/*
In: tau (lattice parameter)
Out: g2 -> g[0]
g3 -> g[1]
*/
void compute_invariants(gsl_complex tau, gsl_complex *g)
{
gsl_complex q, q14;
gsl_complex t2,t3,t24,t34;
gsl_complex g3_term1, g3_term2;
gsl_complex g2, g3;
q = gsl_complex_exp(gsl_complex_mul_imag(tau,M_PI));
q14 = gsl_complex_exp(gsl_complex_mul_imag(tau,M_PI_4));
t2=theta20(q,q14);
t3=theta30(q);
t24 = pow4(t2);
t34 = pow4(t3);
g2 = gsl_complex_mul_real(gsl_complex_sub(gsl_complex_add(gsl_complex_mul(t24,t24),gsl_complex_mul(t34,t34)),gsl_complex_mul(t24,t34)),_CONST_43PI4);
g3_term1 = gsl_complex_add(gsl_complex_mul(t24,gsl_complex_mul(t24,t24)),gsl_complex_mul(t34,gsl_complex_mul(t34,t34)));
g3_term2 = gsl_complex_mul(gsl_complex_add(t24,t34),gsl_complex_mul(t24,t34));
g3 = gsl_complex_sub( gsl_complex_mul_real(g3_term1, _CONST_827PI6),
gsl_complex_mul_real(g3_term2, _CONST_49PI6) );
g[0] = g2;
g[1] = g3;
}
gsl_complex gsl_complex_arcsinh(gsl_complex a)
{ /* z = arcsinh(a) */
gsl_complex z = gsl_complex_mul_imag(a, 1.0);
z = gsl_complex_arcsin(z);
z = gsl_complex_mul_imag(z, -1.0);
return z;
}
void
gsl_complex_arcsinh (complex_t const *a, complex_t *res)
{ /* z = arcsinh(a) */
gsl_complex_mul_imag (a, 1.0, res);
gsl_complex_arcsin (res, res);
gsl_complex_mul_imag (res, -1.0, res);
}
gsl_complex gsl_complex_arctanh(gsl_complex a)
{ /* z = arctanh(a) */
if (GSL_IMAG(a) == 0.0) {
return gsl_complex_arctanh_real(GSL_REAL(a));
} else {
gsl_complex z = gsl_complex_mul_imag(a, 1.0);
z = gsl_complex_arctan(z);
z = gsl_complex_mul_imag(z, -1.0);
return z;
}
}
void
gsl_complex_arctanh (complex_t const *a, complex_t *res)
{ /* z = arctanh(a) */
if (GSL_IMAG (a) == 0.0) {
gsl_complex_arctanh_real (GSL_REAL (a), res);
} else {
gsl_complex_mul_imag (a, 1.0, res);
gsl_complex_arctan (res, res);
gsl_complex_mul_imag (res, -1.0, res);
}
}
complex_spinor complex_spinor::op(OPERATOR_SPIN spinOperator) const{
int i;
double result;
//Spin Parameters
int new_numSites = this->_numSites;
complex_spinor complex_spinor_resu(new_numSites);
if(spinOperator == S_X ){
for(i=0 ; i<new_numSites ; i++){
gsl_complex oldUP = this->complex_spinor_get(i, UP);
gsl_complex oldDOWN = this->complex_spinor_get(i, DOWN);
complex_spinor_resu.complex_spinor_set(i, UP, gsl_complex_mul_real(oldDOWN, 0.5));
complex_spinor_resu.complex_spinor_set(i, DOWN, gsl_complex_mul_real(oldUP, 0.5));
}
}
else if(spinOperator == S_Y){
for(i=0 ; i<new_numSites ; i++){
gsl_complex oldUP = this->complex_spinor_get(i, UP);
gsl_complex oldDOWN = this->complex_spinor_get(i, DOWN);
complex_spinor_resu.complex_spinor_set(i, UP, gsl_complex_mul_imag(oldDOWN, 0.5));
complex_spinor_resu.complex_spinor_set(i, DOWN, gsl_complex_mul_imag(oldUP, -0.5));
}
}
else{ //S_Z
for(i=0 ; i<new_numSites ; i++){
gsl_complex oldUP = this->complex_spinor_get(i, UP);
gsl_complex oldDOWN = this->complex_spinor_get(i, DOWN);
complex_spinor_resu.complex_spinor_set(i, UP, gsl_complex_mul_real(oldUP, 0.5));
complex_spinor_resu.complex_spinor_set(i, DOWN, gsl_complex_mul_real(oldDOWN, -0.5));
}
}
return complex_spinor_resu;
}
gsl_complex
gsl_complex_arccosh (gsl_complex a)
{ /* z = arccosh(a) */
gsl_complex z = gsl_complex_arccos (a);
z = gsl_complex_mul_imag (z, GSL_IMAG(z) > 0 ? -1.0 : 1.0);
return z;
}
