Add tests for wood1().
[octave.git] / central_difference.m
1 function coefficients = central_difference(xs, x)
2 ##
3 ## The first order central difference at x1 is,
4 ##
5 ## f'(x1) = (f(x2) - f(x0))/2
6 ##
7 ## where the index x1 is of course arbitrary but x2, x0 are adjacent
8 ## to x1. The coefficients we seek are the coefficients of f(xj) for
9 ## j = 1,...,N-2, where N is the length of ``xs``. We omit the first
10 ## and last coefficient because at x0 and xN, the previous/next
11 ## value is not available.
12 ##
13 ## This should probably take an 'order' parameter as well; see
14 ## forward_euler().
15 ##
16 ## INPUT:
17 ##
18 ## * ``xs`` - The vector of x-coordinates.
19 ##
20 ## * ``x`` - The point `x` at which you'd like to evaluate the
21 ## derivative of the specified `integer_order`. This should be an
22 ## element of `xs`.
23 ##
24 ## OUTPUT:
25 ##
26 ## * ``coefficients`` - The vector of coefficients, in order, of
27 ## f(x0), f(x1), ..., f(xn).
28 ##
29
30 if (length(xs) < 3)
31 ## We need at least one point other than the first and last.
32 coefficients = NA;
33 return;
34 end
35
36 x_idx = find(xs == x);
37
38 if (x_idx == 1 || x_idx == length(xs))
39 ## You asked for the difference at the first or last element, which
40 ## we can't do.
41 coefficients = NA;
42 return;
43 end
44
45 ## Start with a vector of zeros.
46 coefficients = zeros(1, length(xs));
47
48 ## And fill in the two values that we know.
49 coefficients(x_idx - 1) = -1/2;
50 coefficients(x_idx + 1) = 1/2;
51 end