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gross |
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/* |
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******************************************************************************** |
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* Copyright 2006 by ACcESS MNF * |
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* * |
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* http://www.access.edu.au * |
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* Primary Business: Queensland, Australia * |
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* Licensed under the Open Software License version 3.0 * |
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* http://www.opensource.org/licenses/osl-3.0.php * |
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******************************************************************************** |
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*/ |
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/* Finley_Reduce determines a row and column permutation which, when applied to a given sparse matrix, produces a permuted */ |
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/* matrix with a smaller bandwidth and profile. the input array is a connection table which represents the */ |
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/* indices of the nonzero elements of the matrix, a. the algorithm is described in terms of the adjacency graph which */ |
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/* has the characteristic that there is an edge (connection) between nodes i and j if a(i,j) .ne. 0 and i .ne. j. */ |
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/* pattern_p(N,D1) D1 IS >= MAXIMUM degree_p OF ALL NODES. |
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/* label_p(D2) D2 AND N ARE >= THE TOTAL NUMBER OF |
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/* new_label_p(D2+1) NODES IN THE GRAPH. |
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/* degree_p(D2) STORAGE REQUIREMENTS CAN BE SIGNifICANTLY |
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/* assigned_level_p(D2) DECREASED FOR IBM 360 AND 370 COMPUTERS |
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/* forward_levels_p(D2) BY REPLACING INTEGER pattern_p BY |
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/* backward_levels_p(D2) INTEGER*2 pattern_p IN SUBROUTINES Finley_Reduce, |
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/* ConnectedComponents(D2) Finley_Reduce_setCharacteristics, Finley_Reduce_findDiameter, Paso_SystemMatrixPattern_dropTree AND NUMBER. |
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/* COMMON INFORMATION--THE FOLLOWING COMMON BLOCK MUST BE IN THE |
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/* CALLING ROUTINE. |
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/* COMMON/GRA/N,num_levels,ndeg_max |
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/* EXPLANATION OF INPUT VARIABLES-- |
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/* pattern_p- CONNECTION TABLE REPRESENTING GRAPH. |
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/* pattern_p->index[iptr]=NODE NUMBER OF JTH CONNECTION TO NODE |
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/* NUMBER I. A CONNECTION OF A NODE TO ITSELF IS NOT |
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/* LISTED. EXTRA POSITIONS MUST HAVE ZERO FILL. |
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/* N- ROW DIMENSION ASSIGNED pattern_p IN CALLING PROGRAM. |
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/* label_p[i]- NUMBERING OF ITH NODE UPON INPUT. if NO NUMBERING EXISTS THEN label_p[i]=I. |
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/* N- NUMBER OF NODES IN GRAPH (EQUAL TO ORDER OF MATRIX). |
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/* ndeg_max- MAXIMUM degree_p OF ANY NODE IN THE GRAPH. |
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/* degree_p[i]- THE degree_p OF THE ITH NODE. |
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/* EXPLANATION OF OUTPUT VARIABLES-- |
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/* new_label_p[i]- THE NEW NUMBER FOR THE ITH NODE. |
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/* newBandwidth- THE BANDWIDTH AFTER numbering . |
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/* newProfile- THE PROFILE AFTER numbering . |
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/* num_levels - NUMBER OF LEVELS IN Finley_Reduce LEVEL STRUCTURE. |
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/* */ |
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/* The following only have meaning if the graph was connected: |
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/* assigned_level_p[i]- INDEX INTO forward_levels_p TO THE FIRST NODE IN LEVEL I. assigned_level_p(I+1)-assigned_level_p[i]= number of nodes in ith leveL |
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/* forward_levels_p- node numbers listed by level |
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/* backward_levels_p[i]- the level assigned to node i by Finley_Reduce. |
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/* WORKING STORAGE VARIABLE-- |
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/* ConnectedComponents |
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/* LOCAL STORAGE-- |
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/* COMMON/CC/-SUBROUTINES Finley_Reduce, SORT2 AND PIKassigned_level_p ASSUME THAT |
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/* THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
