forked from bartvdbraak/blender
2584 lines
78 KiB
C
2584 lines
78 KiB
C
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/* ========================================================================== */
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/* === colamd - a sparse matrix column ordering algorithm =================== */
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/* ========================================================================== */
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/*
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colamd: An approximate minimum degree column ordering algorithm.
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Purpose:
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Colamd computes a permutation Q such that the Cholesky factorization of
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(AQ)'(AQ) has less fill-in and requires fewer floating point operations
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than A'A. This also provides a good ordering for sparse partial
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pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
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factorization, and P is computed during numerical factorization via
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conventional partial pivoting with row interchanges. Colamd is the
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column ordering method used in SuperLU, part of the ScaLAPACK library.
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It is also available as user-contributed software for Matlab 5.2,
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available from MathWorks, Inc. (http://www.mathworks.com). This
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routine can be used in place of COLMMD in Matlab. By default, the \
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and / operators in Matlab perform a column ordering (using COLMMD)
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prior to LU factorization using sparse partial pivoting, in the
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built-in Matlab LU(A) routine.
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Authors:
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The authors of the code itself are Stefan I. Larimore and Timothy A.
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Davis (davis@cise.ufl.edu), University of Florida. The algorithm was
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developed in collaboration with John Gilbert, Xerox PARC, and Esmond
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Ng, Oak Ridge National Laboratory.
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Date:
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August 3, 1998. Version 1.0.
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Acknowledgements:
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This work was supported by the National Science Foundation, under
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grants DMS-9504974 and DMS-9803599.
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Notice:
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Copyright (c) 1998 by the University of Florida. All Rights Reserved.
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THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
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EXPRESSED OR IMPLIED. ANY USE IS AT YOUR OWN RISK.
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Permission is hereby granted to use or copy this program for any
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purpose, provided the above notices are retained on all copies.
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User documentation of any code that uses this code must cite the
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Authors, the Copyright, and "Used by permission." If this code is
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accessible from within Matlab, then typing "help colamd" or "colamd"
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(with no arguments) must cite the Authors. Permission to modify the
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code and to distribute modified code is granted, provided the above
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notices are retained, and a notice that the code was modified is
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included with the above copyright notice. You must also retain the
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Availability information below, of the original version.
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This software is provided free of charge.
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Availability:
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This file is located at
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http://www.cise.ufl.edu/~davis/colamd/colamd.c
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The colamd.h file is required, located in the same directory.
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The colamdmex.c file provides a Matlab interface for colamd.
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The symamdmex.c file provides a Matlab interface for symamd, which is
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a symmetric ordering based on this code, colamd.c. All codes are
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purely ANSI C compliant (they use no Unix-specific routines, include
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files, etc.).
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*/
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/* ========================================================================== */
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/* === Description of user-callable routines ================================ */
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/* ========================================================================== */
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/*
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Each user-callable routine (declared as PUBLIC) is briefly described below.
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Refer to the comments preceding each routine for more details.
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----------------------------------------------------------------------------
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colamd_recommended:
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----------------------------------------------------------------------------
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Usage:
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Alen = colamd_recommended (nnz, n_row, n_col) ;
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Purpose:
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Returns recommended value of Alen for use by colamd. Returns -1
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if any input argument is negative.
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Arguments:
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int nnz ; Number of nonzeros in the matrix A. This must
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be the same value as p [n_col] in the call to
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colamd - otherwise you will get a wrong value
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of the recommended memory to use.
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int n_row ; Number of rows in the matrix A.
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int n_col ; Number of columns in the matrix A.
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----------------------------------------------------------------------------
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colamd_set_defaults:
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----------------------------------------------------------------------------
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Usage:
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colamd_set_defaults (knobs) ;
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Purpose:
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Sets the default parameters.
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Arguments:
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double knobs [COLAMD_KNOBS] ; Output only.
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Rows with more than (knobs [COLAMD_DENSE_ROW] * n_col) entries
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are removed prior to ordering. Columns with more than
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(knobs [COLAMD_DENSE_COL] * n_row) entries are removed
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prior to ordering, and placed last in the output column
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ordering. Default values of these two knobs are both 0.5.
