4621 lines
137 KiB
C
4621 lines
137 KiB
C
/* ========================================================================== */
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/* === CCOLAMD/CSYMAMD - a constrained column ordering algorithm ============ */
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/* ========================================================================== */
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/* ----------------------------------------------------------------------------
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* CCOLAMD, Copyright (C) Univ. of Florida. Authors: Timothy A. Davis,
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* Sivasankaran Rajamanickam, and Stefan Larimore
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* See License.txt for the Version 2.1 of the GNU Lesser General Public License
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* http://www.cise.ufl.edu/research/sparse
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* -------------------------------------------------------------------------- */
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/*
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* ccolamd: a constrained approximate minimum degree column ordering
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* algorithm, LU factorization of symmetric or unsymmetric matrices,
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* QR factorization, least squares, interior point methods for
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* linear programming problems, and other related problems.
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*
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* csymamd: a constrained approximate minimum degree ordering algorithm for
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* Cholesky factorization of symmetric matrices.
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*
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* Purpose:
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*
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* CCOLAMD 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. CCOLAMD is an
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* extension of COLAMD, available as built-in function in MATLAB Version 6,
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* available from MathWorks, Inc. (http://www.mathworks.com). This
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* routine can be used in place of COLAMD in MATLAB.
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*
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* CSYMAMD computes a permutation P of a symmetric matrix A such that the
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* Cholesky factorization of PAP' has less fill-in and requires fewer
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* floating point operations than A. CSYMAMD constructs a matrix M such
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* that M'M has the same nonzero pattern of A, and then orders the columns
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* of M using colmmd. The column ordering of M is then returned as the
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* row and column ordering P of A. CSYMAMD is an extension of SYMAMD.
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*
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* Authors:
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*
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* Timothy A. Davis and S. Rajamanickam wrote CCOLAMD, based directly on
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* COLAMD by Stefan I. Larimore and Timothy A. Davis, University of
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* Florida. The algorithm was developed in collaboration with John
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* Gilbert, (UCSB, then at Xerox PARC), and Esmond Ng, (Lawrence Berkeley
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* National Lab, then at Oak Ridge National Laboratory).
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*
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* Acknowledgements:
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*
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* This work was supported by the National Science Foundation, under
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* grants DMS-9504974 and DMS-9803599, CCR-0203270, and a grant from the
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* Sandia National Laboratory (Dept. of Energy).
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*
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* Copyright and License:
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*
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* Copyright (c) 1998-2005 by the University of Florida.
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* All Rights Reserved.
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* COLAMD is also available under alternate licenses, contact T. Davis
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* for details.
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*
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* This library is free software; you can redistribute it and/or
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* modify it under the terms of the GNU Lesser General Public
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* License as published by the Free Software Foundation; either
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* version 2.1 of the License, or (at your option) any later version.
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*
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* This library is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public
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* License along with this library; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301
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* USA
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*
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* Permission is hereby granted to use or copy this program under the
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* terms of the GNU LGPL, provided that the Copyright, this License,
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* and the Availability of the original version is retained on all copies.
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* User documentation of any code that uses this code or any modified
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* version of this code must cite the Copyright, this License, the
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* Availability note, and "Used by permission." Permission to modify
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* the code and to distribute modified code is granted, provided the
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* Copyright, this License, and the Availability note are retained,
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* and a notice that the code was modified is included.
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*
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* Availability:
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*
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* The CCOLAMD/CSYMAMD library is available at
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*
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* http://www.cise.ufl.edu/research/sparse/ccolamd/
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*
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* This is the http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd.c
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* file.
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*
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* See the ChangeLog file for changes since Version 1.0.
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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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/* CCOLAMD includes both int and UF_long versions of all its routines. The
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* description below is for the int version. For UF_long, all int arguments
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* become UF_long integers. UF_long is normally defined as long, except for
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* WIN64 */
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/* ----------------------------------------------------------------------------
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* ccolamd_recommended:
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* ----------------------------------------------------------------------------
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*
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* C syntax:
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*
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* #include "ccolamd.h"
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* size_t ccolamd_recommended (int nnz, int n_row, int n_col) ;
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* size_t ccolamd_l_recommended (UF_long nnz, UF_long n_row,
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* UF_long n_col) ;
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*
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* Purpose:
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*
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* Returns recommended value of Alen for use by ccolamd. Returns 0
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* if any input argument is negative. The use of this routine
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* is optional. Not needed for csymamd, which dynamically allocates
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* its own memory.
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*
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* Arguments (all input arguments):
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*
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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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* ccolamd - otherwise you will get a wrong value
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* of the recommended memory to use.
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*
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* int n_row ; Number of rows in the matrix A.
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*
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* int n_col ; Number of columns in the matrix A.
