Add Matrix#antisymmetric? and Matrix#reflexive? #1730

fang-niuwa · 2017-10-27T15:14:34Z

Add two methods (“antisymmetric?” and “reflexive?”) determine if the
matrix is reflexive, antisymmetric or not.

Add two methods (“antisymmetric?” and “reflexive?”) determine if the matrix is reflexive, antisymmetric or not.

marcandre · 2017-12-14T06:59:07Z

Thanks for the PR.
These look like valid additions to the library.
The PR some issues though:

needs specs, ideally in `ruby/spec/library/matrix/
the code for antisymmetric looks wrong
would probably be nicer to use all? instead of the return true/false

Would you like to amend your PR?

# Conflicts: # lib/matrix.rb

1. implement method — antisymmetric? 2. use all? instead of the return true/false 3. add specs for both methods

marcandre · 2017-12-26T22:59:50Z

lib/matrix.rb

@@ -28,6 +28,7 @@ module ExceptionForMatrix # :nodoc:
 #
 # The +Matrix+ class represents a mathematical matrix. It provides methods for creating
 # matrices, operating on them arithmetically and algebraically,
+<<<<<<< HEAD


Ooops

stomar · 2017-12-27T13:45:42Z

antisymmetric_spec.rb

+
+describe "Matrix.antisymmetric?" do
+  it "returns true for an antisymmetric matrix" do
+    Matrix[[1, 2, 3], [4, 5, 6], [7, 8, 9]].antisymmetric?.should be_true


this is not an antisymmetric matrix

stomar · 2017-12-27T13:46:12Z

antisymmetric_spec.rb

+  end
+
+  it "returns true for a 0x0 empty matrix" do
+    Matrix.empty.symmetric?should be_true


wrong method

stomar · 2017-12-27T13:51:00Z

antisymmetric_spec.rb

+    Matrix.empty.symmetric?should be_true
+  end
+
+  it "returns false for an asymmetric Matrix" do


??? (An asymmetric matrix can be antisymmetric; what‘s the point of this test?)

stomar · 2017-12-27T13:51:10Z

antisymmetric_spec.rb

+  end
+
+  it "returns false for an asymmetric Matrix" do
+    Matrix[[1, 2],[-2, 1]].symmetric?.should be_false


wrong method

stomar · 2017-12-27T13:52:40Z

antisymmetric_spec.rb

+    Matrix[[1, 2],[-2, 1]].symmetric?.should be_false
+  end
+
+  it "raises an error for rectangular matrices" do


IMO clearer: non-square matrices

stomar · 2017-12-27T13:55:31Z

lib/matrix.rb

+  # Returns +true+ if this is a antisymmetric matrix.
+  # Raises an error if matrix is not square.
+  #
+  def antisymmetric?


implementation does not test for antisymmetric!

stomar · 2017-12-27T13:57:50Z

spec/ruby/library/matrix/reflexive_spec.rb

+  end
+
+  it "returns true for a 0x0 empty matrix" do
+    Matrix.empty.symmetric?.should be_true


wrong method

Thank you for being so patient. Most of the code were follow the style of method "symmetric?". I've learned 1-0 matrix, and it seems to me that reflexive relation cannot applied in a general matrix, this method might not be very helpful, but I'll still fix this problem.

stomar · 2017-12-27T13:58:12Z

spec/ruby/library/matrix/reflexive_spec.rb

+    Matrix.empty.symmetric?.should be_true
+  end
+
+  it "returns true for a non-reflexive Matrix" do


stomar · 2017-12-27T13:58:41Z

spec/ruby/library/matrix/reflexive_spec.rb

+    Matrix[[1, 1],[2, 2]].reflexive?.should be_false
+  end
+
+  it "raises an error for rectangular matrices" do


stomar · 2017-12-27T14:00:53Z

spec/ruby/library/matrix/reflexive_spec.rb

+      Matrix.empty(2, 0),
+    ].each do |rectangular_matrix|
+      lambda {
+        rectangular_matrix.symmetric?


wrong method

stomar · 2017-12-27T14:07:13Z

and: antisymmetric_spec.rb is not in the correct directory

1. in reflexive_spec.rb: change on some wrong code 2.in matrix.rb: method error 3.in antisymmetric_spec.rb: change on some wrong code

marcandre

antisymetric? has already been added, please remove it and keep only reflexive?

