From 56d5728589f9cfea6e1d923d5faab8f1b982d29d Mon Sep 17 00:00:00 2001
From: marcandre <marcandre@b2dd03c8-39d4-4d8f-98ff-823fe69b080e>
Date: Tue, 7 Oct 2014 19:30:48 +0000
Subject: * lib/matrix.rb: Add Matrix#laplace_expansion.   patch by gogo tanaka
 [#10073]

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@47835 b2dd03c8-39d4-4d8f-98ff-823fe69b080e
---
 ChangeLog                  |  5 +++++
 NEWS                       |  2 ++
 lib/matrix.rb              | 33 +++++++++++++++++++++++++++++++++
 test/matrix/test_matrix.rb | 18 ++++++++++++++++++
 4 files changed, 58 insertions(+)

diff --git a/ChangeLog b/ChangeLog
index 6c069a0d55..a860bf88df 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,8 @@
+Wed Oct  8 04:30:29 2014  Marc-Andre Lafortune  <ruby-core@marc-andre.ca>
+
+	* lib/matrix.rb: Add Matrix#laplace_expansion.
+	  patch by gogo tanaka [#10073]
+
 Wed Oct  8 04:29:21 2014  Marc-Andre Lafortune  <ruby-core@marc-andre.ca>
 
 	* lib/matrix.rb: Add Vector.basis.
diff --git a/NEWS b/NEWS
index 8222050f93..021c1f9cb4 100644
--- a/NEWS
+++ b/NEWS
@@ -84,6 +84,8 @@ with all sufficient information, see the ChangeLog file.
       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
diff --git a/lib/matrix.rb b/lib/matrix.rb
index 054c197b52..b56b12819a 100644
--- a/lib/matrix.rb
+++ b/lib/matrix.rb
@@ -62,6 +62,8 @@ end
 # * #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
     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 -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
   #++
diff --git a/test/matrix/test_matrix.rb b/test/matrix/test_matrix.rb
index eb62a326b6..2d99cead42 100644
--- a/test/matrix/test_matrix.rb
+++ b/test/matrix/test_matrix.rb
@@ -293,6 +293,24 @@ class TestMatrix < Test::Unit::TestCase
     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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