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*
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* ----------------------------------------------------------------------------
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* ccolamd_set_defaults:
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* ----------------------------------------------------------------------------
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*
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* C syntax:
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*
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* #include "ccolamd.h"
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* ccolamd_set_defaults (double knobs [CCOLAMD_KNOBS]) ;
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* ccolamd_l_set_defaults (double knobs [CCOLAMD_KNOBS]) ;
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*
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* Purpose:
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*
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* Sets the default parameters. The use of this routine is optional.
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* Passing a (double *) NULL pointer for the knobs results in the
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* default parameter settings.
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*
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* Arguments:
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*
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* double knobs [CCOLAMD_KNOBS] ; Output only.
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*
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* knobs [0] and knobs [1] behave differently than they did in COLAMD.
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* The other knobs are new to CCOLAMD.
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*
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* knobs [0]: dense row control
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*
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* For CCOLAMD, rows with more than
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* max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n_col))
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* entries are removed prior to ordering.
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*
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* For CSYMAMD, rows and columns with more than
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* max (16, knobs [CCOLAMD_DENSE_ROW] * sqrt (n))
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* entries are removed prior to ordering, and placed last in the
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* output ordering (subject to the constraints).
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*
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* If negative, only completely dense rows are removed. If you
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* intend to use CCOLAMD for a Cholesky factorization of A*A', set
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* knobs [CCOLAMD_DENSE_ROW] to -1, which is more appropriate for
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* that case.
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*
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* Default: 10.
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*
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* knobs [1]: dense column control
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*
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* For CCOLAMD, columns with more than
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* max (16, knobs [CCOLAMD_DENSE_COL] * sqrt (MIN (n_row,n_col)))
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* entries are removed prior to ordering, and placed last in the
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* output column ordering (subject to the constraints).
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* Not used by CSYMAMD. If negative, only completely dense
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* columns are removed. Default: 10.
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*
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* knobs [2]: aggressive absorption
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*
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* knobs [CCOLAMD_AGGRESSIVE] controls whether or not to do
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* aggressive absorption during the ordering. Default is TRUE
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* (nonzero). If zero, no aggressive absorption is performed.
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*
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* knobs [3]: optimize ordering for LU or Cholesky
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*
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* knobs [CCOLAMD_LU] controls an option that optimizes the
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* ordering for the LU of A or the Cholesky factorization of A'A.
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* If TRUE (nonzero), an ordering optimized for LU is performed.
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* If FALSE (zero), an ordering for Cholesky is performed.
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* Default is FALSE. CSYMAMD ignores this parameter; it always
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* orders for Cholesky.
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*
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* ----------------------------------------------------------------------------
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* ccolamd:
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* ----------------------------------------------------------------------------
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*
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* C syntax:
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*
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* #include "ccolamd.h"
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* int ccolamd (int n_row, int n_col, int Alen, int *A, int *p,
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* double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS],
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* int *cmember) ;
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*
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* UF_long ccolamd_l (UF_long n_row, UF_long n_col, UF_long Alen,
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* UF_long *A, UF_long *p, double knobs [CCOLAMD_KNOBS],
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* UF_long stats [CCOLAMD_STATS], UF_long *cmember) ;
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*
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* Purpose:
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*
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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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*
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* Returns:
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*
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* TRUE (1) if successful, FALSE (0) otherwise.
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*
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* Arguments (for int version):
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*
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* int n_row ; Input argument.
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*
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* Number of rows in the matrix A.
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* Restriction: n_row >= 0.
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* ccolamd returns FALSE if n_row is negative.
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*
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* int n_col ; Input argument.
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*
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* Number of columns in the matrix A.
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* Restriction: n_col >= 0.
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* ccolamd returns FALSE if n_col is negative.
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*
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* int Alen ; Input argument.
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*
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* Restriction (see note):
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* Alen >= MAX (2*nnz, 4*n_col) + 17*n_col + 7*n_row + 7, where
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* nnz = p [n_col]. ccolamd returns FALSE if this condition is
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* not met. We recommend about nnz/5 more space for better
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* efficiency. This restriction makes an modest assumption
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* regarding the size of two typedef'd structures in ccolamd.h.
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* We do, however, guarantee that
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*
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* Alen >= ccolamd_recommended (nnz, n_row, n_col)
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*
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* will work efficiently.
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*
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* int A [Alen] ; Input argument, undefined on output.
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*
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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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* ccolamd_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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*
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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, ccolamd will
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* work a little faster if both of these conditions are met
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* (ccolamd puts the matrix into this format, if it finds that the
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* the conditions are not met).
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*
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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. ccolamd
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* returns FALSE if any row index is out of range.
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*
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* The contents of A are modified during ordering, and are
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* undefined on output.
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*
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* int p [n_col+1] ; Both input and output argument.
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*
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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 nnz = p [n_col]
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* is thus the total number of entries in the pattern of the
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* matrix A. ccolamd returns FALSE if these conditions are not
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* met.
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*
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* On output, if ccolamd 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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*
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* If ccolamd returns FALSE, then no permutation is returned, and
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* p is undefined on output.
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*
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* double knobs [CCOLAMD_KNOBS] ; Input argument.