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/* SUBROUTINE Finley_Reduce_findDiameter ASSUMES THAT THERE ARE AT MOST |
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/* 100 NODES IN THE LAST LEVEL. |
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/* COMMON/assigned_level_pW/-SUBROUTINES Finley_Reduce_setup AND PIKassigned_level_p ASSUME THAT THERE |
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/* ARE AT MOST 100 LEVELS. |
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SUBROUTINE Finley_Reduce(pattern_p, N, label_p, new_label_p, degree_p, assigned_level_p, forward_levels_p,backward_levels_p, ConnectedComponents, newBandwidth, newProfile, NIN, ndeg_maxIN) |
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/* USE INTEGER*2 pattern_p WITH AN IBM 360 OR 370. |
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integer NIN, ndeg_maxIN |
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INTEGER pattern_p |
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INTEGER start_node, end_node, new_label_p, ConnectedComponentCounter, SORT2, last_available_node_number, ConnectedComponents, |
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* SIZE, STPT, first_available_node_number |
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COMMON /GRA/ N, num_levels, ndeg_max |
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/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
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COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
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COMMON /assigned_level_pW/ NHIGH(100), NLOW(100), NACUM(100) |
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DIMENSION ConnectedComponents(1), label_p(1) |
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DIMENSION pattern_p(N,1), assigned_level_p(1), forward_levels_p(1), backward_levels_p(1), new_label_p(1), |
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* degree_p(1) |
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newBandwidth = 0 |
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newProfile = 0 |
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/* SET new_label_p[i]=0 FOR ALL I TO INDICATE NODE I IS UNNUMBERED |
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c |
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c N = N |
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c do i=0,i<N,++i) |
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c if(ndeg_max<degree_p[i]) then |
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c ndeg_max = degree_p[i] |
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c end if |
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c end do |
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c |
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set degree_p |
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N=NIN |
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ndeg_max = ndeg_maxIN |
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for (i=0,i<N,++i) { |
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degree_p[i]=ptr[i+1]-ptr[i]; |
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new_label_p[i] = 0; |
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} |
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/* COMPUTE degree_p OF EACH NODE AND ORIGINAL BANDWIDTH AND PROFILE*/ |
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=============================== |
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Paso_SystemMatrixpattern_p* pattern_p, |
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long initial_bandwidth, initial_profile |
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dim_t *degree_p=NULL; |
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dim_t N = pattern_p->n_ptr; |
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index_t *label_p_p=NULL; |
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degree_p=MEMALLOC(N,dim_t); |
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label_p_p=MEMALLOC(N,index_t); |
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new_label_p=MEMALLOC(N,index_t); |
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if (sdsadsad) { |
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/* get the initial bandwidth and profile */ |
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for (i=0,i<N,++i) { |
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degree_p[i]=pattern_p->ptr[i+1]-pattern_p->ptr[i]-1; |
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label_p[i]=i; |
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new_label_p[i]=0; |
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} |
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Finley_Reduce_setCharacteristics(pattern_p, degree_p, label_p, *initial_bandwidth, *initial_profile) |
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printf("initial bandwidth and profile: %dl %dl\n",initial_bandwidth, initial_profile); |
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/* first_available_node_number = low end of available numbers for numbering */ |
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/* last_available_node_number = high end of available numbers for numbering */ |
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first_available_node_number = 0; |
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last_available_node_number = N; |
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/* number the nodes of degree_p zero are last: */ |
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for (i=0,i<N,++i) { |
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if (degree_p[i]==0) { |
