!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !> Methods for analyzing the results of electronic structure calculations. MODULE AnalysisModule USE CholeskyModule, ONLY : ConstructRankLookup, AppendToVector, & & BroadcastVector, ConstructDiag, DotAllHelper, DotAllPivoted, & & GatherMatrixColumn, GetPivot, UnpackCholesky USE DataTypesModule, ONLY : NTREAL, MPINTREAL USE DMatrixModule, ONLY : Matrix_ldr, DestructMatrix, & & ConstructMatrixDFromS USE LoggingModule, ONLY : EnterSubLog, ExitSubLog, WriteElement, & & WriteHeader, WriteListElement USE PSMatrixModule, ONLY : Matrix_ps, ConstructEmptyMatrix, & & TransposeMatrix, DestructMatrix, ConjugateMatrix, CopyMatrix, & & FillMatrixIdentity, PrintMatrixInformation, MergeMatrixLocalBlocks USE SMatrixModule, ONLY : Matrix_lsr USE SolverParametersModule, ONLY : SolverParameters_t, PrintParameters, & & DestructSolverParameters IMPLICIT NONE PRIVATE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! PUBLIC :: PivotedCholeskyDecomposition CONTAINS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !> Compute The Pivoted Cholesky Decomposition of a Hermitian Semi-Definite !> matrix. This is one way to generate localized orbitals. SUBROUTINE PivotedCholeskyDecomposition(AMat, LMat, rank_in, & & solver_parameters_in) !> The matrix A, must be hermitian, positive semi-definite. TYPE(Matrix_ps), INTENT(IN) :: AMat !> The matrix computed. TYPE(Matrix_ps), INTENT(INOUT) :: LMat !> The target rank of the matrix. INTEGER, INTENT(IN) :: rank_in !> Tarameters for the solver TYPE(SolverParameters_t), INTENT(IN), OPTIONAL :: solver_parameters_in !! Handling Optional Parameters TYPE(SolverParameters_t) :: solver_parameters !! For Pivoting INTEGER, DIMENSION(:), ALLOCATABLE :: pivot_vector REAL(NTREAL), DIMENSION(:), ALLOCATABLE :: diag INTEGER :: pi_j !! Local Variables TYPE(Matrix_lsr) :: sparse_a TYPE(Matrix_lsr) :: acol TYPE(Matrix_ldr) :: dense_a !! For Storing The Results INTEGER, DIMENSION(:), ALLOCATABLE :: values_per_column_l INTEGER, DIMENSION(:,:), ALLOCATABLE :: index_l REAL(NTREAL), DIMENSION(:,:), ALLOCATABLE :: values_l !! Broadcasted Column INTEGER, DIMENSION(:), ALLOCATABLE :: recv_index REAL(NTREAL), DIMENSION(:), ALLOCATABLE :: recv_values INTEGER :: recv_num_values !! Which pivots to treat locally INTEGER, DIMENSION(:), ALLOCATABLE :: local_pivots INTEGER :: num_local_pivots !! Root Lookups INTEGER, DIMENSION(:), ALLOCATABLE :: col_root_lookup !! Temporary Variables REAL(NTREAL), DIMENSION(:), ALLOCATABLE :: a_buf INTEGER :: II, JJ, local_JJ INTEGER :: local_pi_i, local_pi_j REAL(NTREAL) :: Aval, insert_value, inverse_factor REAL(NTREAL), DIMENSION(:), ALLOCATABLE :: dot_values INTEGER :: col_root INTEGER :: ierr !! Optional Parameters IF (PRESENT(solver_parameters_in)) THEN solver_parameters = solver_parameters_in ELSE solver_parameters = SolverParameters_t() END IF !! Print out parameters IF (solver_parameters%be_verbose) THEN CALL WriteHeader("Linear Solver") CALL EnterSubLog CALL WriteElement(key="Method", VALUE="Pivoted Cholesky Decomposition") CALL WriteElement(key="Target_Rank", VALUE=rank_in) CALL WriteHeader("Citations") CALL EnterSubLog CALL WriteListElement("aquilante2006fast") CALL ExitSubLog CALL PrintParameters(solver_parameters) END IF CALL ConstructEmptyMatrix(LMat, AMat) !! Construct the pivot vector ALLOCATE(pivot_vector(AMat%actual_matrix_dimension)) DO JJ = 1, AMat%actual_matrix_dimension pivot_vector(JJ) = JJ END DO !! First get the local matrix in a dense recommendation for quick lookup CALL MergeMatrixLocalBlocks(AMat, sparse_a) CALL ConstructMatrixDFromS(sparse_a, dense_a) ALLOCATE(local_pivots(sparse_a%columns)) !! Extract