Program f08befe ! F08BEF Example Program Text ! Mark 24 Release. NAG Copyright 2012. ! .. Use Statements .. Use nag_library, Only: dgeqpf, dormqr, dtrsv, nag_wp, x04caf ! .. Implicit None Statement .. Implicit None ! .. Parameters .. Real (Kind=nag_wp), Parameter :: zero = 0.0E0_nag_wp Integer, Parameter :: nin = 5, nout = 6 ! .. Local Scalars .. Real (Kind=nag_wp) :: tol Integer :: i, ifail, info, k, lda, ldb, ldx, & lwork, m, n, nrhs ! .. Local Arrays .. Real (Kind=nag_wp), Allocatable :: a(:,:), b(:,:), tau(:), work(:), & x(:,:) Integer, Allocatable :: jpvt(:) ! .. Intrinsic Procedures .. Intrinsic :: abs ! .. Executable Statements .. Write (nout,*) 'F08BEF Example Program Results' ! Skip heading in data file Read (nin,*) Read (nin,*) m, n, nrhs lda = m ldb = m ldx = m lwork = 64*n Allocate (a(lda,n),b(ldb,nrhs),tau(n),work(lwork),x(ldx,nrhs),jpvt(n)) ! Read A and B from data file Read (nin,*)(a(i,1:n),i=1,m) Read (nin,*)(b(i,1:nrhs),i=1,m) ! Initialize JPVT to be zero so that all columns are free jpvt(1:n) = 0 ! Compute the QR factorization of A ! The NAG name equivalent of dgeqpf is f08bef Call dgeqpf(m,n,a,lda,jpvt,tau,work,info) ! Choose TOL to reflect the relative accuracy of the input data tol = 0.01E0_nag_wp ! Determine which columns of R to use loop: Do k = 1, n If (abs(a(k,k))<=tol*abs(a(1,1))) Exit loop End Do loop ! Compute C = (Q**T)*B, storing the result in B k = k - 1 ! The NAG name equivalent of dormqr is f08agf Call dormqr('Left','Transpose',m,nrhs,n,a,lda,tau,b,ldb,work,lwork,info) ! Compute least-squares solution by backsubstitution in R*B = C Do i = 1, nrhs ! The NAG name equivalent of dtrsv is f06pjf Call dtrsv('Upper','No transpose','Non-Unit',k,a,lda,b(1,i),1) ! Set the unused elements of the I-th solution vector to zero b(k+1:n,i) = zero End Do ! Unscramble the least-squares solution stored in B Do i = 1, n x(jpvt(i),1:nrhs) = b(i,1:nrhs) End Do ! Print least-squares solution Write (nout,*) Flush (nout) ! ifail: behaviour on error exit ! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft ifail = 0 Call x04caf('General',' ',n,nrhs,x,ldx,'Least-squares solution',ifail) End Program f08befe