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! This example computes the Schur decomposition of a real-valued square matrix.
program example_schur_real
use stdlib_linalg, only: schur
use stdlib_linalg_constants, only: dp
implicit none
integer, parameter :: n = 3
real(dp), dimension(n,n) :: A, T, Z
! Initialize a real-valued square matrix
A = reshape([ 0, 2, 2, &
0, 1, 2, &
1, 0, 1], shape=[n,n])
! Compute the Schur decomposition: A = Z T Z^T
call schur(A, T, Z)
! Output results
print *, "Original Matrix A:"
print *, A
print *, "Schur Form Matrix T:"
print *, T
print *, "Orthogonal Matrix Z:"
print *, Z
! 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_real
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