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*
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* See ccolamd_set_defaults for a description.
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*
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* int stats [CCOLAMD_STATS] ; Output argument.
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*
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* Statistics on the ordering, and error status.
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* See ccolamd.h for related definitions.
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* ccolamd returns FALSE if stats is not present.
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*
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* stats [0]: number of dense or empty rows ignored.
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*
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* stats [1]: number of dense or empty columns ignored (and
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* ordered last in the output permutation p, subject to the
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* constraints). Note that a row can become "empty" if it
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* contains only "dense" and/or "empty" columns, and similarly
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* a column can become "empty" if it only contains "dense"
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* and/or "empty" rows.
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*
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* stats [2]: number of garbage collections performed. This can
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* be excessively high if Alen is close to the minimum
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* required value.
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*
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* stats [3]: status code. < 0 is an error code.
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* > 1 is a warning or notice.
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*
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* 0 OK. Each column of the input matrix contained row
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* indices in increasing order, with no duplicates.
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*
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* 1 OK, but columns of input matrix were jumbled (unsorted
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* columns or duplicate entries). CCOLAMD had to do some
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* extra work to sort the matrix first and remove
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* duplicate entries, but it still was able to return a
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* valid permutation (return value of ccolamd was TRUE).
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*
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* stats [4]: highest column index of jumbled columns
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* stats [5]: last seen duplicate or unsorted row index
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* stats [6]: number of duplicate or unsorted row indices
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*
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* -1 A is a null pointer
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*
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* -2 p is a null pointer
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*
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* -3 n_row is negative. stats [4]: n_row
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*
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* -4 n_col is negative. stats [4]: n_col
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*
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* -5 number of nonzeros in matrix is negative
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*
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* stats [4]: number of nonzeros, p [n_col]
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*
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* -6 p [0] is nonzero
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*
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* stats [4]: p [0]
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*
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* -7 A is too small
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*
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* stats [4]: required size
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* stats [5]: actual size (Alen)
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*
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* -8 a column has a negative number of entries
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*
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* stats [4]: column with < 0 entries
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* stats [5]: number of entries in col
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*
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* -9 a row index is out of bounds
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*
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* stats [4]: column with bad row index
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* stats [5]: bad row index
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* stats [6]: n_row, # of rows of matrx
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*
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* -10 (unused; see csymamd)
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*
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* int cmember [n_col] ; Input argument.
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*
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* cmember is new to CCOLAMD. It did not appear in COLAMD.
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* It places contraints on the output ordering. s = cmember [j]
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* gives the constraint set s that contains the column j
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* (Restriction: 0 <= s < n_col). In the output column
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* permutation, all columns in set 0 appear first, followed by
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* all columns in set 1, and so on. If NULL, all columns are
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* treated as if they were in a single constraint set, and you
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* will obtain the same ordering as COLAMD (with one exception:
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* the dense row/column threshold and other default knobs in
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* CCOLAMD and COLAMD are different).
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*
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* Example:
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*
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* See
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* http://www.cise.ufl.edu/research/sparse/ccolamd/ccolamd_example.c
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* for a complete example.
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*
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* To order the columns of a 5-by-4 matrix with 11 nonzero entries in
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* the following nonzero pattern
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*
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* x 0 x 0
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* x 0 x x
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* 0 x x 0
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* 0 0 x x
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* x x 0 0
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*
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* with default knobs, no output statistics, and no ordering
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* constraints, do the following:
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*
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* #include "ccolamd.h"
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* #define ALEN 144
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* int A [ALEN] = {0, 1, 4, 2, 4, 0, 1, 2, 3, 1, 3} ;
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* int p [ ] = {0, 3, 5, 9, 11} ;
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* int stats [CCOLAMD_STATS] ;
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* ccolamd (5, 4, ALEN, A, p, (double *) NULL, stats, NULL) ;
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*
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* The permutation is returned in the array p, and A is destroyed.
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*
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* ----------------------------------------------------------------------------
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* csymamd:
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* ----------------------------------------------------------------------------
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*
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* C syntax:
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*
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* #include "ccolamd.h"
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*
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* int csymamd (int n, int *A, int *p, int *perm,
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* double knobs [CCOLAMD_KNOBS], int stats [CCOLAMD_STATS],
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* void (*allocate) (size_t, size_t), void (*release) (void *),
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* int *cmember, int stype) ;
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*
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* UF_long csymamd_l (UF_long n, UF_long *A, UF_long *p, UF_long *perm,
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* double knobs [CCOLAMD_KNOBS], UF_long stats [CCOLAMD_STATS],
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* void (*allocate) (size_t, size_t), void (*release) (void *),
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* UF_long *cmember, UF_long stype) ;
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*
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|
* Purpose:
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*
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|
* The csymamd routine computes an ordering P of a symmetric sparse
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* matrix A such that the Cholesky factorization PAP' = LL' remains
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* sparse. It is based on a column ordering of a matrix M constructed
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* so that the nonzero pattern of M'M is the same as A. Either the
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* lower or upper triangular part of A can be used, or the pattern
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* A+A' can be used. You must pass your selected memory allocator
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* (usually calloc/free or mxCalloc/mxFree) to csymamd, for it to
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* allocate memory for the temporary matrix M.