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Currently, only knobs [0] and knobs [1] are used, but future
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versions may use more knobs. If so, they will be properly set
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to their defaults by the future version of colamd_set_defaults,
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so that the code that calls colamd will not need to change,
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assuming that you either use colamd_set_defaults, or pass a
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(double *) NULL pointer as the knobs array to colamd.
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----------------------------------------------------------------------------
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colamd:
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----------------------------------------------------------------------------
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Usage:
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colamd (n_row, n_col, Alen, A, p, knobs) ;
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Purpose:
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Computes a column ordering (Q) of A such that P(AQ)=LU or
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(AQ)'AQ=LL' have less fill-in and require fewer floating point
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operations than factorizing the unpermuted matrix A or A'A,
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respectively.
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Arguments:
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int n_row ;
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Number of rows in the matrix A.
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Restriction: n_row >= 0.
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Colamd returns FALSE if n_row is negative.
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int n_col ;
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Number of columns in the matrix A.
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Restriction: n_col >= 0.
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Colamd returns FALSE if n_col is negative.
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int Alen ;
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Restriction (see note):
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Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col + COLAMD_STATS
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Colamd returns FALSE if these conditions are not met.
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Note: this restriction makes an modest assumption regarding
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the size of the two typedef'd structures, below. We do,
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however, guarantee that
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Alen >= colamd_recommended (nnz, n_row, n_col)
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will be sufficient.
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int A [Alen] ; Input argument, stats on output.
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A is an integer array of size Alen. Alen must be at least as
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large as the bare minimum value given above, but this is very
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low, and can result in excessive run time. For best
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performance, we recommend that Alen be greater than or equal to
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colamd_recommended (nnz, n_row, n_col), which adds
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nnz/5 to the bare minimum value given above.
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On input, the row indices of the entries in column c of the
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matrix are held in A [(p [c]) ... (p [c+1]-1)]. The row indices
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in a given column c need not be in ascending order, and
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duplicate row indices may be be present. However, colamd will
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work a little faster if both of these conditions are met
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(Colamd puts the matrix into this format, if it finds that the
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the conditions are not met).
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The matrix is 0-based. That is, rows are in the range 0 to
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n_row-1, and columns are in the range 0 to n_col-1. Colamd
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returns FALSE if any row index is out of range.
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The contents of A are modified during ordering, and are thus
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undefined on output with the exception of a few statistics
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about the ordering (A [0..COLAMD_STATS-1]):
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A [0]: number of dense or empty rows ignored.
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A [1]: number of dense or empty columns ignored (and ordered
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last in the output permutation p)
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A [2]: number of garbage collections performed.
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A [3]: 0, if all row indices in each column were in sorted
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order, and no duplicates were present.
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1, otherwise (in which case colamd had to do more work)
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Note that a row can become "empty" if it contains only
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"dense" and/or "empty" columns, and similarly a column can
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become "empty" if it only contains "dense" and/or "empty" rows.
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Future versions may return more statistics in A, but the usage
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of these 4 entries in A will remain unchanged.
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int p [n_col+1] ; Both input and output argument.
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p is an integer array of size n_col+1. On input, it holds the
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"pointers" for the column form of the matrix A. Column c of
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the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
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entry, p [0], must be zero, and p [c] <= p [c+1] must hold
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for all c in the range 0 to n_col-1. The value p [n_col] is
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thus the total number of entries in the pattern of the matrix A.
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Colamd returns FALSE if these conditions are not met.
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On output, if colamd returns TRUE, the array p holds the column
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permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
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the first column index in the new ordering, and p [n_col-1] is
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the last. That is, p [k] = j means that column j of A is the
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kth pivot column, in AQ, where k is in the range 0 to n_col-1
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(p [0] = j means that column j of A is the first column in AQ).
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If colamd returns FALSE, then no permutation is returned, and
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p is undefined on output.
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double knobs [COLAMD_KNOBS] ; Input only.