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new_label_p[i] = last_available_node_number; |
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last_available_node_number--; |
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} |
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} |
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} |
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} |
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/* find an unnumbered node of min degree to start on */ |
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while (first_available_node_number<=last_available_node_number) { |
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reverse_diameter_tree = FALSE; |
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SDIR = 1; |
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/* find the node with smallest degree and use this one as start node */ |
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smallest_degree = N + 1; |
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for (i=0,i<N,++i) { |
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if (degree_p[i]<smallest_degree && new_label_p[i]<=0) { |
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smallest_degree = degree_p[i]; |
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start_node = i; |
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} |
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} |
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/* find pseudo-diameter and associated level structures marked assigned_level_p: */ |
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/* start_node and end_node are the ends of the diameter and |
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forward_levels_p and backward_levels_p are the respective level structures. */ |
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Finley_Reduce_findDiameter(*start_node, end_node, pattern_p, degree_p, |
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assigned_level_p, forward_levels_p,backward_levels_p, ConnectedComponents, IDFLT) |
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/* reverse_diameter_tree INDICATES THE END TO BEGIN NUMBERING ON */ |
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if (degree_p(start_node)>degree_p(end_node)) { |
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reverse_diameter_tree = TRUE; |
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start_node = end_node; |
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} else { |
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reverse_diameter_tree = FALSE; |
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} |
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######### |
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CALL Finley_Reduce_setup(assigned_level_p, forward_levels_p, backward_levels_p) |
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/* find all the connected components (ConnectedComponentCounter counts them) */ |
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ConnectedComponentCounter = 0; |
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LROOT = 1 |
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first_available_in_list_of_tree_nodes = 1 |
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for (i=0,i<N,++i) { |
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if (assigned_level_p[i]==0) { |
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ConnectedComponentCounter++; |
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STPT(ConnectedComponentCounter) = LROOT |
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CALL Paso_SystemMatrixPattern_dropTree(I, pattern_p, N, assigned_level_p, ConnectedComponents, degree_p, last_level_width, first_node_in_bottom_level,first_available_in_list_of_tree_nodes, max_level_width, N) |
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SIZE(ConnectedComponentCounter) = first_node_in_bottom_level + last_level_width - LROOT |
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LROOT = first_node_in_bottom_level + last_level_width |
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first_available_in_list_of_tree_nodes = LROOT |
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} |
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} |
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/* on return from PIKassigned_level_p, DirectionLargestComponent indicates the direction the largest component fell. */ |
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/* DirectionLargestComponent is modIFied now to indicate the numbering direction. num is set to the proper value for this direction. */ |
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if (SORT2(DMY)!=0) PIKassigned_level_p(forward_levels_p, backward_levels_p, ConnectedComponents, IDFLT, DirectionLargestComponent) |
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DirectionLargestComponent = DirectionLargestComponent*reverse_diameter_tree; |
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NUM= (DirectionLargestComponent<0) ? last_available_node_number :first_available_node_number; |
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CALL NUMBER(start_node, NUM, pattern_p, backward_levels_p, degree_p, new_label_p, forward_levels_p, |
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* assigned_level_p, N, reverse_diameter_tree, newBandwidth, newProfile, ConnectedComponents, DirectionLargestComponent) |
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/* update last_available_node_number or first_available_node_number after numbering */ |
