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! This example includes eigenvalue computation in addition to
! the Schur decomposition for a randomly generated matrix.
program example_schur_eigenvalues
use stdlib_linalg, only: schur
use stdlib_linalg_constants, only: dp
implicit none
integer, parameter :: n = 5
real(dp), dimension(n,n) :: A, T, Z
complex(dp), dimension(n) :: eigenvalues
! Create a random real-valued square matrix
call random_number(A)
! Compute the Schur decomposition and eigenvalues
call schur(A, T, Z, eigenvalues)
! Output results
print *, "Random Matrix A:"
print *, A
print *, "Schur Form Matrix T:"
print *, T
print *, "Orthogonal Matrix Z:"
print *, Z
print *, "Eigenvalues:"
print *, eigenvalues
! Test factorization: Z*T*Z^T = A
print *, "Max error in reconstruction:", maxval(abs(matmul(Z, matmul(T, transpose(Z))) - A))
end program example_schur_eigenvalues
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