program main

!*****************************************************************************80
!
!! rbf_interp_1d_test() tests rbf_interp_1d().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    03 July 2018
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  integer nd
  external phi1
  external phi2
  external phi3
  external phi4
  external phi5
  external phi6
  external phi7
  integer prob
  integer prob_num
  real ( kind = rk ) r0
  real ( kind = rk ), allocatable :: xd(:)
  real ( kind = rk ) xmax
  real ( kind = rk ) xmin
  real ( kind = rk ), allocatable :: xy(:,:)

  call timestamp ( )
  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'RBF_INTERP_1D_TEST():'
  write ( *, '(a)' ) '  FORTRAN90 version'
  write ( *, '(a)' ) '  Test RBF_INTERP_1D().'
  write ( *, '(a)' ) '  The R8LIB library is needed.'
  write ( *, '(a)' ) '  The test needs the TEST_INTERP library.'

  call p00_prob_num ( prob_num )

  do prob = 1, prob_num
!
!  Determine an appropriate value of R0, the spacing parameter.
!
    call p00_data_num ( prob, nd )
    allocate ( xy(1:2,1:nd) )
    call p00_data ( prob, 2, nd, xy )
    allocate ( xd(1:nd) )
    xd(1:nd) = xy(1,1:nd)
    xmax = maxval ( xd )
    xmin = minval ( xd )
    r0 = 3.0D+00 * ( xmax - xmin ) / real ( nd - 1, kind = rk )
    deallocate ( xd )
    deallocate ( xy )

    call test01 ( prob, phi1, 'phi1', r0 )
    call test01 ( prob, phi2, 'phi2', r0 )
    call test01 ( prob, phi3, 'phi3', r0 )
    call test01 ( prob, phi4, 'phi4', r0 )
    call test01 ( prob, phi5, 'phi5', r0 )
    call test01 ( prob, phi6, 'phi6', r0 )
    call test01 ( prob, phi7, 'phi7', r0 )

  end do
!
!  Terminate.
!
  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'RBF_INTERP_1D_TEST:'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ''
  call timestamp ( )

  stop
end
subroutine test01 ( prob, phi, phi_name, r0 )

!*****************************************************************************80
!
!! TEST01 tests RBF_INTERP_1D.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 September 2012
!
!  Author:
!
!    John Burkardt
!
!  Parameters:
!
!    Input, integer PROB, the index of the problem.
!
!    Input, external PHI, the name of the radial basis function.
!
!    Input, character ( len = * ) PHI_NAME, the name of the radial basis function.
!
!    Input, real ( kind = rk ) R0, the scale factor.  Typically, this might be
!    a small multiple of the average distance between points.
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  real ( kind = rk ) int_error
  real ( kind = rk ) ld
  real ( kind = rk ) li
  integer m
  integer nd
  integer ni
  external phi
  character ( len = * ) phi_name
  integer prob
  real ( kind = rk ) r0
  real ( kind = rk ) r8vec_norm_affine
  real ( kind = rk ), allocatable :: w(:)
  real ( kind = rk ), allocatable :: xd(:)
  real ( kind = rk ), allocatable :: xi(:)
  real ( kind = rk ) xmax
  real ( kind = rk ) xmin
  real ( kind = rk ), allocatable :: xy(:,:)
  real ( kind = rk ), allocatable :: yd(:)
  real ( kind = rk ), allocatable :: yi(:)
  real ( kind = rk ) ymax
  real ( kind = rk ) ymin

  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'TEST01:'
  write ( *, '(a,i4)' ) '  Interpolate data from TEST_INTERP problem #', prob
  write ( *, '(a)' ) '  using radial basis function "' // trim ( phi_name ) // '".'
  write ( *, '(a,g14.6)' ) '  Scale factor R0 = ', r0

  call p00_data_num ( prob, nd )
  write ( *, '(a,i4)' ) '  Number of data points = ', nd

  allocate ( xy(1:2,1:nd) )
  call p00_data ( prob, 2, nd, xy )
  
  call r8mat_transpose_print ( 2, nd, xy, '  Data array:' )

  allocate ( xd(1:nd) )
  allocate ( yd(1:nd) )
  xd(1:nd) = xy(1,1:nd)
  yd(1:nd) = xy(2,1:nd)

  m = 1
  allocate ( w(1:nd) )
  call rbf_weight ( m, nd, xd, r0, phi, yd, w )
!
!  #1:  Does interpolant match function at interpolation points?
!
  ni = nd
  allocate ( xi(1:ni) )
  allocate ( yi(1:ni) )
  xi(1:nd) = xd(1:nd)
  call rbf_interp ( m, nd, xd, r0, phi, w, ni, xi, yi )

  int_error = r8vec_norm_affine ( ni, yi, yd ) / real ( ni, kind = rk )

  write ( *, '(a)' ) ''
  write ( *, '(a,g14.6)' ) &
    '  L2 interpolation error averaged per interpolant node = ', int_error

  deallocate ( xi )
  deallocate ( yi )
!
!  #2: Compare estimated curve length to piecewise linear (minimal) curve length.
!  Assume data is sorted, and normalize X and Y dimensions by (XMAX-XMIN) and
!  (YMAX-YMIN).
!
  xmin = minval ( xd(1:nd) )
  xmax = maxval ( xd(1:nd) )
  ymin = minval ( yd(1:nd) )
  ymax = maxval ( yd(1:nd) )

  ni = 501
  allocate ( xi(1:ni) )
  allocate ( yi(1:ni) )
  call r8vec_linspace ( ni, xmin, xmax, xi )
  call rbf_interp ( m, nd, xd, r0, phi, w, ni, xi, yi )

  ld = sum ( sqrt ( ( ( xd(2:nd) - xd(1:nd-1) ) / ( xmax - xmin ) ) ** 2 &
                  + ( ( yd(2:nd) - yd(1:nd-1) ) / ( ymax - ymin ) ) ** 2 ) )

  li = sum ( sqrt ( ( ( xi(2:ni) - xi(1:ni-1) ) / ( xmax - xmin ) ) ** 2 &
                  + ( ( yi(2:ni) - yi(1:ni-1) ) / ( ymax - ymin ) ) ** 2 ) )

  write ( *, '(a)' ) ''
  write ( *, '(a,g14.6)' ) '  Normalized length of piecewise linear interpolant = ', ld
  write ( *, '(a,g14.6)' ) '  Normalized length of polynomial interpolant       = ', li

  deallocate ( w )
  deallocate ( xd )
  deallocate ( xi )
  deallocate ( xy )
  deallocate ( yd )
  deallocate ( yi )

  return
end
subroutine timestamp ( )

!*****************************************************************************80
!
!! timestamp() prints the current YMDHMS date as a time stamp.
!
!  Example:
!
!    31 May 2001   9:45:54.872 AM
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    15 August 2021
!
!  Author:
!
!    John Burkardt
!
  implicit none

  character ( len = 8 ) ampm
  integer d
  integer h
  integer m
  integer mm
  character ( len = 9 ), parameter, dimension(12) :: month = (/ &
    'January  ', 'February ', 'March    ', 'April    ', &
    'May      ', 'June     ', 'July     ', 'August   ', &
    'September', 'October  ', 'November ', 'December ' /)
  integer n
  integer s
  integer values(8)
  integer y

  call date_and_time ( values = values )

  y = values(1)
  m = values(2)
  d = values(3)
  h = values(5)
  n = values(6)
  s = values(7)
  mm = values(8)

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

  write ( *, '(i2.2,1x,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