! Copyright (c) 2018 Kannan Masilamani <kannan.masilamani@uni-siegen.de> ! Copyright (c) 2018-2019 Harald Klimach <harald.klimach@uni-siegen.de> ! Copyright (c) 2019 Peter Vitt <peter.vitt2@uni-siegen.de> ! ! Redistribution and use in source and binary forms, with or without ! modification, are permitted provided that the following conditions are met: ! ! 1. Redistributions of source code must retain the above copyright notice, this ! list of conditions and the following disclaimer. ! ! 2. Redistributions in binary form must reproduce the above copyright notice, ! this list of conditions and the following disclaimer in the documentation ! and/or other materials provided with the distribution. ! ! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" ! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE ! DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE ! FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ! OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ! ****************************************************************************** ! !> Contains data_types and function for matrix operations !! ! Copyright (c) 2012-2013 Simon Zimny <s.zimny@grs-sim.de> ! Copyright (c) 2012 Manuel Hasert <m.hasert@grs-sim.de> ! Copyright (c) 2012-2016 Harald Klimach <harald.klimach@uni-siegen.de> ! Copyright (c) 2012, 2015-2016 Kannan Masilamani <kannan.masilamani@uni-siegen.de> ! Copyright (c) 2013 Daniel Harlacher <d.harlacher@grs-sim.de> ! Copyright (c) 2014 Kartik Jain <kartik.jain@uni-siegen.de> ! Copyright (c) 2014 Verena Krupp <verena.krupp@uni-siegen.de> ! Copyright (c) 2015-2017 Jiaxing Qi <jiaxing.qi@uni-siegen.de> ! Copyright (c) 2015-2016 Peter Vitt <peter.vitt2@uni-siegen.de> ! Copyright (c) 2016 Daniel Fleischer <daniel.fleischer@student.uni-siegen.de> ! Copyright (c) 2016 Tobias Schneider <tobias1.schneider@student.uni-siegen.de> ! Copyright (c) 2017 Daniel Petró <daniel.petro@student.uni-siegen.de> ! ! Parts of this file were written by Harald Klimach, Simon Zimny and Manuel ! Hasert for German Research School for Simulation Sciences GmbH. ! ! Parts of this file were written by Harald Klimach, Kannan Masilamani, ! Daniel Harlacher, Kartik Jain, Verena Krupp, Jiaxing Qi, Peter Vitt, ! Daniel Fleischer, Tobias Girresser and Daniel Petró for University Siegen. ! ! Redistribution and use in source and binary forms, with or without ! modification, are permitted provided that the following conditions are met: ! ! 1. Redistributions of source code must retain the above copyright notice, this ! list of conditions and the following disclaimer. ! ! 2. Redistributions in binary form must reproduce the above copyright notice, ! this list of conditions and the following disclaimer in the documentation ! and/or other materials provided with the distribution. ! ! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" ! AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ! IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE ! DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE ! FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ! DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ! SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ! CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ! OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ! OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ! This file contains the source code for growing and dynamic arrays. ! This is used for arrays of primitives (int, long_int, real, ...) as well as ! for arrays of derived datatypes (tem_variable_type,...). ! ! To use these macros include the following to your source file. ! ! Smart growing array (GA) for ?tstring? ! Growing Arrays: ! ! declaration ! ! ! implementation ! ! ----------------------------------------------------------------- ! 2d Array, which can grow in second dimension only (GA2d) ! tname ... indicates type of dynamic array (long, int, real, ...) ! !------------------------------------------------------------------------------ ! ! dynamic Arrays: ! ! declaration ! ! ! implementation ! !! module tem_matrix_module use env_module, only: rk, minLength, zeroLength use tem_aux_module, only: tem_abort use tem_logging_module, only: logUnit use tem_debug_module, only: dbgUnit use tem_dyn_array_module, only: dyn_intArray_type, init, append, truncate, & & destroy use tem_grow_array_module, only: grw_logicalArray_type, init, append, & & truncate, destroy use tem_param_module, only: c_x, c_y, c_z use tem_float_module, only: operator(.feq.) implicit none private public :: tem_matrix_type public :: invert_matrix public :: tem_intpMatrixLSF_type public :: tem_matrix_dump public :: init, append, truncate, destroy, empty, placeAt integer, parameter :: maxIntp_order = 2 ! Number of coefffs for quadratic interpolation ! (/ linear, quadratic /) !