```Issue #15233 has been reported by octonion (Christopher Long).

----------------------------------------
Bug #15233: Speeding Up Matrix Powers
https://bugs.ruby-lang.org/issues/15233

* Author: octonion (Christopher Long)
* Status: Open
* Priority: Normal
* Assignee:
* Target version:
* ruby -v: ruby 2.5.1p57 (2018-03-29 revision 63029) [x86_64-linux-gnu]
* Backport: 2.3: UNKNOWN, 2.4: UNKNOWN, 2.5: UNKNOWN
----------------------------------------
I've been looking at SymPy's slow matrix power speed, and noticed that replacing Ruby's matrix power code with the equivalent code from SymPy makes it significantly faster. As this is a recursively defined function, presumably it can be made even faster with a proper iterative version.

Base:

~~~ ruby
require 'matrix'

Q = Matrix[[0,0,1,0,2,0],
[0,0,0,1,0,0],
[1,0,0,1,0,2],
[0,2,1,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0]]

r = Vector[1,0,0,0,0,0]

p = (Q**100000000*r).sum

puts p.to_s.size
~~~

Output:

~~~
time ruby main.rb
35950264

real    1m42.250s
user    1m41.050s
sys     0m1.184s
~~~

Modified:

~~~ ruby
require 'matrix'

def pow(a,num)
if (num==1)
return a
end
if (num%2)==1
return a*pow(a,num-1)
end
ret = pow(a,(num/2))
ret*ret
end

Q = Matrix[[0,0,1,0,2,0],
[0,0,0,1,0,0],
[1,0,0,1,0,2],
[0,2,1,0,0,0],
[1,0,0,0,0,0],
[0,0,1,0,0,0]]

r = Vector[1,0,0,0,0,0]

p = (pow(Q,100000000)*r).sum

puts p.to_s.size
~~~

Output:

~~~
time ruby main.rb
35950264

real    1m9.489s
user    1m8.661s
sys     0m0.828s
~~~

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