cubicSpline.py

## module cubicSpline
''' k = curvatures(xData,yData).
    Returns the curvatures of cubic spline at its knots.

    y = evalSpline(xData,yData,k,x).
    Evaluates cubic spline at x. The curvatures k can be
    computed with the function 'curvatures'.
'''   
from numpy import zeros,ones
from LUdecomp3 import *

def curvatures(xData,yData):
    n = len(xData) - 1
    c = zeros(n)
    d = ones(n+1)
    e = zeros(n)
    k = zeros(n+1)
    c[0:n-1] = xData[0:n-1] - xData[1:n]
    d[1:n] = 2.0*(xData[0:n-1] - xData[2:n+1])
    e[1:n] = xData[1:n] - xData[2:n+1]
    k[1:n] =6.0*(yData[0:n-1] - yData[1:n]) \
                 /(xData[0:n-1] - xData[1:n]) \
             -6.0*(yData[1:n] - yData[2:n+1])   \
                 /(xData[1:n] - xData[2:n+1])
    LUdecomp3(c,d,e)
    LUsolve3(c,d,e,k)
    return k

def evalSpline(xData,yData,k,x):
    
    def findSegment(xData,x):
        iLeft = 0
        iRight = len(xData)- 1
        while 1:
            if (iRight-iLeft) <= 1: return iLeft
            i =(iLeft + iRight)/2
            if x < xData[i]: iRight = i
            else: iLeft = i
    
    i = findSegment(xData,x)
    h = xData[i] - xData[i+1]
    y = ((x - xData[i+1])**3/h - (x - xData[i+1])*h)*k[i]/6.0 \
      - ((x - xData[i])**3/h - (x - xData[i])*h)*k[i+1]/6.0   \
      + (yData[i]*(x - xData[i+1])                            \
       - yData[i+1]*(x - xData[i]))/h
    return y