NAG Library Manual, Mark 27.3
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f08yyfe

!     F08YYF Example Program Text

!     Mark 27.3 Release. NAG Copyright 2021.

!     .. Use Statements ..
      Use nag_library, Only: f06bnf, f06uaf, nag_wp, x02ajf, ztgevc, ztgsna
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: eps, snorm, stnrm, tnorm
      Integer                          :: i, info, lda, ldb, ldvl, ldvr,       &
                                          lwork, m, n
!     .. Local Arrays ..
      Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), vl(:,:), vr(:,:),  &
      Real (Kind=nag_wp), Allocatable  :: dif(:), rwork(:), s(:)
      Integer, Allocatable             :: iwork(:)
      Logical                          :: select(1)
!     .. Executable Statements ..
      Write (nout,*) 'F08YYF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      lda = n
      ldb = n
      ldvl = n
      ldvr = n
      lwork = 2*n*n
      Allocate (a(lda,n),b(ldb,n),vl(ldvl,n),vr(ldvr,n),work(lwork),dif(n),    &

!     Read A and B from data file

      Read (nin,*)(a(i,1:n),i=1,n)
      Read (nin,*)(b(i,1:n),i=1,n)

!     Calculate the left and right generalized eigenvectors of the
!     pair (A,B).

!     The NAG name equivalent of ztgevc is f08yxf
      Call ztgevc('Both','All',select,n,a,lda,b,ldb,vl,ldvl,vr,ldvr,n,m,work,  &

!     Estimate condition numbers for all the generalized eigenvalues
!     and right eigenvectors of the pair (A,B)

!     The NAG name equivalent of ztgsna is f08yyf
      Call ztgsna('Both','All',select,n,a,lda,b,ldb,vl,ldvl,vr,ldvr,s,dif,n,m, &

!     Print condition numbers of eigenvalues and right eigenvectors

      Write (nout,*) 'S'
      Write (nout,99999) s(1:m)
      Write (nout,*)
      Write (nout,*) 'DIF'
      Write (nout,99999) dif(1:m)

!     Calculate approximate error estimates

!     Compute the 1-norms of A and B and then compute
!     SQRT(snorm**2 + tnorm**2)

      eps = x02ajf()
      snorm = f06uaf('1-norm',n,n,a,lda,rwork)
      tnorm = f06uaf('1-norm',n,n,b,ldb,rwork)
      stnrm = f06bnf(snorm,tnorm)
      Write (nout,*)
      Write (nout,*) 'Approximate error estimates for eigenvalues of (A,B)'
      Write (nout,99999)(eps*stnrm/s(i),i=1,m)
      Write (nout,*)
      Write (nout,*)                                                           &
        'Approximate error estimates for right eigenvectors of (A,B)'
      Write (nout,99999)(eps*stnrm/dif(i),i=1,m)

99999 Format ((3X,1P,7E11.1))
    End Program f08yyfe