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Diffstat (limited to 'intern/opennl/superlu/colamd.c')
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diff --git a/intern/opennl/superlu/colamd.c b/intern/opennl/superlu/colamd.c new file mode 100644 index 00000000000..b60718f9938 --- /dev/null +++ b/intern/opennl/superlu/colamd.c @@ -0,0 +1,2583 @@ +/* ========================================================================== */ +/* === colamd - a sparse matrix column ordering algorithm =================== */ +/* ========================================================================== */ + +/* + colamd: An approximate minimum degree column ordering algorithm. + + Purpose: + + Colamd computes a permutation Q such that the Cholesky factorization of + (AQ)'(AQ) has less fill-in and requires fewer floating point operations + than A'A. This also provides a good ordering for sparse partial + pivoting methods, P(AQ) = LU, where Q is computed prior to numerical + factorization, and P is computed during numerical factorization via + conventional partial pivoting with row interchanges. Colamd is the + column ordering method used in SuperLU, part of the ScaLAPACK library. + It is also available as user-contributed software for Matlab 5.2, + available from MathWorks, Inc. (http://www.mathworks.com). This + routine can be used in place of COLMMD in Matlab. By default, the \ + and / operators in Matlab perform a column ordering (using COLMMD) + prior to LU factorization using sparse partial pivoting, in the + built-in Matlab LU(A) routine. + + Authors: + + The authors of the code itself are Stefan I. Larimore and Timothy A. + Davis (davis@cise.ufl.edu), University of Florida. The algorithm was + developed in collaboration with John Gilbert, Xerox PARC, and Esmond + Ng, Oak Ridge National Laboratory. + + Date: + + August 3, 1998. Version 1.0. + + Acknowledgements: + + This work was supported by the National Science Foundation, under + grants DMS-9504974 and DMS-9803599. + + Notice: + + Copyright (c) 1998 by the University of Florida. All Rights Reserved. + + THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY + EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK. + + Permission is hereby granted to use or copy this program for any + purpose, provided the above notices are retained on all copies. + User documentation of any code that uses this code must cite the + Authors, the Copyright, and "Used by permission." If this code is + accessible from within Matlab, then typing "help colamd" or "colamd" + (with no arguments) must cite the Authors. Permission to modify the + code and to distribute modified code is granted, provided the above + notices are retained, and a notice that the code was modified is + included with the above copyright notice. You must also retain the + Availability information below, of the original version. + + This software is provided free of charge. + + Availability: + + This file is located at + + http://www.cise.ufl.edu/~davis/colamd/colamd.c + + The colamd.h file is required, located in the same directory. + The colamdmex.c file provides a Matlab interface for colamd. + The symamdmex.c file provides a Matlab interface for symamd, which is + a symmetric ordering based on this code, colamd.c. All codes are + purely ANSI C compliant (they use no Unix-specific routines, include + files, etc.). +*/ + +/* ========================================================================== */ +/* === Description of user-callable routines ================================ */ +/* ========================================================================== */ + +/* + Each user-callable routine (declared as PUBLIC) is briefly described below. + Refer to the comments preceding each routine for more details. + + ---------------------------------------------------------------------------- + colamd_recommended: + ---------------------------------------------------------------------------- + + Usage: + + Alen = colamd_recommended (nnz, n_row, n_col) ; + + Purpose: + + Returns recommended value of Alen for use by colamd. Returns -1 + if any input argument is negative. + + Arguments: + + int nnz ; Number of nonzeros in the matrix A. This must + be the same value as p [n_col] in the call to + colamd - otherwise you will get a wrong value + of the recommended memory to use. + int n_row ; Number of rows in the matrix A. + int n_col ; Number of columns in the matrix A. + + ---------------------------------------------------------------------------- + colamd_set_defaults: + ---------------------------------------------------------------------------- + + Usage: + + colamd_set_defaults (knobs) ; + + Purpose: + + Sets the default parameters. + + Arguments: + + double knobs [COLAMD_KNOBS] ; Output only. + + Rows with more than (knobs [COLAMD_DENSE_ROW] * n_col) entries + are removed prior to ordering. Columns with more than + (knobs [COLAMD_DENSE_COL] * n_row) entries are removed + prior to ordering, and placed last in the output column + ordering. Default values of these two knobs are both 0.5. + Currently, only knobs [0] and knobs [1] are used, but future + versions may use more knobs. If so, they will be properly set + to their defaults by the future version of colamd_set_defaults, + so that the code that calls colamd will not need to change, + assuming that you either use colamd_set_defaults, or pass a + (double *) NULL pointer as the knobs array to colamd. + + ---------------------------------------------------------------------------- + colamd: + ---------------------------------------------------------------------------- + + Usage: + + colamd (n_row, n_col, Alen, A, p, knobs) ; + + Purpose: + + Computes a column ordering (Q) of A such that P(AQ)=LU or + (AQ)'AQ=LL' have less fill-in and require fewer floating point + operations than factorizing the unpermuted matrix A or A'A, + respectively. + + Arguments: + + int n_row ; + + Number of rows in the matrix A. + Restriction: n_row >= 0. + Colamd returns FALSE if n_row is negative. + + int n_col ; + + Number of columns in the matrix A. + Restriction: n_col >= 0. + Colamd returns FALSE if n_col is negative. + + int Alen ; + + Restriction (see note): + Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col + COLAMD_STATS + Colamd returns FALSE if these conditions are not met. + + Note: this restriction makes an modest assumption regarding + the size of the two typedef'd structures, below. We do, + however, guarantee that + Alen >= colamd_recommended (nnz, n_row, n_col) + will be sufficient. + + int A [Alen] ; Input argument, stats on output. + + A is an integer array of size Alen. Alen must be at least as + large as the bare minimum value given above, but this is very + low, and can result in excessive run time. For best + performance, we recommend that Alen be greater than or equal to + colamd_recommended (nnz, n_row, n_col), which adds + nnz/5 to the bare minimum value given above. + + On input, the row indices of the entries in column c of the + matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices + in a given column c need not be in ascending order, and + duplicate row indices may be be present. However, colamd will + work a little faster if both of these conditions are met + (Colamd puts the matrix into this format, if it finds that the + the conditions are not met). + + The matrix is 0-based. That is, rows are in the range 0 to + n_row-1, and columns are in the range 0 to n_col-1. Colamd + returns FALSE if any row index is out of range. + + The contents of A are modified during ordering, and are thus + undefined on output with the exception of a few statistics + about the ordering (A [0..COLAMD_STATS-1]): + A [0]: number of dense or empty rows ignored. + A [1]: number of dense or empty columns ignored (and ordered + last in the output permutation p) + A [2]: number of garbage collections performed. + A [3]: 0, if all row indices in each column were in sorted + order, and no duplicates were present. + 1, otherwise (in which case colamd had to do more work) + Note that a row can become "empty" if it contains only + "dense" and/or "empty" columns, and similarly a column can + become "empty" if it only contains "dense" and/or "empty" rows. + Future versions may return more statistics in A, but the usage + of these 4 entries in A will remain unchanged. + + int p [n_col+1] ; Both input and output argument. + + p is an integer array of size n_col+1. On input, it holds the + "pointers" for the column form of the matrix A. Column c of + the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first + entry, p [0], must be zero, and p [c] <= p [c+1] must hold + for all c in the range 0 to n_col-1. The value p [n_col] is + thus the total number of entries in the pattern of the matrix A. + Colamd returns FALSE if these conditions are not met. + + On output, if colamd returns TRUE, the array p holds the column + permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is + the first column index in the new ordering, and p [n_col-1] is + the last. That is, p [k] = j means that column j of A is the + kth pivot column, in AQ, where k is in the range 0 to n_col-1 + (p [0] = j means that column j of A is the first column in AQ). + + If colamd returns FALSE, then no permutation is returned, and + p is undefined on output. + + double knobs [COLAMD_KNOBS] ; Input only. + + See colamd_set_defaults for a description. If the knobs array + is not present (that is, if a (double *) NULL pointer is passed + in its place), then the default values of the parameters are + used instead. + +*/ + + +/* ========================================================================== */ +/* === Include files ======================================================== */ +/* ========================================================================== */ + +/* limits.h: the largest positive integer (INT_MAX) */ +#include <limits.h> + +/* colamd.h: knob array size, stats output size, and global prototypes */ +#include "colamd.h" + +/* ========================================================================== */ +/* === Scaffolding code definitions ======================================== */ +/* ========================================================================== */ + +/* Ensure that debugging is turned off: */ +#ifndef NDEBUG +#define NDEBUG +#endif + +/* assert.h: the assert macro (no debugging if NDEBUG is defined) */ +#include <assert.h> + +/* + Our "scaffolding code" philosophy: In our opinion, well-written library + code should keep its "debugging" code, and just normally have it turned off + by the compiler so as not to interfere with performance. This serves + several purposes: + + (1) assertions act as comments to the reader, telling you what the code + expects at that point. All assertions will always be true (unless + there really is a bug, of course). + + (2) leaving in the scaffolding code assists anyone who would like to modify + the code, or understand the algorithm (by reading the debugging output, + one can get a glimpse into what the code is doing). + + (3) (gasp!) for actually finding bugs. This code has been heavily tested + and "should" be fully functional and bug-free ... but you never know... + + To enable debugging, comment out the "#define NDEBUG" above. The code will + become outrageously slow when debugging is enabled. To control the level of + debugging output, set an environment variable D to 0 (little), 1 (some), + 2, 3, or 4 (lots). +*/ + +/* ========================================================================== */ +/* === Row and Column structures ============================================ */ +/* ========================================================================== */ + +typedef struct ColInfo_struct +{ + int start ; /* index for A of first row in this column, or DEAD */ + /* if column is dead */ + int length ; /* number of rows in this column */ + union + { + int thickness ; /* number of original columns represented by this */ + /* col, if the column is alive */ + int parent ; /* parent in parent tree super-column structure, if */ + /* the column is dead */ + } shared1 ; + union + { + int score ; /* the score used to maintain heap, if col is alive */ + int order ; /* pivot ordering of this column, if col is dead */ + } shared2 ; + union + { + int headhash ; /* head of a hash bucket, if col is at the head of */ + /* a degree list */ + int hash ; /* hash value, if col is not in a degree list */ + int prev ; /* previous column in degree list, if col is in a */ + /* degree list (but not at the head of a degree list) */ + } shared3 ; + union + { + int degree_next ; /* next column, if col is in a degree list */ + int hash_next ; /* next column, if col is in a hash list */ + } shared4 ; + +} ColInfo ; + +typedef struct RowInfo_struct +{ + int start ; /* index for A of first col in this row */ + int length ; /* number of principal columns in this row */ + union + { + int degree ; /* number of principal & non-principal columns in row */ + int p ; /* used as a row pointer in init_rows_cols () */ + } shared1 ; + union + { + int mark ; /* for computing set differences and marking dead rows*/ + int first_column ;/* first column in row (used in garbage collection) */ + } shared2 ; + +} RowInfo ; + +/* ========================================================================== */ +/* === Definitions ========================================================== */ +/* ========================================================================== */ + +#define MAX(a,b) (((a) > (b)) ? (a) : (b)) +#define MIN(a,b) (((a) < (b)) ? (a) : (b)) + +#define ONES_COMPLEMENT(r) (-(r)-1) + +#define TRUE (1) +#define FALSE (0) +#define EMPTY (-1) + +/* Row and column status */ +#define ALIVE (0) +#define DEAD (-1) + +/* Column status */ +#define DEAD_PRINCIPAL (-1) +#define DEAD_NON_PRINCIPAL (-2) + +/* Macros for row and column status update and checking. */ +#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark) +#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE) +#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE) +#define COL_IS_DEAD(c) (Col [c].start < ALIVE) +#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE) +#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL) +#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; } +#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; } +#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; } + +/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */ +#define PUBLIC +#define PRIVATE static + +/* ========================================================================== */ +/* === Prototypes of PRIVATE routines ======================================= */ +/* ========================================================================== */ + +PRIVATE int init_rows_cols +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [], + int p [] +) ; + +PRIVATE void init_scoring +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [], + int head [], + double knobs [COLAMD_KNOBS], + int *p_n_row2, + int *p_n_col2, + int *p_max_deg +) ; + +PRIVATE int find_ordering +( + int n_row, + int n_col, + int Alen, + RowInfo Row [], + ColInfo Col [], + int A [], + int head [], + int n_col2, + int max_deg, + int pfree +) ; + +PRIVATE void order_children +( + int n_col, + ColInfo Col [], + int p [] +) ; + +PRIVATE void detect_super_cols +( +#ifndef NDEBUG + int n_col, + RowInfo Row [], +#endif + ColInfo Col [], + int A [], + int head [], + int row_start, + int row_length +) ; + +PRIVATE int garbage_collection +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [], + int *pfree +) ; + +PRIVATE int clear_mark +( + int n_row, + RowInfo Row [] +) ; + +/* ========================================================================== */ +/* === Debugging definitions ================================================ */ +/* ========================================================================== */ + +#ifndef NDEBUG + +/* === With debugging ======================================================= */ + +/* stdlib.h: for getenv and atoi, to get debugging level from environment */ +#include <stdlib.h> + +/* stdio.h: for printf (no printing if debugging is turned off) */ +#include <stdio.h> + +PRIVATE void debug_deg_lists +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int head [], + int min_score, + int should, + int max_deg +) ; + +PRIVATE void debug_mark +( + int n_row, + RowInfo Row [], + int tag_mark, + int max_mark +) ; + +PRIVATE void debug_matrix +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [] +) ; + +PRIVATE void debug_structures +( + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [], + int n_col2 +) ; + +/* the following is the *ONLY* global variable in this file, and is only */ +/* present when debugging */ + +PRIVATE int debug_colamd ; /* debug print level */ + +#define DEBUG0(params) { (void) printf params ; } +#define DEBUG1(params) { if (debug_colamd >= 1) (void) printf params ; } +#define DEBUG2(params) { if (debug_colamd >= 2) (void) printf params ; } +#define DEBUG3(params) { if (debug_colamd >= 3) (void) printf params ; } +#define DEBUG4(params) { if (debug_colamd >= 4) (void) printf params ; } + +#else + +/* === No debugging ========================================================= */ + +#define DEBUG0(params) ; +#define DEBUG1(params) ; +#define DEBUG2(params) ; +#define DEBUG3(params) ; +#define DEBUG4(params) ; + +#endif + +/* ========================================================================== */ + + +/* ========================================================================== */ +/* === USER-CALLABLE ROUTINES: ============================================== */ +/* ========================================================================== */ + + +/* ========================================================================== */ +/* === colamd_recommended =================================================== */ +/* ========================================================================== */ + +/* + The colamd_recommended routine returns the suggested size for Alen. This + value has been determined to provide good balance between the number of + garbage collections and the memory requirements for colamd. +*/ + +PUBLIC int colamd_recommended /* returns recommended value of Alen. */ +( + /* === Parameters ======================================================= */ + + int nnz, /* number of nonzeros in A */ + int n_row, /* number of rows in A */ + int n_col /* number of columns in A */ +) +{ + /* === Local variables ================================================== */ + + int minimum ; /* bare minimum requirements */ + int recommended ; /* recommended value of Alen */ + + if (nnz < 0 || n_row < 0 || n_col < 0) + { + /* return -1 if any input argument is corrupted */ + DEBUG0 (("colamd_recommended error!")) ; + DEBUG0 ((" nnz: %d, n_row: %d, n_col: %d\n", nnz, n_row, n_col)) ; + return (-1) ; + } + + minimum = + 2 * (nnz) /* for A */ + + (((n_col) + 1) * sizeof (ColInfo) / sizeof (int)) /* for Col */ + + (((n_row) + 1) * sizeof (RowInfo) / sizeof (int)) /* for Row */ + + n_col /* minimum elbow room to guarrantee success */ + + COLAMD_STATS ; /* for output statistics */ + + /* recommended is equal to the minumum plus enough memory to keep the */ + /* number garbage collections low */ + recommended = minimum + nnz/5 ; + + return (recommended) ; +} + + +/* ========================================================================== */ +/* === colamd_set_defaults ================================================== */ +/* ========================================================================== */ + +/* + The colamd_set_defaults routine sets the default values of the user- + controllable parameters for colamd: + + knobs [0] rows with knobs[0]*n_col entries or more are removed + prior to ordering. + + knobs [1] columns with knobs[1]*n_row entries or more are removed + prior to ordering, and placed last in the column + permutation. + + knobs [2..19] unused, but future versions might use this +*/ + +PUBLIC void colamd_set_defaults +( + /* === Parameters ======================================================= */ + + double knobs [COLAMD_KNOBS] /* knob array */ +) +{ + /* === Local variables ================================================== */ + + int i ; + + if (!knobs) + { + return ; /* no knobs to initialize */ + } + for (i = 0 ; i < COLAMD_KNOBS ; i++) + { + knobs [i] = 0 ; + } + knobs [COLAMD_DENSE_ROW] = 0.5 ; /* ignore rows over 50% dense */ + knobs [COLAMD_DENSE_COL] = 0.5 ; /* ignore columns over 50% dense */ +} + + +/* ========================================================================== */ +/* === colamd =============================================================== */ +/* ========================================================================== */ + +/* + The colamd routine computes a column ordering Q of a sparse matrix + A such that the LU factorization P(AQ) = LU remains sparse, where P is + selected via partial pivoting. The routine can also be viewed as + providing a permutation Q such that the Cholesky factorization + (AQ)'(AQ) = LL' remains sparse. + + On input, the nonzero patterns of the columns of A are stored in the + array A, in order 0 to n_col-1. A is held in 0-based form (rows in the + range 0 to n_row-1 and columns in the range 0 to n_col-1). Row indices + for column c are located in A [(p [c]) ... (p [c+1]-1)], where p [0] = 0, + and thus p [n_col] is the number of entries in A. The matrix is + destroyed on output. The row indices within each column do not have to + be sorted (from small to large row indices), and duplicate row indices + may be present. However, colamd will work a little faster if columns are + sorted and no duplicates are present. Matlab 5.2 always passes the matrix + with sorted columns, and no duplicates. + + The integer array A is of size Alen. Alen must be at least of size + (where nnz is the number of entries in A): + + nnz for the input column form of A + + nnz for a row form of A that colamd generates + + 6*(n_col+1) for a ColInfo Col [0..n_col] array + (this assumes sizeof (ColInfo) is 6 int's). + + 4*(n_row+1) for a RowInfo Row [0..n_row] array + (this assumes sizeof (RowInfo) is 4 int's). + + elbow_room must be at least n_col. We recommend at least + nnz/5 in addition to that. If sufficient, + changes in the elbow room affect the ordering + time only, not the ordering itself. + + COLAMD_STATS for the output statistics + + Colamd returns FALSE is memory is insufficient, or TRUE otherwise. + + On input, the caller must specify: + + n_row the number of rows of A + n_col the number of columns of A + Alen the size of the array A + A [0 ... nnz-1] the row indices, where nnz = p [n_col] + A [nnz ... Alen-1] (need not be initialized by the user) + p [0 ... n_col] the column pointers, p [0] = 0, and p [n_col] + is the number of entries in A. Column c of A + is stored in A [p [c] ... p [c+1]-1]. + knobs [0 ... 19] a set of parameters that control the behavior + of colamd. If knobs is a NULL pointer the + defaults are used. The user-callable + colamd_set_defaults routine sets the default + parameters. See that routine for a description + of the user-controllable parameters. + + If the return value of Colamd is TRUE, then on output: + + p [0 ... n_col-1] the column permutation. p [0] is the first + column index, and p [n_col-1] is the last. + That is, p [k] = j means that column j of A + is the kth column of AQ. + + A is undefined on output (the matrix pattern is + destroyed), except for the following statistics: + + A [0] the number of dense (or empty) rows ignored + A [1] the number of dense (or empty) columms. These + are ordered last, in their natural order. + A [2] the number of garbage collections performed. + If this is excessive, then you would have + gotten your results faster if Alen was larger. + A [3] 0, if all row indices in each column were in + sorted order and no duplicates were present. + 1, if there were unsorted or duplicate row + indices in the input. You would have gotten + your results faster if A [3] was returned as 0. + + If the return value of Colamd is FALSE, then A and p are undefined on + output. +*/ + +PUBLIC int colamd /* returns TRUE if successful */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows in A */ + int n_col, /* number of columns in A */ + int Alen, /* length of A */ + int A [], /* row indices of A */ + int p [], /* pointers to columns in A */ + double knobs [COLAMD_KNOBS] /* parameters (uses defaults if NULL) */ +) +{ + /* === Local variables ================================================== */ + + int i ; /* loop index */ + int nnz ; /* nonzeros in A */ + int Row_size ; /* size of Row [], in integers */ + int Col_size ; /* size of Col [], in integers */ + int elbow_room ; /* remaining free space */ + RowInfo *Row ; /* pointer into A of Row [0..n_row] array */ + ColInfo *Col ; /* pointer into A of Col [0..n_col] array */ + int n_col2 ; /* number of non-dense, non-empty columns */ + int n_row2 ; /* number of non-dense, non-empty rows */ + int ngarbage ; /* number of garbage collections performed */ + int max_deg ; /* maximum row degree */ + double default_knobs [COLAMD_KNOBS] ; /* default knobs knobs array */ + int init_result ; /* return code from initialization */ + +#ifndef NDEBUG + debug_colamd = 0 ; /* no debug printing */ + /* get "D" environment variable, which gives the debug printing level */ + if (getenv ("D")) debug_colamd = atoi (getenv ("D")) ; + DEBUG0 (("debug version, D = %d (THIS WILL BE SLOOOOW!)\n", debug_colamd)) ; +#endif + + /* === Check the input arguments ======================================== */ + + if (n_row < 0 || n_col < 0 || !A || !p) + { + /* n_row and n_col must be non-negative, A and p must be present */ + DEBUG0 (("colamd error! %d %d %d\n", n_row, n_col, Alen)) ; + return (FALSE) ; + } + nnz = p [n_col] ; + if (nnz < 0 || p [0] != 0) + { + /* nnz must be non-negative, and p [0] must be zero */ + DEBUG0 (("colamd error! %d %d\n", nnz, p [0])) ; + return (FALSE) ; + } + + /* === If no knobs, set default parameters ============================== */ + + if (!knobs) + { + knobs = default_knobs ; + colamd_set_defaults (knobs) ; + } + + /* === Allocate the Row and Col arrays from array A ===================== */ + + Col_size = (n_col + 1) * sizeof (ColInfo) / sizeof (int) ; + Row_size = (n_row + 1) * sizeof (RowInfo) / sizeof (int) ; + elbow_room = Alen - (2*nnz + Col_size + Row_size) ; + if (elbow_room < n_col + COLAMD_STATS) + { + /* not enough space in array A to perform the ordering */ + DEBUG0 (("colamd error! elbow_room %d, %d\n", elbow_room,n_col)) ; + return (FALSE) ; + } + Alen = 2*nnz + elbow_room ; + Col = (ColInfo *) &A [Alen] ; + Row = (RowInfo *) &A [Alen + Col_size] ; + + /* === Construct the row and column data structures ===================== */ + + init_result = init_rows_cols (n_row, n_col, Row, Col, A, p) ; + if (init_result == -1) + { + /* input matrix is invalid */ + DEBUG0 (("colamd error! matrix invalid\n")) ; + return (FALSE) ; + } + + /* === Initialize scores, kill dense rows/columns ======================= */ + + init_scoring (n_row, n_col, Row, Col, A, p, knobs, + &n_row2, &n_col2, &max_deg) ; + + /* === Order the supercolumns =========================================== */ + + ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p, + n_col2, max_deg, 2*nnz) ; + + /* === Order the non-principal columns ================================== */ + + order_children (n_col, Col, p) ; + + /* === Return statistics in A =========================================== */ + + for (i = 0 ; i < COLAMD_STATS ; i++) + { + A [i] = 0 ; + } + A [COLAMD_DENSE_ROW] = n_row - n_row2 ; + A [COLAMD_DENSE_COL] = n_col - n_col2 ; + A [COLAMD_DEFRAG_COUNT] = ngarbage ; + A [COLAMD_JUMBLED_COLS] = init_result ; + + return (TRUE) ; +} + + +/* ========================================================================== */ +/* === NON-USER-CALLABLE ROUTINES: ========================================== */ +/* ========================================================================== */ + +/* There are no user-callable routines beyond this point in the file */ + + +/* ========================================================================== */ +/* === init_rows_cols ======================================================= */ +/* ========================================================================== */ + +/* + Takes the column form of the matrix in A and creates the row form of the + matrix. Also, row and column attributes are stored in the Col and Row + structs. If the columns are un-sorted or contain duplicate row indices, + this routine will also sort and remove duplicate row indices from the + column form of the matrix. Returns -1 on error, 1 if columns jumbled, + or 0 if columns not