/*
* FUNCTION
* Name: entropy_of_state
* Description: Calculate the Von Neumann entropy of state 'rho'
*
*/
double entropy_of_state ( const gsl_vector* rho )
{
double entr = 0 ;
/* Finding the eigenvalues */
gsl_eigen_herm_workspace* rho_ei = gsl_eigen_herm_alloc(2);
gsl_matrix_complex* dens = gsl_matrix_complex_calloc (2,2);
gsl_matrix_complex_set (dens, 0, 0, gsl_complex_rect(1+VECTOR(rho, 3),0));
gsl_matrix_complex_set (dens,0,1,gsl_complex_rect(VECTOR(rho,1),-VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,0,gsl_complex_rect(VECTOR(rho,1),VECTOR(rho,2)));
gsl_matrix_complex_set (dens,1,1,gsl_complex_rect(1-VECTOR(rho,3),0));
gsl_matrix_complex_scale (dens, gsl_complex_rect(0.5,0));
gsl_vector* eigenvalues = gsl_vector_calloc(2) ;
gsl_eigen_herm (dens, eigenvalues, rho_ei) ;
/* Calculating entropy */
double norm = gsl_hypot3( VECTOR(rho,1), VECTOR(rho,2), VECTOR(rho,3) ) ;
if ( gsl_fcmp(norm, 1, 1e-9) > 0 )
entr = 0 ;
else
entr = - (VECTOR(eigenvalues,0)*gsl_sf_log(VECTOR(eigenvalues,0)) +
VECTOR(eigenvalues,1)*gsl_sf_log(VECTOR(eigenvalues,1))) ;
return (entr);
} /* ----- end of function entropy_of_state ----- */
static VALUE rb_gsl_hypot3(VALUE obj, VALUE x, VALUE y, VALUE z)
{
Need_Float(x);
Need_Float(y);
Need_Float(z);
return rb_float_new(gsl_hypot3(NUM2DBL(x), NUM2DBL(y), NUM2DBL(z)));
}
static size_t
swarm_filter_asmvfm(const double thresh, satdata_mag *data)
{
size_t i;
size_t nflag = 0;
for (i = 0; i < data->n; ++i)
{
double F_asm = data->F[i];
double B[3], F_vfm;
B[0] = SATDATA_VEC_X(data->B, i);
B[1] = SATDATA_VEC_Y(data->B, i);
B[2] = SATDATA_VEC_Z(data->B, i);
F_vfm = gsl_hypot3(B[0], B[1], B[2]);
if (fabs(F_asm - F_vfm) > thresh)
{
data->flags[i] |= SATDATA_FLG_INSTERR;
++nflag;
}
}
return nflag;
}
void Particle::NormalizeSpeed(void)
{
//long double scale = (long double) PARTICLE_SPEED/pow((long double)vx*vx + vy*vy + vz*vz, (long double) 0.5);
long double scale = (long double) PARTICLE_SPEED/gsl_hypot3(vx, vy, vz);
vx *= scale;
vy *= scale;
vz *= scale;
}
int
doplot(const satdata_mag *data, mfield_workspace *w)
{
size_t i;
estist_workspace *est_p = estist_alloc(ESTIST_IDX_FILE);
double rms_f = 0.0;
double rms_z = 0.0;
size_t n = 0;
for (i = 0; i < data->n; ++i)
{
double B_ext[4], B_ext_pomme[4];
double r = data->altitude[i] + data->R;
double theta = M_PI / 2.0 - data->latitude[i] * M_PI / 180.0;
double phi = data->longitude[i] * M_PI / 180.0;
double E_st, I_st;
time_t unix_time = satdata_epoch2timet(data->t[i]);
#if 0
estist_get(unix_time, &E_st, &I_st, est_p);
mfield_eval_ext(data->t[i], r, theta, phi, E_st, I_st, B_ext, w);
#endif
B_ext_pomme[0] = SATDATA_VEC_X(data->B_ext, i);
B_ext_pomme[1] = SATDATA_VEC_Y(data->B_ext, i);
B_ext_pomme[2] = SATDATA_VEC_Z(data->B_ext, i);
B_ext_pomme[3] = gsl_hypot3(B_ext_pomme[0], B_ext_pomme[1], B_ext_pomme[2]);
rms_f += pow(B_ext[3] - B_ext_pomme[3], 2.0);
rms_z += pow(B_ext[2] - B_ext_pomme[2], 2.0);
++n;
#if 1
printf("%f %f %f %f %f %f %f\n",
data->altitude[i],
data->latitude[i],
data->longitude[i],
B_ext[3],
B_ext_pomme[3],
B_ext[2],
B_ext_pomme[2]);
#endif
}
rms_f = sqrt(rms_f / n);
rms_z = sqrt(rms_z / n);
