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added Abdallah's non hermit davidson
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src/dav_general_mat/dav_ext_rout_nonsym_B1space.irp.f
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608
src/dav_general_mat/dav_ext_rout_nonsym_B1space.irp.f
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@ -0,0 +1,608 @@
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! ---
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subroutine davidson_general_ext_rout_nonsym_b1space(u_in, H_jj, energies, sze, N_st, N_st_diag_in, converged, hcalc)
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use mmap_module
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BEGIN_DOC
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! Generic modified-Davidson diagonalization
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!
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! H_jj : specific diagonal H matrix elements to diagonalize de Davidson
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!
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! u_in : guess coefficients on the various states. Overwritten on exit by right eigenvectors
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!
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! sze : Number of determinants
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!
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! N_st : Number of eigenstates
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!
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! N_st_diag_in : Number of states in which H is diagonalized. Assumed > N_st
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!
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! Initial guess vectors are not necessarily orthonormal
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!
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! hcalc subroutine to compute W = H U (see routine hcalc_template for template of input/output)
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END_DOC
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implicit none
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integer, intent(in) :: sze, N_st, N_st_diag_in
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double precision, intent(in) :: H_jj(sze)
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logical, intent(inout) :: converged
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double precision, intent(inout) :: u_in(sze,N_st_diag_in)
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double precision, intent(out) :: energies(N_st)
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external hcalc
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character*(16384) :: write_buffer
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integer :: iter, N_st_diag
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integer :: i, j, k, m
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integer :: iter2, itertot
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logical :: disk_based
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integer :: shift, shift2, itermax
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integer :: nproc_target
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integer :: order(N_st_diag_in)
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double precision :: to_print(2,N_st)
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double precision :: r1, r2, alpha
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double precision :: cpu, wall
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double precision :: cmax
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double precision :: energy_shift(N_st_diag_in*davidson_sze_max)
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double precision, allocatable :: U(:,:)
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double precision, allocatable :: y(:,:), h(:,:), lambda(:)
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double precision, allocatable :: residual_norm(:)
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integer :: i_omax
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double precision :: lambda_tmp
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double precision, allocatable :: U_tmp(:), overlap(:)
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double precision, allocatable :: W(:,:)
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!double precision, pointer :: W(:,:)
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double precision, external :: u_dot_v, u_dot_u
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include 'constants.include.F'
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N_st_diag = N_st_diag_in
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!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: U, W, y, h, lambda
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if(N_st_diag*3 > sze) then
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print *, 'error in Davidson :'
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print *, 'Increase n_det_max_full to ', N_st_diag*3
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stop -1
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endif
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itermax = max(2, min(davidson_sze_max, sze/N_st_diag)) + 1
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provide threshold_nonsym_davidson
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call write_time(6)
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write(6,'(A)') ''
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write(6,'(A)') 'Davidson Diagonalization'
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write(6,'(A)') '------------------------'
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write(6,'(A)') ''
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! Find max number of cores to fit in memory
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! -----------------------------------------
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nproc_target = nproc
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double precision :: rss
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integer :: maxab
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maxab = sze
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m=1
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disk_based = .False.
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call resident_memory(rss)
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do
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r1 = 8.d0 * &! bytes
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( dble(sze)*(N_st_diag*itermax) &! U
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+ 1.d0*dble(sze*m)*(N_st_diag*itermax) &! W
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+ 2.d0*(N_st_diag*itermax)**2 &! h,y
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+ 2.d0*(N_st_diag*itermax) &! s2,lambda
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+ 1.d0*(N_st_diag) &! residual_norm
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! In H_S2_u_0_nstates_zmq
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+ 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on collector
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+ 3.d0*(N_st_diag*N_det) &! u_t, v_t, s_t on slave
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+ 0.5d0*maxab &! idx0 in H_S2_u_0_nstates_openmp_work_*
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+ nproc_target * &! In OMP section
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( 1.d0*(N_int*maxab) &! buffer
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+ 3.5d0*(maxab) ) &! singles_a, singles_b, doubles, idx
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) / 1024.d0**3
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if(nproc_target == 0) then
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call check_mem(r1, irp_here)
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nproc_target = 1
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exit
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endif
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if(r1+rss < qp_max_mem) then
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exit
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endif
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if(itermax > 4) then
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itermax = itermax - 1
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else if (m==1.and.disk_based_davidson) then
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m = 0
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disk_based = .True.
