Program g13eafe ! G13EAF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. 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 Procedures .. 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 100 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 100 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 100 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 100 Continue 99999 Format (6F12.4) 99998 Format (A,E13.4) End Program g13eafe