ZGGES(複素一般化非対称固有値問題) LAPACKサンプルソースコード

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概要

本サンプルはFortran言語によりLAPACKルーチンZGGESを利用するサンプルプログラムです。

行列対

の一般化Schur分解を行います。

$\begin{displaymath} A = \left( \begin{array}{rrrr} -21.10 - 22.50i & 53.50 - ... ...3.30i & -32.50 - 46.00i & -19.00 - 32.50i \end{array} \right) \end{displaymath}$

及び

$\begin{displaymath} B = \left( \begin{array}{rrrr} 1.00 - 5.00i & 1.60 + 1.20... ...80 + 2.40i & 0.00 - 4.00i & 4.00 - 5.00i \end{array} \right). \end{displaymath}$

入力データ

（本ルーチンの詳細はZGGES のマニュアルページを参照）

このデータをダウンロード

ZGGES Example Program Data
  4                                                               : Value of N
  (-21.10,-22.50) ( 53.50,-50.50) (-34.50,127.50) (  7.50,  0.50)
  ( -0.46, -7.78) ( -3.50,-37.50) (-15.50, 58.50) (-10.50, -1.50)
  (  4.30, -5.50) ( 39.70,-17.10) (-68.50, 12.50) ( -7.50, -3.50)
  (  5.50,  4.40) ( 14.40, 43.30) (-32.50,-46.00) (-19.00,-32.50) : End of A
  (  1.00, -5.00) (  1.60,  1.20) ( -3.00,  0.00) (  0.00, -1.00)
  (  0.80, -0.60) (  3.00, -5.00) ( -4.00,  3.00) ( -2.40, -3.20)
  (  1.00,  0.00) (  2.40,  1.80) ( -4.00, -5.00) (  0.00, -3.00)
  (  0.00,  1.00) ( -1.80,  2.40) (  0.00, -4.00) (  4.00, -5.00) : End of B

出力結果

（本ルーチンの詳細はZGGES のマニュアルページを参照）

この出力例をダウンロード

 ZGGES Example Program Results

 Generalized Eigenvalues
  1   (  3.00, -9.00)
  2   (  4.00, -5.00)
  3   (  2.00, -5.00)
  4   (  3.00, -1.00)

ソースコード

（本ルーチンの詳細はZGGES のマニュアルページを参照）

※本サンプルソースコードのご利用手順は「サンプルのコンパイル及び実行方法」をご参照下さい。

このソースコードをダウンロード

    Module zgges_mod

!     ZGGES Example Program Module:

!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Private
      Public :: selctg
    Contains
      Function selctg(a, b)
!       .. Use Statements ..
        Use lapack_precision, Only: dp
!       .. Implicit None Statement ..
        Implicit None
!       .. Function Return Value ..
        Logical :: selctg
!       .. Scalar Arguments ..
        Complex (Kind=dp), Intent (In) :: a, b
!       .. Intrinsic Procedures ..
        Intrinsic :: abs
!       .. Executable Statements ..
        Continue

!       Dummy function - it is not called by ZGGES when sorting is not required.
        selctg = (abs(a)<6.0_dp*abs(b))

        Return
      End Function
    End Module
    Program zgges_example

!     ZGGES Example Program Text

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

!     .. Use Statements ..
      Use blas_interfaces, Only: zgemm
      Use lapack_example_aux, Only: nagf_sort_realvec_rank, &
        nagf_file_print_matrix_complex_gen_comp, &
        nagf_sort_cmplxvec_rank_rearrange
      Use lapack_interfaces, Only: zgges, zlange
      Use lapack_precision, Only: dp
      Use zgges_mod, Only: selctg
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter :: nb = 64, nin = 5, nout = 6
      Logical, Parameter :: chkfac = .False., prmat = .False.
!     .. Local Scalars ..
      Complex (Kind=dp) :: alph, bet
      Real (Kind=dp) :: normd, norme
      Integer :: i, ifail, info, lda, ldb, ldc, ldd, lde, ldvsl, ldvsr, lwork, &
        n, sdim
      Logical :: factor
!     .. Local Arrays ..
      Complex (Kind=dp), Allocatable :: a(:, :), alpha(:), b(:, :), beta(:), &
        c(:, :), d(:, :), e(:, :), vsl(:, :), vsr(:, :), work(:)
      Complex (Kind=dp) :: wdum(1)
      Real (Kind=dp), Allocatable :: rwork(:)
      Integer, Allocatable :: irank(:)
      Logical, Allocatable :: bwork(:)
      Character (1) :: clabs(1), rlabs(1)
!     .. Intrinsic Procedures ..
      Intrinsic :: abs, all, cmplx, epsilon, max, nint, real
!     .. Executable Statements ..
      Write (nout, *) 'ZGGES Example Program Results'
      Write (nout, *)
      Flush (nout)
!     Skip heading in data file
      Read (nin, *)
      Read (nin, *) n
      lda = n
      ldb = n
      ldc = n
      ldd = n
      lde = n
      ldvsl = n
      ldvsr = n
      Allocate (a(lda,n), alpha(n), b(ldb,n), beta(n), c(ldc,n), d(ldd,n), &
        e(lde,n), vsl(ldvsl,n), vsr(ldvsr,n), rwork(8*n), bwork(n), irank(n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
      Call zgges('Vectors (left)', 'Vectors (right)', 'No sort', selctg, n, a, &
        lda, b, ldb, sdim, alpha, beta, vsl, ldvsl, vsr, ldvsr, wdum, lwork, &
        rwork, bwork, info)