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itermax = 6
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else
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nproc_target = nproc_target - 1
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endif
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enddo
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nthreads_davidson = nproc_target
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TOUCH nthreads_davidson
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call write_int(6, N_st, 'Number of states')
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call write_int(6, N_st_diag, 'Number of states in diagonalization')
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call write_int(6, sze, 'Number of basis functions')
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call write_int(6, nproc_target, 'Number of threads for diagonalization')
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call write_double(6, r1, 'Memory(Gb)')
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if(disk_based) then
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print *, 'Using swap space to reduce RAM'
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endif
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!---------------
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write(6,'(A)') ''
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write_buffer = '====='
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ==========='
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enddo
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write(6,'(A)') write_buffer(1:6+41*N_st)
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write_buffer = 'Iter'
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do i=1,N_st
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write_buffer = trim(write_buffer)//' Energy Residual '
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enddo
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write(6,'(A)') write_buffer(1:6+41*N_st)
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write_buffer = '====='
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do i=1,N_st
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write_buffer = trim(write_buffer)//' ================ ==========='
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enddo
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write(6,'(A)') write_buffer(1:6+41*N_st)
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! ---
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allocate( W(sze,N_st_diag*itermax) )
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allocate( &
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! Large
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U(sze,N_st_diag*itermax), &
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! Small
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h(N_st_diag*itermax,N_st_diag*itermax), &
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y(N_st_diag*itermax,N_st_diag*itermax), &
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lambda(N_st_diag*itermax), &
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residual_norm(N_st_diag) &
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)
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U = 0.d0
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h = 0.d0
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y = 0.d0
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lambda = 0.d0
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residual_norm = 0.d0
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ASSERT (N_st > 0)
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ASSERT (N_st_diag >= N_st)
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ASSERT (sze > 0)
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! Davidson iterations
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! ===================
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converged = .False.
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! Initialize from N_st to N_st_diag with gaussian random numbers
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! to be sure to have overlap with any eigenvectors
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do k = N_st+1, N_st_diag
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u_in(k,k) = 10.d0
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do i = 1, sze
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call random_number(r1)
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call random_number(r2)
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r1 = dsqrt(-2.d0*dlog(r1))
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r2 = dtwo_pi*r2
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u_in(i,k) = r1*dcos(r2)
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enddo
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enddo
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! Normalize all states
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do k = 1, N_st_diag
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call normalize(u_in(1,k), sze)
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enddo
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! Copy from the guess input "u_in" to the working vectors "U"
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do k = 1, N_st_diag
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do i = 1, sze
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U(i,k) = u_in(i,k)
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enddo
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enddo
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! ---
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itertot = 0
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do while (.not.converged)
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itertot = itertot + 1
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if(itertot == 8) then
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exit
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endif
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do iter = 1, itermax-1
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shift = N_st_diag * (iter-1)
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shift2 = N_st_diag * iter
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if( (iter > 1) .or. (itertot == 1) ) then
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! Gram-Schmidt to orthogonalize all new guess with the previous vectors
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call ortho_qr(U, size(U, 1), sze, shift2)
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call ortho_qr(U, size(U, 1), sze, shift2)
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! W = H U
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call hcalc(W(1,shift+1), U(1,shift+1), N_st_diag, sze)
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else
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! Already computed in update below
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continue
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endif
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! Compute h_kl = <u_k | W_l> = <u_k| H |u_l>
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! -------------------------------------------
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call dgemm( 'T', 'N', shift2, shift2, sze, 1.d0 &
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, U, size(U, 1), W, size(W, 1) &
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, 0.d0, h, size(h, 1) )
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! Diagonalize h y = lambda y
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! ---------------------------
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call diag_nonsym_right(shift2, h(1,1), size(h, 1), y(1,1), size(y, 1), lambda(1), size(lambda, 1))
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! Express eigenvectors of h in the determinant basis:
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! ---------------------------------------------------
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! y(:,k) = rk
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! U(:,k) = Bk
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! U(:,shift2+k) = Rk = Bk x rk
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call dgemm( 'N', 'N', sze, N_st_diag, shift2, 1.d0 &
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, U, size(U, 1), y, size(y, 1) &
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, 0.d0, U(1,shift2+1), size(U, 1) )
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do k = 1, N_st_diag
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call normalize(U(1,shift2+k), sze)
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enddo
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! ---
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! select the max overlap
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!
