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Date: 2021-01-08 13:03:42 Functions: 7 7 100.0 %
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      42             : 
      43             : !>  \brief This module contains tests of the module [Integration_mod](@ref integration_mod).
      44             : !>  \author Amir Shahmoradi
      45             : 
      46             : module Test_Integration_mod
      47             : 
      48             :     use Integration_mod
      49             :     !use QuadPackDouble_mod, only: dqagi
      50             :     use Constants_mod, only: IK, RK
      51             :     use Err_mod, only: Err_type
      52             :     use Test_mod, only: Test_type
      53             :     implicit none
      54             : 
      55             :     private
      56             :     public :: test_Integration
      57             : 
      58             :     type(Test_type) :: Test
      59             : 
      60             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      61             : 
      62             : contains
      63             : 
      64             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      65             : 
      66           1 :     subroutine test_Integration()
      67             :         implicit none
      68           1 :         Test = Test_type(moduleName=MODULE_NAME)
      69           1 :         call Test%run(test_doQuadRombOpen_1, "test_doQuadRombOpen_1")
      70           1 :         call Test%run(test_doQuadRombOpen_2, "test_doQuadRombOpen_2")
      71           1 :         call Test%run(test_doQuadRombOpen_3, "test_doQuadRombOpen_3")
      72           1 :         call Test%run(test_doQuadRombOpen_4, "test_doQuadRombOpen_4")
      73           1 :         call Test%run(test_doQuadRombClosed_1, "test_doQuadRombClosed_1")
      74           1 :         call Test%finalize()
      75           1 :     end subroutine test_Integration
      76             : 
      77             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
      78             : 
      79             :     ! integrate the Gaussian PDF via the midexp routine on the open interval \f$[0, +\infty)\f$.
      80           1 :     function test_doQuadRombOpen_1() result(assertion)
      81             : 
      82           1 :         use Constants_mod, only: RK, IK, POSINF_RK
      83             :         use Integration_mod
      84             : 
      85             :         implicit none
      86             : 
      87             :         logical                 :: assertion
      88           1 :         real(RK)                :: integral, relativeError, difference 
      89             :         real(RK), parameter     :: integral_ref = 0.5_RK
      90             :         real(RK), parameter     :: tolerance = 1.e-10_RK
      91             :         integer(IK)             :: numFuncEval, ierr
      92             : 
      93             :         call doQuadRombOpen ( getFunc = getTestFuncOpenInterval_1 &
      94             :                             , integrate = midexp &
      95             :                             , lowerLim = 0._RK &
      96             :                             , upperLim = POSINF_RK & ! do not set this to huge() as GNU Fortran in debug mode crashes
      97             :                             , maxRelativeError = 0.1*tolerance &
      98             :                             , nRefinement = 10_IK &
      99             :                             , integral = integral &
     100             :                             , relativeError = relativeError &
     101             :                             , numFuncEval = numFuncEval &
     102             :                             , ierr = ierr &
     103           1 :                             )
     104             : 
     105           1 :         assertion = ierr == 0_IK
     106             : 
     107           1 :         if (Test%isDebugMode .and. .not. assertion) then
     108             :             ! LCOV_EXCL_START
     109             :             if (Test%isDebugMode .and. .not. assertion) then
     110             :                 write(Test%outputUnit,"(*(g0))") "ierr = ", ierr, " /= 0"
     111             :             end if
     112             :             return
     113             :             ! LCOV_EXCL_STOP
     114             :         end if
     115             : 
     116           1 :         difference = abs(integral - integral_ref) / abs(integral_ref)
     117           1 :         assertion = difference < tolerance
     118           1 :         assertion = assertion .and. relativeError <= tolerance
     119             : 
     120             :         ! LCOV_EXCL_START
     121             :         if (Test%isDebugMode .and. .not. assertion) then
     122             :             write(Test%outputUnit,"(*(g0))")
     123             :             write(Test%outputUnit,"(*(g0))") "integral_ref  = ", integral_ref
     124             :             write(Test%outputUnit,"(*(g0))") "integral      = ", integral
     125             :             write(Test%outputUnit,"(*(g0))") "difference    = ", difference
     126             :             write(Test%outputUnit,"(*(g0))") "relativeError = ", relativeError
     127             :             write(Test%outputUnit,"(*(g0))")
