gsl_complex gsl_complex_sqrt(gsl_complex a)
{ /* z=sqrt(a) */
gsl_complex z;
if (GSL_REAL(a) == 0.0 && GSL_IMAG(a) == 0.0) {
GSL_SET_COMPLEX(&z, 0, 0);
} else {
double x = fabs(GSL_REAL(a));
double y = fabs(GSL_IMAG(a));
double w;
if (x >= y) {
double t = y / x;
w = sqrt(x) * sqrt(0.5 * (1.0 + sqrt(1.0 + t * t)));
} else {
double t = x / y;
w = sqrt(y) * sqrt(0.5 * (t + sqrt(1.0 + t * t)));
}
if (GSL_REAL(a) >= 0.0) {
double ai = GSL_IMAG(a);
GSL_SET_COMPLEX(&z, w, ai / (2.0 * w));
} else {
double ai = GSL_IMAG(a);
double vi = (ai >= 0) ? w : -w;
GSL_SET_COMPLEX(&z, ai / (2.0 * vi), vi);
}
}
return z;
}
int
gsl_sf_complex_psi_e(
const double x,
const double y,
gsl_sf_result * result_re,
gsl_sf_result * result_im
)
{
if(x >= 0.0)
{
gsl_complex z = gsl_complex_rect(x, y);
return psi_complex_rhp(z, result_re, result_im);
}
else
{
/* reflection formula [Abramowitz+Stegun, 6.3.7] */
gsl_complex z = gsl_complex_rect(x, y);
gsl_complex omz = gsl_complex_rect(1.0 - x, -y);
gsl_complex zpi = gsl_complex_mul_real(z, M_PI);
gsl_complex cotzpi = gsl_complex_cot(zpi);
int ret_val = psi_complex_rhp(omz, result_re, result_im);
if(GSL_IS_REAL(GSL_REAL(cotzpi)) && GSL_IS_REAL(GSL_IMAG(cotzpi)))
{
result_re->val -= M_PI * GSL_REAL(cotzpi);
result_im->val -= M_PI * GSL_IMAG(cotzpi);
return ret_val;
}
else
{
GSL_ERROR("singularity", GSL_EDOM);
}
}
}
//
// we update shadowing and pathloss coefficients for all the links tx -> rx
//
void MCPMPCoeffs::SpatialChannelUpdate() {
for (int i=0; i<_M; i++) { // user i (tx)
for (int ii=0;ii<=i;ii++) { // user ii (rx)
// we are considering the spatial channel tx-rx, so we get the sostheta(j) vector
// and we compute the shadowing coefficient for the position of rx (rx_lon,rx_lat)
gsl_complex txPos = gsl_vector_complex_get(geoPositions,i); // lat,lon
gsl_complex rxPos = gsl_vector_complex_get(geoPositions,ii+_M); // lat,lon
double txPosLat = GSL_REAL(txPos);
double txPosLon = GSL_IMAG(txPos);
double rxPosLat = GSL_REAL(rxPos);
double rxPosLon = GSL_IMAG(rxPos);
double deltaLat = rxPosLat-txPosLat; // ok
double deltaLon = rxPosLon-txPosLon; // be careful around 180E/W
double meanLat = (rxPosLat+txPosLat)/2.0; // be careful around poles
if (deltaLon > 180) // es Lon1 =-179 Lon2=179 D=2
deltaLon -= 360;
if (deltaLon < -180)
deltaLon += 360;
double x= deltaLon * 111111 * gsl_sf_cos(meanLat*M_PI_OVER_180); // cartesian x position around tx (in m)
double y= deltaLat * 111111; // cartesian y position arond tx (in m)
// shadowing i->ii
double shadowdb=0;
for (int j=0; j<SOSN; j++){
double th = gsl_matrix_get(sostheta,i*_M+ii,j);
double fxn = gsl_vector_get(sosfxn,j);
double fyn = gsl_vector_get(sosfyn,j);
shadowdb += sosc * gsl_sf_cos(2.0 * M_PI * ( fxn * x + fyn * y + th));
} // for j
//
// PATHLOSS MODEL
//
double dist = sqrt(x*x+y*y); // metres
double plossdb = mudisp::OkumuraHataCitydB(dist,1500);
//double plossdb = mudisp::OkumuraHataMetrodB(dist,1500);
//cout << "rx[" << i << "] x=" << x << " y=" << y << " ploss="
// << -plossdb << " shadow=" << shadowdb << " dist=" << dist << endl;
//
double cx = mudisp::dbtolin(-0.5 * plossdb + SOSsigma() * shadowdb );
gsl_matrix_set(pathLoss,i,ii,cx);
gsl_matrix_set(pathLoss,ii,i,cx); // it's symmetric !