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! start test ------------------------------------------------------------------------
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!
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!double precision, allocatable :: Utest(:,:), Otest(:)
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!allocate( Utest(sze,shift2), Otest(shift2) )
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!call dgemm( 'N', 'N', sze, shift2, shift2, 1.d0 &
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! , U, size(U, 1), y, size(y, 1), 0.d0, Utest(1,1), size(Utest, 1) )
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!do k = 1, shift2
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! call normalize(Utest(1,k), sze)
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!enddo
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!do j = 1, sze
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! write(455, '(100(1X, F16.10))') (Utest(j,k), k=1,shift2)
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!enddo
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!do k = 1, shift2
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! Otest(k) = 0.d0
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! do i = 1, sze
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! Otest(k) += Utest(i,k) * u_in(i,1)
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! enddo
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! Otest(k) = dabs(Otest(k))
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! print *, ' Otest =', k, Otest(k), lambda(k)
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!enddo
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!deallocate(Utest, Otest)
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!
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! end test ------------------------------------------------------------------------
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!
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allocate( overlap(N_st_diag) )
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do k = 1, N_st_diag
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overlap(k) = 0.d0
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do i = 1, sze
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overlap(k) = overlap(k) + U(i,shift2+k) * u_in(i,1)
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enddo
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overlap(k) = dabs(overlap(k))
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!print *, ' overlap =', k, overlap(k)
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enddo
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lambda_tmp = 0.d0
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do k = 1, N_st_diag
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if(overlap(k) .gt. lambda_tmp) then
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i_omax = k
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lambda_tmp = overlap(k)
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endif
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enddo
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deallocate(overlap)
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if( lambda_tmp .lt. 0.8d0) then
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print *, ' very small overlap..'
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print*, ' max overlap = ', lambda_tmp, i_omax
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stop
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endif
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! lambda_tmp = lambda(1)
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! lambda(1) = lambda(i_omax)
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! lambda(i_omax) = lambda_tmp
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!
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! allocate( U_tmp(sze) )
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! do i = 1, sze
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! U_tmp(i) = U(i,shift2+1)
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! U(i,shift2+1) = U(i,shift2+i_omax)
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! U(i,shift2+i_omax) = U_tmp(i)
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! enddo
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! deallocate(U_tmp)
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!
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! allocate( U_tmp(N_st_diag*itermax) )
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! do i = 1, shift2
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! U_tmp(i) = y(i,1)
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! y(i,1) = y(i,i_omax)
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! y(i,i_omax) = U_tmp(i)
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! enddo
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! deallocate(U_tmp)
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! ---
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!do k = 1, N_st_diag
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! call normalize(U(1,shift2+k), sze)
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!enddo
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! ---
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! y(:,k) = rk
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! W(:,k) = H x Bk
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! W(:,shift2+k) = H x Bk x rk
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! = Wk
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call dgemm( 'N', 'N', sze, N_st_diag, shift2, 1.d0 &
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, W, size(W, 1), y, size(y, 1) &
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, 0.d0, W(1,shift2+1), size(W, 1) )
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! ---
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! Compute residual vector and davidson step
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! -----------------------------------------
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!$OMP PARALLEL DO DEFAULT(SHARED) PRIVATE(i,k)
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do k = 1, N_st_diag
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do i = 1, sze
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U(i,shift2+k) = (lambda(k) * U(i,shift2+k) - W(i,shift2+k)) / max(H_jj(i)-lambda(k), 1.d-2)
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enddo
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!if(k <= N_st) then
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! residual_norm(k) = u_dot_u(U(1,shift2+k), sze)
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! to_print(1,k) = lambda(k)
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! to_print(2,k) = residual_norm(k)
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!endif
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enddo
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!$OMP END PARALLEL DO
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residual_norm(1) = u_dot_u(U(1,shift2+i_omax), sze)
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to_print(1,1) = lambda(i_omax)
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to_print(2,1) = residual_norm(1)
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if( (itertot > 1) .and. (iter == 1) ) then
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!don't print
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continue
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else
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write(*, '(1X, I3, 1X, 100(1X, F16.10, 1X, F16.10, 1X, F16.10))') iter-1, to_print(1:2,1:N_st)
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endif
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! Check convergence
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if(iter > 1) then
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converged = dabs(maxval(residual_norm(1:N_st))) < threshold_nonsym_davidson
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endif
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do k = 1, N_st
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if(residual_norm(k) > 1.e8) then
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print *, 'Davidson failed'
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stop -1
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endif
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enddo
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if(converged) then
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exit
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endif
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logical, external :: qp_stop
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if(qp_stop()) then
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converged = .True.
