! Copyright (c) 2015 Nikhil Anand ! Copyright (c) 2015,2020 Harald Klimach ! Copyright (c) 2017 Daniel PetrĂ³ ! Copyright (c) 2017 Peter Vitt ! Copyright (c) 2019 Neda Ebrahimi Pour ! ! Parts of this file were written by Nikhil Anand, Harald Klimach, Daniel PetrĂ³, ! Peter Vitt and Neda Ebrahimi Pour for University of Siegen. ! ! Permission to use, copy, modify, and distribute this software for any ! purpose with or without fee is hereby granted, provided that the above ! copyright notice and this permission notice appear in all copies. ! ! THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES ! WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF ! MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ! ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES ! WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ! ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF ! OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. ! **************************************************************************** ! !> The FXT method offers a transformation from Legendre modes to nodes by a !! fast multipole approach implemented in the !! [FXTPACK](http://sudalab.is.s.u-tokyo.ac.jp/~reiji/fxtpack.html) library by !! Reiji Suda: !! R. Suda, "Fast Spherical Harmonic Transform Algorithm based on !! Generalized Fast Multiple Method", RIMS Kokyuroku vol 1606, !! pp. 18-29, Jun. 2008, RIMS, Kyoto University. !! !! Besides the oversampling `factor` that can be used to increase the number !! points in the nodal representation to achieve an de-aliasing, there is only !! one other option to this method: !! The `prec` parameter configures the precision up to which the FXTPACK !! should compute the transformation. !! It defaults to the square root of the epsilon for the real kind. With !! double precision this would something around 1.4e-8. !! !! This transformation utilizes the Gauss Legendre integration points in the !! nodal representation. !! !! Thus, the configuration for a FXT projection takes the following form: !! !!```lua !! projection = { !! kind = 'fxt', !! prec = 1.e-10 !! } !!``` !! module ply_fxt_header_module use env_module, only: rk use aotus_module, only: flu_State, aot_get_val use aot_out_module, only: aot_out_type, aot_out_val use tem_aux_module, only: tem_abort use tem_logging_module, only: logUnit use tem_float_module use ply_nodes_header_module, only: ply_nodes_header_type, & & operator(==), & & operator(/=), & & operator(<=), & & operator(>=), & & operator(<), & & operator(>) implicit none private !> Fxt projection header type, consisting of the node header which give !! information about the type and number of points for the projection type ply_fxt_header_type type(ply_nodes_header_type) :: nodes_header real(kind=rk) :: factor = 1.0 real(kind=rk) :: prec = epsilon(1.0) end type ply_fxt_header_type interface assignment(=) module procedure Copy_fxt_header end interface interface operator(==) module procedure isEqual end interface interface operator(/=) module procedure isUnequal end interface interface operator(<) module procedure isSmaller end interface interface operator(<=) module procedure isSmallerOrEqual end interface interface operator(>) module procedure isGreater end interface interface operator(>=) module procedure isGreaterOrEqual end interface public :: operator(==), operator(/=), operator(<), operator(<=) public :: operator(>), operator(>=) public :: assignment(=) public :: ply_fxt_header_type public :: ply_fxt_header_load, ply_fxt_header_display public :: ply_fxt_header_out contains ! ------------------------------------------------------------------------ ! pure subroutine Copy_fxt_header( left, right ) ! -------------------------------------------------------------------- ! !> fpt to copy to type(ply_fxt_header_type), intent(out) :: left !> fpt to copy from type(ply_fxt_header_type), intent(in) :: right ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! left%factor = right%factor left%prec = right%prec left%nodes_header = right%nodes_header end subroutine Copy_fxt_header ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> Load settings to describe a projection method from a Lua table. subroutine ply_fxt_header_load( me, conf, thandle ) ! -------------------------------------------------------------------- ! type(ply_fxt_header_type), intent(out) :: me type(flu_State) :: conf integer, intent(in) :: thandle ! -------------------------------------------------------------------- ! integer :: iError ! -------------------------------------------------------------------- ! ! for fxt gauss-legendre points are used me%nodes_header%nodes_kind = 'gauss-legendre' ! fill up fxt header call aot_get_val( L = conf, & & thandle = thandle, & & key = 'factor', & & val = me%factor, & & default = 1.0_rk, & & ErrCode = iError ) if (me%factor <= 0) then write(logUnit(1),*) 'ERROR in loading projection: factor for' & & // ' projection has to be larger than 0!' write(logUnit(1),*) 'But it is set to ', me%factor call tem_abort() end if call aot_get_val( L = conf, & & thandle = thandle, & & key = 'prec', & & val = me%prec, & & default = sqrt(epsilon(1.0_rk)), & & ErrCode = iError ) !