} // for ii
} // for i
}
gsl_complex gsl_complex_add(gsl_complex a, gsl_complex b)
{ /* z=a+b */
double ar = GSL_REAL(a), ai = GSL_IMAG(a);
double br = GSL_REAL(b), bi = GSL_IMAG(b);
gsl_complex z;
GSL_SET_COMPLEX(&z, ar + br, ai + bi);
return z;
}
gsl_complex gsl_complex_sub(gsl_complex a, gsl_complex b)
{ /* z=a-b */
double ar = GSL_REAL(a), ai = GSL_IMAG(a);
double br = GSL_REAL(b), bi = GSL_IMAG(b);
gsl_complex z;
GSL_SET_COMPLEX(&z, ar - br, ai - bi);
return z;
}
gsl_complex gsl_complex_mul(gsl_complex a, gsl_complex b)
{ /* z=a*b */
double ar = GSL_REAL(a), ai = GSL_IMAG(a);
double br = GSL_REAL(b), bi = GSL_IMAG(b);
gsl_complex z;
GSL_SET_COMPLEX(&z, ar * br - ai * bi, ar * bi + ai * br);
return z;
}
std::ostream& operator<<(std::ostream &os, const complex_spinor & c_spinor){
int i;
int nSitios = c_spinor._numSites;
for(i=0;i<nSitios;i++){
os << "[(" << GSL_REAL(c_spinor.complex_spinor_get(i,UP))<<" + i. "<<GSL_IMAG(c_spinor.complex_spinor_get(i,UP))<<")]"<<std::endl;
os << "[(" << GSL_REAL(c_spinor.complex_spinor_get(i,DOWN))<<" + i. "<<GSL_IMAG(c_spinor.complex_spinor_get(i,DOWN))<<")]"<<std::endl;
}
return os;
}
void
test_eigen_genherm_results (const gsl_matrix_complex * A,
const gsl_matrix_complex * B,
const gsl_vector * eval,
const gsl_matrix_complex * evec,
size_t count,
const char * desc,
const char * desc2)
{
const size_t N = A->size1;
size_t i, j;
gsl_vector_complex * x = gsl_vector_complex_alloc(N);
gsl_vector_complex * y = gsl_vector_complex_alloc(N);
/* check A v = lambda B v */
for (i = 0; i < N; i++)
{
double ei = gsl_vector_get (eval, i);
gsl_vector_complex_const_view vi =
gsl_matrix_complex_const_column(evec, i);
double norm = gsl_blas_dznrm2(&vi.vector);
/* check that eigenvector is normalized */
gsl_test_rel(norm, 1.0, N * GSL_DBL_EPSILON,
"genherm(N=%u,cnt=%u), %s, normalized(%d), %s", N, count,
desc, i, desc2);
/* compute y = A z */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, A, &vi.vector, GSL_COMPLEX_ZERO, y);
/* compute x = B z */
gsl_blas_zgemv (CblasNoTrans, GSL_COMPLEX_ONE, B, &vi.vector, GSL_COMPLEX_ZERO, x);
/* compute x = lambda B z */
gsl_blas_zdscal(ei, x);
/* now test if y = x */
for (j = 0; j < N; j++)
{
gsl_complex xj = gsl_vector_complex_get (x, j);
gsl_complex yj = gsl_vector_complex_get (y, j);
gsl_test_rel(GSL_REAL(yj), GSL_REAL(xj), 1e9 * GSL_DBL_EPSILON,
"genherm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), real, %s", N, count, desc, i, j, desc2);
gsl_test_abs(GSL_IMAG(yj), GSL_IMAG(xj), 1e9 * GSL_DBL_EPSILON,
"genherm(N=%u,cnt=%u), %s, eigenvalue(%d,%d), imag, %s", N, count, desc, i, j, desc2);
}
}
gsl_vector_complex_free(x);
gsl_vector_complex_free(y);
}
void
FUNCTION (test, trap) (size_t stride, size_t N)
{
TYPE (gsl_vector) * vc = FUNCTION (create, vector) (stride, N);
