gsl_complex theta4(gsl_complex z, gsl_complex q)
{
int n=0;
gsl_complex accum = gsl_complex_rect(0.5,0.0);
gsl_complex q2 = gsl_complex_mul(q,q);
gsl_complex nextm = gsl_complex_negative(gsl_complex_mul(q,q2));
gsl_complex qpower = gsl_complex_negative(q);
gsl_complex term = gsl_complex_rect(1.0,0.0);
while ((gsl_complex_abs(qpower) > 2.0*GSL_DBL_EPSILON) && (n < THETA_ITER_MAX)) {
term = gsl_complex_mul(qpower, gsl_complex_cos(gsl_complex_mul_real(z,2*(n+1))));
accum = gsl_complex_add(accum, term);
qpower = gsl_complex_mul(qpower, nextm);
nextm = gsl_complex_mul(nextm, q2);
n++;
}
if (n >= THETA_ITER_MAX)
return(gsl_complex_rect(0.0,0.0));
return gsl_complex_mul_real(accum,2.0);
}
gsl_complex theta2(gsl_complex z, gsl_complex q, gsl_complex q14)
{
int n=0;
gsl_complex accum = gsl_complex_rect(0.0,0.0);
gsl_complex q2 = gsl_complex_mul(q,q);
gsl_complex nextm = q2;
gsl_complex qpower = gsl_complex_rect(1.0,0.0);
gsl_complex term = gsl_complex_rect(1.0,0.0);
while ((gsl_complex_abs(term) > 2.0*GSL_DBL_EPSILON) && (n < THETA_ITER_MAX)) {
term = gsl_complex_mul(qpower, gsl_complex_cos(gsl_complex_mul_real(z,2*n+1)));
accum = gsl_complex_add(accum, term);
qpower = gsl_complex_mul(qpower, nextm);
nextm = gsl_complex_mul(nextm, q2);
n++;
}
if (n >= THETA_ITER_MAX)
return(gsl_complex_rect(0.0,0.0));
return gsl_complex_mul_real(gsl_complex_mul(q14,accum),2.0);
}
/* The Lattes map */
gsl_complex P_doubler(gsl_complex p, const gsl_complex *g)
{
gsl_complex p2, p3;
gsl_complex num;
gsl_complex denom;
gsl_complex term;
p2 = gsl_complex_mul(p,p);
p3 = gsl_complex_mul(p2,p);
/* denom = 4p^3 - g2p - g3 */
denom = gsl_complex_sub(gsl_complex_mul_real(p3,4.0),
gsl_complex_add(gsl_complex_mul(p,g[0]),g[1]));
/* num = (p^2 + g2/4)^2 + 2g3p */
term = gsl_complex_add(p2,gsl_complex_mul_real(g[0],0.25));
num = gsl_complex_add(gsl_complex_mul(p,gsl_complex_mul_real(g[1],2.0)),
gsl_complex_mul(term,term));
return gsl_complex_div(num,denom);
}
int
print_Lcurve(const char *filename, poltor_workspace *w)
{
int s = 0;
FILE *fp;
const size_t p = w->p;
double rnorm, Lnorm;
gsl_vector_complex_view v = gsl_vector_complex_subvector(w->rhs, 0, p);
size_t i;
fp = fopen(filename, "a");
if (!fp)
{
fprintf(stderr, "print_Lcurve: unable to open %s: %s\n",
filename, strerror(errno));
return -1;
}
/* construct A and b, and calculate chi^2 = ||b - A c||^2 */
poltor_build_ls(0, w);
rnorm = sqrt(w->chisq);
/* compute v = L c; L is stored in w->L by poltor_solve() */
for (i = 0; i < p; ++i)
{
gsl_complex ci = gsl_vector_complex_get(w->c, i);
double li = gsl_vector_get(w->L, i);
gsl_complex val = gsl_complex_mul_real(ci, li);
gsl_vector_complex_set(&v.vector, i, val);
}
/* compute || L c || */
Lnorm = gsl_blas_dznrm2(&v.vector);
fprintf(fp, "%.12e %.12e %.6e %.6e %.6e\n",
log(rnorm),
log(Lnorm),
w->alpha_int,
w->alpha_sh,
w->alpha_tor);
printcv_octave(w->residuals, "r");
printcv_octave(w->c, "c");
printv_octave(w->L, "L");
fclose(fp);
return s;
} /* print_Lcurve() */
double line_segment_integrand_wrapper(double t, void *data)
{
const LineSegmentParams *params = (const LineSegmentParams *)data;
gsl_complex p = gsl_complex_add(params->p0,
gsl_complex_mul_real(params->k, t));
gsl_complex v = f_envelope(p, params->params);
double v_part = (params->part == REAL) ? GSL_REAL(v) : GSL_IMAG(v);
double damped = exp( - params->damping * t) * v_part;
return damped;
}
/* NOTE: Assumes z is in fundamental parallelogram */
gsl_complex wP(gsl_complex z, gsl_complex tau, const gsl_complex *g)
{
int N = 6;
int i;
gsl_complex z0;
gsl_complex z02;
gsl_complex p;
z = near_origin(z,tau);
z0 = gsl_complex_div_real(z,(double)(1 << N));
z02 = gsl_complex_mul(z0,z0);
/* Laurent expansion: P \approx 1/z^2 + (g2/20)z^2 + (g3/28) z^4 */
p = gsl_complex_add(gsl_complex_inverse(z02),
gsl_complex_add(gsl_complex_mul(z02,gsl_complex_mul_real(g[0],0.05)),
gsl_complex_mul(gsl_complex_mul(z02,z02),gsl_complex_mul_real(g[1],_CONST_1_28))));
for (i=0;i<N;i++) {
p = P_doubler(p,g);
}
return p;
}
gsl_complex f_envelope(gsl_complex p, const Params *params)
{
double m = params->m;
gsl_complex env = gsl_complex_div(
p,
gsl_complex_sqrt(gsl_complex_add_real(gsl_complex_mul(p,p), m*m)));
if (params->smear)
{
gsl_complex sp = gsl_complex_mul_real(p, params->sigma);
env = gsl_complex_mul(env, gsl_complex_exp(gsl_complex_negative(gsl_complex_mul(sp, sp))));
}
return env;
}
gsl_complex theta30(gsl_complex q)
{
int n=0;
gsl_complex accum = gsl_complex_rect(0.5,0.0);
gsl_complex q2 = gsl_complex_mul(q,q);
gsl_complex nextm = gsl_complex_mul(q,q2);
gsl_complex qpower = q;
while ((gsl_complex_abs(qpower) > 2.0*GSL_DBL_EPSILON) && (n < THETA_ITER_MAX)) {
accum = gsl_complex_add(accum, qpower);
qpower = gsl_complex_mul(qpower, nextm);
nextm = gsl_complex_mul(nextm, q2);
n++;
}
if (n >= THETA_ITER_MAX)
return(gsl_complex_rect(0.0,0.0));
return gsl_complex_mul_real(accum,2.0);
}
void CModel::FacetHarmonics(int fh, int bw, double r, gsl_complex *coeff){
int i, j, sign;
gsl_complex err;
Triangle_3 tr;
tr = Triangle_3(plist[flist[fh*3+0]],plist[flist[fh*3+1]],plist[flist[fh*3+2]]);
Tetrahedron_3 tetr;
tetr = Tetrahedron_3(Point_3(0.0, 0.0, 0.0),plist[flist[fh*3+0]],plist[flist[fh*3+1]],plist[flist[fh*3+2]]);
if(tetr.is_degenerate()) return;
sign = (tetr.volume()<0 ? -1 : 1);
for(i=0; i<bw; i++){
for(j=0; j<=i; j++){
Integrate(i, j, r, tetr, &coeff[i*bw+j], &err);
coeff[i*bw+j] = gsl_complex_mul_real(coeff[i*bw+j], (double)sign);
}
}
}
void MCPMPCoeffs::GeoUpdate(double seconds) {
for (int i=0;i<2*M();i++) {
gsl_complex v = gsl_vector_complex_get(geoVelocities,i); // expressed in deltalon/s,deltalat/s
gsl_complex p = gsl_vector_complex_get(geoPositions,i); // expressed in lon,lat
gsl_complex np = gsl_complex_add(p,gsl_complex_mul_real(v, seconds));
gsl_vector_complex_set(geoPositions,i,np);
// cout << "node " << i << " position = " << GSL_IMAG(np) << ", " << GSL_REAL(np) << endl;
}
}
void tabulate(FILE *os,
ComplexFunction fun,
void *params,
gsl_complex z0,
gsl_complex z1,
int n)
{
gsl_complex k = gsl_complex_sub(z1, z0);
for (int i = 0; i < n; ++i)
{
double t = (double)i / (n - 1);
gsl_complex z = gsl_complex_add(z0, gsl_complex_mul_real(k, t));
gsl_complex f = fun(z, params);
double abs = gsl_complex_abs(f);
fprintf(os, "%g %g %g %g %g %g %g\n",
t,
GSL_REAL(z), GSL_IMAG(z),
GSL_REAL(f), GSL_IMAG(f), abs, -abs);
}
}
//go through all sets of Bethe rapidities and calculate g1 for all identical sets. return value is sum of all these terms.
gsl_complex exact_integrationDE(double orteins, double ortzwei, double** kEp_plusminus, int anzahl_sets, double** coeffoverlap)
{
//variables to make loop easily readable, could delete from final version
double c, Energie, Energieprime, normierung, normierungprime;
double k[N];
double kprime[N];//corresponds to primed Bethe rapidity set in papers
gsl_complex overlap, overlapprime, integral;
GSL_SET_COMPLEX(&integral, 0.0, 0.0);//sum of all values, technically no needed but good for quick check of initial shape of g1
int zaehler_integrale = 0;//counter of total sets of integrals
double Nminusone_fak = 1.0;//(N-1) factorial, see definition of integrals on restricted spatial domain
for(int j=1; j<=(N-1); j++)
Nminusone_fak = Nminusone_fak * ((double) j);
for(int zaehler_eigenstate = 0 ; zaehler_eigenstate < anzahl_sets; zaehler_eigenstate++){//loop over all Bethe rapidity sets
c = kEp_plusminus[zaehler_eigenstate][0];//interaction strength
for(int bb=0; bb<N; bb++)
k[bb]=kEp_plusminus[zaehler_eigenstate][bb+1];//Bethe rapidities
Energie = kEp_plusminus[zaehler_eigenstate][N+1];//energy
normierung=kEp_plusminus[zaehler_eigenstate][N+6];//norm
GSL_SET_COMPLEX(&overlap, coeffoverlap[zaehler_eigenstate][0], coeffoverlap[zaehler_eigenstate][1]);//overlap of set with initial state
//calculate g1_DE for this Bethe set
gsl_complex integralwert = integraleigenfunction(k, k, c, normierung, normierung, orteins, ortzwei);
integralwert = gsl_complex_mul_real(integralwert, (Nminusone_fak*Laenge));//integral evaluated in Rp only -> missing factor of (N-1)!. Laenge (=system length): definition of g1 has prefactor of N!/(n*(N-1)!) = Laenge
integral = gsl_complex_add(integral, gsl_complex_mul(gsl_complex_mul(overlap, gsl_complex_conjugate(overlap)), integralwert));
}//end for loop zaehler_eigenstate
return integral;
};
/* NOTE: Assumes z is in fundamental parallelogram */
void wP_and_prime(gsl_complex z, gsl_complex tau, const gsl_complex *g, gsl_complex *p, gsl_complex *pp)
{
int N = 6; /* Enough iterations for good P, not so good P' */
int i;
gsl_complex z0;
gsl_complex z02;
gsl_complex pout, ppout;
gsl_complex ppsolve;
z = near_origin(z,tau);
z0 = gsl_complex_div_real(z,(double)(1 << N));
z02 = gsl_complex_mul(z0,z0);
/* Laurent expansion: P \approx 1/z^2 + (g2/20)z^2 + (g3/28) z^4 */
pout = gsl_complex_add(gsl_complex_inverse(z02),
gsl_complex_add(gsl_complex_mul(z02,gsl_complex_mul_real(g[0],0.05)),
gsl_complex_mul(gsl_complex_mul(z02,z02),gsl_complex_mul_real(g[1],_CONST_1_28))));
/* Laurent expansion: P' \approx -2/z^3 + g2/10z + g3/7 z^3 */
ppout = gsl_complex_add(gsl_complex_mul_real(gsl_complex_inverse(gsl_complex_mul(z0,z02)),-2.0),
gsl_complex_add(gsl_complex_mul(z0,gsl_complex_mul_real(g[0],0.1)),
gsl_complex_mul(gsl_complex_mul(z0,z02),gsl_complex_mul_real(g[1],_CONST_1_7))));
for (i=0;i<N;i++) {
P_and_Pprime_doubler(&pout, &ppout, g);
}
/* At this point ppout is a decent but not great approximation of P'(z) */
/* Instead of using it directly, we use it as a guide for which square root of */
/* (4P^3 - g2 P - g3) should be selected. */
ppsolve = gsl_complex_sqrt(
gsl_complex_sub(
gsl_complex_mul_real(gsl_complex_mul(pout,gsl_complex_mul(pout,pout)),4.0),
gsl_complex_add(gsl_complex_mul(g[0],pout),g[1])
)
);
*p = pout;
if (gsl_complex_abs(gsl_complex_sub(ppsolve,ppout)) < gsl_complex_abs(gsl_complex_add(ppsolve,ppout)))
*pp = ppsolve;
else
*pp = gsl_complex_negative(ppsolve);
}
/*
computes the svd of a complex matrix. Missing in gsl.
