* lib/matrix.rb: Add Matrix#cofactor [fix GH-568]

Patch by gogotanaka

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@45528 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

ChangeLog

@@ -1,3 +1,10 @@
+Mon Apr  7 02:39:48 2014  Marc-Andre Lafortune  <ruby-core@marc-andre.ca>
+
+	* lib/matrix.rb: Add Matrix#cofactor [fix GH-568]
+	  Add first_minor [fix GH-568]
+	  Handle empty diagonal matrix case [fix GH-576]
+	  Patches by gogotanaka
+
 Sun Apr  6 08:52:50 2014  Bugra Barin  <bugrabarin@hotmail.com>
 
 	* dln.c (dln_load): use wchar version to load a library in

NEWS

@@ -31,6 +31,8 @@ with all sufficient information, see the ChangeLog file.
   * New methods:
     * Matrix#first_minor(row, column) returns the submatrix obtained
       by deleting the specified row and column.
+    * Matrix#cofactor(row, column) returns the (row, column) cofactor
+      which is obtained by multiplying the first minor by (-1)**(row + column).
 
 === Core classes compatibility issues (excluding feature bug fixes)
 

lib/matrix.rb

@@ -59,6 +59,7 @@ end
 # * #find_index
 # * #minor(*param)
 # * #first_minor(row, column)
+# * #cofactor(row, column)
 #
 # Properties of a matrix:
 # * #diagonal?
@@ -545,6 +546,7 @@ class Matrix
     nil
   end
   alias_method :find_index, :index
+
   #
   # Returns a section of the matrix.  The parameters are either:
   # *  start_row, nrows, start_col, ncols; OR
@@ -619,6 +621,21 @@ class Matrix
     new_matrix arrays, column_count - 1
   end
 
+  #
+  # Returns the (row, column) cofactor which is obtained by multiplying
+  # the first minor by (-1)**(row + column).
+  #
+  #   Matrix.diagonal(9, 5, -3, 4).cofactor(1, 1)
+  #     => -108
+  #
+  def cofactor(row, column)
+    raise RuntimeError, "cofactor of empty matrix is not defined" if empty?
+    Matrix.Raise ErrDimensionMismatch unless square?
+
+    det_of_minor = first_minor(row, column).determinant
+    det_of_minor * (-1) ** (row + column)
+  end
+
   #--
   # TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
   #++

test/matrix/test_matrix.rb

@@ -262,6 +262,17 @@ class TestMatrix < Test::Unit::TestCase
     assert_raise(ArgumentError) { @m1.first_minor(-1, 4) }
   end
 
+  def test_cofactor
+    assert_equal(1, Matrix[[1]].cofactor(0, 0))
+    assert_equal(9, Matrix[[7,6],[3,9]].cofactor(0, 0))
+    assert_equal(0, Matrix[[0,0],[0,0]].cofactor(0, 0))
+    assert_equal(3, Matrix[[0,0,1],[0,7,6],[1,3,9]].cofactor(1, 0))
+    assert_equal(-21, Matrix[[7,0,1,0,12],[8,1,1,9,1],[4,0,0,-7,17],[-1,0,0,-4,8],[10,1,1,8,6]].cofactor(2, 3))
+    assert_raise(RuntimeError) { Matrix.empty(0, 0).cofactor(0, 0) }
+    assert_raise(ArgumentError) { Matrix[[0,0],[0,0]].cofactor(-1, 4) }
+    assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { Matrix[[2,0,1],[0,-2,2]].cofactor(0, 0) }
+  end
+
   def test_regular?
     assert(Matrix[[1, 0], [0, 1]].regular?)
     assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].regular?)