def test_prob_wrong_input_negative_float(self):
"""
If the input value n is negative float, probability(n)
would raise ValueError('Input not of integer instance')
"""
with self.assertRaisesRegexp(ValueError, "instance"):
mpmath.nstr(probability(-4.3), 8)
def test_prob_wrong_input_negative_number(self):
"""
If the input value n is negative number, probability(n)
would raise ValueError('Input not a positive integer')
"""
with self.assertRaisesRegexp(ValueError, "positive"):
mpmath.nstr(probability(-4), 8)
def test_prob_wrong_input_string(self):
"""
If the input value n is a string, probability(n)
would raise ValueError('Input not of integer instance')
"""
with self.assertRaisesRegexp(ValueError, "instance"):
mpmath.nstr(probability("die"), 8)
def test_prob_wrong_input_zero(self):
"""
If the input value n is zero, probability(n)
would raise ValueError('Input not a positive integer')
"""
with self.assertRaisesRegexp(ValueError, "positive"):
mpmath.nstr(probability(0), 8)
def test_nstr():
m = matrix([[0.75, 0.190940654, -0.0299195971],
[0.190940654, 0.65625, 0.205663228],
[-0.0299195971, 0.205663228, 0.64453125e-20]])
assert nstr(m, 4, min_fixed=-inf) == \
'''[ 0.75 0.1909 -0.02992]
[ 0.1909 0.6563 0.2057]
[-0.02992 0.2057 0.000000000000000000006445]'''
assert nstr(m, 4) == \
'''[ 0.75 0.1909 -0.02992]
def test_nstr():
m = matrix([[0.75, 0.190940654, -0.0299195971],
[0.190940654, 0.65625, 0.205663228],
[-0.0299195971, 0.205663228, 0.64453125e-20]])
assert nstr(m, 4, min_fixed=-inf) == \
'''[ 0.75 0.1909 -0.02992]
[ 0.1909 0.6563 0.2057]
[-0.02992 0.2057 0.000000000000000000006445]'''
assert nstr(m, 4) == \
'''[ 0.75 0.1909 -0.02992]
def test_matrix_basic():
A1 = matrix(3)
for i in xrange(3):
A1[i,i] = 1
assert A1 == eye(3)
assert A1 == matrix(A1)
A2 = matrix(3, 2)
assert not A2._matrix__data
A3 = matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
assert list(A3) == range(1, 10)
A3[1,1] = 0
assert not (1, 1) in A3._matrix__data
A4 = matrix([[1, 2, 3], [4, 5, 6]])
A5 = matrix([[6, -1], [3, 2], [0, -3]])
assert A4 * A5 == matrix([[12, -6], [39, -12]])
assert A1 * A3 == A3 * A1 == A3
try:
A2 * A2
assert False
except ValueError:
pass
l = [[10, 20, 30], [40, 0, 60], [70, 80, 90]]
A6 = matrix(l)
assert A6.tolist() == l
assert A6 == eval(repr(A6))
A6 = matrix(A6, force_type=float)
assert A6 == eval(repr(A6))
assert A6*1j == eval(repr(A6*1j))
assert A3 * 10 == 10 * A3 == A6
assert A2.rows == 3
assert A2.cols == 2
A3.rows = 2
A3.cols = 2
assert len(A3._matrix__data) == 3
assert A4 + A4 == 2*A4
try:
A4 + A2
except ValueError:
pass
assert sum(A1 - A1) == 0
A7 = matrix([[1, 2], [3, 4], [5, 6], [7, 8]])
x = matrix([10, -10])
assert A7*x == matrix([-10, -10, -10, -10])
A8 = ones(5)
assert sum((A8 + 1) - (2 - zeros(5))) == 0
assert (1 + ones(4)) / 2 - 1 == zeros(4)
assert eye(3)**10 == eye(3)
try:
A7**2
assert False
except ValueError:
pass
A9 = randmatrix(3)
A10 = matrix(A9)
A9[0,0] = -100
assert A9 != A10
A11 = matrix(randmatrix(2, 3), force_type=mpi)
for a in A11:
assert isinstance(a, mpi)
assert nstr(A9)
def main():
for N in range(2,100):
# get dbN coeffients
dbN = daubechis(N)
# write coeffients
f = open('db' + str(N).zfill(2) +'_coefficients.txt', 'w')
f.write('# db' + str(N) + ' scaling coefficients\n')
for i, h in enumerate(dbN):
f.write('h['+ str(i) + ']='+ sm.nstr(h,40) + '\n')
f.close()
# get an approximation of scaling function
x, phi, psi = scipy.signal.cascade(dbN)
# plot scaling function
plt.plot(x, phi, 'k')
plt.grid()
plt.title('db' + str(N) + ' scaling function')
plt.savefig('db' + str(N).zfill(2) + '_scaling' + '.png')
plt.clf()
# plot wavelet
plt.plot(x, psi, 'k')
plt.grid()
plt.title( 'db' + str(N) + " wavelet" )
plt.savefig('db' + str(N).zfill(2) + '_wavelet' + '.png')
plt.clf()
def test_prob_2_sided_die(self):
""" test for n = 2 : P(n=1) = 0.5. This is like a coin toss.
