diff --git a/CHANGELOG.md b/CHANGELOG.md index 3e98d6c..7953608 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,4 +1,10 @@ +# Version 0.0.5 + +### New + + * Select the initial orthonormal basis set based on the lowest diagonal elements of the matrix + # Version 0.0.4 ## changed diff --git a/src/array_utils.f90 b/src/array_utils.f90 index 771651c..b242712 100644 --- a/src/array_utils.f90 +++ b/src/array_utils.f90 @@ -2,13 +2,14 @@ module array_utils use numeric_kinds, only: dp use lapack_wrapper, only: lapack_generalized_eigensolver, lapack_matmul, lapack_matrix_vector, & - lapack_qr, lapack_solver + lapack_qr, lapack_solver, lapack_sort implicit none !> \private private !> \public - public :: concatenate, diagonal,eye, generate_diagonal_dominant, norm + public :: concatenate, diagonal,eye, generate_diagonal_dominant, norm, & + generate_preconditioner contains @@ -33,7 +34,7 @@ pure function eye(m, n, alpha) do i=1, m do j=1, n if (i /= j) then - eye(i, j) = 0 + eye(i, j) = 0.d0 else eye(i, i) = x end if @@ -132,4 +133,49 @@ function diagonal(matrix) end function diagonal + function generate_preconditioner(diag, dim_sub) result(precond) + !> \brief generates a diagonal preconditioner for `matrix`. + !> \return diagonal matrix + + ! input variable + real(dp), dimension(:), intent(inout) :: diag + integer, intent(in) :: dim_sub + + ! local variables + real(dp), dimension(size(diag), dim_sub) :: precond + integer, dimension(size(diag)) :: keys + integer :: i, k + + ! sort diagonal + keys = lapack_sort('I', diag) + ! Fill matrix with zeros + precond = 0.0_dp + + ! Add one depending on the order of the matrix diagonal + do i=1, dim_sub + k = search_key(keys, i) + precond(k, i) = 1.d0 + end do + + end function generate_preconditioner + + function search_key(keys, i) result(k) + !> \brief Search for a given index `i` in a vector `keys` + !> \param keys Vector of index + !> \param i Index to search for + !> \return index of i inside keys + + integer, dimension(:), intent(in) :: keys + integer, intent(in) :: i + integer :: j, k + + do j=1,size(keys) + if (keys(j) == i) then + k = j + exit + end if + end do + + end function search_key + end module array_utils diff --git a/src/davidson.f90 b/src/davidson.f90 index fe22934..f723b10 100644 --- a/src/davidson.f90 +++ b/src/davidson.f90 @@ -1,12 +1,20 @@ !> \namespace Davidson eigensolver !> \author Felipe Zapata +!> The current implementation uses a general davidson algorithm, meaning +!> that it compute all the eigenvalues simultaneusly using a variable size block approach. +!> The family of Davidson algorithm only differ in the way that the correction +!> vector is computed. +!> Computed pairs of eigenvalues/eigenvectors are deflated using algorithm +!> described at: https://doi.org/10.1023/A:101919970 + + module davidson_dense !> Submodule containing the implementation of the Davidson diagonalization method !> for dense matrices use numeric_kinds, only: dp use lapack_wrapper, only: lapack_generalized_eigensolver, lapack_matmul, lapack_matrix_vector, & - lapack_qr, lapack_solver - use array_utils, only: concatenate, eye, norm + lapack_qr, lapack_solver, lapack_sort + use array_utils, only: concatenate, diagonal, eye, generate_preconditioner, norm implicit none @@ -41,11 +49,8 @@ end function compute_correction_generalized_dense subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, method, max_iters, & tolerance, iters, max_dim_sub, stx) - !> The current implementation uses a general davidson algorithm, meaning - !> that it compute all the eigenvalues simultaneusly using a block approach. - !> The family of Davidson algorithm only differ in the way that the correction - !> vector is computed. - + !> Implementation storing in memory the initial densed matrix mtx. + !