From 79deafc20bc4cb3704f7f2cfcf845ed09d31eee3 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 3 May 2013 21:51:30 -0400
Subject: [PATCH] Add rank_k_approximation() and its tests.

---
 rank_k_approximation.m             | 19 +++++++++++++++++++
 tests/rank_k_approximation_tests.m | 20 ++++++++++++++++++++
 2 files changed, 39 insertions(+)
 create mode 100644 rank_k_approximation.m
 create mode 100644 tests/rank_k_approximation_tests.m

diff --git a/rank_k_approximation.m b/rank_k_approximation.m
new file mode 100644
index 0000000..ff42f58
--- /dev/null
+++ b/rank_k_approximation.m
@@ -0,0 +1,19 @@
+function Ak = rank_k_approximation(A,k)
+  %
+  % Compute the rank-k approximation to A from the ``k`` largest
+  % singular values of A.
+  %
+  % INPUT:
+  %
+  %   - ``A`` -- The matrix to approximate.
+  %
+  %   - ``k`` -- The rank of the resulting matrix; i.e. the number
+  %              of (large) singular values to keep.
+  %
+  % OUTPUT:
+  %
+  %   - ``Ak`` -- The rank-k approximation to ``A``.
+  %
+  [U, S, V] = svds(A, k);
+  Ak = U*S*V';
+end
diff --git a/tests/rank_k_approximation_tests.m b/tests/rank_k_approximation_tests.m
new file mode 100644
index 0000000..8288752
--- /dev/null
+++ b/tests/rank_k_approximation_tests.m
@@ -0,0 +1,20 @@
+U = [4/5, 3/5, 0  ; ...
+     0  , 4/5, 3/5; ...
+     3/5, 0  , 4/5 ];
+
+S = [ 1, 0, 0;
+      0, 2, 0;
+      0, 0, 3 ];
+
+V = [ 0, 1, 0;
+      1, 0, 0;
+      0, 0, 1 ];
+
+A = U*S*V';
+
+expected = A;
+actual = rank_k_approximation(A, 3);
+
+unit_test_equals("Full rank approximation of a matrix is itself", ...
+		 expected, ...
+		 actual);
-- 
2.43.2