Program zupmtr_example
! ZUPMTR 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: dstebz, zhptrd, zstein, zupmtr
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 ..
Complex (Kind=dp) :: scal
Real (Kind=dp) :: vl, vu
Integer :: i, ifail, info, j, k, ldc, m, n, nsplit
Character (1) :: uplo
! .. Local Arrays ..
Complex (Kind=dp), Allocatable :: ap(:), c(:, :), tau(:), work(:)
Real (Kind=dp), Allocatable :: d(:), e(:), rwork(:), w(:)
Integer, Allocatable :: iblock(:), ifailv(:), isplit(:), iwork(:)
Character (1) :: clabs(1), rlabs(1)
! .. Intrinsic Procedures ..
Intrinsic :: abs, conjg, maxloc
! .. Executable Statements ..
Write (nout, *) 'ZUPMTR Example Program Results'
! Skip heading in data file
Read (nin, *)
Read (nin, *) n
ldc = n
Allocate (ap(n*(n+1)/2), c(ldc,n), tau(n), work(n), d(n), e(n), rwork(5* &
n), w(n), iblock(n), ifailv(n), isplit(n), iwork(3*n))
! Read A from data file
Read (nin, *) uplo
If (uplo=='U') Then
Read (nin, *)((ap(i+j*(j-1)/2),j=i,n), i=1, n)
Else If (uplo=='L') Then
Read (nin, *)((ap(i+(2*n-j)*(j-1)/2),j=1,i), i=1, n)
End If
! Reduce A to tridiagonal form T = (Q**H)*A*Q
Call zhptrd(uplo, n, ap, d, e, tau, info)
! Calculate the two smallest eigenvalues of T (same as A)
Call dstebz('I', 'B', n, vl, vu, 1, 2, zero, d, e, m, nsplit, w, iblock, &
isplit, rwork, iwork, info)
Write (nout, *)
If (info>0) Then
Write (nout, *) 'Failure to converge.'
Else
Write (nout, *) 'Eigenvalues'
Write (nout, 100) w(1:m)
! Calculate the eigenvectors of T, storing the result in C
Call zstein(n, d, e, m, w, iblock, isplit, c, ldc, rwork, iwork, &
ifailv, info)
If (info>0) Then
Write (nout, *) 'Failure to converge.'
Else
! Calculate the eigenvectors of A = Q * (eigenvectors of T)
Call zupmtr('Left', uplo, 'No transpose', n, m, ap, tau, c, ldc, &
work, info)
! Print eigenvectors
Write (nout, *)
Flush (nout)
! Normalize the eigenvectors, largest element real
Do i = 1, m
rwork(1:n) = abs(c(1:n,i))
k = maxloc(rwork(1:n), 1)
scal = conjg(c(k,i))/abs(c(k,i))/dznrm2(n, c(1,i), 1)
c(1:n, i) = c(1:n, i)*scal
End Do
! 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, m, &
c, ldc, 'Bracketed', 'F7.4', 'Eigenvectors', 'Integer', rlabs, &
'Integer', clabs, 80, 0, ifail)
End If
End If
100 Format (8X, 4(F7.4,11X,:))
End Program