jumbled. Not user-callable. +*/ + +PRIVATE int init_rows_cols /* returns status code */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + RowInfo Row [], /* of size n_row+1 */ + ColInfo Col [], /* of size n_col+1 */ + int A [], /* row indices of A, of size Alen */ + int p [] /* pointers to columns in A, of size n_col+1 */ +) +{ + /* === Local variables ================================================== */ + + int col ; /* a column index */ + int row ; /* a row index */ + int *cp ; /* a column pointer */ + int *cp_end ; /* a pointer to the end of a column */ + int *rp ; /* a row pointer */ + int *rp_end ; /* a pointer to the end of a row */ + int last_start ; /* start index of previous column in A */ + int start ; /* start index of column in A */ + int last_row ; /* previous row */ + int jumbled_columns ; /* indicates if columns are jumbled */ + + /* === Initialize columns, and check column pointers ==================== */ + + last_start = 0 ; + for (col = 0 ; col < n_col ; col++) + { + start = p [col] ; + if (start < last_start) + { + /* column pointers must be non-decreasing */ + DEBUG0 (("colamd error! last p %d p [col] %d\n",last_start,start)); + return (-1) ; + } + Col [col].start = start ; + Col [col].length = p [col+1] - start ; + Col [col].shared1.thickness = 1 ; + Col [col].shared2.score = 0 ; + Col [col].shared3.prev = EMPTY ; + Col [col].shared4.degree_next = EMPTY ; + last_start = start ; + } + /* must check the end pointer for last column */ + if (p [n_col] < last_start) + { + /* column pointers must be non-decreasing */ + DEBUG0 (("colamd error! last p %d p [n_col] %d\n",p[col],last_start)) ; + return (-1) ; + } + + /* p [0..n_col] no longer needed, used as "head" in subsequent routines */ + + /* === Scan columns, compute row degrees, and check row indices ========= */ + + jumbled_columns = FALSE ; + + for (row = 0 ; row < n_row ; row++) + { + Row [row].length = 0 ; + Row [row].shared2.mark = -1 ; + } + + for (col = 0 ; col < n_col ; col++) + { + last_row = -1 ; + + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + + while (cp < cp_end) + { + row = *cp++ ; + + /* make sure row indices within range */ + if (row < 0 || row >= n_row) + { + DEBUG0 (("colamd error! col %d row %d last_row %d\n", + col, row, last_row)) ; + return (-1) ; + } + else if (row <= last_row) + { + /* row indices are not sorted or repeated, thus cols */ + /* are jumbled */ + jumbled_columns = TRUE ; + } + /* prevent repeated row from being counted */ + if (Row [row].shared2.mark != col) + { + Row [row].length++ ; + Row [row].shared2.mark = col ; + last_row = row ; + } + else + { + /* this is a repeated entry in the column, */ + /* it will be removed */ + Col [col].length-- ; + } + } + } + + /* === Compute row pointers ============================================= */ + + /* row form of the matrix starts directly after the column */ + /* form of matrix in A */ + Row [0].start = p [n_col] ; + Row [0].shared1.p = Row [0].start ; + Row [0].shared2.mark = -1 ; + for (row = 1 ; row < n_row ; row++) + { + Row [row].start = Row [row-1].start + Row [row-1].length ; + Row [row].shared1.p = Row [row].start ; + Row [row].shared2.mark = -1 ; + } + + /* === Create row form ================================================== */ + + if (jumbled_columns) + { + /* if cols jumbled, watch for repeated row indices */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + row = *cp++ ; + if (Row [row].shared2.mark != col) + { + A [(Row [row].shared1.p)++] = col ; + Row [row].shared2.mark = col ; + } + } + } + } + else + { + /* if cols not jumbled, we don't need the mark (this is faster) */ + for (col = 0 ; col < n_col ; col++) + { + cp = &A [p [col]] ; + cp_end = &A [p [col+1]] ; + while (cp < cp_end) + { + A [(Row [*cp++].shared1.p)++] = col ; + } + } + } + + /* === Clear the row marks and set row degrees ========================== */ + + for (row = 0 ; row < n_row ; row++) + { + Row [row].shared2.mark = 0 ; + Row [row].shared1.degree = Row [row].length ; + } + + /* === See if we need to re-create columns ============================== */ + + if (jumbled_columns) + { + +#ifndef NDEBUG + /* make sure column lengths are correct */ + for (col = 0 ; col < n_col ; col++) + { + p [col] = Col [col].length ; + } + for (row = 0 ; row < n_row ; row++) + { + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + p [*rp++]-- ; + } + } + for (col = 0 ; col < n_col ; col++) + { + assert (p [col] == 0) ; + } + /* now p is all zero (different than when debugging is turned off) */ +#endif + + /* === Compute col pointers ========================================= */ + + /* col form of the matrix starts at A [0]. */ + /* Note, we may have a gap between the col form and the row */ + /* form if there were duplicate entries, if so, it will be */ + /* removed upon the first garbage collection */ + Col [0].start = 0 ; + p [0] = Col [0].start ; + for (col = 1 ; col < n_col ; col++) + { + /* note that the lengths here are for pruned columns, i.e. */ + /* no duplicate row indices will exist for these columns */ + Col [col].start = Col [col-1].start + Col [col-1].length ; + p [col] = Col [col].start ; + } + + /* === Re-create col form =========================================== */ + + for (row = 0 ; row < n_row ; row++) + { + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + A [(p [*rp++])++] = row ; + } + } + return (1) ; + } + else + { + /* no columns jumbled (this is faster) */ + return (0) ; + } +} + + +/* ========================================================================== */ +/* === init_scoring ========================================================= */ +/* ========================================================================== */ + +/* + Kills dense or empty columns and rows, calculates an initial score for + each column, and places all columns in the degree lists. Not user-callable. +*/ + +PRIVATE void init_scoring +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + RowInfo Row [], /* of size n_row+1 */ + ColInfo Col [], /* of size n_col+1 */ + int A [], /* column form and row form of A */ + int head [], /* of size n_col+1 */ + double knobs [COLAMD_KNOBS],/* parameters */ + int *p_n_row2, /* number of non-dense, non-empty rows */ + int *p_n_col2, /* number of non-dense, non-empty columns */ + int *p_max_deg /* maximum row degree */ +) +{ + /* === Local variables ================================================== */ + + int c ; /* a column index */ + int r, row ; /* a row index */ + int *cp ; /* a column pointer */ + int deg ; /* degree (# entries) of a row or column */ + int *cp_end ; /* a pointer to the end of a column */ + int *new_cp ; /* new column pointer */ + int col_length ; /* length of pruned column */ + int score ; /* current column score */ + int n_col2 ; /* number of non-dense, non-empty columns */ + int n_row2 ; /* number of non-dense, non-empty rows */ + int dense_row_count ; /* remove rows with more entries than this */ + int dense_col_count ; /* remove cols with more entries than this */ + int min_score ; /* smallest column score */ + int max_deg ; /* maximum row degree */ + int next_col ; /* Used to add to degree list.*/ +#ifndef NDEBUG + int debug_count ; /* debug only. */ +#endif + + /* === Extract knobs ==================================================== */ + + dense_row_count = MAX (0, MIN (knobs [COLAMD_DENSE_ROW] * n_col, n_col)) ; + dense_col_count = MAX (0, MIN (knobs [COLAMD_DENSE_COL] * n_row, n_row)) ; + DEBUG0 (("densecount: %d %d\n", dense_row_count, dense_col_count)) ; + max_deg = 0 ; + n_col2 = n_col ; + n_row2 = n_row ; + + /* === Kill empty columns =============================================== */ + + /* Put the empty columns at the end in their natural, so that LU */ + /* factorization can proceed as far as possible. */ + for (c = n_col-1 ; c >= 0 ; c--) + { + deg = Col [c].length ; + if (deg == 0) + { + /* this is a empty column, kill and order it last */ + Col [c].shared2.order = --n_col2 ; + KILL_PRINCIPAL_COL (c) ; + } + } + DEBUG0 (("null columns killed: %d\n", n_col - n_col2)) ; + + /* === Kill dense columns =============================================== */ + + /* Put the dense columns at the end, in their natural order */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip any dead columns */ + if (COL_IS_DEAD (c)) + { + continue ; + } + deg = Col [c].length ; + if (deg > dense_col_count) + { + /* this is a dense column, kill and order it last */ + Col [c].shared2.order = --n_col2 ; + /* decrement the row degrees */ + cp = &A [Col [c].start] ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + Row [*cp++].shared1.degree-- ; + } + KILL_PRINCIPAL_COL (c) ; + } + } + DEBUG0 (("Dense and null columns killed: %d\n", n_col - n_col2)) ; + + /* === Kill dense and empty rows ======================================== */ + + for (r = 0 ; r < n_row ; r++) + { + deg = Row [r].shared1.degree ; + assert (deg >= 0 && deg <= n_col) ; + if (deg > dense_row_count || deg == 0) + { + /* kill a dense or empty row */ + KILL_ROW (r) ; + --n_row2 ; + } + else + { + /* keep track of max degree of remaining rows */ + max_deg = MAX (max_deg, deg) ; + } + } + DEBUG0 (("Dense and null rows killed: %d\n", n_row - n_row2)) ; + + /* === Compute initial column scores ==================================== */ + + /* At this point the row degrees are accurate. They reflect the number */ + /* of "live" (non-dense) columns in each row. No empty rows exist. */ + /* Some "live" columns may contain only dead rows, however. These are */ + /* pruned in the code below. */ + + /* now find the initial matlab score for each column */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* skip