solve function of gem NMatrix

When I tried to use the function "solve" in gem NMatrix, I find wrong result...

I am trying to solve the linear system a*x = b where

a = [[1,  0, 0], 
     [4, -5, 1],
     [0,  0, 1]]

and

b = [0, 0, 729]

Which should give the answer

x = [0, 145.8, 729]

I call the solve function doing a.solve(b) (as explained at http://www.rubydoc.info/gems/nmatrix/0.2.1/NMatrix#solve-instance_method) but it returns

x = [0, 1.013500790889141e-30, 1.013500790889141e-30]

Therefore, I have two questions:

1. Am I doing something wrong?
2. If not, what would be the other solution (excluding GSL) to solve matrix systems with ruby?

Thank you !

To answer part 2 of your question, you can use Ruby's built-in Matrix class.

require 'matrix'

m = Matrix[[1, 0, 0], [4, -5, 1], [0, 0, 1]]
  #=> Matrix[[1, 0, 0], [4, -5, 1], [0, 0, 1]]
b = Vector[0, 0, 729]
  #=> Vector[0, 0, 729]

a = m.lup.solve(b).to_a
  #=> [(0/1), (729/5), (729/1)]

If one prefers floats (rather than rational numbers),

a.map(&:to_f)
  #=> [0.0, 145.8, 729.0]

See Matrix#lup and Matrix::LUPDecomposition#solve, which solve the linear system using LU decomposition.

If the system of linear equations has no solution (e.g., [[0,0], [0,0]]*x = b) or an infinite number of solutions (that is, m is singular), Ruby will raise an exception. For example,

Matrix[[0,0],[0,0]].lup.solve [1, 1]
  #=> ExceptionForMatrix::ErrNotRegular: Not Regular Matrix

require matrix makes both the Matrix and Vector classes (and subclasses) available for use.