> \param[in] mtx: Matrix to diagonalize !> \param[in, opt] Optional matrix to solve the general eigenvalue problem: !> \f$ mtx \lambda = V stx \lambda \f$ @@ -78,6 +83,7 @@ subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, !local variables integer :: i, j, dim_sub, max_dim + integer :: n_converged ! Number of converged eigenvalue/eigenvector pairs ! Basis of subspace of approximants real(dp), dimension(size(mtx, 1)) :: guess, rs @@ -87,12 +93,22 @@ subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, real(dp), dimension(:), allocatable :: eigenvalues_sub real(dp), dimension(:, :), allocatable :: correction, eigenvectors_sub, mtx_proj, stx_proj, V + ! Diagonal matrix + real(dp), dimension(size(mtx, 1)) :: d + ! generalize problem logical :: gev + ! indices of the eigenvalues/eigenvectors pair that have not converged + logical, dimension(lowest) :: has_converged + ! Iteration subpsace dimension dim_sub = lowest * 2 + ! Initial number of converged eigenvalue/eigenvector pairs + n_converged = 0 + has_converged = .False. + ! maximum dimension of the basis for the subspace if (present(max_dim_sub)) then max_dim = max_dim_sub @@ -104,8 +120,10 @@ subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, gev = present(stx) ! 1. Variables initialization - V = eye(size(ritz_vectors, 1), dim_sub) ! Initial orthonormal basis - + ! Select the initial ortogonal subspace based on lowest elements + ! of the diagonal of the matrix + d = diagonal(mtx) + V = generate_preconditioner(d, dim_sub) ! 2. Generate subpace matrix problem by projecting into V mtx_proj = lapack_matmul('T', 'N', V, lapack_matmul('N', 'N', mtx, V)) @@ -145,9 +163,16 @@ subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, end if rs = lapack_matrix_vector('N', mtx, ritz_vectors(:, j)) - guess errors(j) = norm(rs) + ! Check which eigenvalues has converged + if (errors(j) < tolerance) then + has_converged(j) = .true. + end if end do - - if (all(errors < tolerance)) then + + ! Count converged pairs of eigenvalues/eigenvectors + n_converged = n_converged + count(errors < tolerance) + + if (all(has_converged)) then iters = i exit end if @@ -197,7 +222,8 @@ subroutine generalized_eigensolver_dense(mtx, eigenvalues, ritz_vectors, lowest, end do outer_loop ! 8. Check convergence - if (i > max_iters / dim_sub) then + if (i > max_iters) then + iters = i print *, "Warning: Algorithm did not converge!!" end if @@ -265,7 +291,7 @@ module davidson_free use numeric_kinds, only: dp use lapack_wrapper, only: lapack_generalized_eigensolver, lapack_matmul, lapack_matrix_vector, & lapack_qr, lapack_solver - use array_utils, only: concatenate, eye, norm + use array_utils, only: concatenate, generate_preconditioner, norm use davidson_dense, only: generalized_eigensolver_dense implicit none @@ -343,7 +369,7 @@ end function fun_stx_gemv ! ! Basis of subspace of approximants real(dp), dimension(size(ritz_vectors, 1),1) :: guess, rs - real(dp), dimension(size(ritz_vectors, 1) ) :: diag_mtx, diag_stx + real(dp), dimension(size(ritz_vectors, 1) ) :: diag_mtx, diag_stx, copy_d real(dp), dimension(lowest):: errors ! ! Working arrays @@ -368,7 +394,10 @@ end function fun_stx_gemv diag_stx = extract_diagonal_free(fun_stx_gemv,dim_mtx) ! 1. Variables initialization - V = eye(dim_mtx, dim_sub) ! Initial orthonormal basis + ! Select the initial ortogonal subspace based on lowest elements + ! of the diagonal of the matrix + copy_d = diag_mtx + V = generate_preconditioner(copy_d, dim_sub) ! Initial orthonormal basis ! 