Program d03ubfe ! D03UBF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: d03ubf, 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, root2, x1, x2, y1, & y2, yy, z1, z2 Integer :: i, ifail, it, j, k, lda, n1, n2, n3, & nits, sda ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:,:), b(:,:,:), c(:,:,:), & d(:,:,:), e(:,:,:), f(:,:,:), & g(:,:,:), q(:,:,:), r(:,:,:), & t(:,:,:), wrksp1(:,:,:), & wrksp2(:,:,:), wrksp3(:,:,:), x(:), & y(:), z(:) ! .. Intrinsic Procedures .. Intrinsic :: abs, cos, exp, max, real, sqrt ! .. Executable Statements .. Write (nout,*) 'D03UBF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n1, n2, n3, nits lda = n1 sda = n2 Allocate (a(lda,sda,n3),b(lda,sda,n3),c(lda,sda,n3),d(lda,sda,n3), & e(lda,sda,n3),f(lda,sda,n3),g(lda,sda,n3),q(lda,sda,n3),r(lda,sda,n3), & t(lda,sda,n3),wrksp1(lda,sda,n3),wrksp2(lda,sda,n3), & wrksp3(lda,sda,n3),x(n1),y(n2),z(n3)) Read (nin,*) x(1:n1) Read (nin,*) y(1:n2) Read (nin,*) z(1:n3) root2 = sqrt(two) aparam = one ! Set up difference equation coefficients, source terms and ! initial approximation a(1:n1,1:n2,1:n3) = zero b(1:n1,1:n2,1:n3) = zero c(1:n1,1:n2,1:n3) = zero e(1:n1,1:n2,1:n3) = zero f(1:n1,1:n2,1:n3) = zero g(1:n1,1:n2,1:n3) = zero q(1:n1,1:n2,1:n3) = zero t(1:n1,1:n2,1:n3) = zero ! Specification for internal nodes Do k = 2, n3 - 1 a(2:n1-1,2:n2-1,k) = two/((z(k)-z(k-1))*(z(k+1)-z(k-1))) g(2:n1-1,2:n2-1,k) = two/((z(k+1)-z(k))*(z(k+1)-z(k-1))) End Do Do j = 2, n2 - 1 b(2:n1-1,j,2:n3-1) = two/((y(j)-y(j-1))*(y(j+1)-y(j-1))) f(2:n1-1,j,2:n3-1) = two/((y(j+1)-y(j))*(y(j+1)-y(j-1))) End Do Do i = 2, n1 - 1 c(i,2:n2-1,2:n3-1) = two/((x(i)-x(i-1))*(x(i+1)-x(i-1))) e(i,2:n2-1,2:n3-1) = two/((x(i+1)-x(i))*(x(i+1)-x(i-1))) End Do d(1:n1,1:n2,1:n3) = -a(1:n1,1:n2,1:n3) - b(1:n1,1:n2,1:n3) - & c(1:n1,1:n2,1:n3) - e(1:n1,1:n2,1:n3) - f(1:n1,1:n2,1:n3) - & g(1:n1,1:n2,1:n3) ! Specification for boundary nodes yy = one/y(n2) x1 = (x(1)+one)*yy x2 = (x(n1)+one)*yy Do j = 1, n2 y1 = root2*y(j)*yy q(1,j,1:n3) = exp(x1)*cos(y1)*exp((-z(1:n3)-one)*yy) q(n1,j,1:n3) = exp(x2)*cos(y1)*exp((-z(1:n3)-one)*yy) End Do y1 = root2*y(1)*yy y2 = root2*y(n2)*yy Do i = 1, n1 x1 = (x(i)+one)*yy q(i,1,1:n3) = exp(x1)*cos(y1)*exp((-z(1:n3)-one)*yy) q(i,n2,1:n3) = exp(x1)*cos(y2)*exp((-z(1:n3)-one)*yy) End Do z1 = (-z(1)-one)*yy z2 = (-z(n3)-one)*yy Do i = 1, n1 x1 = (x(i)+one)*yy q(i,1:n2,1) = exp(x1)*cos(root2*y(1:n2)*yy)*exp(z1) q(i,1:n2,n3) = exp(x1)*cos(root2*y(1:n2)*yy)*exp(z2) End Do ! Iterative loop Do it = 1, nits resmax = zero resmn = zero Do k = 1, n3 Do j = 1, n2 Do i = 1, n1 If (d(i,j,k)/=zero) Then ! Seven point molecule formula r(i,j,k) = q(i,j,k) - a(i,j,k)*t(i,j,k-1) - & b(i,j,k)*t(i,j-1,k) - c(i,j,k)*t(i-1,j,k) - & d(i,j,k)*t(i,j,k) - e(i,j,k)*t(i+1,j,k) - & f(i,j,k)*t(i,j+1,k) - g(i,j,k)*t(i,j,k+1) Else ! Explicit equation r(i,j,k) = q(i,j,k) - t(i,j,k) End If ares = abs(r(i,j,k)) resmax = max(resmax,ares) resmn = resmn + ares End Do End Do End Do resmn = resmn/(real(n1*n2*n3,kind=nag_wp)) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call d03ubf(n1,n2,n3,lda,sda,a,b,c,d,e,f,g,aparam,it,r,wrksp1,wrksp2, & wrksp3,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 k = 1, n3 Do j = 1, n2 Do i = 1, n1 t(i,j,k) = t(i,j,k) + r(i,j,k) adel = abs(r(i,j,k)) delmax = max(delmax,adel) delmn = delmn + adel End Do End Do End Do delmn = delmn/(real(n1*n2*n3,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,99995) Write (nout,*) Write (nout,99998)((k,j,(i,t(i,j,k),i=1,n1),j=1,n2),k=1,n3) 99999 Format (1X,I5,4(2X,E11.4)) 99998 Format ((1X,I1,I3,1X,4(1X,I3,2X,F8.3))) 99997 Format (1X,A,6X,A,19X,A) 99996 Format (2X,A,7X,A,8X,A,11X,A,6X,A/) 99995 Format (1X,'K J',2X,4(1X,'(I T )')) End Program d03ubfe