fprintf(stderr, "RMS F = %f [nT]\n", rms_f);
fprintf(stderr, "RMS Z = %f [nT]\n", rms_z);
estist_free(est_p);
return 0;
}
/*
* FUNCTION
* Name: entropy_production
* Description:
*
*/
double entropy_production ( const gsl_vector* rho, const gsl_vector* rhoeq,
const gsl_matrix* L )
{
/* l1, l2, l3 */
double l[3] ; unsigned int i, j ;
for ( i = 1 ; i < 3 ; i++ )
{
l[i] = 0 ;
for ( j = 0 ; j < 3 ; j++ )
l[i] += gsl_matrix_get(L,i,j)*VECTOR(rho,j) ;
}
/* L[rho] */
double Lr = 0 ;
for ( i = 1 ; i < 3 ; i++ )
Lr += l[i]*VECTOR(rho,i) ;
/* L[rhoeq] */
double Leq = 0 ;
for ( i = 1 ; i < 3 ; i++ )
Leq += l[i]*VECTOR(rhoeq,i) ;
/* r , req */
double r, req ;
r = req = 0 ;
r = gsl_hypot3(VECTOR(rho,1),VECTOR(rho,2),VECTOR(rho,3)) ;
req = gsl_hypot3(VECTOR(rhoeq,1),VECTOR(rhoeq,2),
VECTOR(rhoeq,3)) ;
/* internal entropy s */
double s ;
if ( r < 1 && req < 1 )
s = -(gsl_sf_log((1+r)/(1-r))*Lr/r -gsl_sf_log((1+req)/(1-req))*Leq/req);
else if ( r < 1 && req >= 0 )
s = -gsl_sf_log((1+r)/(1-r))*Lr/r ;
else
s = 0 ;
return s;
} /* ----- end of function entropy_production ----- */
int
main (void)
{
double y, y_expected;
int e, e_expected;
gsl_ieee_env_setup ();
/* Test for expm1 */
y = gsl_expm1 (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.0)");
y = gsl_expm1 (1e-10);
y_expected = 1.000000000050000000002e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(1e-10)");
y = gsl_expm1 (-1e-10);
y_expected = -9.999999999500000000017e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-1e-10)");
y = gsl_expm1 (0.1);
y_expected = 0.1051709180756476248117078264902;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(0.1)");
y = gsl_expm1 (-0.1);
y_expected = -0.09516258196404042683575094055356;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-0.1)");
y = gsl_expm1 (10.0);
y_expected = 22025.465794806716516957900645284;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(10.0)");
y = gsl_expm1 (-10.0);
y_expected = -0.99995460007023751514846440848444;
gsl_test_rel (y, y_expected, 1e-15, "gsl_expm1(-10.0)");
/* Test for log1p */
y = gsl_log1p (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.0)");
y = gsl_log1p (1e-10);
y_expected = 9.9999999995000000000333333333308e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(1e-10)");
y = gsl_log1p (0.1);
y_expected = 0.095310179804324860043952123280765;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(0.1)");
y = gsl_log1p (10.0);
y_expected = 2.3978952727983705440619435779651;
gsl_test_rel (y, y_expected, 1e-15, "gsl_log1p(10.0)");
/* Test for gsl_hypot */
y = gsl_hypot (0.0, 0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(0.0, 0.0)");
y = gsl_hypot (1e-10, 1e-10);
y_expected = 1.414213562373095048801688e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, 1e-10)");
y = gsl_hypot (1e-38, 1e-38);
y_expected = 1.414213562373095048801688e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-38, 1e-38)");
y = gsl_hypot (1e-10, -1.0);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e-10, -1)");
y = gsl_hypot (-1.0, 1e-10);
y_expected = 1.000000000000000000005;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(-1, 1e-10)");
