CAMLprim value ml_gsl_cheb_init(value cs, value f, value a, value b)
{
CAMLparam2(cs, f);
GSLFUN_CLOSURE(gf, f);
gsl_cheb_init(CHEB_VAL(cs), &gf, Double_val(a), Double_val(b));
CAMLreturn(Val_unit);
}
static VALUE rb_gsl_cheb_init(VALUE obj, VALUE ff, VALUE aa, VALUE bb)
{
gsl_cheb_series *p = NULL;
gsl_function *fff = NULL;
double a, b;
CHECK_FUNCTION(ff);
Need_Float(aa); Need_Float(bb);
Data_Get_Struct(obj, gsl_cheb_series, p);
Data_Get_Struct(ff, gsl_function, fff);
a = NUM2DBL(aa);
b = NUM2DBL(bb);
gsl_cheb_init(p, fff, a, b);
return obj;
}
void
test_dim (const size_t n, const double a, const double b,
gsl_function * F, gsl_function * DF, gsl_function *IF)
{
double tol = 100.0 * GSL_DBL_EPSILON;
double x;
gsl_cheb_series * cs = gsl_cheb_alloc(n);
gsl_cheb_series * csd = gsl_cheb_alloc(n);
gsl_cheb_series * csi = gsl_cheb_alloc(n);
gsl_cheb_init(cs, F, a, b);
for(x=a; x<b; x += (b-a)/100.0) {
double r = gsl_cheb_eval(cs, x);
gsl_test_abs(r, GSL_FN_EVAL(F, x), tol, "gsl_cheb_eval, F(%.3g)", x);
}
/* Test derivative */
gsl_cheb_calc_deriv(csd, cs);
for(x=a; x<b; x += (b-a)/100.0) {
double r = gsl_cheb_eval(csd, x);
gsl_test_abs(r, GSL_FN_EVAL(DF, x), tol, "gsl_cheb_eval, deriv F(%.3g)", x);
}
/* Test integral */
gsl_cheb_calc_integ(csi, cs);
for(x=a; x<b; x += (b-a)/100.0) {
double r = gsl_cheb_eval(csi, x);
gsl_test_abs(r, GSL_FN_EVAL(IF, x), tol, "gsl_cheb_eval, integ F(%.3g)", x);
}
gsl_cheb_free(csi);
gsl_cheb_free(csd);
gsl_cheb_free(cs);
}
int
main(void)
{
double tol = 100.0 * GSL_DBL_EPSILON;
double ftol = 20.0;
double x;
size_t i;
gsl_cheb_series * cs = gsl_cheb_alloc(40);
gsl_cheb_series * csd = gsl_cheb_alloc(40);
gsl_cheb_series * csi = gsl_cheb_alloc(40);
gsl_function F_sin, F_T0, F_T1, F_T2, F_DP, F_P, F_IP1, F_IP2;
F_sin.function = f_sin;
F_sin.params = 0;
F_T0.function = f_T0;
F_T0.params = 0;
F_T1.function = f_T1;
F_T1.params = 0;
F_T2.function = f_T2;
F_T2.params = 0;
F_P.function = f_P;
F_P.params = 0;
F_DP.function = f_DP;
F_DP.params = 0;
F_IP1.function = f_IP1;
F_IP1.params = 0;
F_IP2.function = f_IP2;
F_IP2.params = 0;
gsl_ieee_env_setup();
gsl_cheb_init(cs, &F_T0, -1.0, 1.0);
{
size_t expected = 40;
size_t order = gsl_cheb_order (cs);
size_t size = gsl_cheb_size (cs);
double * p = gsl_cheb_coeffs (cs);
gsl_test(order != expected, "gsl_cheb_order");
gsl_test(size != expected + 1, "gsl_cheb_size");
gsl_test(p != cs->c, "gsl_cheb_coeffs");
}
for (i = 0; i<cs->order; i++)
{
double c_exp = (i == 0) ? 2.0 : 0.0;
gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_0(x)", i);
}
gsl_cheb_init(cs, &F_T1, -1.0, 1.0);
for (i = 0; i<cs->order; i++)
{
double c_exp = (i == 1) ? 1.0 : 0.0;
gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_1(x)", i);
}
gsl_cheb_init(cs, &F_T2, -1.0, 1.0);
for (i = 0; i<cs->order; i++)
{
double c_exp = (i == 2) ? 1.0 : 0.0;
gsl_test_abs (cs->c[i], c_exp, tol, "c[%d] for T_2(x)", i);
}
gsl_cheb_init(cs, &F_sin, -M_PI, M_PI);
gsl_test_abs (cs->c[0], 0.0, tol, "c[0] for F_sin(x)");
gsl_test_abs (cs->c[1], 5.69230686359506e-01, tol, "c[1] for F_sin(x)");
gsl_test_abs (cs->c[2], 0.0, tol, "c[2] for F_sin(x)");
gsl_test_abs (cs->c[3], -6.66916672405979e-01, tol, "c[3] for F_sin(x)");
