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Ruby script to do LU-decomposition by outer-product form.
#! /usr/local/bin/ruby
# ***********************************************
# LU 分解(外積形式ガウス法(outer-product form))
# ***********************************************
#
class LuDecomposition
# 元の行列
A = [
[2, -3, 1],
[1, 1, -1],
[3, 5, -7]
]
# 実行
def exec
display("A", A) # 元の行列 A
lu = lu_decompose(A) # LU 分解
display("LU", lu) # 結果出力
end
private
# LU 分解
# * L の対角要素を 1 とする
#
# @param a: 元の正方行列 A(n, n)
# @return a: LU 分解後の正方行列 A(n, n)
def lu_decompose(a)
n = a.size
begin
0.upto(n - 1) do |k|
if a[k][k] == 0
puts "Can't divide by 0 ..."
exit
end
tmp = 1.0 / a[k][k]
(k + 1).upto(n - 1) { |i| a[i][k] *= tmp }
(k + 1).upto(n - 1) do |j|
tmp = a[k][j]
(k + 1).upto(n - 1) { |i| a[i][j] -= a[i][k] * tmp }
end
end
return a
rescue => e
raise
end
end
# 行列出力
#
# @param s: 行列名
# @param a: 行列(n * n)
def display(s, a)
n = a.size
begin
puts "#{s} = "
n.times do |i|
n.times { |j| print " %10.2f" % a[i][j] }
puts
end
rescue => e
raise
end
end
end
LuDecomposition.new.exec if __FILE__ == $0
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