> For 1D stencil, !! 2 unknown coeffs: p(x)=a0+a1 x for linear 1st order interpolation !! 3 unknown coeffs: p(x)=a0+a1 x+a2 x^2 for quadratic 2nd order interpolation integer, dimension(maxIntp_order), parameter :: nCoeffs_1D = (/ 2, 3 /) !> For 2D stencil, !! 3 unknown coeffs for linear 1st order interpolation: !! p(x,y)=a0+a1 x+a2 y !! 6 unknown coeffs for quadratic 2nd order interpolation: !! p(x,y)=a0+a1 x+a2 y+a3 x^2+a4 y^2+ a5 xy integer, dimension(maxIntp_order), parameter :: nCoeffs_2D = (/ 3, 6 /) !> For 3D stencil, !! 4 unknown coeffs for linear 1st order interpolation: !! p(x,y,z)=a0+a1 x+a2 y+a3 z !! 10 unknown coeffs for quadratic 2nd order interpolation: !! p(x,y,z)=a0+a1 x+a2 y+a3 z+a4 x^2+a5 y^2+ a6 z^2+ a7 xy + a8 yz + a9 zx integer, dimension(maxIntp_order), parameter :: nCoeffs_3D = (/ 4, 10 /) !> This derived type encapsulates the definition of the matrix type tem_matrix_type !> inverted matrix to solve linear system of equation real(kind=rk), allocatable :: A(:,:) !> how many entries are in the 2d matrix? integer :: nEntries(2) end type tem_matrix_type !> growing array type for type(tem_matrix_type) type grw_matrixarray_type integer :: nvals = 0 integer :: containersize = 0 type(tem_matrix_type), allocatable :: val(:) end type !> initialize the dynamic array interface init module procedure init_ga_matrix end interface !> truncate the array, meaning !! cut off the trailing empty entries interface truncate module procedure truncate_ga_matrix end interface !> empty the entries without changing arrays interface empty module procedure empty_ga_matrix end interface !> destroy the dynamic array interface destroy module procedure destroy_ga_matrix end interface !> insert an element at a given position interface placeat module procedure placeat_ga_matrix module procedure placeat_ga_matrix_vec end interface !> append a value to the dynamic array !! and return its position. interface append module procedure append_ga_matrix module procedure append_ga_matrix_vec end interface !> increase the size of the container !! for the array. interface expand module procedure expand_ga_matrix end interface !> This derived type encapsulates the definition of least square fit matrix !! for interpolation method which is required for every combination of !! available nSourceFromCoarser type tem_intpMatrixLSF_type type(grw_matrixArray_type) :: matArray !> Unique hash ID to identify different combination of available !! nSourceFromCoarser type(dyn_intArray_type) :: ID !> nCoeffs required for least square fit. !! Depends on nDims and order of interpolation integer:: nCoeffs !> For every matrix in matArray, store if its invertible or not !! to avoid rebuilding singular matrix type(grw_logicalArray_type) :: isInvertible end type tem_intpMatrixLSF_type interface init module procedure init_intpMatrixLSF end interface init interface append module procedure append_intpMatrixLSF end interface append interface truncate module procedure truncate_intpMatrixLSF end interface truncate interface destroy module procedure destroy_intpMatrixLSF end interface destroy interface assignment(=) module procedure copy_matrix end interface contains subroutine init_ga_matrix(me, length) type(grw_matrixarray_type), intent(out) :: me !< dynamic array to init integer, intent(in), optional :: length !< initial length of the container if (present(length)) then me%containersize = length else me%containersize = zerolength end if ! deallocate ... if( allocated( me%val )) & deallocate(me%val) ! ... and reallocate allocate(me%val(me%containersize)) me%nvals = 0 end subroutine init_ga_matrix subroutine destroy_ga_matrix(me) type(grw_matrixarray_type), intent(inout) :: me !< dynamic array to destroy me%containersize = 0 me%nvals = 0 if( allocated( me%val ) ) deallocate(me%val) end subroutine destroy_ga_matrix subroutine truncate_ga_matrix(me) !------------------------------------------------------------------------ type(grw_matrixarray_type) :: me !< array to truncate !------------------------------------------------------------------------ type(tem_matrix_type), allocatable :: tarray(:) !------------------------------------------------------------------------ integer :: ii !