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SingleColExpBase.F90
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SingleColExpBase.F90
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! MIT License
!
! Copyright (c) 2021 Florian Goth
!
! 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.
!--------------------------------------------------------------------
!> @author
!> Florian Goth
!
!> @file SingleColExpBase.F90
!> @brief This file contains the interface class for all checkerboard objects.
!--------------------------------------------------------------------
module SingleColExpBase_mod
implicit none
!--------------------------------------------------------------------
!> @author
!> Florian Goth
!
!> @class SingleColExpBase
!> @brief This defines the interface for all four checkerboard types.
!>
!> We require a common base class to distinguish for optimization purposes
!> between matrices where the diagonal is zero,
!> those that have the same value on the entire diagonal(i.e. homogeneous)
!> and those that have an arbitrary diagonal.
!--------------------------------------------------------------------
type, abstract :: SingleColExpBase
integer :: nrofentries
integer, allocatable :: xy(:)
complex (kind=kind(0.d0)), allocatable :: s(:), s2(:)
real (kind=kind(0.d0)), allocatable :: c(:), c2(:)
contains
procedure(vecmultinterface), deferred :: vecmult
procedure(rmultinterface), deferred :: rmult
procedure(lmultinterface), deferred :: lmult
procedure(rmultinvinterface), deferred :: rmultinv
procedure(lmultinvinterface), deferred :: lmultinv
procedure(adjointactioninterface), deferred :: adjointaction
procedure(adjointactionovertwointerface), deferred :: adjoint_over_two
procedure(initinterface), deferred :: init
procedure(deallocinterface), deferred :: dealloc
end type SingleColExpBase
abstract interface
!--------------------------------------------------------------------
!> @brief
!> Multiplies this with mat from the right.
!
!> @param[in] this
!> @param[inout] mat a complex matrix.
!--------------------------------------------------------------------
subroutine rmultinterface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:) :: mat
end subroutine
!--------------------------------------------------------------------
!> @brief
!> Multiplies this with mat from the left.
!
!> @param[in] this
!> @param[inout] mat
!--------------------------------------------------------------------
subroutine lmultinterface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:), contiguous :: mat
end subroutine
!--------------------------------------------------------------------
!> @brief
!> Multiplies this with a vector from the left.
!
!> @param[in] this
!> @param[inout] vec
!--------------------------------------------------------------------
subroutine vecmultinterface(this, vec)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:) :: vec
end subroutine
!--------------------------------------------------------------------
!> @brief
!> multiplies this^-1 with mat from the right.
!
!> @param[in] this
!--------------------------------------------------------------------
subroutine rmultinvinterface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:) :: mat
end subroutine
!--------------------------------------------------------------------
!> @brief
!> multiplies this^-1 with mat from the left.
!
!> @param[in] this
!--------------------------------------------------------------------
subroutine lmultinvinterface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:), contiguous :: mat
end subroutine
!--------------------------------------------------------------------
!> @brief
!> This inititializes an object.
!
!> @param[in] this
!> @param nodes the array of Nodes
!> @param nredges how many nodes are there
!> @param mys an array with the diagonal entries
!> @param a possible prefactor
!--------------------------------------------------------------------
subroutine initinterface(this, nodes, nredges, mys, weight)
Use Node_mod
import SingleColExpBase
class(SingleColExpBase), intent(inout) :: this
type(node), dimension(:), intent(in) :: nodes
real(kind=kind(0.D0)), intent(in), dimension(:) :: mys
integer, intent(in) :: nredges
real(kind=kind(0.D0)), intent(in) :: weight
end subroutine
!--------------------------------------------------------------------
!> @brief
!> Free the used memory.
!
!> @param[in] this
!--------------------------------------------------------------------
subroutine deallocinterface(this)
import SingleColExpBase
class(SingleColExpBase), intent(inout) :: this
end subroutine
!--------------------------------------------------------------------
!> @brief
!> Perform the similarity transform e^{-T} arg e^{T}
!
!> @param[in] this
!> @param[inout] mat the matrix that we intend to transform.
!--------------------------------------------------------------------
subroutine adjointactioninterface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:) :: mat
end subroutine
!--------------------------------------------------------------------
!> @brief
!> Perform the similarity transform e^{-T/2} arg e^{T/2}
!
!> @param[in] this
!> @param[inout] mat the matrix that we intend to transform.
!--------------------------------------------------------------------
subroutine adjointactionovertwointerface(this, mat)
import SingleColExpBase
class(SingleColExpBase), intent(in) :: this
Complex(kind=kind(0.d0)), intent(inout), dimension(:,:) :: mat
end subroutine
end interface
contains
!--------------------------------------------------------------------
!> @author
!> Florian Goth
!
!> @brief
!> Perform the multiplication of an checkerboard exponential with a matrix.