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if (DirectionLargestComponent<0) last_available_node_number = NUM; |
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if (DirectionLargestComponent>0) first_available_node_number = NUM; |
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} |
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/* if original numbering is better than new one, set up to return it */ |
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if (newBandwidth > initial_bandwidth) { |
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for (i=0,i<N,++i) |
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new_label_p[i] = label_p[i]; |
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*newBandwidth = initial_bandwidth; |
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*newProfile = initial_profile; |
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} |
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} |
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=============================================== |
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/* Finley_Reduce_setCharacteristics computes the degree_p of each node and stores it in the array degree_p. */ |
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/* the bandwidth and profile for the original or input numbering of the graph is computed also. */ |
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void Finley_Reduce_setCharacteristics(Paso_SystemMatrixpattern_p *pattern_p, |
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dim_t *degree_p, |
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dim_t* label_p, |
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long *bandwidth,long *initial_profile) { |
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long max_diff; |
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dim_t i; |
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*bandwidth = 0; |
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*profile = 0; |
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for (i=0,i<pattern_p->n_ptr,++i) { |
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max_diff = 0; |
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for (iptr=pattern_p->ptr[i],iptr<pattern_p->ptr[i+1],++i) { |
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diff = label_p[i] - label_p(pattern_p->index[iptr]); |
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max_diff = MAX(max_diff,diff); |
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} |
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*profile + = max_diff; |
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*bandwidth=MAX(*bandwidth,max_diff); |
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} |
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} |
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void Paso_SystemMatrixPattern_sortByDegree(index_t* node_index1, index_t* node_index2, dim_t* num_nodes1, dim_t num_nodes2, dim_t* degree_p) |
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{ |
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/* Paso_SystemMatrixPattern_sortByDegree sorts node_index2 by degree_p of the NODE AND ADDS IT TO THE END |
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OF node_index1 IN ORDER OF LOWEST TO HIGHEST degree_p. num_nodes1 AND num_nodes2 ARE THE |
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NUMBER OF NODES IN node_index1 AND node_index2 RESPECTIVELY. |
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*/ |
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register bool_t swapped=TRUE; |
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register dim_t i, ipp; |
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register index_t node_index2_i, node_index2_ipp, temp; |
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register dim_t j=num_nodes2; |
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while (swapped && j>1) { |
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j--; |
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swapped = FALSE; |
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for (i=0; i<j; ++i) { |
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ipp=i+1 |
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node_index2_i = node_index2[i] |
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node_index2_ipp = node_index2[ipp] |
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if (degree_p[node_index2_i]>degree_p[node_index2_ipp]) { |
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swapped= TRUE; |
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temp = node_index2[i]; |
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node_index2[i] = node_index2[ipp]; |
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node_index2[ipp] = temp; |
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} |
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} |
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} |
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for (i=0; i< num_nodes2; ++i) { |
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(*num_nodes1)++; |
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node_index1[num_nodes1] = node_index2[i] |
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} |
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return; |
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} |
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void Finley_Reduce_findDiameter(index_t *start_node, |
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index_t *end_node, |
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Paso_SystemMatrixPattern *pattern_p, |