------------------------------------------------------------------------ ! nothing to do if container size is not larger than the number of values ! in the array. if (me%containersize > me%nvals) then allocate(tarray(me%nvals)) do ii = 1, me%nvals tarray(ii) = me%val(ii) end do call move_alloc(tarray, me%val) me%containersize = me%nvals end if end subroutine truncate_ga_matrix subroutine empty_ga_matrix(me) !------------------------------------------------------------------------ type(grw_matrixarray_type) :: me !< array to sorttruncate !------------------------------------------------------------------------ me%nvals = 0 end subroutine empty_ga_matrix !> adds the value to a given position inside the growing array. !! !! if the requested position is outside the current array bounds, the array !! will be resized accordingly. if it is inside the current array bounds, the !! element at the requested position will be replaced. subroutine placeat_ga_matrix(me, val, pos, length) type(grw_matrixarray_type) :: me !< array to place the value into type(tem_matrix_type), intent(in) :: val !< value to place at the given position integer, intent(in) :: pos !< predefined position !> optional length to expand the array integer, intent(in), optional :: length ! value to append is larger than all existing ones, ! just put it to the end of the list, this captures ! also the case of empty lists. ! in this case foundpos = me%nvals + 1 holds. if (pos > me%containersize) then ! expand the array, if its boundary is reached call expand(me = me, pos = pos, length = length) end if me%nvals = max( pos, me%nvals ) me%val(pos) = val end subroutine placeat_ga_matrix !> adds the values starting from a given position inside the growing array. !! !! if the requested position is outside the current array bounds, the array !! will be resized accordingly. if it is inside the current array bounds, the !! elements starting from the requested position will be replaced up to !! the element at position `pos + size(val) - 1`. subroutine placeat_ga_matrix_vec(me, val, pos, length) type(grw_matrixarray_type) :: me !< array to append the value to type(tem_matrix_type), intent(in) :: val(:) !< values to append integer, intent(in) :: pos !< predefined position !> optional length to expand the array integer, intent(in), optional :: length integer :: ub, ii if (me%nvals == huge(me%nvals)) then write(*,*) "reached end of integer range for growing array!" write(*,*) "aborting!!" stop end if ub = pos + size(val) - 1 if (ub > me%containersize) then ! expand the array, if its boundary is reached call expand(me = me, pos = ub, length = length) end if me%nvals = max( ub, me%nvals ) do ii = pos, ub me%val(ii) = val(1+ii-pos) end do end subroutine placeat_ga_matrix_vec subroutine append_ga_matrix(me, val, length) type(grw_matrixarray_type) :: me !< array to append the value to type(tem_matrix_type), intent(in) :: val !< value to append !> optional length to expand the array integer, intent(in), optional :: length ! value to append is larger than all existing ones, ! just put it to the end of the list, this captures ! also the case of empty lists. ! in this case foundpos = me%nvals + 1 holds. if (me%nvals+1 > me%containersize) then ! expand the array, if its boundary is reached call expand(me = me, length = length) end if me%nvals = me%nvals+1 me%val(me%nvals) = val end subroutine append_ga_matrix subroutine append_ga_matrix_vec(me, val, length) type(grw_matrixarray_type) :: me !< array to append the value to type(tem_matrix_type), intent(in) :: val(:) !< values to append !> optional length to expand the array integer, intent(in), optional :: length integer :: lb, ub, ii if (me%nvals == huge(me%nvals)) then write(*,*) "reached end of integer range for growing array!" write(*,*) "aborting!!" stop end if lb = me%nvals + 1 ub = lb + size(val) - 1 if (ub > me%containersize) then ! expand the array, if its boundary is reached call expand(me = me, pos = ub, length = length) end if me%nvals = max( ub, me%nvals ) do ii = lb, ub me%val(ii) = val(1+ii-lb) end do end subroutine append_ga_matrix_vec subroutine expand_ga_matrix(me, pos, length) type(grw_matrixarray_type) :: me !< array to resize integer, intent(in), optional :: pos !< optional predefined position !