Program zgeqrf_example
! ZGEQRF Example Program Text
! Copyright 2017, Numerical Algorithms Group Ltd. http://www.nag.com
! .. Use Statements ..
Use blas_interfaces, Only: dznrm2
Use lapack_example_aux, Only: nagf_file_print_matrix_complex_gen_comp
Use lapack_interfaces, Only: zgeqrf, ztrtrs, zunmqr
Use lapack_precision, Only: dp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Integer, Parameter :: nb = 64, nin = 5, nout = 6
! .. Local Scalars ..
Integer :: i, ifail, info, j, lda, ldb, lwork, m, n, nrhs
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: a(:, :), b(:, :), tau(:), work(:)
Real (Kind=dp), Allocatable :: rnorm(:)
Character (1) :: clabs(1), rlabs(1)
! .. Executable Statements ..
Write (nout, *) 'ZGEQRF Example Program Results'
Write (nout, *)
Flush (nout)
! Skip heading in data file
Read (nin, *)
Read (nin, *) m, n, nrhs
lda = m
ldb = m
lwork = nb*n
Allocate (a(lda,n), b(ldb,nrhs), tau(n), work(lwork), rnorm(nrhs))
! 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)
! Compute the QR factorization of A
Call zgeqrf(m, n, a, lda, tau, work, lwork, info)
! Compute C = (C1) = (Q**H)*B, storing the result in B
! (C2)
Call zunmqr('Left', 'Conjugate transpose', m, nrhs, n, a, lda, tau, b, &
ldb, work, lwork, info)
! Compute least squares solutions by back-substitution in
! R*X = C1
Call ztrtrs('Upper', 'No transpose', 'Non-Unit', n, nrhs, a, lda, b, &
ldb, 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
! Print least squares solutions
! ifail: behaviour on error exit
! =0 for hard exit, =1 for quiet-soft, =-1 for noisy-soft
ifail = 0
Call nagf_file_print_matrix_complex_gen_comp('General', ' ', n, nrhs, &
b, ldb, 'Bracketed', 'F7.4', 'Least squares solution(s)', 'Integer', &
rlabs, 'Integer', clabs, 80, 0, ifail)
! Compute and print estimates of the square roots of the residual
! sums of squares
Do j = 1, nrhs
rnorm(j) = dznrm2(m-n, b(n+1,j), 1)
End Do
Write (nout, *)
Write (nout, *) 'Square root(s) of the residual sum(s) of squares'
Write (nout, 100) rnorm(1:nrhs)
End If
100 Format (3X, 1P, 7E11.2)
End Program