''' p = evalPoly(a,xData,x).
  Evaluates Newton's polynomial p at x. The coefficient
  vector 'a' can be computed by the function 'coeffts'.
  a = coeffts(xData,yData).
  Computes the coefficients of Newton's polynomial.
'''  
def evalPoly(a,xData,x):
  n = len(xData) - 1 # Degree of polynomial
  p = a[n]
  for k in range(1,n+1):
    p = a[n-k] + (x -xData[n-k])*p
  return p
def coeffts(xData,yData):
  m = len(xData) # Number of data points
  a = yData.copy()
  for k in range(1,m):
    a[k:m] = (a[k:m] - a[k-1])/(xData[k:m] - xData[k-1])
  return a