dead column */ + if (COL_IS_DEAD (c)) + { + continue ; + } + score = 0 ; + cp = &A [Col [c].start] ; + new_cp = cp ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + /* skip if dead */ + if (ROW_IS_DEAD (row)) + { + continue ; + } + /* compact the column */ + *new_cp++ = row ; + /* add row's external degree */ + score += Row [row].shared1.degree - 1 ; + /* guard against integer overflow */ + score = MIN (score, n_col) ; + } + /* determine pruned column length */ + col_length = (int) (new_cp - &A [Col [c].start]) ; + if (col_length == 0) + { + /* a newly-made null column (all rows in this col are "dense" */ + /* and have already been killed) */ + DEBUG0 (("Newly null killed: %d\n", c)) ; + Col [c].shared2.order = --n_col2 ; + KILL_PRINCIPAL_COL (c) ; + } + else + { + /* set column length and set score */ + assert (score >= 0) ; + assert (score <= n_col) ; + Col [c].length = col_length ; + Col [c].shared2.score = score ; + } + } + DEBUG0 (("Dense, null, and newly-null columns killed: %d\n",n_col-n_col2)) ; + + /* At this point, all empty rows and columns are dead. All live columns */ + /* are "clean" (containing no dead rows) and simplicial (no supercolumns */ + /* yet). Rows may contain dead columns, but all live rows contain at */ + /* least one live column. */ + +#ifndef NDEBUG + debug_structures (n_row, n_col, Row, Col, A, n_col2) ; +#endif + + /* === Initialize degree lists ========================================== */ + +#ifndef NDEBUG + debug_count = 0 ; +#endif + + /* clear the hash buckets */ + for (c = 0 ; c <= n_col ; c++) + { + head [c] = EMPTY ; + } + min_score = n_col ; + /* place in reverse order, so low column indices are at the front */ + /* of the lists. This is to encourage natural tie-breaking */ + for (c = n_col-1 ; c >= 0 ; c--) + { + /* only add principal columns to degree lists */ + if (COL_IS_ALIVE (c)) + { + DEBUG4 (("place %d score %d minscore %d ncol %d\n", + c, Col [c].shared2.score, min_score, n_col)) ; + + /* === Add columns score to DList =============================== */ + + score = Col [c].shared2.score ; + + assert (min_score >= 0) ; + assert (min_score <= n_col) ; + assert (score >= 0) ; + assert (score <= n_col) ; + assert (head [score] >= EMPTY) ; + + /* now add this column to dList at proper score location */ + next_col = head [score] ; + Col [c].shared3.prev = EMPTY ; + Col [c].shared4.degree_next = next_col ; + + /* if there already was a column with the same score, set its */ + /* previous pointer to this new column */ + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = c ; + } + head [score] = c ; + + /* see if this score is less than current min */ + min_score = MIN (min_score, score) ; + +#ifndef NDEBUG + debug_count++ ; +#endif + } + } + +#ifndef NDEBUG + DEBUG0 (("Live cols %d out of %d, non-princ: %d\n", + debug_count, n_col, n_col-debug_count)) ; + assert (debug_count == n_col2) ; + debug_deg_lists (n_row, n_col, Row, Col, head, min_score, n_col2, max_deg) ; +#endif + + /* === Return number of remaining columns, and max row degree =========== */ + + *p_n_col2 = n_col2 ; + *p_n_row2 = n_row2 ; + *p_max_deg = max_deg ; +} + + +/* ========================================================================== */ +/* === find_ordering ======================================================== */ +/* ========================================================================== */ + +/* + Order the principal columns of the supercolumn form of the matrix + (no supercolumns on input). Uses a minimum approximate column minimum + degree ordering method. Not user-callable. +*/ + +PRIVATE int find_ordering /* return the number of garbage collections */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows of A */ + int n_col, /* number of columns of A */ + int Alen, /* size of A, 2*nnz + elbow_room or larger */ + RowInfo Row [], /* of size n_row+1 */ + ColInfo Col [], /* of size n_col+1 */ + int A [], /* column form and row form of A */ + int head [], /* of size n_col+1 */ + int n_col2, /* Remaining columns to order */ + int max_deg, /* Maximum row degree */ + int pfree /* index of first free slot (2*nnz on entry) */ +) +{ + /* === Local variables ================================================== */ + + int k ; /* current pivot ordering step */ + int pivot_col ; /* current pivot column */ + int *cp ; /* a column pointer */ + int *rp ; /* a row pointer */ + int pivot_row ; /* current pivot row */ + int *new_cp ; /* modified column pointer */ + int *new_rp ; /* modified row pointer */ + int pivot_row_start ; /* pointer to start of pivot row */ + int pivot_row_degree ; /* # of columns in pivot row */ + int pivot_row_length ; /* # of supercolumns in pivot row */ + int pivot_col_score ; /* score of pivot column */ + int needed_memory ; /* free space needed for pivot row */ + int *cp_end ; /* pointer to the end of a column */ + int *rp_end ; /* pointer to the end of a row */ + int row ; /* a row index */ + int col ; /* a column index */ + int max_score ; /* maximum possible score */ + int cur_score ; /* score of current column */ + unsigned int hash ; /* hash value for supernode detection */ + int head_column ; /* head of hash bucket */ + int first_col ; /* first column in hash bucket */ + int tag_mark ; /* marker value for mark array */ + int row_mark ; /* Row [row].shared2.mark */ + int set_difference ; /* set difference size of row with pivot row */ + int min_score ; /* smallest column score */ + int col_thickness ; /* "thickness" (# of columns in a supercol) */ + int max_mark ; /* maximum value of tag_mark */ + int pivot_col_thickness ; /* number of columns represented by pivot col */ + int prev_col ; /* Used by Dlist operations. */ + int next_col ; /* Used by Dlist operations. */ + int ngarbage ; /* number of garbage collections performed */ +#ifndef NDEBUG + int debug_d ; /* debug loop counter */ + int debug_step = 0 ; /* debug loop counter */ +#endif + + /* === Initialization and clear mark ==================================== */ + + max_mark = INT_MAX - n_col ; /* INT_MAX defined in <limits.h> */ + tag_mark = clear_mark (n_row, Row) ; + min_score = 0 ; + ngarbage = 0 ; + DEBUG0 (("Ordering.. n_col2=%d\n", n_col2)) ; + + /* === Order the columns ================================================ */ + + for (k = 0 ; k < n_col2 ; /* 'k' is incremented below */) + { + +#ifndef NDEBUG + if (debug_step % 100 == 0) + { + DEBUG0 (("\n... Step k: %d out of n_col2: %d\n", k, n_col2)) ; + } + else + { + DEBUG1 (("\n----------Step k: %d out of n_col2: %d\n", k, n_col2)) ; + } + debug_step++ ; + debug_deg_lists (n_row, n_col, Row, Col, head, + min_score, n_col2-k, max_deg) ; + debug_matrix (n_row, n_col, Row, Col, A) ; +#endif + + /* === Select pivot column, and order it ============================ */ + + /* make sure degree list isn't empty */ + assert (min_score >= 0) ; + assert (min_score <= n_col) ; + assert (head [min_score] >= EMPTY) ; + +#ifndef NDEBUG + for (debug_d = 0 ; debug_d < min_score ; debug_d++) + { + assert (head [debug_d] == EMPTY) ; + } +#endif + + /* get pivot column from head of minimum degree list */ + while (head [min_score] == EMPTY && min_score < n_col) + { + min_score++ ; + } + pivot_col = head [min_score] ; + assert (pivot_col >= 0 && pivot_col <= n_col) ; + next_col = Col [pivot_col].shared4.degree_next ; + head [min_score] = next_col ; + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = EMPTY ; + } + + assert (COL_IS_ALIVE (pivot_col)) ; + DEBUG3 (("Pivot col: %d\n", pivot_col)) ; + + /* remember score for defrag check */ + pivot_col_score = Col [pivot_col].shared2.score ; + + /* the pivot column is the kth column in the pivot order */ + Col [pivot_col].shared2.order = k ; + + /* increment order count by column thickness */ + pivot_col_thickness = Col [pivot_col].shared1.thickness ; + k += pivot_col_thickness ; + assert (pivot_col_thickness > 0) ; + + /* === Garbage_collection, if necessary ============================= */ + + needed_memory = MIN (pivot_col_score, n_col - k) ; + if (pfree + needed_memory >= Alen) + { + pfree = garbage_collection (n_row, n_col, Row, Col, A, &A [pfree]) ; + ngarbage++ ; + /* after garbage collection we will have enough */ + assert (pfree + needed_memory < Alen) ; + /* garbage collection has wiped out the Row[].shared2.mark array */ + tag_mark = clear_mark (n_row, Row) ; +#ifndef NDEBUG + debug_matrix (n_row, n_col, Row, Col, A) ; +#endif + } + + /* === Compute pivot row pattern ==================================== */ + + /* get starting location for this new merged row */ + pivot_row_start = pfree ; + + /* initialize new row counts to zero */ + pivot_row_degree = 0 ; + + /* tag pivot column as having been visited so it isn't included */ + /* in merged pivot row */ + Col [pivot_col].shared1.thickness = -pivot_col_thickness ; + + /* pivot row is the union of all rows in the pivot column pattern */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + DEBUG4 (("Pivot col pattern %d %d\n", ROW_IS_ALIVE (row), row)) ; + /* skip if row is dead */ + if (ROW_IS_DEAD (row)) + { + continue ; + } + rp = &A [Row [row].start] ; + rp_end = rp + Row [row].length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + /* add the column, if alive and untagged */ + col_thickness = Col [col].shared1.thickness ; + if (col_thickness > 0 && COL_IS_ALIVE (col)) + { + /* tag column in pivot row */ + Col [col].shared1.thickness = -col_thickness ; + assert (pfree < Alen) ; + /* place column in pivot row */ + A [pfree++] = col ; + pivot_row_degree += col_thickness ; + } + } + } + + /* clear tag on pivot column */ + Col [pivot_col].shared1.thickness = pivot_col_thickness ; + max_deg = MAX (max_deg, pivot_row_degree) ; + +#ifndef NDEBUG + DEBUG3 (("check2\n")) ; + debug_mark (n_row, Row, tag_mark, max_mark) ; +#endif + + /* === Kill all rows used to construct pivot row ==================== */ + + /* also kill pivot row, temporarily */ + cp = &A [Col [pivot_col].start] ; + cp_end = cp + Col [pivot_col].length ; + while (cp < cp_end) + { + /* may be killing an already dead row */ + row = *cp++ ; + DEBUG2 (("Kill row in pivot col: %d\n", row)) ; + KILL_ROW (row) ; + } + + /* === Select a row index to use as the new pivot row =============== */ + + pivot_row_length = pfree - pivot_row_start ; + if (pivot_row_length > 0) + { + /* pick the "pivot" row arbitrarily (first row in col) */ + pivot_row = A [Col [pivot_col].start] ; + DEBUG2 (("Pivotal row is %d\n", pivot_row)) ; + } + else + { + /* there is no pivot row, since it is of zero length */ + pivot_row = EMPTY ; + assert (pivot_row_length == 0) ; + } + assert (Col [pivot_col].length > 0 || pivot_row_length == 0) ; + + /* === Approximate degree computation =============================== */ + + /* Here begins the computation of the approximate degree. The column */ + /* score is the sum of the pivot row "length", plus the size of the */ + /* set differences of each row in the column minus the pattern of the */ + /* pivot row itself. The column ("thickness") itself is also */ + /* excluded from the column score (we thus use an approximate */ + /* external degree). */ + + /* The time taken by the following code (compute set differences, and */ + /* add them up) is proportional to the size of the data structure */ + /* being scanned - that is, the sum of the sizes of each column in */ + /* the pivot row. Thus, the amortized time to compute a column score */ + /* is proportional to the size of that column (where size, in this */ + /* context, is the column "length", or the number of row indices */ + /* in that column). The number of row indices in a column is */ + /* monotonically non-decreasing, from the length of the original */ + /* column on input to colamd. */ + + /* === Compute set differences ====================================== */ + + DEBUG1 (("** Computing set differences phase. **\n")) ; + + /* pivot row is currently dead - it will be revived later. */ + + DEBUG2 (("Pivot row: ")) ; + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + assert (COL_IS_ALIVE (col) && col != pivot_col) ; + DEBUG2 (("Col: %d\n", col)) ; + + /* clear tags used to construct pivot row pattern */ + col_thickness = -Col [col].shared1.thickness ; + assert (col_thickness > 0) ; + Col [col].shared1.thickness = col_thickness ; + + /* === Remove column from degree list =========================== */ + + cur_score = Col [col].shared2.score ; + prev_col = Col [col].shared3.prev ; + next_col = Col [col].shared4.degree_next ; + assert (cur_score >= 0) ; + assert (cur_score <= n_col) ; + assert (cur_score >= EMPTY) ; + if (prev_col == EMPTY) + { + head [cur_score] = next_col ; + } + else + { + Col [prev_col].shared4.degree_next = next_col ; + } + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = prev_col ; + } + + /* === Scan the column ========================================== */ + + cp = &A [Col [col].start] ; + cp_end = cp + Col [col].length ; + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + continue ; + } + assert (row != pivot_row) ; + set_difference = row_mark - tag_mark ; + /* check if the row has been seen yet */ + if (set_difference < 0) + { + assert (Row [row].shared1.degree <= max_deg) ; + set_difference = Row [row].shared1.degree ; + } + /* subtract column thickness from this row's set difference */ + set_difference -= col_thickness ; + assert (set_difference >= 0) ; + /* absorb this row if the set difference becomes zero */ + if (set_difference == 0) + { + DEBUG1 (("aggressive absorption. Row: %d\n", row)) ; + KILL_ROW (row) ; + } + else + { + /* save the new mark */ + Row [row].shared2.mark = set_difference + tag_mark ; + } + } + } + +#ifndef NDEBUG + debug_deg_lists (n_row, n_col, Row, Col, head, + min_score, n_col2-k-pivot_row_degree, max_deg) ; +#endif + + /* === Add up set differences for each column ======================= */ + + DEBUG1 (("** Adding set differences phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + /* get a column */ + col = *rp++ ; + assert (COL_IS_ALIVE (col) && col != pivot_col) ; + hash = 0 ; + cur_score = 0 ; + cp = &A [Col [col].start] ; + /* compact the column */ + new_cp = cp ; + cp_end = cp + Col [col].length ; + + DEBUG2 (("Adding set diffs for Col: %d.\n", col)) ; + + while (cp < cp_end) + { + /* get a row */ + row = *cp++ ; + assert(row >= 0 && row < n_row) ; + row_mark = Row [row].shared2.mark ; + /* skip if dead */ + if (ROW_IS_MARKED_DEAD (row_mark)) + { + continue ; + } + assert (row_mark > tag_mark) ; + /* compact the column */ + *new_cp++ = row ; + /* compute hash function */ + hash += row ; + /* add set difference */ + cur_score += row_mark - tag_mark ; + /* integer overflow... */ + cur_score = MIN (cur_score, n_col) ; + } + + /* recompute the column's length */ + Col [col].length = (int) (new_cp - &A [Col [col].start]) ; + + /* === Further mass elimination ================================= */ + + if (Col [col].length == 0) + { + DEBUG1 (("further mass elimination. Col: %d\n", col)) ; + /* nothing left but the pivot row in this column */ + KILL_PRINCIPAL_COL (col) ; + pivot_row_degree -= Col [col].shared1.thickness ; + assert (pivot_row_degree >= 0) ; + /* order it */ + Col [col].shared2.order = k ; + /* increment order count by column thickness */ + k += Col [col].shared1.thickness ; + } + else + { + /* === Prepare for supercolumn detection ==================== */ + + DEBUG2 (("Preparing supercol detection for Col: %d.\n", col)) ; + + /* save score so far */ + Col [col].shared2.score = cur_score ; + + /* add column to hash table, for supercolumn detection */ + hash %= n_col + 1 ; + + DEBUG2 ((" Hash = %d, n_col = %d.\n", hash, n_col)) ; + assert (hash <= n_col) ; + + head_column = head [hash] ; + if (head_column > EMPTY) + { + /* degree list "hash" is non-empty, use prev (shared3) of */ + /* first column in degree list as head of hash bucket */ + first_col = Col [head_column].shared3.headhash ; + Col [head_column].shared3.headhash = col ; + } + else + { + /* degree list "hash" is empty, use head as hash bucket */ + first_col = - (head_column + 2) ; + head [hash] = - (col + 2) ; + } + Col [col].shared4.hash_next = first_col ; + + /* save hash function in Col [col].shared3.hash */ + Col [col].shared3.hash = (int) hash ; + assert (COL_IS_ALIVE (col)) ; + } + } + + /* The approximate external column degree is now computed. */ + + /* === Supercolumn detection ======================================== */ + + DEBUG1 (("** Supercolumn detection phase. **\n")) ; + + detect_super_cols ( +#ifndef NDEBUG + n_col, Row, +#endif + Col, A, head, pivot_row_start, pivot_row_length) ; + + /* === Kill the pivotal column ====================================== */ + + KILL_PRINCIPAL_COL (pivot_col) ; + + /* === Clear mark =================================================== */ + + tag_mark += (max_deg + 1) ; + if (tag_mark >= max_mark) + { + DEBUG1 (("clearing tag_mark\n")) ; + tag_mark = clear_mark (n_row, Row) ; + } +#ifndef NDEBUG + DEBUG3 (("check3\n")) ; + debug_mark (n_row, Row, tag_mark, max_mark) ; +#endif + + /* === Finalize the new pivot row, and column scores ================ */ + + DEBUG1 (("** Finalize scores phase. **\n")) ; + + /* for each column in pivot row */ + rp = &A [pivot_row_start] ; + /* compact the pivot row */ + new_rp = rp ; + rp_end = rp + pivot_row_length ; + while (rp < rp_end) + { + col = *rp++ ; + /* skip dead columns */ + if (COL_IS_DEAD (col)) + { + continue ; + } + *new_rp++ = col ; + /* add new pivot row to column */ + A [Col [col].start + (Col [col].length++)] = pivot_row ; + + /* retrieve score so far and add on pivot row's degree. */ + /* (we wait until here for this in case the pivot */ + /* row's degree was reduced due to mass elimination). */ + cur_score = Col [col].shared2.score + pivot_row_degree ; + + /* calculate the max possible score as the number of */ + /* external columns minus the 'k' value minus the */ + /* columns thickness */ + max_score = n_col - k - Col [col].shared1.thickness ; + + /* make the score the external degree of the union-of-rows */ + cur_score -= Col [col].shared1.thickness ; + + /* make sure score is less or equal than the max score */ + cur_score = MIN (cur_score, max_score) ; + assert (cur_score >= 0) ; + + /* store updated score */ + Col [col].shared2.score = cur_score ; + + /* === Place column back in degree list ========================= */ + + assert (min_score >= 0) ; + assert (min_score <= n_col) ; + assert (cur_score >= 0) ; + assert (cur_score <= n_col) ; + assert (head [cur_score] >= EMPTY) ; + next_col = head [cur_score] ; + Col [col].shared4.degree_next = next_col ; + Col [col].shared3.prev = EMPTY ; + if (next_col != EMPTY) + { + Col [next_col].shared3.prev = col ; + } + head [cur_score] = col ; + + /* see if this score is less than current min */ + min_score = MIN (min_score, cur_score) ; + + } + +#ifndef NDEBUG + debug_deg_lists (n_row, n_col, Row, Col, head, + min_score, n_col2-k, max_deg) ; +#endif + + /* === Resurrect the new pivot row ================================== */ + + if (pivot_row_degree > 0) + { + /* update pivot row length to reflect any cols that were killed */ + /* during super-col detection and mass elimination */ + Row [pivot_row].start = pivot_row_start ; + Row [pivot_row].length = (int) (new_rp - &A[pivot_row_start]) ; + Row [pivot_row].shared1.degree = pivot_row_degree ; + Row [pivot_row].shared2.mark = 0 ; + /* pivot row is no longer dead */ + } + } + + /* === All principal columns have now been ordered ====================== */ + + return (ngarbage) ; +} + + +/* ========================================================================== */ +/* === order_children ======================================================= */ +/* ========================================================================== */ + +/* + The find_ordering routine has ordered all of the principal columns (the + representatives of the supercolumns). The non-principal columns have not + yet been ordered. This routine orders those columns by walking up the + parent tree (a column is a child of the column which absorbed it). The + final permutation vector is then placed in p [0 ... n_col-1], with p [0] + being the first column, and p [n_col-1] being the last. It doesn't look + like it at first glance, but be assured that this routine takes time linear + in the number of columns. Although not immediately obvious, the time + taken by this routine is O (n_col), that is, linear in the number of + columns. Not user-callable. +*/ + +PRIVATE void order_children +( + /* === Parameters ======================================================= */ + + int n_col, /* number of columns of A */ + ColInfo Col [], /* of size n_col+1 */ + int p [] /* p [0 ... n_col-1] is the column permutation*/ +) +{ + /* === Local variables ================================================== */ + + int i ; /* loop counter for all columns */ + int c ; /* column index */ + int parent ; /* index of column's parent */ + int order ; /* column's order */ + + /* === Order each non-principal column ================================== */ + + for (i = 0 ; i < n_col ; i++) + { + /* find an un-ordered non-principal column */ + assert (COL_IS_DEAD (i)) ; + if (!COL_IS_DEAD_PRINCIPAL (i) && Col [i].shared2.order == EMPTY) + { + parent = i ; + /* once found, find its principal parent */ + do + { + parent = Col [parent].shared1.parent ; + } while (!COL_IS_DEAD_PRINCIPAL (parent)) ; + + /* now, order all un-ordered non-principal columns along path */ + /* to this parent. collapse tree at the same time */ + c = i ; + /* get order of parent */ + order = Col [parent].shared2.order ; + + do + { + assert (Col [c].shared2.order == EMPTY) ; + + /* order this column */ + Col [c].shared2.order = order++ ; + /* collaps tree */ + Col [c].shared1.parent = parent ; + + /* get immediate parent of this column */ + c = Col [c].shared1.parent ; + + /* continue until we hit an ordered column. There are */ + /* guarranteed not to be anymore unordered columns */ + /* above an ordered column */ + } while (Col [c].shared2.order == EMPTY) ; + + /* re-order the super_col parent to largest order for this group */ + Col [parent].shared2.order = order ; + } + } + + /* === Generate the permutation ========================================= */ + + for (c = 0 ; c < n_col ; c++) + { + p [Col [c].shared2.order] = c ; + } +} + + +/* ========================================================================== */ +/* === detect_super_cols ==================================================== */ +/* ========================================================================== */ + +/* + Detects supercolumns by finding matches between columns in the hash buckets. + Check amongst columns in the set A [row_start ... row_start + row_length-1]. + The columns under consideration are currently *not* in the degree lists, + and have already been placed in the hash buckets. + + The hash bucket for columns whose hash function is equal to h is stored + as follows: + + if head [h] is >= 0, then head [h] contains a degree list, so: + + head [h] is the first column in degree bucket h. + Col [head [h]].headhash gives the first column in hash bucket h. + + otherwise, the degree list is empty, and: + + -(head [h] + 2) is the first column in hash bucket h. + + For a column c in a hash bucket, Col [c].shared3.prev is NOT a "previous + column" pointer. Col [c].shared3.hash is used instead as the hash number + for that column. The value of Col [c].shared4.hash_next is the next column + in the same hash bucket. + + Assuming no, or "few" hash collisions, the time taken by this routine is + linear in the sum of the sizes (lengths) of each column whose score has + just been computed in the approximate degree computation. + Not user-callable. +*/ + +PRIVATE void detect_super_cols +( + /* === Parameters ======================================================= */ + +#ifndef NDEBUG + /* these two parameters are only needed when debugging is enabled: */ + int n_col, /* number of columns of A */ + RowInfo Row [], /* of size n_row+1 */ +#endif + ColInfo Col [], /* of size n_col+1 */ + int A [], /* row indices of A */ + int head [], /* head of degree lists and hash buckets */ + int row_start, /* pointer to set of columns to check */ + int row_length /* number of columns to check */ +) +{ + /* === Local variables ================================================== */ + + int hash ; /* hash # for a column */ + int *rp ; /* pointer to a row */ + int c ; /* a column index */ + int super_c ; /* column index of the column to absorb into */ + int *cp1 ; /* column pointer for column super_c */ + int *cp2 ; /* column pointer for column c */ + int length ; /* length of column super_c */ + int prev_c ; /* column preceding c in hash bucket */ + int i ; /* loop counter */ + int *rp_end ; /* pointer to the end of the row */ + int col ; /* a column index in the row to check */ + int head_column ; /* first column in hash bucket or degree list */ + int first_col ; /* first column in hash bucket */ + + /* === Consider each column in the row ================================== */ + + rp = &A [row_start] ; + rp_end = rp + row_length ; + while (rp < rp_end) + { + col = *rp++ ; + if (COL_IS_DEAD (col)) + { + continue ; + } + + /* get hash number for this column */ + hash = Col [col].shared3.hash ; + assert (hash <= n_col) ; + + /* === Get the first column in this hash bucket ===================== */ + + head_column = head [hash] ; + if (head_column > EMPTY) + { + first_col = Col [head_column].shared3.headhash ; + } + else + { + first_col = - (head_column + 2) ; + } + + /* === Consider each column in the hash bucket ====================== */ + + for (super_c = first_col ; super_c != EMPTY ; + super_c = Col [super_c].shared4.hash_next) + { + assert (COL_IS_ALIVE (super_c)) ; + assert (Col [super_c].shared3.hash == hash) ; + length = Col [super_c].length ; + + /* prev_c is the column preceding column c in the hash bucket */ + prev_c = super_c ; + + /* === Compare super_c with all columns after it ================ */ + + for (c = Col [super_c].shared4.hash_next ; + c != EMPTY ; c = Col [c].shared4.hash_next) + { + assert (c != super_c) ; + assert (COL_IS_ALIVE (c)) ; + assert (Col [c].shared3.hash == hash) ; + + /* not identical if lengths or scores are different */ + if (Col [c].length != length || + Col [c].shared2.score != Col [super_c].shared2.score) + { + prev_c = c ; + continue ; + } + + /* compare the two columns */ + cp1 = &A [Col [super_c].start] ; + cp2 = &A [Col [c].start] ; + + for (i = 0 ; i < length ; i++) + { + /* the columns are "clean" (no dead rows) */ + assert (ROW_IS_ALIVE (*cp1)) ; + assert (ROW_IS_ALIVE (*cp2)) ; + /* row indices will same order for both supercols, */ + /* no gather scatter nessasary */ + if (*cp1++ != *cp2++) + { + break ; + } + } + + /* the two columns are different if the for-loop "broke" */ + if (i != length) + { + prev_c = c ; + continue ; + } + + /* === Got it! two columns are identical =================== */ + + assert (Col [c].shared2.score == Col [super_c].shared2.score) ; + + Col [super_c].shared1.thickness += Col [c].shared1.thickness ; + Col [c].shared1.parent = super_c ; + KILL_NON_PRINCIPAL_COL (c) ; + /* order c later, in order_children() */ + Col [c].shared2.order = EMPTY ; + /* remove c from hash bucket */ + Col [prev_c].shared4.hash_next = Col [c].shared4.hash_next ; + } + } + + /* === Empty this hash bucket ======================================= */ + + if (head_column > EMPTY) + { + /* corresponding degree list "hash" is not empty */ + Col [head_column].shared3.headhash = EMPTY ; + } + else + { + /* corresponding degree list "hash" is empty */ + head [hash] = EMPTY ; + } + } +} + + +/* ========================================================================== */ +/* === garbage_collection =================================================== */ +/* ========================================================================== */ + +/* + Defragments and compacts columns and rows in the workspace A. Used when + all avaliable memory has been used while performing row merging. Returns + the index of the first free position in A, after garbage collection. The + time taken by this routine is linear is the size of the array A, which is + itself linear in the number of nonzeros in the input matrix. + Not user-callable. +*/ + +PRIVATE int garbage_collection /* returns the new value of pfree */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows */ + int n_col, /* number of columns */ + RowInfo Row [], /* row info */ + ColInfo Col [], /* column info */ + int A [], /* A [0 ... Alen-1] holds the matrix */ + int *pfree /* &A [0] ... pfree is in use */ +) +{ + /* === Local variables ================================================== */ + + int *psrc ; /* source pointer */ + int *pdest ; /* destination pointer */ + int j ; /* counter */ + int r ; /* a row index */ + int c ; /* a column index */ + int length ; /* length of a row or column */ + +#ifndef NDEBUG + int debug_rows ; + DEBUG0 (("Defrag..