!     Make sure that there is enough workspace for block size nb.
      lwork = max((nb+1)*n, nint(real(wdum(1))))
      Allocate (work(lwork))

!     Read in the matrices A and B
      Read (nin, *)(a(i,1:n), i=1, n)
      Read (nin, *)(b(i,1:n), i=1, n)

!     Copy A and B into D and E respectively
      d(1:n, 1:n) = a(1:n, 1:n)
      e(1:n, 1:n) = b(1:n, 1:n)

      If (prmat) Then
!       Print matrices A and B
!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0
        Call nagf_file_print_matrix_complex_gen_comp('General', ' ', n, n, a, &
          lda, 'Bracketed', 'F8.4', 'Matrix A', 'Integer', rlabs, 'Integer', &
          clabs, 80, 0, ifail)
        Write (nout, *)
        Flush (nout)

        ifail = 0
        Call nagf_file_print_matrix_complex_gen_comp('General', ' ', n, n, b, &
          ldb, 'Bracketed', 'F8.4', 'Matrix B', 'Integer', rlabs, 'Integer', &
          clabs, 80, 0, ifail)
        Write (nout, *)
        Flush (nout)
      End If

      factor = .True.
!     Find the generalized Schur form
      Call zgges('Vectors (left)', 'Vectors (right)', 'No sort', selctg, n, a, &
        lda, b, ldb, sdim, alpha, beta, vsl, ldvsl, vsr, ldvsr, work, lwork, &
        rwork, bwork, info)

      If (info>0) Then
        Write (nout, 100) 'Failure in ZGGES. INFO =', info
        factor = .False.
      Else If (chkfac) Then

!       Compute A - Q*S*Z^H from the factorization of (A,B) and store in
!       matrix D
        alph = cmplx(1, kind=dp)
        bet = cmplx(0, kind=dp)
        Call zgemm('N', 'N', n, n, n, alph, vsl, ldvsl, a, lda, bet, c, ldc)
        alph = cmplx(-1, kind=dp)
        bet = cmplx(1, kind=dp)
        Call zgemm('N', 'C', n, n, n, alph, c, ldc, vsr, ldvsr, bet, d, ldd)

!       Compute B - Q*T*Z^H from the factorization of (A,B) and store in
!       matrix E
        alph = cmplx(1, kind=dp)
        bet = cmplx(0, kind=dp)
        Call zgemm('N', 'N', n, n, n, alph, vsl, ldvsl, b, ldb, bet, c, ldc)
        alph = cmplx(-1, kind=dp)
        bet = cmplx(1, kind=dp)
        Call zgemm('N', 'C', n, n, n, alph, c, ldc, vsr, ldvsr, bet, e, lde)

!       Find norms of matrices D and E and warn if either is too large
        normd = zlange('O', ldd, n, d, ldd, rwork)
        norme = zlange('O', lde, n, e, lde, rwork)
        If (normd>epsilon(1.0E0_dp)**0.75_dp) Then
          Write (nout, *) 'Norm of A-(Q*S*Z^H) is much greater than 0.'
          factor = .False.
        End If
        If (norme>epsilon(1.0E0_dp)**0.75_dp) Then
          Write (nout, *) 'Norm of B-(Q*T*Z^H) is much greater than 0.'
          factor = .False.
        End If
      End If
      If (factor) Then
!       Sort and print generalized eigenvalues if none are infinite
        If (all(real(beta(1:n))>0.0_dp)) Then
          work(1:n) = alpha(1:n)/beta(1:n)
          rwork(1:n) = abs(work(1:n))

!         Rank eigenvalues
          ifail = 0
          Call nagf_sort_realvec_rank(rwork, 1, n, 'Descending', irank, ifail)

!         Sort eigenvalues in work(1:n)
          Call nagf_sort_cmplxvec_rank_rearrange(work, 1, n, irank, ifail)
          Write (nout, *) 'Generalized Eigenvalues'
          Do i = 1, n
            Write (nout, 110) i, work(i)
          End Do
        End If
      Else
        Write (nout, *) 'Schur factorization has failed.'
      End If

100   Format (1X, A, I4)
110   Format (1X, I2, 3X, '(', F6.2, ',', F6.2, ')')
    End Program

ご案内

複素一般化非対称固有値問題: 非対称行列ペア : (一般化固有値と一般化実シュール形)

LAPACKサンプルソースコード : 使用ルーチン名：ZGGES

概要

入力データ

出力結果

ソースコード