#### Convenience Functions to be moved to kerneltools ####
from __future__ import division
from statsmodels.compat.python import range
import numpy as np

def forrt(X,m=None):
"""
RFFT with order like Munro (1976) FORTT routine.
"""
if m is None:
m = len(X)
y = np.fft.rfft(X,m)/m
return np.r_[y.real,y[1:-1].imag]

def revrt(X,m=None):
"""
Inverse of forrt. Equivalent to Munro (1976) REVRT routine.
"""
if m is None:
m = len(X)
i = int(m // 2+1)
y = X[:i] + np.r_[0,X[i:],0]*1j
return np.fft.irfft(y)*m

def silverman_transform(bw, M, RANGE):
"""
FFT of Gaussian kernel following to Silverman AS 176.

Notes
-----
Underflow is intentional as a dampener.
"""
J = np.arange(M/2+1)
FAC1 = 2*(np.pi*bw/RANGE)**2
JFAC = J**2*FAC1
BC = 1 - 1./3 * (J*1./M*np.pi)**2
FAC = np.exp(-JFAC)/BC
kern_est = np.r_[FAC,FAC[1:-1]]
return kern_est

def counts(x,v):
"""
Counts the number of elements of x that fall within the grid points v

Notes
-----
Using np.digitize and np.bincount
"""
idx = np.digitize(x,v)
try: # numpy 1.6
return np.bincount(idx, minlength=len(v))
except:
bc = np.bincount(idx)
return np.r_[bc,np.zeros(len(v)-len(bc))]

def kdesum(x,axis=0):
return np.asarray([np.sum(x[i] - x, axis) for i in range(len(x))])