gsl_test_abs (cs->c[4], 0.0, tol, "c[4] for F_sin(x)");
gsl_test_abs (cs->c[5], 1.04282368734237e-01, tol, "c[5] for F_sin(x)");
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval(cs, x);
gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval, sin(%.3g)", x);
}
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_err(cs, x, &r, &e);
gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval_err, sin(%.3g)", x);
gsl_test_factor(fabs(r-sin(x)) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_err, error sin(%.3g)", x);
}
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval_n(cs, 25, x);
gsl_test_abs(r, sin(x), tol, "gsl_cheb_eval_n, sin(%.3g)", x);
}
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_n_err(cs, 25, x, &r, &e);
gsl_test_abs(r, sin(x), 100.0 * tol, "gsl_cheb_eval_n_err, deriv sin(%.3g)", x);
gsl_test_factor(fabs(r-sin(x)) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_n_err, error sin(%.3g)", x);
}
/* Test derivative */
gsl_cheb_calc_deriv(csd, cs);
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval(csd, x);
gsl_test_abs(r, cos(x), 1600 * tol, "gsl_cheb_eval, deriv sin(%.3g)", x);
}
#ifdef TEST_DERIVATIVE_ERR
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_err(csd, x, &r, &e);
gsl_test_abs(r, cos(x), tol, "gsl_cheb_eval_err, deriv sin(%.3g)", x);
gsl_test_factor(fabs(r-cos(x)) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_err, deriv error sin(%.3g)", x);
}
#endif
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval_n(csd, 25, x);
gsl_test_abs(r, cos(x), 1600 * tol, "gsl_cheb_eval_n, deriv sin(%.3g)", x);
}
#ifdef TEST_DERIVATIVE_ERR
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_n_err(csd, 25, x, &r, &e);
gsl_test_abs(r, cos(x), 100.0 * tol, "gsl_cheb_eval_n_err, deriv sin(%.3g)", x);
gsl_test_factor(fabs(r-cos(x)) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_n_err, deriv error sin(%.3g)", x);
}
#endif
/* Test integral */
gsl_cheb_calc_integ(csi, cs);
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval(csi, x);
gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval, integ sin(%.3g)", x);
}
#ifdef TEST_INTEGRAL_ERR
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_err(csi, x, &r, &e);
gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval_err, integ sin(%.3g)", x);
gsl_test_factor(fabs(r-(-1-cos(x))) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_err, integ error sin(%.3g)", x);
}
#endif
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r = gsl_cheb_eval_n(csi, 25, x);
gsl_test_abs(r, -(1+cos(x)), tol, "gsl_cheb_eval_n, integ sin(%.3g)", x);
}
#ifdef TEST_INTEGRAL_ERR
for(x=-M_PI; x<M_PI; x += M_PI/100.0) {
double r, e;
gsl_cheb_eval_n_err(csi, 25, x, &r, &e);
gsl_test_abs(r, -(1+cos(x)), 100.0 * tol, "gsl_cheb_eval_n_err, integ sin(%.3g)", x);
gsl_test_factor(fabs(r-(-1-cos(x))) + GSL_DBL_EPSILON, e, ftol,
"gsl_cheb_eval_n_err, integ error sin(%.3g)", x);
}
#endif
gsl_cheb_free(csi);
gsl_cheb_free(csd);
gsl_cheb_free(cs);
/* Test low order cases */
test_dim (2, -5.0, 5.0, &F_P, &F_DP, &F_IP2);
test_dim (1, -5.0, 5.0, &F_P, &F_DP, &F_IP1);
exit (gsl_test_summary());
}
