''' c = polyFit(xData,yData,m).
    Returns coefficients of the polynomial
    p(x) = c[0] + c[1]x + c[2]x^2 +...+ c[m]x^m
    that fits the specified data in the least
    squares sense.
 
    sigma = stdDev(c,xData,yData).
    Computes the std. deviation between p(x)
    and the data.
'''    
from numpy import zeros
from math import sqrt
from gaussPivot import *
 
def polyFit(xData,yData,m):
    a = zeros((m+1,m+1))
    b = zeros(m+1)
    s = zeros(2*m+1)
    for i in range(len(xData)):
        temp = yData[i]
        for j in range(m+1):
            b[j] = b[j] + temp
            temp = temp*xData[i]
        temp = 1.0
        for j in range(2*m+1):
            s[j] = s[j] + temp
            temp = temp*xData[i]
    for i in range(m+1):
        for j in range(m+1):
            a[i,j] = s[i+j]
    return gaussPivot(a,b)
 
def stdDev(c,xData,yData):
 
    def evalPoly(c,x):
        m = len(c) - 1
        p = c[m]
        for j in range(m):
            p = p*x + c[m-j-1]
        return p    
 
    n = len(xData) - 1
    m = len(c) - 1
    sigma = 0.0
    for i in range(n+1):
        p = evalPoly(c,xData[i])
        sigma = sigma + (yData[i] - p)**2
    sigma = sqrt(sigma/(n - m))
    return sigma
#//python/7406