Program dgeqpf_example
! DGEQPF Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use blas_interfaces, Only: dtrsv
Use lapack_example_aux, Only: nagf_file_print_matrix_real_gen
Use lapack_interfaces, Only: dgeqp3, dormqr
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=dp), Parameter :: zero = 0.0E0_dp
Integer, Parameter :: nin = 5, nout = 6
! .. Local Scalars ..
Real (Kind=dp) :: tol
Integer :: i, ifail, info, k, lda, ldb, ldx, lwork, m, n, nrhs
! .. Local Arrays ..
Real (Kind=dp), Allocatable :: a(:, :), b(:, :), tau(:), work(:), &
x(:, :)
Integer, Allocatable :: jpvt(:)
! .. Intrinsic Procedures ..
Intrinsic :: abs
! .. Executable Statements ..
Write (nout, *) 'DGEQPF 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
Call dgeqp3(m, n, a, lda, jpvt, tau, work, lwork, info)
! Choose TOL to reflect the relative accuracy of the input data
tol = 0.01E0_dp
! Determine which columns of R to use
loop: Do k = 1, n
If (abs(a(k,k))<=tol*abs(a(1,1))) Then
Exit loop
End If
End Do loop
! Compute C = (Q**T)*B, storing the result in B
k = k - 1
Call dormqr('Left', 'Transpose', m, nrhs, n, a, lda, tau, b, ldb, work, &
lwork, info)
! Compute least squares solution by back-substitution in R*B = C
Do i = 1, nrhs
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 nagf_file_print_matrix_real_gen('General', ' ', n, nrhs, x, ldx, &
'Least squares solution', ifail)
End Program