y = gsl_hypot (1e307, 1e301);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e301)");
y = gsl_hypot (1e301, 1e307);
y_expected = 1.000000000000499999999999e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e301, 1e307)");
y = gsl_hypot (1e307, 1e307);
y_expected = 1.414213562373095048801688e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1e307, 1e307)");
/* Test +-Inf, finite */
y = gsl_hypot (GSL_POSINF, 1.2);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_POSINF, 1.2)");
y = gsl_hypot (GSL_NEGINF, 1.2);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NEGINF, 1.2)");
y = gsl_hypot (1.2, GSL_POSINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_POSINF)");
y = gsl_hypot (1.2, GSL_NEGINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_NEGINF)");
/* Test NaN, finite */
y = gsl_hypot (GSL_NAN, 1.2);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, 1.2)");
y = gsl_hypot (1.2, GSL_NAN);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(1.2, GSL_NAN)");
/* Test NaN, NaN */
y = gsl_hypot (GSL_NAN, GSL_NAN);
y_expected = GSL_NAN;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_NAN)");
/* Test +Inf, NaN */
y = gsl_hypot (GSL_POSINF, GSL_NAN);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_POSINF, GSL_NAN)");
/* Test -Inf, NaN */
y = gsl_hypot (GSL_NEGINF, GSL_NAN);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NEGINF, GSL_NAN)");
/* Test NaN, +Inf */
y = gsl_hypot (GSL_NAN, GSL_POSINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_POSINF)");
/* Test NaN, -Inf */
y = gsl_hypot (GSL_NAN, GSL_NEGINF);
y_expected = GSL_POSINF;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot(GSL_NAN, GSL_NEGINF)");
/* Test for gsl_hypot3 */
y = gsl_hypot3 (0.0, 0.0, 0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(0.0, 0.0, 0.0)");
y = gsl_hypot3 (1e-10, 1e-10, 1e-10);
y_expected = 1.732050807568877293527446e-10;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, 1e-10, 1e-10)");
y = gsl_hypot3 (1e-38, 1e-38, 1e-38);
y_expected = 1.732050807568877293527446e-38;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-38, 1e-38, 1e-38)");
y = gsl_hypot3 (1e-10, 1e-10, -1.0);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, 1e-10, -1)");
y = gsl_hypot3 (1e-10, -1.0, 1e-10);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e-10, -1, 1e-10)");
y = gsl_hypot3 (-1.0, 1e-10, 1e-10);
y_expected = 1.000000000000000000099;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(-1, 1e-10, 1e-10)");
y = gsl_hypot3 (1e307, 1e301, 1e301);
y_expected = 1.0000000000009999999999995e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e301, 1e301)");
y = gsl_hypot3 (1e307, 1e307, 1e307);
y_expected = 1.732050807568877293527446e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e307, 1e307)");
y = gsl_hypot3 (1e307, 1e-307, 1e-307);
y_expected = 1.0e307;
gsl_test_rel (y, y_expected, 1e-15, "gsl_hypot3(1e307, 1e-307, 1e-307)");
/* Test for acosh */
y = gsl_acosh (1.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.0)");
y = gsl_acosh (1.1);
y_expected = 4.435682543851151891329110663525e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1.1)");
y = gsl_acosh (10.0);