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See colamd_set_defaults for a description. If the knobs array
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is not present (that is, if a (double *) NULL pointer is passed
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in its place), then the default values of the parameters are
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used instead.
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*/
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/* ========================================================================== */
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/* === Include files ======================================================== */
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/* ========================================================================== */
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/* limits.h: the largest positive integer (INT_MAX) */
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#include <limits.h>
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/* colamd.h: knob array size, stats output size, and global prototypes */
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#include "colamd.h"
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/* ========================================================================== */
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/* === Scaffolding code definitions ======================================== */
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/* ========================================================================== */
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/* Ensure that debugging is turned off: */
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#ifndef NDEBUG
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#define NDEBUG
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#endif
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/* assert.h: the assert macro (no debugging if NDEBUG is defined) */
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#include <assert.h>
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/*
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Our "scaffolding code" philosophy: In our opinion, well-written library
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code should keep its "debugging" code, and just normally have it turned off
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by the compiler so as not to interfere with performance. This serves
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several purposes:
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(1) assertions act as comments to the reader, telling you what the code
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expects at that point. All assertions will always be true (unless
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there really is a bug, of course).
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(2) leaving in the scaffolding code assists anyone who would like to modify
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the code, or understand the algorithm (by reading the debugging output,
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one can get a glimpse into what the code is doing).
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(3) (gasp!) for actually finding bugs. This code has been heavily tested
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and "should" be fully functional and bug-free ... but you never know...
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To enable debugging, comment out the "#define NDEBUG" above. The code will
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become outrageously slow when debugging is enabled. To control the level of
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debugging output, set an environment variable D to 0 (little), 1 (some),
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2, 3, or 4 (lots).
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*/
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/* ========================================================================== */
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/* === Row and Column structures ============================================ */
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/* ========================================================================== */
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typedef struct ColInfo_struct
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{
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int start ; /* index for A of first row in this column, or DEAD */
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/* if column is dead */
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int length ; /* number of rows in this column */
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union
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{
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int thickness ; /* number of original columns represented by this */
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/* col, if the column is alive */
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int parent ; /* parent in parent tree super-column structure, if */
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/* the column is dead */
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} shared1 ;
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union
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{
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int score ; /* the score used to maintain heap, if col is alive */
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int order ; /* pivot ordering of this column, if col is dead */
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} shared2 ;
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union
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{
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int headhash ; /* head of a hash bucket, if col is at the head of */
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/* a degree list */
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int hash ; /* hash value, if col is not in a degree list */
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int prev ; /* previous column in degree list, if col is in a */
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/* degree list (but not at the head of a degree list) */
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} shared3 ;
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union
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{
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int degree_next ; /* next column, if col is in a degree list */
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int hash_next ; /* next column, if col is in a hash list */
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} shared4 ;
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} ColInfo ;
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typedef struct RowInfo_struct
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{
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int start ; /* index for A of first col in this row */
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int length ; /* number of principal columns in this row */
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union
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{
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int degree ; /* number of principal & non-principal columns in row */
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int p ; /* used as a row pointer in init_rows_cols () */
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} shared1 ;
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union
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{
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int mark ; /* for computing set differences and marking dead rows*/
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int first_column ;/* first column in row (used in garbage collection) */
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} shared2 ;
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} RowInfo ;
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/* ========================================================================== */
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/* === Definitions ========================================================== */
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||
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/* ========================================================================== */
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#define MAX(a,b) (((a) > (b)) ? (a) : (b))
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#define MIN(a,b) (((a) < (b)) ? (a) : (b))
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#define ONES_COMPLEMENT(r) (-(r)-1)
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#define TRUE (1)
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#define FALSE (0)
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#define EMPTY (-1)
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/* Row and column status */
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#define ALIVE (0)
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#define DEAD (-1)
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/* Column status */
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#define DEAD_PRINCIPAL (-1)
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#define DEAD_NON_PRINCIPAL (-2)
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/* Macros for row and column status update and checking. */
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#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
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#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
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#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
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#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
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#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
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#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
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#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
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|
|
#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
|
||
|
|
|