*/
int
svd(gsl_matrix_complex *A, gsl_matrix_complex *V, gsl_vector *S)
{
int n = A->size1;
gsl_eigen_hermv_workspace *gsl_work = gsl_eigen_hermv_alloc(n);
gsl_matrix_complex *Asq = gsl_matrix_complex_alloc(n, n);
gsl_complex zero = gsl_complex_rect(0., 0.);
gsl_complex one = gsl_complex_rect(1., 0.);
gsl_vector *e = gsl_vector_alloc(n);
gsl_matrix_complex *U = gsl_matrix_complex_alloc(n, n);
gsl_blas_zgemm(CblasNoTrans, CblasConjTrans, one, A, A, zero, Asq);
gsl_eigen_hermv(Asq, e, U, gsl_work);
gsl_eigen_hermv_sort(e, U, GSL_EIGEN_SORT_VAL_DESC);
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, A, A, zero, Asq);
gsl_eigen_hermv(Asq, e, V, gsl_work);
gsl_eigen_hermv_sort(e, V, GSL_EIGEN_SORT_VAL_DESC);
gsl_blas_zgemm(CblasNoTrans, CblasNoTrans, one, A, V, zero, Asq);
gsl_blas_zgemm(CblasConjTrans, CblasNoTrans, one, U, Asq, zero, A);
for(int i=0; i<n; i++){
gsl_complex x = gsl_matrix_complex_get(A, i, i);
double phase = gsl_complex_arg(gsl_complex_mul_real(x, 1./sqrt(e->data[i])));
gsl_vector_complex_view U_col = gsl_matrix_complex_column(U, i);
gsl_vector_complex_scale(&U_col.vector, gsl_complex_polar(1., phase));
gsl_vector_set(S, i, sqrt(gsl_vector_get(e, i)));
}
gsl_matrix_complex_memcpy(A, U);
gsl_vector_free(e);
gsl_matrix_complex_free(U);
gsl_matrix_complex_free(Asq);
gsl_eigen_hermv_free(gsl_work);
return 0;
}
/******************************************************************************
* calc_A()
* This function calcs the A's for a given theta.
*
* Parameters
* ---------
*
* Returns
* -------
*
* Notes
* -----
* This function assumes that the X[j] and g[j] values have already
* been calculated (see calc_X())
*
* Note: X[j] = Ar[j]/Ai[j]
* And we can derive:
*
* Ai[j] = phase*Ai[j+1]*t[j+1] / ( 1 + phase^2 * X[j] * r[j+1])
* Ar[j] = Ai[j]*X[j]
*
* where Ar[j] and Ai[j] are the field amplitudes within layer j at
* the j/j-1 interface.
*
* For the top layer Ai[nlayer-1] = 1. ie everything is referenced to
* unit intensity (Io=|Ai|^2) within the top layer. Therefore Ar[0] = X[0].
*
* Given the known values for the top layer we can procede to calculate each Ai and Ar
* value starting at the top.
*
* For the base layer X[0] = 0, ie Ar[0] = 0
*
* The values of r[j+1] and t[j+1] are the reflection and transmission coefficients
* for the j+1/j interface, respectively, and calculated from:
*
* r[j+1] = (g[j+1]-g[j])/(g[j+1]+g[j])
* t[j+1] = 2*g[j+1]/(g[j+1] + g[j]) = 1 + r[j+1]
*
* This function also includes an interfacial roughness term mult into
* the reflection coefficient for the j+1/j interface:
*
* r[j+1] = r[j+1]*exp(-1.0(q*sig[j+1])^2)
*
* Note we include roughness in the t calc using the below:
* t[j+1] = 1 + r[j+1]*exp(-1.0(q*sig[j+1])^2)
*
* Therefore as r-> 0, t-> 1. This is only done if calc_params[10] > 0.
* Otherwise t is calc explicitley from the g's
*
* The phase term accounts for the phase shift and attentuation of the field
* traversing the j layer (ie from the j+1/j interface to the j/j-1 interface),
* ie the Ai[j] and Ar[j] are the field amplitudes at the j/j-1 interface:
*
* phase = exp( -i*k*d[j] * g[j])
*
* Note if j == 0 then the phase for layer j is 0.0, and X[0] = 0
* ie in the infinitley thick base layer we assumer the is no reflected
* field (Ar[0] = 0.0) and we are calculating the the field amplitude at the
* top of layer 0 rather than the bottom of layer 0.
*
*
* Note: double check how doing the phase calc below, is that the best way??
* e.g. could we use:
* phase = gsl_complex_exp( gsl_complex_mul_real(g1,-1.0*k*d[j]));
* instead of
* phase = gsl_complex_exp( gsl_complex_mul(phase,g1));
*
*
******************************************************************************/
int calc_A(double theta, ref_model *ref, angle_calc *ang_c, layer_calc *lay_c){
int i, j, idx;
double cos_sqr_thet, k, q, dw;
double *d, *sig;
gsl_complex g1, g2, num, den, r, t, Ai_2, Ar_2, Ai_1, Ar_1, X1, phase, phase_sqr;
//gsl_complex n1, n2;
// convenience vars
cos_sqr_thet = square(cos(theta*M_PI/180.));
k = ref->k;
q = 2.0*k*sin((theta*M_PI/180.));
d = ref->d;
sig = ref->sigma;
// start at top
idx = ref->nlayer - 1;
// get g for upper layer, ie air/vaccum slab
// ie del ~ bet ~ 0.
// n = 1 - del -i*bet ~ 1
// g2 = sqrt( n^2 - cos(theta)^2 )
//GSL_REAL(n2) = 1.0 - lay_c->del[idx];
//GSL_IMAG(n2) = -1.0*lay_c->bet[idx];
//g2 = gsl_complex_sqrt( gsl_complex_sub_real(gsl_complex_mul(n2, n2), cos_sqr_thet) );
GSL_SET_COMPLEX(&g2,ang_c->Re_g[idx],ang_c->Im_g[idx]);
// for the top (j=nlayer-1) layer, Ai =1.0
// therefore Ar = Ai*X = X
// store these in A arrays
ang_c->Re_Ai[idx] = GSL_REAL(Ai_2) = 1.0;
ang_c->Im_Ai[idx] = GSL_IMAG(Ai_2) = 0.0;
ang_c->Re_Ar[idx] = GSL_REAL(Ar_2) = ang_c->Re_X[idx];
ang_c->Im_Ar[idx] = GSL_IMAG(Ar_2) = ang_c->Im_X[idx];
// loop over all layers, start at top - 1
// ie loop from j = nlayer-2 --> j = 0
// note j is lower layer in the r and t calcs
// therefore we are considering the j+1/j interface
// i is the interface number, ie which interface
// are the r's and t's calc for
i = idx - 1;
for ( j = idx - 1; j > -1 ; j--){
// calc g and phase for lower layer
// n = 1 - del -i*bet
// g1 = sqrt( n^2 - cos(theta)^2 )
//GSL_REAL(n1) = 1.0 - xpar->del[j];
//GSL_IMAG(n1) = -1.0 * xpar->bet[j];
//g1 = gsl_complex_sqrt( gsl_complex_sub_real(gsl_complex_mul(n1, n1), cos_sqr_thet) );
GSL_SET_COMPLEX(&g1,ang_c->Re_g[j],ang_c->Im_g[j]);
//calc phase and attenuation
// phase = exp( -i*k*d[j] * g1)
// phase_sqr = (phase)^2
if (j == 0){
GSL_REAL(phase) = 1.0;
GSL_IMAG(phase) = 0.0;
GSL_REAL(phase_sqr) = 1.0;
GSL_IMAG(phase_sqr) = 0.0;
} else {
GSL_REAL(phase) = 0.0;
GSL_IMAG(phase) = -1.0*k*d[j];
phase = gsl_complex_exp( gsl_complex_mul(phase,g1));
GSL_REAL(phase_sqr) = 0.0;
GSL_IMAG(phase_sqr) = -2.0*k*d[j];
phase_sqr = gsl_complex_exp( gsl_complex_mul(phase_sqr,g1));
}
// calc r for upper layer
// r = (g2-g1)/(g2+g1)
GSL_SET_COMPLEX(&num,0.0,0.0);
GSL_SET_COMPLEX(&den,0.0,0.0);
num = gsl_complex_sub(g2,g1);
den = gsl_complex_add(g2,g1);
r = gsl_complex_div(num,den);
// include simple dw type roughness
// r = r*exp(-1.0(q*sig)^2)
if (ref->sigma[j+1] > 0.0){
//dw = exp(-1.0*square(q*ref->sigma[j+1]));
dw = exp(-1.0*square(q*ref->sigma[i]));
r = gsl_complex_mul_real(r,dw);
}
// calc t for upper layer
// t = 2*g2/(g2 + g1)
if (ref->calc_params[10] == 0.0){
GSL_SET_COMPLEX(&num,0.0,0.0);
num = gsl_complex_mul_real(g2, 2.0);
t = gsl_complex_div(num,den);
} else {
// note as as r->0, t->1
// ie t = 1+r, so we could just calc t from r?
