Mercurial > repos > public > sbplib
changeset 660:184833fe4c0e feature/grids
Add monomial, vandermonde and stencil cretation tools
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 14 Nov 2017 16:46:07 +0100 |
| parents | 11a39b274260 |
| children | 905612b7f3d4 |
| files | mononomial.m stencilEquation.m vandermonde.m |
| diffstat | 3 files changed, 31 insertions(+), 0 deletions(-) [+] |
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--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/mononomial.m Tue Nov 14 16:46:07 2017 +0100 @@ -0,0 +1,8 @@ +function y = mononomial(x, k) + if k < 0 + y = x*0; + return + end + y = x.^k/factorial(k); +end +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/stencilEquation.m Tue Nov 14 16:46:07 2017 +0100 @@ -0,0 +1,13 @@ +% Find the equation for the stencil for d^k/dx^k +function [A,b] = stencilEquation(k, offsets, order) + q = sym('q', [1, length(offsets)]); + + p = 0:(order-1+k); + + v = vandermonde(offsets, p); + vdiff = vandermonde( 0, p-k); + + eq = q*v == vdiff; + + [A,b] = equationsToMatrix(eq, q); +end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/vandermonde.m Tue Nov 14 16:46:07 2017 +0100 @@ -0,0 +1,10 @@ +% Create vandermonde matrix for points x and polynomials of order p +% x and p are vectors +% v is a length(x) by length(p) matrix +function V = vandermonde(x, p) + V = sym(zeros(length(x), length(p))); % Is there a way to make this work for both double and sym + + for i = 1:length(p) + V(:, i) = mononomial(x,p(i)); + end +end