/usr/share/doc/ruby-gsl/examples/linalg/SV_solve.rb is in ruby-gsl 2.1.0.3+dfsg1-1build1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | #!/usr/bin/env ruby
require("gsl")
include GSL
m = Matrix[[-2, 1, 1], [1, -2, 1], [1, 1, -2], [-2, 1, 1]]
u, v, s = m.SV_decomp
p u.class
p v.class
p s.class
m2 = Matrix[[5, 6, 8, 4], [6, 2, 4, 2], [8, 2, 3, 5], [1, 7, 2, 3]]
u2, v2, s2 = m2.SV_decomp
p u2
p v2
p s2
m = GSL::Matrix[[0.18, 0.60, 0.57, 0.96], [0.41, 0.24, 0.99, 0.58],
[0.14, 0.30, 0.97, 0.66], [0.51, 0.13, 0.19, 0.85]]
u, v, s = Linalg::SV.decomp_jacobi(m)
b = [1, 2, 3, 4].to_gv
p Linalg::SV.solve(u, v, s, b)
p Linalg::SV.solve(u, v, s, [1, 2, 3, 4])
puts "OK"
p m.SV_solve(b)
p Linalg::SV.solve(m, b)
####
A = Matrix[1..4, 2, 2]
I = Matrix.identity(2)
Ainv = A.inv
u, v, s = A.SV_decomp
sm = s.to_m_diagonal
sinv = s.collect { |elm| 1.0/elm }.to_m_diagonal
a = u*sm*v.trans
ainv = v*sinv*u.trans
p a == A
p ainv == Ainv
p (u.trans*u) == I
p (v.trans*v) == I
p A*v == u*sm
p A.trans*u == v*sm
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