""" regressione funzione potenza 'pagine' n 19 pag 114 Impedovo
    la funzione cercata e' y=a*x^b , si passa ai logaritmi"""
from graftarta2 import Graf
from graphics import *
import math

# metri
X=[100,200,400,800,1500,5000,10000,42195]
# primati in s
Y=[9.77,19.32,43.18,101.11,206.00,757.35,1577.53,7440.55]

def media(Lista):
    """ media, varianza dei valori in Lista, sqm
    """
    somma = 0
    sommaqua = 0
    n = len(Lista)
    for k in Lista:
        somma = somma+k
        sommaqua = sommaqua+k*k
    m = float(somma)/n
    varian = float(sommaqua)/n-m*m
    sqm=varian**0.5
    #print 'media ',m, ' varianza ', varian,'  sqm ', sqm
    return m, varian, sqm

def covarianza(X,Y):
    prod=[]
    for i in range(len(X)):
        prod.append(X[i]*Y[i])
    mediaX=media(X)
    mediaY=media(Y)
    mediaXY=media(prod)
    return mediaXY[0]-mediaX[0]*mediaY[0]

logX=[]
for i in X:
    logX.append(math.log10(i))
                
logY=[]
for i in Y:
    logY.append(math.log10(i))

print logX, logY
medX, varX, sqmX=media(logX)
medY, varY, sqmY=media(logY)
cov=covarianza(logX,logY)
m=cov/varX
q=medY-m*medX
print 'm ', m
print 'q ', q
#print m[0]
gr=Graf("regressione con funzione potenza",600,400)
gr.coordinate(-1,-0.5,5,4.5,True)
for i in range(len(logX)):
    Point(logX[i],logY[i]).draw(gr)
def f(x):
    return m*x+q
gr.colorePenna("red")
gr.grafico(f,2,4.6253,0.02)

a=math.pow(10,q)
b=abs(m)
b=1.104
print a, b
gr1=Graf("regressione con funzione potenza II",600,400)
gr1.coordinate(-5000,-1000,45000,9000,True)
for i in range(len(X)):
    Point(X[i],Y[i]).draw(gr1)
def f(x):
    return a*(x**b)
gr1.colorePenna("red")
gr1.grafico(f,0,43000,100)
print f(42195)
print f(42195/2.0)