add examples: eig, eigh, eigvals, eigvalsh

Author: perazz

example/linalg/CMakeLists.txt

@@ -13,6 +13,10 @@ ADD_EXAMPLE(is_square)
 ADD_EXAMPLE(is_symmetric)
 ADD_EXAMPLE(is_triangular)
 ADD_EXAMPLE(outer_product)
+ADD_EXAMPLE(eig)
+ADD_EXAMPLE(eigh)
+ADD_EXAMPLE(eigvals)
+ADD_EXAMPLE(eigvalsh)
 ADD_EXAMPLE(trace)
 ADD_EXAMPLE(state1)
 ADD_EXAMPLE(state2)

example/linalg/example_eig.f90

@@ -0,0 +1,27 @@
+! Eigendecomposition of a real square matrix 
+program example_eig
+  use stdlib_linalg_constants, only: sp
+  use stdlib_linalg, only: eig
+  implicit none
+
+  integer :: i
+  real(sp), allocatable :: A(:,:)
+  complex(sp), allocatable :: lambda(:),vectors(:,:)
+
+  ! Decomposition of this square matrix
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape( [ [2, 2, 4], &
+                           [1, 3, 5], &
+                           [2, 3, 4] ], [3,3] )) 
+
+  ! Get eigenvalues and right eigenvectors
+  allocate(lambda(3),vectors(3,3))
+  
+  call eig(A, lambda, right=vectors)
+  
+  do i=1,3
+     print *, 'eigenvalue  ',i,': ',lambda(i)
+     print *, 'eigenvector ',i,': ',vectors(:,i)
+  end do
+  
+end program example_eig

example/linalg/example_eigh.f90

@@ -0,0 +1,39 @@
+! Eigendecomposition of a real symmetric matrix 
+program example_eigh
+  use stdlib_linalg_constants, only: sp
+  use stdlib_linalg, only: eigh
+  implicit none
+
+  integer :: i
+  real(sp), allocatable :: A(:,:),lambda(:),v(:,:)
+  complex(sp), allocatable :: cA(:,:),cv(:,:)
+
+  ! Decomposition of this symmetric matrix
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape( [ [2, 1, 4], &
+                           [1, 3, 5], &
+                           [4, 5, 4] ], [3,3] )) 
+
+  ! Note: real symmetric matrices have real (orthogonal) eigenvalues and eigenvectors
+  allocate(lambda(3),v(3,3))  
+  call eigh(A, lambda, vectors=v)
+  
+  print *, 'Real matrix'
+  do i=1,3
+     print *, 'eigenvalue  ',i,': ',lambda(i)
+     print *, 'eigenvector ',i,': ',v(:,i)
+  end do
+  
+  ! Complex hermitian matrices have real (orthogonal) eigenvalues and complex eigenvectors
+  cA = A
+  
+  allocate(cv(3,3))  
+  call eigh(cA, lambda, vectors=cv)
+  
+  print *, 'Complex matrix'
+  do i=1,3
+     print *, 'eigenvalue  ',i,': ',lambda(i)
+     print *, 'eigenvector ',i,': ',cv(:,i)
+  end do  
+  
+end program example_eigh

example/linalg/example_eigvals.f90

@@ -0,0 +1,25 @@
+! Eigenvalues of a general real / complex matrix 
+program example_eigvals
+  use stdlib_linalg_constants, only: sp
+  use stdlib_linalg, only: eigvals
+  implicit none
+
+  integer :: i
+  real(sp), allocatable :: A(:,:),lambda(:)
+  complex(sp), allocatable :: cA(:,:),clambda(:)
+
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape( [ [2, 8, 4], &
+                           [1, 3, 5], &
+                           [9, 5,-2] ], [3,3] )) 
+
+  ! Note: real symmetric matrix
+  lambda = eigvals(A)
+  print *, 'Real    matrix eigenvalues: ',lambda
+  
+  ! Complex general matrix
+  cA = cmplx(A, -2*A, kind=sp)
+  clambda = eigvals(cA)
+  print *, 'Complex matrix eigenvalues: ',clambda
+  
+end program example_eigvals

example/linalg/example_eigvalsh.f90

@@ -0,0 +1,26 @@
+! Eigenvalues of a real symmetric / complex hermitian matrix 
+program example_eigvalsh
+  use stdlib_linalg_constants, only: sp
+  use stdlib_linalg, only: eigvalsh
+  implicit none
+
+  integer :: i
+  real(sp), allocatable :: A(:,:),lambda(:)
+  complex(sp), allocatable :: cA(:,:)
+
+  ! Decomposition of this symmetric matrix
+  ! NB Fortran is column-major -> transpose input
+  A = transpose(reshape( [ [2, 1, 4], &
+                           [1, 3, 5], &
+                           [4, 5, 4] ], [3,3] )) 
+
+  ! Note: real symmetric matrices have real (orthogonal) eigenvalues and eigenvectors
+  lambda = eigvalsh(A)
+  print *, 'Symmetric matrix eigenvalues: ',lambda
+  
+  ! Complex hermitian matrices have real (orthogonal) eigenvalues and complex eigenvectors
+  cA = A
+  lambda = eigvalsh(cA)
+  print *, 'Hermitian matrix eigenvalues: ',lambda
+  
+end program example_eigvalsh