!----------------------------------------------------------------------
!     Copyright (c) 2016 Shin-ichi Takehiro. All rights reserved.
!----------------------------------------------------------------------
!
!表題  w_spectrum_module_svpack テストプログラム :: スペクトル解析関数のテスト
!
!履歴  2016/03/09  竹広真一   w_test_spectrum.f90 を改造, SVPACK 対応
!
program w_spectrum_module_svpack_test

  use dc_message, only : MessageNotify
  use dc_test, only : AssertEqual
  use w_module_svpack
  implicit none

  integer, parameter :: im=32, jm=16, nm=10


  real(8), dimension((nm+1)**2)   ::  w_data
  real(8), dimension(0:im-1,1:jm) ::  xy_data

  real(8), dimension(0:nm,-nm:nm) ::  nm_data
  real(8), dimension(0:nm)        ::  n_data
  real(8)                         ::  data

  ! 判定誤差設定
  integer, parameter :: check_digits = 10
  integer, parameter :: ignore = -11

  integer :: n,m

  call w_Initial( nm, im, jm )

  call MessageNotify('M','w_test_spectrum','w_spectrum_module tests') 

  !================= 2Y_1^0+3Y_2^1 のテスト ================
  xy_data = 2*sqrt(3.0D0)*sin(xy_Lat) &        ! 2Y_1^0+3Y_2^1
       + 3*sqrt(5.0D0/6)*3.0*sin(xy_Lat)*cos(xy_Lat) * cos(xy_Lon)! 
  w_data = w_xy(xy_data)

  !--------- Energy spectrum ---------
  nm_data=w_spectrum_VMiss
  do n=0,nm
     do m=-n,n
        nm_data(n,m) = 0.0
     enddo
  enddo
  nm_data(1,0) = 1*2*(2**2)/2
  nm_data(2,1) = 2*3*(3.0D0/2)**2/2
  nm_data(2,-1) =  nm_data(2,1)
  call AssertEqual(&
    message='nm_EnergyFromStreamfunc_w with 2Y_1^0+3Y_2^1 ',      &
    answer = nm_data,                                             &
    check = nm_EnergyFromStreamfunc_w(w_data),                    &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  n_data = 0.0; n_data(1) = 4.0D0 ;   n_data(2) = 2*3*(3.0D0/2)**2
  call AssertEqual(&
    message='n_EnergyFromStreamfunc_w with 2Y_1^0+3Y_2^1 ',       &
    answer = n_data,                                              &
    check = n_EnergyFromStreamfunc_w(w_data),                     &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  nm_Data = nm_EnergyFromStreamfunc_w(w_data)
  data = 0.0D0
  do n=0,nm
     do m=-n,n
        data = data + nm_Data(n,m)
     enddo
  enddo

  call AssertEqual(&
    message='total energy by nm-spectrum with 2Y_1^0+3Y_2^1 ',    &
    answer = AvrLonLat_xy( &
         0.5*(xy_GradLon_w(w_data)**2+xy_GradLat_w(w_data)**2) ), &
    check = data,                                                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  data = AvrLonLat_xy( 0.5*(xy_GradLon_w(w_data)**2+xy_GradLat_w(w_data)**2) )
  call AssertEqual(&
    message='total energy by n-spectrum with 2Y_1^0+3Y_2^1 ',     &
    answer = data,                                                &
    check = sum(n_EnergyFromStreamfunc_w(w_data)),                &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  !--------- Enstrophy spectrum ---------
  nm_data=w_spectrum_VMiss
  do n=0,nm
     do m=-n,n
        nm_data(n,m) = 0.0
     enddo
  enddo
  nm_data(1,0) = (1**2)*(2**2)*(2**2)/2
  nm_data(2,1) = (2**2)*(3**2)*(3.0D0/2.0D0)**2/2
  nm_data(2,-1) = nm_data(2,1)
  call AssertEqual(&
    message='nm_EnstrophyFromStreamfunc_w with 2Y_1^0+3Y_2^1 ',   &
    answer = nm_data,                                             &
    check = nm_EnstrophyFromStreamfunc_w(w_data),                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  n_data = 0.0; 
  n_data(1) = (1**2)*(2**2)*(2**2)/2
  n_data(2) = (2**2)*(3**2)*(3.0D0/2.0D0)**2
  call AssertEqual(&
    message='n_EnstrophyFromStreamfunc_w with 2Y_1^0+3Y_2^1 ',    &
    answer = n_data,                                              &
    check = n_EnstrophyFromStreamfunc_w(w_data),                  &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  nm_Data = nm_EnstrophyFromStreamfunc_w(w_data)
  data = 0.0D0
  do n=0,nm
     do m=-n,n
        data = data + nm_Data(n,m)
     enddo
  enddo

  call AssertEqual(&
    message='total enstrophy by nm-spectrum with 2Y_1^0+3Y_2^1 ', &
    answer =  AvrLonLat_xy( 0.5*(xy_w(w_Lapla_w(w_data))**2)),    &
    check = data,                                                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  data = AvrLonLat_xy( 0.5*(xy_w(w_Lapla_w(w_data))**2))
  call AssertEqual(&
    message='total enstrophy by n-spectrum with 2Y_1^0+3Y_2^1 ',  &
    answer = data,                                                &
    check = sum(n_EnstrophyFromStreamfunc_w(w_data)),             &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  !======== 3*Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2 のテスト ========
  xy_data = 3*sqrt(3.0D0)*sin(xy_Lat) &        ! 2Y_1^0+3Y_2^1
          + 2* sqrt(3.0D0/2)*cos(xy_Lat)*cos(xy_Lon) &
          + 2*sqrt(5.0D0)*(3.0/2*sin(xy_Lat)**2-1/2.0) &
          - sqrt(5.0D0/24)*3.0*cos(xy_Lat)**2*sin(2*xy_Lon)
  w_data = w_xy(xy_data)