gsl_complex f_integrand(gsl_complex p, const Params *params)
{
double r = params->r;
return gsl_complex_mul(
f_envelope(p, params),
gsl_complex_exp(gsl_complex_mul_imag(p, r)));
}
void LALInferenceTemplateROQ(LALInferenceModel *model)
{
double m1,m2,mc,eta,q,iota=0;
/* Prefer m1 and m2 if available (i.e. for injection template) */
if(LALInferenceCheckVariable(model->params,"mass1")&&LALInferenceCheckVariable(model->params,"mass2"))
{
m1=*(REAL8 *)LALInferenceGetVariable(model->params,"mass1");
m2=*(REAL8 *)LALInferenceGetVariable(model->params,"mass2");
eta=m1*m2/((m1+m2)*(m1+m2));
mc=pow(eta , 0.6)*(m1+m2);
}
else
{
if (LALInferenceCheckVariable(model->params,"q")) {
q = *(REAL8 *)LALInferenceGetVariable(model->params,"q");
q2eta(q, &eta);
}
else
eta = *(REAL8*) LALInferenceGetVariable(model->params, "eta");
mc = *(REAL8*) LALInferenceGetVariable(model->params, "chirpmass");
mc2masses(mc, eta, &m1, &m2);
}
iota = acos(LALInferenceGetREAL8Variable(model->params, "costheta_jn")); /* zenith angle between J and N in radians */
double cosiota = cos(iota);
double plusCoef = 0.5 * (1.0 + cosiota*cosiota);
double crossCoef = cosiota;
/* external: SI; internal: solar masses */
const REAL8 m = m1 + m2;
const REAL8 m_sec = m * LAL_MTSUN_SI; /* total mass in seconds */
const REAL8 etap2 = eta * eta;
const REAL8 etap3 = etap2 * eta;
const REAL8 piM = LAL_PI * m_sec;
const REAL8 mSevenBySix = -7./6.;
const REAL8 phic = *(REAL8 *)LALInferenceGetVariable(model->params,"phase");
const REAL8 r = 1e6*LAL_PC_SI;
REAL8 logv0 = log(1.); //the standard tf2 definition is log(v0), but I've changed it to reflect Scott's convention
REAL8 shft, amp0;//, f_max;
REAL8 psiNewt, psi2, psi3, psi4, psi5, psi6, psi6L, psi7, psi3S, psi4S, psi5S;
REAL8 eta_fac = -113. + 76. * eta;
REAL8 chi=0; //NOTE: chi isn't used here yet, so we just set it to zero
gsl_complex h_i;
/* extrinsic parameters */
amp0 = -pow(m_sec, 5./6.) * sqrt(5.*eta / 24.) / (Pi_p2by3 * r / LAL_C_SI);
shft = 0;//LAL_TWOPI * (tStart.gpsSeconds + 1e-9 * tStart.gpsNanoSeconds);
/* spin terms in the amplitude and phase (in terms of the reduced
* spin parameter */
psi3S = 113.*chi/3.;
psi4S = 63845.*(-81. + 4.*eta)*chi*chi/(8. * eta_fac * eta_fac);
psi5S = -565.*(-146597. + 135856.*eta + 17136.*etap2)*chi/(2268.*eta_fac);
/* coefficients of the phase at PN orders from 0 to 3.5PN */
psiNewt = 3./(128.*eta);
psi2 = 3715./756. + 55.*eta/9.;
psi3 = psi3S - 16.*LAL_PI;
psi4 = 15293365./508032. + 27145.*eta/504. + 3085.*eta*eta/72. + psi4S;
psi5 = (38645.*LAL_PI/756. - 65.*LAL_PI*eta/9. + psi5S);
psi6 = 11583231236531./4694215680. - (640.*Pi_p2)/3. - (6848.*LAL_GAMMA)/21.
+ (-5162.983708047263 + 2255.*Pi_p2/12.)*eta
+ (76055.*etap2)/1728. - (127825.*etap3)/1296.;
psi6L = -6848./21.;
psi7 = (77096675.*LAL_PI)/254016. + (378515.*LAL_PI*eta)/1512.
- (74045.*LAL_PI*eta*eta)/756.;
for (unsigned int i = 0; i < model->roq->frequencyNodes->size; i++) {
/* fourier frequency corresponding to this bin */
const REAL8 f = gsl_vector_get(model->roq->frequencyNodes, i);
const REAL8 v3 = piM*f;
/* PN expansion parameter */
REAL8 v, v2, v4, v5, v6, v7, logv, Psi, amp;
v = cbrt(v3);
v2 = v*v; v4 = v3*v; v5 = v4*v; v6 = v3*v3; v7 = v6*v;
logv = log(v);
/* compute the phase and amplitude */
Psi = psiNewt / v5 * (1.