t = gsl_complex_add_real(r,1.0);
}
// calc Ai_1 and Ar_1
// these are field mag in the lower slab (layer j)
// at the bottom of the slab, relative to Ai in the top layer (j=nlayer-1)
// Ai_1 = phase*Ai_2*t / ( 1 + phase^2 * X1 * r)
// Ar_1 = Ai_1*X1
GSL_REAL(X1) = ang_c->Re_X[j];
GSL_IMAG(X1) = ang_c->Im_X[j];
GSL_SET_COMPLEX(&num,0.0,0.0);
GSL_SET_COMPLEX(&den,0.0,0.0);
num = gsl_complex_mul(t,gsl_complex_mul(Ai_2,phase));
den = gsl_complex_add_real(gsl_complex_mul(phase_sqr,gsl_complex_mul(X1,r)),1.0);
Ai_1 = gsl_complex_div(num,den);
if (fabs(GSL_REAL(Ai_1)) < 1.0e-12){
GSL_REAL(Ai_1) = 0.0;
}
if (fabs(GSL_IMAG(Ai_1)) < 1.0e-12){
GSL_IMAG(Ai_1) = 0.0;
}
Ar_1 = gsl_complex_mul(Ai_1,X1);
//store results
ang_c->Re_Ai[j] = GSL_REAL(Ai_1);
ang_c->Im_Ai[j] = GSL_IMAG(Ai_1);
ang_c->Re_Ar[j] = GSL_REAL(Ar_1);
ang_c->Im_Ar[j] = GSL_IMAG(Ar_1);
// this is the field intensity at the bottom of layer j
// except for layer j = 0, this is the intensity at the top
// of the base layer (bc of how phase is calc above)
// use bottom layer as top for next time through
GSL_REAL(Ai_2) = GSL_REAL(Ai_1);
GSL_IMAG(Ai_2) = GSL_IMAG(Ai_1);
GSL_REAL(Ar_2) = GSL_REAL(Ar_1);
GSL_IMAG(Ar_2) = GSL_IMAG(Ar_1);
// do the same for g's
GSL_REAL(g2) = GSL_REAL(g1);
GSL_IMAG(g2) = GSL_IMAG(g1);
// increment interface number
i--;
}
return (SUCCESS);
}
double Calculator::getIntensity(double Q)
{
std::complex<double> cppf1, cppf2;
gsl_complex alpha, beta;
gsl_complex gslf1, gslf2;
int s;
double avFactor;
cppf1 = m_sf1->F(0.0, 0.0, Q, m_energy);
cppf2 = m_sf2->F(0.0, 0.0, Q, m_energy);
gslf1 = gsl_complex_rect(cppf1.real(), cppf1.imag());
gslf2 = gsl_complex_rect(cppf2.real(), cppf2.imag());
avFactor = exp(-2.0 / m_N);
alpha = gsl_complex_rect (1.0, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*set vector F (scattering factors)*/
gsl_vector_complex_set(F, 0, gslf1);
gsl_vector_complex_set(F, 1, gslf2);
/*set vector conj(F) (scattering factors)*/
gsl_vector_complex_set(Fconj, 0, gsl_complex_conjugate(gslf1));
gsl_vector_complex_set(Fconj, 1, gsl_complex_conjugate(gslf2));
/*set exp matrix*/
setMatrixExp(m_Exp, Q);
/*find W = P * Exp * Ps * conj(F) vector:*/
/* (1) W = alpha * Ps * conj(F) + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, W);
/*printf("W(1):\n");
gsl_vector_complex_fprintf (stdout, W, "%g");*/
/* (2) W = alpha * Exp * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Exp, W, beta, tmp_vec);
/*printf("W(2):\n");
gsl_vector_complex_fprintf (stdout, tmp_vec, "%g");*/
/* (3) W = alpha * P * tmp_vec + beta * W */
gsl_blas_zgemv (CblasNoTrans, alpha, m_P, tmp_vec, beta, W);
/*Find J0 = F.(Ps * conj(F)) */
gsl_blas_zgemv (CblasNoTrans, alpha, m_Ps, Fconj, beta, tmp_vec);
gsl_blas_zdotu (F, tmp_vec, &J0);
/*alpha = exp(-2 / N)*/
alpha = gsl_complex_rect (avFactor, 0.0);
beta = gsl_complex_rect (0.0, 0.0);
/*find T matrix: T = alpha * P * exp + beta * T*/
gsl_blas_zgemm (CblasNoTrans, CblasNoTrans, alpha, m_P, m_Exp, beta, T);
/*printf("T:\n");
gsl_matrix_complex_fprintf (stdout, T, "%g");*/
/*Find Jns = F. (G * W) */
/*tmp_mat = I */
gsl_matrix_complex_set_identity (tmp_mat);
/*tmp_mat = I - T */
gsl_matrix_complex_sub (tmp_mat, T);
/*LU decomposition*/
gsl_linalg_complex_LU_decomp(tmp_mat, perm, &s);
/*calculate product G * W = (I - T)^(-1) W directly using LU decomposition*/
gsl_linalg_complex_LU_solve (tmp_mat, perm, W, tmp_vec);
/*calculate F.(G * W)*/
gsl_blas_zdotu (F, tmp_vec, &Jns);
/*Find Js = F.(G^2 * (I - T^N) * W) however, this term should be negligible*/
/*result = N *(2 * Jns + J0) - Js */
alpha = gsl_complex_mul_real (Jns, 2.0 * avFactor);
alpha = gsl_complex_add (alpha, J0);
return m_N * m_I0 * GSL_REAL(alpha) * getPLGfactor(getTheta(Q)) + m_Ibg;
}
gsl_complex gsl_complex_log10(gsl_complex a)
{ /* z = log10(a) */
return gsl_complex_mul_real(gsl_complex_log(a), 1 / log(10.));
}
void distribuzione_luce(grano* g){
int i;
double eta, h, fi, C, S;
tilacoide* tilacoide_figlio;
gsl_matrix* L_1 = gsl_matrix_alloc(2, 2);
gsl_matrix* L_2 = gsl_matrix_alloc(2, 2);
gsl_matrix* L_3 = gsl_matrix_alloc(2, 2);
gsl_matrix* L = gsl_matrix_alloc(2, 2);
// calcolo della matrice L
// itero sui tilacoidi
// primo stroma
// carico dati nella matrice L_1
tilacoide_figlio = g->tilacoidi_figli;//[0];
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_1, 0, 0, C);
gsl_matrix_set(L_1, 0, 1, -S/eta);
gsl_matrix_set(L_1, 1, 0, eta*S);
gsl_matrix_set(L_1, 1, 1, C);
// itero dal secondo strato in poi
for(i = 0; i < g->N; i++) {
tilacoide_figlio = g->tilacoidi_figli +i;// [i];
// MEMEBRANA
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// LUMEN
eta = in.n_lu * in.k_onda;
h = tilacoide_figlio->lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// MEMEBRANA
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
// stroma
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto L_3 <- L_1 x L_2
gsl_matrix_set(L_3, 0, 0, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 0, 1, gsl_matrix_get(L_1, 0, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
gsl_matrix_set(L_3, 1, 0, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 0) + gsl_matrix_get(L_1, 1, 1) * gsl_matrix_get(L_2, 1, 0));
gsl_matrix_set(L_3, 1, 1, gsl_matrix_get(L_1, 1, 0) * gsl_matrix_get(L_2, 0, 1) + gsl_matrix_get(L_1, 0, 1) * gsl_matrix_get(L_2, 1, 1));
// L_1 <- L_3
gsl_matrix_memcpy (L_1, L_3);
}
// L <- L_3 - L CALCOLATA
gsl_matrix_memcpy (L, L_3);
// calcolo di A_n ampiezza del campo rifratto nell'ultimo mezzo
double eta_1, eta_n;
eta_1 = eta_n = in.n_st*in.k_onda;
double c11 = gsl_matrix_get(L, 0, 0);
double c12 = gsl_matrix_get(L, 0, 1);
double c21 = gsl_matrix_get(L, 1, 0);
double c22 = gsl_matrix_get(L, 1, 1);
//gsl_complex A_n = gsl_complex_rect(0, 0);
gsl_complex A_n = gsl_complex_div(gsl_complex_rect(2* eta_1 * in.A_1, 0),
gsl_complex_rect(eta_1 * c11+ eta_n * c22, eta_1 * eta_n * c12 - c21));
// output - cacolo intensita nelle membrane (a ritroso)
gsl_complex v_2[2];
gsl_complex v_1[2];
// primo passo, calcolo v_n, corrisponde allo stroma
v_2[0] = A_n;
v_2[1] = gsl_complex_mul_real(A_n, eta_n);
// calcolo v_{n-1}, corrisponde alla membrana
v_1[0] = v_2[0];
v_1[1] = v_2[1];
gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
g->tilacoidi_figli[(g->N-1)].me2->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// calcolo ultimo lumen
eta = in.n_lu * in.k_onda;
//h = g->tilacoidi_figli[(g->N-1)]->lu->dim;
h = g->tilacoidi_figli[(g->N-1)].lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// penultima membrana
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
//g->tilacoidi_figli[(g->N-1)]->me1->I_luce = intensita(A, B);
g->tilacoidi_figli[(g->N-1)].me1->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// su tutti i tilacoidi
for(i = g->N-2; i >= 0; i--) {
tilacoide_figlio = g->tilacoidi_figli+i;//[i];
// stroma
eta = in.n_st * in.k_onda;
h = tilacoide_figlio->st_succ->dim;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
tilacoide_figlio->me2->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// calcolo ultimo lumen
eta = in.n_lu * in.k_onda;
h = tilacoide_figlio->lu->dim;
fi = in.n_lu * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L, 0, 0, C);
gsl_matrix_set(L, 0, 1, -S/eta);
gsl_matrix_set(L, 1, 0, eta*S);
gsl_matrix_set(L, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
v_2[0] = v_1[0];
v_2[1] = v_1[1];
// penultima membrana
eta = in.n_me * in.k_onda;
h = in.D_me;
fi = in.n_me * in.k_onda * h;
C = cos(fi);
S = sin(fi);
gsl_matrix_set(L_2, 0, 0, C);
gsl_matrix_set(L_2, 0, 1, -S/eta);
gsl_matrix_set(L_2, 1, 0, eta*S);
gsl_matrix_set(L_2, 1, 1, C);
// prodotto v_1 <- L x v_2
v_1[0] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 0, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 0, 1)));
v_1[1] = gsl_complex_add(gsl_complex_mul_real(v_2[0], gsl_matrix_get(L, 1, 0)), gsl_complex_mul_real(v_2[1], gsl_matrix_get(L_1, 1, 1)));
//gsl_complex P, Q;
P = v_1[0];
Q = v_1[1];
//gsl_complex A, B; // ampiezze del campo ottico
eta = in.n_me * in.k_onda;
A = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, -eta)), 2);
B = gsl_complex_div_real(gsl_complex_add(P, gsl_complex_div_real(Q, eta)), 2);
// A e B determinano il campo
// calcolo dell'intensita media
tilacoide_figlio->me1->I_luce = intensita(A, B);
v_2[0] = v_1[0];
v_2[1] = v_1[1];
}
// libera memoria matrici
gsl_matrix_free(L_1);
gsl_matrix_free(L_2);
gsl_matrix_free(L_3);
gsl_matrix_free(L);
}
complex&
complex::operator*=(const double& a)
{
_complex = gsl_complex_mul_real(_complex,a);
return *this;
}
complex complex::operator*(const double& a) const
{
gsl_complex rl = gsl_complex_mul_real(_complex,a);
return complex(rl);
}
void Spectrometer::countAmplitudes_bulk_B(Medium &Osrodek, QString DataName, QProgressBar *Progress, QTextBrowser *Browser, double kx, double ky, double w, int polarisation, double x_lenght, double y_lenght, double precision) {
