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mo_integrate.f90
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mo_integrate.f90
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!> \file mo_integrate.f90
!> \brief Provides integration routines
!> \details This module provides routine for numerical integration such a Newton-Cotes formulas, etc.
!> \authors Matthias Cuntz
!> \date Mar 2013
MODULE mo_integrate
! Provide numerical integration.
! Written Matthias Cuntz, Mar 2013
! License
! -------
! This file is part of the JAMS Fortran package, distributed under the MIT License.
!
! Copyright (c) 2013 Matthias Cuntz - mc (at) macu (dot) de
!
! Permission is hereby granted, free of charge, to any person obtaining a copy
! of this software and associated documentation files (the "Software"), to deal
! in the Software without restriction, including without limitation the rights
! to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
! copies of the Software, and to permit persons to whom the Software is
! furnished to do so, subject to the following conditions:
!
! The above copyright notice and this permission notice shall be included in all
! copies or substantial portions of the Software.
!
! THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
! IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
! FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
! AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
! LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
! OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
! SOFTWARE.
USE mo_kind, ONLY: i4, sp, dp
IMPLICIT NONE
PUBLIC :: int_regular ! Integrate regularily spaced data
! ------------------------------------------------------------------
! NAME
! int_regular
! PURPOSE
!> \brief Integrate regularily spaced data.
!> \details Integrates regularily spaced data with a 5-point Newton-Cotes formula:
!> \f[ \int y = \frac{2}{45} dx \sum_{i=5,n-4,4} 7 y_{i-4} + 32 y_{i-3} + 12 y_{i-2} + 32 y_{i-1} + 7 y_{i} \f]
!> dx=1 if not given.
! INTENT(IN)
!> \param[in] "real(sp/dp) :: dat(:)" \f$ y_i \f$ 1D-array with y-values.
! INTENT(INOUT)
! None
! INTENT(OUT)
! None
! INTENT(IN), OPTIONAL
!> \param[in] "real(sp/dp) :: dx" x-spacing (default=1.)
! INTENT(INOUT), OPTIONAL
! None
! INTENT(OUT), OPTIONAL
! None
! RETURN
!> \return real(sp/dp) :: integral — \f$ \int y \f$ integral of y values
! RESTRICTIONS
! None
! EXAMPLE
! vec = (/ 1., 2, 3., 4., 5., 6., 7., 8., 9. /)
! m = int_regular(vec)
! -> see also example in test directory
! LITERATURE
! None
! HISTORY
!> \author Matthias Cuntz
!> \date Mar 2013
INTERFACE int_regular
MODULE PROCEDURE int_regular_sp, int_regular_dp
END INTERFACE int_regular
! ------------------------------------------------------------------
PRIVATE
! ------------------------------------------------------------------
CONTAINS
! ------------------------------------------------------------------
! integrates tabulated function with equal distant points usign 5-point Newton-Cotes formula
FUNCTION int_regular_dp(dat, dx)
IMPLICIT NONE
REAL(dp), DIMENSION(:), INTENT(IN) :: dat
REAL(dp), OPTIONAL, INTENT(IN) :: dx
REAL(dp) :: int_regular_dp
INTEGER(i4) :: n, n0
REAL(dp) :: ddx
if (size(dat,1) < 5) stop 'Error int_regular_dp: size(dat) < 5'
if (present(dx)) then
ddx = dx*2.0_dp/45.0_dp
else
ddx = 2.0_dp/45.0_dp
endif
n0 = 5
n = size(dat,1)
if (ddx .gt. 0.0_dp) then
int_regular_dp = sum( &
(7.0_dp*(dat(n0-4:n-4:4) + dat(n0:n:4)) + &
32.0_dp*(dat(n0-3:n-3:4) + dat(n0-1:n-1:4)) + &
12.0_dp*dat(n0-2:n-2:4)) )
! to avoid underflow issues
if ( ddx .lt. 1.0_dp ) then
if ( int_regular_dp .gt. tiny(1.0_dp)/ddx ) then
int_regular_dp = ddx * int_regular_dp
else
int_regular_dp = tiny(1.0_dp)
end if
else
int_regular_dp = ddx * int_regular_dp
end if
else
int_regular_dp = 0.0_dp
end if
END FUNCTION int_regular_dp
FUNCTION int_regular_sp(dat, dx)
IMPLICIT NONE
REAL(sp), DIMENSION(:), INTENT(IN) :: dat
REAL(sp), OPTIONAL, INTENT(IN) :: dx
REAL(sp) :: int_regular_sp
INTEGER(i4) :: n, n0
REAL(sp) :: ddx
if (size(dat,1) < 5) stop 'Error int_regular_sp: size(dat) < 5'
if (present(dx)) then
ddx = dx*2.0_sp/45.0_sp
else
ddx = 2.0_sp/45.0_sp
endif
n0 = 5
n = size(dat,1)
if (ddx .gt. 0.0_sp) then
int_regular_sp = sum( &
(7.0_sp*(dat(n0-4:n-4:4) + dat(n0:n:4)) + &
32.0_sp*(dat(n0-3:n-3:4) + dat(n0-1:n-1:4)) + &
12.0_sp*dat(n0-2:n-2:4)) )
! to avoid underflow issues
if ( ddx .lt. 1.0_sp ) then
if ( int_regular_sp .gt. tiny(1.0_sp)/ddx ) then
int_regular_sp = ddx * int_regular_sp
else
int_regular_sp = tiny(1.0_sp)
end if
else
int_regular_sp = ddx * int_regular_sp
end if
else
int_regular_sp = 0.0_sp
end if
END FUNCTION int_regular_sp
END MODULE mo_integrate