mjo/interpolation.py: use xrange everywhere.

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index dc061077eda70879682048775c3ca69e423e9450..a5ad78ddb32589137b72658afa4fe6401f17b202 100644 (file)
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -18,7 +18,7 @@ def lagrange_denominator(k, xs):
     The product of all xs[j] with j != k.
 
     """
-    return product([xs[k] - xs[j] for j in range(0, len(xs)) if j != k])
+    return product([xs[k] - xs[j] for j in xrange(len(xs)) if j != k])
 
 
 def lagrange_coefficient(k, x, xs):
@@ -96,8 +96,8 @@ def lagrange_polynomial(x, xs, ys):
         True
 
     """
-    ls = [ lagrange_coefficient(k, x, xs) for k in range(0, len(xs)) ]
-    sigma = sum([ ys[k] * ls[k] for k in range(0, len(xs)) ])
+    ls = [ lagrange_coefficient(k, x, xs) for k in xrange(len(xs)) ]
+    sigma = sum([ ys[k] * ls[k] for k in xrange(len(xs)) ])
     return sigma
 
 
@@ -161,7 +161,7 @@ def divided_difference_coefficients(xs):
         [1/2/pi^2, -1/pi^2, 1/2/pi^2]
 
     """
-    coeffs = [ QQ(1)/lagrange_denominator(k, xs) for k in range(0, len(xs)) ]
+    coeffs = [ QQ(1)/lagrange_denominator(k, xs) for k in xrange(len(xs)) ]
     return coeffs
 
 
@@ -253,7 +253,7 @@ def newton_polynomial(x, xs, ys):
 
     N = SR(0)
 
-    for k in range(0, degree+1):
+    for k in xrange(degree+1):
         term  = divided_difference(xs[:k+1], ys[:k+1])
         term *= lagrange_psi(x, xs[:k])
         N += term
@@ -347,10 +347,10 @@ def hermite_interpolant(x, xs, ys, y_primes):
 
     """
     s1 = sum([ ys[k] * hermite_coefficient(k, x, xs)
-               for k in range(0, len(xs)) ])
+               for k in xrange(len(xs)) ])
 
     s2 = sum([ y_primes[k] * hermite_deriv_coefficient(k, x, xs)
-               for k in range(0, len(xs)) ])
+               for k in xrange(len(xs)) ])
 
     return (s1 + s2)