PROGRAM g13eafe ! G13EAF Example Program Text ! Mark 23 Release. NAG Copyright 2011. ! .. Use Statements .. USE nag_library, ONLY : daxpy, ddot, dgemv, dpotrf, dtrmv, dtrsv, & g13eaf, nag_wp, x04caf ! .. Implicit None Statement .. IMPLICIT NONE ! .. Parameters .. REAL (KIND=nag_wp), PARAMETER :: one = 1.0_nag_wp REAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp INTEGER, PARAMETER :: inc1 = 1, nin = 5, nout = 6 ! .. Local Scalars .. REAL (KIND=nag_wp) :: dev, tol INTEGER :: i, ifail, info, istep, l, ldm, ldq, & lds, lwk, m, n, ncall, tdq LOGICAL :: full, is_const, read_matrix, stq ! .. Local Arrays .. REAL (KIND=nag_wp), ALLOCATABLE :: a(:,:), ax(:), b(:,:), c(:,:), & h(:,:), k(:,:), p(:,:), q(:,:), & r(:,:), s(:,:), wk(:), x(:), y(:), & ymean(:) INTEGER, ALLOCATABLE :: iwk(:) ! .. Intrinsic Functions .. INTRINSIC log ! .. Executable Statements .. WRITE (nout,*) 'G13EAF Example Program Results' WRITE (nout,*) ! Skip heading in data file READ (nin,*) ! Read in the problem size READ (nin,*) n, m, l, stq, is_const lds = n IF ( .NOT. stq) THEN ldq = l tdq = l ELSE ldq = 1 tdq = 1 END IF ldm = m lwk = (n+m)*(n+m+l) ALLOCATE (a(lds,n),b(lds,l),q(ldq,tdq),c(ldm,n),r(ldm,m),s(lds,n), & k(lds,m),h(ldm,m),iwk(m),wk(lwk),x(n),ymean(m),y(m),ax(n),p(lds,n)) ! Read in the state covariance matrix, S READ (nin,*) (s(i,1:n),i=1,n) ! Read in flag indicating whether S is the full matrix, or its ! Cholesky decomposition READ (nin,*) full ! If required (full), perform the Cholesky decomposition on S IF (full) THEN ! The NAG name equivalent of dpotrf is f07fdf CALL dpotrf('L',n,s,lds,info) IF (info>0) THEN WRITE (nout,*) ' S not positive definite' GO TO 20 END IF END IF ! Read in initial state vector READ (nin,*) x(1:n) ! Read in mean of the series READ (nin,*) ymean(1:m) ! Read in control parameter READ (nin,*) ncall, tol ! Display titles WRITE (nout,*) ' Residuals' WRITE (nout,*) ! Initialise variables dev = zero read_matrix = .TRUE. ! Loop through data DO istep = 1, ncall ! Read in the various matrices. If the series is constant ! then this only happens at the first call IF (read_matrix) THEN ! Read in transition matrix, A READ (nin,*) (a(i,1:n),i=1,n) ! Read in noise coefficient matrix, B READ (nin,*) (b(i,1:l),i=1,n) ! Read in measurement coefficient matrix, C READ (nin,*) (c(i,1:n),i=1,m) ! Read in measurement noise covariance matrix, R READ (nin,*) (r(i,1:m),i=1,m) ! Read in flag indicating whether R is the full matrix, or its ! Cholesky decomposition READ (nin,*) full ! If required (full), perform the Cholesky decomposition on R IF (full) THEN ! The NAG name equivalent of dpotrf is f07fdf CALL dpotrf('L',m,r,ldm,info) IF (info>0) THEN WRITE (nout,*) ' R not positive definite' GO TO 20 END IF END IF ! Read in state noise matrix Q, if not assume to be identity matrix IF ( .NOT. stq) THEN READ (nin,*) (q(i,1:l),i=1,l) ! Read in flag indicating whether Q is the full matrix, or its ! Cholesky decomposition READ (nin,*) full ! Perform Cholesky factorisation on Q, if full matrix is supplied IF (full) THEN ! The NAG name equivalent of dpotrf is f07fdf CALL dpotrf('L',l,q,ldq,info) IF (info>0) THEN WRITE (nout,*) ' Q not positive definite' GO TO 20 END IF END IF END IF ! If series is constant set flag to false read_matrix = .NOT. is_const END IF ! Read in observed values READ (nin,*) y(1:m) ! Call G13EAF ifail = 0 CALL g13eaf(n,m,l,a,lds,b,stq,q,ldq,c,ldm,r,s,k,h,tol,iwk,wk,ifail) ! Subtract the mean y:= y-ymean ! The NAG name equivalent of daxpy is f06ecf CALL daxpy(m,-one,ymean,inc1,y,inc1) ! Perform time and measurement update x <= Ax + K(y-Cx) ! The NAG name equivalent of dgemv is f06paf CALL dgemv('N',m,n,-one,c,ldm,x,inc1,one,y,1) CALL dgemv('N',n,n,one,a,lds,x,inc1,zero,ax,1) CALL dgemv('N',n,m,one,k,lds,y,inc1,one,ax,1) x(1:n) = ax(1:n) ! Display the residuals WRITE (nout,99999) y(1:m) ! Update loglikelihood. ! The NAG name equivalent of dtrsv is f06pjf CALL dtrsv('L','N','N',m,h,ldm,y,1) ! The NAG name equivalent of ddot is f06eaf dev = dev + ddot(m,y,1,y,1) DO i = 1, m dev = dev + 2.0_nag_wp*log(h(i,i)) END DO END DO ! Compute P from S ! The NAG name equivalent of dtrmv is f06pff DO i = 1, n p(1:i,i) = s(i,1:i) CALL dtrmv('L','N','N',i,s,lds,p(1,i),inc1) p(i,1:i-1) = p(1:i-1,i) END DO ! Display final results WRITE (nout,*) WRITE (nout,*) ' Final X(I+1:I) ' WRITE (nout,*) WRITE (nout,99999) x(1:n) WRITE (nout,*) FLUSH (nout) ifail = 0 CALL x04caf('Lower','Non-Diag',n,n,p,lds,'Final Value of P',ifail) WRITE (nout,*) WRITE (nout,99998) ' Deviance = ', dev 20 CONTINUE 99999 FORMAT (6F12.4) 99998 FORMAT (A,E13.4) END PROGRAM g13eafe