BASE z = {{(ATOMIC)1.2, (ATOMIC)3.4}};
BASE z1 = {{(ATOMIC)4.5, (ATOMIC)6.7}};
size_t j = 0;
status = 0;
FUNCTION (gsl_vector, set) (vc, j - 1, z);
gsl_test (!status,
NAME (gsl_vector) "_set traps index below lower bound");
status = 0;
FUNCTION (gsl_vector, set) (vc, N + 1, z);
gsl_test (!status,
NAME (gsl_vector) "_set traps index above upper bound");
status = 0;
FUNCTION (gsl_vector, set) (vc, N, z);
gsl_test (!status, NAME (gsl_vector) "_set traps index at upper bound");
status = 0;
z1 = FUNCTION (gsl_vector, get) (vc, j - 1);
gsl_test (!status,
NAME (gsl_vector) "_get traps index below lower bound");
gsl_test (GSL_REAL (z1) != 0,
NAME (gsl_vector) "_get returns zero real below lower bound");
gsl_test (GSL_IMAG (z1) != 0,
NAME (gsl_vector) "_get returns zero imag below lower bound");
status = 0;
z1 = FUNCTION (gsl_vector, get) (vc, N + 1);
gsl_test (!status,
NAME (gsl_vector) "_get traps index above upper bound");
gsl_test (GSL_REAL (z1) != 0,
NAME (gsl_vector) "_get returns zero real above upper bound");
gsl_test (GSL_IMAG (z1) != 0,
NAME (gsl_vector) "_get returns zero imag above upper bound");
status = 0;
z1 = FUNCTION (gsl_vector, get) (vc, N);
gsl_test (!status, NAME (gsl_vector) "_get traps index at upper bound");
gsl_test (GSL_REAL (z1) != 0,
NAME (gsl_vector) "_get returns zero real at upper bound");
gsl_test (GSL_IMAG (z1) != 0,
NAME (gsl_vector) "_get returns zero imag at upper bound");
FUNCTION (gsl_vector, free) (vc);
}
void MCPMPCoeffs::GeoRender() {
ostringstream kmltmp;
// kmlobject.seekp(ios_base::beg);
for (int i=0;i<M();i++) { // tx loop
gsl_complex pos = gsl_vector_complex_get(geoPositions,i);
kmltmp.precision(10);
kmltmp << "\t<Placemark>" << endl
<< "\t\t<name>Tx_" << i << "</name>" << endl
<< "\t\t<description>^</description>" << endl
<< "\t\t<styleUrl>#greenIcon</styleUrl>" << endl
<< "\t\t<Point>" << endl
<< "\t\t\t<coordinates>" << GSL_IMAG(pos) << ","
<< GSL_REAL(pos) << ","
<< 0 << "</coordinates>" << endl
<< "\t\t</Point>" << endl
<< "\t</Placemark>" << endl;
}
for (int i=0;i<M();i++) { // rx loop
gsl_complex pos = gsl_vector_complex_get(geoPositions,i+_M);
kmltmp.precision(10);
kmltmp << "\t<Placemark>" << endl
<< "\t\t<name>Rx_" << i << "</name>" << endl
<< "\t\t<description>^</description>" << endl
<< "\t\t<styleUrl>#blueIcon</styleUrl>" << endl
<< "\t\t<Point>" << endl
<< "\t\t\t<coordinates>" << GSL_IMAG(pos) << ","
<< GSL_REAL(pos) << ","
<< 0 << "</coordinates>" << endl
<< "\t\t</Point>" << endl
<< "\t</Placemark>" << endl;
}
ofs.open(GeoFn());
if (! ofs ) {
cerr << BlockName << ": error opening "
<< GeoFn() << endl;
exit(_ERROR_OPEN_FILE_);
}
ofs << kmlhead.str() << kmltmp.str() << kmlheadend.str();
ofs.close();
}
int
main (void)
{
double data[] = { -1.0, 1.0, -1.0, 1.0,
-8.0, 4.0, -2.0, 1.0,
27.0, 9.0, 3.0, 1.0,