     128             :         end if
     129             :         ! LCOV_EXCL_STOP
     130             : 
     131           1 :     end function test_doQuadRombOpen_1
     132             : 
     133             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     134             : 
     135           1 :     function test_doQuadRombOpen_2() result(assertion)
     136             : 
     137           1 :         use Constants_mod, only: RK, IK, POSINF_RK
     138             :         use Integration_mod
     139             : 
     140             :         implicit none
     141             : 
     142             :         logical                 :: assertion
     143           1 :         real(RK)                :: relativeError, difference
     144           1 :         real(RK)                :: integral
     145             :         real(RK), parameter     :: integral_ref = 0.078649603525143_RK
     146             :         real(RK), parameter     :: tolerance = 1.e-10_RK
     147             :         integer(IK)             :: numFuncEval, ierr
     148             : 
     149             :         call doQuadRombOpen ( getFunc = getTestFuncOpenInterval_1 &
     150             :                             , integrate = midinf &
     151             :                             , lowerLim = 1._RK &
     152             :                             , upperLim = POSINF_RK & ! do not set this to huge() as GNU Fortran in debug mode crashes
     153             :                             , maxRelativeError = 0.1*tolerance &
     154             :                             , nRefinement = 10_IK &
     155             :                             , integral = integral &
     156             :                             , relativeError = relativeError &
     157             :                             , numFuncEval = numFuncEval &
     158             :                             , ierr = ierr &
     159           1 :                             )
     160             : 
     161           1 :         assertion = ierr == 0_IK
     162             : 
     163           1 :         if (Test%isDebugMode .and. .not. assertion) then
     164             :             ! LCOV_EXCL_START
     165             :             if (Test%isDebugMode .and. .not. assertion) then
     166             :                 write(Test%outputUnit,"(*(g0))") "ierr = ", ierr, " /= 0"
     167             :             end if
     168             :             return
     169             :             ! LCOV_EXCL_STOP
     170             :         end if
     171             : 
     172           1 :         difference = abs(integral - integral_ref) / abs(integral_ref)
     173           1 :         assertion = difference < tolerance
     174           1 :         assertion = assertion .and. relativeError <= tolerance
     175             : 
     176           1 :         if (Test%isDebugMode .and. .not. assertion) then
     177             :         ! LCOV_EXCL_START
     178             :             write(Test%outputUnit,"(*(g0))")
     179             :             write(Test%outputUnit,"(*(g0))") "integral_ref  = ", integral_ref
     180             :             write(Test%outputUnit,"(*(g0))") "integral      = ", integral
     181             :             write(Test%outputUnit,"(*(g0))") "difference    = ", difference
     182             :             write(Test%outputUnit,"(*(g0))") "relativeError = ", relativeError
     183             :             write(Test%outputUnit,"(*(g0))")
     184             :         end if
     185             :         ! LCOV_EXCL_STOP
     186             : 
     187           1 :     end function test_doQuadRombOpen_2
     188             : 
     189             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     190             : 
     191           1 :     function test_doQuadRombOpen_3() result(assertion)
     192             : 
     193           1 :         use Constants_mod, only: RK, IK, POSINF_RK
     194             :         use Integration_mod
     195             : 
     196             :         implicit none
     197             : 
     198             :         logical                 :: assertion
     199           1 :         real(RK)                :: relativeError, difference
     200           1 :         real(RK)                :: integral
     201             :         real(RK), parameter     :: integral_ref = 0.078649603525143_RK
     202             :         real(RK), parameter     :: tolerance = 1.e-4_RK
     203             :         integer(IK)             :: numFuncEval, ierr
     204             : 
     205             :         call doQuadRombOpen ( getFunc = getTestFuncOpenInterval_1 &
     206             :                             , integrate = midinf &
     207             :                             , lowerLim = POSINF_RK & ! do not set this to huge() as GNU Fortran in debug mode crashes
     208             :                             , upperLim = -1._RK &
     209             :                             , maxRelativeError = 1.e-10_RK &
     210             :                             , nRefinement = 10_IK &
     211             :                             , integral = integral &
     212             :                             , relativeError = relativeError &