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dim_t* degree_p, |
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index_t* forward_levels_p, |
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index_t* backward_levels_p, |
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*IDFLT, |
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index_t* work1_p, |
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index_t* work2_p, |
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index_t* node_list_p, |
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) |
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/* |
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Finley_Reduce_findDiameter is the control procedure for finding the pseudo-diameter of pattern |
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as well as the level structure from each end |
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start_node- on input this is the node number of the first attempt at finding a diameter. |
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on output it contains the actual number used. |
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end_node - on output contains other end of diameter |
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forward_levels_p- ARRAY CONTAINING LEVEL STRUCTURE WITH start_node AS ROOT |
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backward_levels_p- ARRAY CONTAINING LEVEL STRUCTURE WITH end_node AS ROOT |
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IDFLT- reverse_diameter_tree USED IN PICKING FINAL LEVEL STRUCTURE, SET |
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=1 if WIDTH OF forward_levels_p <= WIDTH OF backward_levels_p, OTHERWISE =2 |
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assigned_level_p, list_of_tree_nodes_p- WORKING STORAGE |
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*/ |
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/* COMMON /GRA/ N, num_levels, ndeg_max |
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IT IS ASSUMED THAT THE LAST LEVEL HAS AT MOST 100 NODES. |
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COMMON /CC/ node_list(100) |
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DIMENSION pattern_p(N,1), degree_p(1), assigned_level_p(1), forward_levels_p(1), backward_levels_p(1),list_of_tree_nodes_p(1) |
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*/ |
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dim_t num_tree_nodes; |
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dim_t N= pattern->n_ptr; |
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bool_t find_new_starting_nodes=TRUE; |
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/* find initial set of nodes as the end points of the tree created by root */ |
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while (find_new_starting_nodes) { |
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num_tree_nodes = 0; |
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/* zero assigned_level_p to indicate all nodes are available to Paso_SystemMatrixPattern_dropTree */ |
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for (i=0,i<N,++i) forward_levels_p[i] = -1; |
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Paso_SystemMatrixPattern_dropTree(*(start_node), |
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pattern_p, |
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forward_levels_p, |
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work2_p, |
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degree_p, |
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num_tree_nodes, first_node_in_bottom_level, |
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first_available_in_list_of_tree_nodes, |
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|
|
num_levels, max_level_width_abort1, N) |
| 309 |
|
|
|
| 310 |
|
|
node_list_len = 0; |
| 311 |
|
|
/* sort last level by degree_p and store in node_list_p */ |
| 312 |
|
|
Paso_SystemMatrixPattern_sortByDegree(node_list_p, &(work2_p[first_node_in_bottom_level]), |
| 313 |
|
|
*node_list_len, last_level_width, degree_p) |
| 314 |
|
|
|
| 315 |
|
|
find_new_starting_nodes=FALSE; |
| 316 |
|
|
/* now start searching from the ends points of the initial search */ |
| 317 |
|
|
NDXN=0; |
| 318 |
|
|
while (NDXN < node_list_len) { |
| 319 |
|
|
start_node2 = node_list[NDXN]; |
| 320 |
|
|
|
| 321 |
|
|
/* drop a tree from start_node2 */ |
| 322 |
|
|
for (i=0;i<N;++i) assigned_level_p[i] = -1; |
| 323 |
|
|
num_tree_nodes = 0; |
| 324 |
|
|
Paso_SystemMatrixPattern_dropTree(start_node2, |
| 325 |
|
|
pattern_p, |
| 326 |
|
|
work1_p, |
| 327 |
|
|
work2_p, |
| 328 |
|
|
degree_p, last_level_width, first_node_in_bottom_level, |
| 329 |
|
|
num_tree_nodes, |
| 330 |
|
|
num_levels2, |
| 331 |
|
|
max_level_width, max_level_width_abort); |
| 332 |
|
|
if (num_levels2<num_levels) { |
| 333 |
|
|
start_node = start_node2 |
| 334 |
|
|
find_new_starting_nodes=TRUE; |
| 335 |
|
|
break; |
| 336 |
|
|
} |
| 337 |
|
|
/* STORE NARROWEST REVERSE LEVEL STRUCTURE IN backward_levels_p */ |
| 338 |
|
|
if (max_level_width<max_level_width_abort) { |
| 339 |
|
|
max_level_width_abort = max_level_width; |
| 340 |
|
|
end_node = start_node2; |
| 341 |
|
|
for (i=0;i<N;++i) backward_levels_p[i] = work1_p[i]; |
| 342 |
|
|
} |
| 343 |
|
|
NDXN++; |
| 344 |
|
|
} |
| 345 |
|
|
if (max_level_width_abort2<=max_level_width_abort1) |
| 346 |
|
|
*IDFLT = 2 |
| 347 |
|
|
} else { |
| 348 |
|
|
*IDFLT=1 |
| 349 |
|
|
} |
| 350 |
|
|
return |
| 351 |
|
|
} |
| 352 |
|
|
|
| 353 |
|
|
void Paso_SystemMatrixPattern_dropTree(index_t root, |
