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
---
 lib/matrix.rb | 33 +++++++++++++++++++++++++++++++++
 1 file changed, 33 insertions(+)

(limited to 'lib/matrix.rb')

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 -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
   #++
-- 
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