marcandre · 2018-02-09T18:52:40Z

lib/matrix.rb

+  #
+  def reflexive?
+    Matrix.Raise ErrDimensionMismatch unless square?
+    self.each(:diagonal) do |e|


self is superfluous. consider using each(:diagonal).all?

marcandre · 2018-02-09T18:53:06Z

lib/matrix.rb

+    self.each(:diagonal) do |e|
+      return false if e != 1
+    end
+    all?


marcandre · 2018-09-20T18:25:25Z

Implementation fixed, code merged 😄

Thanks @Yiloo!

Adapted from a patch by Yilo git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@64796 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

ruby/ruby#1730 ruby/ruby@19fe655

mame · 2018-09-21T14:55:59Z

Is "reflexive" a common word to indicate a matrix whose diagonals are all 1s?

I couldn't (easily) find such a usage by searching with "reflexive matrix" diagonal. I could find some articles including the definition by searching with "matrix is reflexive", but its hit count is just 44. I guess that the word came from "reflexive relation", but I'm unsure if it is also common for matrix.

@marcandre What do you think? /cc @znz

marcandre · 2018-09-21T15:30:57Z

Hmmm, it looks like indeed it's not needed (and easy to do anyways). I'll revert this.

mame · 2018-09-21T17:20:09Z

/cc @stomar @marcandre

Well, there seems to be confusion about the word "antisymmetric".

I believe the OP expected antisymmetric relation: a_ij = 0 or a_ji = 0 for all i ≠ j. However, the PR's implementation checks if a_ij != a_ji for all i ≠ j. I guess it was a bug.
Matrix#antisymmetric in @stomar's #1788, which is the current implementation in trunk, checks if the matrix is skew-symmetric: a_ij == -a_ji for all i != j.
I think that antisymmetric relation is not directly related to antisymmetric matrix. Anyway, the current implementation is different than the OP expected.

Wikipedia's "Skew-symmetric matrix" says (emphasized by me):

In mathematics, particularly in linear algebra, a skew-symmetric (or antisymmetric or antimetric[1]) matrix is a square matrix whose transpose equals its negative

If we have Matrix#antisymmetric?, it should use this definition of "antisymmetric matrix", not "antisymmetric relation". So, @stomar's implementation is the best, I think.

However, I'm not sure whether the name "antisymmetric?" is best. Isn't "skew_symmetric?" better? I'm unfamiliar with math. Wolfram uses the name AntisymmetricMatrix, but it also says:

Antisymmetric matrices are commonly called "skew symmetric matrices" by mathematicians.

Strictly speaking, there is no actual request for the current Matrix#antisymmetric?. Is it really needed? Again, I'm unfamiliar with math.

mame · 2018-09-21T17:36:57Z

@mrkn found: https://physics.stackexchange.com/questions/96687/what-is-the-difference-between-a-skew-symmetric-and-an-antisymmetric-tensor

Physicists tend to favor the term "antisymmetric" and mathematicians tend to favor the term "skew-symmetric" in my experience.

marcandre · 2018-09-21T18:46:27Z

Strictly speaking, there is no actual request for the current Matrix#antisymmetric?. Is it really needed? Again, I'm unfamiliar with math.

I think that antisymmetric? is well defined and thus could be useful to many (contrary to reflexive?). I could add an alias for skew_symmetric? though.

stomar · 2018-09-29T19:49:37Z

Actually, I am a physicist 😄. I thought the concept useful and used enough to have it added to Matrix. An alias might be a good idea.

fang-niuwa · 2018-10-03T18:49:25Z

Is "reflexive" a common word to indicate a matrix whose diagonals are all 1s?

I couldn't (easily) find such a usage by searching with "reflexive matrix" diagonal. I could find some articles including the definition by searching with "matrix is reflexive", but its hit count is just 44. I guess that the word came from "reflexive relation", but I'm unsure if it is also common for matrix.

