Feature #10056: [PATCH 0/1]Add #adjugate method to matrix class

• Status: Closed
• Assignee: marcandre (Marc-Andre Lafortune)
• Target version: -

[gogotanaka (Kazuki Tanaka)]

Add Matrix#adjugate to make a matrix adjugate.

Adjugate is really important operator to handle matrix (especially Exploring Data with ruby)

# Property

* Any n-th matrix  `m`(object of Matrix class) Satisfy the following conditions

Matrix.identity(n) == (m.adjugate * m) / m.det

# Differential vector or matrix
Let A = (a(i, j)) is n-th matrix, A(i, j) is adjugate matrix excluding the j and column i row A.

def. ∂det(A)/∂a(i,j) = (-1) ** (i + j) * det(A(i, j))

Some people regards adjugate matrix as Hermitian adjoint.

I regard adjuate matrix as transpose of the cofactor matrix by referencing http://en.wikipedia.org/wiki/Adjugate_matrix.

[gogotanaka (Kazuki Tanaka)]

• File add_matrix#adjugate_method.patch add_matrix#adjugate_method.patch added

[hsbt (Hiroshi SHIBATA)]

• Status changed from Open to Assigned
• Assignee set to marcandre (Marc-Andre Lafortune)

[nagachika (Tomoyuki Chikanaga)]

Hello,

The patch seems fine to me.
I'd like to add some assertions for the testcase.
These are deribed from "Properties of Adjugate matrix" in Wikipedia. tanaka san, how about it?

## adj(I) = I
assert_equal(Matrix.identity(2), Matrix.identity(2).adjugate)
assert_equal(Matrix.identity(3), Matrix.identity(3).adjugate)
## adj(A * B) = ajd(B) * adj(A)
a = Matrix[[4, 1, -3], [0, 3, 7], [11, -4, 2]]
b = Matrix[[-7, 7, -10], [9, -3, -2], [-1, 3, 9]]
assert_equal((a * b).adjugate, b.adjugate * a.adjugate)
## adj(cA) = c^(n-1) * adj(A)
assert_equal((3**2) * a.adjugate, (3 * a).adjugate)

Marc-Andre, how do you think?

[gogotanaka (Kazuki Tanaka)]

• File update_news.patch update_news.patch added
• File implement.patch implement.patch added
• File add_test.patch add_test.patch added

@Tomoyuki Chikanaga san

Sorry for my delay. I was little bit puzzled about how to test well.

I suppose it's better to add not only #adjugate but also all of such a testcase about properties by instance variable.

I'm gonna make another ticket :)

Right now, I added testcase for Matrix#adjugate and separated patches. It ready for merging.

Take your time.

[marcandre (Marc-Andre Lafortune)]

• Category set to lib
• Status changed from Assigned to Closed

Committed, thanks for this request!