2. Generate subspace matrix problem by projecting into V mtx_proj = lapack_matmul('T', 'N', V, fun_mtx_gemv(V)) @@ -757,7 +786,7 @@ function compute_DPR_generalized_dense(mtx, V, eigenvalues, eigenvectors, stx) r real(dp), dimension(:, :), intent(in) :: mtx, V, eigenvectors real(dp), dimension(:, :), intent(in), optional :: stx real(dp), dimension(size(mtx, 1), size(V, 2)) :: correction - + ! local variables integer :: ii,j, m real(dp), dimension(size(mtx, 1), size(mtx, 2)) :: diag, arr @@ -780,12 +809,12 @@ function compute_DPR_generalized_dense(mtx, V, eigenvalues, eigenvectors, stx) r correction(:, j) = lapack_matrix_vector('N', arr, vec) do ii=1,size(correction,1) - if (gev) then - correction(ii, j) = correction(ii, j) / (eigenvalues(j) * stx(ii,ii) - mtx(ii, ii)) - else - correction(ii, j) = correction(ii, j) / (eigenvalues(j) - mtx(ii, ii)) - end if - end do + if (gev) then + correction(ii, j) = correction(ii, j) / (eigenvalues(j) * stx(ii,ii) - mtx(ii, ii)) + else + correction(ii, j) = correction(ii, j) / (eigenvalues(j) - mtx(ii, ii)) + endif + end do end do end function compute_DPR_generalized_dense diff --git a/src/lapack_wrapper.f90 b/src/lapack_wrapper.f90 index 9015fd4..3355b5f 100644 --- a/src/lapack_wrapper.f90 +++ b/src/lapack_wrapper.f90 @@ -7,7 +7,7 @@ module lapack_wrapper private !> \public public :: lapack_generalized_eigensolver, lapack_matmul, lapack_matrix_vector, & - lapack_qr, lapack_solver + lapack_qr, lapack_solver, lapack_sort contains @@ -280,6 +280,35 @@ function lapack_matrix_vector(transA, mtx, vector, alpha) result(rs) end function lapack_matrix_vector + + function lapack_sort(id, vector) result(keys) + !> \brief sort a vector of douboles + !> \param vector Array to sort + !> \param keys Indices of the sorted array + !> \param id Sorted either `I` increasing or `D` decreasing + real(dp), dimension(:), intent(inout) :: vector + character(len=1), intent(in) :: id + integer, dimension(size(vector)) :: keys + + ! local variables + real(dp), dimension(size(vector)) :: xs + integer :: i, j, info + xs = vector + + call DLASRT(id, size(vector), vector, info) + call check_lapack_call(info, "DLASRT") + + do i=1,size(vector) + do j=1, size(vector) + if (abs(vector(j) - xs(i)) < 1e-16) then + keys(i) = j + end if + end do + end do + + end function lapack_sort + + subroutine check_lapack_call(info, name) !> Check if a subroutine finishes sucessfully !> \param info: Termination signal diff --git a/src/main.f90 b/src/main.f90 index dbec38e..c614124 100644 --- a/src/main.f90 +++ b/src/main.f90 @@ -37,7 +37,7 @@ program main implicit none - integer, parameter :: dim = 50 + integer, parameter :: dim = 100 real(dp), dimension(3) :: eigenvalues_DPR, eigenvalues_GJD real(dp), dimension(dim, 3) :: eigenvectors_DPR, eigenvectors_GJD real(dp), dimension(dim, dim) :: mtx @@ -46,27 +46,29 @@ program main real(dp), dimension(dim) :: xs integer :: iter_i, j - mtx = generate_diagonal_dominant(dim, 1d-4) - stx = generate_diagonal_dominant(dim, 1d-4, 1d0) - - call generalized_eigensolver(mtx, eigenvalues_GJD, eigenvectors_GJD, 3, "GJD", 1000, 1d-8, iter_i, 10, stx) - call generalized_eigensolver(mtx, eigenvalues_DPR, eigenvectors_DPR, 3, "DPR", 1000, 1d-8, iter_i, 10, stx) + mtx = generate_diagonal_dominant(dim, 1d-3) + stx = generate_diagonal_dominant(dim, 1d-3, 1d0) + call generalized_eigensolver(mtx, eigenvalues_GJD, eigenvectors_GJD, 3, "GJD", 100, 1d-5, iter_i, 10, stx) + print *, "GJD algorithm converged in: ", iter_i, " iterations!" + call generalized_eigensolver(mtx, eigenvalues_DPR, eigenvectors_DPR, 3, "DPR", 100, 1d-5, iter_i, 10, stx) + print *, "DPR algorithm converged in: ", iter_i, " iterations!" + print *, "Test 1" test_norm_eigenvalues = norm(eigenvalues_GJD - eigenvalues_DPR) print *, "Check that eigenvalues norm computed by different methods are the same: ", test_norm_eigenvalues < 1e-6 print *, "Test 2" - print *, "Check that eigenvalue equation: H V = l S V " + print *, "Check that eigenvalue equation: H V = l