64.0, 16.0, 4.0, 1.0 };
gsl_matrix_view m
= gsl_matrix_view_array (data, 4, 4);
gsl_vector_complex *eval = gsl_vector_complex_alloc (4);
gsl_matrix_complex *evec = gsl_matrix_complex_alloc (4, 4);
gsl_eigen_nonsymmv_workspace * w =
gsl_eigen_nonsymmv_alloc (4);
gsl_eigen_nonsymmv (&m.matrix, eval, evec, w);
gsl_eigen_nonsymmv_free (w);
gsl_eigen_nonsymmv_sort (eval, evec,
GSL_EIGEN_SORT_ABS_DESC);
{
int i, j;
for (i = 0; i < 4; i++)
{
gsl_complex eval_i
= gsl_vector_complex_get (eval, i);
gsl_vector_complex_view evec_i
= gsl_matrix_complex_column (evec, i);
printf ("eigenvalue = %g + %gi\n",
GSL_REAL(eval_i), GSL_IMAG(eval_i));
printf ("eigenvector = \n");
for (j = 0; j < 4; ++j)
{
gsl_complex z = gsl_vector_complex_get(&evec_i.vector, j);
printf("%g + %gi\n", GSL_REAL(z), GSL_IMAG(z));
}
}
}
gsl_vector_complex_free(eval);
gsl_matrix_complex_free(evec);
return 0;
}
gsl_complex
gsl_complex_pow_real (gsl_complex a, double b)
{ /* z=a^b */
gsl_complex z;
if (GSL_REAL (a) == 0 && GSL_IMAG (a) == 0)
{
if (b == 0)
{
GSL_SET_COMPLEX (&z, 1, 0);
}
else
{
GSL_SET_COMPLEX (&z, 0, 0);
}
}
else
{
double logr = gsl_complex_logabs (a);
double theta = gsl_complex_arg (a);
double rho = exp (logr * b);
double beta = theta * b;
GSL_SET_COMPLEX (&z, rho * cos (beta), rho * sin (beta));
}
return z;
}
bool VECTOR_ensure_not_complex(CVECTOR *_object)
{
gsl_vector *v;
int size = SIZE(THIS);
int i;
gsl_complex c;
if (!COMPLEX(THIS))
return FALSE;
for (i = 0; i < size; i++)
{
c = gsl_vector_complex_get(CVEC(THIS), i);
if (GSL_IMAG(c) != 0.0)
return TRUE;
}
v = gsl_vector_alloc(size);
for (i = 0; i < size; i++)
gsl_vector_set(v, i, GSL_REAL(gsl_vector_complex_get(CVEC(THIS), i)));
gsl_vector_complex_free(CVEC(THIS));
THIS->vector = v;
THIS->complex = FALSE;
return FALSE;
}
static int
matlab_dlmwrite_complex(FILE * fp, const gsl_matrix_complex * A)
{
const size_t M = A->size1;
const size_t N = A->size2;
size_t i, j;
for (i = 0; i < M; ++i)
{
for (j = 0; j < N; ++j)
{
gsl_complex z = gsl_matrix_complex_get(A, i, j);
double zr = GSL_REAL(z);
double zi = GSL_IMAG(z);
fprintf(fp, "%.12e%s%.12ei%s",
zr,
(zi < 0.0) ? "" : "+",
zi,
(j < N - 1) ? "," : "\n");
}
}
return 0;
}
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
gsl_complex_tan (gsl_complex a)
{ /* z = tan(a) */
double R = GSL_REAL (a), I = GSL_IMAG (a);
gsl_complex z;
if (fabs (I) < 1)
{
double D = pow (cos (R), 2.0) + pow (sinh (I), 2.0);
GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) / D, 0.5 * sinh (2 * I) / D);
}
else
{
double u = exp (-I);
double C = 2 * u / (1 - pow (u, 2.0));
double D = 1 + pow (cos (R), 2.0) * pow (C, 2.0);
double S = pow (C, 2.0);
double T = 1.0 / tanh (I);
GSL_SET_COMPLEX (&z, 0.5 * sin (2 * R) * S / D, T / D);
}
return z;
}
gsl_complex
gsl_complex_add_real (gsl_complex a, double x)
