marcandre	2014-10-08 04:30:48 +0900 (Wed, 08 Oct 2014)

  New Revision: 47835

  http://svn.ruby-lang.org/cgi-bin/viewvc.cgi?view=revision&revision=47835

  Log:
    * lib/matrix.rb: Add Matrix#laplace_expansion.
      patch by gogo tanaka [#10073]

  Modified files:
    trunk/ChangeLog
    trunk/NEWS
    trunk/lib/matrix.rb
    trunk/test/matrix/test_matrix.rb
Index: ChangeLog
===================================================================
--- ChangeLog	(revision 47834)
+++ ChangeLog	(revision 47835)
@@ -1,3 +1,8 @@ https://github.com/ruby/ruby/blob/trunk/ChangeLog#L1
+Wed Oct  8 04:30:29 2014  Marc-Andre Lafortune  <ruby-core@m...>
+
+	* lib/matrix.rb: Add Matrix#laplace_expansion.
+	  patch by gogo tanaka [#10073]
+
 Wed Oct  8 04:29:21 2014  Marc-Andre Lafortune  <ruby-core@m...>
 
 	* lib/matrix.rb: Add Vector.basis.
Index: lib/matrix.rb
===================================================================
--- lib/matrix.rb	(revision 47834)
+++ lib/matrix.rb	(revision 47835)
@@ -62,6 +62,8 @@ end https://github.com/ruby/ruby/blob/trunk/lib/matrix.rb#L62
 # * #minor(*param)
 # * #first_minor(row, column)
 # * #cofactor(row, column)
+# * #laplace_expansion(row_or_column: num)
+# * #cofactor_expansion(row_or_column: num)
 #
 # Properties of a matrix:
 # * #diagonal?
@@ -685,6 +687,37 @@ class Matrix https://github.com/ruby/ruby/blob/trunk/lib/matrix.rb#L687
     det_of_minor * (-1) ** (row + column)
   end
 
+  #
+  # Returns the Laplace expansion along given row or column.
+  #
+  #    Matrix[[7,6], [3,9]].laplace_expansion(column: 1)
+  #     => 45
+  #
+  #    Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0)
+  #     => Vector[3, -2]
+  #
+  #
+  def laplace_expansion(row: nil, column: nil)
+    num = row || column
+
+    if !num || (row && column)
+      raise ArgumentError, "exactly one the row or column arguments must be specified"
+    end
+
+    Matrix.Raise ErrDimensionMismatch unless square?
+    raise RuntimeError, "laplace_expansion of empty matrix is not defined" if empty?
+
+    unless 0 <= num && num < row_count
+      raise ArgumentError, "invalid num (#{num.inspect} for 0..#{row_count - 1})"
+    end
+
+    send(row ? :row : :column, num).map.with_index { |e, k|
+      e * cofactor(*(row ? [num, k] : [k,num]))
+    }.inject(:+)
+  end
+  alias_method :cofactor_expansion, :laplace_expansion
+
+
   #--
   # TESTING -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
   #++
Index: NEWS
===================================================================
--- NEWS	(revision 47834)
+++ NEWS	(revision 47835)
@@ -84,6 +84,8 @@ with all sufficient information, see the https://github.com/ruby/ruby/blob/trunk/NEWS#L84
       which is obtained by multiplying the first minor by (-1)**(row + column).
     * hstack and vstack are new instance and class methods to stack matrices
       horizontally and vertically.
+    * Matrix#laplace_expansion(row_or_column: num) returns the laplace_expansion
+      along the +num+ -th row or column.
     * Vector.basis(size:, index:) returns the specified basis vector
 
 * Method
Index: test/matrix/test_matrix.rb
===================================================================
--- test/matrix/test_matrix.rb	(revision 47834)
+++ test/matrix/test_matrix.rb	(revision 47835)
@@ -293,6 +293,24 @@ class TestMatrix < Test::Unit::TestCase https://github.com/ruby/ruby/blob/trunk/test/matrix/test_matrix.rb#L293
     assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { Matrix[[2,0,1],[0,-2,2]].cofactor(0, 0) }
   end
 
+  def test_laplace_expansion
+    assert_equal(1, Matrix[[1]].laplace_expansion(row: 0))
+    assert_equal(45, Matrix[[7,6], [3,9]].laplace_expansion(row: 1))
+    assert_equal(0, Matrix[[0,0],[0,0]].laplace_expansion(column: 0))
+    assert_equal(-7, Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(column: 2))
+
+    assert_equal(Vector[3, -2], Matrix[[Vector[1, 0], Vector[0, 1]], [2, 3]].laplace_expansion(row: 0))
+
+    assert_raise(ExceptionForMatrix::ErrDimensionMismatch) { @m1.laplace_expansion(row: 1) }
+    assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion() }
+    assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(foo: 1) }
+    assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(row: 1, column: 1) }
+    assert_raise(ArgumentError) { Matrix[[7,6], [3,9]].laplace_expansion(row: 2) }
+    assert_raise(ArgumentError) { Matrix[[0,0,1],[0,7,6],[1,3,9]].laplace_expansion(column: -1) }
+
+    assert_raise(RuntimeError) { Matrix.empty(0, 0).laplace_expansion(row: 0) }
+  end
+
   def test_regular?
     assert(Matrix[[1, 0], [0, 1]].regular?)
     assert(Matrix[[1, 0, 0], [0, 1, 0], [0, 0, 1]].regular?)

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