Program f08sqfe ! F08SQF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: ddisna, nag_wp, x02ajf, x04daf, zhegvd, & zlanhe => f06ucf, ztrcon ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: one = 1.0E+0_nag_wp Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: anorm, bnorm, eps, rcond, rcondb, & t1, t2, t3 Integer :: i, ifail, info, lda, ldb, liwork, & lrwork, lwork, n ! .. Local Arrays .. Complex (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), work(:) Complex (Kind=nag_wp) :: cdum(1) Real (Kind=nag_wp), Allocatable :: eerbnd(:), rcondz(:), rwork(:), & w(:), zerbnd(:) Real (Kind=nag_wp) :: rdum(1) Integer :: idum(1) Integer, Allocatable :: iwork(:) ! .. Intrinsic Procedures .. Intrinsic :: abs, max, nint, real ! .. Executable Statements .. Write (nout,*) 'F08SQF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n lda = n ldb = n Allocate (a(lda,n),b(ldb,n),eerbnd(n),rcondz(n),w(n),zerbnd(n)) ! Use routine workspace query to get optimal workspace. lwork = -1 liwork = -1 lrwork = -1 ! The NAG name equivalent of zhegvd is f08sqf Call zhegvd(2,'Vectors','Upper',n,a,lda,b,ldb,w,cdum,lwork,rdum,lrwork, & idum,liwork,info) ! Make sure that there is enough workspace for blocksize nb. lwork = max((nb+2+n)*n,nint(real(cdum(1)))) lrwork = max(1+(5+2*n)*n,nint(rdum(1))) liwork = max(3+5*n,idum(1)) Allocate (work(lwork),rwork(lrwork),iwork(liwork)) ! 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) ! Compute the one-norms of the symmetric matrices A and B ! f06ucf is the NAG name equivalent of the LAPACK auxiliary zlanhe anorm = zlanhe('One norm','Upper',n,a,lda,rwork) bnorm = zlanhe('One norm','Upper',n,b,ldb,rwork) ! Solve the generalized Hermitian eigenvalue problem ! A*B*x = lambda*x (itype = 2) ! The NAG name equivalent of zhegvd is f08sqf Call zhegvd(2,'Vectors','Upper',n,a,lda,b,ldb,w,work,lwork,rwork,lrwork, & iwork,liwork,info) If (info==0) Then ! Print solution Write (nout,*) 'Eigenvalues' Write (nout,99999) w(1:n) Flush (nout) ! Normalize the eigenvectors Do i = 1, n a(1:n,i) = a(1:n,i)/a(1,i) 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) ! Call ZTRCON (F07TUF) to estimate the reciprocal condition ! number of the Cholesky factor of B. Note that: ! cond(B) = 1/rcond**2 Call ztrcon('One norm','Upper','Non-unit',n,b,ldb,rcond,work,rwork, & info) ! Print the reciprocal condition number of B rcondb = rcond**2 Write (nout,*) Write (nout,*) 'Estimate of reciprocal condition number for B' Write (nout,99998) rcondb Flush (nout) ! Get the machine precision, eps, and if rcondb is not less ! than eps**2, compute error estimates for the eigenvalues and ! eigenvectors eps = x02ajf() If (rcond>=eps) Then ! Call DDISNA (F08FLF) to estimate reciprocal condition ! numbers for the eigenvectors of (A*B - lambda*I) Call ddisna('Eigenvectors',n,n,w,rcondz,info) ! Compute the error estimates for the eigenvalues and ! eigenvectors t1 = one/rcond t2 = eps*t1 t3 = anorm*bnorm Do i = 1, n eerbnd(i) = eps*(t3+abs(w(i))/rcondb) zerbnd(i) = t2*(t3/rcondz(i)+t1) End Do ! Print the approximate error bounds for the eigenvalues ! and vectors Write (nout,*) Write (nout,*) 'Error estimates for the eigenvalues' Write (nout,99998) eerbnd(1:n) Write (nout,*) Write (nout,*) 'Error estimates for the eigenvectors' Write (nout,99998) zerbnd(1:n) Else Write (nout,*) Write (nout,*) 'B is very ill-conditioned, error ', & 'estimates have not been computed' End If Else If (info>n) Then i = info - n Write (nout,99997) 'The leading minor of order ', i, & ' of B is not positive definite' Else Write (nout,99996) 'Failure in ZHEGVD. INFO =', info End If 99999 Format (3X,(6F11.4)) 99998 Format (4X,1P,6E11.1) 99997 Format (1X,A,I4,A) 99996 Format (1X,A,I4) End Program f08sqfe