quadrature.py File Reference

Namespaces
	quadrature

Functions
def	quadrature.ExactIntegrationOfSinus (t, a=None, b=None)
def	quadrature.ExactIntegrationOfSinusWithExponentialKernel (t, ti, alpha=None, beta=None)
def	quadrature.ExactIntegrationOfTail (end_time, end_time_minus_tw, initial_time, ais, tis)
def	quadrature.ApproximateQuadrature (times, f)
def	quadrature.NaiveQuadrature (times, f)
def	quadrature.Alpha (n, j)
def	quadrature.Beta (n, j)
def	quadrature.Gamma (n, j)
def	quadrature.Coefficient (order, n, j)
def	quadrature.Daitche (times, f, order)
def	quadrature.DaitcheTimesAndIntegrands (times, integrands, order)
def	quadrature.Phi (t)
def	quadrature.Hinsberg (m, t_win, times, f, which_set_of_points='hinsberg')
def	quadrature.OmegaTaylorTerms (alpha, bi, pi)
def	quadrature.A (alpha, p, f, t, times, c=1)
def	quadrature.Bombardelli (times, f_to_integrate, order=1)
def	quadrature.SubstituteRichardsons (approx_successive_values, k, order, level=- 1)
def	quadrature.SubstituteEmpiricalRichardsons (approx_successive_values, k, order, level=- 1)
def	quadrature.SubstituteShanks (approx_sequence)
def	quadrature.LogInterpolation (a, b)

