複素一般化エルミート固有値問題: パック形式のエルミート定値一般化行列 : (分割統治法)

LAPACKサンプルソースコード : 使用ルーチン名：ZHPGVD

ホーム > LAPACKサンプルプログラム目次 > 複素一般化エルミート固有値問題 > パック形式のエルミート定値一般化行列

概要

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

一般化エルミート固有値問題 $ A B x = \lambda x$の全ての固有値と固有ベクトルを求めます。

\begin{displaymath} A = \left( \begin{array}{cccc} -7.36 & 0.77 - 0.43i & -0.... ...97i & 1.90 - 3.73i & 2.88 + 3.17i & -2.54 \end{array} \right) \end{displaymath}

及び

\begin{displaymath} B = \left( \begin{array}{cccc} 3.23 & 1.51 - 1.92i & 1.90... ...0i & -1.18 - 1.37i & 2.33 + 0.14i & 4.29 \end{array} \right), \end{displaymath}

$ B$の条件数の推定値と計算された固有値と固有ベクトルの誤差限界の近似値も合わせて求めます。

ZHPGVの例題プログラムは一般化エルミート固有値問題 $ A x = \lambda B x$の解き方を示します。

入力データ

（本ルーチンの詳細はZHPGVD のマニュアルページを参照）
このデータをダウンロード 
ZHPGVD Example Program Data

   4                                                        :Value of N

 (-7.36, 0.00) ( 0.77, -0.43) (-0.64, -0.92) ( 3.01, -6.97)
               ( 3.49,  0.00) ( 2.19,  4.45) ( 1.90,  3.73)
                              ( 0.12,  0.00) ( 2.88, -3.17)
                                             (-2.54,  0.00) :End of matrix A

 ( 3.23, 0.00) ( 1.51, -1.92) ( 1.90,  0.84) ( 0.42,  2.50)
               ( 3.58,  0.00) (-0.23,  1.11) (-1.18,  1.37)
                              ( 4.09,  0.00) ( 2.33, -0.14)
                                             ( 4.29,  0.00) :End of matrix B

出力結果

（本ルーチンの詳細はZHPGVD のマニュアルページを参照）
この出力例をダウンロード 
 ZHPGVD Example Program Results

 Eigenvalues
      -61.7321    -6.6195     0.0725    43.1883

 Estimate of reciprocal condition number for B
        2.5E-03

 Error estimates (relative to machine precision)
 for the eigenvalues:
        2.4E+04    2.8E+03    2.3E+02    1.7E+04

ソースコード

（本ルーチンの詳細はZHPGVD 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 
    Program zhpgvd_example

!     ZHPGVD Example Program Text

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

!     .. Use Statements ..
      Use lapack_interfaces, Only: zhpgvd, zlanhp, ztpcon
      Use lapack_precision, Only: dp
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter :: nin = 5, nout = 6
      Character (1), Parameter :: uplo = 'U'
!     .. Local Scalars ..
      Real (Kind=dp) :: anorm, bnorm, eps, rcond, rcondb, t1
      Integer :: aplen, i, info, j, liwork, lrwork, lwork, n
!     .. Local Arrays ..
      Complex (Kind=dp), Allocatable :: ap(:), bp(:), work(:)
      Complex (Kind=dp) :: dummy(1, 1)
      Real (Kind=dp), Allocatable :: eerbnd(:), rwork(:), w(:)
      Real (Kind=dp) :: rdum(1)
      Integer :: idum(1)
      Integer, Allocatable :: iwork(:)
!     .. Intrinsic Procedures ..
      Intrinsic :: abs, epsilon, max, nint, real
!     .. Executable Statements ..
      Write (nout, *) 'ZHPGVD Example Program Results'
      Write (nout, *)
!     Skip heading in data file
      Read (nin, *)
      Read (nin, *) n
      aplen = (n*(n+1))/2
      Allocate (ap(aplen), bp(aplen), eerbnd(n), w(n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
      liwork = -1
      lrwork = -1
      Call zhpgvd(2, 'No vectors', uplo, n, ap, bp, w, dummy, 1, dummy, lwork, &
        rdum, lrwork, idum, liwork, info)

!     Make sure that there is at least the minimum workspace
      lwork = max(2*n, nint(real(dummy(1,1))))
      lrwork = max(n, nint(rdum(1)))
      liwork = max(1, idum(1))
      Allocate (work(lwork), rwork(lrwork), iwork(liwork))

!     Read the upper or lower triangular parts of the matrices A and
!     B from data file

      If (uplo=='U') Then
        Read (nin, *)((ap(i+(j*(j-1))/2),j=i,n), i=1, n)
        Read (nin, *)((bp(i+(j*(j-1))/2),j=i,n), i=1, n)
      Else If (uplo=='L') Then
        Read (nin, *)((ap(i+((2*n-j)*(j-1))/2),j=1,i), i=1, n)
        Read (nin, *)((bp(i+((2*n-j)*(j-1))/2),j=1,i), i=1, n)
      End If

!     Compute the one-norms of the symmetric matrices A and B

      anorm = zlanhp('One norm', uplo, n, ap, rwork)
      bnorm = zlanhp('One norm', uplo, n, bp, rwork)

!     Solve the generalized symmetric eigenvalue problem
!     A*B*x = lambda*x (itype = 2)

      Call zhpgvd(2, 'No vectors', uplo, n, ap, bp, w, dummy, 1, work, lwork, &
        rwork, lrwork, iwork, liwork, info)

      If (info==0) Then

!       Print solution

        Write (nout, *) 'Eigenvalues'
        Write (nout, 100) w(1:n)

!       Call ZTPCON to estimate the reciprocal condition
!       number of the Cholesky factor of B.  Note that:
!       cond(B) = 1/rcond**2.  ZTPCON requires WORK and RWORK to be
!       of length at least 2*n and n respectively

        Call ztpcon('One norm', uplo, 'Non-unit', n, bp, rcond, work, rwork, &
          info)

!       Print the reciprocal condition number of B

        rcondb = rcond**2
        Write (nout, *)
        Write (nout, *) 'Estimate of reciprocal condition number for B'
        Write (nout, 110) rcondb

!       Get the machine precision, eps, and if rcondb is not less
!       than eps**2, compute error estimates for the eigenvalues

        eps = epsilon(1.0E0_dp)
        If (rcond>=eps) Then
          t1 = anorm*bnorm
          Do i = 1, n
            eerbnd(i) = t1 + abs(w(i))/rcondb
          End Do

!         Print the approximate error bounds for the eigenvalues

          Write (nout, *)
          Write (nout, *) 'Error estimates (relative to machine precision)'
          Write (nout, *) 'for the eigenvalues:'
          Write (nout, 110) eerbnd(1:n)
        Else
          Write (nout, *)
          Write (nout, *) 'B is very ill-conditioned, error ', &
            'estimates have not been computed'
        End If
      Else If (info>n .And. info<=2*n) Then
        i = info - n
        Write (nout, 120) 'The leading minor of order ', i, &
          ' of B is not positive definite'
      Else
        Write (nout, 130) 'Failure in ZHPGVD. INFO =', info
      End If

100   Format (3X, (6F11.4))
110   Format (4X, 1P, 6E11.1)
120   Format (1X, A, I4, A)
130   Format (1X, A, I4)
    End Program


ご案内
関連情報
Privacy Policy  /  Trademarks