Program f08frfe ! F08FRF Example Program Text ! Mark 31.1 Release. nAG Copyright 2025. ! .. Use Statements .. Use nag_library, Only: nag_wp, x04daf, zheevr, zscal ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: zero = 0.0E+0_nag_wp Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: abstol, vl, vu Integer :: i, ifail, il, info, iu, k, lda, ldz, & liwork, lrwork, lwork, m, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), work(:), z(:,:) Complex (Kind=nag_wp) :: dummy(1) Real (Kind=nag_wp) :: rdum(1) Real (Kind=nag_wp), Allocatable :: rwork(:), w(:) Integer :: idum(1) Integer, Allocatable :: isuppz(:), iwork(:) ! .. Intrinsic Procedures .. Intrinsic :: abs, cmplx, conjg, max, maxloc, & nint, real ! .. Executable Statements .. Write (nout,*) 'F08FRF Example Program Results' Write (nout,*) ! Skip heading in data file and read N and the lower and upper ! indices of the smallest and largest eigenvalues to be found Read (nin,*) Read (nin,*) n, il, iu lda = n ldz = n m = n Allocate (a(lda,n),z(ldz,m),w(n),isuppz(2*m)) ! Use routine workspace query to get optimal workspace. lwork = -1 liwork = -1 lrwork = -1 ! The NAG name equivalent of zheevr is f08frf Call zheevr('Vectors','I','Upper',n,a,lda,vl,vu,il,iu,abstol,m,w,z,ldz, & isuppz,dummy,lwork,rdum,lrwork,idum,liwork,info) ! Make sure that there is enough workspace for block size nb. lwork = max((nb+1)*n,nint(real(dummy(1)))) lrwork = max(24*n,nint(rdum(1))) liwork = max(10*n,idum(1)) Allocate (work(lwork),rwork(lrwork),iwork(liwork)) ! Read the upper triangular part of the matrix A from data file Read (nin,*)(a(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 symmetric eigenvalue problem ! The NAG name equivalent of zheevr is f08frf Call zheevr('Vectors','I','Upper',n,a,lda,vl,vu,il,iu,abstol,m,w,z,ldz, & isuppz,work,lwork,rwork,lrwork,iwork,liwork,info) If (info==0) Then ! Print solution Write (nout,*) 'Selected eigenvalues' Write (nout,99999) w(1:m) Flush (nout) ! Normalize the eigenvectors so that the element of largest absolute ! value is real. Do i = 1, m rwork(1:n) = abs(z(1:n,i)) k = maxloc(rwork(1:n),1) Call zscal(n,conjg(z(k,i))/cmplx(abs(z(k,i)),kind=nag_wp),z(1,i),1) End Do ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04daf('General',' ',n,m,z,ldz,'Selected eigenvectors',ifail) Else Write (nout,99998) 'Failure in ZHEEVR. INFO =', info End If 99999 Format (3X,(8F8.4)) 99998 Format (1X,A,I5) End Program f08frfe