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exit
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endif
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enddo ! loop over iter
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! Re-contract U and update W
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! --------------------------------
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call dgemm( 'N', 'N', sze, N_st_diag, shift2, 1.d0 &
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, W, size(W, 1), y, size(y, 1) &
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, 0.d0, u_in, size(u_in, 1) )
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do k = 1, N_st_diag
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do i = 1, sze
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W(i,k) = u_in(i,k)
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enddo
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enddo
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call dgemm( 'N', 'N', sze, N_st_diag, shift2, 1.d0 &
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, U, size(U, 1), y, size(y, 1) &
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, 0.d0, u_in, size(u_in, 1) )
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do k = 1, N_st_diag
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do i = 1, sze
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U(i,k) = u_in(i,k)
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enddo
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enddo
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call ortho_qr(U, size(U, 1), sze, N_st_diag)
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call ortho_qr(U, size(U, 1), sze, N_st_diag)
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do j = 1, N_st_diag
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k = 1
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do while( (k < sze) .and. (U(k,j) == 0.d0) )
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k = k+1
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enddo
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if(U(k,j) * u_in(k,j) < 0.d0) then
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do i = 1, sze
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W(i,j) = -W(i,j)
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enddo
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endif
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enddo
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enddo ! loop over while
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! ---
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do k = 1, N_st
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energies(k) = lambda(k)
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enddo
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write_buffer = '====='
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do i = 1, N_st
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||||
write_buffer = trim(write_buffer)//' ================ ==========='
|
||||
enddo
|
||||
write(6,'(A)') trim(write_buffer)
|
||||
write(6,'(A)') ''
|
||||
call write_time(6)
|
||||
|
||||
deallocate(W)
|
||||
deallocate(U, h, y, lambda, residual_norm)
|
||||
|
||||
FREE nthreads_davidson
|
||||
|
||||
end subroutine davidson_general_ext_rout_nonsym_b1space
|
||||
|
||||
! ---
|
||||
|
||||
subroutine diag_nonsym_right(n, A, A_ldim, V, V_ldim, energy, E_ldim)
|
||||
|
||||
implicit none
|
||||
|
||||
integer, intent(in) :: n, A_ldim, V_ldim, E_ldim
|
||||
double precision, intent(in) :: A(A_ldim,n)
