! G13EKF Example Program Text
! Mark 27.2 Release. NAG Copyright 2021.
Module g13ekfe_mod
! G13EKF Example Program Module:
! User-defined Routines
! .. Use Statements ..
Use nag_library, Only: nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: f, h, read_problem_data
! .. Parameters ..
Integer, Parameter, Public :: mx = 3, my = 2, nin = 5, nout = 6
Contains
Subroutine f(mx,n,xt,fxt,iuser,ruser,info)
! .. Scalar Arguments ..
Integer, Intent (Inout) :: info
Integer, Intent (In) :: mx, n
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: fxt(mx,n)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: xt(mx,n)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Real (Kind=nag_wp) :: d, phi_lt, phi_rt, r, t1, t3
Integer :: i
! .. Intrinsic Procedures ..
Intrinsic :: cos, sin
! .. Executable Statements ..
Continue
r = ruser(3)
d = ruser(4)
phi_rt = ruser(5)
phi_lt = ruser(6)
t1 = 0.5_nag_wp*r*(phi_rt+phi_lt)
t3 = (r/d)*(phi_rt-phi_lt)
Do i = 1, n
fxt(1,i) = xt(1,i) + cos(xt(3,i))*t1
fxt(2,i) = xt(2,i) + sin(xt(3,i))*t1
fxt(3,i) = xt(3,i) + t3
End Do
! Set info nonzero to terminate execution for any reason.
info = 0
Return
End Subroutine f
Subroutine h(mx,my,n,yt,hyt,iuser,ruser,info)
! .. Use Statements ..
Use nag_library, Only: x01aaf
! .. Scalar Arguments ..
Integer, Intent (Inout) :: info
Integer, Intent (In) :: mx, my, n
! .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: hyt(my,n)
Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
Real (Kind=nag_wp), Intent (In) :: yt(mx,n)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Real (Kind=nag_wp) :: a, delta, tmp
Integer :: i
! .. Intrinsic Procedures ..
Intrinsic :: cos, sin
! .. Executable Statements ..
Continue
delta = ruser(1)
a = ruser(2)
Do i = 1, n
hyt(1,i) = delta - yt(1,i)*cos(a) - yt(2,i)*sin(a)
hyt(2,i) = yt(3,i) - a
! Make sure that the theta is in the same range as the observed
! data, which in this case is [0, 2*pi)
If (hyt(2,i)<0.0_nag_wp) Then
hyt(2,i) = hyt(2,i) + 2*x01aaf(tmp)
End If
End Do
! Set info nonzero to terminate execution for any reason.
info = 0
Return
End Subroutine h
Subroutine read_problem_data(t,iuser,ruser,read_ok)
! Read in any data specific to the F and H subroutines
! .. Scalar Arguments ..
Integer, Intent (In) :: t
Logical, Intent (Out) :: read_ok
! .. Array Arguments ..
Real (Kind=nag_wp), Allocatable, Intent (Inout) :: ruser(:)
Integer, Allocatable, Intent (Inout) :: iuser(:)
! .. Local Scalars ..
Real (Kind=nag_wp) :: a, d, delta, phi_lt, phi_rt, r
Integer :: tt
! .. Executable Statements ..
Continue
If (t==0) Then
! Allocate the arrays to hold the data
Allocate (ruser(6),iuser(0))
! Read in the data that is constant across all time points
Read (nin,*) r, d, delta, a
! Store the data in RUSER
ruser(1) = delta
ruser(2) = a
ruser(3) = r
ruser(4) = d
read_ok = .True.
Else
! Read in data for time point t
Read (nin,*) tt, phi_rt, phi_lt
If (tt/=t) Then
! Sanity check
Write (nout,99999) 'Expected to read in data for time point ', t
Write (nout,99999) 'Data that was read in was for time point ', tt
99999 Format (A,E22.15)
read_ok = .False.
Else
read_ok = .True.
End If
! Store the data in RUSER
ruser(5) = phi_rt
ruser(6) = phi_lt
End If
End Subroutine read_problem_data
End Module g13ekfe_mod
Program g13ekfe
! .. Use Statements ..
Use g13ekfe_mod, Only: f, h, mx, my, nin, nout, read_problem_data
Use nag_library, Only: g13ekf, nag_wp
! .. Implicit None Statement ..
Implicit None
! .. Local Scalars ..
Integer :: i, ifail, ntime, t
Logical :: read_ok
! .. Local Arrays ..
Real (Kind=nag_wp), Allocatable :: lx(:,:), ly(:,:), ruser(:), st(:,:), &
x(:), y(:)
Integer, Allocatable :: iuser(:)
! .. Intrinsic Procedures ..
Intrinsic :: repeat
! .. Executable Statements ..
Write (nout,*) 'G13EKF Example Program Results'
Write (nout,*)
! Skip heading in data file
Read (nin,*)
! Allocate arrays
Allocate (lx(mx,mx),ly(my,my),x(mx),st(mx,mx),y(my))
! Read in the Cholesky factorization of the covariance matrix for the
! process noise
Do i = 1, mx
Read (nin,*) lx(i,1:i)
End Do
! Read in the Cholesky factorization of the covariance matrix for the
! observation noise
Do i = 1, my
Read (nin,*) ly(i,1:i)
End Do
! Read in the initial state vector
Read (nin,*) x(1:mx)
! Read in the Cholesky factorization of the initial state covariance
! matrix
Do i = 1, mx
Read (nin,*) st(i,1:i)
End Do
! Read in the number of time points to run the system for
Read (nin,*) ntime
! Read in any problem specific data that is constant
Call read_problem_data(0,iuser,ruser,read_ok)
If (.Not. read_ok) Then
Go To 100
End If
! Title for first set of output
Write (nout,*) ' Time ', repeat(' ',(11*mx-16)/2), 'Estimate of State'
Write (nout,*) repeat('-',7+11*mx)
! Loop over each time point
Do t = 1, ntime
! Read in any problem specific data that is time dependent
Call read_problem_data(t,iuser,ruser,read_ok)
If (.Not. read_ok) Then
Go To 100
End If
! Read in the observed data for time t
Read (nin,*) y(1:my)
! Call Unscented Kalman Filter routine
ifail = 0
Call g13ekf(mx,my,y,lx,ly,f,h,x,st,iuser,ruser,ifail)
! Display the current state estimates
Write (nout,99999) t, x(1:mx)
End Do
Write (nout,*)
Write (nout,*) 'Estimate of Cholesky Factorization of the State'
Write (nout,*) 'Covariance Matrix at the Last Time Point'
Do i = 1, mx
Write (nout,99998) st(i,1:i)
End Do
100 Continue
99999 Format (1X,I3,4X,10(1X,F10.3))
99998 Format (10(1X,E10.3))
End Program g13ekfe