Update the lagrange_polynomial() function to take a list of y-values instead of a...

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index 4cb58740c8d2b4611bb4e4ec4ebc6b1e8bd8f47d..0cafc283e7b445f0ec8af9487f3964195a291cc5 100644 (file)
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -38,27 +38,28 @@ def lagrange_coefficient(k, x, xs):
 
 
 
-def lagrange_polynomial(f, x, xs):
+def lagrange_polynomial(x, xs, ys):
     """
     Return the Lagrange form of the interpolation polynomial in `x` of
-    `f` at the points `xs`.
+    at the points (xs[k], ys[k]).
 
     INPUT:
 
-      - ``f`` - The function to interpolate.
-
       - ``x`` - The independent variable of the resulting polynomial.
 
       - ``xs`` - The list of points at which we interpolate `f`.
 
+      - ``ys`` - The function values at `xs`.
+
     OUTPUT:
 
-    A symbolic function (polynomial) interpolating `f` at `xs`.
+    A symbolic function (polynomial) interpolating each (xs[k], ys[k]).
 
     TESTS::
 
         sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
-        sage: L = lagrange_polynomial(sin, x, xs)
+        sage: ys = map(sin, xs)
+        sage: L = lagrange_polynomial(x, xs, ys)
         sage: expected  = 27/16*(pi - 6*x)*(pi - 2*x)*(pi + 2*x)*x/pi^4
         sage: expected -= 1/8*(pi - 6*x)*(pi - 2*x)*(pi + 6*x)*x/pi^4
         sage: expected -= 1/8*(pi - 6*x)*(pi + 2*x)*(pi + 6*x)*x/pi^4
@@ -67,7 +68,6 @@ def lagrange_polynomial(f, x, xs):
         True
 
     """
-    ys = [ f(xs[k]) for k in range(0, len(xs)) ]
     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)) ])
     return sigma
@@ -145,7 +145,8 @@ def newton_polynomial(f, x, xs):
     TESTS:
 
         sage: xs = [ -pi/2, -pi/6, 0, pi/6, pi/2 ]
-        sage: L = lagrange_polynomial(sin, x, xs)
+        sage: ys = map(sin, xs)
+        sage: L = lagrange_polynomial(x, xs, ys)
         sage: N = newton_polynomial(sin, x, xs)
         sage: bool(N == L)
         True