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*
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|
* Returns:
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*
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* TRUE (1) if successful, FALSE (0) otherwise.
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*
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|
* Arguments:
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*
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* int n ; Input argument.
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*
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* Number of rows and columns in the symmetrix matrix A.
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|
* Restriction: n >= 0.
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* csymamd returns FALSE if n is negative.
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*
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|
* int A [nnz] ; Input argument.
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*
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|
* A is an integer array of size nnz, where nnz = p [n].
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|
*
|
|
* The row indices of the entries in column c of the matrix are
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|
* held in A [(p [c]) ... (p [c+1]-1)]. The row indices in a
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|
* given column c need not be in ascending order, and duplicate
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|
* row indices may be present. However, csymamd will run faster
|
|
* if the columns are in sorted order with no duplicate entries.
|
|
*
|
|
* The matrix is 0-based. That is, rows are in the range 0 to
|
|
* n-1, and columns are in the range 0 to n-1. csymamd
|
|
* returns FALSE if any row index is out of range.
|
|
*
|
|
* The contents of A are not modified.
|
|
*
|
|
* int p [n+1] ; Input argument.
|
|
*
|
|
* p is an integer array of size n+1. On input, it holds the
|
|
* "pointers" for the column form of the matrix A. Column c of
|
|
* the matrix A is held in A [(p [c]) ... (p [c+1]-1)]. The first
|
|
* entry, p [0], must be zero, and p [c] <= p [c+1] must hold
|
|
* for all c in the range 0 to n-1. The value p [n] is
|
|
* thus the total number of entries in the pattern of the matrix A.
|
|
* csymamd returns FALSE if these conditions are not met.
|
|
*
|
|
* The contents of p are not modified.
|
|
*
|
|
* int perm [n+1] ; Output argument.
|
|
*
|
|
* On output, if csymamd returns TRUE, the array perm holds the
|
|
* permutation P, where perm [0] is the first index in the new
|
|
* ordering, and perm [n-1] is the last. That is, perm [k] = j
|
|
* means that row and column j of A is the kth column in PAP',
|
|
* where k is in the range 0 to n-1 (perm [0] = j means
|
|
* that row and column j of A are the first row and column in
|
|
* PAP'). The array is used as a workspace during the ordering,
|
|
* which is why it must be of length n+1, not just n.
|
|
*
|
|
* double knobs [CCOLAMD_KNOBS] ; Input argument.
|
|
*
|
|
* See colamd_set_defaults for a description.
|
|
*
|
|
* int stats [CCOLAMD_STATS] ; Output argument.
|
|
*
|
|
* Statistics on the ordering, and error status.
|
|
* See ccolamd.h for related definitions.
|
|
* csymand returns FALSE if stats is not present.
|
|
*
|
|
* stats [0]: number of dense or empty row and columns ignored
|
|
* (and ordered last in the output permutation perm, subject
|
|
* to the constraints). Note that a row/column can become
|
|
* "empty" if it contains only "dense" and/or "empty"
|
|
* columns/rows.
|
|
*
|
|
* stats [1]: (same as stats [0])
|
|
*
|
|
* stats [2]: number of garbage collections performed.
|
|
*
|
|
* stats [3]: status code. < 0 is an error code.
|
|
* > 1 is a warning or notice.
|
|
*
|
|
* 0 to -9: same as ccolamd, with n replacing n_col and n_row,
|
|
* and -3 and -7 are unused.
|
|
*
|
|
* -10 out of memory (unable to allocate temporary workspace
|
|
* for M or count arrays using the "allocate" routine
|
|
* passed into csymamd).
|
|
*
|
|
* void * (*allocate) (size_t, size_t)
|
|
*
|
|
* A pointer to a function providing memory allocation. The
|
|
* allocated memory must be returned initialized to zero. For a
|
|
* C application, this argument should normally be a pointer to
|
|
* calloc. For a MATLAB mexFunction, the routine mxCalloc is
|
|
* passed instead.
|
|
*
|
|
* void (*release) (size_t, size_t)
|
|
*
|
|
* A pointer to a function that frees memory allocated by the
|
|
* memory allocation routine above. For a C application, this
|
|
* argument should normally be a pointer to free. For a MATLAB
|
|
* mexFunction, the routine mxFree is passed instead.
|
|
*
|
|
* int cmember [n] ; Input argument.
|
|
*
|
|
* Same as ccolamd, except that cmember is of size n, and it places
|
|
* contraints symmetrically, on both the row and column ordering.
|
|
* Entries in cmember must be in the range 0 to n-1.
|
|
*
|
|
* int stype ; Input argument.