| 354 |
|
|
Paso_SystemMatrixPattern *pattern_p, |
| 355 |
|
|
index_t *assigned_level_p, |
| 356 |
|
|
index_t *list_of_tree_nodes_p, |
| 357 |
|
|
index_t *last_level_width, |
| 358 |
|
|
index_t *first_node_in_bottom_level, |
| 359 |
|
|
index_t *first_available_in_list_of_tree_nodes, |
| 360 |
|
|
dim_t *num_levels, |
| 361 |
|
|
dim_t *max_level_width, dim_t max_level_width_abort) |
| 362 |
|
|
|
| 363 |
|
|
/* |
| 364 |
|
|
Paso_SystemMatrixPattern_dropTree drops a tree in pattern_p from root |
| 365 |
|
|
|
| 366 |
|
|
assigned_level_p- array of length length pattern_p->N indicating available nodes with -1 entries. |
| 367 |
|
|
Paso_SystemMatrixPattern_dropTree enters level numbers . |
| 368 |
|
|
|
| 369 |
|
|
list_of_tree_nodes_p - on output contains node numbers used in tree (array of length pattern_p->N) |
| 370 |
|
|
sorted by levels where list_of_tree_nodes_p[first_available_in_list_of_tree_nodes] |
| 371 |
|
|
contains root and list_of_tree_nodes_p[first_node_in_bottom_level+last_level_width-1] |
| 372 |
|
|
contains last node entered) |
| 373 |
|
|
|
| 374 |
|
|
last_level_width - on output contains width of last level |
| 375 |
|
|
first_node_in_bottom_level - on output contains index into list_of_tree_nodes_p of first node in last level |
| 376 |
|
|
|
| 377 |
|
|
first_available_in_list_of_tree_nodes- |
| 378 |
|
|
on input the first available location in list_of_tree_nodes_p |
| 379 |
|
|
usually zero but if list_of_tree_nodes_p is used to store previous |
| 380 |
|
|
connected components, first_available_in_list_of_tree_nodes is |
| 381 |
|
|
next available location. on output the |
| 382 |
|
|
|
| 383 |
|
|
num_levels - number of levels |
| 384 |
|
|
|
| 385 |
|
|
max_level_width - on output contains the maximum level width |
| 386 |
|
|
max_level_width_abort- input param which triggers early return if max_level_width becomes >= max_level_width_abort |
| 387 |
|
|
|
| 388 |
|
|
*/ |
| 389 |
|
|
|
| 390 |
|
|
dim_t j; |
| 391 |
|
|
index_t node_now; |
| 392 |
|
|
index_t i_top = first_available_in_list_of_tree_nodes; |
| 393 |
|
|
index_t i_now = first_available_in_list_of_tree_nodes; |
| 394 |
|
|
*max_level_width = 0; |
| 395 |
|
|
*first_node_in_bottom_level = first_available_in_list_of_tree_nodes; |
| 396 |
|
|
*top_level = first_available_in_list_of_tree_nodes + 1; |
| 397 |
|
|
*num_levels = 0 |
| 398 |
|
|
|
| 399 |
|
|
assigned_level_p[root] = *num_levels; |
| 400 |
|
|
list_of_tree_nodes_p[i_top] = root; |
| 401 |
|
|
|
| 402 |
|
|
while ( ( max_level_width<max_level_width_abort ) && ( i_top >=top_level ) ) { |
| 403 |
|
|
|
| 404 |
|
|
num_levels++; |
| 405 |
|
|
|
| 406 |
|
|
while (i_now>=top_level) { |
| 407 |
|
|
node_now = list_of_tree_nodes_p[i_now]; |
| 408 |
|
|
for (j=pattern_p->iptr[node_now],j<pattern_p->iptr[node_now+1],++j) { |
| 409 |
|
|
index = pattern_p->index[j]; |
| 410 |
|
|
if (assigned_level_p[index]<0) { |
| 411 |
|
|
assigned_level_p[index] = (*num_levels); |
| 412 |
|
|
i_top++; |
| 413 |
|
|
list_of_tree_nodes_p[i_top] = index |
| 414 |
|
|
} |
| 415 |
|
|
} |
| 416 |
|
|
i_now++; |
| 417 |
|
|
} |
| 418 |
|
|
*last_level_width = top_level - first_node_in_bottom_level; |
| 419 |
|
|
*max_level_width = MAX(*max_level_width, last_level_width); |
| 420 |
|
|
*first_node_in_bottom_level = i_now; |
| 421 |
|
|
*top_level = i_top + 1; |
| 422 |
|
|
} |
| 423 |
|
|
} |
| 424 |
|
|
|
| 425 |
|
|
SUBROUTINE Finley_Reduce_setup(assigned_level_p, forward_levels_p, backward_levels_p) SET 10 |
| 426 |
|
|
/* Finley_Reduce_setup COMPUTES THE REVERSE LEVELING INFO FROM backward_levels_p AND STORES |
| 427 |
|
|
/* IT INTO backward_levels_p. NACUM[i] IS INITIALIZED TO NODES/ITH LEVEL FOR NODES |
| 428 |
|
|
/* ON THE PSEUDO-diameter OF THE GRAPH. assigned_level_p IS INITIALIZED TO NON- |
| 429 |
|
|
/* ZERO FOR NODES ON THE PSEUDO-diameter AND NODES IN A DifFERENT |
| 430 |
|
|
/* COMPONENT OF THE GRAPH. |
| 431 |
|
|
COMMON /GRA/ N, num_levels, ndeg_max |
| 432 |
|
|
/* IT IS ASSUMED THAT THERE ARE AT MOST 100 LEVELS. |
| 433 |
|
|
COMMON /assigned_level_pW/ NHIGH(100), NLOW(100), NACUM(100) |
| 434 |
|
|
DIMENSION assigned_level_p(1), forward_levels_p(1), backward_levels_p(1) |
| 435 |
|
|
for (10 I=1,num_levels |
| 436 |
|
|
NACUM[i] = 0 |
| 437 |
|
|
10 CONTINUE |
| 438 |
|
|
for (30 i=0,i<N,++i) |
| 439 |
|
|
assigned_level_p[i] = 1 |
| 440 |
|
|
backward_levels_p[i] = num_levels + 1 - backward_levels_p[i] |
| 441 |
|
|
Itemp = backward_levels_p[i] |
| 442 |
|
|
if (Itemp>num_levels) GO TO 30 |
| 443 |
|
|
if (Itemp!=forward_levels_p[i]) GO TO 20 |
| 444 |
|
|
NACUM(Itemp) = NACUM(Itemp) + 1 |
| 445 |
|
|
GO TO 30 |
| 446 |
|
|
20 assigned_level_p[i] = 0 |
| 447 |
|
|
30 CONTINUE |
| 448 |
|
|
RETURN |
| 449 |
|
|
END |
| 450 |
|
|
INTEGER FUNCTION SORT2(DMY) SOR 10 |
| 451 |
|
|
/* SORT2 SORTS SIZE AND STPT INTO DESCENDING ORDER ACCORDING TO |
| 452 |
|
|
/* VALUES OF SIZE. ConnectedComponentCounter=NUMBER OF ENTRIES IN EACH ARRAY |
| 453 |
|
|
INTEGER temp, ConnectedComponents, SIZE, STPT, ConnectedComponentCounter |
| 454 |
|
|
/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 CONNECTED COMPONENTS. |
| 455 |
|
|
COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
| 456 |
|
|
SORT2 = 0 |
| 457 |
|
|
if (ConnectedComponentCounter.EQ.0) RETURN |
| 458 |
|
|
SORT2 = 1 |
| 459 |
|
|
IND = ConnectedComponentCounter |
| 460 |
|
|
10 ITEST = 0 |
| 461 |
|
|
IND = IND - 1 |
| 462 |
|
|
if (IND<1) RETURN |
| 463 |
|
|
for (20 I=1,IND |
| 464 |
|
|
J = I + 1 |
| 465 |
|
|
if (SIZE[i]>=SIZE(J)) GO TO 20 |
| 466 |
|
|
ITEST = 1 |
| 467 |
|
|
temp = SIZE[i] |
| 468 |
|
|
SIZE[i] = SIZE(J) |
| 469 |
|
|
SIZE(J) = temp |
| 470 |
|
|
temp = STPT[i] |