y_expected = 2.9932228461263808979126677137742e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(10.0)");
y = gsl_acosh (1e10);
y_expected = 2.3718998110500402149594646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_acosh(1e10)");
/* Test for asinh */
y = gsl_asinh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.0)");
y = gsl_asinh (1e-10);
y_expected = 9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (-1e-10);
y_expected = -9.9999999999999999999833333333346e-11;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e-10)");
y = gsl_asinh (0.1);
y_expected = 9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(0.1)");
y = gsl_asinh (-0.1);
y_expected = -9.983407889920756332730312470477e-2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-0.1)");
y = gsl_asinh (1.0);
y_expected = 8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1.0)");
y = gsl_asinh (-1.0);
y_expected = -8.8137358701954302523260932497979e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1.0)");
y = gsl_asinh (10.0);
y_expected = 2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(10)");
y = gsl_asinh (-10.0);
y_expected = -2.9982229502979697388465955375965e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-10)");
y = gsl_asinh (1e10);
y_expected = 2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(1e10)");
y = gsl_asinh (-1e10);
y_expected = -2.3718998110500402149599646668302e1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_asinh(-1e10)");
/* Test for atanh */
y = gsl_atanh (0.0);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.0)");
y = gsl_atanh (1e-20);
y_expected = 1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(1e-20)");
y = gsl_atanh (-1e-20);
y_expected = -1e-20;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-1e-20)");
y = gsl_atanh (0.1);
y_expected = 1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.1)");
y = gsl_atanh (-0.1);
y_expected = -1.0033534773107558063572655206004e-1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(-0.1)");
y = gsl_atanh (0.9);
y_expected = 1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
y = gsl_atanh (-0.9);
y_expected = -1.4722194895832202300045137159439e0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_atanh(0.9)");
/* Test for pow_int */
y = gsl_pow_2 (-3.14);
y_expected = pow (-3.14, 2.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_2(-3.14)");
y = gsl_pow_3 (-3.14);
y_expected = pow (-3.14, 3.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_3(-3.14)");
y = gsl_pow_4 (-3.14);
y_expected = pow (-3.14, 4.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_4(-3.14)");
y = gsl_pow_5 (-3.14);
y_expected = pow (-3.14, 5.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_5(-3.14)");
y = gsl_pow_6 (-3.14);
y_expected = pow (-3.14, 6.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_6(-3.14)");
y = gsl_pow_7 (-3.14);
y_expected = pow (-3.14, 7.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_7(-3.14)");
y = gsl_pow_8 (-3.14);
y_expected = pow (-3.14, 8.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_8(-3.14)");
y = gsl_pow_9 (-3.14);
y_expected = pow (-3.14, 9.0);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_9(-3.14)");
