Add diffusion_matrix_sparse() and its tests.

diff --git a/diffusion_matrix_sparse.m b/diffusion_matrix_sparse.m
new file mode 100644 (file)
index 0000000..dbe4e2a
--- /dev/null
+++ b/diffusion_matrix_sparse.m
@@ -0,0 +1,26 @@
+function K = diffusion_matrix_sparse(integerN)
+  ##
+  ## A sparse representation of the matrix K in the advection-diffusion
+  ## equation. See advection_matrix.m for details.
+  ##
+
+  if (integerN < 2)
+    K = NA;
+    return
+  end
+
+  ## The negative ones directly above the diagonal.
+  top = [ [zeros(integerN-1, 1), -speye(integerN-1)]; ...
+          zeros(1, integerN)];
+
+  ## The negative ones directly below the diagonal.
+  bottom = [ [zeros(1, integerN-1); ...
+            -speye(integerN-1)    ], zeros(integerN, 1)];
+
+  ## Combine the top and bottom.
+  K = top + bottom + 2*speye(integerN);
+
+  ## Fill in the entries in the corner.
+  K(1, integerN) = -1;
+  K(integerN, 1) = -1;
+end

diff --git a/tests/diffusion_matrix_sparse_tests.m b/tests/diffusion_matrix_sparse_tests.m
new file mode 100644 (file)
index 0000000..735c79b
--- /dev/null
+++ b/tests/diffusion_matrix_sparse_tests.m
@@ -0,0 +1,11 @@
+expected_K = [2, -1, 0, 0, -1;
+             -1, 2, -1, 0, 0;
+             0, -1, 2, -1, 0;
+             0, 0, -1, 2, -1;
+             -1, 0, 0, -1, 2];
+
+actual_K = diffusion_matrix_sparse(5);
+
+unit_test_equals("diffusion_matrix_sparse(5) looks right", ...
+                true, ...
+                isequal(actual_K, expected_K));