def selb_formu_list_up_to_x(x, format, sample_rate=1):
selb_sum_list = []
sum_1st_part_list = []
sum_2nd_part_list = []
# calculate prime_list, von_mang list, cheby_list out side of loop,
# so that we do not need to calculate it every time.in the loop
if(format == 1):
primes_list = get_prime_list(x)
if ((format == 2) or (format == 3)):
von_mang_list = von_mang_upto(x)
if (format == 3):
cheby_list = cheby_fun_integer(x)
if(format == 4):
primes_list = get_prime_list(x)
primes_and_log_2d_list = get_primes_and_log_2d_list(primes_list)
print primes_and_log_2d_list
print 'Before loop, format = ', format
count = 0
for n in range(2, x+1, sample_rate):
# format 1, log only
if(format == 1):
selb_sum, sum_1st_part, sum_2nd_part = selb_formu_for_one_x_log_only(n, primes_list)
# format 2, use von_mang
if(format == 2):
# print n
selb_sum, sum_1st_part, sum_2nd_part = selb_formu_for_one_x_using_von_mang(n, von_mang_list )
# format 3: use cheby_fun
if(format == 3):
selb_sum, sum_1st_part, sum_2nd_part = selb_formu_for_one_x_using_cheby(n, von_mang_list, cheby_list )
# format 4, log only, formula is same as 1, with some speed optimization
if(format == 4):
selb_sum, sum_1st_part, sum_2nd_part = selb_formu_for_one_x_log_only_optimized(n, primes_and_log_2d_list)
# show some progress, print every 100 steps,
count += 1
if((count%100) == 0):
print 'Total = ', x, 'current n = ', n
# Save results
selb_sum_list.append(selb_sum)
sum_1st_part_list.append(sum_1st_part)
sum_2nd_part_list.append(sum_2nd_part)
return selb_sum_list, sum_1st_part_list, sum_2nd_part_list
def compare_mert_log_sum_with_cheby(n, mert_list):
cheby_list = cheby_fun_integer(n)
cheby_approx_list = mert_related_to_cheby(mert_list)
range_list = range(1, n+1)
# plot cheby_fun(x) against x
plt.figure(1)
plot_one_list(cheby_list, n, range_list, 'b-*')
plot_one_list(range_list, n, range_list, 'g-*')
plot_one_list(cheby_approx_list, n, range_list, 'r-*')
plt.xlabel('blue, cheby; red: mert_approx; green: x')
# it turns out cheby_list and cheby_approx_list are EXACT same.
print 'cheby_list[1] = ', cheby_list[1]
print 'cheby_approx_list[1] = ', cheby_approx_list[1]
plt.show()
# NOTE: It is better to test n = 10,000, 1,000, 10, to see
# the difference. When n = 10,000, one can zoom in some interesting region to see
# fine details.
parser = OptionParser()
(options, args) = parser.parse_args()
if(len(args) != 2):
print 'Wrong arguments, require parameters: max_num factor_list_option'
print 'factor_list_option = 1: TRUE_PRIME, 2: PRIME_XLOGX_NON_PRECISE, 3: LIOUVI_FACTOR, 4: PRIME_XLOGX_PRECISE'
sys.exit(0)
n = int(args[0])
factor_list_option = int(args[1])
cheby_list = cheby_fun_integer(n)
range_list = range(1, n+1)
# plot cheby_fun(x) against x
plt.figure(1)
plot_one_list(cheby_list, n, range_list, 'b-*')
plot_one_list(range_list, n, range_list, 'g-*')
plt.xlabel('blue, cheby; green: x')
title_str = 'cheby_fun, target_num %d'%(n)
plt.title(title_str)
# plt.show()
# plot cheby_fun(x) - x
plt.figure(2)
cheby_minus_x_arr = cheby_minus_x(cheby_list, range_list)