> optional length to expand the array integer, intent(in), optional :: length type(tem_matrix_type), allocatable :: swpval(:) integer :: explen, ii explen = 0 ! increase the container by the requested length of double it if( present(length) ) then explen = max( length, minlength ) else ! set the global minimum length, if doubling would be smaller than that explen = max(me%containersize, minlength) end if ! if a position is given, increase the container to at least the size to ! fit the position. if( present(pos) ) explen = max(explen, pos-me%containersize) ! if the current size plus explen exceeds the max container size, ! reduce the size to the max container size. if( (huge(me%containersize) - explen) <= me%containersize) then ! set max container size me%containersize = huge(me%containersize) else ! set the new container size me%containersize = me%containersize + explen end if if ( me%nvals > 0 ) then allocate(swpval(me%containersize)) do ii = 1, me%nvals swpval(ii) = me%val(ii) end do call move_alloc( swpval, me%val ) else ! me%nvals == 0 if ( allocated(me%val) ) deallocate( me%val ) allocate( me%val(me%containersize) ) end if end subroutine expand_ga_matrix ! **************************************************************************** ! !> This routine initialize interpolation matrix for least square fit subroutine init_intpMatrixLSF(me, length, nDims, order) ! -------------------------------------------------------------------------- type(tem_intpMatrixLSF_type), intent(out) :: me integer, intent(in) :: length integer, intent(in) :: nDims integer, intent(in) :: order ! -------------------------------------------------------------------------- call init(me = me%matArray, length = length) call init(me = me%ID, length = length) call init(me = me%isInvertible, length = length) ! Set coeffs required for each order if (order > 0 .and. order <= maxIntp_order) then select case(nDims) case(1) me%nCoeffs = nCoeffs_1D(order) case(2) me%nCoeffs = nCoeffs_2D(order) case(3) me%nCoeffs = nCoeffs_3D(order) end select else call tem_abort('Unsupported interpolation order') end if end subroutine init_intpMatrixLSF ! **************************************************************************** ! ! ************************************************************************** ! !> This routine builds up the matrix for least square fit used in !! linear and quadratic interpolation. !! !! Compute interpolation matrix for least square fit using stencil !! direction of available sources !! The parent of target childs coord is 0,0,0 so we could !! just use of stencil%cxDir to build up this matrix entries !! Every row in matrix is evaluated with coord of source element subroutine append_intpMatrixLSF(me, order, QQ, nDims, nSources, cxDirRK, & & neighDir, pos, success) ! -------------------------------------------------------------------------- !> intpMatrix for LSF fill type(tem_intpMatrixLSF_type), intent(inout) :: me !> interpolation order calculated for current element depending on nSources !! if quadratic LSF matrix is singular fall back to linear integer, intent(inout) :: order !> Number of stencil directions integer, intent(in) :: QQ !> Number of dimensions integer, intent(in) :: nDims !> Number of sources from coarser found integer, intent(in) :: nSources !> Stencil directions real(kind=rk), intent(in) :: cxDirRK(3,QQ) !> direction in which sources are found integer, intent(in) :: neighDir(nSources) !> Pointer to position of interpolation matrix in growing array of matrix integer, intent(out) :: pos !> success if false if matrix is singular reduce interpolation order logical, intent(out) :: success ! -------------------------------------------------------------------------- integer :: hashID type(tem_matrix_type) :: matLSF_tmp logical :: wasAdded integer :: iNeigh, iSrc ! -------------------------------------------------------------------------- write(dbgUnit(4),"(A,I0)") 'Inside append least square fit matrix for intp ' & & //'order: ', order ! hashID to identify unique combination of available nSources hashID = 0 do iSrc = 1, nSources iNeigh = neighDir(iSrc) hashID = ibset(hashID, iNeigh) end do write(dbgUnit(4),"(A,I0)") ' hashID: ', hashID call append( me = me%ID, & & val = hashID, & & pos = pos, & & wasAdded = wasAdded ) write(dbgUnit(4),"(A,L5)") ' wasAdded: ', wasAdded write(dbgUnit(4),"(A,I5)") ' pos: ', pos if (wasAdded) then select case(order) case(1) ! linear call build_matrixLSF_linearIntp( me = matLSF_tmp, & & QQ = QQ, & & nDims = nDims, & & nSources = nSources, & & cxDirRK = cxDirRK, & & neighDir = neighDir, & & nCoeffs = me%nCoeffs, & & success = success ) case(2) ! quadratic call build_matrixLSF_quadIntp( me = matLSF_tmp, & & QQ = QQ, & & nDims = nDims, & & nSources = nSources, & & cxDirRK = cxDirRK, & & neighDir = neighDir, & & nCoeffs = me%nCoeffs, & & success = success ) case default write(logUnit(1),*) 'Unsupported interpolation order to build matrix ' & & //'for LSF: ', order end select call append( me = me%isInvertible, val = success ) call append( me = me%matArray, val = matLSF_tmp ) else ! hashID already exist then return success depends on matrix isInvertible if (me%isInvertible%val(pos)) then success = .true. else success = .false. end if end if write(dbgUnit(4),"(A,L5)") ' success : ', success end subroutine append_intpMatrixLSF ! ************************************************************************** ! ! ************************************************************************** ! !