! F12FBF Example Program Text ! Mark 24 Release. NAG Copyright 2012. Module f12fbfe_mod ! F12FBF Example Program Module: ! Parameters and User-defined Routines ! .. Use Statements .. Use nag_library, Only: nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: one = 1.0_nag_wp Real (Kind=nag_wp), Parameter :: two = 2.0_nag_wp Real (Kind=nag_wp), Parameter :: zero = 0.0_nag_wp Integer, Parameter :: imon = 0, licomm = 140, nin = 5, & nout = 6 Contains Subroutine av(m,n,x,w) ! Computes w <- A*x. ! .. Scalar Arguments .. Integer, Intent (In) :: m, n ! .. Array Arguments .. Real (Kind=nag_wp), Intent (Out) :: w(m) Real (Kind=nag_wp), Intent (In) :: x(n) ! .. Local Scalars .. Real (Kind=nag_wp) :: h, k, s, t Integer :: i, j ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. h = one/real(m+1,kind=nag_wp) k = one/real(n+1,kind=nag_wp) w(1:m) = zero t = zero Do j = 1, n t = t + k s = zero Do i = 1, j s = s + h w(i) = w(i) + k*s*(t-one)*x(j) End Do Do i = j + 1, m s = s + h w(i) = w(i) + k*t*(s-one)*x(j) End Do End Do Return End Subroutine av Subroutine atv(m,n,w,y) ! Computes y <- A'*w. ! .. Scalar Arguments .. Integer, Intent (In) :: m, n ! .. Array Arguments .. Real (Kind=nag_wp), Intent (In) :: w(m) Real (Kind=nag_wp), Intent (Out) :: y(n) ! .. Local Scalars .. Real (Kind=nag_wp) :: h, k, s, t Integer :: i, j ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. h = one/real(m+1,kind=nag_wp) k = one/real(n+1,kind=nag_wp) y(1:n) = zero t = zero Do j = 1, n t = t + k s = zero Do i = 1, j s = s + h y(j) = y(j) + k*s*(t-one)*w(i) End Do Do i = j + 1, m s = s + h y(j) = y(j) + k*t*(s-one)*w(i) End Do End Do Return End Subroutine atv End Module f12fbfe_mod Program f12fbfe ! F12FBF Example Main Program ! .. Use Statements .. Use f12fbfe_mod, Only: nout ! .. Implicit None Statement .. Implicit None ! .. Executable Statements .. Write (nout,*) 'F12FBF Example Program Results' Call ex1 Call ex2 Contains Subroutine ex1 ! .. Use Statements .. Use nag_library, Only: dgttrf, dgttrs, dnrm2, f12faf, f12fbf, f12fcf, & f12fdf, f12fef, nag_wp Use f12fbfe_mod, Only: imon, licomm, nin, one, two, zero ! .. Local Scalars .. Real (Kind=nag_wp) :: h2, sigma Integer :: ifail, info, irevcm, j, lcomm, & ldv, n, nconv, ncv, nev, & niter, nshift ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: ad(:), adl(:), adu(:), & adu2(:), comm(:), d(:,:), & mx(:), resid(:), v(:,:), x(:) Integer :: icomm(licomm) Integer, Allocatable :: ipiv(:) ! .. Intrinsic Procedures .. Intrinsic :: real ! .. Executable Statements .. Write (nout,*) Write (nout,*) 'F12FBF Example 1' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) Read (nin,*) n, nev, ncv ldv = n lcomm = 3*n + ncv*ncv + 8*ncv + 60 Allocate (ad(n),adl(n),adu(n),adu2(n),comm(lcomm),d(ncv,2),mx(n), & resid(n),v(ldv,ncv),x(n),ipiv(n)) ifail = 0 Call f12faf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! Set the region of the spectrum that is required. Call f12fdf('LARGEST MAGNITUDE',icomm,comm,ifail) ! Use the Shifted Inverse mode. Call f12fdf('SHIFTED INVERSE',icomm,comm,ifail) h2 = one/real((n+1)*(n+1),kind=nag_wp) sigma = zero ad(1:n) = two/h2 - sigma adl(1:n) = -one/h2 adu(1:n) = adl(1:n) ! The NAG name equivalent of dgttrf is f07cdf Call dgttrf(n,adl,ad,adu,adu2,ipiv,info) irevcm = 0 ifail = -1 revcm: Do Call f12fbf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) If (irevcm==5) Then Exit revcm Else If (irevcm==-1 .Or. irevcm==1) Then ! Perform matrix vector multiplication ! y <--- inv[A-sigma*I]*x ! The NAG name equivalent of dgttrs is f07cef Call dgttrs('N',n,1,adl,ad,adu,adu2,ipiv,x,n,info) Else If (irevcm==4 .And. imon/=0) Then ! Output monitoring information Call f12fef(niter,nconv,d,d(1,2),icomm,comm) ! The NAG name equivalent of dnrm2 is f06ejf Write (6,99999) niter, nconv, dnrm2(nev,d(1,2),1) Flush (nout) End If End Do revcm If (ifail==0) Then ! Post-Process using F12FCF to compute eigenvalues/vectors. Call f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail) Write (nout,99998) nconv, sigma Write (nout,99997)(j,d(j,1),j=1,nconv) End If Deallocate (ad,adl,adu,adu2,comm,d,mx,resid,v,x,ipiv) Return 99999 Format (1X,'Iteration',1X,I3,', No. converged =',1X,I3,', norm o', & 'f estimates =',E16.8) 99998 Format (1X/' The ',I4,' Ritz values of closest to ',F8.4,' are:'/) 99997 Format (1X,I8,5X,F12.4) End Subroutine ex1 Subroutine ex2 ! .. Use Statements .. Use nag_library, Only: daxpy, dnrm2, dscal, f12faf, f12fbf, f12fcf, & nag_wp, x04caf Use f12fbfe_mod, Only: atv, av, licomm, nin, one ! .. Local Scalars .. Real (Kind=nag_wp) :: sigma, temp Integer :: ifail, ifail1, irevcm, j, & lcomm, ldu, ldv, m, n, nconv, & ncv, nev, nshift ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: ax(:), comm(:), d(:,:), mx(:), & resid(:), u(:,:), v(:,:), x(:) Integer :: icomm(licomm) ! .. Intrinsic Procedures .. Intrinsic :: sqrt ! .. Executable Statements .. Write (nout,*) Write (nout,*) 'F12FBF Example 2' Write (nout,*) Flush (nout) ! Skip heading in data file Read (nin,*) Read (nin,*) m, n, nev, ncv ldu = m ldv = n lcomm = 3*n + ncv*ncv + 8*ncv + 60 Allocate (ax(m),comm(lcomm),d(ncv,2),mx(m),resid(n),u(ldu,nev), & v(ldv,ncv),x(m)) ! Initialize for problem. ifail = 0 Call f12faf(n,nev,ncv,icomm,licomm,comm,lcomm,ifail) ! Main reverse communication loop. irevcm = 0 ifail = -1 revcm: Do Call f12fbf(irevcm,resid,v,ldv,x,mx,nshift,comm,icomm,ifail) If (irevcm==5) Then Exit revcm Else If (irevcm==-1 .Or. irevcm==1) Then ! Perform the operation X <- A'AX Call av(m,n,x,ax) Call atv(m,n,ax,x) End If End Do revcm If (ifail==0) Then ! Post-Process using F12FCF. ! Computed singular values may be extracted. ! Singular vectors may also be computed now if desired. ifail1 = 0 Call f12fcf(nconv,d,v,ldv,sigma,resid,v,ldv,comm,icomm,ifail1) ! Singular values (squared) are returned in the first column ! of D and the corresponding right singular vectors are ! returned in the first NEV columns of V. Do j = 1, nconv d(j,1) = sqrt(d(j,1)) ! Compute the left singular vectors from the formula ! u = Av/sigma/norm(Av). Call av(m,n,v(1,j),ax) u(1:m,j) = ax(1:m) ! The NAG name equivalent of dnrm2 is f06ejf temp = one/dnrm2(m,u(1,j),1) ! The NAG name equivalent of dscal is f06edf Call dscal(m,temp,u(1,j),1) ! Compute the residual norm ||A*v - sigma*u|| for the nconv ! accurately computed singular values and vectors. ! Store the result in 2nd column of array D. ! The NAG name equivalent of daxpy is f06ecf Call daxpy(m,-d(j,1),u(1,j),1,ax,1) d(j,2) = dnrm2(m,ax,1) End Do ! Print computed residuals Call x04caf('G','N',nconv,2,d,ncv, & ' Singular values and direct residuals',ifail1) End If Deallocate (ax,comm,d,mx,resid,u,v,x) Return End Subroutine ex2 End Program f12fbfe