def plot_x_p_pair_using_direct_calculation(num_of_zeros, upto_n):
input_file_name = 'first_1000_zeros.txt'
gamma_list = read_zeros_to_array(input_file_name)
# print gamma_list
assert(num_of_zeros >= 1)
# this function only support up to 1000 zeros
assert(num_of_zeros <= 1000)
assert(upto_n > 2)
rou_list, rou_conj_list = get_rou_rou_conj_list(gamma_list[:num_of_zeros])
x_p_x_p_conj_pair_sum_list, x_range_arr = get_x_p_pair_directly(rou_list, rou_conj_list, upto_n)
x_p_x_p_conj_pair_sum_list = np.asarray(x_p_x_p_conj_pair_sum_list, dtype=complex)
# get real part, even though imag part of x_p_x_p_conj_pair_sum_list should be zero
# maybe because of some numerical calculation issue, it can have very tiny left,
# so we get real part, because we only can plot real part anyway
x_p_x_p_conj_pair_sum_list_real = x_p_x_p_conj_pair_sum_list.real
plt.figure()
titlestr = 'sum of x^p pairs, %d zeros, direct calculation'%(num_of_zeros)
plot_one_list(x_p_x_p_conj_pair_sum_list_real, upto_n, x_range_arr,titlestr)
# calculate 'x - sum(x_p_x_p_conj)'
x_p_x_p_conj_pair_sum_list_real_arr = np.asarray( x_p_x_p_conj_pair_sum_list_real)
x_minus_x_p_x_p_conj_pair = np.subtract(x_range_arr, x_p_x_p_conj_pair_sum_list_real_arr)
# plot 'x - sum(x_p_x_p_conj)' against x
plt.figure()
titlestr = 'x - (sum of x^p pair), %d zeros, direct calculation'%(num_of_zeros)
plot_one_list(x_minus_x_p_x_p_conj_pair, upto_n, x_range_arr, titlestr)
def mapping_zeros_on_unit_circle_s_1_minus_s(num_of_zeros):
input_file_name = 'first_1000_zeros.txt'
gamma_list = read_zeros_to_array(input_file_name)
assert(num_of_zeros >= 1)
# this function only support up to 1000 zeros
assert(num_of_zeros <= 1000)
rou_list, rou_conj_list = get_rou_rou_conj_list(gamma_list[:num_of_zeros])
rou_on_circle_list = convert_critline_to_unit_circle_s_1_minus_s(rou_list)
rou_conj_on_circle_list = convert_critline_to_unit_circle_s_1_minus_s(rou_conj_list)
return rou_on_circle_list, rou_conj_on_circle_list
def lamda_n_from_zet_zeros(num_of_lamda, num_of_terms):
input_file_name = 'first_10000_zeros.txt'
gamma_list = read_zeros_to_array(input_file_name)
assert(num_of_terms >= 1)
# this function only support up to 10000 zeros
assert(num_of_terms <= 10000)
rou_list, rou_conj_list = get_rou_rou_conj_list(gamma_list[:num_of_terms])
lamda_lst = []
for n in range(1, num_of_lamda):
lamda = lamda_n(n, num_of_terms, rou_list, rou_conj_list)
print 'n = ', n, ', lamda_n:', lamda
lamda_lst.append(lamda)
return lamda_lst
def verify_slow_converge_sign_change_of_x_p_pair_sequence(num_of_zeros, x):
input_file_name = 'first_1000_zeros.txt'
gamma_list = read_zeros_to_array(input_file_name)
# print gamma_list
assert(num_of_zeros >= 1)
# this function only support up to 1000 zeros
assert(num_of_zeros <= 1000)
rou_list, rou_conj_list = get_rou_rou_conj_list(gamma_list[:num_of_zeros])
x_p_x_p_conj_pair_list = get_x_p_pair_sequences(rou_list, rou_conj_list, x)
x_p_x_p_conj_pair_list = np.asarray(x_p_x_p_conj_pair_list, dtype=complex)
# get real part, even though imag part of x_p_x_p_conj_pair_sum_list should be zero
# maybe because of some numerical calculation issue, it can have very tiny left,
# so we get real part, because we only can plot real part anyway
x_p_x_p_conj_pair_list_real = x_p_x_p_conj_pair_list.real
plt.figure()
titlestr = 'x^p pair sequences, x = %10.2f, %d zeros'%(x, num_of_zeros)
x_range_arr = range(1, num_of_zeros + 1)
plot_one_list(x_p_x_p_conj_pair_list_real, x_range_arr,titlestr)
target_num = int(args[0])
factor_list_option = int(args[1])
num_of_zeros = int(args[2]) # 1 to see the contribution from 1st zero, 50 for good approximation
assert(num_of_zeros >= 1) and (num_of_zeros <= 1000)
input_file_name = 'first_1000_zeros.txt'
gamma_list = read_zeros_to_array(input_file_name)
print gamma_list
assert(num_of_zeros >= 1)
# this function only support up to 1000 zeros
assert(num_of_zeros <= 1000)
rou_list, rou_conj_list = get_rou_rou_conj_list(gamma_list[:num_of_zeros])
zet_2_pk_list, zet_deri_pk_list = pre_calculated_needed_zet_values_to_list(num_of_zeros, rou_list)
check_lx_at_poly_conj_failed_x(num_of_zeros, rou_list, zet_2_pk_list, zet_deri_pk_list)
summatory_approx_list = []
if(factor_list_option == 1):
for x in range(1, target_num + 1):
# mx = lx_from_zet_zeros(num_of_zeros, x, rou_list)
mx = mx_from_zet_zeros_using_pre_cal_zets(num_of_zeros, x, rou_list, zet_2_pk_list, zet_deri_pk_list)
summatory_approx_list.append(mx)
print 'x = ', x, ', mx = ', mx