> This routine builds up the matrix for least square fit used in !! quadratic interpolation. !! We extract momentum information completely on the view of the source !! coordinate system !! Set the right hand side of the equation system !! Solve the problem, where b = rhs, x = coefficients !! A*x = b !! overdetermined, solve the least Square fit problem !! (A^T)A*x = (A^T)b !! x = ((A^T)A)^-1*(A^T)b !! Solve linear system of equation with inverted matrix. !! Size of matrix: (nCoeffs, QQ) !! matrix_LSF = ((A^T)A)^-1*(A^T) subroutine build_matrixLSF_quadIntp(me, QQ, nDims, nSources, cxDirRK, & & neighDir, nCoeffs, success) ! -------------------------------------------------------------------------- !> Matrix to fill type(tem_matrix_type), intent(out) :: me !> Number of stencil directions integer, intent(in) :: QQ !> Number of dimensions integer, intent(in) :: nDims !> Number of sources from coarser found integer, intent(in) :: nSources !> Stencil directions real(kind=rk), intent(in) :: cxDirRK(3,QQ) !> direction in which sources are found integer, intent(in) :: neighDir(nSources) !> nUnknown coeffs integer, intent(in) :: nCoeffs !> success if false if matrix is singular reduce interpolation order logical, intent(out) :: success ! -------------------------------------------------------------------------- integer :: iDir, iSrc !> Each row represents a polynomial evaluated at coord of elements in ! stencil directions type(tem_matrix_type) :: tmp_matrix real(kind=rk) :: inv_AtA(nCoeffs,nCoeffs), AtA(nCoeffs,nCoeffs) integer :: errCode ! -------------------------------------------------------------------------- write(dbgUnit(4),"(A)") 'Inside build least square fit matrix for quadratic' ! me%A = ((A^T)A)^-1*(A^T) ! inv_AtA = ((A^T)A)^-1 call alloc_matrix(tmp_matrix, nSources, nCoeffs) select case(nDims) case (1) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyQuadratic_1D( cxDirRK(:,iDir) ) end do case (2) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyQuadratic_2D( cxDirRK(:,iDir) ) end do case (3) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyQuadratic_3D( cxDirRK(:,iDir) ) end do case default write(logUnit(1),*) 'Unknown nDims for quadratic interpolation' call tem_abort() end select write(dbgUnit(4),"(A)") ' tmp matrix:' call tem_matrix_dump(tmp_matrix, dbgUnit(4)) flush(dbgUnit(4)) AtA = matmul( transpose(tmp_matrix%A), tmp_matrix%A) inv_AtA = invert_matrix(AtA, errCode) if (errCode == 0) then ! matrix_LSF size is transpose of tmp_matrix call alloc_matrix(me, nCoeffs, nSources) me%A = matmul( inv_AtA, transpose(tmp_matrix%A) ) success = .true. else ! singular matrix, reduce interpolation order call alloc_matrix(me, 1, 1) success = .false. return end if write(dbgUnit(4),"(A)") ' matrix LSF:' call tem_matrix_dump(me, dbgUnit(4)) flush(dbgUnit(4)) !write(*,*) 'Matrix_LSF ' !do iDir = 1, nCoeffs ! write(*,*) 'iDir ', iDir, me%A(iDir, :) !end do end subroutine build_matrixLSF_quadIntp ! ************************************************************************** ! ! ************************************************************************** ! !> This routine builds up the matrix for least square fit used in !! linear interpolation. subroutine build_matrixLSF_linearIntp(me, QQ, nDims, nSources, cxDirRK, & & neighDir, nCoeffs, success) ! -------------------------------------------------------------------------- !> Matrix to fill type(tem_matrix_type), intent(out) :: me !> Number of stencil directions integer, intent(in) :: QQ !> Number of dimensions integer, intent(in) :: nDims !> Number of sources from coarser found integer, intent(in) :: nSources !> Stencil directions real(kind=rk), intent(in) :: cxDirRK(3,QQ) !> direction in which sources are found integer, intent(in) :: neighDir(nSources) !> nUnknown coeffs integer, intent(in) :: nCoeffs !> success if false if matrix is singular reduce interpolation order logical, intent(out) :: success ! -------------------------------------------------------------------------- integer :: iDir, iSrc !