     213             :                             , numFuncEval = numFuncEval &
     214             :                             , ierr = ierr &
     215           1 :                             )
     216             : 
     217           1 :         assertion = ierr == 0_IK
     218           1 :         if (Test%isDebugMode .and. .not. assertion) then
     219             :             ! LCOV_EXCL_START
     220             :             if (Test%isDebugMode .and. .not. assertion) then
     221             :                 write(Test%outputUnit,"(*(g0))") "ierr = ", ierr, " /= 0"
     222             :             end if
     223             :             return
     224             :             ! LCOV_EXCL_STOP
     225             :         end if
     226             : 
     227           1 :         difference = abs(integral - integral_ref) / abs(integral_ref)
     228           1 :         assertion = difference < tolerance
     229           1 :         assertion = assertion .and. relativeError <= tolerance
     230             : 
     231           1 :         if (Test%isDebugMode .and. .not. assertion) then
     232             :         ! LCOV_EXCL_START
     233             :             write(Test%outputUnit,"(*(g0))")
     234             :             write(Test%outputUnit,"(*(g0))") "integral_ref  = ", integral_ref
     235             :             write(Test%outputUnit,"(*(g0))") "integral      = ", integral
     236             :             write(Test%outputUnit,"(*(g0))") "difference    = ", difference
     237             :             write(Test%outputUnit,"(*(g0))") "relativeError = ", relativeError
     238             :             write(Test%outputUnit,"(*(g0))")
     239             :         end if
     240             :         ! LCOV_EXCL_STOP
     241             : 
     242           1 :     end function test_doQuadRombOpen_3
     243             : 
     244             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     245             : 
     246           1 :     function test_doQuadRombOpen_4() result(assertion)
     247             : 
     248           1 :         use Constants_mod, only: RK, IK
     249             :         use Integration_mod
     250             : 
     251             :         implicit none
     252             : 
     253             :         logical                 :: assertion
     254           1 :         real(RK)                :: relativeError, difference
     255           1 :         real(RK)                :: integral
     256             :         real(RK), parameter     :: integral_ref = 1._RK
     257             :         real(RK), parameter     :: tolerance = 1.e-10_RK
     258             :         integer(IK)             :: numFuncEval, ierr
     259             : 
     260             :         call doQuadRombOpen ( getFunc = getTestFuncOpenInterval_1 &
     261             :                             , integrate = midpnt &
     262             :                             , lowerLim = -5._RK &
     263             :                             , upperLim = +5._RK &
     264             :                             , maxRelativeError = 1.e-10_RK &
     265             :                             , nRefinement = 10_IK &
     266             :                             , integral = integral &
     267             :                             , relativeError = relativeError &
     268             :                             , numFuncEval = numFuncEval &
     269             :                             , ierr = ierr &
     270           1 :                             )
     271             : 
     272           1 :         assertion = ierr == 0_IK
     273           1 :         if (Test%isDebugMode .and. .not. assertion) then
     274             :             ! LCOV_EXCL_START
     275             :             if (Test%isDebugMode .and. .not. assertion) then
     276             :                 write(Test%outputUnit,"(*(g0))") "ierr = ", ierr, " /= 0"
     277             :             end if
     278             :             return
     279             :             ! LCOV_EXCL_STOP
     280             :         end if
     281             : 
     282           1 :         difference = abs(integral - integral_ref) / abs(integral_ref)
     283           1 :         assertion = difference < tolerance
     284           1 :         assertion = assertion .and. relativeError <= tolerance
     285             : 
     286           1 :         if (Test%isDebugMode .and. .not. assertion) then
     287             :         ! LCOV_EXCL_START
     288             :             write(Test%outputUnit,"(*(g0))")
     289             :             write(Test%outputUnit,"(*(g0))") "integral_ref  = ", integral_ref
     290             :             write(Test%outputUnit,"(*(g0))") "integral      = ", integral
     291             :             write(Test%outputUnit,"(*(g0))") "difference    = ", difference
     292             :             write(Test%outputUnit,"(*(g0))") "relativeError = ", relativeError
     293             :             write(Test%outputUnit,"(*(g0))")
     294             :         end if
     295             :         ! LCOV_EXCL_STOP
     296             : 
     297           1 :     end function test_doQuadRombOpen_4
     298             : 
     299             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     300             : 