!> This is an internal helper function that finds reuse in multiple places.
!
!> @param[in] c the diagonal data
!> @param[in] s the off-diagonal data
!> @param[in] xy the used matrix positions
!> @param[in] nrofentries how many vertices are in this family.
!> @param[inout] mat the matrix that we modify.
!--------------------------------------------------------------------
pure subroutine rmultbase(c, s, xy, nrofentries, mat)
real (kind=kind(0.d0)), allocatable, intent(in) :: c(:)
complex (kind=kind(0.d0)), allocatable, intent(in) :: s(:)
integer, allocatable, intent(in) :: xy(:)
integer, intent(in) ::nrofentries
complex(kind=kind(0.D0)), dimension(:, :), intent(inout) :: mat
integer :: i, j, ndim
complex(kind=kind(0.D0)) :: t1, t2
ndim = size(mat,1)
do i = 1, nrofentries! for every matrix
do j = 1, ndim
t1 = mat(j, xy(2*i-1))
t2 = mat(j, xy(2*i))
mat(j, xy(2*i-1)) = c(i) * t1 + s(i)* t2
mat(j, xy(2*i)) = c(i) * t2 + conjg(s(i))* t1
enddo
enddo
end subroutine
!--------------------------------------------------------------------
!> @author
!> Florian Goth
!
!> @brief
!> Perform the multiplication of this exponential with a matrix: out = this*mat
!
!> Notes: unifying x and y into one array gave some speedup.
!> Unifying c and s did not...
!> FIXME: ndim divisible by two...
!> This is an internal helper function that finds reuse in multiple places.
!
!> @param[in] c the diagonal data
!> @param[in] s the off-diagonal data
!> @param[in] x the used matrix positions
!> @param[in] nrofentries how many vertices are in this family.
!> @param[inout] mat the matrix that we modify.
!--------------------------------------------------------------------
pure subroutine lmultbase(c, s, xy, nrofentries, mat)
real (kind=kind(0.d0)), allocatable, intent(in) :: c(:)
complex (kind=kind(0.d0)), allocatable, intent(in) :: s(:)
integer, allocatable, intent(in) :: xy(:)
integer, intent(in) ::nrofentries
complex(kind=kind(0.D0)), dimension(:, :), intent(inout), contiguous :: mat
integer :: i, j, k, ndim, loopend
integer, parameter :: step = 2 ! determined to be fastest on 6x6 hubbard
complex(kind=kind(0.D0)) :: t1(step), t2(step)
integer, allocatable, dimension(:) :: xyarray
complex(kind=kind(0.D0)), allocatable, dimension(:) :: snh
real(kind=kind(0.D0)), allocatable, dimension(:) :: csh
! The intel compiler is really helped by using these temporary arrays
allocate(xyarray(size(xy)), csh(nrofentries), snh(nrofentries) )
xyarray = xy
csh = c
snh = s
ndim = size(mat,1)
loopend = (ndim/step)*step
! ifort 2017
!DIR$ UNROLL_AND_JAM(4)
do j = 1, loopend, step
do i = 1, nrofentries! for every matrix
do k = 1,step
t1(k) = mat(xyarray(2*i-1), j+k-1)
t2(k) = mat(xyarray(2*i), j+k-1)
enddo
do k = 1, step
mat(xyarray(2*i-1), j+k-1) = csh(i) * t1(k) + snh(i) * t2(k)
mat(xyarray(2*i), j+k-1) = csh(i) * t2(k) + conjg(snh(i)) * t1(k)
enddo
enddo
enddo
! remainder loop
if ((ndim - loopend) .ne. 0) then
do i = 1, nrofentries! for every matrix
t1(1) = mat(xyarray(2*i-1), ndim)
t2(1) = mat(xyarray(2*i), ndim)
mat(xyarray(2*i-1), ndim) = csh(i) * t1(1) + snh(i) * t2(1)
mat(xyarray(2*i), ndim) = csh(i) * t2(1) + conjg(snh(i)) * t1(1)
enddo
endif
deallocate(xyarray, csh, snh)
end subroutine
!--------------------------------------------------------------------
!> @author
!> Florian Goth
!
!> @brief
!> A function to calculate the Frobenius norm of hermitian 2x2 matrices.
!
!> @param[in] d1 first diagonal entry
!> @param[in] d2 second diagonal entry
!> @param[in] o off-diagonal entry
!> @return The value of the frobenius norm
!--------------------------------------------------------------------
function frobnorm(d1, d2, o) result(fn)
real (kind=kind(0.d0)) :: fn, d1, d2
complex(kind=kind(0.D0)), intent(in) :: o
fn = sqrt(d1*d1+d2*d2 + 2*dble(o * conjg(o)))
end function
end module SingleColExpBase_mod