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! Eigendecomposition of a real symmetric matrix
program example_eigh
use stdlib_linalg, only: eigh
implicit none
integer :: i
real, allocatable :: A(:,:),lambda(:),vectors(:,:)
complex, allocatable :: cA(:,:),cvectors(:,:)
! Decomposition of this symmetric matrix
! NB Fortran is column-major -> transpose input
A = transpose(reshape( [ [2, 1, 4], &
[1, 3, 5], &
[4, 5, 4] ], [3,3] ))
! Note: real symmetric matrices have real (orthogonal) eigenvalues and eigenvectors
allocate(lambda(3),vectors(3,3))
call eigh(A, lambda, vectors=vectors)
print *, 'Real matrix'
do i=1,3
print *, 'eigenvalue ',i,': ',lambda(i)
print *, 'eigenvector ',i,': ',vectors(:,i)
end do
! Complex hermitian matrices have real (orthogonal) eigenvalues and complex eigenvectors
cA = A
allocate(cvectors(3,3))
call eigh(cA, lambda, vectors=cvectors)
print *, 'Complex matrix'
do i=1,3
print *, 'eigenvalue ',i,': ',lambda(i)
print *, 'eigenvector ',i,': ',cvectors(:,i)
end do
end program example_eigh
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