+ psi2 * v2 + psi3 * v3 + psi4 * v4
+ psi5 * v5 * (1. + 3. * (logv - logv0))
+ (psi6 + psi6L * (log4 + logv)) * v6 + psi7 * v7);
amp = amp0 * pow(f, mSevenBySix);
GSL_SET_COMPLEX(&h_i, amp * cos(Psi + shft * f - 2.*phic - LAL_PI_4), - amp * sin(Psi + shft * f - 2.*phic - LAL_PI_4));
gsl_vector_complex_set(model->roq->hplus, i, gsl_complex_mul_real(h_i,plusCoef));
gsl_vector_complex_set(model->roq->hcross, i, gsl_complex_mul_real(gsl_complex_mul_imag(h_i,-1.0),crossCoef));
}
return;
}
gsl_complex integrate_line_segment(Params *params,
gsl_complex p0,
gsl_complex p1)
{
gsl_complex k = gsl_complex_sub(p1, p0);
const double r = params->r;
const double a = 0.0; // parameter interval start
const double b = 1.0; // parameter interval end
const double L = b - a; // length of parameter interval
const size_t table_size = 1000;
// calculate frequency of oscillatory part
double omega = GSL_REAL(k) * r;
gsl_integration_workspace *ws = gsl_integration_workspace_alloc(table_size);
// prepare sine/cosine tables for integration
gsl_integration_qawo_table *table_cos = gsl_integration_qawo_table_alloc(omega, L, GSL_INTEG_COSINE, table_size);
gsl_integration_qawo_table *table_sin = gsl_integration_qawo_table_alloc(omega, L, GSL_INTEG_SINE, table_size);
LineSegmentParams lsp;
lsp.p0 = p0;
lsp.k = k;
lsp.damping = params->r * GSL_IMAG(k);
lsp.params = params;
//fprintf(stderr, "p0 = %g %g, p1 = %g %g, k = %g %g, r = %g, omega = %g, damping = %g\n",
// GSL_REAL(p0), GSL_IMAG(p0), GSL_REAL(p1), GSL_IMAG(p1),
// GSL_REAL(k), GSL_IMAG(k), r, omega, lsp.damping);
gsl_function F;
F.function = &line_segment_integrand_wrapper;
F.params = &lsp;
double result_real_cos, abserr_real_cos;
double result_real_sin, abserr_real_sin;
double result_imag_cos, abserr_imag_cos;
double result_imag_sin, abserr_imag_sin;
double epsabs = 1e-9;
double epsrel = 1e-9;
lsp.part = REAL;
gsl_integration_qawo(&F, a, epsabs, epsrel, table_size, ws, table_cos, &result_real_cos, &abserr_real_cos);
gsl_integration_qawo(&F, a, epsabs, epsrel, table_size, ws, table_sin, &result_real_sin, &abserr_real_sin);
lsp.part = IMAG;
gsl_integration_qawo(&F, a, epsabs, epsrel, table_size, ws, table_cos, &result_imag_cos, &abserr_imag_cos);
gsl_integration_qawo(&F, a, epsabs, epsrel, table_size, ws, table_sin, &result_imag_sin, &abserr_imag_sin);
//fprintf(stderr, " cos: %g (+- %g) %g (+- %g) sin: %g (+- %g) %g (+- %g)\n",
// result_real_cos, abserr_real_cos, result_imag_cos, abserr_imag_cos,
// result_real_sin, abserr_real_sin, result_imag_sin, abserr_imag_sin);
gsl_complex cos_part = gsl_complex_rect(result_real_cos, result_imag_cos);
gsl_complex sin_part = gsl_complex_rect(-result_imag_sin, result_real_sin);
gsl_complex sum = gsl_complex_add(cos_part, sin_part);
gsl_complex result = gsl_complex_mul(
k,
gsl_complex_mul(sum, gsl_complex_exp(gsl_complex_mul_imag(p0, params->r))));
gsl_integration_qawo_table_free(table_sin);
gsl_integration_qawo_table_free(table_cos);
gsl_integration_workspace_free(ws);
return result;
}
void
gsl_complex_arccosh (complex_t const *a, complex_t *res)
{ /* z = arccosh(a) */
gsl_complex_arccos (a, res);
gsl_complex_mul_imag (res, GSL_IMAG (res) > 0 ? -1.0 : 1.0, res);
}