def test_correctness_and_precision_of_solve_diff_eqn(number=20, verbosity=1):
"""
``number`` is how many different random distributions to check.
Currently, avoids the prime 2.
"""
from sage.misc.prandom import randint
from sage.rings.arith import random_prime
from sage.rings.padics.factory import ZpCA
from sage.modular.pollack_stevens.coeffmod_OMS_space import OverconvergentDistributions
from sage.structure.sage_object import dumps
errors = []
munus = []
for i in range(number):
Mspace = randint(1, 20) #Moments of space
M = randint(max(0, Mspace - 5), Mspace)
p = random_prime(13, lbound=3)
k = randint(0, 6)
Rprec = Mspace + randint(0, 5)
R = ZpCA(p, Rprec)
D = OverconvergentDistributions(k, base=R, prec_cap=Mspace)
S0 = D.action().actor()
Delta_mat = S0([1,1,0,1])
mu = D.random_element(M)
mu_save = dumps(mu)#[deepcopy(mu.ordp), deepcopy(mu._moments)]
if verbosity > 0:
print "\nTest #{0} data (Mspace, M, p, k, Rprec) =".format(i+1), (Mspace, M, p, k, Rprec)
print "mu =", mu
nu = mu * Delta_mat - mu
nu_save = [deepcopy(nu.ordp), deepcopy(nu._moments)]
mu2 = nu.solve_diff_eqn()
nu_abs_prec = nu.precision_absolute()
expected = nu_abs_prec - nu_abs_prec.exact_log(p) - 1
if M != 1:
try:
agree = (mu - mu2).is_zero(expected)
except PrecisionError:
print (Mspace, M, p, k, Rprec), mu_save._repr_(), nu_save
assert False
else:
agree = mu2.is_zero(expected)
if verbosity > 1:
print " Just so you know:"
print " mured =", mu.reduce_precision_absolute(expected)
print " mu2 =", mu2
print " nu = ", nu
if not agree:
errors.append((i+1, 1))
munus.append((mu_save, nu_save, mu2, (Mspace, M, p, k, Rprec)))
if verbosity > 0:
print " Test finding mu from mu|Delta accurate: %s"%(agree)
print " nu_abs_prec soln_abs_prec_expected actual agree"
mu2_abs_prec = mu2.precision_absolute()
agree = (expected == mu2_abs_prec)
if verbosity > 0:
print " %s %s %s %s"%(nu_abs_prec, expected, mu2_abs_prec, agree)
if not agree:
errors.append((i+1, 2))
munus.append((mu_save, nu_save, mu2, (Mspace, M, p, k, Rprec)))
if mu.precision_relative() > 0:
mu._moments[0] = R(0, mu.precision_relative())
mu_save = [deepcopy(mu.ordp), deepcopy(mu._moments)]
if verbosity > 0:
print " mu modified =", mu
nu = mu.solve_diff_eqn()
mu_abs_prec = mu.precision_absolute()
expected = mu_abs_prec - mu_abs_prec.exact_log(p) - 1
nud = nu * Delta_mat - nu
nu_save = [deepcopy(nu.ordp), deepcopy(nu._moments)]
agree = (nud - mu).is_zero(expected)
if verbosity > 1:
print " Just so you know:"
print " mu =", mu
print " mured =", mu.reduce_precision_absolute(expected)
print " nud =", nud
if not agree:
errors.append((i+1, 3))
munus.append((mu_save, nu_save, (Mspace, M, p, k, Rprec)))
if verbosity > 0:
print " Test finding nu with nu|Delta == mu: %s"%(agree)
print " mu_abs_prec soln_abs_prec_expected actual agree"
nu_abs_prec = nu.precision_absolute()
agree = (expected == nu_abs_prec)
if verbosity > 0:
print " %s %s %s %s"%(mu_abs_prec, expected, nu_abs_prec, agree)
if not agree:
errors.append((i+1, 4))
munus.append((mu_save, nu_save, (Mspace, M, p, k, Rprec)))
if len(errors) == 0:
if verbosity > 0:
print "\nTest passed with no errors."
return
if verbosity > 0:
print "\nTest failed with errors: %s\n"%(errors)
return errors, munus
