program main

c*********************************************************************72
c
cc test_eigen_test() tests test_eigen().
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    09 March 2018
c
c  Author:
c
c    John Burkardt
c
      implicit none

      call timestamp ( )
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'test_eigen_test():'
      write ( *, '(a)' ) '  Fortran77 version'
      write ( *, '(a)' ) '  Test test_eigen().'

      call r8symm_gen_test ( )
      call r8nsymm_gen_test ( )
c
c  Terminate.
c
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'test_eigen_test():'
      write ( *, '(a)' ) '  Normal end of execution.'
      write ( *, '(a)') ' '
      call timestamp ( )

      stop 0
      end
      subroutine r8symm_gen_test ( )

c*********************************************************************72
c
cc r8symm_gen_test() tests r8symm_gen().
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    09 March 2018
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer n
      parameter ( n = 5 )
 
      double precision a(n,n)
      double precision aq(n,n)
      integer i
      integer j
      integer k
      double precision lambda(n)
      double precision lambda2(n)
      double precision lambda_dev
      parameter ( lambda_dev = 5.0D+00 )
      double precision lambda_mean
      parameter ( lambda_mean = 10.0D+00 )
      double precision q(n,n)
      integer seed

      seed = 123456789

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'r8symm_gen_test():'
      write ( *, '(a)' ) '  r8symm_gen() makes an arbitrary size '
      write ( *, '(a)' ) '  symmetric matrix with known eigenvalues '
      write ( *, '(a)' ) '  and eigenvectors.'
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 
     &  '  Real data is declared as "DOUBLE PRECISION".'

      call r8symm_gen ( n, lambda_mean, lambda_dev, seed, a, q, 
     &  lambda )

      call r8mat_print ( n, n, a, '  The matrix A:' )
      call r8mat_print ( n, n, q, '  The eigenvector matrix Q:' )
      call r8vec_print ( n, lambda, '  The eigenvalue vector LAMBDA:' )

      do i = 1, n
        do j = 1, n
          aq(i,j) = 0.0D+00
          do k = 1, n
            aq(i,j) = aq(i,j) + a(i,k) * q(k,j)
          end do
        end do
      end do

      do j = 1, n
        lambda2(j) = 0.0D+00
        do i = 1, n
          lambda2(j) = lambda2(j) + aq(i,j) ** 2
        end do
        lambda2(j) = sqrt ( lambda2(j) )
      end do

      call r8vec2_print ( n, lambda, lambda2, 
     &  '  LAMBDA versus the column norms of A*Q:' )

      return
      end
      subroutine r8nsymm_gen_test ( )

c*********************************************************************72
c
cc r8nsymm_gen_test() tests r8nsymm_gen().
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    05 June 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer n
      parameter ( n = 5 )
 
      double precision A(n,n)
      integer i
      double precision lambda(n)
      double precision lambda_dev
      parameter ( lambda_dev = 5.0D+00 )
      double precision lambda_mean
      parameter ( lambda_mean = 10.0D+00 )
      double precision Q(n,n)
      integer seed
      double precision T(n,n)

      seed = 123456789

      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'r8nsymm_gen_test()'
      write ( *, '(a)' ) '  r8nsymm_gen() makes an arbitrary size '
      write ( *, '(a)' ) '  nonsymmetric matrix with known eigenvalues '
      write ( *, '(a)' ) '  and eigenvectors.'
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 
     &  '  Real data is declared as "DOUBLE PRECISION".'

      call r8nsymm_gen ( n, lambda_mean, lambda_dev, seed, A, Q, T )

      do i = 1, n
        lambda(i) = T(i,i)
      end do

      call r8vec_sort_bubble_a ( n, lambda )

      call r8mat_print ( n, n, A, '  The nonsymmetric matrix A:' )
      call r8mat_print ( n, n, Q, '  The orthogonal factor Q:' )
      call r8mat_print ( n, n, T, '  The upper triangular matrix T:' )
      call r8vec_print ( n, lambda, '  The sorted eigenvalues LAMBDA:' )

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc timestamp() prints out the current YMDHMS date as a timestamp.
c
c  Discussion:
c
c    This Fortran77 version is made available for cases where the
c    Fortran90 version cannot be used.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    12 January 2007
c
c  Author:
c
c    John Burkardt
c
c  Parameters:
c
c    None
c
      implicit none

      character * ( 8 ) ampm
      integer d
      character * ( 8 ) date
      integer h
      integer m
      integer mm
      character * ( 9 ) month(12)
      integer n
      integer s
      character * ( 10 ) time
      integer y

      save month

      data month /
     &  'January  ', 'February ', 'March    ', 'April    ',
     &  'May      ', 'June     ', 'July     ', 'August   ',
     &  'September', 'October  ', 'November ', 'December ' /

      call date_and_time ( date, time )

      read ( date, '(i4,i2,i2)' ) y, m, d
      read ( time, '(i2,i2,i2,1x,i3)' ) h, n, s, mm

      if ( h .lt. 12 ) then
        ampm = 'AM'
      else if ( h .eq. 12 ) then
        if ( n .eq. 0 .and. s .eq. 0 ) then
          ampm = 'Noon'
        else
          ampm = 'PM'
        end if
      else
        h = h - 12
        if ( h .lt. 12 ) then
          ampm = 'PM'
        else if ( h .eq. 12 ) then
          if ( n .eq. 0 .and. s .eq. 0 ) then
            ampm = 'Midnight'
          else
            ampm = 'AM'
          end if
        end if
      end if

      write ( *,
     &  '(i2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' )
     &  d, month(m), y, h, ':', n, ':', s, '.', mm, ampm

      return
      end