!---------------------------------------------------------------------- ! Copyright (c) 2024 Shin-ichi Takehiro. All rights reserved. !---------------------------------------------------------------------- ! !表題 w_zonal_module テストプログラム :: 微分関数のテスト ! !履歴 2024/02/15 竹広真一 ! program w_zonal_module_deriv_test use dc_message, only : MessageNotify use dc_test, only : AssertEqual use w_zonal_module implicit none integer, parameter :: im=1, jm=16, nm=10 real(8), dimension(0:im-1,1:jm) :: xy_data1 ! 元の関数 real(8), dimension(0:im-1,1:jm) :: xy_ddata ! 微分の正解 real(8), dimension(0:im-1,1:jm) :: xy_mu ! μ=sinφ ! 判定誤差設定 integer, parameter :: check_digits = 11 integer, parameter :: ignore = -12 integer :: j call MessageNotify('M','w_zonal_module_deriv_test', & 'w_zonal_module tests of derivative functions') call w_Initial( nm, im, jm ) !============== 微分計算 (φ座標系用) のテスト ============== !---- P_1^0 のテスト ---- xy_data1 = sqrt(3.0D0)*sin(xy_Lat) ! P_1^0 xy_ddata = -2*sqrt(3.0D0)*sin(xy_Lat) ! w_Lapla_w call AssertEqual(& message='P_1^0 Test of w_Lapla_w', & answer = xy_ddata, & check = xy_w(w_Lapla_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = -0.5*sqrt(3.0D0)*sin(xy_Lat) ! w_LaplaInv_l call AssertEqual(& message='P_1^0 Test of w_LaplaInv_w', & answer = xy_ddata, & check = xy_w(w_LaplaInv_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = 0.0D0 ! w_DLon_w call AssertEqual(& message='P_1^0 Test of w_DLon_w', & answer = xy_ddata, & check = xy_w(w_DLon_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = 0.0D0 ! xy_GradLon_w call AssertEqual(& message='P_1^0 Test of xy_GradLon_w', & answer = xy_ddata, & check = xy_GradLon_w(w_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = sqrt(3.0D0)*cos(xy_Lat) ! xy_GradLat_w call AssertEqual(& message='P_1^0 Test of xy_GradLat_w', & answer = xy_ddata, & check = xy_GradLat_w(w_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) !---- P_1^0 cosφ のテスト ---- xy_data1 = sqrt(3.0D0)*sin(xy_Lat)*cos(xy_Lat) ! P_1^0 xy_ddata = 0.0D0 ! w_DivLon_xy call AssertEqual(& message='P_1^0 cos(phi) Test of w_DivLon_xy', & answer = xy_ddata, & check = xy_w(w_DivLon_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = sqrt(3.0D0)*(1.0D0-3.0D0*sin(xy_Lat)**2) ! xy_DivLat_xy call AssertEqual(& message='P_1^0 cos(phi) Test of w_DivLat_xy', & answer = xy_ddata, & check = xy_w(w_DivLat_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) !---- P_2^0 のテスト ---- xy_data1 = sqrt(5.0D0)*(3.0D0*sin(xy_Lat)**2-1.0D0)/2.0D0 ! P_2 xy_ddata = -6*xy_data1 ! w_Lapla_w call AssertEqual(& message='P_2^0 Test of w_Lapla_w', & answer = xy_ddata, & check = xy_w(w_Lapla_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = -xy_data1/6.0D0 ! w_Lapla_w call AssertEqual(& message='P_2^0 Test of w_LaplaInv_w', & answer = xy_ddata, & check = xy_w(w_LaplaInv_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = 0.0D0 ! w_DLon_w call AssertEqual(& message='P_2^0 Test of w_DLon_w', & answer = xy_ddata, & check = xy_w(w_DLon_w(w_xy(xy_data1))), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = 0.0D0 ! xy_GradLon_w call AssertEqual(& message='P_2^0 Test of xy_GradLon_w', & answer = xy_ddata, & check = xy_GradLon_w(w_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = sqrt(5.0D0)*3.0D0*sin(xy_Lat)*cos(xy_Lat) ! xy_GradLat_w call AssertEqual(& message='P_2^0 Test of xy_GradLat_w', & answer = xy_ddata, & check = xy_GradLat_w(w_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) !---- P_2^0 cosφ のテスト ---- xy_data1 = sqrt(5.0D0)*(3.0D0*sin(xy_Lat)**2-1.0D0)/2.0D0*cos(xy_Lat) ! P_2^1 cosφ xy_ddata = 0.0D0 ! w_DivLat_xy call AssertEqual(& message='P_2^0 cos(phi) Test of w_DivLon_xy', & answer = xy_ddata, & check = xy_w(w_DivLon_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) xy_ddata = sqrt(5.0D0)*sin(xy_Lat)*(3.0D0*cos(2*xy_Lat)+1.0D0) call AssertEqual(& message='P_2^0 cos(phi) Test of w_DivLat_xy', & answer = xy_ddata, & check = xy_w(w_DivLat_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) !============== 微分計算 (μ座標系用) のテスト ============== xy_mu = sin(xy_Lat) !----- P_2^0 のテスト ----- xy_data1 = (3.0D0*xy_mu**2-1.0D0)/2.0D0 ! P_2^0 xy_ddata = (1-xy_mu**2)*3*xy_mu ! (1-μ^2)∂/∂μ call AssertEqual(& message='P_2^0 Test of xy_GradMu_w', & answer = xy_ddata, & check = xy_GradMu_w(w_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) !----- P_2^0 (1-μ^2) のテスト ----- xy_data1 = (3.0D0*xy_mu**2-1.0D0)/2.0D0*(1-xy_mu**2) ! P_2^0 (1-μ^2) xy_ddata = -6*xy_mu**3+4*xy_mu ! ∂/∂μ call AssertEqual(& message='P_2^0 (1-mu^2) Test of xy_DivMu_w', & answer = xy_ddata, & check = xy_w(w_DivMu_xy(xy_data1)), & significant_digits = check_digits, ignore_digits = ignore & ) call MessageNotify('M','w_module_deriv_test', & 'w_module tests of derivative functions succeeded!') end program w_zonal_module_deriv_test