| 471 |
|
|
STPT[i] = STPT(J) |
| 472 |
|
|
STPT(J) = temp |
| 473 |
|
|
20 CONTINUE |
| 474 |
|
|
if (ITEST.EQ.1) GO TO 10 |
| 475 |
|
|
RETURN |
| 476 |
|
|
END |
| 477 |
|
|
SUBROUTINE PIKassigned_level_p(forward_levels_p, backward_levels_p, ConnectedComponents, IDFLT, DirectionLargestComponent) PIK 10 |
| 478 |
|
|
/* PIKassigned_level_p CHOOSES THE LEVEL STRUCTURE USED IN NUMBERING GRAPH |
| 479 |
|
|
/* forward_levels_p- ON INPUT CONTAINS FORWARD LEVELING INFO |
| 480 |
|
|
/* backward_levels_p- ON INPUT CONTAINS REVERSE LEVELING INFO |
| 481 |
|
|
/* ON OUTPUT THE FINAL LEVEL STRUCTURE CHOSEN |
| 482 |
|
|
/* ConnectedComponents- ON INPUT CONTAINS CONNECTED COMPONENT INFO |
| 483 |
|
|
/* IDFLT- ON INPUT =1 if WDTH forward_levels_p<=WDTH backward_levels_p, =2 OTHERWISE |
| 484 |
|
|
/* NHIGH KEEPS TRACK OF LEVEL WIDTHS FOR HIGH NUMBERING |
| 485 |
|
|
/* NLOW- KEEPS TRACK OF LEVEL WIDTHS FOR LOW NUMBERING |
| 486 |
|
|
/* NACUM- KEEPS TRACK OF LEVEL WIDTHS FOR CHOSEN LEVEL STRUCTURE |
| 487 |
|
|
/* ConnectedComponentCounter- NUMBER OF CONNECTED COMPONENTS |
| 488 |
|
|
/* SIZE[i]- SIZE OF ITH CONNECTED COMPONENT |
| 489 |
|
|
/* STPT[i]- INDEX INTO ConnectedComponentsE OF 1ST NODE IN ITH CON COMPT |
| 490 |
|
|
/* DirectionLargestComponent- reverse_diameter_tree WHICH INDICATES WHICH WAY THE LARGEST CONNECTED |
| 491 |
|
|
/* COMPONENT FELL. =+1 if LOW AND -1 if HIGH |
| 492 |
|
|
INTEGER ConnectedComponents, SIZE, STPT, ConnectedComponentCounter, END |
| 493 |
|
|
COMMON /GRA/ N, num_levels, ndeg_max |
| 494 |
|
|
/* IT IS ASSUMED THAT THE GRAPH HAS AT MOST 50 COMPONENTS AND |
| 495 |
|
|
/* THAT THERE ARE AT MOST 100 LEVELS. |
| 496 |
|
|
COMMON /assigned_level_pW/ NHIGH(100), NLOW(100), NACUM(100) |
| 497 |
|
|
COMMON /CC/ ConnectedComponentCounter, SIZE(50), STPT(50) |
| 498 |
|
|
DIMENSION forward_levels_p(1), backward_levels_p(1), ConnectedComponents(1) |
| 499 |
|
|
/* FOR EACH CONNECTED COMPONENT DO |
| 500 |
|
|
for (80 I=1,ConnectedComponentCounter |
| 501 |
|
|
J = STPT[i] |
| 502 |
|
|
END = SIZE[i] + J - 1 |
| 503 |
|
|
/* SET NHIGH AND NLOW EQUAL TO NACUM |
| 504 |
|
|
for (10 K=1,num_levels |
| 505 |
|
|
NHIGH(K) = NACUM(K) |
| 506 |
|
|
NLOW(K) = NACUM(K) |
| 507 |
|
|
10 CONTINUE |
| 508 |
|
|
/* UPDATE NHIGH AND NLOW FOR EACH NODE IN CONNECTED COMPONENT |
| 509 |
|
|
for (20 K=J,END |
| 510 |
|
|
INODE = ConnectedComponents(K) |
| 511 |
|
|
first_available_in_list_of_tree_nodesH = forward_levels_p(INODE) |
| 512 |
|
|
NHIGH(first_available_in_list_of_tree_nodesH) = NHIGH(first_available_in_list_of_tree_nodesH) + 1 |
| 513 |
|
|
first_available_in_list_of_tree_nodesL = backward_levels_p(INODE) |
| 514 |
|
|
NLOW(first_available_in_list_of_tree_nodesL) = NLOW(first_available_in_list_of_tree_nodesL) + 1 |
| 515 |
|
|
20 CONTINUE |
| 516 |
|
|
MAnum_nodes1 = 0 |
| 517 |
|
|
MAnum_nodes2 = 0 |
| 518 |
|
|
/* SET MAnum_nodes1=LARGEST NEW NUMBER IN NHIGH |
| 519 |
|
|
/* SET MAnum_nodes2=LARGEST NEW NUMBER IN NLOW |
| 520 |
|
|
for (30 K=1,num_levels |
| 521 |
|
|
if (2*NACUM(K).EQ.NLOW(K)+NHIGH(K)) GO TO 30 |
| 522 |
|
|
if (NHIGH(K)>MAnum_nodes1) MAnum_nodes1 = NHIGH(K) |
| 523 |
|
|
if (NLOW(K)>MAnum_nodes2) MAnum_nodes2 = NLOW(K) |
| 524 |
|
|
30 CONTINUE |
| 525 |
|
|
/* SET IT= NUMBER OF LEVEL STRUCTURE TO BE USED |
| 526 |
|
|
IT = 1 |
| 527 |
|
|
if (MAnum_nodes1>MAnum_nodes2) IT = 2 |
| 528 |
|
|
if (MAnum_nodes1.EQ.MAnum_nodes2) IT = IDFLT |
| 529 |
|
|
if (IT.EQ.2) GO TO 60 |
| 530 |
|
|
if (I.EQ.1) DirectionLargestComponent = -1 |
| 531 |
|
|
/* COPY forward_levels_p INTO backward_levels_p FOR EACH NODE IN CONNECTED COMPONENT |
| 532 |
|
|
for (40 K=J,END |
| 533 |
|
|
INODE = ConnectedComponents(K) |
| 534 |
|
|
backward_levels_p(INODE) = forward_levels_p(INODE) |
| 535 |
|
|
40 CONTINUE |
| 536 |
|
|
/* UPDATE NACUM TO BE THE SAME AS NHIGH |
| 537 |
|
|
for (50 K=1,num_levels |
| 538 |
|
|
NACUM(K) = NHIGH(K) |
| 539 |
|
|
50 CONTINUE |
| 540 |
|
|
GO TO 80 |
| 541 |
|
|
/* UPDATE NACUM TO BE THE SAME AS NLOW |
| 542 |
|
|
60 for (70 K=1,num_levels |
| 543 |
|
|
NACUM(K) = NLOW(K) |
| 544 |
|
|
70 CONTINUE |
| 545 |
|
|
80 CONTINUE |
| 546 |
|
|
RETURN |
| 547 |
|
|
END |
| 548 |
|
|
SUBROUTINE NUMBER(start_node2, NUM, pattern_p, backward_levels_p, degree_p, new_label_p, assigned_level_pST, NUM 10 |
| 549 |
|
|
* LSTPT, N, reverse_diameter_tree, newBandwidth, newProfile, IPFA, DirectionLargestComponent) |
| 550 |
|
|
/* NUMBER PRODUCES THE NUMBERING OF THE GRAPH FOR MIN BANDWIDTH |
| 551 |
|
|
/* start_node2- ON INPUT THE NODE TO BEGIN NUMBERING ON |
| 552 |
|
|
/* NUM- ON INPUT AND OUTPUT, THE NEXT AVAILABLE NUMBER |
| 553 |
|
|
/* backward_levels_p- THE LEVEL STRUCTURE TO BE USED IN NUMBERING |
| 554 |
|
|
/* new_label_p- THE ARRAY USED TO STORE THE NEW NUMBERING |
| 555 |
|
|
/* assigned_level_pST- ON OUTPUT CONTAINS LEVEL STRUCTURE |
| 556 |
|
|
/* LSTPT[i]- ON OUTPUT, INDEX INTO assigned_level_pST TO FIRST NODE IN ITH assigned_level_p |
| 557 |
|
|
/* LSTPT(I+1) - LSTPT[i] = NUMBER OF NODES IN ITH assigned_level_p |
| 558 |
|
|
/* reverse_diameter_tree- =+1 if start_node2 IS FORWARD END OF PSEUDO-diameter |
| 559 |
|
|
/* =-1 if start_node2 IS REVERSE END OF PSEUDO-diameter |
| 560 |
|
|
/* newBandwidth- BANDWIDTH OF NEW NUMBERING COMPUTED BY NUMBER |
| 561 |
|
|
/* newProfile- PROFILE OF NEW NUMBERING COMPUTED BY NUMBER |
| 562 |
|
|
/* IPFA- WORKING STORAGE USED TO COMPUTE PROFILE AND BANDWIDTH |
| 563 |
|
|
/* DirectionLargestComponent- INDICATES STEP DIRECTION USED IN NUMBERING(+1 OR -1) |
| 564 |
|
|
/* USE INTEGER*2 pattern_p WITH AN IBM 360 OR 370. |
| 565 |
|
|
INTEGER pattern_p |
| 566 |
|
|
INTEGER start_node2, node_indexA, node_indexB, node_indexC, node_indexD, XA, XB, ConnectedComponentCounter, XD, CX, END, |