> Each row represents a polynomial evaluated at coord of elements in ! stencil directions type(tem_matrix_type) :: tmp_matrix real(kind=rk) :: inv_AtA(nCoeffs,nCoeffs), AtA(nCoeffs,nCoeffs) integer :: errCode ! -------------------------------------------------------------------------- write(dbgUnit(4),"(A)") 'Inside build least square fit matrix for linear' ! me%A = ((A^T)A)^-1*(A^T) ! inv_AtA = ((A^T)A)^-1 call alloc_matrix(tmp_matrix, nSources, nCoeffs) select case(nDims) case (1) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyLinear_1D( cxDirRK(:,iDir) ) end do case (2) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyLinear_2D( cxDirRK(:,iDir) ) end do case (3) do iSrc = 1, nSources iDir = neighDir(iSrc) tmp_matrix%A(iSrc,:) = polyLinear_3D( cxDirRK(:,iDir) ) end do case default write(logUnit(1),*) 'Unknown nDims for quadratic interpolation' call tem_abort() end select write(dbgUnit(4),"(A)") ' tmp matrix:' call tem_matrix_dump(tmp_matrix, dbgUnit(4)) flush(dbgUnit(4)) AtA = matmul( transpose(tmp_matrix%A), tmp_matrix%A) inv_AtA = invert_matrix(AtA, errCode) if (errCode == 0) then ! matrix_LSF size is transpose of tmp_matrix call alloc_matrix(me, nCoeffs, nSources) me%A = matmul( inv_AtA, transpose(tmp_matrix%A) ) success = .true. else ! singular matrix, reduce interpolation order call alloc_matrix(me, 1, 1) success = .false. return end if write(dbgUnit(4),"(A)") ' Matrix LSF:' call tem_matrix_dump(me, dbgUnit(4)) flush(dbgUnit(4)) end subroutine build_matrixLSF_linearIntp ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for quadratic polynomial for 1D !! stencil pure function polyQuadratic_1D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(3) ! -------------------------------------------------------------------------- phi(1) = 1.0_rk phi(2) = cxDir(c_x) phi(3) = cxDir(c_x)**2 end function polyQuadratic_1D ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for quadratic polynomial for 2D !! stencil pure function polyQuadratic_2D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(6) ! -------------------------------------------------------------------------- phi(1) = 1.0_rk phi(2) = cxDir(c_x) phi(3) = cxDir(c_y) phi(4) = cxDir(c_x)**2 phi(5) = cxDir(c_y)**2 phi(6) = cxDir(c_x)*cxDir(c_y) end function polyQuadratic_2D ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for quadratic polynomial for 3D !! stencil pure function polyQuadratic_3D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(10) ! -------------------------------------------------------------------------- phi( 1) = 1.0_rk phi( 2) = cxDir(c_x) phi( 3) = cxDir(c_y) phi( 4) = cxDir(c_z) phi( 5) = cxDir(c_x)**2 phi( 6) = cxDir(c_y)**2 phi( 7) = cxDir(c_z)**2 phi( 8) = cxDir(c_x)*cxDir(c_y) phi( 9) = cxDir(c_y)*cxDir(c_z) phi(10) = cxDir(c_z)*cxDir(c_x) end function polyQuadratic_3D ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for Linear polynomial for 1D !! stencil pure function polyLinear_1D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(2) ! -------------------------------------------------------------------------- phi(1) = 1.0_rk phi(2) = cxDir(c_x) end function polyLinear_1D ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for Linear polynomial for 2D !! stencil pure function polyLinear_2D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(3) ! -------------------------------------------------------------------------- phi(1) = 1.0_rk phi(2) = cxDir(c_x) phi(3) = cxDir(c_y) end function polyLinear_2D ! ************************************************************************** ! ! ************************************************************************** ! !> This function returns matrix entries for Linear polynomial for 3D !! stencil pure function polyLinear_3D(cxDir) result (phi) ! -------------------------------------------------------------------------- real(kind=rk), intent(in) :: cxDir(3) real(kind=rk) :: phi(4) ! -------------------------------------------------------------------------- phi( 1) = 1.0_rk phi( 2) = cxDir(c_x) phi( 3) = cxDir(c_y) phi( 4) = cxDir(c_z) end function polyLinear_3D ! ************************************************************************** ! ! ************************************************************************** ! subroutine truncate_intpMatrixLSF(me) ! -------------------------------------------------------------------------- type(tem_intpMatrixLSF_type), intent(inout) :: me ! -------------------------------------------------------------------------- call truncate(me%matArray) call truncate(me%ID) call truncate(me%isInvertible) end subroutine truncate_intpMatrixLSF ! ************************************************************************** ! ! ************************************************************************** ! subroutine destroy_intpMatrixLSF(me) ! -------------------------------------------------------------------------- type(tem_intpMatrixLSF_type), intent(inout) :: me ! -------------------------------------------------------------------------- call destroy(me%matArray) call destroy(me%ID) call truncate(me%isInvertible) end subroutine destroy_intpMatrixLSF ! ************************************************************************** ! ! ************************************************************************** ! subroutine tem_matrix_dump(me, outUnit) ! -------------------------------------------------------------------------- type(tem_matrix_type), intent(in) :: me integer, intent(in) :: outUnit ! -------------------------------------------------------------------------- integer :: iRow ! -------------------------------------------------------------------------- write(outUnit, "(A,i2,A,i2)") 'Matrix dimension: ', & & me%nEntries(1), ' x ', me%nEntries(2) do iRow = 1, me%nEntries(1) write(outUnit, *) 'iRow ', iRow ,'Val ', me%A(iRow, :) end do end subroutine tem_matrix_dump ! ************************************************************************** ! ! ************************************************************************** ! !> This routine provides assignment operator of tem_matrix_type subroutine copy_matrix(left, right) ! -------------------------------------------------------------------------- type(tem_matrix_type), intent(out) :: left type(tem_matrix_type), intent(in) :: right ! -------------------------------------------------------------------------- left%nEntries = right%nEntries if (allocated(right%A)) then allocate(left%A(right%nEntries(1), right%nEntries(2))) left%A = right%A end if end subroutine copy_matrix ! **************************************************************************** ! ! **************************************************************************** ! !> This routine allocates matrix with given dimentions subroutine alloc_matrix( me, dim1, dim2 ) ! -------------------------------------------------------------------------- type( tem_matrix_type ) :: me integer, intent(in) :: dim1 integer, intent(in) :: dim2 ! -------------------------------------------------------------------------- if ( dim1 > 0 .and. dim2 > 0 ) then me%nEntries(1) = dim1 me%nEntries(2) = dim2 allocate( me%A( dim1, dim2 ) ) me%A = 0.0_rk else write( logUnit(1), "(A)" ) & & 'Failed to allocate matrix. Dimension is negative number.' call tem_abort() end if end subroutine alloc_matrix ! **************************************************************************** ! ! **************************************************************************** ! !> Returns the inverse of a matrix calculated by finding the LU !! decomposition. Depends on LAPACK. !! function invert_matrix(A, errCode) result(Ainv) ! --------------------------------------------------------------------------- !> Matrix to invert real(kind=rk), dimension(:,:), intent(in) :: A !> If error code is present return error code and do not abort integer, optional, intent(out) :: errCode !> inverse of A real(kind=rk), dimension(size(A,1),size(A,2)) :: Ainv ! --------------------------------------------------------------------------- real(kind=rk), dimension(size(A,1)) :: work ! work array for LAPACK integer, dimension(size(A,1)) :: ipiv ! pivot indices integer :: n, info ! External procedures defined in LAPACK external DGETRF external DGETRI ! --------------------------------------------------------------------------- ! Store A in Ainv to prevent it from being overwritten by LAPACK Ainv = A n = size(A,1) ! DGETRF computes an LU factorization of a general M-by-N matrix A ! using partial pivoting with row interchanges. call DGETRF(n, n, Ainv, n, ipiv, info) if (info /= 0) then if (present(errCode)) then errCode = info write(logUnit(5),*) 'WARNING: Matrix is numerically singular!' return else call tem_abort('Matrix is numerically singular!') end if end if ! DGETRI computes the inverse of a matrix using the LU factorization ! computed by DGETRF. call DGETRI(n, Ainv, n, ipiv, work, n, info) if (info /= 0) then if (present(errCode)) then errCode = info write(logUnit(5),*) 'WARNING: Matrix inversion failed!' return else call tem_abort('Matrix inversion failed!') end if end if ! successfull if (present(errCode)) errCode = 0 end function invert_matrix ! **************************************************************************** ! end module tem_matrix_module