\n")) ; + for (psrc = &A[0] ; psrc < pfree ; psrc++) assert (*psrc >= 0) ; + debug_rows = 0 ; +#endif + + /* === Defragment the columns =========================================== */ + + pdest = &A[0] ; + for (c = 0 ; c < n_col ; c++) + { + if (COL_IS_ALIVE (c)) + { + psrc = &A [Col [c].start] ; + + /* move and compact the column */ + assert (pdest <= psrc) ; + Col [c].start = (int) (pdest - &A [0]) ; + length = Col [c].length ; + for (j = 0 ; j < length ; j++) + { + r = *psrc++ ; + if (ROW_IS_ALIVE (r)) + { + *pdest++ = r ; + } + } + Col [c].length = (int) (pdest - &A [Col [c].start]) ; + } + } + + /* === Prepare to defragment the rows =================================== */ + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + if (Row [r].length == 0) + { + /* this row is of zero length. cannot compact it, so kill it */ + DEBUG0 (("Defrag row kill\n")) ; + KILL_ROW (r) ; + } + else + { + /* save first column index in Row [r].shared2.first_column */ + psrc = &A [Row [r].start] ; + Row [r].shared2.first_column = *psrc ; + assert (ROW_IS_ALIVE (r)) ; + /* flag the start of the row with the one's complement of row */ + *psrc = ONES_COMPLEMENT (r) ; +#ifndef NDEBUG + debug_rows++ ; +#endif + } + } + } + + /* === Defragment the rows ============================================== */ + + psrc = pdest ; + while (psrc < pfree) + { + /* find a negative number ... the start of a row */ + if (*psrc++ < 0) + { + psrc-- ; + /* get the row index */ + r = ONES_COMPLEMENT (*psrc) ; + assert (r >= 0 && r < n_row) ; + /* restore first column index */ + *psrc = Row [r].shared2.first_column ; + assert (ROW_IS_ALIVE (r)) ; + + /* move and compact the row */ + assert (pdest <= psrc) ; + Row [r].start = (int) (pdest - &A [0]) ; + length = Row [r].length ; + for (j = 0 ; j < length ; j++) + { + c = *psrc++ ; + if (COL_IS_ALIVE (c)) + { + *pdest++ = c ; + } + } + Row [r].length = (int) (pdest - &A [Row [r].start]) ; +#ifndef NDEBUG + debug_rows-- ; +#endif + } + } + /* ensure we found all the rows */ + assert (debug_rows == 0) ; + + /* === Return the new value of pfree ==================================== */ + + return ((int) (pdest - &A [0])) ; +} + + +/* ========================================================================== */ +/* === clear_mark =========================================================== */ +/* ========================================================================== */ + +/* + Clears the Row [].shared2.mark array, and returns the new tag_mark. + Return value is the new tag_mark. Not user-callable. +*/ + +PRIVATE int clear_mark /* return the new value for tag_mark */ +( + /* === Parameters ======================================================= */ + + int n_row, /* number of rows in A */ + RowInfo Row [] /* Row [0 ... n_row-1].shared2.mark is set to zero */ +) +{ + /* === Local variables ================================================== */ + + int r ; + + DEBUG0 (("Clear mark\n")) ; + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + Row [r].shared2.mark = 0 ; + } + } + return (1) ; +} + + +/* ========================================================================== */ +/* === debugging routines =================================================== */ +/* ========================================================================== */ + +/* When debugging is disabled, the remainder of this file is ignored. */ + +#ifndef NDEBUG + + +/* ========================================================================== */ +/* === debug_structures ===================================================== */ +/* ========================================================================== */ + +/* + At this point, all empty rows and columns are dead. All live columns + are "clean" (containing no dead rows) and simplicial (no supercolumns + yet). Rows may contain dead columns, but all live rows contain at + least one live column. +*/ + +PRIVATE void debug_structures +( + /* === Parameters ======================================================= */ + + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [], + int n_col2 +) +{ + /* === Local variables ================================================== */ + + int i ; + int c ; + int *cp ; + int *cp_end ; + int len ; + int score ; + int r ; + int *rp ; + int *rp_end ; + int deg ; + + /* === Check A, Row, and Col ============================================ */ + + for (c = 0 ; c < n_col ; c++) + { + if (COL_IS_ALIVE (c)) + { + len = Col [c].length ; + score = Col [c].shared2.score ; + DEBUG4 (("initial live col %5d %5d %5d\n", c, len, score)) ; + assert (len > 0) ; + assert (score >= 0) ; + assert (Col [c].shared1.thickness == 1) ; + cp = &A [Col [c].start] ; + cp_end = cp + len ; + while (cp < cp_end) + { + r = *cp++ ; + assert (ROW_IS_ALIVE (r)) ; + } + } + else + { + i = Col [c].shared2.order ; + assert (i >= n_col2 && i < n_col) ; + } + } + + for (r = 0 ; r < n_row ; r++) + { + if (ROW_IS_ALIVE (r)) + { + i = 0 ; + len = Row [r].length ; + deg = Row [r].shared1.degree ; + assert (len > 0) ; + assert (deg > 0) ; + rp = &A [Row [r].start] ; + rp_end = rp + len ; + while (rp < rp_end) + { + c = *rp++ ; + if (COL_IS_ALIVE (c)) + { + i++ ; + } + } + assert (i > 0) ; + } + } +} + + +/* ========================================================================== */ +/* === debug_deg_lists ====================================================== */ +/* ========================================================================== */ + +/* + Prints the contents of the degree lists. Counts the number of columns + in the degree list and compares it to the total it should have. Also + checks the row degrees. +*/ + +PRIVATE void debug_deg_lists +( + /* === Parameters ======================================================= */ + + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int head [], + int min_score, + int should, + int max_deg +) +{ + /* === Local variables ================================================== */ + + int deg ; + int col ; + int have ; + int row ; + + /* === Check the degree lists =========================================== */ + + if (n_col > 10000 && debug_colamd <= 0) + { + return ; + } + have = 0 ; + DEBUG4 (("Degree lists: %d\n", min_score)) ; + for (deg = 0 ; deg <= n_col ; deg++) + { + col = head [deg] ; + if (col == EMPTY) + { + continue ; + } + DEBUG4 (("%d:", deg)) ; + while (col != EMPTY) + { + DEBUG4 ((" %d", col)) ; + have += Col [col].shared1.thickness ; + assert (COL_IS_ALIVE (col)) ; + col = Col [col].shared4.degree_next ; + } + DEBUG4 (("\n")) ; + } + DEBUG4 (("should %d have %d\n", should, have)) ; + assert (should == have) ; + + /* === Check the row degrees ============================================ */ + + if (n_row > 10000 && debug_colamd <= 0) + { + return ; + } + for (row = 0 ; row < n_row ; row++) + { + if (ROW_IS_ALIVE (row)) + { + assert (Row [row].shared1.degree <= max_deg) ; + } + } +} + + +/* ========================================================================== */ +/* === debug_mark =========================================================== */ +/* ========================================================================== */ + +/* + Ensures that the tag_mark is less that the maximum and also ensures that + each entry in the mark array is less than the tag mark. +*/ + +PRIVATE void debug_mark +( + /* === Parameters ======================================================= */ + + int n_row, + RowInfo Row [], + int tag_mark, + int max_mark +) +{ + /* === Local variables ================================================== */ + + int r ; + + /* === Check the Row marks ============================================== */ + + assert (tag_mark > 0 && tag_mark <= max_mark) ; + if (n_row > 10000 && debug_colamd <= 0) + { + return ; + } + for (r = 0 ; r < n_row ; r++) + { + assert (Row [r].shared2.mark < tag_mark) ; + } +} + + +/* ========================================================================== */ +/* === debug_matrix ========================================================= */ +/* ========================================================================== */ + +/* + Prints out the contents of the columns and the rows. +*/ + +PRIVATE void debug_matrix +( + /* === Parameters ======================================================= */ + + int n_row, + int n_col, + RowInfo Row [], + ColInfo Col [], + int A [] +) +{ + /* === Local variables ================================================== */ + + int r ; + int c ; + int *rp ; + int *rp_end ; + int *cp ; + int *cp_end ; + + /* === Dump the rows and columns of the matrix ========================== */ + + if (debug_colamd < 3) + { + return ; + } + DEBUG3 (("DUMP MATRIX:\n")) ; + for (r = 0 ; r < n_row ; r++) + { + DEBUG3 (("Row %d alive? %d\n", r, ROW_IS_ALIVE (r))) ; + if (ROW_IS_DEAD (r)) + { + continue ; + } + DEBUG3 (("start %d length %d degree %d\n", + Row [r].start, Row [r].length, Row [r].shared1.degree)) ; + rp = &A [Row [r].start] ; + rp_end = rp + Row [r].length ; + while (rp < rp_end) + { + c = *rp++ ; + DEBUG3 ((" %d col %d\n", COL_IS_ALIVE (c), c)) ; + } + } + + for (c = 0 ; c < n_col ; c++) + { + DEBUG3 (("Col %d alive? %d\n", c, COL_IS_ALIVE (c))) ; + if (COL_IS_DEAD (c)) + { + continue ; + } + DEBUG3 (("start %d length %d shared1 %d shared2 %d\n", + Col [c].start, Col [c].length, + Col [c].shared1.thickness, Col [c].shared2.score)) ; + cp = &A [Col [c].start] ; + cp_end = cp + Col [c].length ; + while (cp < cp_end) + { + r = *cp++ ; + DEBUG3 ((" %d row %d\n", ROW_IS_ALIVE (r), r)) ; + } + } +} + +#endif + |