How do I extract a submatrix from a matrix in ruby - ruby

Question

What would be the idiomatic way of extracting a submatrix from a matrix in ruby.
I have a matrix like, this is an object of Matrix
[131, 673, 234, 103, 18]
[201, 96, 342, 965, 150]
[630, 803, 746, 422, 111]
[537, 699, 497, 121, 956]
[805, 732, 524, 37, 331]
I'm looking for a method with a signature like
matrix.submatrix(1,1) this should return
[96, 342, 965, 150]
[803, 746, 422, 111]
[699, 497, 121, 956]
[732, 524, 37, 331]
matrix.submatrix(2,2) would return
[746, 422, 111]
[497, 121, 956]
[524, 37, 331]
I browsed through the rubydoc but couldn't find any method that would give me what I wanted. How would I do this in ruby?
For a 2D array I have come up with
def submatrix(matrix)
submatrix = matrix.collect{|row| row.slice(1..-1)}
# Pop off the first row
submatrix[1..-1]
end
I am wondering if I should reinvent the wheel or could I use something from the Matrix class.

Answer 1

Take a look at Matrix#minor:
a = [[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]]
m = Matrix[*a]
m1 = m.minor(1..4, 1..4)
=> Matrix[[96, 342, 965, 150], [803, 746, 422, 111],
[699, 497, 121, 956], [732, 524, 37, 331]]
m2 = m1.minor(1..3, 1..3)
=> Matrix[[746, 422, 111], [497, 121, 956], [524, 37, 331]]
You can also do:
m1 = m.minor(1..-1, 1..-1)
m2 = m1.minor(1..-1, 1..-1)
Or:
class Matrix
def submatrix(x, y)
self.minor(x..-1, y..-1)
end
end
m.submatrix(2, 2)
=> Matrix[[746, 422, 111], [497, 121, 956], [524, 37, 331]]

Answer 2

If you are using Ruby 2.2.0 or later, you can use Matrix#first_minor, which removes a specified row and column. I'm not sure how efficient it is, but here is some code that solves your problem:
require 'matrix'
def my_submatrix(matrix, n)
matrix = matrix.first_minor(0, 0) while matrix.row_count > n
matrix
end
m = Matrix[[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]]
p my_submatrix(m, 3)
# => Matrix[[746, 422, 111], [497, 121, 956], [524, 37, 331]]

Answer 3

Here are a couple of ways, one using a Matrix object, the other just manipulating an array.
Manipulating a Matrix object
Code
require 'matrix'
def doit(matrix,i,j)
selection_matrix(matrix.row_count,i) * matrix *
selection_matrix(matrix.row_size,j)
end
def selection_matrix(n,m)
Matrix.diagonal(*(0...n).map { |i| (i<m) ? 0 : 1 })
end
Use doit(matrix,i,j).to_a to return an Array object.
Examples
a = [[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]]
matrix = Matrix[*a]
doit(matrix,2,2)
#=> Matrix[[0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0],
# [0, 0, 746, 422, 111],
# [0, 0, 497, 121, 956],
# [0, 0, 524, 37, 331]]
doit(matrix,1,1)
#=> Matrix[[0, 0, 0, 0, 0],
# [0, 96, 342, 965, 150],
# [0, 803, 746, 422, 111],
# [0, 699, 497, 121, 956],
# [0, 732, 524, 37, 331]]
Explanation
selection_matrix(n,m) returns a diagonal matrix whose diagonal elements are ones and zeros, the ones stabing out the appropriate rows or columns of the matrix. The matrix is pre-multiplied (post-multiplied) by a diagonal matrix whose order equals the number of rows (columns) of the matrix.
selection_matrix(5,2)
#=> Matrix[[0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0],
# [0, 0, 1, 0, 0],
# [0, 0, 0, 1, 0],
# [0, 0, 0, 0, 1]]
a = selection_matrix(5,2) * matrix
#=> Matrix[[ 0, 0, 0, 0, 0],
# [ 0, 0, 0, 0, 0],
# [630, 803, 746, 422, 111],
# [537, 699, 497, 121, 956],
# [805, 732, 524, 37, 331]]
b = a * selection_matrix(5,2)
#=> Matrix[[0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0],
# [0, 0, 746, 422, 111],
# [0, 0, 497, 121, 956],
# [0, 0, 524, 37, 331]]
b.to_a
#=> [[0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0],
# [0, 0, 746, 422, 111],
# [0, 0, 497, 121, 956],
# [0, 0, 524, 37, 331]]
Manipulating an Array object
Without creating a Matrix object, you could just do this:
Code
def doit(a,i,j)
a[i..-1].transpose[j..-1].transpose
end
Examples
a = [[131, 673, 234, 103, 18],
[201, 96, 342, 965, 150],
[630, 803, 746, 422, 111],
[537, 699, 497, 121, 956],
[805, 732, 524, 37, 331]]
doit(a,1,1)
#=> [[ 96, 342, 965, 150],
# [803, 746, 422, 111],
# [699, 497, 121, 956],
# [732, 524, 37, 331]]
doit(a,2,2)
#=> [[746, 422, 111],
# [497, 121, 956],
# [524, 37, 331]]