{
int n;
for (n = -9; n < 10; n++)
{
y = gsl_pow_int (-3.14, n);
y_expected = pow (-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_int(-3.14,%d)", n);
}
}
{
unsigned int n;
for (n = 0; n < 10; n++)
{
y = gsl_pow_uint (-3.14, n);
y_expected = pow (-3.14, n);
gsl_test_rel (y, y_expected, 1e-15, "gsl_pow_uint(-3.14,%d)", n);
}
}
/* Test case for n at INT_MAX, INT_MIN */
{
double u = 1.0000001;
int n = INT_MAX;
y = gsl_pow_int (u, n);
y_expected = pow (u, n);
gsl_test_rel (y, y_expected, 1e-6, "gsl_pow_int(%.7f,%d)", u, n);
n = INT_MIN;
y = gsl_pow_int (u, n);
y_expected = pow (u, n);
gsl_test_rel (y, y_expected, 1e-6, "gsl_pow_int(%.7f,%d)", u, n);
}
/* Test for ldexp */
y = gsl_ldexp (M_PI, -2);
y_expected = M_PI_4;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(pi,-2)");
y = gsl_ldexp (1.0, 2);
y_expected = 4.000000;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(1.0,2)");
y = gsl_ldexp (0.0, 2);
y_expected = 0.0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(0.0,2)");
y = gsl_ldexp (9.999999999999998890e-01, 1024);
y_expected = GSL_DBL_MAX;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp DBL_MAX");
y = gsl_ldexp (1e308, -2000);
y_expected = 8.7098098162172166755761e-295;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(1e308,-2000)");
y = gsl_ldexp (GSL_DBL_MIN, 2000);
y_expected = 2.554675596204441378334779940e294;
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(DBL_MIN,2000)");
/* Test subnormals */
{
int i = 0;
volatile double x = GSL_DBL_MIN;
y_expected = 2.554675596204441378334779940e294;
x /= 2;
while (x > 0)
{
i++ ;
y = gsl_ldexp (x, 2000 + i);
gsl_test_rel (y, y_expected, 1e-15, "gsl_ldexp(DBL_MIN/2**%d,%d)",i,2000+i);
x /= 2;
}
}
/* Test for frexp */
y = gsl_frexp (0.0, &e);
y_expected = 0;
e_expected = 0;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0) exponent");
y = gsl_frexp (M_PI, &e);
y_expected = M_PI_4;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(pi) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(pi) exponent");
y = gsl_frexp (2.0, &e);
y_expected = 0.5;
e_expected = 2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(2.0) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(2.0) exponent");
y = gsl_frexp (1.0 / 4.0, &e);
y_expected = 0.5;
e_expected = -1;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25) exponent");
y = gsl_frexp (1.0 / 4.0 - 4.0 * GSL_DBL_EPSILON, &e);
y_expected = 0.999999999999996447;
e_expected = -2;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(0.25-eps) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(0.25-eps) exponent");
y = gsl_frexp (GSL_DBL_MAX, &e);
y_expected = 9.999999999999998890e-01;
e_expected = 1024;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MAX) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MAX) exponent");
y = gsl_frexp (-GSL_DBL_MAX, &e);
y_expected = -9.999999999999998890e-01;
e_expected = 1024;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(-DBL_MAX) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(-DBL_MAX) exponent");
y = gsl_frexp (GSL_DBL_MIN, &e);
y_expected = 0.5;
