Program f08tafe ! F08TAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dspgv, dtpcon, f06rdf, nag_wp, x02ajf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Integer, Parameter :: nin = 5, nout = 6 Character (1), Parameter :: uplo = 'U' ! .. Local Scalars .. Real (Kind=nag_wp) :: anorm, bnorm, eps, rcond, rcondb, & t1, t2 Integer :: i, info, j, n ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: ap(:), bp(:), eerbnd(:), w(:), work(:) Real (Kind=nag_wp) :: dummy(1,1) Integer, Allocatable :: iwork(:) ! .. Intrinsic Procedures .. Intrinsic :: abs ! .. Executable Statements .. Write (nout,*) 'F08TAF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n Allocate (ap((n*(n+1))/2),bp((n*(n+1))/2),eerbnd(n),w(n),work(3*n),iwork & (n)) ! Read the upper or lower triangular parts of the matrices A and ! B from data file If (uplo=='U') Then Read (nin,*)((ap(i+(j*(j-1))/2),j=i,n),i=1,n) Read (nin,*)((bp(i+(j*(j-1))/2),j=i,n),i=1,n) Else If (uplo=='L') Then Read (nin,*)((ap(i+((2*n-j)*(j-1))/2),j=1,i),i=1,n) Read (nin,*)((bp(i+((2*n-j)*(j-1))/2),j=1,i),i=1,n) End If ! Compute the one-norms of the symmetric matrices A and B anorm = f06rdf('One norm',uplo,n,ap,work) bnorm = f06rdf('One norm',uplo,n,bp,work) ! Solve the generalized symmetric eigenvalue problem ! A*x = lambda*B*x (itype = 1) ! The NAG name equivalent of dspgv is f08taf Call dspgv(1,'No vectors',uplo,n,ap,bp,w,dummy,1,work,info) If (info==0) Then ! Print solution Write (nout,*) 'Eigenvalues' Write (nout,99999) w(1:n) ! Call DTPCON (F07UGF) to estimate the reciprocal condition ! number of the Cholesky factor of B. Note that: ! cond(B) = 1/rcond**2 Call dtpcon('One norm',uplo,'Non-unit',n,bp,rcond,work,iwork,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 ! Get the machine precision, eps, and if rcondb is not less ! than eps**2, compute error estimates for the eigenvalues eps = x02ajf() If (rcond>=eps) Then t1 = eps/rcondb t2 = anorm/bnorm Do i = 1, n eerbnd(i) = t1*(t2+abs(w(i))) End Do ! Print the approximate error bounds for the eigenvalues Write (nout,*) Write (nout,*) 'Error estimates for the eigenvalues' Write (nout,99998) eerbnd(1:n) Else Write (nout,*) Write (nout,*) 'B is very ill-conditioned, error ', & 'estimates have not been computed' End If Else If (info>n .And. info<=2*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 DSPGV. 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 f08tafe