*
* circular adressing
*/
j = (j + resst->MASK) & resst->MASK;
}
/*
* scale the data
*/
/* output[*numOutputSamples]*=(REAL)interpFactor; */
*outptr = Cscl (*outptr, (REAL) resst->interpFactor);
resst->numOutputSamples += 1;
/*
* increment interpolation phase # by decimation factor
*/
resst->filterPhaseNum += (resst->deciFactor);
} /* end while *filterPhaseNum < interpFactor */
resst->filterPhaseNum -= resst->interpFactor;
} /* end for inputArrayLength */
} /* end PolyPhaseFir */
int CarrMethod_old_verison(double S0,
double T,
double K,
double CallPut,
double r,
double divid,
double sigma,
void * Model,
dcomplex (*ln_phi)(dcomplex u,double t,void * model),
double *ptprice,
double *ptdelta)
{
int n;
dcomplex dzeta,dzetaBS;
double alpha=0.0;
//taking account of dividends
int Nlimit = 2048;
//number of integral discretization steps
double logstrikestep = 0.01;
double k0 = log(K/(S0*exp(-divid*T)));
double h = M_2PI/Nlimit/logstrikestep; //integral discretization step
double A = (Nlimit-1)*h; // integration domain is (-A/2,A/2)
PnlVectComplex * z =pnl_vect_complex_create(Nlimit);
PnlVectComplex * y =pnl_vect_complex_create(Nlimit);
double vn = -A/2;
dcomplex vn_minus_alpha_plus_uno = Complex(-A/2,-(alpha+1));
dcomplex i_vn_plus_alpha = Complex(alpha,-A/2);
double weight = 1./3; //Simpson's rule weights
dcomplex uno_plus_alpha_plus_ivn=Complex(1+alpha,vn);
//delta
for(n=0; n<Nlimit; n++)
{
dzeta= Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,vn*(r*T-k0)));
dzetaBS= Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,vn*(r*T-k0)));
dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS));
dzeta = Cdiv(dzeta,i_vn_plus_alpha);
dzeta = RCmul(weight,dzeta);
pnl_vect_complex_set(z,n,dzeta);
dzeta=Cdiv(dzeta,uno_plus_alpha_plus_ivn);
pnl_vect_complex_set(y,n,dzeta);
//>> Update value
vn += h;
vn_minus_alpha_plus_uno.r+=h;
i_vn_plus_alpha.i+=h;
uno_plus_alpha_plus_ivn.i+=h;
weight = (weight<1) ? 4./3 : 2./3; //Simpson's rule weights
weight = (n==(Nlimit-2)) ?2./3. :weight;
}
//pnl_vect_complex_print(z);
pnl_fft_inplace(z);
pnl_fft_inplace(y);
//pnl_vect_complex_print(z);
//Black-Scholes formula
pnl_cf_call_bs(S0,K,T,r,divid,sigma,ptprice,ptdelta);
S0 *= exp(-divid*T);
/*Call Case*/
*ptprice += S0*A/M_2PI/(Nlimit-1)*exp(-alpha*k0)*GET_REAL(y,0);
*ptdelta += exp(-divid*T)*(A/M_2PI/(Nlimit-1)*exp(-alpha*k0)*GET_REAL(z,0));
//Put Case via parity*/
if (CallPut==2)
{
*ptprice =*ptprice-S0+K*exp(-r*T);
*ptdelta =*ptdelta-exp(-divid*T);
}
//memory desallocation
pnl_vect_complex_free(&z);
pnl_vect_complex_free(&y);
return OK;
}
static double charact_func(double k)
{
double X,tau,roeps,u,b,I,eps,eps2;
dcomplex Ak,Bk,Ck,Dk,Lambdak,z1,z2,z3,zeta,psi_moins,psi_plus,expo,ans;
dcomplex dlk;
tau = T;
eps = sigma;
roeps = rho*eps;
X = log(S/K) + (r - divid)*tau;
eps2 = eps*eps;
if(func_type==1)
{
u = 1.;
b = kappa - roeps;
I = 1.;
}