e_expected = -1021;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MIN) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MIN) exponent");
y = gsl_frexp (-GSL_DBL_MIN, &e);
y_expected = -0.5;
e_expected = -1021;
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(-DBL_MIN) fraction");
gsl_test_int (e, e_expected, "gsl_frexp(-DBL_MIN) exponent");
/* Test subnormals */
{
int i = 0;
volatile double x = GSL_DBL_MIN;
y_expected = 0.5;
e_expected = -1021;
x /= 2;
while (x > 0)
{
e_expected--;
i++ ;
y = gsl_frexp (x, &e);
gsl_test_rel (y, y_expected, 1e-15, "gsl_frexp(DBL_MIN/2**%d) fraction",i);
gsl_test_int (e, e_expected, "gsl_frexp(DBL_MIN/2**%d) exponent", i);
x /= 2;
}
}
/* Test for approximate floating point comparison */
{
double x, y;
int i;
x = M_PI;
y = 22.0 / 7.0;
/* test the basic function */
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (x, y, tol);
gsl_test_int (res, -(i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", x, y, tol);
}
for (i = 0; i < 10; i++)
{
double tol = pow (10, -i);
int res = gsl_fcmp (y, x, tol);
gsl_test_int (res, (i >= 4), "gsl_fcmp(%.5f,%.5f,%g)", y, x, tol);
}
}
#if HAVE_IEEE_COMPARISONS
/* Test for isinf, isnan, finite */
{
double zero, one, inf, nan;
int s;
zero = 0.0;
one = 1.0;
inf = exp (1.0e10);
nan = inf / inf;
s = gsl_isinf (zero);
gsl_test_int (s, 0, "gsl_isinf(0)");
s = gsl_isinf (one);
gsl_test_int (s, 0, "gsl_isinf(1)");
s = gsl_isinf (inf);
gsl_test_int (s, 1, "gsl_isinf(inf)");
s = gsl_isinf (-inf);
gsl_test_int (s, -1, "gsl_isinf(-inf)");
s = gsl_isinf (nan);
gsl_test_int (s, 0, "gsl_isinf(nan)");
s = gsl_isnan (zero);
gsl_test_int (s, 0, "gsl_isnan(0)");
s = gsl_isnan (one);
gsl_test_int (s, 0, "gsl_isnan(1)");
s = gsl_isnan (inf);
gsl_test_int (s, 0, "gsl_isnan(inf)");
s = gsl_isnan (-inf);
gsl_test_int (s, 0, "gsl_isnan(-inf)");
s = gsl_isnan (nan);
gsl_test_int (s, 1, "gsl_isnan(nan)");
s = gsl_finite (zero);
gsl_test_int (s, 1, "gsl_finite(0)");
s = gsl_finite (one);
gsl_test_int (s, 1, "gsl_finite(1)");
s = gsl_finite (inf);
gsl_test_int (s, 0, "gsl_finite(inf)");
s = gsl_finite (-inf);
gsl_test_int (s, 0, "gsl_finite(-inf)");
s = gsl_finite (nan);
gsl_test_int (s, 0, "gsl_finite(nan)");
}
#endif
{
double x = gsl_fdiv (2.0, 3.0);
gsl_test_rel (x, 2.0 / 3.0, 4 * GSL_DBL_EPSILON, "gsl_fdiv(2,3)");
}
/* Test constants in gsl_math.h */
{
double x = log(M_E);
gsl_test_rel (x, 1.0, 4 * GSL_DBL_EPSILON, "ln(M_E)");
}
{
double x=pow(2.0,M_LOG2E);
gsl_test_rel (x, exp(1.0), 4 * GSL_DBL_EPSILON, "2^M_LOG2E");
}
{
double x=pow(10.0,M_LOG10E);
gsl_test_rel (x, exp(1.0), 4 * GSL_DBL_EPSILON, "10^M_LOG10E");
}
{
double x=pow(M_SQRT2, 2.0);
gsl_test_rel (x, 2.0, 4 * GSL_DBL_EPSILON, "M_SQRT2^2");
}
{
double x=pow(M_SQRT1_2, 2.0);
gsl_test_rel (x, 1.0/2.0, 4 * GSL_DBL_EPSILON, "M_SQRT1_2");
}
{
double x=pow(M_SQRT3, 2.0);
gsl_test_rel (x, 3.0, 4 * GSL_DBL_EPSILON, "M_SQRT3^2");
}
{
double x = M_PI;
gsl_test_rel (x, 3.1415926535897932384626433832795, 4 * GSL_DBL_EPSILON, "M_PI");
}
{
double x = 2 * M_PI_2;
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "2*M_PI_2");
}
{
double x = 4 * M_PI_4;
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "4*M_PI_4");
