bombardelli_test Namespace Reference

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

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

Function Documentation

ExactIntegrationOfSinusKernel()

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

Variable Documentation

a

list bombardelli_test.a = recent_times[0]

coeff

list bombardelli_test.coeff = h ** (- q)

constant_initial_correction

int bombardelli_test.constant_initial_correction = 2 * sqrt(t) * f(t)

dt

float bombardelli_test.dt = end_time / n_steps

end_time

list bombardelli_test.end_time = 1.0

f

bombardelli_test.f = math.sin

h

list bombardelli_test.h = t / N

initial_approx_deriv

bombardelli_test.initial_approx_deriv = cos(a)

linear_correction_option

int bombardelli_test.linear_correction_option = 0

linear_initial_correction

int bombardelli_test.linear_initial_correction = 2. / 3 * sqrt(t) * (2 * t) * initial_approx_deriv

N

int bombardelli_test.N = len(times) - 1

n_steps

int bombardelli_test.n_steps = 100

old_coeff

list bombardelli_test.old_coeff = h ** (- q)

old_correction

int bombardelli_test.old_correction = 2 * (sqrt(end_time) - sqrt(end_time - t)) * f(t)

old_times

list bombardelli_test.old_times = [time * times[i] / times[-1] for time in times]

old_values

list bombardelli_test.old_values = [gamma(k - q) / gamma(k + 1) * (f(t - k * h) - f(t)) for k in range(N + 1)]

q

float bombardelli_test.q = - 0.5

recent_coeff_1

list bombardelli_test.recent_coeff_1 = h ** (- q)

recent_coeff_2

list bombardelli_test.recent_coeff_2 = h ** (- q) * gamma(- q)

recent_correction_1

int bombardelli_test.recent_correction_1 = constant_initial_correction

recent_correction_2

bombardelli_test.recent_correction_2 = gamma(- q) * (constant_initial_correction + linear_correction_option * linear_initial_correction)

recent_times

list bombardelli_test.recent_times = [times[i] + time * (times[-1] - times[0] - times[i]) / (times[-1] - times[0]) for time in times]

recent_values_1

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)]

recent_values_2

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)]

t

list bombardelli_test.t = times[- 1]

t_win

list bombardelli_test.t_win = times[0] + 0.5 * times[- 1]

times

list bombardelli_test.times = [dt * i for i in range(n_steps)]

values

list bombardelli_test.values = [gamma(k - q) / gamma(k + 1) * f(t - k * h) for k in range(N)]