Program f08fnfe ! F08FNF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: blas_zamax_val, ddisna, nag_wp, x02ajf, x04daf, & zheev ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: eerrbd, eps, r Integer :: i, ifail, info, k, lda, lwork, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), work(:) Complex (Kind=nag_wp) :: dummy(1) Real (Kind=nag_wp), Allocatable :: rcondz(:), rwork(:), w(:), zerrbd(:) ! .. Intrinsic Procedures .. Intrinsic :: abs, cmplx, conjg, max, nint, real ! .. Executable Statements .. Write (nout,*) 'F08FNF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n lda = n Allocate (a(lda,n),rcondz(n),rwork(3*n-2),w(n),zerrbd(n)) ! Use routine workspace query to get optimal workspace. ! The NAG name equivalent of zheev is f08fnf lwork = -1 Call zheev('Vectors','Upper',n,a,lda,w,dummy,lwork,rwork,info) ! Make sure that there is enough workspace for blocksize nb. lwork = max((nb+1)*n,nint(real(dummy(1)))) Allocate (work(lwork)) ! Read the upper triangular part of the matrix A from data file Read (nin,*)(a(i,i:n),i=1,n) ! Solve the Hermitian eigenvalue problem ! The NAG name equivalent of zheev is f08fnf Call zheev('Vectors','Upper',n,a,lda,w,work,lwork,rwork,info) If (info==0) Then ! Print solution Write (nout,*) 'Eigenvalues' Write (nout,99999) w(1:n) Write (nout,*) Flush (nout) ! Normalize the eigenvectors so that the element of largest absolute ! value is real. Do i = 1, n Call blas_zamax_val(n,a(1,i),1,k,r) a(1:n,i) = a(1:n,i)*(conjg(a(k,i))/cmplx(abs(a(k,i)),kind=nag_wp)) 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,n,a,lda,'Eigenvectors',ifail) ! Get the machine precision, EPS and compute the approximate ! error bound for the computed eigenvalues. Note that for ! the 2-norm, max( abs(W(i)) ) = norm(A), and since the ! eigenvalues are returned in descending order ! max( abs(W(i)) ) = max( abs(W(1)), abs(W(n))) eps = x02ajf() eerrbd = eps*max(abs(w(1)),abs(w(n))) ! Call DDISNA (F08FLF) to estimate reciprocal condition ! numbers for the eigenvectors Call ddisna('Eigenvectors',n,n,w,rcondz,info) ! Compute the error estimates for the eigenvectors Do i = 1, n zerrbd(i) = eerrbd/rcondz(i) End Do ! Print the approximate error bounds for the eigenvalues ! and vectors Write (nout,*) Write (nout,*) 'Error estimate for the eigenvalues' Write (nout,99998) eerrbd Write (nout,*) Write (nout,*) 'Error estimates for the eigenvectors' Write (nout,99998) zerrbd(1:n) Else Write (nout,99997) 'Failure in ZHEEV. INFO =', info End If 99999 Format (3X,(8F8.4)) 99998 Format (4X,1P,6E11.1) 99997 Format (1X,A,I4) End Program f08fnfe