/
EigValVecSym.f95
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EigValVecSym.f95
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subroutine EigValVecSym(ain, n, eig, evec, ul, K)
!-------------------------------------------------------------------------------
!
! This subroutine will return the eigenvalues and eigenvectors
! of the symmetric square matrix Ain. The output eigenvectors
! are ordered from greatest to least, and the norm of the eigenvectors
! is unity. If the optional parameter K is specified, only the K largest
! eigenvalues and corresponding vectors will be output.
!
! Calling Parameters
!
! IN
! Ain Input symmetric matrix. By default, only the
! upper portion is used.
! n Order of the matrix Ain.
! OUT
! eig Vector of length n of the eigenvalues of Ain.
! evec Matrix of dimension n of the eigenvectors of Ain.
!
! OPTIONAL
! ul Use the upper 'U' or lower 'L' portion of the
! input symmetric matrix.
! K The K largest eigenvalues and corresponding eigenvectors
! to calculate and output.
!
! Notes:
!
! 1. The eigenvalues and eigenvectors are determined by reducing the
! matrix to
! A = Z L Z = Q (S L S') Q'
! by the two operations:
!
! (1) The real symmetric square matrix is reduced to tridiagonal form
! A = Q T Q'
! where Q is orthogonal, and T is symmetric tridiagonal.
! (2) The tridiagonal matrix is reduced to
! T = S L S'
!
! The eigenvalues of A correspond to the L (which is a diagonal), and the
! eigenvectors correspond to Z = Q S.
!
! 2. The sign convention for the eigenvalues might want to be changed.
! For instance, IMSL chooses the sign such that the value with
! max(abs(evec)) is positive.
!
! Dependencies: LAPACK, BLAS
!
! Copyright (c) 2015, Mark A. Wieczorek
! All rights reserved.
!
!-------------------------------------------------------------------------------
implicit none
real*8, intent(in) :: ain(:,:)
integer, intent(in) :: n
real*8, intent(out) :: eig(:), evec(:,:)
character, intent(in), optional :: ul
integer, intent(in), optional :: K
integer, parameter :: nb = 80, nbl = 10
character :: uplo
real*8 :: d(n), e(n), tau(n-1), work(nb*n), vl, vu, abstol, w(n)
real*8, allocatable :: a(:,:), z(:,:)
integer :: lwork, info, il, iu, m, isuppz(2*n), liwork, iwork(nbl*n), &
i, astat(2)
external dsytrd, dstegr, dormtr
if (size(ain(:,1)) < n .or. size(ain(1,:)) < n) then
print*, "Error --- EigValVecSym"
print*, "AIN must be dimensioned as (N, N) where N is ", n
print*, "Input array is dimensioned as ", size(ain(:,1)), size(ain(1,:))
stop
end if
if (present(K)) then
if (K > n .or. K < 1) then
print*, "Error --- EigValVecSym"
print*, "The number of eigenvalues to output must " // &
"be between 0 and N."
print*, "N = ", n
print*, "K = ", k
stop
end if
if (size(eig) < K) then
print*, "Error --- EigValVecSym"
print*, "EIG must be dimensioned as (K) where K is ", K
print*, "Input array is dimensioned as ", size(eig)
stop
else if(size(evec(:,1)) < n .or. size(evec(1,:)) < K) then
print*, "Error --- EigValVecSym"
print*, "EVEC must be dimensioned as (N, K)."
print*, "N = ", n
print*, "K = ", k
print*, "Input array is dimensioned as ", size(evec(:,1)), &
size(evec(1,:))
stop
end if
else
if (size(eig) < n) then
print*, "Error --- EigValVecSym"
print*, "EIG must be dimensioned as (N) where N is ", n
print*, "Input array is dimensioned as ", size(eig)
stop
else if (size(evec(:,1)) < n .or. size(evec(1,:)) < n) then
print*, "Error --- EigValVecSym"
print*, "EVEC must be dimensioned as (N, N) where N is ", n
print*, "Input array is dimensioned as ", size(evec(:,1)), &
size(evec(1,:))
stop
end if
end if
allocate (a(n,n), stat = astat(1))
allocate (z(n,n), stat = astat(2))
if (astat(1) /= 0 .or. astat(2) /= 0) then
print*, "Error --- EigValVecSym2"
print*, "Problem allocating arrays A and Z", astat(1), astat(2)
stop
end if
lwork = nb * n
liwork = nbl * n
eig = 0.0d0
evec = 0.0d0
a(1:n,1:n) = ain(1:n,1:n)
if (present(ul)) then
uplo = ul
else
uplo = "U"
end if
!---------------------------------------------------------------------------
!
! Factor A to Q T Q' where T is a tridiagonal matrix.
!
!---------------------------------------------------------------------------
call dsytrd(uplo, n, a, n, d, e(1:n-1), tau, work, lwork, info)
if (info /= 0) then
print*, "Error --- EigValVecSym"
print*, "Problem tri-diagonalizing input matrix"
print*, "DSYTRD info = ", info
stop
else
if (work(1) > dble(lwork)) then
print*, "Warning --- EigValVecSym"
print*, "Consider changing value of nb to ", work(1)/n, &
" and recompile."
end if
end if
!---------------------------------------------------------------------------
!
! Factor T to S L S' where L is a diagonal matrix.
!
!---------------------------------------------------------------------------
abstol = 0.0d0
if (present(K)) then
call dstegr('v','I', n, d, e, vl, vu, n-K+1, n, abstol, m, w, &
z, n, isuppz, work, lwork, iwork, liwork, info)
else
call dstegr('v','I', n, d, e, vl, vu, il, iu, abstol, m, w, &
z, n, isuppz, work, lwork, iwork, liwork, info)
end if
if (info /= 0) then
print*, "Error --- EigValVecSym"
print*, "Problem determining eigenvalues and eigenvectors " // &
"of tridiagonal matrix."
if (info == 1) print*, "Internal error in DLARRE"
if (info == 2) print*, "Internal error in DLARRV"
print*, "DSTEGR info = ", info
stop
else
if (work(1) > dble(lwork)) then
print*, "Warning --- EigValVecSym"
print*, "Consider changing value of nb to ", work(1)/n, &
" and recompile SHTOOLS archive."
endif
if (iwork(1) > liwork) then
print*, "Warning --- EigValVecSym"
print*, "Consider changing value of nb to ", iwork(1)/n, &
" and recompile SHTOOLS archive."
end if
end if
!---------------------------------------------------------------------------
!
! Determine eigenvalues Z = Q S (note that Q is stored in a
! bizarre manner, see LAPACK notes), and reorder eigenvalues and
! eigenvectors from greatest to least.
!
!---------------------------------------------------------------------------
call dormtr('L', uplo, 'N', n, n, a, n, tau, z, n, work, lwork, info)
if (info /= 0) then
print*, "Error --- EigValVecSym"
print*, "Problem multiplying matrices."
print*, "DORMTR info = ", info
stop
else
if (work(1) > dble(lwork)) then
print*, "Warning --- EigValVecSym"
print*, "Consider changing value of nb to ", work(1)/n, &
" and recompile."
end if
end if
if (present(k)) then
do i = n-K+1, n
eig(i-n+k) = w(n+1-i)
evec(1:n,i-n+k) = z(1:n,n+1-i)
end do
else
do i = 1, n
eig(i) = w(n+1-i)
evec(1:n,i) = z(1:n,n+1-i)
end do
end if
deallocate (a)
deallocate (z)
end subroutine EigValVecSym