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! This example demonstrates the Schur decomposition for a complex-valued matrix.
program example_schur_complex
use stdlib_linalg, only: schur
use stdlib_linalg_constants, only: dp
implicit none
integer, parameter :: n = 3
complex(dp), dimension(n,n) :: A, T, Z
! Initialize a complex-valued square matrix
A = reshape([ (1, 2), (3,-1), (4, 1), &
(0,-1), (2, 0), (1,-2), &
(2, 3), (1, 1), (0,-1) ], shape=[n,n])
! Compute the Schur decomposition: A = Z T Z^H
call schur(A, T, Z)
! Output results
print *, "Original Matrix A:"
print *, A
print *, "Schur Form Matrix T:"
print *, T
print *, "Unitary Matrix Z:"
print *, Z
! Test factorization: Z*T*Z^H = A
print *, "Max error in reconstruction:", maxval(abs(matmul(Z, matmul(T, conjg(transpose(Z)))) - A))
end program example_schur_complex
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