{ /* z=a+x */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a) + x, GSL_IMAG (a));
return z;
}
double gsl_complex_abs2(gsl_complex z)
{ /* return |z|^2 */
double x = GSL_REAL(z);
double y = GSL_IMAG(z);
return (x * x + y * y);
}
gsl_complex
gsl_complex_div_imag (gsl_complex a, double y)
{ /* z=a/(iy) */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_IMAG (a) / y, - GSL_REAL (a) / y);
return z;
}
gsl_complex
gsl_complex_div_real (gsl_complex a, double x)
{ /* z=a/x */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a) / x, GSL_IMAG (a) / x);
return z;
}
gsl_complex
gsl_complex_mul_imag (gsl_complex a, double y)
{ /* z=a*iy */
gsl_complex z;
GSL_SET_COMPLEX (&z, -y * GSL_IMAG (a), y * GSL_REAL (a));
return z;
}
void
gsl_complex_cosh (complex_t const *a, complex_t *res)
{ /* z = cosh(a) */
gnm_float R = GSL_REAL (a), I = GSL_IMAG (a);
complex_init (res, cosh (R) * gnm_cos (I), gnm_sinh (R) * gnm_sin (I));
}
gsl_complex
gsl_complex_sub_imag (gsl_complex a, double y)
{ /* z=a-iy */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a), GSL_IMAG (a) - y);
return z;
}
gsl_complex
gsl_complex_sub_real (gsl_complex a, double x)
{ /* z=a-x */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a) - x, GSL_IMAG (a));
return z;
}
gsl_complex
gsl_complex_add_imag (gsl_complex a, double y)
{ /* z=a+iy */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a), GSL_IMAG (a) + y);
return z;
}
gsl_complex
gsl_complex_conjugate (gsl_complex a)
{ /* z=conj(a) */
gsl_complex z;
GSL_SET_COMPLEX (&z, GSL_REAL (a), -GSL_IMAG (a));
return z;
}
static VALUE rb_gsl_sf_lngamma_complex_e(int argc, VALUE *argv, VALUE obj)
{
gsl_sf_result *lnr, *arg;
gsl_complex *z;
double re, im;
VALUE vlnr, varg;
int status;
switch (argc) {
case 1:
CHECK_COMPLEX(argv[0]);
Data_Get_Struct(argv[0], gsl_complex, z);
re = GSL_REAL(*z);
im = GSL_IMAG(*z);
break;
case 2:
Need_Float(argv[0]); Need_Float(argv[1]);
re = NUM2DBL(argv[0]);
im = NUM2DBL(argv[1]);
default:
rb_raise(rb_eArgError, "wrong number of arguments (%d for 1 or 2)", argc);
}
vlnr = Data_Make_Struct(cgsl_sf_result, gsl_sf_result, 0, free, lnr);
varg = Data_Make_Struct(cgsl_sf_result, gsl_sf_result, 0, free, arg);
status = gsl_sf_lngamma_complex_e(re, im, lnr, arg);
return rb_ary_new3(3, vlnr, varg, INT2FIX(status));
}
gsl_complex
gsl_complex_negative (gsl_complex a)
{ /* z=-a */
gsl_complex z;
GSL_SET_COMPLEX (&z, -GSL_REAL (a), -GSL_IMAG (a));
return z;
}
gsl_complex
gsl_complex_mul_real (gsl_complex a, double x)
{ /* z=a*x */
gsl_complex z;
GSL_SET_COMPLEX (&z, x * GSL_REAL (a), x * GSL_IMAG (a));
return z;
}
void
gsl_complex_inverse (complex_t const *a, complex_t *res)
{ /* z=1/a */
gnm_float s = 1.0 / complex_mod (a);
complex_init (res, (GSL_REAL (a) * s) * s, -(GSL_IMAG (a) * s) * s);
}