>\todo Check, wether Lobatto Points could be used with FXTPACK. me%nodes_header%lobattoPoints = .false. !!call aot_get_val(L = conf, & !! & thandle = thandle, & !! & key = 'lobattoPoints', & !! & val = me%nodes_header%lobattoPoints, & !! & ErrCode = iError, & !! & default = .false. ) end subroutine ply_fxt_header_load ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> Write FXT settings into a Lua table. subroutine ply_fxt_header_out( me, conf ) ! -------------------------------------------------------------------- ! type(ply_fxt_header_type), intent(in) :: me type(aot_out_type) :: conf ! -------------------------------------------------------------------- ! call aot_out_val( put_conf = conf, & & vname = 'factor', & & val = me%factor ) call aot_out_val( put_conf = conf, & & vname = 'lobattoPoints', & & val = me%nodes_header%lobattoPoints ) end subroutine ply_fxt_header_out ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! subroutine ply_fxt_header_display( me ) ! -------------------------------------------------------------------- ! type(ply_fxt_header_type), intent(in) :: me ! -------------------------------------------------------------------- ! write(logUnit(1),*) ' * Kind of projection method = fxt' write(logUnit(1),*) ' * Precision for the fast multipole: ', me%prec write(logUnit(1),*) ' * Factor to use in projection = ', me%factor write(logUnit(1),*) ' * using LobattoPoints = ', & & me%nodes_header%lobattoPoints if (me%factor < 2.0_rk) then write(logUnit(1),*) '' write(logUnit(1),*) & & '+-----------------------------------------------------+' write(logUnit(1),*) & & '| WARNING, the oversampling factor is smaller than 2! |' write(logUnit(1),*) & & '| this might lead to bad projections! |' write(logUnit(1),*) & & '+-----------------------------------------------------+' end if end subroutine ply_fxt_header_display ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides the test for equality of two projections. !! !! Two fxt header are considered to be equal, if their node_header, !! and the factor are equal. pure function isEqual( left, right ) result( equality ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is equal?? logical :: equality ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! equality = ( left%nodes_header == right%nodes_header ) & & .and. ( left%factor .feq. right%factor ) end function isEqual ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides the test for unequality of two projections. !! !! Two fxt header are considered to be unequal, if their node_header, !! or the factor are not equal. pure function isUnequal( left, right ) result( unequality ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is unequal?? logical :: unequality ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! unequality = ( left%nodes_header /= right%nodes_header ) & & .or. ( left%factor .fne. right%factor) end function isUnequal ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides a < comparison of two projections. !! !! Sorting of fxt header is given by node_header and by the factor. pure function isSmaller( left, right ) result( small ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is smaller?? logical :: small ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! small = .false. if (left%nodes_header < right%nodes_header) then small = .true. else if (left%nodes_header == right%nodes_header) then small = (left%factor < right%factor) end if end if end function isSmaller ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides a <= comparison of two projections. !! !! Sorting of fxt header is given by node_header, fxt_blocksize and !! last by factor. pure function isSmallerOrEqual( left, right ) result( small ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is smaller?? logical :: small ! -------------------------------------------------------------------- ! small = .false. if (left%nodes_header < right%nodes_header) then small = .true. else if (left%nodes_header == right%nodes_header) then small = (left%factor <= right%factor) end if end if end function isSmallerOrEqual ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides a > comparison of two projections. !! !! Sorting of fxt header is given by node_header, fxt_blocksize and !! last by factor. pure function isGreater( left, right ) result( great ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is greater?? logical :: great ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! great = .false. if (left%nodes_header > right%nodes_header) then great = .true. else if (left%nodes_header == right%nodes_header) then great = (left%factor > right%factor) end if end if end function isGreater ! ------------------------------------------------------------------------ ! ! ------------------------------------------------------------------------ ! !> This function provides a >= comparison of two projections. !! !! Sorting of fxt header is given by node_header, fxt_blocksize and !! last by factor. pure function isGreaterOrEqual( left, right ) result( great ) ! -------------------------------------------------------------------- ! !> projection to compare type(ply_fxt_header_type), intent(in) :: left !> projection to compare against type(ply_fxt_header_type), intent(in) :: right !> is greater?? logical :: great ! -------------------------------------------------------------------- ! ! -------------------------------------------------------------------- ! great = .false. if (left%nodes_header > right%nodes_header) then great = .true. else if (left%nodes_header == right%nodes_header) then great = (left%factor >= right%factor) end if end if end function isGreaterOrEqual ! ------------------------------------------------------------------------ ! end module ply_fxt_header_module