#def mean(x):
#  import Numeric, caching
#  reload(caching)#
#
#  sum = caching.cache(Numeric.sum,x,verbose=0)
#  #sum = Numeric.sum(x)  
#  avg = float(sum)/len(x)
#
#  return(avg)

def mean(x):
  import Numeric

  sum = Numeric.sum(x)  
  avg = float(sum)/len(x)

  return(avg)


def cov(x,y=None):
  import Numeric
  if y is None:
    y = x 

  assert(len(x)==len(y))
  N = len(x)
 
  cx = x - mean(x)  
  cy = y - mean(y)  

  p = Numeric.innerproduct(cx,cy) / N


  return(p)


def err(x,y=0,n=2):
  """Relative error of ||x-y|| to ||y||
     n = 2:    Two norm
     n = None: Max norm

     If denominator evaluates to zero, absolute error is returned
  """

  
  if n == 2:
      err = norm(x-y)
      try:
          err = err/norm(y)
      except:
          pass

  else:
      err = max(abs(x-y))
      try:
          err = err/max(abs(y))    
      except:
          pass
        
  return err
  

def norm(x):
  """2-norm of x
  """
  
  import Numeric  
  y = Numeric.ravel(x)
  p = Numeric.sqrt(Numeric.innerproduct(y,y))
  return p
    
  
def corr(x,y=None):
  import caching  
  from math import sqrt
  if y is None:
    y = x 

  varx = caching.cache(cov,x,verbose=0)
  vary = caching.cache(cov,y,verbose=0)
  #varx = cov(x)
  #vary = cov(y)

  if varx == 0 or vary == 0:
    C = 0
  else:  
    C = cov(x,y)/ sqrt(varx * vary)   

  return(C)