@marcandre What do you think? /cc @znz

It was my idea to implement this method, as I was taking Discrete Mathematics course in the college. You are right, the reflexive matrix is representing a reflexive relation by using 0-1 matrix. I was not sure if this method would be widely used since a general matrix can have more values than just 0 and 1.

mame · 2018-11-01T05:25:33Z

Thank you for your reply. Now I'm satisfied about antisymmetric?.

@marcandre May I remove reflexive?? I'd like to remove it before 2.6.0 preview 3 if possible.

marcandre · 2018-11-01T12:54:53Z

I'll do it tomorrow, and merge the mutable matrix too, assuming that's ok for you, @mame?

This reverts commit 19fe655.

This reverts commit 19fe655. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@65500 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

Add two methods.

aed48f8

Add two methods (“antisymmetric?” and “reflexive?”) determine if the matrix is reflexive, antisymmetric or not.

hsbt assigned marcandre Dec 14, 2017

marcandre changed the title ~~Add two methods.~~ Add two methods to the Matrix library. Dec 14, 2017

marcandre changed the title ~~Add two methods to the Matrix library.~~ Add Matrix#antisymmetric? and Matrix#reflexive? Dec 14, 2017

Yilo added 3 commits December 25, 2017 12:41

Merge remote-tracking branch 'ruby/trunk' into trunk

3fee1b8

# Conflicts: # lib/matrix.rb

Merge remote-tracking branch 'ruby/trunk' into trunk

a7d453e

Add Matrix#antisymmetric? and Matrix#reflexive? #1730

24102d5

1. implement method — antisymmetric? 2. use all? instead of the return true/false 3. add specs for both methods

marcandre reviewed Dec 26, 2017

View reviewed changes

Yilo added 2 commits December 26, 2017 19:06

Merge remote-tracking branch 'ruby/trunk' into trunk

75f00e8

update file from ruby/trunk

0872247

Ooops

stomar reviewed Dec 27, 2017

View reviewed changes

Yilo added 8 commits December 27, 2017 10:06

Merge remote-tracking branch 'ruby/trunk' into trunk

b9c93f1

Merge remote-tracking branch 'ruby/trunk' into trunk

b99d61b

fix some problems on the code

32ae910

1. in reflexive_spec.rb: change on some wrong code 2.in matrix.rb: method error 3.in antisymmetric_spec.rb: change on some wrong code

Merge remote-tracking branch 'ruby/trunk' into trunk

e974533

typo

c38a244

Merge remote-tracking branch 'ruby/trunk' into trunk

b12acec

Merge remote-tracking branch 'ruby/trunk' into trunk

cce8ab1

typo

bbbb1c6

stomar mentioned this pull request Jan 10, 2018

Add Matrix#antisymmetric? #1788

Closed

matzbot force-pushed the trunk branch from 2677ddd to ce7ad3a Compare January 18, 2018 15:27

marcandre requested changes Feb 9, 2018

View reviewed changes

marcandre closed this Sep 20, 2018

matzbot pushed a commit that referenced this pull request Sep 20, 2018

Matrix: Add #reflexive? method. [Fix GH-1730]

19fe655

Adapted from a patch by Yilo git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@64796 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

znz added a commit to znz/doctree that referenced this pull request Sep 21, 2018

Add Matrix#reflexive?

19710f1

ruby/ruby#1730 ruby/ruby@19fe655

znz mentioned this pull request Nov 1, 2018

Add Matrix#antisymmetric? and Matrix#reflexive? since 2.6.0 rurema/doctree#1014

Merged

marcandre added a commit to marcandre/ruby that referenced this pull request Nov 2, 2018

Revert "Matrix: Add #reflexive? method. [Fix rubyGH-1730]"

875c58a

This reverts commit 19fe655.

matzbot pushed a commit that referenced this pull request Nov 2, 2018

Revert "Matrix: Add #reflexive? method. [Fix GH-1730]"

55961ac

This reverts commit 19fe655. git-svn-id: svn+ssh://ci.ruby-lang.org/ruby/trunk@65500 b2dd03c8-39d4-4d8f-98ff-823fe69b080e

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Add Matrix#antisymmetric? and Matrix#reflexive? #1730

Add Matrix#antisymmetric? and Matrix#reflexive? #1730

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Add Matrix#antisymmetric? and Matrix#reflexive? #1730

Add Matrix#antisymmetric? and Matrix#reflexive? #1730

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