program polynomial_conversion_test

c*********************************************************************72
c
cc polynomial_conversion_test() tests polynomial_conversion().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    16 April 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      call timestamp ( )
      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'polynomial_conversion_test():'
      write ( *, '(a)' ) '  Fortran77 version'
      write ( *, '(a)' ) '  Test polynomial_conversion().'

      call chebyshev_to_monomial_test ( )
      call monomial_to_chebyshev_test ( )
      call chebyshev_monomial_chebyshev_test ( )

      call gegenbauer_to_monomial_matrix_test ( )

      call legendre_to_monomial_matrix_test ( )
c
c  Terminate.
c
      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'polynomial_conversion_test():'
      write ( *, '(a)' ) '  Normal end of execution.'

      call timestamp ( )

      stop
      end
      subroutine chebyshev_monomial_chebyshev_test ( )

c*********************************************************************72
c
cc chebyshev_monomial_chebyshev_test() tests accuracy.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    18 February 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer n
      parameter ( n = 10 )

      double precision ccoef(0:n)
      double precision ccoef2(0:n)
      double precision e
      double precision mcoef(0:n)
      double precision r8vec_diff_norm_l2

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'chebyshev_monomial_chebyshev_test ( )'
      write ( *, '(a)' ) '  Convert a polynomial from Chebyshev form'
      write ( *, '(a)' ) '  to monomial form and back.'

      call random_number ( ccoef(0:n) )
      call chebyshev_to_monomial ( n, ccoef, mcoef )
      call monomial_to_chebyshev ( n, mcoef, ccoef2 )

      e = r8vec_diff_norm_l2 ( n, ccoef, ccoef2 )
      write ( *, '(a)' ) ''
      write ( *, '(a,g14.6)' ) '  L2 difference = ', e

      return
      end
      subroutine chebyshev_to_monomial_test ( )

c*********************************************************************72
c
cc chebyshev_to_monomial_test() tests chebyshev_to_monomial().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    18 February 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer nmax
      parameter ( nmax = 6 )

      double precision ccoef(0:nmax)
      integer k
      double precision mcoef(0:nmax)
      integer n

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'chebyshev_to_monomial_test ( )'
      write ( *, '(a)' ) '  chebyshev_to_monomial() converts a'
      write ( *, '(a)' ) '  polynomial from Chebyshev form'
      write ( *, '(a)' ) '  to monomial form.'

      write ( *, '(a)' ) ''
      write ( *, '(10x,7(''X**'',i1,''    ''))' ) ( k, k = 0, nmax )
      write ( *, '(a)' ) ''
      do n = 0, nmax
        do k = 0, n - 1
          ccoef(k) = 0.0D+00
        end do
        ccoef(n) = 1.0D+00
        call chebyshev_to_monomial ( n, ccoef, mcoef )
        write ( *, '(a,i1,a,f7.3,8f8.3)' ) 
     &    'T', n, '(x) = ', ( mcoef(k), k = 0, n )
      end do

      return
      end
      subroutine gegenbauer_to_monomial_matrix_test ( )

c*********************************************************************72
c
cc gegenbauer_to_monomial_matrix_test() tests gegenbauer_to_monomial_matrix().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    16 April 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 4

      double precision A(0:n,0:n)
      double precision alpha
      integer i
      integer j

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'gegenbauer_to_monomial_matrix_test ( )'
      write ( *, '(a)' ) '  gegenbauer_to_monomial_matrix() returns the'
      write ( *, '(a)' ) '  matrix which converts a polynomial from'
      write ( *, '(a)' ) '  Gegenbauer form to monomial form.'

      alpha = 0.5D+00
      write ( *, '(a,g14.6)' ) '  alpha = ', alpha

      call gegenbauer_to_monomial_matrix ( n + 1, alpha, A )

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) '  A:'
      write ( *, '(a)' ) ''
      do i = 0, n
        do j = 0, n
          write ( *, '(f8.5)', advance = 'no' ) A(i,j)
        end do
        write ( *, '(a)' ) ''
      end do

      return
      end
      subroutine legendre_to_monomial_matrix_test ( )

c*********************************************************************72
c
cc legendre_to_monomial_matrix_test() tests legendre_to_monomial_matrix().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    20 February 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 4

      double precision A(0:n,0:n)
      integer i
      integer j

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'legendre_to_monomial_matrix_test ( )'
      write ( *, '(a)' ) '  legendre_to_monomial_matrix() returns the'
      write ( *, '(a)' ) '  matrix which converts a polynomial from'
      write ( *, '(a)' ) '  Legendre form to monomial form.'

      call legendre_to_monomial_matrix ( n + 1, A )

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) '  A:'
      write ( *, '(a)' ) ''
      do i = 0, n
        do j = 0, n
          write ( *, '(f8.5)', advance = 'no' ) A(i,j)
        end do
        write ( *, '(a)' ) ''
      end do

      return
      end
      subroutine monomial_to_chebyshev_test ( )

c*********************************************************************72
c
cc monomial_to_chebyshev_test() tests monomial_to_chebyshev().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    18 February 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer nmax
      parameter ( nmax = 6 )

      double precision ccoef(0:nmax)
      integer k
      double precision mcoef(0:nmax)
      integer n

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'monomial_to_chebyshev_test ( )'
      write ( *, '(a)' ) '  monomial_to_chebyshev() converts a'
      write ( *, '(a)' ) '  polynomial from monomial form to '
      write ( *, '(a)' ) '  Chebyshev form.'

      write ( *, '(a)' ) ''
      write ( *, '(8x,7(''T'',i1,''(x)   ''))' ) ( k, k = 0, nmax )
      write ( *, '(a)' ) ''
      do n = 0 , nmax
        do k = 0, n - 1
          mcoef(k) = 0.0D+00
        end do
        mcoef(n) = 1.0D+00
        call monomial_to_chebyshev ( n, mcoef, ccoef )
        write ( *, '(a,i1,a,8f8.5)' ) 
     &    'X**', n, ' = ', ( ccoef(k), k = 0, n )
      end do

      return
      end
      function r8vec_diff_norm_l2 ( n, a, b )

c*********************************************************************72
c
cc r8vec_diff_norm_l2() returns the L2 norm of the difference of R8VEC's.
c
c  Discussion:
c
c    An R8VEC is a vector of R8 values.
c
c    The vector L2 norm is defined as:
c
c      R8VEC_NORM_L2 = sqrt ( sum ( 1 <= I <= N ) A(I)^2 ).
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 June 2010
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    integer N, the number of entries in A.
c
c    double precision A(N), B(N), the vectors.
c
c  Output:
c
c    double precision R8VEC_DIFF_NORM_L2, the L2 norm of A - B.
c
      implicit none

      integer n

      double precision a(n)
      double precision b(n)
      integer i
      double precision r8vec_diff_norm_l2
      double precision value

      value = 0.0D+00
      do i = 1, n
        value = value + ( a(i) - b(i) )**2
      end do
      value = sqrt ( value )

      r8vec_diff_norm_l2 = value

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc timestamp() prints the YMDHMS date as a timestamp.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 June 2014
c
c  Author:
c
c    John Burkardt
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, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, 
     &  trim ( ampm )

      return
      end