|
|
*
|
|
* If stype < 0, then only the strictly lower triangular part of
|
|
* A is accessed. The upper triangular part is assumed to be the
|
|
* transpose of the lower triangular part. This is the same as
|
|
* SYMAMD, which did not have an stype parameter.
|
|
*
|
|
* If stype > 0, only the strictly upper triangular part of A is
|
|
* accessed. The lower triangular part is assumed to be the
|
|
* transpose of the upper triangular part.
|
|
*
|
|
* If stype == 0, then the nonzero pattern of A+A' is ordered.
|
|
*
|
|
* ----------------------------------------------------------------------------
|
|
* ccolamd_report:
|
|
* ----------------------------------------------------------------------------
|
|
*
|
|
* C syntax:
|
|
*
|
|
* #include "ccolamd.h"
|
|
* ccolamd_report (int stats [CCOLAMD_STATS]) ;
|
|
* ccolamd_l_report (UF_long stats [CCOLAMD_STATS]) ;
|
|
*
|
|
* Purpose:
|
|
*
|
|
* Prints the error status and statistics recorded in the stats
|
|
* array on the standard error output (for a standard C routine)
|
|
* or on the MATLAB output (for a mexFunction).
|
|
*
|
|
* Arguments:
|
|
*
|
|
* int stats [CCOLAMD_STATS] ; Input only. Statistics from ccolamd.
|
|
*
|
|
*
|
|
* ----------------------------------------------------------------------------
|
|
* csymamd_report:
|
|
* ----------------------------------------------------------------------------
|
|
*
|
|
* C syntax:
|
|
*
|
|
* #include "ccolamd.h"
|
|
* csymamd_report (int stats [CCOLAMD_STATS]) ;
|
|
* csymamd_l_report (UF_long stats [CCOLAMD_STATS]) ;
|
|
*
|
|
* Purpose:
|
|
*
|
|
* Prints the error status and statistics recorded in the stats
|
|
* array on the standard error output (for a standard C routine)
|
|
* or on the MATLAB output (for a mexFunction).
|
|
*
|
|
* Arguments:
|
|
*
|
|
* int stats [CCOLAMD_STATS] ; Input only. Statistics from csymamd.
|
|
*
|
|
*/
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === Scaffolding code definitions ======================================== */
|
|
/* ========================================================================== */
|
|
|
|
/* Ensure that debugging is turned off: */
|
|
#ifndef NDEBUG
|
|
#define NDEBUG
|
|
#endif
|
|
|
|
/* turn on debugging by uncommenting the following line
|
|
#undef NDEBUG
|
|
*/
|
|
|
|
/* ========================================================================== */
|
|
/* === Include files ======================================================== */
|
|
/* ========================================================================== */
|
|
|
|
#include "ccolamd.h"
|
|
|
|
#include <stdlib.h>
|
|
#include <math.h>
|
|
#include <limits.h>
|
|
|
|
#ifdef MATLAB_MEX_FILE
|
|
#include "mex.h"
|
|
#include "matrix.h"
|
|
#endif
|
|
|
|
#if !defined (NPRINT) || !defined (NDEBUG)
|
|
#include <stdio.h>
|
|
#endif
|
|
|
|
#ifndef NULL
|
|
#define NULL ((void *) 0)
|
|
#endif
|
|
|
|
/* ========================================================================== */
|
|
/* === int or UF_long ======================================================= */
|
|
/* ========================================================================== */
|
|
|
|
/* define UF_long */
|
|
#include "UFconfig.h"
|
|
|
|
#ifdef DLONG
|
|
|
|
#define Int UF_long
|
|
#define ID UF_long_id
|
|
#define Int_MAX UF_long_max
|
|
|
|
#define CCOLAMD_recommended ccolamd_l_recommended
|
|
#define CCOLAMD_set_defaults ccolamd_l_set_defaults
|
|
#define CCOLAMD_2 ccolamd2_l
|
|
#define CCOLAMD_MAIN ccolamd_l
|
|
#define CCOLAMD_apply_order ccolamd_l_apply_order
|
|
#define CCOLAMD_postorder ccolamd_l_postorder
|
|
#define CCOLAMD_post_tree ccolamd_l_post_tree
|
|
#define CCOLAMD_fsize ccolamd_l_fsize
|
|
#define CSYMAMD_MAIN csymamd_l
|
|
#define CCOLAMD_report ccolamd_l_report
|
|
#define CSYMAMD_report csymamd_l_report
|
|
|
|
#else
|
|
|
|
#define Int int
|
|
#define ID "%d"
|
|
#define Int_MAX INT_MAX
|
|
|
|
#define CCOLAMD_recommended ccolamd_recommended
|
|
#define CCOLAMD_set_defaults ccolamd_set_defaults
