Program f08wbfe

!     F08WBF Example Program Text

!     Mark 26.2 Release. NAG Copyright 2017.

!     .. Use Statements ..
      Use nag_library, Only: dggevx, dnrm2, m01daf, m01eaf, nag_wp, x02ajf,    &
                             x02amf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Integer, Parameter               :: nb = 64, nin = 5, nout = 6
      Logical, Parameter               :: verbose = .False.
!     .. Local Scalars ..
      Complex (Kind=nag_wp)            :: eig
      Real (Kind=nag_wp)               :: abnrm, bbnrm, eps, jswap, rcnd,      &
                                          scal_i, scal_r, small
      Integer                          :: i, ifail, ihi, ilo, info, j, k, lda, &
                                          ldb, ldvr, lwork, n
      Logical                          :: pair
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: a(:,:), alphai(:), alphar(:),        &
                                          b(:,:), beta(:), lscale(:),          &
                                          rconde(:), rcondv(:), rscale(:),     &
                                          vr(:,:), vr_row(:), work(:)
      Real (Kind=nag_wp)               :: dummy(1,1)
      Integer, Allocatable             :: iwork(:)
      Logical, Allocatable             :: bwork(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: abs, all, cmplx, max, maxloc, nint,  &
                                          sqrt, sum
!     .. Executable Statements ..
      Write (nout,*) 'F08WBF Example Program Results'
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      lda = n
      ldb = n
      ldvr = n
      Allocate (a(lda,n),alphai(n),alphar(n),b(ldb,n),beta(n),lscale(n),       &
        rconde(n),rcondv(n),rscale(n),vr(ldvr,n),iwork(n+6),bwork(n))

!     Use routine workspace query to get optimal workspace.
      lwork = -1
!     The NAG name equivalent of dggevx is f08wbf
      Call dggevx('Balance','No vectors (left)','Vectors (right)',             &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,alphar,alphai,beta,  &
        dummy,1,vr,ldvr,ilo,ihi,lscale,rscale,abnrm,bbnrm,rconde,rcondv,dummy, &
        lwork,iwork,bwork,info)

!     Make sure that there is enough workspace for block size nb.
      lwork = max((nb+2*n)*n,nint(dummy(1,1)))
      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)

!     Solve the generalized eigenvalue problem

!     The NAG name equivalent of dggevx is f08wbf
      Call dggevx('Balance','No vectors (left)','Vectors (right)',             &
        'Both reciprocal condition numbers',n,a,lda,b,ldb,alphar,alphai,beta,  &
        dummy,1,vr,ldvr,ilo,ihi,lscale,rscale,abnrm,bbnrm,rconde,rcondv,work,  &
        lwork,iwork,bwork,info)

      If (info>0) Then
        Write (nout,*)
        Write (nout,99999) 'Failure in DGGEVX. INFO =', info
      Else

!       Compute the machine precision and the safe range parameter
!       small

        eps = x02ajf()
        small = x02amf()

!       If beta(:) > eps, Order eigenvalues by ascending real parts
        If (all(abs(beta(1:n))>eps)) Then
          work(1:n) = alphar(1:n)/beta(1:n)
          ifail = 0
          Call m01daf(work,1,n,'Ascending',iwork,ifail)
          Call m01eaf(alphar,1,n,iwork,ifail)
          Call m01eaf(alphai,1,n,iwork,ifail)
          Call m01eaf(beta,1,n,iwork,ifail)
!         Order the eigenvectors in the same way
          Allocate (vr_row(n))
          Do j = 1, n
            vr_row(1:n) = vr(j,1:n)
            Call m01eaf(vr_row,1,n,iwork,ifail)
            vr(j,1:n) = vr_row(1:n)
          End Do
          Deallocate (vr_row)
        End If

!       Print out eigenvalues and vectors and associated condition
!       number and bounds

        pair = .False.
        Do j = 1, n

!         Print out information on the j-th eigenvalue

          Write (nout,*)
          If ((abs(alphar(j))+abs(alphai(j)))*small>=abs(beta(j))) Then
            Write (nout,99998) 'Eigenvalue(', j, ')',                          &
              ' is numerically infinite or undetermined', 'ALPHAR(', j,        &
              ') = ', alphar(j), ', ALPHAI(', j, ') = ', alphai(j), ', BETA(', &
              j, ') = ', beta(j)
          Else
            If (.Not. pair) Then
              jswap = 1.0_nag_wp
              If (alphai(j)>0.0_nag_wp) Then
                jswap = -jswap
              End If
            End If
            If (alphai(j)==0.0E0_nag_wp) Then
              Write (nout,99997) 'Eigenvalue(', j, ') = ', alphar(j)/beta(j)
            Else
              eig = cmplx(alphar(j),jswap*alphai(j),kind=nag_wp)/              &
                cmplx(beta(j),kind=nag_wp)
              Write (nout,99996) 'Eigenvalue(', j, ') = ', eig
            End If
          End If

          If (verbose) Then
            rcnd = rconde(j)
            Write (nout,*)
            Write (nout,99995) '  Reciprocal condition number = ', rcnd
          End If

!         Print out information on the j-th eigenvector

          Write (nout,*)
          Write (nout,99994) 'Eigenvector(', j, ')'
          If (alphai(j)==0.0E0_nag_wp) Then
!           Let largest element be positive
            work(1:n) = abs(vr(1:n,j))
            k = maxloc(work(1:n),1)
            If (vr(k,j)<0.0_nag_wp) Then
              vr(1:n,j) = -vr(1:n,j)/dnrm2(n,vr(1,j),1)
            End If
            Write (nout,99993)(vr(i,j),i=1,n)
          Else
            If (pair) Then
              Write (nout,99992)(vr(i,j-1),-jswap*vr(i,j),i=1,n)
            Else
!             Let largest element be real (and positive).
              work(1:n) = vr(1:n,j)**2 + vr(1:n,j+1)**2
              k = maxloc(work(1:n),1)
              scal_r = vr(k,j)/sqrt(work(k))/sqrt(sum(work(1:n)))
              scal_i = -vr(k,j+1)/sqrt(work(k))/sqrt(sum(work(1:n)))
              work(1:n) = vr(1:n,j)
              vr(1:n,j) = scal_r*work(1:n) - scal_i*vr(1:n,j+1)
              vr(1:n,j+1) = scal_r*vr(1:n,j+1) + scal_i*work(1:n)
              vr(k,j+1) = 0.0_nag_wp
              Write (nout,99992)(vr(i,j),jswap*vr(i,j+1),i=1,n)
            End If
            pair = .Not. pair
          End If
          If (verbose) Then
            rcnd = rcondv(j)
            Write (nout,*)
            Write (nout,99995) '  Reciprocal condition number = ', rcnd
          End If
        End Do

      End If

99999 Format (1X,A,I4)
99998 Format (/,1X,A,I2,2A,/,1X,2(A,I2,A,F11.5),A,I2,A,F11.5)
99997 Format (/,1X,A,I2,A,F11.5)
99996 Format (/,1X,A,I2,A,'(',F11.5,',',F11.5,')')
99995 Format (1X,A,1P,E8.1)
99994 Format (1X,A,I2,A)
99993 Format (1X,F11.5)
99992 Format (1X,'(',F11.5,',',F11.5,')')
    End Program f08wbfe