the diagonal ALLOCATE(diag(sparse_a%columns)) CALL ConstructDiag(AMat, Lmat%process_grid, dense_a, diag) !! Root Lookups ALLOCATE(col_root_lookup(AMat%logical_matrix_dimension)) CALL ConstructRankLookup(AMat, LMat%process_grid, col_root_lookup) !! Allocate space for L ALLOCATE(values_per_column_l(sparse_a%columns)) ALLOCATE(index_l(sparse_a%rows, sparse_a%columns)) ALLOCATE(values_l(sparse_a%rows, sparse_a%columns)) values_per_column_l = 0 !! Buffer for fast indexing of A ALLOCATE(a_buf(sparse_a%columns)) a_buf = 0 !! Allocate space for a received column ALLOCATE(recv_index(sparse_a%rows)) ALLOCATE(recv_values(sparse_a%rows)) ALLOCATE(dot_values(sparse_a%columns)) !! Pregather the full column of A. CALL GatherMatrixColumn(sparse_a, acol, LMat%process_grid) !! Main Loop DO JJ = 1, rank_in !! Pick a pivot vector local_JJ = JJ - AMat%start_row + 1 CALL GetPivot(AMat, LMat%process_grid, JJ, pivot_vector, diag, pi_j, & & insert_value, local_pivots, num_local_pivots) !! l[pi[j],j] = sqrt(d[pi[j]]) IF (pi_j .GE. AMat%start_column .AND. pi_j .LT. AMat%end_column) THEN local_pi_j = pi_j - AMat%start_column + 1 insert_value = SQRT(insert_value) inverse_factor = 1.0_NTREAL/insert_value !! Insert IF (JJ .GE. AMat%start_row .AND. JJ .LT. AMat%end_row) THEN CALL AppendToVector(values_per_column_l(local_pi_j), & & index_l(:,local_pi_j), values_l(:, local_pi_j), & & local_JJ, insert_value) END IF !! Extract column J for sending later recv_num_values = values_per_column_l(local_pi_j) recv_index(:recv_num_values) = index_l(:recv_num_values,local_pi_j) recv_values(:recv_num_values) = values_l(:recv_num_values, local_pi_j) END IF col_root = col_root_lookup(pi_j) !! Broadcast column JJ, and Inverse Factor CALL BroadcastVector(recv_num_values, recv_index, recv_values, & & col_root, LMat%process_grid%row_comm) CALL MPI_Bcast(inverse_factor, 1, MPINTREAL, col_root, & & LMat%process_grid%row_comm, ierr) !! Extract the row of A to a dense matrix for easy lookup DO II = MAX(acol%outer_index(pi_j),1), acol%outer_index(pi_j+1) a_buf(acol%inner_index(II)) = acol%values(II) END DO !! Compute Dot Products CALL DotAllPivoted(recv_num_values, recv_index, recv_values, & & values_per_column_l, index_l, values_l, local_pivots, & & num_local_pivots, dot_values, LMat%process_grid%column_comm) !! Loop over other columns DO II = 1, num_local_pivots !! Insert Into L local_pi_i = local_pivots(II) Aval = a_buf(local_pi_i) insert_value = inverse_factor * (Aval - dot_values(II)) IF (ABS(insert_value) .GT. solver_parameters%threshold) THEN IF (JJ .GE. AMat%start_row .AND. JJ .LT. AMat%end_row) THEN CALL AppendToVector(values_per_column_l(local_pi_i), & & index_l(:,local_pi_i), values_l(:, local_pi_i), & & local_JJ, insert_value) END IF END IF !! Update Diagonal Array diag(local_pi_i) = diag(local_pi_i) - insert_value**2 END DO !! Clear up the A buffer DO II = MAX(acol%outer_index(pi_j),1), acol%outer_index(pi_j+1) a_buf(acol%inner_index(II)) = 0 END DO END DO !! Unpack CALL UnpackCholesky(values_per_column_l, index_l, values_l, LMat) !! Cleanup IF (solver_parameters%be_verbose) THEN CALL PrintMatrixInformation(LMat) CALL ExitSubLog END IF DEALLOCATE(local_pivots) DEALLOCATE(pivot_vector) DEALLOCATE(diag) CALL DestructMatrix(dense_a) DEALLOCATE(values_per_column_l) DEALLOCATE(index_l) DEALLOCATE(values_l) DEALLOCATE(recv_index) DEALLOCATE(recv_values) DEALLOCATE(dot_values) DEALLOCATE(a_buf) DEALLOCATE(col_root_lookup) CALL DestructMatrix(sparse_a) CALL DestructMatrix(acol) END SUBROUTINE PivotedCholeskyDecomposition !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! END MODULE AnalysisModule