! D02EJF Example Program Text
! Mark 23 Release. NAG Copyright 2011.
MODULE d02ejfe_mod
! Data for D02EJF example program
! .. Use Statements ..
USE nag_library, ONLY : nag_wp
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Parameters ..
REAL (KIND=nag_wp), PARAMETER :: alpha = 0.04_nag_wp
REAL (KIND=nag_wp), PARAMETER :: beta = 1.0E4_nag_wp
REAL (KIND=nag_wp), PARAMETER :: gamma = 3.0E7_nag_wp
REAL (KIND=nag_wp), PARAMETER :: zero = 0.0_nag_wp
INTEGER, PARAMETER :: n = 3, nin = 5, nout = 6
! .. Local Scalars ..
REAL (KIND=nag_wp) :: h, xend
INTEGER, SAVE :: k
CONTAINS
SUBROUTINE fcn(x,y,f)
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Scalar Arguments ..
REAL (KIND=nag_wp), INTENT (IN) :: x
! .. Array Arguments ..
REAL (KIND=nag_wp), INTENT (OUT) :: f(*)
REAL (KIND=nag_wp), INTENT (IN) :: y(*)
! .. Executable Statements ..
f(1) = -alpha*y(1) + beta*y(2)*y(3)
f(2) = alpha*y(1) - beta*y(2)*y(3) - gamma*y(2)*y(2)
f(3) = gamma*y(2)*y(2)
RETURN
END SUBROUTINE fcn
SUBROUTINE pederv(x,y,pw)
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Scalar Arguments ..
REAL (KIND=nag_wp), INTENT (IN) :: x
! .. Array Arguments ..
REAL (KIND=nag_wp), INTENT (OUT) :: pw(*)
REAL (KIND=nag_wp), INTENT (IN) :: y(*)
! .. Executable Statements ..
pw(1) = -alpha
pw(2) = alpha
pw(3) = zero
pw(4) = beta*y(3)
pw(5) = -beta*y(3) - 2.0_nag_wp*gamma*y(2)
pw(6) = 2.0_nag_wp*gamma*y(2)
pw(7) = beta*y(2)
pw(8) = -beta*y(2)
pw(9) = zero
RETURN
END SUBROUTINE pederv
FUNCTION g(x,y)
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Function Return Value ..
REAL (KIND=nag_wp) :: g
! .. Scalar Arguments ..
REAL (KIND=nag_wp), INTENT (IN) :: x
! .. Array Arguments ..
REAL (KIND=nag_wp), INTENT (IN) :: y(*)
! .. Executable Statements ..
g = y(1) - 0.9E0_nag_wp
RETURN
END FUNCTION g
SUBROUTINE output(xsol,y)
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Scalar Arguments ..
REAL (KIND=nag_wp), INTENT (INOUT) :: xsol
! .. Array Arguments ..
REAL (KIND=nag_wp), INTENT (IN) :: y(*)
! .. Local Scalars ..
INTEGER :: j
! .. Intrinsic Functions ..
INTRINSIC real
! .. Executable Statements ..
WRITE (nout,99999) xsol, (y(j),j=1,n)
xsol = xend - real(k,kind=nag_wp)*h
k = k - 1
RETURN
99999 FORMAT (1X,F8.2,3F13.5)
END SUBROUTINE output
END MODULE d02ejfe_mod
PROGRAM d02ejfe
! D02EJF Example Main Program
! .. Use Statements ..
USE nag_library, ONLY : d02ejf, d02ejw, d02ejx, d02ejy, nag_wp
USE d02ejfe_mod, ONLY : fcn, g, h, k, n, nin, nout, output, pederv, xend
! .. Implicit None Statement ..
IMPLICIT NONE
! .. Local Scalars ..
REAL (KIND=nag_wp) :: tol, x, xinit
INTEGER :: i, icase, ifail, iw, j, kinit
! .. Local Arrays ..
REAL (KIND=nag_wp), ALLOCATABLE :: w(:), y(:), yinit(:)
! .. Intrinsic Functions ..
INTRINSIC real
! .. Executable Statements ..
WRITE (nout,*) 'D02EJF Example Program Results'
iw = (12+n)*n + 50
ALLOCATE (w(iw),y(n),yinit(n))
! Skip heading in data file
READ (nin,*)
! xinit: initial x value, xend: final x value
! y: initial solution values
READ (nin,*) xinit, xend
READ (nin,*) yinit(1:n)
READ (nin,*) kinit
DO icase = 1, 5
IF (icase/=2) THEN
WRITE (nout,99995) icase, 'Jacobian internally'
ELSE
WRITE (nout,99995) icase, 'Jacobian by PEDERV'
END IF
SELECT CASE (icase)
CASE (1,2)
WRITE (nout,99994) 'intermediate output, root-finding'
CASE (3)
WRITE (nout,99994) 'no intermediate output, root-finding'
CASE (4)
WRITE (nout,99994) 'intermediate output, no root-finding'
CASE (5)
WRITE (nout,99994) &
'no intermediate output, no root-finding (integrate to XEND)'
END SELECT
DO j = 3, 4
tol = 10.0E0_nag_wp**(-j)
WRITE (nout,99999) ' Calculation with TOL =', tol
x = xinit
y(1:n) = yinit(1:n)
IF (icase/=3) THEN
WRITE (nout,*) ' X Y(1) Y(2) Y(3)'
k = kinit
h = (xend-x)/real(k+1,kind=nag_wp)
END IF
ifail = 0
SELECT CASE (icase)
CASE (1)
CALL d02ejf(x,xend,n,y,fcn,d02ejy,tol,'Default',output,g,w,iw, &
ifail)
WRITE (nout,99998) ' Root of Y(1)-0.9 at', x
WRITE (nout,99997) ' Solution is', (y(i),i=1,n)
CASE (2)
CALL d02ejf(x,xend,n,y,fcn,pederv,tol,'Default',output,g,w,iw, &
ifail)
WRITE (nout,99998) ' Root of Y(1)-0.9 at', x
WRITE (nout,99997) ' Solution is', (y(i),i=1,n)
CASE (3)
CALL d02ejf(x,xend,n,y,fcn,d02ejy,tol,'Default',d02ejx,g,w,iw, &
ifail)
WRITE (nout,99998) ' Root of Y(1)-0.9 at', x
WRITE (nout,99997) ' Solution is', (y(i),i=1,n)
CASE (4)
ifail = 0
CALL d02ejf(x,xend,n,y,fcn,d02ejy,tol,'Default',output,d02ejw, &
w,iw,ifail)
CASE (5)
WRITE (nout,99996) x, (y(i),i=1,n)
CALL d02ejf(x,xend,n,y,fcn,d02ejy,tol,'Default',d02ejx,d02ejw, &
w,iw,ifail)
WRITE (nout,99996) x, (y(i),i=1,n)
END SELECT
IF (tol<0.0E0_nag_wp) WRITE (nout,*) ' Range too short for TOL'
END DO
IF (icase<5) THEN
WRITE (nout,*)
END IF
END DO
99999 FORMAT (/1X,A,E8.1)
99998 FORMAT (1X,A,F7.3)
99997 FORMAT (1X,A,3F13.5)
99996 FORMAT (1X,F8.2,3F13.5)
99995 FORMAT (/1X,'Case ',I1,': calculating ',A,',')
99994 FORMAT (8X,A)
END PROGRAM d02ejfe