From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 21 Jul 2013 21:19:35 +0000 (-0400)
Subject: Rename 'diagonal' to 'diagonal_part'.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=c160f3101ddb9797fd30007d6f628da394628538

Rename 'diagonal' to 'diagonal_part'.
Add functions to pull out the (strict) lower/upper triangular parts of a matrix.
---

diff --git a/src/Linear/Matrix.hs b/src/Linear/Matrix.hs
index 105acef..e4743b5 100644
--- a/src/Linear/Matrix.hs
+++ b/src/Linear/Matrix.hs
@@ -530,13 +530,83 @@ angle v1 v2 =
 --   Examples:
 --
 --   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
---   >>> diagonal m
+--   >>> diagonal_part m
 --   ((1,0,0),(0,5,0),(0,0,9))
 --
-diagonal :: (Arity m, Ring.C a)
+diagonal_part :: (Arity m, Ring.C a)
          => Mat m m a
          -> Mat m m a
-diagonal matrix =
+diagonal_part matrix =
   construct lambda
   where
     lambda i j = if i == j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the on-diagonal and below-diagonal entries of
+--   @matrix@. The above-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> lt_part m
+--   ((1,0,0),(4,5,0),(7,8,9))
+--
+lt_part :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+lt_part matrix =
+  construct lambda
+  where
+    lambda i j = if i >= j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the below-diagonal entries of @matrix@. The on-
+--   and above-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> lt_part_strict m
+--   ((0,0,0),(4,0,0),(7,8,0))
+--
+lt_part_strict :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+lt_part_strict matrix =
+  construct lambda
+  where
+    lambda i j = if i > j then matrix !!! (i,j) else 0
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the on-diagonal and above-diagonal entries of
+--   @matrix@. The below-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> ut_part m
+--   ((1,2,3),(0,5,6),(0,0,9))
+--
+ut_part :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+ut_part = transpose . lt_part . transpose
+
+
+-- | Given a square @matrix@, return a new matrix of the same size
+--   containing only the above-diagonal entries of @matrix@. The on-
+--   and below-diagonal entries are set to zero.
+--
+--   Examples:
+--
+--   >>> let m = fromList [[1,2,3],[4,5,6],[7,8,9]] :: Mat3 Int
+--   >>> ut_part_strict m
+--   ((0,2,3),(0,0,6),(0,0,0))
+--
+ut_part_strict :: (Arity m, Ring.C a)
+        => Mat m m a
+        -> Mat m m a
+ut_part_strict = transpose . lt_part_strict . transpose