|
|
#define CCOLAMD_2 ccolamd2
|
|
#define CCOLAMD_MAIN ccolamd
|
|
#define CCOLAMD_apply_order ccolamd_apply_order
|
|
#define CCOLAMD_postorder ccolamd_postorder
|
|
#define CCOLAMD_post_tree ccolamd_post_tree
|
|
#define CCOLAMD_fsize ccolamd_fsize
|
|
#define CSYMAMD_MAIN csymamd
|
|
#define CCOLAMD_report ccolamd_report
|
|
#define CSYMAMD_report csymamd_report
|
|
|
|
#endif
|
|
|
|
/* ========================================================================== */
|
|
/* === Row and Column structures ============================================ */
|
|
/* ========================================================================== */
|
|
|
|
typedef struct CColamd_Col_struct
|
|
{
|
|
/* size of this struct is 8 integers if no padding occurs */
|
|
|
|
Int start ; /* index for A of first row in this column, or DEAD */
|
|
/* if column is dead */
|
|
Int length ; /* number of rows in this column */
|
|
union
|
|
{
|
|
Int thickness ; /* number of original columns represented by this */
|
|
/* col, if the column is alive */
|
|
Int parent ; /* parent in parent tree super-column structure, if */
|
|
/* the column is dead */
|
|
} shared1 ;
|
|
union
|
|
{
|
|
Int score ;
|
|
Int order ;
|
|
} shared2 ;
|
|
union
|
|
{
|
|
Int headhash ; /* head of a hash bucket, if col is at the head of */
|
|
/* a degree list */
|
|
Int hash ; /* hash value, if col is not in a degree list */
|
|
Int prev ; /* previous column in degree list, if col is in a */
|
|
/* degree list (but not at the head of a degree list) */
|
|
} shared3 ;
|
|
union
|
|
{
|
|
Int degree_next ; /* next column, if col is in a degree list */
|
|
Int hash_next ; /* next column, if col is in a hash list */
|
|
} shared4 ;
|
|
|
|
Int nextcol ; /* next column in this supercolumn */
|
|
Int lastcol ; /* last column in this supercolumn */
|
|
|
|
} CColamd_Col ;
|
|
|
|
|
|
typedef struct CColamd_Row_struct
|
|
{
|
|
/* size of this struct is 6 integers if no padding occurs */
|
|
|
|
Int start ; /* index for A of first col in this row */
|
|
Int length ; /* number of principal columns in this row */
|
|
union
|
|
{
|
|
Int degree ; /* number of principal & non-principal columns in row */
|
|
Int p ; /* used as a row pointer in init_rows_cols () */
|
|
} shared1 ;
|
|
union
|
|
{
|
|
Int mark ; /* for computing set differences and marking dead rows*/
|
|
Int first_column ;/* first column in row (used in garbage collection) */
|
|
} shared2 ;
|
|
|
|
Int thickness ; /* number of original rows represented by this row */
|
|
/* that are not yet pivotal */
|
|
Int front ; /* -1 if an original row */
|
|
/* k if this row represents the kth frontal matrix */
|
|
/* where k goes from 0 to at most n_col-1 */
|
|
|
|
} CColamd_Row ;
|
|
|
|
/* ========================================================================== */
|
|
/* === basic definitions ==================================================== */
|
|
/* ========================================================================== */
|
|
|
|
#define EMPTY (-1)
|
|
#define MAX(a,b) (((a) > (b)) ? (a) : (b))
|
|
#define MIN(a,b) (((a) < (b)) ? (a) : (b))
|
|
|
|
/* Routines are either PUBLIC (user-callable) or PRIVATE (not user-callable) */
|
|
#define GLOBAL
|
|
#define PUBLIC
|
|
#define PRIVATE static
|
|
|
|
#define DENSE_DEGREE(alpha,n) \
|
|
((Int) MAX (16.0, (alpha) * sqrt ((double) (n))))
|
|
|
|
#define CMEMBER(c) ((cmember == (Int *) NULL) ? (0) : (cmember [c]))
|
|
|
|
/* True if x is NaN */
|
|
#define SCALAR_IS_NAN(x) ((x) != (x))
|
|
|
|
/* true if an integer (stored in double x) would overflow (or if x is NaN) */
|
|
#define INT_OVERFLOW(x) ((!((x) * (1.0+1e-8) <= (double) Int_MAX)) \
|
|
|| SCALAR_IS_NAN (x))
|
|
|
|
#define ONES_COMPLEMENT(r) (-(r)-1)
|
|
#undef TRUE
|
|
#undef FALSE
|
|
#define TRUE (1)
|
|
#define FALSE (0)
|
|
|
|
/* Row and column status */
|
|
#define ALIVE (0)
|
|
#define DEAD (-1)
|
|
|
|
/* Column status */
|
|
#define DEAD_PRINCIPAL (-1)
|
|
#define DEAD_NON_PRINCIPAL (-2)
