計算ルーチン: 実三重対角行列の LU 分解

DGTTRF Example Program Data
   5                           :Value of N
        2.1  -1.0   1.9   8.0
  3.0   2.3  -5.0  -0.9   7.1
  3.4   3.6   7.0  -6.0        :End of matrix A

 DGTTRF Example Program Results

 Details of factorization

  Second superdiagonal of U
   -1.0000   1.9000   8.0000

  First superdiagonal of U
    2.3000  -5.0000  -0.9000   7.1000

  Main diagonal of U
    3.4000   3.6000   7.0000  -6.0000  -1.0154

  Multipliers
    0.8824   0.0196   0.1401  -0.0148

  Vector of interchanges
         2        3        4        5        5

    Program dgttrf_example

!     DGTTRF Example Program Text

!     Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com

!     .. Use Statements ..
      Use lapack_interfaces, Only: dgttrf
      Use lapack_precision, Only: dp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter :: nin = 5, nout = 6
!     .. Local Scalars ..
      Integer :: info, n
!     .. Local Arrays ..
      Real (Kind=dp), Allocatable :: d(:), dl(:), du(:), du2(:)
      Integer, Allocatable :: ipiv(:)
!     .. Executable Statements ..
      Write (nout, *) 'DGTTRF Example Program Results'
      Write (nout, *)
!     Skip heading in data file
      Read (nin, *)
      Read (nin, *) n

      Allocate (d(n), dl(n-1), du(n-1), du2(n-2), ipiv(n))

!     Read the tridiagonal matrix A from data file

      Read (nin, *) du(1:n-1)
      Read (nin, *) d(1:n)
      Read (nin, *) dl(1:n-1)

!     Factorize the tridiagonal matrix A
      Call dgttrf(n, dl, d, du, du2, ipiv, info)

      If (info>0) Then
        Write (nout, 100) 'The (', info, ',', info, ')', &
          ' element of the factor U is zero'
      End If

!     Print details of the factorization

      Write (nout, *) 'Details of factorization'
      Write (nout, *)
      Write (nout, *) ' Second superdiagonal of U'
      Write (nout, 110) du2(1:n-2)
      Write (nout, *)
      Write (nout, *) ' First superdiagonal of U'
      Write (nout, 110) du(1:n-1)
      Write (nout, *)
      Write (nout, *) ' Main diagonal of U'
      Write (nout, 110) d(1:n)
      Write (nout, *)
      Write (nout, *) ' Multipliers'
      Write (nout, 110) dl(1:n-1)
      Write (nout, *)
      Write (nout, *) ' Vector of interchanges'
      Write (nout, 120) ipiv(1:n)

100   Format (1X, A, I3, A, I3, A, A)
110   Format (1X, 8F9.4)
120   Format (1X, 5I9)
    End Program