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Ruby script to do LU-decomposition by Crout method.
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#! /usr/local/bin/ruby | |
# *********************************************** | |
# LU 分解(クラウト法(Crout method)) | |
# *********************************************** | |
# | |
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 | |
# * U 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| | |
k.upto(n - 1) do |i| | |
sum = 0 | |
0.upto(k - 1) { |j| sum += a[i][j] * a[j][k] } | |
a[i][k] -= sum | |
end | |
if a[k][k] == 0 | |
puts "Can't divide by 0 ..." | |
exit | |
end | |
tmp = 1.0 / a[k][k] | |
(k + 1).upto(n - 1) do |j| | |
sum = 0 | |
0.upto(k - 1) { |i| sum += a[k][i] * a[i][j] } | |
a[k][j] = (a[k][j] - sum) * 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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