finding PCC,CPCC,SPCC,Jaccard,MSD,JMSD,COS and ACOS similarity metrics for a and b dicts {'item1':rating1,'item2':rating2..}

metrics.py

#!/usr/bin/env python
# -*- coding: utf-8 -*-
from math import *

# summ XY for 'both' common elements
def scal(x,y,both):
    return sum(x[i]*y[i] for i in both)

# summ X for 'both' common elements
def one(x,both):
    return sum(x[i] for i in both)

# calculating common elements
def bothcalc(a,b):
    return dict([(i,1) for i in a if i in b])

# PCC - Pearson correlation coefficient
def PCC(a,b):
    both=bothcalc(a,b)
    if both == {}: return 0
    n = len(both)
    onea = one(a,a)/len(a)
    oneb = one(b,b)/len(b)
    up = sum((a[i]-onea)*(b[i]-oneb) for i in both)
    down = sqrt(sum((a[i]-onea)**2 for i in both)) * sqrt(sum((b[i]-oneb)**2 for i in both))
    if down == 0:
        return 0
    return up/down

# CPCC - Constrained Pearson correlation coefficient
def CPCC(a,b,rsm=3):#rsm - rating scale median
    both=bothcalc(a,b)
    if both == {}: return 0
    up = sum((a[i]-rsm)*(b[i]-rsm) for i in both)
    down = sqrt(sum((a[i]-rsm)**2 for i in both)) * sqrt(sum((b[i]-rsm)**2 for i in both))
    if down == 0:
        return 0
    return up/down

# SPCC - Sigmoid function based Pearson coefficient
def SPCC(a,b):
    both=bothcalc(a,b)
    if both == {}: return 0
    return PCC(a,b) * 1/(1+exp(-len(both)/2))

# COS - Cosine measure
def COS(a,b):
    both=bothcalc(a,b)
    if both == {}: return 0
    return scal(a,b,both)/(sqrt(scal(a,a,a))*sqrt(scal(b,b,b)))

# ACOS - Adjusted cosine measure
def ACOS(a,b):
    al = set(a)&set(b)
    a2 = dict([(i,a[i]) if i in a else (i,0) for i in al])
    b2 = dict([(i,b[i]) if i in b else (i,0) for i in al])
    onea = one(a,a)/len(a)
    oneb = one(b,b)/len(b)
    up = sum((a2[i]-onea)*(b2[i]-oneb) for i in al)
    down = sqrt(sum((a2[i]-onea)**2 for i in al)) * sqrt(sum((b2[i]-oneb)**2 for i in al))
    if down == 0:
        return 0
    return up/down

# Jaccard - Jaccard similarity
def Jaccard(a,b):
    both=bothcalc(a,b)
    if both == {}: return 0
    return len(both)/(len(a)+len(b)-len(both))

# MSD - Mean squared differences
def MSD(a,b,scale=5):
    both=bothcalc(a,b)
    if both == {}: return 0
    return 1 - sum(((a[i]-b[i])/scale)**2 for i in both)/len(both)

# JMSD - Jaccard and MSD combined
def JMSD(a,b,scale=5):
    return Jaccard(a,b)*MSD(a,b)

This is really nice effort I have ever seen, would you please explain how can I use these functions to get similarity matrix for ML100K or similar dataset..? Thanks in advance