Variables
int	quadrature.end_time = 10
float	quadrature.t_win = 1.0
int	quadrature.n_discretizations = 7
int	quadrature.min_exp = 3
int	quadrature.k = 2
int	quadrature.m = 10
int	quadrature.order_bomb = 1
	quadrature.f = math.sin
list	quadrature.n_div = [k ** (min_exp + i) for i in range(n_discretizations)]
list	quadrature.n_sizes = [end_time / number for number in n_div]
int	quadrature.n_theor_slopes = 2
	quadrature.n_samples = int(min(8, n_div[0]))
list	quadrature.exact_values = [0] * n_discretizations
list	quadrature.approx_values_naive = [0] * n_discretizations
list	quadrature.approx_values_1 = [0] * n_discretizations
list	quadrature.approx_values_2 = [0] * n_discretizations
list	quadrature.approx_values_3 = [0] * n_discretizations
list	quadrature.approx_values_bomb = [0] * n_discretizations
list	quadrature.approx_values_hins = [0] * n_discretizations
list	quadrature.approx_values_hins_t_norm = [0] * n_discretizations
list	quadrature.approx_values_hins_abs = [0] * n_discretizations
list	quadrature.errors_naive = [0] * n_discretizations
list	quadrature.errors_1 = [0] * n_discretizations
list	quadrature.errors_2 = [0] * n_discretizations
list	quadrature.errors_3 = [0] * n_discretizations
list	quadrature.errors_bomb = [0] * n_discretizations
list	quadrature.errors_hins = [0] * n_discretizations
list	quadrature.errors_hins_t_norm = [0] * n_discretizations
list	quadrature.errors_hins_abs = [0] * n_discretizations
list	quadrature.errors_naive_rich = [0] * n_discretizations
list	quadrature.errors_1_rich = [0] * n_discretizations
list	quadrature.errors_2_rich = [0] * n_discretizations
list	quadrature.errors_3_rich = [0] * n_discretizations
list	quadrature.errors_bomb_rich = [0] * n_discretizations
list	quadrature.errors_hins_rich = [0] * n_discretizations
list	quadrature.errors_naive_rich_emp = [0] * n_discretizations
list	quadrature.errors_1_rich_emp = [0] * n_discretizations
list	quadrature.errors_2_rich_emp = [0] * n_discretizations
list	quadrature.errors_3_rich_emp = [0] * n_discretizations
list	quadrature.errors_bomb_rich_emp = [0] * n_discretizations
list	quadrature.errors_hins_rich_emp = [0] * n_discretizations
list	quadrature.errors_naive_shank = [0] * n_discretizations
list	quadrature.errors_1_shank = [0] * n_discretizations
list	quadrature.errors_2_shank = [0] * n_discretizations
list	quadrature.errors_3_shank = [0] * n_discretizations
list	quadrature.errors_bomb_shank = [0] * n_discretizations
list	quadrature.errors_hins_shank = [0] * n_discretizations
int	quadrature.j = 0
int	quadrature.h = end_time / n_divisions
list	quadrature.times = [h * delta for delta in range(n_divisions * i // n_samples)]
	quadrature.exact_value = float(ExactIntegrationOfSinus(times[-1]))
def	quadrature.approx_value_1 = Daitche(times, f, 1)
def	quadrature.approx_value_2 = Daitche(times, f, 2)
def	quadrature.approx_value_3 = Daitche(times, f, 3)
def	quadrature.approx_value_bomb = Bombardelli(times, f, order_bomb)
def	quadrature.approx_value_hins = Hinsberg(m, t_win, times, f)
def	quadrature.approx_value_hins_t_norm = Hinsberg(m, t_win, times, f, 't-norm')
def	quadrature.approx_value_hins_abs = Hinsberg(m, t_win, times, f, 'abs-norm')
int	quadrature.approx_value_naive = 1
	quadrature.error_naive = abs(approx_value_naive - exact_value)
	quadrature.error_1 = abs(approx_value_1 - exact_value)
	quadrature.error_2 = abs(approx_value_2 - exact_value)
	quadrature.error_3 = abs(approx_value_3 - exact_value)
	quadrature.error_bomb = abs(approx_value_bomb - exact_value)
	quadrature.error_hins = abs(approx_value_hins - exact_value)
	quadrature.error_hins_t_norm = abs(approx_value_hins_t_norm - exact_value)
	quadrature.error_hins_abs = abs(approx_value_hins_abs - exact_value)
list	quadrature.approx_values_naive_rich = [value for value in approx_values_naive]
list	quadrature.approx_values_1_rich = [value for value in approx_values_1]
list	quadrature.approx_values_2_rich = [value for value in approx_values_2]
list	quadrature.approx_values_3_rich = [value for value in approx_values_3]
list	quadrature.approx_values_bomb_rich = [value for value in approx_values_bomb]
list	quadrature.approx_values_hins_rich = [value for value in approx_values_hins]
list	quadrature.approx_values_naive_rich_emp = [value for value in approx_values_naive]
list	quadrature.approx_values_1_rich_emp = [value for value in approx_values_1]
list	quadrature.approx_values_2_rich_emp = [value for value in approx_values_2]
list	quadrature.approx_values_3_rich_emp = [value for value in approx_values_3]
list	quadrature.approx_values_bomb_rich_emp = [value for value in approx_values_bomb]
list	quadrature.approx_values_hins_rich_emp = [value for value in approx_values_hins]
list	quadrature.approx_values_naive_shank = [value for value in approx_values_naive]
list	quadrature.approx_values_1_shank = [value for value in approx_values_1]
list	quadrature.approx_values_2_shank = [value for value in approx_values_2]
list	quadrature.approx_values_3_shank = [value for value in approx_values_3]
list	quadrature.approx_values_bomb_shank = [value for value in approx_values_bomb]
list	quadrature.approx_values_hins_shank = [value for value in approx_values_hins]
list	quadrature.theoretical_slope_naive = []
list	quadrature.theoretical_slope_1 = [errors_1[- 1] / 0.5 ** (2 * (n_theor_slopes - i) - 0.5) for i in range(n_theor_slopes)]
list	quadrature.theoretical_slope_2 = [errors_2[- 1] / 0.5 ** (3 * (n_theor_slopes - i) - 1.5) for i in range(n_theor_slopes)]
list	quadrature.theoretical_slope_3 = [errors_3[- 1] / 0.5 ** (4 * (n_theor_slopes - i) - 2.5) for i in range(n_theor_slopes)]
list	quadrature.theoretical_slope_bomb = [errors_bomb[- 1] / 0.5 ** (1 * (n_theor_slopes - i) + 0.5) for i in range(n_theor_slopes)]
list	quadrature.theoretical_slope_hins = [errors_hins[- 1] / 0.5 ** (2 * (n_theor_slopes - i) - 0.5) for i in range(n_theor_slopes)]
	quadrature.color
	quadrature.linestyle
	quadrature.linewidth
	quadrature.ms
	quadrature.marker
	quadrature.label
list	quadrature.bomb_sizes = [size / 1 for size in n_sizes]
	quadrature.mew
list	quadrature.annotation_cooors_naive = [LogInterpolation(n_sizes[- 1], n_sizes[- 2]), LogInterpolation(theoretical_slope_naive[- 1], theoretical_slope_naive[- 2])]
list	quadrature.annotation_cooors_1 = [LogInterpolation(n_sizes[- 1], n_sizes[- 2]), LogInterpolation(theoretical_slope_1[- 1], theoretical_slope_1[- 2])]
list	quadrature.annotation_cooors_2 = [LogInterpolation(n_sizes[- 1], n_sizes[- 2]), LogInterpolation(theoretical_slope_2[- 1], theoretical_slope_2[- 2])]
	quadrature.xy
	quadrature.xycoords
	quadrature.xytext
	quadrature.textcoords
	quadrature.fontsize
	quadrature.arrowprops
list	quadrature.annotation_cooors_3 = [LogInterpolation(n_sizes[- 1], n_sizes[- 2]), LogInterpolation(theoretical_slope_3[- 1], theoretical_slope_3[- 2])]
list	quadrature.annotation_cooors_bomb = [LogInterpolation(n_sizes[- 1], n_sizes[- 2]), LogInterpolation(theoretical_slope_bomb[- 1], theoretical_slope_bomb[- 2])]
	quadrature.loc
	quadrature.prop
	quadrature.frameon
	quadrature.format
	quadrature.dpi