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more efficient restore symmetry
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@ -1574,79 +1574,110 @@ subroutine nullify_small_elements(m,n,A,LDA,thresh)
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end
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subroutine restore_symmetry(m,n,A,LDA,thresh)
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implicit none
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BEGIN_DOC
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! Tries to find the matrix elements that are the same, and sets them
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! to the average value.
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! If restore_symm is False, only nullify small elements
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! Tries to find the matrix elements that are the same, and sets them
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! to the average value.
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! If restore_symm is False, only nullify small elements
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END_DOC
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integer, intent(in) :: m,n,LDA
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double precision, intent(inout) :: A(LDA,n)
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double precision, intent(in) :: thresh
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integer :: i,j,k,l
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logical, allocatable :: done(:,:)
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double precision :: f, g, count, thresh2
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double precision, allocatable :: copy(:), copy_sign(:)
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integer, allocatable :: key(:), ii(:), jj(:)
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integer :: sze, pi, pf, idx, i,j,k
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double precision :: average, val, thresh2
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thresh2 = dsqrt(thresh)
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call nullify_small_elements(m,n,A,LDA,thresh)
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! if (.not.restore_symm) then
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! return
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! endif
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sze = m * n
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! TODO: Costs O(n^4), but can be improved to (2 n^2 * log(n)):
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! - copy all values in a 1D array
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! - sort 1D array
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! - average nearby elements
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! - for all elements, find matching value in the sorted 1D array
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allocate(copy(sze),copy_sign(sze),key(sze),ii(sze),jj(sze))
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allocate(done(m,n))
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do j=1,n
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do i=1,m
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done(i,j) = A(i,j) == 0.d0
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! Copy to 1D
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!$OMP PARALLEL if (m>100) &
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!$OMP SHARED(A,m,n,sze,copy_sign,copy,key,ii,jj) &
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!$OMP PRIVATE(i,j,k) &
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!$OMP DEFAULT(NONE)
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!$OMP DO
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do j = 1, n
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do i = 1, m
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k = i+(j-1)*m
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copy(k) = A(i,j)
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copy_sign(k) = sign(1.d0,copy(k))
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copy(k) = -dabs(copy(k))
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key(k) = k
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ii(k) = i
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jj(k) = j
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enddo
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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do j=1,n
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do i=1,m
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if ( done(i,j) ) cycle
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done(i,j) = .True.
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count = 1.d0
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f = 1.d0/A(i,j)
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do l=1,n
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do k=1,m
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if ( done(k,l) ) cycle
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g = f * A(k,l)
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if ( dabs(dabs(g) - 1.d0) < thresh2 ) then
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count = count + 1.d0
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if (g>0.d0) then
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A(i,j) = A(i,j) + A(k,l)
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else
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A(i,j) = A(i,j) - A(k,l)
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end if
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endif
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enddo
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enddo
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if (count > 1.d0) then
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A(i,j) = A(i,j) / count
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do l=1,n
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do k=1,m
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if ( done(k,l) ) cycle
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g = f * A(k,l)
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if ( dabs(dabs(g) - 1.d0) < thresh2 ) then
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done(k,l) = .True.
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if (g>0.d0) then
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A(k,l) = A(i,j)
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else
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A(k,l) = -A(i,j)
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end if
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endif
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enddo
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enddo
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! Sort
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call dsort(copy,key,sze)
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call iset_order(ii,key,sze)
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call iset_order(jj,key,sze)
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call dset_order(copy_sign,key,sze)
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!TODO
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! Parallelization with OMP
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! Symmetrize
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i = 1
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do while (i < sze)
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pi = i
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pf = i
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! Exit if the remaining elements are below thresh
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if (-copy(i) <= thresh) exit
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val = 1d0/copy(i)
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do while (dabs(val * copy(pf+1) - 1d0) < thresh2)
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pf = pf + 1
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! if pf == sze, copy(pf+1) will not be valid
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if (pf == sze) then
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exit
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endif
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enddo
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! if pi and pf are different do the average from pi to pf
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if (pf - pi > 0) then
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average = 0d0
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do j = pi, pf
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average = average + copy(j)
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enddo
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average = average / (pf-pi+1.d0)
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do j = pi, pf
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copy(j) = average
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enddo
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! Update i
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i = pf
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endif
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! Update i
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i = i + 1
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enddo
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copy(i:) = 0.d0
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!$OMP PARALLEL if (sze>10000) &
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!$OMP SHARED(m,sze,copy_sign,copy,key,A,ii,jj) &
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!$OMP PRIVATE(i,j,k,idx) &
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!$OMP DEFAULT(NONE)
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! copy -> A
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!$OMP DO
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do k = 1, sze
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i = ii(k)
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j = jj(k)
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A(i,j) = sign(copy(k),copy_sign(k))
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enddo
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!$OMP END DO
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!$OMP END PARALLEL
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deallocate(copy,copy_sign,key,ii,jj)
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end
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