}
{
double x = pow(M_SQRTPI, 2.0);
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "M_SQRTPI^2");
}
{
double x = pow(M_2_SQRTPI, 2.0);
gsl_test_rel (x, 4/M_PI, 4 * GSL_DBL_EPSILON, "M_SQRTPI^2");
}
{
double x = M_1_PI;
gsl_test_rel (x, 1/M_PI, 4 * GSL_DBL_EPSILON, "M_1_SQRTPI");
}
{
double x = M_2_PI;
gsl_test_rel (x, 2.0/M_PI, 4 * GSL_DBL_EPSILON, "M_2_PI");
}
{
double x = exp(M_LN10);
gsl_test_rel (x, 10, 4 * GSL_DBL_EPSILON, "exp(M_LN10)");
}
{
double x = exp(M_LN2);
gsl_test_rel (x, 2, 4 * GSL_DBL_EPSILON, "exp(M_LN2)");
}
{
double x = exp(M_LNPI);
gsl_test_rel (x, M_PI, 4 * GSL_DBL_EPSILON, "exp(M_LNPI)");
}
{
double x = M_EULER;
gsl_test_rel (x, 0.5772156649015328606065120900824, 4 * GSL_DBL_EPSILON, "M_EULER");
}
exit (gsl_test_summary ());
}
/*
* FUNCTION
* Name: red_evol
* Description:
*
*/
int red_evol ( void* params, const double r[], double time_end, double step,
const gsl_vector* req_red, gsl_matrix* red_m )
{
struct f_params* pars = (struct f_params*) params ;
unsigned int i ; /* counter for the for loops */
/*
*
* evolving the systems
*
*/
double t = 0 ;
/* setting the initial vector */
gsl_vector* init_red = gsl_vector_calloc(4) ;
for ( i = 0 ; i < 4 ; i++ )
gsl_vector_set ( init_red, i, r[i] ) ;
/*
*
* Initializing the system for Redfield dynamics
*
*/
gsl_odeiv2_system red_sys = { generator, jac, 4, (void*) red_m } ;
/* Choosing the step function type: Runge-Kutta-Fehlberg (4,5) */
/* gsl_odeiv2_step* s = gsl_odeiv2_step_alloc ( gsl_odeiv2_step_rkf45 , 4 ) ; */
/* Choosing the step function type: Runge-Kutta Cash-Karp (4,5) */
gsl_odeiv2_step* r_s = gsl_odeiv2_step_alloc ( gsl_odeiv2_step_rkck , 4 ) ;
/* Setting the step control: abserr=1e-9, relerr=1e-3 */
gsl_odeiv2_control* r_c = gsl_odeiv2_control_standard_new ( 1e-9, 1e-3, 1, 1 ) ;
/* Allocating the space for evolution function */
gsl_odeiv2_evolve* r_e = gsl_odeiv2_evolve_alloc ( 4 ) ;
/* opening the files */
FILE* f_red = fopen ( "RED-EVOLUTION.dat", "w" ) ;
FILE* g_red = fopen ( "RED-ENTROPY-PROD.dat", "w" ) ;
FILE* h_red = fopen ( "RED-CURRENT.dat", "w" ) ;
FILE* i_red = fopen ( "RED-ENTROPY.dat", "w" ) ;
/* writing data */
while ( t < t_end )
{
evol ( t, init_red, step, r_e, r_c, r_s, &red_sys ) ;
fprintf ( f_red, "%.2f %.9f %.9f %.9f %.9f\n", t,
VECTOR(init_red,1), VECTOR(init_red,2),
VECTOR(init_red,3),
gsl_hypot3(VECTOR(init_red,1),VECTOR(init_red,2),
VECTOR(init_red,3)) ) ;
fprintf ( g_red, "%.2f %.9f\n",
t, entropy_production( init_red, req_red, red_m )) ;
fprintf ( h_red, "%.2f %.9f\n", t, tot_current(init_red, pars) ) ;
fprintf ( i_red, "%.2f %.9f\n",
t, entropy_of_state(init_red) ) ;
t += step ;
}
/* final entropy */
printf("Final entropy: %g\n", entropy_of_state(init_red) ) ;
/* close the files */
fclose (f_red) ;
fclose (g_red) ;
fclose (h_red) ;
fclose (i_red) ;
/* free memory for evolution */
gsl_odeiv2_evolve_free (r_e) ;
gsl_odeiv2_control_free (r_c) ;
gsl_odeiv2_step_free (r_s) ;
return 0;
} /* ----- end of function red_evol ----- */
/**
* C++ version of gsl_hypot3(). Avoids overflow.
* @param x A real value.
* @param y A real value.
* @param z A real value.
* @return \f$\sqrt{x^2+y^2+z^2}\f$.