|
||||
double precision, intent(out) :: energy(E_ldim), V(V_ldim,n)
|
||||
|
||||
character*1 :: JOBVL, JOBVR, BALANC, SENSE
|
||||
integer :: i, j
|
||||
integer :: ILO, IHI, lda, ldvl, ldvr, LWORK, INFO
|
||||
double precision :: ABNRM
|
||||
integer, allocatable :: iorder(:), IWORK(:)
|
||||
double precision, allocatable :: WORK(:), SCALE_array(:), RCONDE(:), RCONDV(:)
|
||||
double precision, allocatable :: Atmp(:,:), WR(:), WI(:), VL(:,:), VR(:,:), Vtmp(:)
|
||||
double precision, allocatable :: energy_loc(:), V_loc(:,:)
|
||||
|
||||
allocate( Atmp(n,n), WR(n), WI(n), VL(1,1), VR(n,n) )
|
||||
do i = 1, n
|
||||
do j = 1, n
|
||||
Atmp(j,i) = A(j,i)
|
||||
enddo
|
||||
enddo
|
||||
|
||||
JOBVL = "N" ! computes the left eigenvectors
|
||||
JOBVR = "V" ! computes the right eigenvectors
|
||||
BALANC = "B" ! Diagonal scaling and Permutation for optimization
|
||||
SENSE = "V" ! Determines which reciprocal condition numbers are computed
|
||||
lda = n
|
||||
ldvr = n
|
||||
ldvl = 1
|
||||
|
||||
allocate( WORK(1), SCALE_array(n), RCONDE(n), RCONDV(n), IWORK(2*n-2) )
|
||||
|
||||
LWORK = -1 ! to ask for the optimal size of WORK
|
||||
call dgeevx( BALANC, JOBVL, JOBVR, SENSE & ! CHARACTERS
|
||||
, n, Atmp, lda & ! MATRIX TO DIAGONALIZE
|
||||
, WR, WI & ! REAL AND IMAGINARY PART OF EIGENVALUES
|
||||
, VL, ldvl, VR, ldvr & ! LEFT AND RIGHT EIGENVECTORS
|
||||
, ILO, IHI, SCALE_array, ABNRM, RCONDE, RCONDV & ! OUTPUTS OF OPTIMIZATION
|
||||
, WORK, LWORK, IWORK, INFO )
|
||||
|
||||
if(INFO .ne. 0) then
|
||||
print*, 'dgeevx failed !!', INFO
|
||||
stop
|
||||
endif
|
||||
|
||||
LWORK = max(int(work(1)), 1) ! this is the optimal size of WORK
|
||||
deallocate(WORK)
|
||||
allocate(WORK(LWORK))
|
||||
call dgeevx( BALANC, JOBVL, JOBVR, SENSE &
|
||||
, n, Atmp, lda &
|
||||
, WR, WI &
|
||||
, VL, ldvl, VR, ldvr &
|
||||
, ILO, IHI, SCALE_array, ABNRM, RCONDE, RCONDV &
|
||||
, WORK, LWORK, IWORK, INFO )
|
||||
if(INFO .ne. 0) then
|
||||
print*, 'dgeevx failed !!', INFO
|
||||
stop
|
||||
endif
|
||||
|
||||
deallocate( WORK, SCALE_array, RCONDE, RCONDV, IWORK )
|
||||
deallocate( VL, Atmp )
|
||||
|
||||
|
||||
allocate( energy_loc(n), V_loc(n,n) )
|
||||
energy_loc = 0.d0
|
||||
V_loc = 0.d0
|
||||
|
||||
i = 1
|
||||
do while(i .le. n)
|
||||
|
||||
! print*, i, WR(i), WI(i)
|
||||
|
||||
if( dabs(WI(i)) .gt. 1e-7 ) then
|
||||
|
||||
print*, ' Found an imaginary component to eigenvalue'
|
||||
print*, ' Re(i) + Im(i)', i, WR(i), WI(i)
|
||||
|
||||
energy_loc(i) = WR(i)
|
||||
do j = 1, n
|
||||
V_loc(j,i) = WR(i) * VR(j,i) - WI(i) * VR(j,i+1)
|
||||
enddo
|
||||
energy_loc(i+1) = WI(i)
|
||||
do j = 1, n
|
||||
V_loc(j,i+1) = WR(i) * VR(j,i+1) + WI(i) * VR(j,i)
|
||||
enddo
|
||||
i = i + 2
|
||||
|
||||
else
|
||||
|
||||
energy_loc(i) = WR(i)
|
||||
do j = 1, n
|
||||
V_loc(j,i) = VR(j,i)
|
||||
enddo
|
||||
i = i + 1
|
||||
|
||||
endif
|
||||
|
||||
enddo
|
||||
|
||||
deallocate(WR, WI, VR)
|
||||
|
||||
|
||||
! ordering
|
||||
! do j = 1, n
|
||||
! write(444, '(100(1X, F16.10))') (V_loc(j,i), i=1,5)
|
||||
! enddo
|
||||
allocate( iorder(n) )
|
||||
do i = 1, n
|
||||
iorder(i) = i
|
||||
enddo
|
||||
call dsort(energy_loc, iorder, n)
|
||||
do i = 1, n
|
||||
energy(i) = energy_loc(i)
|
||||
do j = 1, n
|
||||
V(j,i) = V_loc(j,iorder(i))
|
||||
enddo
|
||||
enddo
|
||||
deallocate(iorder)
|
||||
! do j = 1, n
|
||||
! write(445, '(100(1X, F16.10))') (V_loc(j,i), i=1,5)
|
||||
! enddo
|
||||
deallocate(V_loc, energy_loc)
|
||||
|
||||
end subroutine diag_nonsym_right
|
||||
|
||||
! ---
|
||||
|
Loading…
Reference in New Issue
Block a user