S V holds!" print *, "DPR method:" do j=1,3 xs = matmul(mtx, eigenvectors_DPR(:, j)) - (eigenvalues_DPR(j) * matmul(stx, eigenvectors_DPR(:, j))) - print *, "eigenvalue ", j, ": ", eigenvalues_DPR(j), " : ", norm(xs) , " : ", norm(xs)< 1.d-7 + print *, "eigenvalue ", j, ": ", eigenvalues_DPR(j), "||Error||: ", norm(xs) end do print *, "GJD method:" do j=1,3 xs = matmul(mtx, eigenvectors_GJD(:, j)) - (eigenvalues_GJD(j) * matmul( stx, eigenvectors_GJD(:, j))) - print *, "eigenvalue ", j, ": ",eigenvalues_GJD(j), " : ", norm(xs), " : ", norm(xs)< 1.d-7 + print *, "eigenvalue ", j, ": ",eigenvalues_GJD(j), "||Error||: ", norm(xs) end do end program main diff --git a/src/tests/CMakeLists.txt b/src/tests/CMakeLists.txt index 3d36e19..253b742 100644 --- a/src/tests/CMakeLists.txt +++ b/src/tests/CMakeLists.txt @@ -17,7 +17,8 @@ foreach(PROG ${SOURCE_DAVIDSON}) endforeach(PROG) # set(NUMPY_TEST_SRC ${CMAKE_SOURCE_DIR}/src/davidson.f90 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diff --git a/src/tests/test_free_properties.f90 b/src/tests/test_free_properties.f90 index d3259b2..28af17f 100644 --- a/src/tests/test_free_properties.f90 +++ b/src/tests/test_free_properties.f90 @@ -23,21 +23,21 @@ program main call generalized_eigensolver(apply_mtx_to_vect, eigenvalues_DPR, eigenvectors_DPR, 3, "DPR", 1000, & 1d-8, iter_i, 20, apply_stx_to_vect) - print *, "eigenvalues: ", eigenvalues_DPR + print "(a, 3f8.4)", "eigenvalues: ", eigenvalues_DPR print *, "Test 1" print *, "Check that eigenvalue equation: H V = l B V holds" print *, "DPR method:" do j=1,3 xs = matmul(mtx, eigenvectors_DPR(:, j)) - (eigenvalues_DPR(j) * matmul(stx, eigenvectors_DPR(:, j))) - print *, "error: ", norm(xs) - print *, "eigenvalue ", j, ": ", eigenvalues_DPR(j), " succeeded: ", norm(xs) < 1d-8 + print "(a, e10.3)", "error: ", norm(xs) + print "(a, i2, a, e12.5, a, l)", "eigenvalue ", j, ": ", eigenvalues_DPR(j), " succeeded: ", norm(xs) < 1d-8 end do print *, "Test 2" print *, "If V are the eigenvector then V * V^T = I" zs = diagonal(matmul(eigenvectors_DPR, transpose(eigenvectors_DPR))) ! There are only 3 eigenvectors - print *, "DPR method: ", norm(zs(:3)) < sqrt(3.d0) + print "(a, l)", "DPR method: ", norm(zs(:3)) < sqrt(3.d0) end program main diff --git a/src/tests/test_reorder.f90 b/src/tests/test_reorder.f90 new file mode 100644 index 0000000..890c81f --- /dev/null +++ b/src/tests/test_reorder.f90 @@ -0,0 +1,36 @@ +program main + + use array_utils, only: diagonal, norm + use davidson, only: generalized_eigensolver + use numeric_kinds, only: dp + use test_utils, only: read_matrix + + implicit none + + integer, parameter :: dim = 864 + integer, parameter :: lowest = 6 + real(dp), dimension(lowest) :: eigenvalues_DPR, eigenvalues_GJD, expected + real(dp), dimension(dim, lowest) :: eigenvectors_DPR, eigenvectors_GJD + real(dp), dimension(dim, dim) :: mtx + integer :: iter_i + + mtx = read_matrix("../src/tests/data/bse_singlet.dat", dim) + + print *, "DPR Method" + call generalized_eigensolver(mtx, eigenvalues_DPR, eigenvectors_DPR, lowest, "DPR", 50, 1d-4, iter_i, lowest*3) + + expected = [0.30445426, 0.31341032, 0.31360998, 0.33246853, 0.34212415, 0.35761287] + + print "(a, i2)", "steps to convergence: ", iter_i + print "(a, 6f8.4)", "Eigenvalues:", eigenvalues_DPR + print "(a, e10.3)", "Relative error with expected eigenvalues: ", norm(eigenvalues_DPR - expected) + + print *, "GJD Method" + + call generalized_eigensolver(mtx, eigenvalues_GJD, eigenvectors_GJD, lowest, "GJD", 10, 1d-4, iter_i, lowest*2) + + print "(a, i2)", "steps to convergence: ", iter_i + print "(a, 6f8.4)", "Eigenvalues:", eigenvalues_GJD + print "(a, e10.3)", "Relative error with expected eigenvalues: ", norm(eigenvalues_GJD - expected) + +end program main