matrix.rb: add Matrix#antisymmetric?

* lib/matrix.rb: add Matrix#antisymmetric?.
  Proposed by Yilo (@yiloo). Patch by Marcus Stollsteimer (@stomar).
  [Fix GH-1788]
* spec/ruby/library/matrix/antisymmetric_spec.rb: add specs.

git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@61775 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

lib/matrix.rb

@@ -801,6 +801,18 @@ class Matrix
     true
   end
 
+  #
+  # Returns +true+ if this is an antisymmetric matrix.
+  # Raises an error if matrix is not square.
+  #
+  def antisymmetric?
+    Matrix.Raise ErrDimensionMismatch unless square?
+    each_with_index(:upper) do |e, row, col|
+      return false unless e == -rows[col][row]
+    end
+    true
+  end
+
   #
   # Returns +true+ if this is a unitary matrix
   # Raises an error if matrix is not square.

spec/ruby/library/matrix/antisymmetric_spec.rb

@@ -0,0 +1,35 @@
+require File.expand_path('../../../spec_helper', __FILE__)
+require 'matrix'
+
+describe "Matrix#antisymmetric?" do
+  it "returns true for an antisymmetric Matrix" do
+    Matrix[[0, -2, Complex(1, 3)], [2, 0, 5], [-Complex(1, 3), -5, 0]].antisymmetric?.should be_true
+  end
+
+  it "returns true for a 0x0 empty matrix" do
+    Matrix.empty.antisymmetric?.should be_true
+  end
+
+  it "returns false for non-antisymmetric matrices" do
+    [
+      Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9]],
+      Matrix[[1, -2, 3], [2, 0, 6], [-3, -6, 0]],  # wrong diagonal element
+      Matrix[[0, 2, -3], [2, 0, 6], [-3, 6, 0]]    # only signs wrong
+    ].each do |matrix|
+      matrix.antisymmetric?.should be_false
+    end
+  end
+
+  it "raises an error for rectangular matrices" do
+    [
+      Matrix[[0], [0]],
+      Matrix[[0, 0]],
+      Matrix.empty(0, 2),
+      Matrix.empty(2, 0),
+    ].each do |rectangular_matrix|
+      lambda {
+        rectangular_matrix.antisymmetric?
+      }.should raise_error(Matrix::ErrDimensionMismatch)
+    end
+  end
+end