def wilcoxon(x,y=None):
"""
Calculates the Wilcoxon signed-rank test for the null hypothesis that two samples come from the same distribution. A non-parametric T-test. (need N > 20)
Returns: t-statistic, two-tailed p-value
"""
if y is None:
d = x
else:
x, y = map(asarray, (x, y))
if len(x) <> len(y):
raise ValueError, 'Unequal N in wilcoxon. Aborting.'
d = x-y
d = compress(not_equal(d,0),d) # Keep all non-zero differences
count = len(d)
if (count < 10):
print "Warning: sample size too small for normal approximation."
r = stats.rankdata(abs(d))
r_plus = sum((d > 0)*r)
r_minus = sum((d < 0)*r)
T = min(r_plus, r_minus)
mn = count*(count+1.0)*0.25
se = math.sqrt(count*(count+1)*(2*count+1.0)/24)
if (len(r) != len(unique(r))): # handle ties in data
replist, repnum = find_repeats(r)
corr = 0.0
for i in range(len(replist)):
si = repnum[i]
corr += 0.5*si*(si*si-1.0)
V = se*se - corr
se = sqrt((count*V - T*T)/(count-1.0))
z = (T - mn)/se
prob = 2*(1.0 -stats.zprob(abs(z)))
return T, prob
def _make_complex_eigvecs(w,vin,cmplx_tcode):
v = scipy_base.array(vin,typecode=cmplx_tcode)
ind = scipy_base.nonzero(scipy_base.not_equal(w.imag,0.0))
vnew = scipy_base.zeros((v.shape[0],len(ind)>>1),cmplx_tcode)
vnew.real = scipy_base.take(vin,ind[::2],1)
vnew.imag = scipy_base.take(vin,ind[1::2],1)
count = 0
conj = scipy_base.conjugate
for i in range(len(ind)/2):
v[:,ind[2*i]] = vnew[:,count]
v[:,ind[2*i+1]] = conj(vnew[:,count])
count += 1
return v