  !--------- Energy spectrum ---------
  nm_data=w_spectrum_VMiss
  do n=0,nm
     do m=-n,n
        nm_data(n,m) = 0.0
     enddo
  enddo
  nm_data(1,0)  = 1*2*3**2/2
  nm_data(1,1)  = 1*2*(2/2)**2/2
  nm_data(1,-1) = nm_data(1,1)
  nm_data(2,0)  = 2*3*2**2/2
  nm_data(2,-2) = 2*3*(1.0D0/2.0D0)**2/2
  nm_data(2,2)  = nm_data(2,-2)
  call AssertEqual(&
    message='nm_EnergyFromStreamfunc_w with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2',&
    answer = nm_data,                                             &
    check = nm_EnergyFromStreamfunc_w(w_data),                    &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  n_data = 0.0
  n_data(1) = 1*2*3**2/2 + 1*2*(2/2)**2
  n_data(2) = 2*3*2**2/2 + 2*3*(1.0D0/2.0D0)**2
  call AssertEqual(&
    message='n_EnergyFromStreamfunc_w with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2', &
    answer = n_data,                                              &
    check = n_EnergyFromStreamfunc_w(w_data),                     &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  nm_Data = nm_EnergyFromStreamfunc_w(w_data)
  data = 0.0D0
  do n=0,nm
     do m=-n,n
        data = data + nm_Data(n,m)
     enddo
  enddo

  call AssertEqual(&
    message='total energy by nm-spectrum with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2', &
    answer = AvrLonLat_xy( &
         0.5*(xy_GradLon_w(w_data)**2+xy_GradLat_w(w_data)**2) ), &
    check = data,                                                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  data = AvrLonLat_xy( 0.5*(xy_GradLon_w(w_data)**2+xy_GradLat_w(w_data)**2) )
  call AssertEqual(&
    message='total energy by n-spectrum with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2', &
    answer = data,                                                &
    check = sum(n_EnergyFromStreamfunc_w(w_data)),                &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  !--------- Enstrophy spectrum ---------
  nm_data=w_spectrum_VMiss
  do n=0,nm
     do m=-n,n
        nm_data(n,m) = 0.0
     enddo
  enddo
  nm_data(1,0)  = (1**2)*(2**2)*3**2/2
  nm_data(1,1)  = (1**2)*(2**2)*(2/2)**2/2
  nm_data(1,-1) = nm_data(1,1)
  nm_data(2,0)  = (2**2)*(3**2)*2**2/2
  nm_data(2,-2) = (2**2)*(3**2)*(1.0D0/2.0D0)**2/2
  nm_data(2,2)  = nm_data(2,-2)
  call AssertEqual(&
    message='nm_EnstrophyFromStreamfunc_w with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2', &
    answer = nm_data,                                             &
    check = nm_EnstrophyFromStreamfunc_w(w_data),                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  n_data = 0.0
  n_data(1) = (1**2)*(2**2)*3**2/2 + (1**2)*(2**2)*(2/2)**2
  n_data(2) = (2**2)*(3**2)*2**2/2 + (2**2)*(3**2)*(1.0D0/2.0D0)**2
  call AssertEqual(&
    message='n_EnstrophyFromStreamfunc_w with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2', &
    answer = n_data,                                              &
    check = n_EnstrophyFromStreamfunc_w(w_data),                  &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  nm_Data = nm_EnstrophyFromStreamfunc_w(w_data)
  data = 0.0D0
  do n=0,nm
     do m=-n,n
        data = data + nm_Data(n,m)
     enddo
  enddo

  call AssertEqual(&
    message='total enstrophy by nm-spectrum with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2',&
    answer =  AvrLonLat_xy( 0.5*(xy_w(w_Lapla_w(w_data))**2)),    &
    check = data,                                                 &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  data = AvrLonLat_xy( 0.5*(xy_w(w_Lapla_w(w_data))**2))
  call AssertEqual(&
    message='total enstrophy by n-spectrum with 3Y_1^0 + 2Y_1^1 + 2Y_2^0 +Y_2^-2',&
    answer = data,                                                &
    check = sum(n_EnstrophyFromStreamfunc_w(w_data)),             &
    significant_digits = check_digits, ignore_digits = ignore     &
    )

  call MessageNotify('M','w_spectrum_module_svpack_test', &
                         'w_spectrum_module_svpack tests succeeded!') 

end program w_spectrum_module_svpack_test