PROGRAM d03uafe

!      D03UAF Example Program Text

!      Mark 23 Release. NAG Copyright 2011.

!      .. Use Statements ..
       USE nag_library, ONLY : d03uaf, 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              :: nin = 5, nout = 6
!      .. Local Scalars ..
       REAL (KIND=nag_wp)              :: adel, aparam, ares, delmax, delmn,   &
                                          resmax, resmn
       INTEGER                         :: i, ifail, it, j, lda, n1, n2, nits
!      .. Local Arrays ..
       REAL (KIND=nag_wp), ALLOCATABLE :: a(:,:), b(:,:), c(:,:), d(:,:),      &
                                          e(:,:), q(:,:), r(:,:), t(:,:),      &
                                          wrksp1(:,:), wrksp2(:,:), x(:), y(:)
!      .. Intrinsic Functions ..
       INTRINSIC                          abs, cos, exp, max, real
!      .. Executable Statements ..
       WRITE (nout,*) 'D03UAF Example Program Results'
       WRITE (nout,*)
!      Skip heading in data file
       READ (nin,*)
       READ (nin,*) n1, n2, nits
       lda = n1
       ALLOCATE (a(lda,n2),b(lda,n2),c(lda,n2),d(lda,n2),e(lda,n2),q(lda,n2), &
          r(lda,n2),t(lda,n2),wrksp1(lda,n2),wrksp2(lda,n2),x(n1),y(n2))
       READ (nin,*) x(1:n1)
       READ (nin,*) y(1:n2)
       aparam = one

!      Set up difference equation coefficients, source terms and
!      initial S
       a(1:n1,1:n2) = zero
       b(1:n1,1:n2) = zero
       d(1:n1,1:n2) = zero
       e(1:n1,1:n2) = zero
       q(1:n1,1:n2) = zero
       t(1:n1,1:n2) = zero
!      Specification for internal nodes
       DO j = 2, n2 - 1
          a(2:n1-1,j) = two/((y(j)-y(j-1))*(y(j+1)-y(j-1)))
          e(2:n1-1,j) = two/((y(j+1)-y(j))*(y(j+1)-y(j-1)))
       END DO
       DO i = 2, n1 - 1
          b(i,2:n2-1) = two/((x(i)-x(i-1))*(x(i+1)-x(i-1)))
          d(i,2:n2-1) = two/((x(i+1)-x(i))*(x(i+1)-x(i-1)))
       END DO
       c(1:n1,1:n2) = -a(1:n1,1:n2) - b(1:n1,1:n2) - d(1:n1,1:n2) - &
          e(1:n1,1:n2)
!      Specification for boundary nodes
       DO j = 1, n2
          q(1,j) = exp((x(1)+one)/y(n2))*cos(y(j)/y(n2))
          q(n1,j) = exp((x(n1)+one)/y(n2))*cos(y(j)/y(n2))
       END DO
       DO i = 1, n1
          q(i,1) = exp((x(i)+one)/y(n2))*cos(y(1)/y(n2))
          q(i,n2) = exp((x(i)+one)/y(n2))*cos(y(n2)/y(n2))
       END DO

!      Iterative loop
       DO it = 1, nits
!         Calculate the residuals
          resmax = zero
          resmn = zero
          DO j = 1, n2
             DO i = 1, n1
                IF (c(i,j)/=zero) THEN
!                  Five point molecule formula
                   r(i,j) = q(i,j) - a(i,j)*t(i,j-1) - b(i,j)*t(i-1,j) - &
                      c(i,j)*t(i,j) - d(i,j)*t(i+1,j) - e(i,j)*t(i,j+1)
                ELSE
!                  Explicit equation
                   r(i,j) = q(i,j) - t(i,j)
                END IF
                ares = abs(r(i,j))
                resmax = max(resmax,ares)
                resmn = resmn + ares
             END DO
          END DO
          resmn = resmn/(real(n1*n2,kind=nag_wp))

!         ifail: behaviour on error exit   
!                =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft  
          ifail = 0
          CALL d03uaf(n1,n2,lda,a,b,c,d,e,aparam,it,r,wrksp1,wrksp2,ifail)

          IF (it==1) THEN
             WRITE (nout,99997) 'Iteration', 'Residual', 'Change'
             WRITE (nout,99996) 'No', 'Max.', 'Mean', 'Max.', 'Mean'
          END IF

!         Update the dependent variable
          delmax = zero
          delmn = zero
          DO j = 1, n2
             DO i = 1, n1
                t(i,j) = t(i,j) + r(i,j)
                adel = abs(r(i,j))
                delmax = max(delmax,adel)
                delmn = delmn + adel
             END DO
          END DO
          delmn = delmn/(real(n1*n2,kind=nag_wp))
          WRITE (nout,99999) it, resmax, resmn, delmax, delmn
!      Convergence tests here if required
       END DO
!      End of iterative loop
       WRITE (nout,*)
       WRITE (nout,*) 'Table of calculated function values'
       WRITE (nout,*)
       WRITE (nout,99995) 'I', 1, (i,i=2,6)
       WRITE (nout,*) ' J'
       DO j = 1, n2
          WRITE (nout,99998) j, (t(i,j),i=1,n1)
       END DO


99999  FORMAT (1X,I3,4(2X,E11.4))
99998  FORMAT (1X,I2,1X,6(F9.3,2X))
99997  FORMAT (1X,A,6X,A,19X,A)
99996  FORMAT (3X,A,7X,A,8X,A,11X,A,6X,A/)
99995  FORMAT (4X,A,4X,I1,5I11)
    END PROGRAM d03uafe