double a=Osrodek.itsBasis.getLatticeConstant();
int RecVec=itsRecVectors;
int dimension=3*(2*RecVec+1)*(2*RecVec+1);
std::ofstream plik;
DataName="results/amplitudes/"+ DataName + ".dat";
QByteArray bytes = DataName.toAscii();
const char * CDataName = bytes.data();
plik.open(CDataName);
//inicjalizacje wektorów i macierzy
gsl_matrix *gamma=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *V=gsl_matrix_calloc(dimension, dimension);
gsl_vector *S=gsl_vector_calloc(dimension);
gsl_vector *work=gsl_vector_calloc(dimension);
//gamma dla Podłoża
/*
S - numeruje transformaty tensora sprężystoci i gestosci
i - numeruje wiersze macierzy
j - numeruje kolumny macierzy
*/
for(int Nx=-RecVec, i=0, S=0; Nx<=RecVec; Nx++) {
for(int Ny=-RecVec; Ny<=RecVec; Ny++, i=i+3) {
for(int Nx_prim=-RecVec, j=0; Nx_prim<=RecVec; Nx_prim++) {
for(int Ny_prim=-RecVec; Ny_prim<=RecVec; Ny_prim++, j=j+3, S++) {
double Elasticity[6][6];
itsRecBasisSubstance[S].getElasticity(Elasticity);
double Density=itsRecBasisSubstance[S].getDensity();
double gx=2*M_PI*Nx/a;
double gy=2*M_PI*Ny/a;
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
gsl_matrix_set(gamma, i, j, Elasticity[0][0]*(kx+gx)*(kx+gx_prim)+Elasticity[3][3]*(ky+gy)*(ky+gy_prim)-Density*w*w);
gsl_matrix_set(gamma, i+1, j, Elasticity[0][1]*(kx+gx_prim)*(ky+gy)+Elasticity[3][3]*(ky+gy_prim)*(kx+gx));
gsl_matrix_set(gamma, i, j+1, Elasticity[0][1]*(ky+gy_prim)*(kx+gx)+Elasticity[3][3]*(kx+gx_prim)*(ky+gy));
gsl_matrix_set(gamma, i+1, j+1, Elasticity[0][0]*(ky+gy_prim)*(ky+gy)+Elasticity[3][3]*(kx+gx_prim)*(kx+gx)-Density*w*w);
gsl_matrix_set(gamma, i+2, j+2, Elasticity[3][3]*(ky+gy_prim)*(ky+gy)+Elasticity[3][3]*(kx+gx_prim)*(kx+gx)-Density*w*w);
}
}
}
}
//rozwiązanie układu równań
gsl_linalg_SV_decomp(gamma, V, S, work);
gsl_complex u;
double Gx, Gy;
if (polarisation==3) {
gsl_complex ux, uy, uz;
for(double x=0; x < x_lenght; x=x+precision) {
for(double y=0; y < y_lenght; y=y+precision) {
ux = gsl_complex_rect(0, 0);
uy = gsl_complex_rect(0, 0);
uz = gsl_complex_rect(0, 0);
//pasek postepu
int postep=int(100*x/x_lenght);
Progress->setValue(postep);
Progress->update();
QApplication::processEvents();
for (int Nx=-RecVec, i=0; Nx <= RecVec; Nx++) {
for (int Ny=-RecVec; Ny <= RecVec; Ny++, i=i+3) {
Gx=2*M_PI*Nx/a;
Gy=2*M_PI*Ny/a;
double Ax = gsl_matrix_get(V, i, dimension-1);
double Ay = gsl_matrix_get(V, i+1, dimension-1);
double Az = gsl_matrix_get(V, i+2, dimension-1);
gsl_complex expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
gsl_complex exp1 = gsl_complex_exp(expin1);
gsl_complex multiply = gsl_complex_mul_real(exp1, Ax);
ux = gsl_complex_add(ux, multiply);
expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
exp1 = gsl_complex_exp(expin1);
multiply = gsl_complex_mul_real(exp1, Ay);
uy = gsl_complex_add(uy, multiply);
expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
exp1 = gsl_complex_exp(expin1);
multiply = gsl_complex_mul_real(exp1, Az);
uz = gsl_complex_add(uz, multiply);
}
}
double U = sqrt(gsl_complex_abs(ux)*gsl_complex_abs(ux)+gsl_complex_abs(uy)*gsl_complex_abs(uy)+gsl_complex_abs(uz)*gsl_complex_abs(uz));
//zapisanie wartości do pliku
QString nazwa = Osrodek.itsBasis.getFillingSubstance().getName();
if(nazwa=="Air")
{
double rad=Osrodek.itsBasis.getRadius();
if(sqrt(x*x+y*y) > rad && sqrt((a-x)*(a-x)+y*y) > rad && sqrt((a-x)*(a-x)+(a-y)*(a-y)) > rad && sqrt((a-y)*(a-y)+x*x) > rad)
{
plik << x << "\t" << y << "\t" << U << "\n";
}
} else {
plik << x << "\t" << y << "\t" << U << "\n";
}
}
plik << "\n";
}
} else if (polarisation==4) {
gsl_complex uxx, uxy, uxz, uyx, uyy, uyz, uzx, uzy, uzz;
double Uxx, Uxy, Uxz, Uyx, Uyy, Uyz, Uzx, Uzy, Uzz;
for(double x=0; x < x_lenght; x=x+precision) {
for(double y=0; y < y_lenght; y=y+precision) {
uxx = gsl_complex_rect(0, 0);
uxy = gsl_complex_rect(0, 0);
uxz = gsl_complex_rect(0, 0);
uyx = gsl_complex_rect(0, 0);
uyy = gsl_complex_rect(0, 0);
uyz = gsl_complex_rect(0, 0);
uzx = gsl_complex_rect(0, 0);
uzy = gsl_complex_rect(0, 0);
uzz = gsl_complex_rect(0, 0);
double rad=Osrodek.itsBasis.getRadius();
double Ela[6][6];
if(sqrt(x*x+y*y) > rad && sqrt((a-x)*(a-x)+y*y) > rad && sqrt((a-x)*(a-x)+(a-y)*(a-y)) > rad && sqrt((a-y)*(a-y)+x*x) > rad)
{
Osrodek.itsBasis.getSubstance().getElasticity(Ela);
} else {
Osrodek.itsBasis.getFillingSubstance().getElasticity(Ela);
}
//pasek postepu
int postep=int(100*x/x_lenght);
Progress->setValue(postep);
Progress->update();
QApplication::processEvents();
for (int Nx=-RecVec, i=0; Nx <= RecVec; Nx++) {
for (int Ny=-RecVec; Ny <= RecVec; Ny++, i=i+3) {
Gx=2*M_PI*Nx/a;
Gy=2*M_PI*Ny/a;
double Ax = gsl_matrix_get(V, i, dimension-1);
double Ay = gsl_matrix_get(V, i+1, dimension-1);
double Az = gsl_matrix_get(V, i+2, dimension-1);
gsl_complex expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
gsl_complex exp1 = gsl_complex_exp(expin1);
gsl_complex multiply = gsl_complex_mul_real(exp1, Ax);
//uxx
gsl_complex multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), kx+Gx));
uxx = gsl_complex_add(uxx, multidiff);
//uxy
multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), ky+Gy));
uxy = gsl_complex_add(uxy, multidiff);
expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
exp1 = gsl_complex_exp(expin1);
//uy
multiply = gsl_complex_mul_real(exp1, Ay);
//uyx
multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), kx+Gx));
uyx = gsl_complex_add(uyx, multidiff);
//uyy
multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), ky+Gy));
uyy = gsl_complex_add(uyy, multidiff);
expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
exp1 = gsl_complex_exp(expin1);
multiply = gsl_complex_mul_real(exp1, Az);
//uzx
multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), kx+Gx));
uzx = gsl_complex_add(uzx, multidiff);
//uzy
multidiff = gsl_complex_mul(multiply, gsl_complex_mul_real(gsl_complex_rect(0,1), ky+Gy));
uzy = gsl_complex_add(uzy, multidiff);
}
}
Uxx=gsl_complex_abs(uxx);
Uxy=gsl_complex_abs(uxy);
Uxz=gsl_complex_abs(uxz);
Uyx=gsl_complex_abs(uyx);
Uyy=gsl_complex_abs(uyy);
Uyz=gsl_complex_abs(uyz);
Uzx=gsl_complex_abs(uzx);
Uzy=gsl_complex_abs(uzy);
Uzz=gsl_complex_abs(uzz);
double U = Ela[0][0]*(Uxx*Uxx+Uyy*Uyy+Uzz*Uzz)+2*Ela[0][1]*(Uxx*Uyy+Uxx*Uzz+Uyy*Uzz)+0.25*Ela[3][3]*((Uyz+Uzy)*(Uyz+Uzy)+(Uxz+Uzx)*(Uxz+Uzx)+(Uxy+Uyx)*(Uxy+Uyx));
//zapisanie wartości do pliku
QString nazwa = Osrodek.itsBasis.getFillingSubstance().getName();
if(nazwa=="Air")
{
double rad=Osrodek.itsBasis.getRadius();
if(sqrt(x*x+y*y) > rad && sqrt((a-x)*(a-x)+y*y) > rad && sqrt((a-x)*(a-x)+(a-y)*(a-y)) > rad && sqrt((a-y)*(a-y)+x*x) > rad)
{
plik << x << "\t" << y << "\t" << U << "\n";
}
} else {
plik << x << "\t" << y << "\t" << U << "\n";
}
}
plik << "\n";
}
} else {
for(double x=0; x < x_lenght; x=x+precision) {
for(double y=0; y < y_lenght; y=y+precision) {
u = gsl_complex_rect(0, 0);
//pasek postepu
int postep=int(100*x/x_lenght);
Progress->setValue(postep);
Progress->update();
QApplication::processEvents();
for (int Nx=-RecVec, i=0; Nx <= RecVec; Nx++) {
for (int Ny=-RecVec; Ny <= RecVec; Ny++, i=i+3) {
Gx=2*M_PI*Nx/a;
Gy=2*M_PI*Ny/a;
double A = gsl_matrix_get(V, i+polarisation, dimension-1);
gsl_complex expin1 = gsl_complex_rect(0, (kx+Gx)*x+(ky+Gy)*y);
gsl_complex exp1 = gsl_complex_exp(expin1);
gsl_complex multiply = gsl_complex_mul_real(exp1, A);
u = gsl_complex_add(u, multiply);
}
}
double U = gsl_complex_abs(u);
//zapisanie wartości do pliku
plik << x << "\t" << y << "\t" << U << "\n";
}
plik << "\n";
}
}
plik.close();
gsl_matrix_free(gamma);
gsl_matrix_free(V);
gsl_vector_free(S);
gsl_vector_free(work);
}
void Spectrometer::countDispersion_BS(Medium &Osrodek, QString DataName, QProgressBar *Progress, int factor) {
//lsfgerhla
double a=Osrodek.itsBasis.getLatticeConstant();
double thickness=Osrodek.itsStructure.getThickness();
int RecVec=itsRecVectors;
int k_prec=itsK_Precision;
double wi=itsFrequencies[0];
double w_prec=itsFrequencies[1];
double wf=itsFrequencies[2];
int half=3*(2*RecVec+1)*(2*RecVec+1);
int dimension=6*(2*RecVec+1)*(2*RecVec+1);
int EigValStrNumber=6*(2*RecVec+1)*(2*RecVec+1);
int EigValNumber=9*(2*RecVec+1)*(2*RecVec+1);
std::ofstream plik;
DataName="results/"+ DataName + ".dat";
QByteArray bytes = DataName.toAscii();
const char * CDataName = bytes.data();
plik.open(CDataName);
//inicjalizacje wektorów i macierzy
gsl_matrix *gammaA=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaB=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaC=gsl_matrix_calloc(dimension, dimension);
gsl_matrix *gammaD=gsl_matrix_calloc(dimension, dimension);
gsl_eigen_genv_workspace *wspce=gsl_eigen_genv_alloc(dimension);
gsl_eigen_genv_workspace *wspce2=gsl_eigen_genv_alloc(dimension);
gsl_vector_complex *StrAlpha =gsl_vector_complex_alloc(dimension);
gsl_vector *StrBeta = gsl_vector_alloc(dimension);
gsl_matrix_complex *StrEigenVec=gsl_matrix_complex_calloc(dimension, dimension);
