Program f08jvfe
! F08JVF Example Program Text
! Mark 30.0 Release. NAG Copyright 2024.
! .. Use Statements ..
Use nag_library, Only: dznrm2, nag_wp, x04dbf, zhbtrd, zstedc
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nin = 5, nout = 6
Character (1), Parameter :: uplo = 'U'
! .. Local Scalars ..
Complex (Kind=nag_wp) :: scal
Integer :: i, ifail, info, j, k, kd, ldab, ldz, &
lgn, liwork, lrwork, lwork, n
! .. Local Arrays ..
Complex (Kind=nag_wp), Allocatable :: ab(:,:), work(:), z(:,:)
Complex (Kind=nag_wp) :: cdum(1)
Real (Kind=nag_wp), Allocatable :: d(:), e(:), rwork(:)
Real (Kind=nag_wp) :: rdum(1)
Integer :: idum(1)
Integer, Allocatable :: iwork(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, ceiling, conjg, log, max, &
maxloc, min, nint, real
! .. Executable Statements ..
Write (nout,*) 'F08JVF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
Read (nin,*) n, kd
ldab = kd + 1
ldz = n
lgn = ceiling(log(real(n,kind=nag_wp))/log(2.0_nag_wp))
Allocate (ab(ldab,n),z(ldz,n),d(n),e(n-1))
! Use routine workspace query to get optimal workspace.
lwork = -1
lrwork = -1
liwork = -1
! The NAG name equivalent of zstedc is f08jvf
Call zstedc('V',n,d,e,z,ldz,cdum,lwork,rdum,lrwork,idum,liwork,info)
! Make sure that there is enough workspace.
lwork = max(n*n,nint(real(cdum(1))))
lrwork = max(1+3*n+2*n*lgn+4*n*n,nint(rdum(1)))
liwork = max(6+6*n+5*n*lgn,idum(1))
Allocate (work(lwork),rwork(lrwork),iwork(liwork))
! Read the upper or lower triangular part of the band matrix A
! from data file
If (uplo=='U') Then
Do i = 1, n
Read (nin,*)(ab(kd+1+i-j,j),j=i,min(n,i+kd))
End Do
Else If (uplo=='L') Then
Do i = 1, n
Read (nin,*)(ab(1+i-j,j),j=max(1,i-kd),i)
End Do
End If
! Reduce A to tridiagonal form T = (Z**T)*A*Z, and form Z
! The NAG name equivalent of zhbtrd is f08hsf
Call zhbtrd('V',uplo,n,kd,ab,ldab,d,e,z,ldz,work,info)
! Calculate all the eigenvalues and eigenvectors of A,
! from T and Z
! The NAG name equivalent of zstedc is f08jvf
Call zstedc('V',n,d,e,z,ldz,work,lwork,rwork,lrwork,iwork,liwork,info)
If (info==0) Then
! Print eigenvalues and eigenvectors
Write (nout,*) 'Eigenvalues'
Write (nout,99999) d(1:n)
Write (nout,*)
Flush (nout)
! Normalize the eigenvectors, largest element real
Do i = 1, n
rwork(1:n) = abs(z(1:n,i))
k = maxloc(rwork(1:n),1)
scal = conjg(z(k,i))/abs(z(k,i))/dznrm2(n,z(1,i),1)
z(1:n,i) = z(1:n,i)*scal
End Do
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call x04dbf('General',' ',n,n,z,ldz,'Bracketed','F7.4','Eigenvectors', &
'Integer',rlabs,'Integer',clabs,80,0,ifail)
Else
Write (nout,99998) 'Failure in ZSTEDC. INFO = ', info
End If
99999 Format (4X,F8.4,3(10X,F8.4))
99998 Format (1X,A,I10)
End Program f08jvfe