all outcomes = {HH, HT, TH, TT}
desired outcomes = {HT, TH}
probability = 2/4 = 0.5
"""
self.assertEqual(mpmath.nstr(probability(2), 8), "0.5")
def cramerVonMises(x, y): try: x = sorted(x); y = sorted(y); pool = x + y; ps, pr = _sortRank(pool) rx = array ( [ pr[ind] for ind in [ ps.index(element) for element in x ] ] ) ry = array ( [ pr[ind] for ind in [ ps.index(element) for element in y ] ] ) n = len(x) m = len(y) i = array(range(1, n+1)) j = array(range(1, m+1)) u = n * sum ( power( (rx - i), 2 ) ) + m * sum ( power((ry - j), 2) ) t = u / (n*m*(n+m)) - (4*n*m-1) / (6 * (n+m)) Tmu = 1/6 + 1 / (6*(n+m)) Tvar = 1/45 * ( (m+n+1) / power((m+n),2) ) * (4*m*n*(m+n) - 3*(power(m,2) + power(n,2)) - 2*m*n) / (4*m*n) t = (t - Tmu) / power(45*Tvar, 0.5) + 1/6 if t < 0: return -1 elif t <= 12: a = 1-mp.nsum(lambda x : ( mp.gamma(x+0.5) / ( mp.gamma(0.5) * mp.fac(x) ) ) * mp.power( 4*x + 1, 0.5 ) * mp.exp ( - mp.power(4*x + 1, 2) / (16*t) ) * mp.besselk(0.25 , mp.power(4*x + 1, 2) / (16*t) ), [0,100] ) / (mp.pi*mp.sqrt(t)) return float(mp.nstr(a,3)) else: return 0 except Exception as e: print e return -1
def fstr(x): s = nstr(x, n=digits) return s + '_pfdp'
def test_prob_1_sided_die(self):
""" test for n = 1 : P(n=1) = 1
"""
self.assertEqual(mpmath.nstr(probability(1), 8), "1.0")
def fstr(x):
s = nstr(x, n=digits)
s = s.replace('e', 'd')
if s.find('d') == -1:
s = s + 'd0'
return s
##
## write python module 'quadrature.py'
##
with open('quadrature.py', 'w') as f:
f.write('# this file was generated by "mksmat.py"\n')
f.write('table = {\n')
for q in quads:
for n in quads[q]:
for r in quads[q][n]:
f.write("('%s',%d,%d): {\n" % (q, n, r))
(nodes, smat) = quads[q][n][r]
f.write(" 'nodes': [" + ',\n'.join(
[nstr(x, digits) for x in nodes]) + '],\n')
f.write(" 'matrix': [ \n")
for row in smat:
f.write('[' + ',\n'.join([nstr(x, digits) for x in row]) + '],\n')
f.write(" ] }, \n")
f.write('}\n\n')
##
## write C++ look-up tables '*.hpp' (no refinements)
##
# First rename quadratures.
quads['gauss_lobatto'] = quads['GL']
del quads['GL']
quads['gauss_radau'] = quads['GR']
# Remez algorithm --step4--
if check_convergence(list_a, list_x):
return list_a, d, list_x, count
else:
raise Exception('[ERROR]Remez algorithm failed')
if __name__ == '__main__':
print('Remez algorithm calculating...', end='')
list_a, d, list_x, count = remez()
print(' OK')
for k, a in enumerate(list_a):
print('a[' + str(k) + ']=', sm.nstr(a, 17))
print('d=', sm.nstr(d, 17))
# -2*s0*s1*s3*x**3 + s0*s2*x + s1**2*s3*x**4 + x**2*(s0**2*s3 - s1*s2)
def f(s0, s1, s2, s3):
return s0*s2 - list_a[1], \
s0**2*s3 - s1*s2 - list_a[2], \
-2*s0*s1*s3 - list_a[3], \
s1**2*s3 - list_a[4]
print()
print('Newton method calculating...', end='')
initilal = (1.2732395447351627, 0.40528473456935109, 0.77633023248007499,
0.22308510060189463)
list_s = sm.findroot(f,
list_x = update_maximum_error_points(list_a)
# Remez algorithm --step4--
if check_convergence(list_a, list_x):
return list_a, d, list_x, count
else:
raise Exception('[ERROR]Remez algorithm failed')
if __name__ == '__main__':
print('Remez algorithm calculating...', end='')
list_a, d, list_x, count = remez()
print(' OK')
for k,a in enumerate(list_a):
print('a[' + str(k) + ']=', sm.nstr(a, 17))
print('d=', sm.nstr(d, 17))
# -2*s0*s1*s3*x**3 + s0*s2*x + s1**2*s3*x**4 + x**2*(s0**2*s3 - s1*s2)
def f(s0,s1,s2,s3):
return s0*s2 - list_a[1], \
s0**2*s3 - s1*s2 - list_a[2], \
-2*s0*s1*s3 - list_a[3], \
s1**2*s3 - list_a[4]
print()
print('Newton method calculating...', end='')
initilal = (1.2732395447351627, 0.40528473456935109, 0.77633023248007499, 0.22308510060189463);
list_s = sm.findroot(
f,
