add examples

Author: perazz

example/linalg/CMakeLists.txt

@@ -24,6 +24,9 @@ ADD_EXAMPLE(eigvalsh)
 ADD_EXAMPLE(trace)
 ADD_EXAMPLE(state1)
 ADD_EXAMPLE(state2)
+ADD_EXAMPLE(schur_real)
+ADD_EXAMPLE(schur_complex)
+ADD_EXAMPLE(schur_eigvals)
 ADD_EXAMPLE(blas_gemv)
 ADD_EXAMPLE(lapack_getrf)
 ADD_EXAMPLE(lstsq1)

example/linalg/example_schur_complex.f90

@@ -0,0 +1,33 @@
+! 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
+  complex(dp), allocatable :: A(:,:), T(:,:), Z(:,:)
+  integer :: n
+
+  ! Initialize a complex-valued square matrix
+  n = 3
+  allocate(A(n,n), T(n,n), Z(n,n))
+  A = reshape([ &
+       (1.0_dp, 2.0_dp), (3.0_dp, -1.0_dp), (4.0_dp, 1.0_dp), &
+       (0.0_dp, -1.0_dp), (2.0_dp, 0.0_dp), (1.0_dp, -2.0_dp), &
+       (2.0_dp, 3.0_dp), (1.0_dp, 1.0_dp), (0.0_dp, -1.0_dp) ], 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))
+
+  deallocate(A, T, Z)
+end program example_schur_complex
+

example/linalg/example_schur_eigvals.f90

@@ -0,0 +1,34 @@
+! 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
+  real(dp), allocatable :: A(:,:), T(:,:), Z(:,:)
+  complex(dp), allocatable :: eigenvalues(:)
+  integer :: n
+
+  ! Create a random real-valued square matrix
+  n = 5
+  allocate(A(n,n), T(n,n), Z(n,n), eigenvalues(n))
+  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))
+
+  deallocate(A, T, Z, eigenvalues)
+end program example_schur_eigenvalues
+

example/linalg/example_schur_real.f90

@@ -0,0 +1,33 @@
+! 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
+  real(dp), allocatable :: A(:,:), T(:,:), Z(:,:)
+  integer :: n
+
+  ! Initialize a real-valued square matrix
+  n = 3
+  allocate(A(n,n), T(n,n), Z(n,n))
+  A = reshape([ &
+       0.0_dp, 2.0_dp, 2.0_dp, &
+       0.0_dp, 1.0_dp, 2.0_dp, &
+       1.0_dp, 0.0_dp, 1.0_dp], 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))
+
+  deallocate(A, T, Z)
+end program example_schur_real
+