/
EigValVecSymTri.F95
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EigValVecSymTri.F95
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subroutine EigValVecSymTri(ain, n, eig, evec, ul, exitstatus)
!------------------------------------------------------------------------------
!
! This subroutine will return the eigenvalues and eigenvectors
! of the symmetric square tridiagonal matrix Ain. The output eigenvectors
! are ordered from greatest to least, and the norm of the eigenvectors
! is unity. The sign convention for the eigenvectors is that the
! first value of each eigenvector is positive.
!
! Calling Parameters
!
! IN
! Ain Input symmetric tridiagonal matrix.
! 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.
!
! IN (OPTIONAL)
! ul Use the upper 'U' or lower 'L' portion of the
! input symmetric matrix. By default, the lower portion
! of the matrix will be used.
!
! OPTIONAL (OUT)
! exitstatus If present, instead of executing a STOP when an error
! is encountered, the variable exitstatus will be
! returned describing the error.
! 0 = No errors;
! 1 = Improper dimensions of input array;
! 2 = Improper bounds for input variable;
! 3 = Error allocating memory;
! 4 = File IO error.
!
! Notes:
!
! 1. The tridiagonal matrix is reduced to A = S L S'.
! 2. If accuracy is a problem, consider changing the value of ABSTOL.
! I have arbitrarily set this to zero, which forces the routines to
! pick a default value (which may or may not be good).
! 3. 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) 2016, SHTOOLS
! 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(out), optional :: exitstatus
integer, parameter :: nb = 80, nbl = 10
real*8 :: d(n), e(n), work(nb*n), vl, vu, abstol, w(n)
real*8, allocatable :: z(:,:)
integer :: lwork, info, il, iu, m, isuppz(2*n), liwork, &
iwork(nbl*n), i, astat
#ifdef LAPACK_UNDERSCORE
#define dstegr dstegr_
#endif
external dstegr
if (present(exitstatus)) exitstatus = 0
if (size(ain(:,1)) < n .or. size(ain(1,:)) < n) then
print*, "Error --- EigValVecSymTri"
print*, "AIN must be dimensioned as (N, N) where N is ", n
print*, "Input array is dimensioned as ", size(ain(:,1)), size(ain(1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(eig) < n) then
print*, "Error --- EigValVecSymTri"
print*, "EIG must be dimensioned as (N) where N is ", n
print*, "Input array is dimensioned as ", size(eig)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(evec(:,1)) < n .or. size(evec(1,:)) < n) then
print*, "Error --- EigValVecSymTri"
print*, "EVEC must be dimensioned as (N, N) where N is ", n
print*, "Input array is dimensioned as ", size(evec(:,1)), &
size(evec(1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
allocate (z(n, n), stat = astat)
if (astat /= 0) then
print*, "Error --- EigValVecSymTri"
print*, "Problem allocating arrays Z", astat
if (present(exitstatus)) then
exitstatus = 3
return
else
stop
end if
end if
lwork = nb * n
liwork = nbl * n
eig = 0.0d0
evec = 0.0d0
d(1) = ain(1,1)
if (present(ul)) then
if (ul == "U" .or. ul == "u") then
do i = 2, n, 1
d(i) = ain(i,i)
e(i-1) = ain(i-1, i)
end do
else if (ul =="L" .or. ul == "l") then
do i = 2, n, 1
d(i) = ain(i,i)
e(i-1) = ain(i, i-1)
end do
else
print*, "Error --- EigValVecSym"
print*, "UL must be either U, u, L, or l"
print*, "Input value is ", ul
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
else
do i = 2, n, 1
d(i) = ain(i,i)
e(i-1) = ain(i, i-1)
end do
end if
e(n) = 0.0d0
!--------------------------------------------------------------------------
!
! Factor tridiagonal matric A = S L S', and re-order
! eignevalues and vectors from greatest to least.
!
!--------------------------------------------------------------------------
abstol = 0.0d0
call dstegr('v','a', n, d, e, vl, vu, il, iu, abstol, m, w, &
z, n, isuppz, work, lwork, iwork, liwork, info)
if (info /= 0) then
print*, "Error --- EigValVecSymTri"
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"
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
else
if (work(1) > dble(lwork)) then
print*, "Warning --- EigValVecSymTri"
print*, "Consider changing value of nb to ", work(1)/n, &
" and recompile SHTOOLS archive."
end if
if (iwork(1) > liwork) then
print*, "Warning --- EigValVecSymTri"
print*, "Consider changing value of nb to ", iwork(1)/n, &
" and recompile SHTOOLS archive."
end if
end if
do i = 1, n
eig(i) = w(n+1-i)
evec(1:n,i) = z(1:n,n+1-i)
if (evec(1,i) < 0.0d0) evec(1:n,i) = -evec(1:n,i)
end do
deallocate (z)
end subroutine EigValVecSymTri