Program f08sbfe
! F08SBF Example Program Text
! Mark 30.3 Release. nAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: blas_damax_val, dsygvx, nag_wp, x04caf
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=nag_wp), Parameter :: zero = 0.0_nag_wp
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=nag_wp) :: abstol, r, vl, vu
Integer :: i, ifail, il, info, iu, k, lda, ldb, &
ldz, lwork, m, n
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), w(:), work(:), &
z(:,:)
Real (Kind=nag_wp) :: dummy(1)
Integer, Allocatable :: iwork(:), jfail(:)
! .. Intrinsic Procedures ..
Intrinsic :: max, nint
! .. Executable Statements ..
Write (nout,*) 'F08SBF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n
lda = n
ldb = n
ldz = n
m = n
Allocate (a(lda,n),b(ldb,n),w(n),z(ldz,m),iwork(5*n),jfail(n))
! Read the lower and upper bounds of the interval to be searched.
Read (nin,*) vl, vu
! Use routine workspace query to get optimal workspace.
lwork = -1
! The NAG name equivalent of dsygvx is f08sbf
Call dsygvx(1,'Vectors','Values in range','Upper',n,a,lda,b,ldb,vl,vu, &
il,iu,abstol,m,w,z,ldz,dummy,lwork,iwork,jfail,info)
! Make sure that there is enough workspace for block size nb.
lwork = max((nb+3)*n,nint(dummy(1)))
Allocate (work(lwork))
! Read the upper triangular parts of the matrices A and B
Read (nin,*)(a(i,i:n),i=1,n)
Read (nin,*)(b(i,i:n),i=1,n)
! 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 dsygvx is f08sbf
Call dsygvx(1,'Vectors','Values in range','Upper',n,a,lda,b,ldb,vl,vu, &
il,iu,abstol,m,w,z,ldz,work,lwork,iwork,jfail,info)
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 =', &
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'
Else
Write (nout,99999) 'Failure in DSYGVX. 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 f08sbfe