To calculate eigenvalues and eigenvectors in Fortran, you can use the LAPACK library, specifically the DGEEV subroutine. This subroutine computes the eigenvalues and eigenvectors of a real general matrix.
Eigenvalues are scalar values that represent how a linear transformation affects the magnitude of a vector, while eigenvectors are the actual vectors that are only scaled by the eigenvalue when the linear transformation is applied to them.
Sure! Here is a simple code snippet using LAPACK's DGEEV subroutine to calculate eigenvalues and eigenvectors:```fortranprogram eigen_example implicit none integer, parameter :: N = 3 real*8 :: A(N,N), WR(N), WI(N), VL(N,N), VR(N,N) integer :: LWORK = 3*N real*8 :: WORK(LWORK) integer :: INFO ! Initialize matrix A A = reshape([1.0d0, 0.0d0, 0.0d0, & 0.0d0, 2.0d0, 0.0d0, & 0.0d0, 0.0d0, 3.0d0], [N,N]) ! Call DGEEV subroutine call DGEEV('N', 'V', N, A, N, WR, WI, VL, N, VR, N, WORK, LWORK, INFO) ! Output eigenvalues and eigenvectors print *, 'Eigenvalues:' print *, WR print *, 'Eigenvectors:' print *, VRend program eigen_example```This code initializes a 3x3 matrix and computes its eigenvalues and eigenvectors using the DGEEV subroutine.
If the DGEEV subroutine returns an error code (INFO < 0), it indicates that an input parameter is invalid. You should check your input matrix and parameters to ensure they are correct.
Yes, besides LAPACK, you can also use the ARPACK library for calculating eigenvalues and eigenvectors in Fortran. ARPACK is specifically designed for large-scale eigenvalue problems and offers additional features compared to LAPACK.