|
|
|
|
/* Macros for row and column status update and checking. */
|
|
#define ROW_IS_DEAD(r) ROW_IS_MARKED_DEAD (Row[r].shared2.mark)
|
|
#define ROW_IS_MARKED_DEAD(row_mark) (row_mark < ALIVE)
|
|
#define ROW_IS_ALIVE(r) (Row [r].shared2.mark >= ALIVE)
|
|
#define COL_IS_DEAD(c) (Col [c].start < ALIVE)
|
|
#define COL_IS_ALIVE(c) (Col [c].start >= ALIVE)
|
|
#define COL_IS_DEAD_PRINCIPAL(c) (Col [c].start == DEAD_PRINCIPAL)
|
|
#define KILL_ROW(r) { Row [r].shared2.mark = DEAD ; }
|
|
#define KILL_PRINCIPAL_COL(c) { Col [c].start = DEAD_PRINCIPAL ; }
|
|
#define KILL_NON_PRINCIPAL_COL(c) { Col [c].start = DEAD_NON_PRINCIPAL ; }
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd reporting mechanism ========================================== */
|
|
/* ========================================================================== */
|
|
|
|
#if defined (MATLAB_MEX_FILE) || defined (MATHWORKS)
|
|
/* In MATLAB, matrices are 1-based to the user, but 0-based internally */
|
|
#define INDEX(i) ((i)+1)
|
|
#else
|
|
/* In C, matrices are 0-based and indices are reported as such in *_report */
|
|
#define INDEX(i) (i)
|
|
#endif
|
|
|
|
/* All output goes through the PRINTF macro. */
|
|
#define PRINTF(params) { if (ccolamd_printf != NULL) (void) ccolamd_printf params ; }
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === Debugging prototypes and definitions ================================= */
|
|
/* ========================================================================== */
|
|
|
|
#ifndef NDEBUG
|
|
|
|
#include <assert.h>
|
|
|
|
/* debug print level, present only when debugging */
|
|
PRIVATE Int ccolamd_debug ;
|
|
|
|
/* debug print statements */
|
|
#define DEBUG0(params) { PRINTF (params) ; }
|
|
#define DEBUG1(params) { if (ccolamd_debug >= 1) PRINTF (params) ; }
|
|
#define DEBUG2(params) { if (ccolamd_debug >= 2) PRINTF (params) ; }
|
|
#define DEBUG3(params) { if (ccolamd_debug >= 3) PRINTF (params) ; }
|
|
#define DEBUG4(params) { if (ccolamd_debug >= 4) PRINTF (params) ; }
|
|
|
|
#ifdef MATLAB_MEX_FILE
|
|
#define ASSERT(expression) (mxAssert ((expression), ""))
|
|
#else
|
|
#define ASSERT(expression) (assert (expression))
|
|
#endif
|
|
|
|
PRIVATE void ccolamd_get_debug
|
|
(
|
|
char *method
|
|
) ;
|
|
|
|
PRIVATE void debug_mark
|
|
(
|
|
Int n_row,
|
|
CColamd_Row Row [],
|
|
Int tag_mark,
|
|
Int max_mark
|
|
) ;
|
|
|
|
PRIVATE void debug_matrix
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [],
|
|
CColamd_Col Col [],
|
|
Int A []
|
|
) ;
|
|
|
|
PRIVATE void debug_structures
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [],
|
|
CColamd_Col Col [],
|
|
Int A [],
|
|
Int in_cset [],
|
|
Int cset_start []
|
|
) ;
|
|
|
|
PRIVATE void dump_super
|
|
(
|
|
Int super_c,
|
|
CColamd_Col Col [],
|
|
Int n_col
|
|
) ;
|
|
|
|
PRIVATE void debug_deg_lists
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int head [ ],
|
|
Int min_score,
|
|
Int should,
|
|
Int max_deg
|
|
) ;
|
|
|
|
#else
|
|
|
|
/* === No debugging ========================================================= */
|
|
|
|
#define DEBUG0(params) ;
|
|
#define DEBUG1(params) ;
|
|
#define DEBUG2(params) ;
|
|
#define DEBUG3(params) ;
|
|
#define DEBUG4(params) ;
|
|
|
|
#define ASSERT(expression)
|
|
|
|
#endif
|
|
|
|
/* ========================================================================== */
|
|
/* === Prototypes of PRIVATE routines ======================================= */
|
|
/* ========================================================================== */
|
|
|
|
PRIVATE Int init_rows_cols
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int p [ ],
|
|
Int stats [CCOLAMD_STATS]
|
|
) ;
|
|
|
|
PRIVATE void init_scoring
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int head [ ],
|
|
double knobs [CCOLAMD_KNOBS],
|
|
Int *p_n_row2,
|
|
Int *p_n_col2,
|
|
Int *p_max_deg,
|
|
Int cmember [ ],
|
|
Int n_cset,
|
|
Int cset_start [ ],
|
|
Int dead_cols [ ],
|
|
Int *p_ndense_row, /* number of dense rows */
