Program f08nffe ! F08NFF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dgehrd, dgemm, dhseqr, dlange => f06raf, dorghr, & nag_wp, x02ajf, x04caf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: alpha, beta, norm Integer :: i, ifail, info, lda, ldc, ldd, ldz, & lwork, n ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), c(:,:), d(:,:), tau(:), & wi(:), work(:), wr(:), z(:,:) ! .. Executable Statements .. Write (nout,*) 'F08NFF Example Program Results' ! Skip heading in data file Read (nin,*) Read (nin,*) n lda = n ldz = n ldc = n ldd = n lwork = 64*(n-1) Allocate (a(lda,n),c(ldc,n),d(ldd,n),tau(n),wi(n),work(lwork),wr(n), & z(ldz,n)) ! Read A from data file Read (nin,*)(a(i,1:n),i=1,n) ! Copy A into D. d(1:n,1:n) = a(1:n,1:n) Write (nout,*) Flush (nout) ! Print Matrix A ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04caf('General',' ',n,n,a,lda,'Matrix A',ifail) Write (nout,*) Flush (nout) ! Reduce A to upper Hessenberg form H = (Q**T)*A*Q ! The NAG name equivalent of dgehrd is f08nef Call dgehrd(n,1,n,a,lda,tau,work,lwork,info) ! Copy A into Z z(1:n,1:n) = a(1:n,1:n) ! Form Q explicitly, storing the result in Z ! The NAG name equivalent of dorghr is f08nff Call dorghr(n,1,n,z,ldz,tau,work,lwork,info) ! Calculate the Schur factorization of H = Y*T*(Y**T) and form ! Q*Y explicitly, storing the result in Z ! Note that A = Z*T*(Z**T), where Z = Q*Y ! The NAG name equivalent of dhseqr is f08pef Call dhseqr('Schur form','Vectors',n,1,n,a,lda,wr,wi,z,ldz,work,lwork, & info) ! Compute A - Z*T*Z^T from the factorization of A and store in matrix D. ! The NAG name equivelent of dgemm is f06yaf. alpha = 1.0_nag_wp beta = 0.0_nag_wp Call dgemm('N','N',n,n,n,alpha,z,ldz,a,lda,beta,c,ldc) alpha = -1.0_nag_wp beta = 1.0_nag_wp Call dgemm('N','T',n,n,n,alpha,c,ldc,z,ldz,beta,d,ldd) ! Find norm of difference matrix D and warn if it is too large; ! f06raf is the NAG name equivalent of the LAPACK auxiliary dlange norm = dlange('O',ldd,n,d,ldd,work) If (norm>x02ajf()**0.8_nag_wp) Then Write (nout,*) 'Norm of A-(Z*T*Z^T) is much greater than 0.' Write (nout,*) 'Schur factorization has failed.' Else ! Print eigenvalues. Write (nout,*) 'Eigenvalues' Write (nout,99999)(' (',wr(i),',',wi(i),')',i=1,n) End If 99999 Format (1X,A,F8.4,A,F8.4,A) End Program f08nffe