     301           1 :     function test_doQuadRombClosed_1() result(assertion)
     302             : 
     303           1 :         use Constants_mod, only: RK, IK
     304             :         use Integration_mod
     305             : 
     306             :         implicit none
     307             : 
     308             :         logical                 :: assertion
     309           1 :         real(RK)                :: relativeError, difference
     310           1 :         real(RK)                :: integral
     311             :         real(RK), parameter     :: integral_ref = 1._RK
     312             :         real(RK), parameter     :: tolerance = 1.e-10_RK
     313             :         integer(IK)             :: numFuncEval, ierr
     314             : 
     315             :         call doQuadRombClosed   ( getFunc = getTestFuncOpenInterval_1 &
     316             :                                 , lowerLim = -5._RK &
     317             :                                 , upperLim = +5._RK &
     318             :                                 , maxRelativeError = 0.1*tolerance &
     319             :                                 , nRefinement = 10_IK &
     320             :                                 , integral = integral &
     321             :                                 , relativeError = relativeError &
     322             :                                 , numFuncEval = numFuncEval &
     323             :                                 , ierr = ierr &
     324           1 :                                 )
     325           1 :         assertion = ierr == 0_IK
     326           1 :         if (Test%isDebugMode .and. .not. assertion) then
     327             :         ! LCOV_EXCL_START
     328             :             if (Test%isDebugMode .and. .not. assertion) then
     329             :                 write(Test%outputUnit,"(*(g0))") "ierr = ", ierr, " /= 0"
     330             :             end if
     331             :             return
     332             :         ! LCOV_EXCL_STOP
     333             :         end if
     334             : 
     335           1 :         difference = abs(integral - integral_ref) / abs(integral_ref)
     336           1 :         assertion = difference < tolerance
     337           1 :         assertion = assertion .and. relativeError <= tolerance
     338             : 
     339           1 :         if (Test%isDebugMode .and. .not. assertion) then
     340             :         ! LCOV_EXCL_START
     341             :             write(Test%outputUnit,"(*(g0))")
     342             :             write(Test%outputUnit,"(*(g0))") "integral_ref  = ", integral_ref
     343             :             write(Test%outputUnit,"(*(g0))") "integral      = ", integral
     344             :             write(Test%outputUnit,"(*(g0))") "difference    = ", difference
     345             :             write(Test%outputUnit,"(*(g0))") "relativeError = ", relativeError
     346             :             write(Test%outputUnit,"(*(g0))")
     347             :         end if
     348             :         ! LCOV_EXCL_STOP
     349             : 
     350           1 :     end function test_doQuadRombClosed_1
     351             : 
     352             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     353             : 
     354             :     ! The Gaussian PDF with sigma = 1/sqrt(2)
     355       79245 :     function getTestFuncOpenInterval_1(x) result(funcVal)
     356           1 :         use Constants_mod, only: RK, INVSQRTPI, NEGLOGINF_RK
     357             :         implicit none
     358             :         real(RK), intent(in)    :: x
     359             :         real(RK)                :: funcVal
     360             :         real(RK), parameter     :: LOGINVSQRTPI = log(INVSQRTPI)
     361       79245 :         funcVal = LOGINVSQRTPI - x**2
     362       79245 :         if (funcVal<NEGLOGINF_RK) then ! This takes care of the GNU Fortran 9.1 test crash in debug mode.
     363        1480 :             funcVal = 0._RK
     364             :         else
     365       77765 :             funcVal = exp(funcVal)
     366             :         end if
     367       79245 :     end function getTestFuncOpenInterval_1
     368             : 
     369             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     370             : 
     371             :     ! requires `midsql`.
     372             :     ! The MATLAB test function: https://www.mathworks.com/help/matlab/ref/integral.html
     373             :     ! LCOV_EXCL_START
     374             :     function getTestFuncOpenIntervalMATLAB(x) result(funcVal)
     375             :         use Constants_mod, only: RK
     376             :         implicit none
     377             :         real(RK), intent(in)    :: x
     378             :         real(RK)                :: funcVal
     379             :         funcVal = exp(-x**2) * log(x)**2
     380             :     end function getTestFuncOpenIntervalMATLAB
     381             :     ! LCOV_EXCL_STOP
     382             : 
     383             : !%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
     384             : 
     385             : end module Test_Integration_mod ! LCOV_EXCL_LINE

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