gsl_vector_complex *BAlpha =gsl_vector_complex_alloc(dimension);
gsl_vector *BBeta = gsl_vector_alloc(dimension);
gsl_matrix_complex *BasisEigenVec=gsl_matrix_complex_calloc(dimension, dimension);
gsl_matrix_complex *ChosenVectors = gsl_matrix_complex_calloc(half, EigValNumber);
gsl_vector_complex *ChosenValues = gsl_vector_complex_calloc(EigValNumber);
gsl_matrix_complex *Boundaries=gsl_matrix_complex_calloc(EigValNumber, EigValNumber);
double kx, ky, krokx, kroky, boundary_x, boundary_y;
double k_zred, k_zred0;
double krok = M_PI/(k_prec*a);
for (int droga=0; droga<3; droga++) {
//int droga = 1;
if (droga==0) //droga M->Gamma
{
kx=-M_PI/a;
krokx=krok;
boundary_x=0;
ky=-M_PI/a;
kroky=krok;
boundary_y=0;
k_zred0=-1*sqrt(pow(kx/(2*M_PI/a), 2)+pow(ky/(2*M_PI/a), 2));
}
else if (droga==1)
{
kx=0; //droga Gamma->X
krokx=krok;
boundary_x=M_PI/a;
ky=0;
kroky=0;
boundary_y=0;
k_zred0=sqrt(2)/2;
//k_zred0=0;
}
else if (droga==2)
{
kx=M_PI/a; //Droga X->M
krokx=0;
boundary_x=M_PI/a;
ky=0;
kroky=krok;
boundary_y=M_PI/a;
k_zred0=sqrt(2)/2;
}
//petla dla wektorów falowych
for (; kx <= boundary_x && ky <= boundary_y; kx=kx+krokx, ky=ky+kroky)
{
if (droga==0) {
k_zred = abs(k_zred0 + sqrt( pow(kx/(2*M_PI/a), 2)+pow(ky/(2*M_PI/a), 2)));
} else {
k_zred = k_zred0 + kx/(2*M_PI/a) + ky/(2*M_PI/a);
}
int postep=int(100*k_zred/1.7);
Progress->setValue(postep);
Progress->update();
QApplication::processEvents();
//pętla dla częstości w
for (double w=wi; w<wf; w=w+w_prec)
{
gsl_matrix_complex_set_all(Boundaries, gsl_complex_rect (0,0)); //ustawienie wartosci wyznacznika na 0
gsl_matrix_set_all(gammaA, 0);
gsl_matrix_set_all(gammaB, 0);
gsl_matrix_set_all(gammaC, 0);
gsl_matrix_set_all(gammaD, 0);
gsl_vector_complex_set_all(StrAlpha, gsl_complex_rect (0,0));
gsl_vector_set_all(BBeta, 0);
gsl_vector_complex_set_all(BAlpha, gsl_complex_rect (0,0));
gsl_vector_set_all(StrBeta, 0);
gsl_matrix_complex_set_all(BasisEigenVec, gsl_complex_rect (0,0));
gsl_matrix_complex_set_all(StrEigenVec, gsl_complex_rect (0,0));
gsl_matrix_complex_set_all(ChosenVectors, gsl_complex_rect (0,0));
gsl_vector_complex_set_all(ChosenValues, gsl_complex_rect (0,0));
//gammaA,B dla struktury
//gammaA,B dla struktury
/*
S - numeruje transformaty tensora sprężystoci i gestosci
i - numeruje wiersze macierzy
j - numeruje kolumny macierzy
half - druga polowa macierzy
*/
for(int Nx=-RecVec, i=0, S=0; Nx<=RecVec; Nx++) {
for(int Ny=-RecVec; Ny<=RecVec; Ny++, i=i+3) {
for(int Nx_prim=-RecVec, j=0; Nx_prim<=RecVec; Nx_prim++) {
for(int Ny_prim=-RecVec; Ny_prim<=RecVec; Ny_prim++, j=j+3, S++) {
double Elasticity[6][6];
itsRecStructureSubstance[S].getElasticity(Elasticity);
double Density=itsRecStructureSubstance[S].getDensity();
double gx=2*M_PI*Nx/a;
double gy=2*M_PI*Ny/a;
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
gsl_matrix_set(gammaA, i, j, Elasticity[3][3]);
gsl_matrix_set(gammaA, i+1, j+1, Elasticity[3][3]);
gsl_matrix_set(gammaA, i+2, j+2, Elasticity[0][0]);
gsl_matrix_set(gammaB, i+2, j, -Elasticity[0][1]*(kx+gx_prim)-Elasticity[3][3]*(kx+gx));
gsl_matrix_set(gammaB, i+2, j+1, -Elasticity[0][1]*(ky+gy_prim)-Elasticity[3][3]*(ky+gy));
gsl_matrix_set(gammaB, i, j+2, -Elasticity[0][1]*(kx+gx)-Elasticity[3][3]*(kx+gx_prim));
gsl_matrix_set(gammaB, i+1, j+2, -Elasticity[0][1]*(ky+gy)-Elasticity[3][3]*(ky+gy_prim));
gsl_matrix_set(gammaB, i, j+half, -Elasticity[0][0]*(kx+gx)*(kx+gx_prim)-Elasticity[3][3]*(ky+gy)*(ky+gy_prim)+Density*w*w);
gsl_matrix_set(gammaB, i+1, j+half, -Elasticity[0][1]*(kx+gx_prim)*(ky+gy)-Elasticity[3][3]*(ky+gy_prim)*(kx+gx));
gsl_matrix_set(gammaB, i, j+half+1, -Elasticity[0][1]*(ky+gy_prim)*(kx+gx)-Elasticity[3][3]*(kx+gx_prim)*(ky+gy));
gsl_matrix_set(gammaB, i+1, j+half+1, -Elasticity[0][0]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
gsl_matrix_set(gammaB, i+2, j+half+2, -Elasticity[3][3]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
if (i==j) {
gsl_matrix_set(gammaA, i+half, j+half, 1);
gsl_matrix_set(gammaA, i+half+1, j+half+1, 1);
gsl_matrix_set(gammaA, i+half+2, j+half+2, 1);
gsl_matrix_set(gammaB, i+half, j, 1);
gsl_matrix_set(gammaB, i+half+1, j+1, 1);
gsl_matrix_set(gammaB, i+half+2, j+2, 1);
}
}
}
}
}
//rozwiazanie zagadnienienia własnego
gsl_eigen_genv(gammaB, gammaA, StrAlpha, StrBeta, StrEigenVec, wspce);
//gammaC,D dla Podłoża
for(int Nx=-RecVec, i=0, S=0; Nx<=RecVec; Nx++) {
for(int Ny=-RecVec; Ny<=RecVec; Ny++, i=i+3) {
for(int Nx_prim=-RecVec, j=0; Nx_prim<=RecVec; Nx_prim++) {
for(int Ny_prim=-RecVec; Ny_prim<=RecVec; Ny_prim++, j=j+3, S++) {
double Elasticity[6][6];
itsRecBasisSubstance[S].getElasticity(Elasticity);
double Density=itsRecBasisSubstance[S].getDensity();
double gx=2*M_PI*Nx/a;
double gy=2*M_PI*Ny/a;
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
gsl_matrix_set(gammaC, i, j, Elasticity[3][3]);
gsl_matrix_set(gammaC, i+1, j+1, Elasticity[3][3]);
gsl_matrix_set(gammaC, i+2, j+2, Elasticity[0][0]);
gsl_matrix_set(gammaD, i+2, j, -Elasticity[0][1]*(kx+gx_prim)-Elasticity[3][3]*(kx+gx));
gsl_matrix_set(gammaD, i+2, j+1, -Elasticity[0][1]*(ky+gy_prim)-Elasticity[3][3]*(ky+gy));
gsl_matrix_set(gammaD, i, j+2, -Elasticity[0][1]*(kx+gx)-Elasticity[3][3]*(kx+gx_prim));
gsl_matrix_set(gammaD, i+1, j+2, -Elasticity[0][1]*(ky+gy)-Elasticity[3][3]*(ky+gy_prim));
gsl_matrix_set(gammaD, i, j+half, -Elasticity[0][0]*(kx+gx)*(kx+gx_prim)-Elasticity[3][3]*(ky+gy)*(ky+gy_prim)+Density*w*w);
gsl_matrix_set(gammaD, i+1, j+half, -Elasticity[0][1]*(kx+gx_prim)*(ky+gy)-Elasticity[3][3]*(ky+gy_prim)*(kx+gx));
gsl_matrix_set(gammaD, i, j+half+1, -Elasticity[0][1]*(ky+gy_prim)*(kx+gx)-Elasticity[3][3]*(kx+gx_prim)*(ky+gy));
gsl_matrix_set(gammaD, i+1, j+half+1, -Elasticity[0][0]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
gsl_matrix_set(gammaD, i+2, j+half+2, -Elasticity[3][3]*(ky+gy_prim)*(ky+gy)-Elasticity[3][3]*(kx+gx_prim)*(kx+gx)+Density*w*w);
if (i==j) {
gsl_matrix_set(gammaC, i+half, j+half, 1);
gsl_matrix_set(gammaC, i+half+1, j+half+1, 1);
gsl_matrix_set(gammaC, i+half+2, j+half+2, 1);
gsl_matrix_set(gammaD, i+half, j, 1);
gsl_matrix_set(gammaD, i+half+1, j+1, 1);
gsl_matrix_set(gammaD, i+half+2, j+2, 1);
}
}
}
}
}
//rozwiazanie zagadnienienia własnego
gsl_eigen_genv(gammaD, gammaC, BAlpha, BBeta, BasisEigenVec, wspce2);
double imagL, realL; //części Re i Im wartości własnych
int n=0;
for (int i = 0; i<dimension; i++)
{
//przepisanie wartości i wektorów własnych struktury do macierzy Chosen*
gsl_complex StrValue;
StrValue= gsl_complex_div_real(gsl_vector_complex_get(StrAlpha, i), gsl_vector_get(StrBeta,i));
gsl_vector_complex_set(ChosenValues, i, StrValue);
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, i, gsl_matrix_complex_get(StrEigenVec, j, i));
}
//wybieranie odpowiednich wartości i wektorów własnych dla podłoża i przepisanie do macierzy Chosen*
gsl_complex BValue;
BValue= gsl_complex_div_real(gsl_vector_complex_get(BAlpha, i), gsl_vector_get(BBeta,i));
imagL=GSL_IMAG(BValue);
realL=GSL_REAL(BValue);
if (imagL > 0.00001 && n+EigValStrNumber<EigValNumber) //warunek na wartości własne && żeby nie było ich więcej niż połowa
{
gsl_vector_complex_set(ChosenValues, n+EigValStrNumber, BValue); //wybranie wartości własnej
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, n+EigValStrNumber, gsl_complex_mul_real(gsl_matrix_complex_get(BasisEigenVec, j, i), -1)); //wybranie drugiej połowy wektora własnego
}
n++;
}
}
if (n+EigValStrNumber<EigValNumber)
{
for (int i = 0; i<dimension; i++)
{
gsl_complex BValue;
BValue= gsl_complex_div_real(gsl_vector_complex_get(BAlpha, i), gsl_vector_get(BBeta,i));
imagL=GSL_IMAG(BValue);
realL=GSL_REAL(BValue);
if (imagL < 0.00001 && imagL > -0.00001 && realL < -0.00001 && n+EigValStrNumber<EigValNumber) //warunek na wartości własne && żeby nie było ich więcej niż połowa
{
gsl_vector_complex_set(ChosenValues, n+EigValStrNumber, BValue); //wybranie wartości własnej
for (int j = half, m=0; j < dimension; j++, m++)
{
gsl_matrix_complex_set(ChosenVectors, m, n+EigValStrNumber, gsl_complex_mul_real(gsl_matrix_complex_get(BasisEigenVec, j, i), -1)); //wybranie drugiej połowy wektora własnego
}
n++;
}
}
}
//wyznacznik warunków brzegowych - konstrukcja
/*
S, S' - numerujš transformaty tensora sprężystoci
i - numeruje wektory własne A w pętli dla G
j - numeruje warunki brzegowe dla kolejnych wektorow odwrotnych G
k - numeruje wektory własne A w pętli dla G'
L - numeruje wartoci własne
*/
for (int Nx=-RecVec, S=0, S_prim=0, i=0, j=0; Nx <= RecVec; Nx++) {
for (int Ny=-RecVec; Ny <= RecVec; Ny++, j=j+9, i=i+3) {
for (int L=0; L < EigValNumber; L++) {
S_prim = S;
for (int Nx_prim=-RecVec, k=0; Nx_prim <= RecVec; Nx_prim++) {
for (int Ny_prim=-RecVec; Ny_prim <= RecVec; Ny_prim++, S_prim++, k=k+3) {
double StrElasticity[6][6];
itsRecStructureSubstance[S_prim].getElasticity(StrElasticity);
double BasisElasticity[6][6];
itsRecBasisSubstance[S_prim].getElasticity(BasisElasticity);
double gx_prim=2*M_PI*Nx_prim/a;
