import sys, string, os, math, re, random, operator, pickle, cPickle, glob, copy, bisect
import array, Numeric, LinearAlgebra, RandomArray, numarray, RandomArray2, LinearAlgebra2
#import pstat, stats, io    # modest statistics module, had some problems
#
# Abbreviations of modules:
O = operator
B = bisect
S = string
M = math
N = Numeric
R = RandomArray      # comes with Numeric
L = LinearAlgebra    # dito
# The above takes some of the tedium out of qualified references ("module.function"),
# and yet it preserves the ability to use "dir()" and "doc()" queries.
#
# Abbreviations of important matrix operations:
N.a = N.array
N.m = N.matrixmultiply
N.t = N.transpose
N.i = N.innerproduct
#
# Some basic linear algebra functions:
N.sqnorm = lambda x: N.i(x,x)
N.norm = lambda x: N.sqrt(N.i(x,x))
N.std = lambda x: N.a(x) / N.norm(x)
N.center = lambda x: N.a(x) - N.sum(x)/N.size(x)
N.cor = lambda x,y: N.i(x,y) / (N.norm(x) * N.norm(y))
N.ang = lambda x,y: N.arccos( N.i(x,y) / (N.norm(x) * N.norm(y)) )
N.ang360 = lambda x,y: N.arccos( N.i(x,y) / (N.norm(x) * N.norm(y)) ) /math.pi * 180.
#
# Use "doc()" parallel with "dir()":
def doc(x): print x.__doc__  
#
# Create a sorted copy (NOT in place!): works only for lists!!!
def sort(x):  from copy import copy; y = copy(x); y.sort(); return y