else if(func_type==2)
{
u = -1.;
b = kappa;
I = 0.;
}
else
{
printf("erreur : dans charact_func il faut initialiser func_type a 1 ou 2.\n");
exit(-1);
}
if(heston==1)
{
z1 = Complex(k*k,-u*k);
z2 = Complex(b,-roeps*k);
z2 = Cmul(z2,z2);
zeta = Cadd(z2,RCmul(eps2,z1));
zeta = Csqrt(zeta);
psi_moins = Complex(b,-roeps*k);
psi_plus = RCmul(-1.,psi_moins);
psi_moins = Cadd(psi_moins,zeta);
psi_plus = Cadd(psi_plus,zeta);
expo = Cexp( RCmul(-tau,zeta) );
z3 = Cadd( psi_moins , Cmul(psi_plus,expo) );
Bk = RCmul(-1.,z1);
Bk = Cmul( Bk , Csub(Complex(1.,0),expo) );
Bk = Cdiv(Bk,z3);
Ak = Cdiv( z3 , RCmul(2.,zeta) );
Ak = Clog(Ak);
if(initlog>0)
{
dlk = Csub(Ak,lk_1);
if(dlk.i < -M_PI)
{
bk = bk + 1;
}
else if(dlk.i > M_PI)
{
bk = bk - 1;
}
initlog++;
lk_1 = Ak;
} else {
initlog++;
lk_1 = Ak;
}
Ak = Cadd(Ak, Complex(0.,2*M_PI*bk));
Ak = RCmul( 2. , Ak );
Ak = Cadd( RCmul(tau,psi_plus) , Ak);
Ak = RCmul( -kappa*teta/eps2 , Ak);
}
else
{
Ak = Complex(0.,0.);
Bk = Complex( -0.5*tau*k*k , 0.5*tau*u*k );
}
if(merton==1)
{
z1 = Complex( -0.5*v*v*k*k + I*(m0+0.5*v*v) , (m0+I*v*v)*k );
z1 = Cexp(z1);
z2 = Complex(I,k);
z2 = RCmul( exp(m0+0.5*v*v) -1, z2);
z2 = Cadd( Complex(1.,0.) , z2 );
Lambdak = Csub(z1,z2);
Ck = Complex(0.,0.);
Dk = RCmul(tau,Lambdak);
}
else
{
Ck = Complex(0.,0.);
Dk = Complex(0.,0.);
}
ans = Cadd( Ak , RCmul(V0,Bk) );
ans = Cadd( ans , Ck );
ans = Cadd( ans , RCmul(lambda0,Dk) );
ans = Cadd( ans , Complex(0.,k*X) );
ans = Cexp(ans);
ans = Cdiv(ans,Complex(0.,k));
return ans.r;
}
/*Computation the double(Mellin+Laplace) transform of the density of arithmetic average */
static dcomplex mellintransform(dcomplex l, dcomplex n, double sg, double r)
{
dcomplex mu,nterm1, nterm2, nterm3, dterm1, dterm2;
dcomplex num, den, cv,cost;
double v;
v= 2*r/(sg*sg)-1.0;
cv =Complex(v,0.0);
mu = Csqrt(Cadd(Complex(v*v,0), RCmul(2.0,l)));
cost=RCmul(log(2.0/(sg*sg)), n);
nterm1 =Clgamma(Cadd(n,CONE));
nterm2 =Clgamma(Cadd(RCmul(0.5, Cadd(mu,cv)),CONE));
nterm3 =Clgamma(Csub(RCmul(0.5, Csub(mu,cv)),n));
num = Cadd(Cadd( nterm1,nterm2),nterm3);
dterm1 =Clgamma(RCmul(0.5, Csub(mu,cv)));
dterm2 =Clgamma(Cadd(Cadd(RCmul(0.5, Cadd(mu,cv)),CONE),n));
den = Cadd( dterm1,dterm2);
return Cdiv(Cexp(Cadd(Csub(num,den),cost)),l);
}
int CarrMethod(double S0,
double T,
double K,
double CallPut,
double r,
double divid,
double sigma,
void * Model,
dcomplex (*ln_phi)(dcomplex u,double t,void * model),
double *ptprice,
double *ptdelta)
{
int n;
dcomplex dzeta,dzetaBS;
double alpha=0.75;
//taking account of dividends
int Nlimit = 2048;//2048;
//number of integral discretization steps
double logstrikestep = 0.01;
double k0 = log(K/S0)-(r-divid)*T;
double h = M_PI/Nlimit/logstrikestep; //integral discretization step
double z,y;
double vn = 0;
dcomplex vn_minus_alpha_plus_uno = Complex(0,-(alpha+1));
dcomplex i_vn_plus_alpha = Complex(alpha,0);