double gy_prim=2*M_PI*Ny_prim/a;
if (L < EigValStrNumber)
{
//eksponens
gsl_complex exponent = gsl_complex_polar(exp(GSL_IMAG(gsl_vector_complex_get(ChosenValues, L))*thickness), -1*GSL_REAL(gsl_vector_complex_get(ChosenValues, L))*thickness);
//warunki zerowania się naprężenia na powierzchni
gsl_complex w1 = gsl_complex_mul_real(exponent, StrElasticity[3][3]);
gsl_complex w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
gsl_complex w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
gsl_complex BCjL = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w3), w1), gsl_matrix_complex_get(Boundaries, j, L));
gsl_matrix_complex_set(Boundaries, j, L, BCjL);
w1 = gsl_complex_mul_real(exponent, StrElasticity[3][3]);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w3), w1), gsl_matrix_complex_get(Boundaries, j+1, L));
gsl_matrix_complex_set(Boundaries, j+1, L, BCjL);
w1 = gsl_complex_mul_real(exponent, StrElasticity[0][0]);
gsl_complex w11 = gsl_complex_mul_real(exponent, StrElasticity[0][1]);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
gsl_complex w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
gsl_complex w4 = gsl_complex_add(gsl_complex_mul(gsl_complex_add(w2, w22), w11), gsl_complex_mul(w3, w1));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+2, L));
gsl_matrix_complex_set(Boundaries, j+2, L, BCjL);
//warunki równości naprężeń na granicy ośrodków - część dla struktury
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), StrElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+3, L));
gsl_matrix_complex_set(Boundaries, j+3, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), StrElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+4, L));
gsl_matrix_complex_set(Boundaries, j+4, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
w4 = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w22), StrElasticity[0][1]), gsl_complex_mul_real(w3, StrElasticity[0][0]));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+5, L));
gsl_matrix_complex_set(Boundaries, j+5, L, BCjL);
} else {
//warunki równości naprężeń na granicy ośrodków - część dla podłoża
gsl_complex w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (kx+gx_prim));
gsl_complex w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k, L));
gsl_complex BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), BasisElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+3, L));
gsl_matrix_complex_set(Boundaries, j+3, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+2, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+1, L));
BCjL = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w3), BasisElasticity[3][3]), gsl_matrix_complex_get(Boundaries, j+4, L));
gsl_matrix_complex_set(Boundaries, j+4, L, BCjL);
w2 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k, L), (kx+gx_prim));
gsl_complex w22 = gsl_complex_mul_real(gsl_matrix_complex_get(ChosenVectors, k+1, L), (ky+gy_prim));
w3 = gsl_complex_mul(gsl_vector_complex_get(ChosenValues, L), gsl_matrix_complex_get(ChosenVectors, k+2, L));
gsl_complex w4 = gsl_complex_add(gsl_complex_mul_real(gsl_complex_add(w2, w22), BasisElasticity[0][1]), gsl_complex_mul_real(w3, BasisElasticity[0][0]));
BCjL = gsl_complex_add(w4, gsl_matrix_complex_get(Boundaries, j+5, L));
gsl_matrix_complex_set(Boundaries, j+5, L, BCjL);
}
}
}
// warunek równości wychyleń na granicy ośrodków
gsl_matrix_complex_set(Boundaries, j+6, L, gsl_matrix_complex_get(ChosenVectors, i, L));
gsl_matrix_complex_set(Boundaries, j+7, L, gsl_matrix_complex_get(ChosenVectors, i+1, L));
gsl_matrix_complex_set(Boundaries, j+8, L, gsl_matrix_complex_get(ChosenVectors, i+2, L));
}
S=S_prim;
}
}
//skalowanie macierzy Boundaries
gsl_complex scale=gsl_complex_rect(pow(10, factor), 0);
gsl_matrix_complex_scale(Boundaries, scale);
//obliczenie wyznacznika z Boundaries
gsl_permutation *Bpermutation = gsl_permutation_alloc(EigValNumber);
int Bsignum;
gsl_linalg_complex_LU_decomp(Boundaries, Bpermutation, &Bsignum);
double DetVal = gsl_linalg_complex_LU_lndet(Boundaries);
//usuwanie NaN
if(DetVal != DetVal) DetVal = 0;
//zapisanie wartości do pliku
plik << k_zred << "\t" << w << "\t" << DetVal << "\n";
}
plik << "\n";
}
}
plik.close();
gsl_matrix_free(gammaA);
gsl_matrix_free(gammaB);
gsl_vector_free(BBeta);
gsl_vector_free(StrBeta);
gsl_matrix_free(gammaC);
gsl_matrix_free(gammaD);
gsl_vector_complex_free(StrAlpha);
gsl_vector_complex_free(BAlpha);
gsl_eigen_genv_free(wspce);
gsl_eigen_genv_free(wspce2);
gsl_matrix_complex_free(Boundaries);
gsl_matrix_complex_free(ChosenVectors);
gsl_vector_complex_free(ChosenValues);
}
void smf_filter_mce( smfFilter *filt, int noinverse, int *status ) {
/* Filter parameters */
double B_1_1;
double B_1_2;
double B_2_1;
double B_2_2;
double CLOCK_PERIOD;
double ROW_DWELL;
double NUM_ROWS=41;
double DELTA_TIME;
double SRATE;
double datechange; /* UTC MJD for change in MCE filter parameters */
AstTimeFrame *tf=NULL; /* time frame for date conversion */
size_t i; /* Loop counter */
if( *status != SAI__OK ) return;
if( !filt ) {
*status = SAI__ERROR;
errRep( FUNC_NAME, "NULL smfFilter supplied.", status );
return;
}
if( filt->ndims != 1 ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": function only generates filters for time-series",
status );
return;
}
if( !filt->fdims[0] ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": 0-length smfFilter supplied.",
status );
return;
}
if( filt->dateobs == VAL__BADD ) {
*status = SAI__ERROR;
errRep( "", FUNC_NAME ": dateobs (date of data to which filter will be "
"applied) is not set - can't determine correct MCE filter "
"parameters.", status );
return;
}
/* If filt->real is NULL, create a complex identity filter first. Similarly,
if the filter is currently only real-valued, add an imaginary part. */
if( !filt->real ) {
smf_filter_ident( filt, 1, status );
if( *status != SAI__OK ) return;
} else if( !filt->imag ) {
filt->imag = astCalloc( filt->fdims[0], sizeof(*filt->imag) );
if( *status != SAI__OK ) return;
filt->isComplex = 1;
}
/* Set up filter parameters */
tf = astTimeFrame( " " );
astSet( tf, "TimeScale=UTC" );
astSet( tf, "TimeOrigin=%s", "2011-06-03T00:00:00" );
datechange = astGetD( tf, "TimeOrigin" );
tf = astAnnul( tf );
if( filt->dateobs > datechange ) {
/* Data taken after 20110603 */
B_1_1 = -1.9712524; /* -2.*32297./2.^15. */
B_1_2 = 0.97253418; /* 2.*15934./2.^15. */
B_2_1 = -1.9337769; /* -2.*31683./2.^15. */
B_2_2 = 0.93505859; /* 2.*15320./2.^15. */
ROW_DWELL = 94.; /* time to dwell at each row (in clocks) */
msgOutiff(MSG__DEBUG, "", FUNC_NAME
": filter for data UTC MJD %lf after %lf", status,
filt->dateobs, datechange );
} else {
/* Older data */
B_1_1 = -1.9587402; /* -2.*32092./2.^15. */
B_1_2 = 0.96130371; /* 2.*15750./2.^15. */
B_2_1 = -1.9066162; /* -2.*31238./2.^15. */
B_2_2 = 0.90911865; /* 2.*14895./2.^15. */
ROW_DWELL = 128.; /* time to dwell at each row (in clocks) */
msgOutiff(MSG__DEBUG, "", FUNC_NAME
": filter for data UTC MJD %lf before %lf", status,
filt->dateobs, datechange );
}
CLOCK_PERIOD = 20E-9; /* 50 MHz clock */
NUM_ROWS = 41.; /* number of rows addressed */
DELTA_TIME = (CLOCK_PERIOD*ROW_DWELL*NUM_ROWS); /* sample length */
SRATE = (1./DELTA_TIME); /* sample rate */
/* Loop over all frequencies in the filter */
for( i=0; i<filt->fdims[0]; i++ ) {
double cos_m_o;
double sin_m_o;
double cos_m_2o;
double sin_m_2o;
double f;
gsl_complex den;
gsl_complex h1_omega;
gsl_complex h2_omega;
gsl_complex h_omega;
gsl_complex num;
gsl_complex temp;
double omega;
f = filt->df[0]*i; /* Frequency at this step */
omega = (f / SRATE)*2*AST__DPI; /* Angular frequency */
cos_m_o = cos(-omega);
sin_m_o = sin(-omega);
cos_m_2o = cos(-2*omega);
sin_m_2o = sin(-2*omega);
/*
h1_omega=(1 + 2*complex(cos_m_o,sin_m_o) + complex(cos_m_2o,sin_m_2o)) /
(1 + b_1_1*complex(cos_m_o,sin_m_o) + b_1_2 * complex(cos_m_2o,sin_m_2o))
*/
/* numerator */
GSL_SET_COMPLEX(&num, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
num = gsl_complex_add( num, gsl_complex_mul_real(temp, 2) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
num = gsl_complex_add( num, temp );
/* denominator */
GSL_SET_COMPLEX(&den, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_1_1) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_1_2) );
/* quotient */
h1_omega = gsl_complex_div( num, den );
/*
h2_omega=(1 + 2*complex(cos_m_o,sin_m_o) + complex(cos_m_2o,sin_m_2o)) /
(1 + b_2_1*complex(cos_m_o,sin_m_o) + b_2_2*complex(cos_m_2o,sin_m_2o))
note: we can re-use numerator from above
*/
/* denominator */
GSL_SET_COMPLEX(&den, 1, 0);
GSL_SET_COMPLEX(&temp, cos_m_o, sin_m_o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_2_1) );
GSL_SET_COMPLEX(&temp, cos_m_2o, sin_m_2o);
den = gsl_complex_add( den, gsl_complex_mul_real(temp,B_2_2) );
/* quotient */
h2_omega = gsl_complex_div( num, den );
/* And finally...
h_omega=h1_omega*h2_omega/2048.
