From 8ca30867e869231f85848dc14e15f11e6d9c732b Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Mon, 25 Feb 2013 10:09:03 -0500
Subject: [PATCH] Add envelope() and its tests.

---
 envelope.m             | 38 ++++++++++++++++++++++++++++++++++++++
 tests/envelope_tests.m | 11 +++++++++++
 2 files changed, 49 insertions(+)
 create mode 100644 envelope.m
 create mode 100644 tests/envelope_tests.m

diff --git a/envelope.m b/envelope.m
new file mode 100644
index 0000000..e54f818
--- /dev/null
+++ b/envelope.m
@@ -0,0 +1,38 @@
+function envelope = envelope(A)
+  ## Compute the envelope of the matrix ``A``. The envelope of a matrix
+  ## is defined as the set of indices,
+  ##
+  ##   E = { (i,j) : i < j, A(k,j) != 0 for some k <= i }
+  ##
+  if (!issymmetric(A) && !is_upper_triangular(A))
+    ## The envelope of a matrix is only defined for U-T or symmetric
+    ## matrices.
+    envelope = {NA};
+    return;
+  end
+
+  ## Start with an empty result, and append to it as we find
+  ## satisfactory indices.
+  envelope = {};
+
+  for j = [ 1 : columns(A) ]
+    ## Everything below the first non-zero element in a column will be
+    ## part of the envelope. Since we're moving from top to bottom, we
+    ## can simply set a flag indicating that we've found the first
+    ## non-zero element. Thereafter, everything we encounter should be
+    ## added to the envelope.
+    found_nonzero = false;
+
+    for i = [ 1 : j-1 ]
+      if (A(i,j) != 0)
+        found_nonzero = true;
+      end
+
+      if (found_nonzero)
+	envelope{end+1} = [i,j];
+      end
+    end
+
+  end
+
+end
diff --git a/tests/envelope_tests.m b/tests/envelope_tests.m
new file mode 100644
index 0000000..88f5b4f
--- /dev/null
+++ b/tests/envelope_tests.m
@@ -0,0 +1,11 @@
+A = [2, 1, 1, 0; ...
+     1, 2, 0, 1; ...
+     1, 0, 2, 0; ...
+     0, 1, 0, 1];
+
+expected = { [1,2], [1,3], [2,3], [2,4], [3,4] };
+actual = envelope(A);
+
+unit_test_equals("envelope works on an example", ...
+		 true, ...
+		 isequal(actual, expected));
-- 
2.43.2