| 567 |
|
|
* new_label_p, TEST |
| 568 |
|
|
COMMON /GRA/ N, num_levels, ndeg_max |
| 569 |
|
|
/* THE STORAGE IN COMMON BLOCKS CC AND assigned_level_pW IS NOW FREE AND CAN |
| 570 |
|
|
/* BE USED FOR STACKS. |
| 571 |
|
|
COMMON /assigned_level_pW/ node_indexA(100), node_indexB(100), node_indexC(100) |
| 572 |
|
|
COMMON /CC/ node_indexD(100) |
| 573 |
|
|
DIMENSION IPFA(1) |
| 574 |
|
|
DIMENSION pattern_p(N,1), backward_levels_p(1), degree_p(1), new_label_p(1), assigned_level_pST(1), |
| 575 |
|
|
* LSTPT(1) |
| 576 |
|
|
/* SET UP assigned_level_pST AND LSTPT FROM backward_levels_p |
| 577 |
|
|
for (10 i=0,i<N,++i) |
| 578 |
|
|
IPFA[i] = 0 |
| 579 |
|
|
10 CONTINUE |
| 580 |
|
|
NSTPT = 1 |
| 581 |
|
|
for (30 I=1,num_levels |
| 582 |
|
|
LSTPT[i] = NSTPT |
| 583 |
|
|
for (20 J=1,N |
| 584 |
|
|
if (backward_levels_p(J)!=I) GO TO 20 |
| 585 |
|
|
assigned_level_pST(NSTPT) = J |
| 586 |
|
|
NSTPT = NSTPT + 1 |
| 587 |
|
|
20 CONTINUE |
| 588 |
|
|
30 CONTINUE |
| 589 |
|
|
LSTPT(num_levels+1) = NSTPT |
| 590 |
|
|
/* node_indexA, node_indexB, node_indexC AND node_indexD ARE STACKS WITH POINTERS |
| 591 |
|
|
/* XA,XB,ConnectedComponentCounter, AND XD. CX IS A SPECIAL POINTER INTO node_indexC WHICH |
| 592 |
|
|
/* INDICATES THE PARTICULAR NODE BEING PROCESSED. |
| 593 |
|
|
/* first_available_in_list_of_tree_nodes KEEPS TRACK OF THE LEVEL WE ARE WORKING AT. |
| 594 |
|
|
/* INITIALLY node_indexC CONTAINS ONLY THE INITIAL NODE, start_node2. |
| 595 |
|
|
first_available_in_list_of_tree_nodes = 0 |
| 596 |
|
|
if (reverse_diameter_tree<0) first_available_in_list_of_tree_nodes = num_levels + 1 |
| 597 |
|
|
ConnectedComponentCounter = 1 |
| 598 |
|
|
node_indexC(ConnectedComponentCounter) = start_node2 |
| 599 |
|
|
40 CX = 1 |
| 600 |
|
|
XD = 0 |
| 601 |
|
|
first_available_in_list_of_tree_nodes = first_available_in_list_of_tree_nodes + reverse_diameter_tree |
| 602 |
|
|
LST = LSTPT(first_available_in_list_of_tree_nodes) |
| 603 |
|
|
LND = LSTPT(first_available_in_list_of_tree_nodes+1) - 1 |
| 604 |
|
|
/* BEGIN PROCESSING NODE node_indexC(CX) |
| 605 |
|
|
50 IPRO = node_indexC(CX) |
| 606 |
|
|
new_label_p(IPRO) = NUM |
| 607 |
|
|
NUM = NUM + DirectionLargestComponent |
| 608 |
|
|
END = degree_p(IPRO) |
| 609 |
|
|
XA = 0 |
| 610 |
|
|
XB = 0 |
| 611 |
|
|
/* CHECK ALL ADJACENT NODES |
| 612 |
|
|
for (80 I=1,END |
| 613 |
|
|
TEST = pattern_p(IPRO,I) |
| 614 |
|
|
INX = new_label_p(TEST) |
| 615 |
|
|
/* ONLY NODES NOT NUMBERED OR ALREADY ON A STACK ARE ADDED |
| 616 |
|
|
if (INX.EQ.0) GO TO 60 |
| 617 |
|
|
if (INX<0) GO TO 80 |
| 618 |
|
|
/* for (PRELIMINARY BANDWIDTH AND PROFILE CALCULATIONS |
| 619 |
|
|
NBW = (new_label_p(IPRO)-INX)*DirectionLargestComponent |
| 620 |
|
|
if (DirectionLargestComponent>0) INX = new_label_p(IPRO) |
| 621 |
|
|
if (IPFA(INX)<NBW) IPFA(INX) = NBW |
| 622 |
|
|
GO TO 80 |
| 623 |
|
|
60 new_label_p(TEST) = -1 |
| 624 |
|
|
/* PUT NODES ON SAME LEVEL ON node_indexA, ALL OTHERS ON node_indexB |
| 625 |
|
|
if (backward_levels_p(TEST).EQ.backward_levels_p(IPRO)) GO TO 70 |
| 626 |
|
|
XB = XB + 1 |
| 627 |
|
|
node_indexB(XB) = TEST |
| 628 |
|
|
GO TO 80 |
| 629 |
|
|
70 XA = XA + 1 |
| 630 |
|
|
node_indexA(XA) = TEST |
| 631 |
|
|
80 CONTINUE |
| 632 |
|
|
/* SORT node_indexA AND node_indexB INTO INCREASING degree_p AND ADD node_indexA TO node_indexC |
| 633 |
|
|
/* AND node_indexB TO node_indexD |
| 634 |
|
|
if (XA.EQ.0) GO TO 100 |
| 635 |
|
|
if (XA.EQ.1) GO TO 90 |
| 636 |
|
|
CALL Paso_SystemMatrixPattern_sortByDegree(node_indexC, node_indexA, ConnectedComponentCounter, XA, degree_p) |
| 637 |
|
|
GO TO 100 |
| 638 |
|
|
90 ConnectedComponentCounter = ConnectedComponentCounter + 1 |
| 639 |
|
|
node_indexC(ConnectedComponentCounter) = node_indexA(XA) |
| 640 |
|
|
100 if (XB.EQ.0) GO TO 120 |
| 641 |
|
|
if (XB.EQ.1) GO TO 110 |
| 642 |
|
|
CALL Paso_SystemMatrixPattern_sortByDegree(node_indexD, node_indexB, XD, XB, degree_p) |
| 643 |
|
|
GO TO 120 |
| 644 |
|
|
110 XD = XD + 1 |
| 645 |
|
|
node_indexD(XD) = node_indexB(XB) |
| 646 |
|
|
/* BE SURE TO PROCESS ALL NODES IN node_indexC |
| 647 |
|
|
120 CX = CX + 1 |
| 648 |
|
|
if (ConnectedComponentCounter>=CX) GO TO 50 |
| 649 |
|
|
/* WHEN node_indexC IS EXHAUSTED LOOK FOR MIN degree_p NODE IN SAME LEVEL |
| 650 |
|
|
/* WHICH HAS NOT BEEN PROCESSED |
| 651 |
|
|
MAX = ndeg_max + 1 |
| 652 |
|
|
start_node2 = N + 1 |
| 653 |
|
|
for (130 I=LST,LND |
| 654 |
|
|
TEST = assigned_level_pST[i] |
| 655 |
|
|
if (new_label_p(TEST)!=0) GO TO 130 |
| 656 |
|
|
if (degree_p(TEST)>=MAX) GO TO 130 |
| 657 |
|
|
new_label_p(start_node2) = 0 |
| 658 |
|
|
new_label_p(TEST) = -1 |
| 659 |
|
|
MAX = degree_p(TEST) |
| 660 |
|
|
start_node2 = TEST |
| 661 |
|
|
130 CONTINUE |
| 662 |
|
|
if (start_node2.EQ.N+1) GO TO 140 |
| 663 |
|
|
ConnectedComponentCounter = ConnectedComponentCounter + 1 |
| 664 |
|
|
node_indexC(ConnectedComponentCounter) = start_node2 |
| 665 |
|
|
GO TO 50 |
| 666 |
|
|
/* if node_indexD IS EMPTY WE ARE DONE, OTHERWISE COPY node_indexD ONTO node_indexC |
| 667 |
|
|
/* AND BEGIN PROCESSING NEW node_indexC |
| 668 |
|
|
140 if (XD.EQ.0) GO TO 160 |
| 669 |
|
|
for (150 I=1,XD |
| 670 |
|
|
node_indexC[i] = node_indexD[i] |
| 671 |
|
|
150 CONTINUE |
| 672 |
|
|
ConnectedComponentCounter = XD |
| 673 |
|
|
GO TO 40 |
| 674 |
|
|
/* for (FINAL BANDWIDTH AND PROFILE CALCULATIONS |
| 675 |
|
|
160 for (170 i=0,i<N,++i) |
| 676 |
|
|
if (IPFA[i]>newBandwidth) newBandwidth = IPFA[i] |
| 677 |
|
|
newProfile = newProfile + IPFA[i] |
| 678 |
|
|
170 CONTINUE |
| 679 |
|
|
RETURN |
| 680 |
|
|
END |
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