add examples

Author: perazz

example/linalg/CMakeLists.txt

@@ -19,8 +19,10 @@ ADD_EXAMPLE(inverse_subroutine)
 ADD_EXAMPLE(outer_product)
 ADD_EXAMPLE(eig)
 ADD_EXAMPLE(eigh)
+ADD_EXAMPLE(eig_generalized)
 ADD_EXAMPLE(eigvals)
 ADD_EXAMPLE(eigvalsh)
+ADD_EXAMPLE(eigvals_generalized)
 ADD_EXAMPLE(trace)
 ADD_EXAMPLE(state1)
 ADD_EXAMPLE(state2)

example/linalg/example_eig_generalized.f90

@@ -0,0 +1,32 @@
+! Eigendecomposition of a real square matrix for the generalized eigenproblem
+program example_eig_generalized
+  use stdlib_linalg, only: eig
+  implicit none
+
+  integer :: i
+  real, allocatable :: A(:,:), B(:,:)
+  complex, allocatable :: lambda(:), vectors(:,:)
+
+  ! Matrices for the generalized eigenproblem: A * v = lambda * B * v
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape([ [2, 2, 4], &
+                           [1, 3, 5], &
+                           [2, 3, 4] ], [3,3]))
+
+  B = transpose(reshape([ [1, 0, 0], &
+                           [0, 1, 0], &
+                           [0, 0, 1] ], [3,3]))
+
+  ! Allocate eigenvalues and right eigenvectors
+  allocate(lambda(3), vectors(3,3))
+
+  ! Get eigenvalues and right eigenvectors for the generalized problem
+  call eig(A, B, lambda, right=vectors)
+
+  do i = 1, 3
+     print *, 'Eigenvalue  ', i, ': ', lambda(i)
+     print *, 'Eigenvector ', i, ': ', vectors(:,i)
+  end do
+
+end program example_eig_generalized
+

example/linalg/example_eigvals_generalized.f90

@@ -0,0 +1,28 @@
+! Eigenvalues of a general real/complex matrix for the generalized eigenproblem
+program example_eigvals_generalized
+  use stdlib_linalg, only: eigvals
+  implicit none
+
+  real, allocatable :: A(:,:), B(:,:), lambda(:)
+  complex, allocatable :: cA(:,:), cB(:,:), clambda(:)
+
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape([ [2, 8, 4], &
+                           [1, 3, 5], &
+                           [9, 5,-2] ], [3,3]))
+
+  B = transpose(reshape([ [1, 0, 0], &
+                           [0, 1, 0], &
+                           [0, 0, 1] ], [3,3]))
+
+  ! Real generalized eigenproblem
+  lambda = eigvals(A, B)
+  print *, 'Real generalized matrix eigenvalues: ', lambda
+
+  ! Complex generalized eigenproblem
+  cA = cmplx(A, -2*A)
+  cB = cmplx(B, 0.5*B)
+  clambda = eigvals(cA, cB)
+  print *, 'Complex generalized matrix eigenvalues: ', clambda
+
+end program example_eigvals_generalized