def get_result_MjMi_for_N_step_with_fixed_Q_t(Q, t, start_num, max_num, loop_step):
assert(Q < t)
MajorA_2d_sorted_arr, MinorA_2d_sorted_arr, smallest_interval = get_MajorA_MinorA(Q, t)
result_list=[]
# We choose a prime, this will determine the interval step.
# An prime number will make numeric calculation less prone to error.
# If N is a multiply of num_of_integration_step, it can cause numeric error in trignometric summation
# num_of_integration_step = 10007 # an old prime
num_of_integration_step = 19997
# try different N
# Note: whenever, N is a multiple of num_of_integration, the value will be invalid
for N in xrange(start_num, max_num+1, loop_step):
if((N% num_of_integration_step) == 0):
print '__WARNIING__, N = %d is a multiply of num_of_integration_step = %d'%(N, num_of_integration_step)
# study the effect of step to see how it affect the result.
for xstep in xrange(1, 2, 1):
# this will give smalltest step = 0.001
step = float(xstep)/num_of_integration_step
# if step is largest than smallest_interval of fare sequence, then
# this integration does not make sense
assert(step < smallest_interval)
result = result_MjMn(N, step, MajorA_2d_sorted_arr, MinorA_2d_sorted_arr, t)
result['smallest_interval'] = smallest_interval
result_list.append(result)
results_all = {'Q': Q,
't': t,
'result_list': result_list, }
return results_all
np.set_printoptions(precision=5)
np.set_printoptions(suppress=True)
N_list, v_bound_list = vino_bound_trend()
# Q =20
# Q =3
# tao must be larger than 2*Q^2
tao = 4*Q*Q + 1
# N = 909
# M = 50000
step = 1./M
MajorA_2d_sorted_arr, MinorA_2d_sorted_arr, smallest_interval, MA_a_q_sorted_arr = get_MajorA_MinorA(Q, tao)
print MajorA_2d_sorted_arr
a_q_list, F_N_a_q_list = F_N_a_q(MA_a_q_sorted_arr, N)
a_q_x_list, F_N_a_q_x_list = F_N_x(MA_a_q_sorted_arr, MajorA_2d_sorted_arr, N, step)
if(A == 0):
# note: t is tao in Pan's book P4, formula 11.
# this is to move interval [0, 1] to [-1/t, 1 - 1/t]
t1 = 99999999999999999 # to get 1/t close to 0, this is to shift interval [0, 1] to [-1/t, 1-1/t]
arc1 = get_arc(t1)
t2 = 333333 # try another t, to get 1/t close to 0
arc2 = get_arc(t2)
if(A == 1):
