Contents

module Stick

  class Matrix

    module LU

      #  Return the Gauss vector, MC, Golub, 3.2.1 Gauss Transformation, p94

      def LU.gauss_vector(mat, k)
        t = mat.column2matrix(k)
        tk = t[k, 0]
        (0..k).each{|i| t[i, 0] = 0}
        return t if tk == 0
        (k+1...mat.row_size).each{|i| t[i, 0] = t[i, 0].to_f / tk}
        t
      end

      # Return the Gauss transformation matrix: M_k = I - tau * e_k^T

      def LU.gauss(mat, k)
        i = Matrix.I(mat.column_size)
        tau = gauss_vector(mat, k)
        e = i.row2matrix(k)
        i - tau * e
      end

      # LU factorization: A = LU
      # where L is lower triangular and U is upper triangular

      def LU.factorization(mat)
        u = mat.clone
        n = u.column_size
        i = Matrix.I(n)
        l = i.clone
        (n-1).times {|k|
          mk = gauss(u, k)
          u = mk * u  # M_{n-1} * ... * M_1 * A = U
          l += i - mk  # L = M_1^{-1} * ... * M_{n-1}^{-1} = I + sum_{k=1}^{n-1} tau * e
        }
        return l, u
      end
    end

    # Return the upper triangular matrix of LU factorization
    # M_{n-1} * ... * M_1 * A = U

    def U
      LU.factorization(self)[1]
    end

    # Return the lower triangular matrix of LU factorization
    # L = M_1^{-1} * ... * M_{n-1}^{-1} = I + sum_{k=1}^{n-1} tau * e

    def L
      LU.factorization(self)[0]
    end

  end

end

Version data entries

1 entries across 1 versions & 1 rubygems

Version	Path
stick-1.3.3	lib/stick/matrix/lu.rb