*/
h_omega = gsl_complex_mul( h1_omega, gsl_complex_div_real(h2_omega,2048.) );
/* Normally we are applying the inverse of the filter to remove
its effect from the time-series. */
if( !noinverse ) {
h_omega = gsl_complex_inverse( h_omega );
}
/* Then apply this factor to the filter. */
GSL_SET_COMPLEX( &temp, filt->real[i], filt->imag[i] );
temp = gsl_complex_mul( temp, h_omega );
filt->real[i] = GSL_REAL( temp );
filt->imag[i] = GSL_IMAG( temp );
}
}
void AbsArg(param_ param, abs_info_ *abs_info, gsl_complex *W, double *absW,
double *argW, gsl_complex *complex_rot) {
/*
* In this function, we calculate the abs and arg
* values for every point on the lattice. We also
* find the total and max values for the abs across
* the entire lattice.
*/
int i, j, tmp_int;
gsl_complex complex_I;
double *max_array, tmp;
int max_num_threads;
int L=param.L;
GSL_SET_COMPLEX(&complex_I,0.,1.);
tmp = 0.;
tmp_int = 0;
(*abs_info).max=0.;
#pragma omp parallel
{
/*
* The optimization here creates an array once in the
* main thread, of length equal to the total number
* of threads, and then updates local maxima along
* the individual threads, storing them in the newly
* created array. At the end, the local maxima are
* compared.
*/
#pragma omp master
{
max_num_threads = omp_get_num_threads();
max_array = (double *)calloc(max_num_threads,sizeof(double));
}
int num;
num=omp_get_thread_num();
#pragma omp barrier //this barrier ensures the array
//is visible to all threads
#pragma omp for reduction(+:tmp)
for(i=0; i<L*L; i++) {
absW[i]=gsl_complex_abs(W[i]);
tmp += absW[i];
if(absW[i] > max_array[num])
max_array[num]=absW[i];
argW[i] = gsl_complex_arg(W[i]);
complex_rot[i] = gsl_complex_exp(gsl_complex_mul_real(\
complex_I,(-0.5)*argW[i]));
}
#pragma omp barrier
#pragma omp master
{
for(i=0; i<max_num_threads; i++)
if(max_array[i] > (*abs_info).max)
(*abs_info).max = max_array[i];
free(max_array);
}
} //end parallel construct
(*abs_info).total = tmp;
/*
* Here, we find the total number of
* points considered active according to
* param.p_thresh.
*/
for(j=0; j<param.pr_range; j++) {
tmp_int = 0;
#pragma omp parallel for reduction(+:tmp_int)
for(i=0; i<L*L; i++)
if(absW[i] >= param.pr_thresh[j]*(*abs_info).max)
tmp_int++;
(*abs_info).int_total[j] = tmp_int;
}
}
void SumProduct::accumulateEigenCounts (vguard<vguard<double> >& rootCounts, vguard<vguard<vguard<gsl_complex> > >& eigenCounts, double weight) const {
LogThisAt(8,"Accumulating eigencounts, column " << join(gappedCol,"") << ", weight " << weight << endl);
accumulateRootCounts (rootCounts, weight);
const auto rootNode = columnRoot();
const int A = model.alphabetSize();
vguard<double> U (A), D (A);
vguard<gsl_complex> Ubasis (A), Dbasis (A);
vguard<double> U0 (A), D0 (A);
for (auto node : ungappedRows)
if (node != rootNode) {
LogThisAt(9,"Accumulating eigencounts, column " << join(gappedCol,"") << " node " << tree.seqName(node) << endl);
const TreeNodeIndex parent = tree.parentNode(node);
const TreeNodeIndex sibling = tree.getSibling(node);
for (int cpt = 0; cpt < components(); ++cpt) {
LogThisAt(9,"Accumulating eigencounts, column " << join(gappedCol,"") << " node " << tree.seqName(node) << " component #" << cpt << endl);
const vguard<double>& U0 = F[cpt][node];
for (AlphTok i = 0; i < A; ++i)
D0[i] = G[cpt][parent][i] * E[cpt][sibling][i];
const double maxU0 = *max_element (U0.begin(), U0.end());
const double maxD0 = *max_element (D0.begin(), D0.end());
const double norm = exp (colLogLike - logCptWeight[cpt] - logF[cpt][node] - logG[cpt][parent] - logE[cpt][sibling]) / (maxU0 * maxD0);
// U[b] = U0[b] / maxU0; Ubasis[l] = sum_b U[b] * evecInv[l][b]
for (AlphTok b = 0; b < A; ++b)
U[b] = U0[b] / maxU0;
for (AlphTok l = 0; l < A; ++l) {
Ubasis[l] = gsl_complex_rect (0, 0);
for (AlphTok b = 0; b < A; ++b)
Ubasis[l] = gsl_complex_add
(Ubasis[l],
gsl_complex_mul_real (gsl_matrix_complex_get (eigen.evecInv[cpt], l, b),
U[b]));
}
// D[a] = D0[a] / maxD0; Dbasis[k] = sum_a D[a] * evec[a][k]
for (AlphTok a = 0; a < A; ++a)
D[a] = D0[a] / maxD0;
for (AlphTok k = 0; k < A; ++k) {
Dbasis[k] = gsl_complex_rect (0, 0);
for (AlphTok a = 0; a < A; ++a)
Dbasis[k] = gsl_complex_add
(Dbasis[k],
gsl_complex_mul_real (gsl_matrix_complex_get (eigen.evec[cpt], a, k),
D[a]));
}
// R = evec * evals * evecInv
// exp(RT) = evec * exp(evals T) * evecInv
// count(i,j|a,b,T) = Q / exp(RT)_ab
// where...
// Q = \sum_a \sum_b \int_{t=0}^T D_a exp(Rt)_ai R_ij exp(R(T-t))_jb U_b dt
// = \sum_a \sum_b \int_{t=0}^T D_a (\sum_k evec_ak exp(eval_k t) evecInv_ki) R_ij (\sum_l evec_jl exp(eval_l (T-t)) evecInv_lb) U_b dt
// = \sum_a \sum_b D_a \sum_k evec_ak evecInv_ki R_ij \sum_l evec_jl evecInv_lb U_b \int_{t=0}^T exp(eval_k t) exp(eval_l (T-t)) dt
// = \sum_a \sum_b D_a \sum_k evec_ak evecInv_ki R_ij \sum_l evec_jl evecInv_lb U_b eigenSubCount(k,l,T)
// = R_ij \sum_k evecInv_ki \sum_l evec_jl (\sum_a D_a evec_ak) (\sum_b U_b evecInv_lb) eigenSubCount(k,l,T)
// = R_ij \sum_k evecInv_ki \sum_l evec_jl Dbasis_k Ubasis_l eigenSubCount(k,l,T)
// eigenCounts[k][l] += Dbasis[k] * eigenSub[k][l] * Ubasis[l] / norm
for (AlphTok k = 0; k < A; ++k)
for (AlphTok l = 0; l < A; ++l)
eigenCounts[cpt][k][l] =
gsl_complex_add
(eigenCounts[cpt][k][l],
gsl_complex_mul_real
(gsl_complex_mul
(Dbasis[k],
gsl_complex_mul
(gsl_matrix_complex_get (branchEigenSubCount[cpt][node], k, l),
Ubasis[l])),
weight / norm));
// LogThisAt(9,"colLogLike=" << colLogLike << " logF[cpt][node]=" << logF[cpt][node] << " logG[cpt][parent]=" << logG[cpt][parent] << " logE[cpt][sibling]=" << logE[cpt][sibling] << " maxU0=" << maxU0 << " maxD0=" << maxD0 << endl);
// LogThisAt(8,"Component #" << cpt << " eigencounts matrix (norm=" << norm << "):" << endl << complexMatrixToString(eigenCounts[cpt]) << endl);
}
}
}
int
gsl_eigen_hermv (gsl_matrix_complex * A, gsl_vector * eval,
gsl_matrix_complex * evec,
gsl_eigen_hermv_workspace * w)
{
if (A->size1 != A->size2)
{
GSL_ERROR ("matrix must be square to compute eigenvalues", GSL_ENOTSQR);
}
else if (eval->size != A->size1)
{
GSL_ERROR ("eigenvalue vector must match matrix size", GSL_EBADLEN);
}
else if (evec->size1 != A->size1 || evec->size2 != A->size1)
{
GSL_ERROR ("eigenvector matrix must match matrix size", GSL_EBADLEN);
}
else
{
const size_t N = A->size1;
double *const d = w->d;
double *const sd = w->sd;
size_t a, b;
/* handle special case */
if (N == 1)
{
gsl_complex A00 = gsl_matrix_complex_get (A, 0, 0);
gsl_vector_set (eval, 0, GSL_REAL(A00));
gsl_matrix_complex_set (evec, 0, 0, GSL_COMPLEX_ONE);
return GSL_SUCCESS;
}
/* Transform the matrix into a symmetric tridiagonal form */
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_view sd_vec = gsl_vector_view_array (sd, N - 1);
gsl_vector_complex_view tau_vec = gsl_vector_complex_view_array (w->tau, N-1);
gsl_linalg_hermtd_decomp (A, &tau_vec.vector);
gsl_linalg_hermtd_unpack (A, &tau_vec.vector, evec, &d_vec.vector, &sd_vec.vector);
}
/* Make an initial pass through the tridiagonal decomposition
to remove off-diagonal elements which are effectively zero */
chop_small_elements (N, d, sd);
/* Progressively reduce the matrix until it is diagonal */
b = N - 1;
while (b > 0)
{
if (sd[b - 1] == 0.0 || isnan(sd[b - 1]))
{
b--;
continue;
}
/* Find the largest unreduced block (a,b) starting from b
and working backwards */
a = b - 1;
while (a > 0)
{
if (sd[a - 1] == 0.0)
{
break;
}
a--;
}
{
size_t i;
const size_t n_block = b - a + 1;
double *d_block = d + a;
double *sd_block = sd + a;
double * const gc = w->gc;
double * const gs = w->gs;
/* apply QR reduction with implicit deflation to the
unreduced block */
qrstep (n_block, d_block, sd_block, gc, gs);
/* Apply Givens rotation Gij(c,s) to matrix Q, Q <- Q G */
for (i = 0; i < n_block - 1; i++)
{
const double c = gc[i], s = gs[i];
size_t k;
for (k = 0; k < N; k++)
{
gsl_complex qki = gsl_matrix_complex_get (evec, k, a + i);
gsl_complex qkj = gsl_matrix_complex_get (evec, k, a + i + 1);
/* qki <= qki * c - qkj * s */
/* qkj <= qki * s + qkj * c */
gsl_complex x1 = gsl_complex_mul_real(qki, c);
gsl_complex y1 = gsl_complex_mul_real(qkj, -s);
gsl_complex x2 = gsl_complex_mul_real(qki, s);
gsl_complex y2 = gsl_complex_mul_real(qkj, c);
gsl_complex qqki = gsl_complex_add(x1, y1);
gsl_complex qqkj = gsl_complex_add(x2, y2);
gsl_matrix_complex_set (evec, k, a + i, qqki);
gsl_matrix_complex_set (evec, k, a + i + 1, qqkj);
}
}
/* remove any small off-diagonal elements */
chop_small_elements (n_block, d_block, sd_block);
}
}
{
gsl_vector_view d_vec = gsl_vector_view_array (d, N);
gsl_vector_memcpy (eval, &d_vec.vector);
}
return GSL_SUCCESS;
}
}
int
lls_complex_stdform(gsl_matrix_complex *A, gsl_vector_complex *b,
const gsl_vector *wts, const gsl_vector *L,
lls_complex_workspace *w)
{
const size_t n = A->size1;
const size_t p = A->size2;
if (p != w->p)
{
fprintf(stderr, "lls_complex_stdform: A has wrong size2\n");
return GSL_EBADLEN;
}
else if (n != b->size)
{
fprintf(stderr, "lls_complex_stdform: b has wrong size\n");
return GSL_EBADLEN;
}
else if (wts != NULL && n != wts->size)
{
fprintf(stderr, "lls_complex_stdform: wts has wrong size\n");
return GSL_EBADLEN;
}
else if (L != NULL && p != L->size)
{
fprintf(stderr, "lls_complex_stdform: L has wrong size\n");
return GSL_EBADLEN;
}
else
{
int s = 0;
size_t i;
if (wts != NULL)
{
for (i = 0; i < n; ++i)
{
gsl_vector_complex_view rv = gsl_matrix_complex_row(A, i);
gsl_complex bi = gsl_vector_complex_get(b, i);
double wi = gsl_vector_get(wts, i);
double sqrtwi = sqrt(wi);
gsl_complex val;
GSL_SET_COMPLEX(&val, sqrtwi, 0.0);
/* A <- sqrt(W) A */
gsl_vector_complex_scale(&rv.vector, val);
/* b <- sqrt(W) b */
val = gsl_complex_mul_real(bi, sqrtwi);
gsl_vector_complex_set(b, i, val);
}
}
if (L != NULL)
{
/* A <- sqrt(W) A L^{-1} */
for (i = 0; i < p; ++i)
{
gsl_vector_complex_view cv = gsl_matrix_complex_column(A, i);
double Li = gsl_vector_get(L, i);
gsl_complex val;
if (Li == 0.0)
{
GSL_ERROR("L matrix is singular", GSL_ESING);
}
GSL_SET_COMPLEX(&val, 1.0 / Li, 0.0);
gsl_vector_complex_scale(&cv.vector, val);
}
}
return s;
}
} /* lls_complex_stdform() */
double OneSim(param_ param, FILE *pipe, arr_info_ arr_info_0,
lattice_point_ **nghb, gsl_complex **K, gsl_complex *W,
gsl_complex *CW, gsl_complex *dW, gsl_complex *complex_rot,
double *argW, double *absW, double *rec, double *prec,
pr_max_ *pr_max){
int i;
double t = 0.;
double *p_levl, *r_levl;
abs_info_ abs_info;
arr_info_ arr_info;
pr_ *rW = NULL, *pW = NULL, *eW = NULL;
/*
* Zero-ing the pr_max array
*/
for(i=0;i<param.pr_range;i++){
pr_max[i].rec = 0.;
pr_max[i].prec = 0.;
}
/*
* Need to allocate the int_total array
* of abs_info.
