bombardelli_test.py File Reference

Namespaces
	bombardelli_test

Functions
def	bombardelli_test.ExactIntegrationOfSinusKernel (t, a=None, b=None)

Variables
	bombardelli_test.f = math.sin
float	bombardelli_test.end_time = 1.0
int	bombardelli_test.n_steps = 100
float	bombardelli_test.dt = end_time / n_steps
list	bombardelli_test.times = [dt * i for i in range(n_steps)]
list	bombardelli_test.t_win = times[0] + 0.5 * times[- 1]
list	bombardelli_test.old_times = [time * times[i] / times[-1] for time in times]
list	bombardelli_test.recent_times = [times[i] + time * (times[-1] - times[0] - times[i]) / (times[-1] - times[0]) for time in times]
float	bombardelli_test.q = - 0.5
list	bombardelli_test.t = times[- 1]
int	bombardelli_test.N = len(times) - 1
list	bombardelli_test.h = t / N
list	bombardelli_test.coeff = h ** (- q)
list	bombardelli_test.values = [gamma(k - q) / gamma(k + 1) * f(t - k * h) for k in range(N)]
list	bombardelli_test.old_coeff = h ** (- q)
list	bombardelli_test.old_values = [gamma(k - q) / gamma(k + 1) * (f(t - k * h) - f(t)) for k in range(N + 1)]
int	bombardelli_test.old_correction = 2 * (sqrt(end_time) - sqrt(end_time - t)) * f(t)
list	bombardelli_test.a = recent_times[0]
	bombardelli_test.initial_approx_deriv = cos(a)
int	bombardelli_test.constant_initial_correction = 2 * sqrt(t) * f(t)
int	bombardelli_test.linear_initial_correction = 2. / 3 * sqrt(t) * (2 * t) * initial_approx_deriv
int	bombardelli_test.linear_correction_option = 0
list	bombardelli_test.recent_coeff_1 = h ** (- q)
list	bombardelli_test.recent_values_1 = [gamma(k - q) / gamma(k + 1) * (f(t - k * h + a) - f(t)) for k in range(N + 1)]
int	bombardelli_test.recent_correction_1 = constant_initial_correction
list	bombardelli_test.recent_coeff_2 = h ** (- q) * gamma(- q)
list	bombardelli_test.recent_values_2 = [(- 1) ** k * gamma(q + 1) / (gamma(k + 1) * gamma(q - k + 1)) * (f(t - (k - 0.5 * q) * h + a) - f(a) - linear_correction_option * (t - (k - 0.5 * q) * h) * initial_approx_deriv) for k in range(N)]
	bombardelli_test.recent_correction_2 = gamma(- q) * (constant_initial_correction + linear_correction_option * linear_initial_correction)