*/
inline double hypot3( double const x, double const y, double const z ){ return gsl_hypot3( x, y, z ); }
int
print_data(const int down_sample, const print_parameters *params,
const satdata_mag *data)
{
int s = 0;
size_t i, j;
f107_workspace *f107_p = f107_alloc(F107_IDX_FILE);
i = 1;
printf("# Field %zu: time (UT)\n", i++);
printf("# Field %zu: time (decimal year)\n", i++);
printf("# Field %zu: UT (hours)\n", i++);
printf("# Field %zu: local time (hours)\n", i++);
printf("# Field %zu: season (day of year)\n", i++);
printf("# Field %zu: EUVAC\n", i++);
printf("# Field %zu: longitude (degrees)\n", i++);
printf("# Field %zu: latitude (degrees)\n", i++);
printf("# Field %zu: altitude (km)\n", i++);
printf("# Field %zu: QD latitude (degrees)\n", i++);
printf("# Field %zu: satellite direction\n", i++);
printf("# Field %zu: electron density (cm^{-3})\n", i++);
printf("# Field %zu: scalar field (nT)\n", i++);
printf("# Field %zu: X field (nT)\n", i++);
printf("# Field %zu: Y field (nT)\n", i++);
printf("# Field %zu: Z field (nT)\n", i++);
printf("# Field %zu: scalar residual (nT)\n", i++);
printf("# Field %zu: X residual (nT)\n", i++);
printf("# Field %zu: Y residual (nT)\n", i++);
printf("# Field %zu: Z residual (nT)\n", i++);
printf("# Field %zu: X main (nT)\n", i++);
printf("# Field %zu: Y main (nT)\n", i++);
printf("# Field %zu: Z main (nT)\n", i++);
printf("# Field %zu: X crust (nT)\n", i++);
printf("# Field %zu: Y crust (nT)\n", i++);
printf("# Field %zu: Z crust (nT)\n", i++);
printf("# Field %zu: X external (nT)\n", i++);
printf("# Field %zu: Y external (nT)\n", i++);
printf("# Field %zu: Z external (nT)\n", i++);
for (i = 0; i < data->n; i += down_sample)
{
time_t unix_time;
double phi = data->longitude[i] * M_PI / 180.0;
double lt, ut, euvac;
double qdlat = data->qdlat[i];
double B_obs[3], B_main[3], B_crust[3], B_ext[3], B_res[4], B_model[4];
if (data->flags[i])
continue; /* nan vector components */
if (qdlat < params->qd_min || qdlat > params->qd_max)
continue;
if (data->altitude[i] < params->alt_min || data->altitude[i] > params->alt_max)
continue;
unix_time = satdata_epoch2timet(data->t[i]);
lt = get_localtime(unix_time, phi);
if (lt < params->lt_min || lt > params->lt_max)
continue;
ut = get_ut(unix_time);
if (ut < params->ut_min || ut > params->ut_max)
continue;
f107_get_euvac(unix_time, &euvac, f107_p);
B_obs[0] = SATDATA_VEC_X(data->B, i);
B_obs[1] = SATDATA_VEC_Y(data->B, i);
B_obs[2] = SATDATA_VEC_Z(data->B, i);
B_main[0] = SATDATA_VEC_X(data->B_main, i);
B_main[1] = SATDATA_VEC_Y(data->B_main, i);
B_main[2] = SATDATA_VEC_Z(data->B_main, i);
B_crust[0] = SATDATA_VEC_X(data->B_crust, i);
B_crust[1] = SATDATA_VEC_Y(data->B_crust, i);
B_crust[2] = SATDATA_VEC_Z(data->B_crust, i);
B_ext[0] = SATDATA_VEC_X(data->B_ext, i);
B_ext[1] = SATDATA_VEC_Y(data->B_ext, i);
B_ext[2] = SATDATA_VEC_Z(data->B_ext, i);
for (j = 0; j < 3; ++j)
{
B_model[j] = B_main[j] + B_crust[j] + B_ext[j];
B_res[j] = B_obs[j] - B_model[j];
}
/* compute scalar residual */
B_model[3] = gsl_hypot3(B_model[0], B_model[1], B_model[2]);
B_res[3] = data->F[i] - B_model[3];
printf("%ld %.8f %.2f %.2f %6.2f %5.1f %10.4f %8.4f %10.4f %10.4f %d %10.4e %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f %10.4f\n",
unix_time,
satdata_epoch2year(data->t[i]),
get_ut(unix_time),
lt,
get_season(unix_time),
euvac,
data->longitude[i],
data->latitude[i],
data->altitude[i],
qdlat,
satdata_mag_satdir(i, data),
data->ne[i],
data->F[i],
SATDATA_VEC_X(data->B, i),
SATDATA_VEC_Y(data->B, i),
SATDATA_VEC_Z(data->B, i),
B_res[3],
B_res[0],
B_res[1],
B_res[2],
B_main[0],
B_main[1],
B_main[2],
B_crust[0],
B_crust[1],
B_crust[2],
B_ext[0],
B_ext[1],
B_ext[2]);
}
f107_free(f107_p);
return s;
}
