NAG Library Manual, Mark 29.3
Interfaces:  FL   CL   CPP   AD 

NAG FL Interface Introduction
Example description
    Program f08tbfe

!     F08TBF Example Program Text

!     Mark 29.3 Release. NAG Copyright 2023.

!     .. Use Statements ..
      Use nag_library, Only: blas_damax_val, dspgvx, nag_wp, x04caf
!     .. Implicit None Statement ..
      Implicit None
!     .. Parameters ..
      Real (Kind=nag_wp), Parameter    :: zero = 0.0E+0_nag_wp
      Integer, Parameter               :: nin = 5, nout = 6
      Character (1), Parameter         :: uplo = 'U'
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: abstol, r, vl, vu
      Integer                          :: i, ifail, il, info, iu, j, k, ldz,   &
                                          m, n
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: ap(:), bp(:), w(:), work(:), z(:,:)
      Integer, Allocatable             :: iwork(:), jfail(:)
!     .. Executable Statements ..
      Write (nout,*) 'F08TBF Example Program Results'
      Write (nout,*)
!     Skip heading in data file
      Read (nin,*)
      Read (nin,*) n
      ldz = n
      m = n
      Allocate (ap((n*(n+1))/2),bp((n*(n+1))/2),w(n),work(8*n),z(ldz,m),iwork( &

!     Read the lower and upper bounds of the interval to be searched,
!     and read the upper or lower triangular parts of the matrices A
!     and B from data file

      Read (nin,*) vl, vu
      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

!     Set the absolute error tolerance for eigenvalues. With abstol
!     set to zero, the default value is used instead

      abstol = zero

!     Solve the generalized symmetric eigenvalue problem
!     A*x = lambda*B*x (itype = 1)

!     The NAG name equivalent of dspgvx is f08tbf
      Call dspgvx(1,'Vectors','Values in range',uplo,n,ap,bp,vl,vu,il,iu,      &

      If (info>=0 .And. info<=n) Then

!       Print solution

        Write (nout,99999) 'Number of eigenvalues found =', m
        Write (nout,*)
        Write (nout,*) 'Eigenvalues'
        Write (nout,99998) w(1:m)
        Flush (nout)

!       Normalize the eigenvectors, largest positive
        Do i = 1, m
          Call blas_damax_val(n,z(1,i),1,k,r)
          If (z(k,i)<zero) Then
            z(1:n,i) = -z(1:n,i)
          End If
        End Do

!       ifail: behaviour on error exit
!              =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
        ifail = 0
        Call x04caf('General',' ',n,m,z,ldz,'Selected eigenvectors',ifail)

        If (info>0) Then
          Write (nout,99999) 'INFO eigenvectors failed to converge, INFO =',   &
          Write (nout,*) 'Indices of eigenvectors that did not converge'
          Write (nout,99997) jfail(1:m)
        End If
      Else If (info>n .And. info<=2*n) Then
        i = info - n
        Write (nout,99996) 'The leading minor of order ', i,                   &
          ' of B is not positive definite'
        Write (nout,99999) 'Failure in DSPGVX. INFO =', info
      End If

99999 Format (1X,A,I5)
99998 Format (3X,(8F8.4))
99997 Format (3X,(8I8))
99996 Format (1X,A,I4,A)
    End Program f08tbfe