Program f08zefe ! F08ZEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dgemv, dggqrf, dnrm2, dormqr, dormrq, dtrtrs, & nag_wp ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: one = 1.0E0_nag_wp Real (Kind=nag_wp), Parameter :: zero = 0.0E0_nag_wp Integer, Parameter :: nb = 64, nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: rnorm Integer :: i, info, lda, ldb, lwork, m, n, p ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), d(:), taua(:), & taub(:), work(:), y(:) ! .. Intrinsic Procedures .. Intrinsic :: max, min ! .. Executable Statements .. Write (nout,*) 'F08ZEF Example Program Results' Write (nout,*) ! Skip heading in data file Read (nin,*) Read (nin,*) n, m, p lda = n ldb = n lwork = nb*(m+p) Allocate (a(lda,m),b(ldb,p),d(n),taua(m),taub(m+p),work(lwork),y(p)) ! Read A, B and D from data file Read (nin,*)(a(i,1:m),i=1,n) Read (nin,*)(b(i,1:p),i=1,n) Read (nin,*) d(1:n) ! Compute the generalized QR factorization of (A,B) as ! A = Q*(R), B = Q*(T11 T12)*Z ! (0) ( 0 T22) ! The NAG name equivalent of dggqrf is f08zef Call dggqrf(n,m,p,a,lda,taua,b,ldb,taub,work,lwork,info) ! Compute c = (c1) = (Q**T)*d, storing the result in D ! (c2) ! The NAG name equivalent of dormqr is f08agf Call dormqr('Left','Transpose',n,1,m,a,lda,taua,d,n,work,lwork,info) ! Putting Z*y = w = (w1), set w1 = 0, storing the result in Y1 ! (w2) y(1:m+p-n) = zero If (n>m) Then ! Copy c2 into Y2 y(m+p-n+1:p) = d(m+1:n) ! Solve T22*w2 = c2 for w2, storing result in Y2 ! The NAG name equivalent of dtrtrs is f07tef Call dtrtrs('Upper','No transpose','Non-unit',n-m,1,b(m+1,m+p-n+1), & ldb,y(m+p-n+1),n-m,info) If (info>0) Then Write (nout,*) & 'The upper triangular factor, T22, of B is singular, ' Write (nout,*) 'the least squares solution could not be computed' Go To 100 End If ! Compute estimate of the square root of the residual sum of squares ! norm(y) = norm(w2) ! The NAG name equivalent of dnrm2 is f06ejf rnorm = dnrm2(n-m,y(m+p-n+1),1) ! Form c1 - T12*w2 in D ! The NAG name equivalent of dgemv is f06paf Call dgemv('No transpose',m,n-m,-one,b(1,m+p-n+1),ldb,y(m+p-n+1),1, & one,d,1) End If ! Solve R*x = c1 - T12*w2 for x ! The NAG name equivalent of dtrtrs is f07tef Call dtrtrs('Upper','No transpose','Non-unit',m,1,a,lda,d,m,info) If (info>0) Then Write (nout,*) 'The upper triangular factor, R, of A is singular, ' Write (nout,*) 'the least squares solution could not be computed' Else ! Compute y = (Z**T)*w ! The NAG name equivalent of dormrq is f08ckf Call dormrq('Left','Transpose',p,1,min(n,p),b(max(1, & n-p+1),1),ldb,taub,y,p,work,lwork,info) ! Print least squares solution x Write (nout,*) 'Generalized least squares solution' Write (nout,99999) d(1:m) ! Print residual vector y Write (nout,*) Write (nout,*) 'Residual vector' Write (nout,99998) y(1:p) ! Print estimate of the square root of the residual sum of squares Write (nout,*) Write (nout,*) 'Square root of the residual sum of squares' Write (nout,99998) rnorm End If 100 Continue 99999 Format (1X,7F11.4) 99998 Format (3X,1P,7E11.2) End Program f08zefe