def factorial(n,exact=0):
"""n! = special.gamma(n+1)
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array argument accepted only for exact=0 case.
- If n<0, the return value is 0.
"""
if exact:
if n < 0:
return 0L
n = long(n)
val = 1L
k = 1L
while (k < n+1L):
val = val*k
k += 1
return val
else:
n = asarray(n)
sv = special.errprint(0)
vals = special.gamma(n+1)
sv = special.errprint(sv)
return where(n>=0,vals,0)
def boxcox(x,lmbda=None,alpha=None):
"""Return a positive dataset tranformed by a Box-Cox power transformation.
If lmbda is not None, do the transformation for that value.
If lmbda is None, find the lambda that maximizes the log-likelihood
function and return it as the second output argument.
If alpha is not None, return the 100(1-alpha)% confidence interval for
lambda as the third output argument.
"""
if any(x < 0):
raise ValueError, "Data must be positive."
if lmbda is not None: # single transformation
lmbda = lmbda*(x==x)
y = where(lmbda == 0, log(x), (x**lmbda - 1)/lmbda)
return y
# Otherwise find the lmbda that maximizes the log-likelihood function.
def tempfunc(lmb, data): # function to minimize
return -boxcox_llf(lmb,data)
lmax = optimize.brent(tempfunc, brack=(-2.0,2.0),args=(x,))
y, lmax = boxcox(x, lmax)
if alpha is None:
return y, lmax
# Otherwise find confidence interval
interval = _boxcox_conf_interval(x, lmax, alpha)
return y, lmax, interval
def comb(N,k,exact=0):
"""Combinations of N things taken k at a time.
If exact==0, then floating point precision is used, otherwise
exact long integer is computed.
Notes:
- Array arguments accepted only for exact=0 case.
- If k > N, N < 0, or k < 0, then a 0 is returned.
"""
if exact:
if (k > N) or (N < 0) or (k < 0):
return 0L
N,k = map(long,(N,k))
top = N
val = 1L
while (top > (N-k)):
val *= top
top -= 1
n = 1L
while (n < k+1L):
val /= n
n += 1
return val
else:
k,N = asarray(k), asarray(N)
lgam = special.gammaln
cond = (k <= N) & (N >= 0) & (k >= 0)
sv = special.errprint(0)
vals = exp(lgam(N+1) - lgam(N-k+1) - lgam(k+1))
sv = special.errprint(sv)
return where(cond, vals, 0.0)