double weight = 1./3; //Simpson's rule weights
dcomplex uno_plus_alpha_plus_ivn=Complex(1+alpha,vn);
//delta
z=0;y=0;
for(n=0; n<Nlimit; n++)
{
dzeta=Cadd(ln_phi(vn_minus_alpha_plus_uno,T,Model),Complex(0,-vn*k0));
// printf("%7.4f + i %7.4f \n",dzeta.r,dzeta.i);
dzetaBS= Cadd(ln_phi_BS(vn_minus_alpha_plus_uno,T,sigma),Complex(0,-vn*k0));
dzeta = Csub(Cexp(dzeta),Cexp(dzetaBS));
dzeta = Cdiv(dzeta,i_vn_plus_alpha);
dzeta = RCmul(weight,dzeta);
//printf(">>%7.4f + i %7.4f \n",dzeta.r,dzeta.i);
z+=dzeta.r;
dzeta=Cdiv(dzeta,uno_plus_alpha_plus_ivn);
y+=dzeta.r;
//>> Update value
vn += h;
vn_minus_alpha_plus_uno.r+=h;
i_vn_plus_alpha.i+=h;
uno_plus_alpha_plus_ivn.i+=h;
weight = (weight<1) ? 4./3 : 2./3; //Simpson's rule weights
weight = (n==(Nlimit-2)) ?2./3. :weight;
}
//Black-Scholes formula
pnl_cf_call_bs(S0,K,T,r,divid,sigma,ptprice,ptdelta);
S0 *= exp(-divid*T);
/*Call Case*/
*ptprice += S0/(Nlimit*logstrikestep)*exp(-alpha*k0)*y;
//*ptprice = y;
*ptdelta += exp(-divid*T)/(Nlimit*logstrikestep)*exp(-alpha*k0)*z;
//Put Case via parity*/
if (CallPut==2)
{
*ptprice =*ptprice-S0+K*exp(-r*T);
*ptdelta =*ptdelta-exp(-divid*T);
}
//memory desallocation
return OK;
}
static double charact_func0(double k)
{
double X,tau,roeps,u,eps,eps2;
dcomplex Ak,Bk,Ck,Dk,Lambdak,z1,z2,z3,zeta,psi_moins,psi_plus,expo,ans;
dcomplex dlk;
tau = T;
eps = sigma;
roeps = rho*eps;
X = log(S/K) + (r - divid)*tau;
u = kappa - roeps/2.;
eps2 = eps*eps;
if(heston==1)
{
zeta.r = k*k*eps2*(1.-rho*rho) + u*u + eps2/4.;
zeta.i = 2.*k*roeps*u;
zeta = Csqrt(zeta);
psi_moins = Complex(u,roeps*k);
psi_plus = RCmul(-1.,psi_moins);
psi_moins = Cadd(psi_moins,zeta);
psi_plus = Cadd(psi_plus,zeta);
expo = Cexp( RCmul(-tau,zeta) );
z3 = Cadd( psi_moins , Cmul(psi_plus,expo) );
Bk = RCmul( -(k*k+0.25) , Csub(Complex(1.,0),expo) );
Bk = Cdiv(Bk,z3);
Ak = Cdiv( z3 , RCmul(2.,zeta) );
Ak = Clog(Ak);
if(initlog>0)
{
dlk = Csub(Ak,lk_1);
if(dlk.i < -M_PI)
{
bk = bk + 1;
}
else if(dlk.i > M_PI)
{
bk = bk - 1;
}
initlog++;
lk_1 = Ak;
} else {
initlog++;
lk_1 = Ak;
}
Ak = Cadd(Ak, Complex(0.,2*M_PI*bk));
Ak = RCmul( 2. , Ak );
Ak = Cadd( RCmul(tau,psi_plus) , Ak);
Ak = RCmul( -kappa*teta/eps2 , Ak);
}
else
{
Ak = Complex(0.,0.);
Bk = Complex( -0.5*tau*(k*k+0.25) ,0.);
}
if(merton==1)
{
z1 = Complex( 0.5*m0-0.5*v*v*(k*k-0.25) , -k*(m0+0.5*v*v) );
z1 = Cexp(z1);
z2 = Complex(0.5,-k);
z2 = RCmul( exp(m0+0.5*v*v) - 1. , z2);
z2 = Cadd( Complex(1.,0.) , z2 );
Lambdak = Csub(z1,z2);
Ck = Complex(0.,0.);
Dk = RCmul(tau,Lambdak);
}
else
{
Ck = Complex(0.,0.);
Dk = Complex(0.,0.);
}
ans = Cadd( Ak , RCmul(V0,Bk) );
ans = Cadd( ans , Ck );
ans = Cadd( ans , RCmul(lambda0,Dk) );
ans = Cadd( ans , RCmul(X,Complex(0.5,-k) ) );
ans = Cexp(ans);
ans = Cdiv(ans,Complex(k*k+0.25,0.));
if(probadelta == 1)
{
ans = Cmul( ans , Complex(0.5,-k) );
ans = RCmul( 1./S , ans );
}
return ans.r;
}