*/
abs_info.int_total = (int *)malloc(param.pr_range*sizeof(int));
arr_info.nghb_N = arr_info_0.nghb_N;
arr_info.r_N = 0;
arr_info.p_N = 0;
arr_info.e_N = 0;
/*
* Clutter needs to be started first
*/
InitZeros(param, CW);
InitAmoeba(param, &arr_info, CW, &rW, &pW, &eW);
InitClutter(param, CW);
/*
* Reset the important arrays before
* generating the real amoeba.
*/
free(rW);
rW = NULL;
free(pW);
pW = NULL;
free(eW);
eW = NULL;
arr_info.r_N = 0;
arr_info.p_N = 0;
arr_info.e_N = 0;
InitZeros(param, W);
InitAmoeba(param, &arr_info, W, &rW, &pW, &eW);
/*
* Reserve memory of the levl arrays
*/
p_levl = (double *)malloc(arr_info.p_N*sizeof(double));
r_levl = (double *)malloc(arr_info.r_N*sizeof(double));
/*
* Check the exclusion zone
*/
ChckExcl(param, arr_info, CW, eW);
/*
* Time to add the clutter to the amoeba
*/
for(i=0;i<param.L*param.L;i++)
if(gsl_complex_abs2(W[i]) < EPS)
W[i] = CW[i];
AbsArg(param, &abs_info, W, absW, argW, complex_rot);
while(t<param.T){
t+=param.dt;
Quiver(param,pipe,absW,argW,abs_info.max,t);
FieldUpdate(param, arr_info, K, W, dW, absW, complex_rot, nghb);
#pragma omp parallel for
for(i=0;i<param.L*param.L;i++)
W[i]=gsl_complex_add(W[i],gsl_complex_mul_real(dW[i],param.dt));
AbsArg(param, &abs_info, W, absW, argW, complex_rot);
FieldRedux(param, W, absW, abs_info);
CalculateRecall(param, rec, arr_info, absW, argW, rW, r_levl);
CalculatePrecision(param, prec, abs_info, arr_info, absW, argW, pW,
p_levl);
/*
* Time to calculate max precision
* and recall for all threshold values.
* We use that to evaluate the performance
* of the current choice of parameters.
*/
for(i=0;i<param.pr_range;i++)
if(rec[i]+prec[i] > pr_max[i].rec + pr_max[i].prec){
pr_max[i].rec = rec[i];
pr_max[i].prec = prec[i];
}
}
free(rW);
free(pW);
free(eW);
free(p_levl);
free(r_levl);
free(abs_info.int_total);
return t;
}
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;
}
/******************************************************************************
* calc_X()
* This function calcs the X's and g's for a given theta.
*
* Parameters
* ---------
*
* Returns
* -------
*
* Notes
* -----
* This function computes
* X[j] = Ar[j]/Ai[j]
* where Ar[j] and Ai[j] are the field amplitdues within layer j at
* the j/j-1 interface. For the base layer X[0] = 0,
* ie there is no reflected field in the substrate. While
* X[nlayers-1] is the field intensity at the top of the multilayer,
* therefore |X[nlayers-1]|^2 = R
*
* The X's are calculated using the optical recursion formlua, starting at the bottom
* where X[0] = 0 and calc X[1], and proceding to calc of X[nlayer-1]:
*
* X[j] = ( r[j] + X[j-1]*phase) / (1 + r[j]*X[j-1]*phase)
*
* The r[j] values are the reflection coefficients for the j/j-1 interface,
* and calculated from:
*
* r[j] = (g[j]-g[j-1])/(g[j]+g[j-1])
*
* This function also includes an interfacial roughness term mult into
* the reflection coefficient for the j/j-1 interface:
*
* r[j] = r[j]*exp(-1.0(q*sig[j])^2)
*
* The phase term accounts for the phase shift and attentuation of the field
* traversing the j-1 layer (ie from the j-1/j-2 interface to the j/j-1 interface)
*
* phase = exp( -i* 2*k*d[j-1] * g[j-1])
*
* Note if j == 1 then the phase for layer j-1 is 0.0,
* ie infinitley thick base layer
*
* Note: g[j] = sqrt( n[j]^2 - cos(theta)^2 )
* where n[j] is the layers index of refraction: n[j] = 1-del[j]-i*bet[j]
* Hence, each layer has a unique g value. We assume here
* that the del[j] and bet[j] have already been calculated
* (see calc_del_bet(), this should be called before this function).
*
*
* Note: double check how doing the phase calc below, is that the best way??
* e.g. could we use:
* phase = gsl_complex_exp( gsl_complex_mul_real(g1,-1.0*k*d[j]));
* instead of
* phase = gsl_complex_exp( gsl_complex_mul(phase,g1));
*
* Note we should move the g and r calc to a new function, possibly calc the
* t values as well and store these so we dont have to recalc in calc_A() (???)
*
******************************************************************************/
int calc_X(double theta, ref_model *ref, angle_calc *ang_c, layer_calc *lay_c){
int i, j;
double cos_sqr_thet, k, q, dw;
double *d, *sig;
gsl_complex g1, g2, num, den, r, X2, X1, n1, n2, phase;
// convenience vars
cos_sqr_thet = square(cos(theta*M_PI/180.));
k = ref->k;
q = 2.0*k*sin((theta*M_PI/180.));
d = ref->d;
sig = ref->sigma;
// start at bottom
// ie interface 0
ang_c->Re_X[0] = GSL_REAL(X1) = 0.0;
ang_c->Im_X[0] = GSL_IMAG(X1) = 0.0;
// calc g for base layer (g[0])
// n = 1 - del -i*bet
// g = sqrt( n^2 - cos(theta)^2 )
GSL_REAL(n1) = 1.0 - lay_c->del[0];
GSL_IMAG(n1) = -1.0*lay_c->bet[0];
g1 = gsl_complex_sqrt( gsl_complex_sub_real(gsl_complex_mul(n1, n1), cos_sqr_thet) );
// store g for base layer
ang_c->Re_g[0] = GSL_REAL(g1);
ang_c->Im_g[0] = GSL_IMAG(g1);
// loop over all layers
// note j is upper layer and i is the interface number
// the loop starts considering the first interface (i=0)
// which is the interface between the base layer (j=0)
// and the first layer (j=1) ie the 1/0 interface
// note there are nlayer-1 interfaces...
i = 0;
for ( j = 1; j < ref->nlayer; j++){
// calc g for upper layer
// n = 1 - del -i*bet
// g2 = sqrt( n^2 - cos(theta)^2 )
GSL_REAL(n2) = 1.0 - lay_c->del[j];
GSL_IMAG(n2) = -1.0 * lay_c->bet[j];
g2 = gsl_complex_sqrt( gsl_complex_sub_real(gsl_complex_mul(n2, n2), cos_sqr_thet) );
// store g for layer j
ang_c->Re_g[j] = GSL_REAL(g2);
ang_c->Im_g[j] = GSL_IMAG(g2);
// calculate r for the j/j-1 interface
// r_j = (g2-g1)/(g2+g1)
//GSL_SET_COMPLEX(&num,0.0,0.0);
//GSL_SET_COMPLEX(&den,0.0,0.0);
//GSL_SET_COMPLEX(&r,0.0,0.0);
num = gsl_complex_sub(g2,g1);
den = gsl_complex_add(g2,g1);
r = gsl_complex_div(num,den);
// calc r including roughness
// simple dw roughness model
// r = r*exp(-1.0(q*sig)^2)
// sigma[i]
if (ref->sigma[j] > 0.0){
//dw = exp(-1.0*square(q*ref->sigma[j]));
dw = exp(-1.0*square(q*ref->sigma[i]));
r = gsl_complex_mul_real(r,dw);
}
//calc phase shift and attentuation for
//field traversing the j-1 layer
//phase = exp( -i* 2*k*d[j-1] * g1)
// if j == 1 then the phase for layer j-1
// is 0.0, ie infinitley thick base layer
if (j == 1){
GSL_REAL(phase) = 0.0;
GSL_IMAG(phase) = 0.0;
} else {
// check here
GSL_REAL(phase) = 0.0;
GSL_IMAG(phase) = -2.0*k*d[j-1];
phase = gsl_complex_exp( gsl_complex_mul(phase,g1));
}
// calc Xj
// X2 = ( r + X1*phase) / (1 + r*X1*phase)
//GSL_SET_COMPLEX(&num,0.0,0.0);
//GSL_SET_COMPLEX(&den,0.0,0.0);
num = gsl_complex_add(r,gsl_complex_mul(X1,phase));
den = gsl_complex_add_real(gsl_complex_mul(r,gsl_complex_mul(X1,phase)), 1.0);
X2 = gsl_complex_div(num,den);
if (fabs(GSL_REAL(X2)) < 1e-10){
GSL_REAL(X2) = 0.0;
}
if (fabs(GSL_IMAG(X2)) < 1e-10){
GSL_IMAG(X2) = 0.0;
}
// store values of Xj
ang_c->Re_X[j] = GSL_REAL(X2);
ang_c->Im_X[j] = GSL_IMAG(X2);
// use top layer as bottom for next time through
GSL_REAL(X1) = GSL_REAL(X2);
GSL_IMAG(X1) = GSL_IMAG(X2);
// do the same for g's
GSL_REAL(g1) = GSL_REAL(g2);
GSL_IMAG(g1) = GSL_IMAG(g2);
//increment the interface number
i++;
}
return (SUCCESS);
}