|
|
Int *p_nempty_row, /* number of original empty rows */
|
|
Int *p_nnewlyempty_row, /* number of newly empty rows */
|
|
Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */
|
|
Int *p_nempty_col, /* number of original empty cols */
|
|
Int *p_nnewlyempty_col /* number of newly empty cols */
|
|
) ;
|
|
|
|
PRIVATE Int find_ordering
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
Int Alen,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int head [ ],
|
|
#ifndef NDEBUG
|
|
Int n_col2,
|
|
#endif
|
|
Int max_deg,
|
|
Int pfree,
|
|
Int cset [ ],
|
|
Int cset_start [ ],
|
|
#ifndef NDEBUG
|
|
Int n_cset,
|
|
#endif
|
|
Int cmember [ ],
|
|
Int Front_npivcol [ ],
|
|
Int Front_nrows [ ],
|
|
Int Front_ncols [ ],
|
|
Int Front_parent [ ],
|
|
Int Front_cols [ ],
|
|
Int *p_nfr,
|
|
Int aggressive,
|
|
Int InFront [ ],
|
|
Int order_for_lu
|
|
) ;
|
|
|
|
PRIVATE void detect_super_cols
|
|
(
|
|
#ifndef NDEBUG
|
|
Int n_col,
|
|
CColamd_Row Row [ ],
|
|
#endif
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int head [ ],
|
|
Int row_start,
|
|
Int row_length,
|
|
Int in_set [ ]
|
|
) ;
|
|
|
|
PRIVATE Int garbage_collection
|
|
(
|
|
Int n_row,
|
|
Int n_col,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int *pfree
|
|
) ;
|
|
|
|
PRIVATE Int clear_mark
|
|
(
|
|
Int tag_mark,
|
|
Int max_mark,
|
|
Int n_row,
|
|
CColamd_Row Row [ ]
|
|
) ;
|
|
|
|
PRIVATE void print_report
|
|
(
|
|
char *method,
|
|
Int stats [CCOLAMD_STATS]
|
|
) ;
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === USER-CALLABLE ROUTINES: ============================================== */
|
|
/* ========================================================================== */
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd_recommended ================================================== */
|
|
/* ========================================================================== */
|
|
|
|
/*
|
|
* The ccolamd_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 ccolamd. If any
|
|
* argument is negative, or if integer overflow occurs, a 0 is returned as
|
|
* an error condition.
|
|
*
|
|
* 2*nnz space is required for the row and column indices of the matrix
|
|
* (or 4*n_col, which ever is larger).
|
|
*
|
|
* CCOLAMD_C (n_col) + CCOLAMD_R (n_row) space is required for the Col and Row
|
|
* arrays, respectively, which are internal to ccolamd. This is equal to
|
|
* 8*n_col + 6*n_row if the structures are not padded.
|
|
*
|
|
* An additional n_col space is the minimal amount of "elbow room",
|
|
* and nnz/5 more space is recommended for run time efficiency.
|
|
*
|
|
* The remaining (((3 * n_col) + 1) + 5 * (n_col + 1) + n_row) space is
|
|
* for other workspace used in ccolamd which did not appear in colamd.
|
|
*/
|
|
|
|
/* add two values of type size_t, and check for integer overflow */
|
|
static size_t t_add (size_t a, size_t b, int *ok)
|
|
{
|
|
(*ok) = (*ok) && ((a + b) >= MAX (a,b)) ;
|
|
return ((*ok) ? (a + b) : 0) ;
|
|
}
|
|
|
|
/* compute a*k where k is a small integer, and check for integer overflow */
|
|
static size_t t_mult (size_t a, size_t k, int *ok)
|
|
{
|
|
size_t i, s = 0 ;
|
|
for (i = 0 ; i < k ; i++)
|
|
{
|
|
s = t_add (s, a, ok) ;
|
|
}
|
|
return (s) ;
|
|
}
|
|
|
|
/* size of the Col and Row structures */
|
|
#define CCOLAMD_C(n_col,ok) \
|
|
((t_mult (t_add (n_col, 1, ok), sizeof (CColamd_Col), ok) / sizeof (Int)))
|
|
|
|
#define CCOLAMD_R(n_row,ok) \
|
|
((t_mult (t_add (n_row, 1, ok), sizeof (CColamd_Row), ok) / sizeof (Int)))
|
|
|
|
/*
|
|
#define CCOLAMD_RECOMMENDED(nnz, n_row, n_col) \
|
|
MAX (2 * nnz, 4 * n_col) + \
|
|
CCOLAMD_C (n_col) + CCOLAMD_R (n_row) + n_col + (nnz / 5) \
|
|
+ ((3 * n_col) + 1) + 5 * (n_col + 1) + n_row
|
|
*/
|
|
|
|
static size_t ccolamd_need (Int nnz, Int n_row, Int n_col, int *ok)
|
|
{
|
|
|
|
/* ccolamd_need, compute the following, and check for integer overflow:
|
|
need = MAX (2*nnz, 4*n_col) + n_col +
|
|
Col_size + Row_size +
|
|
(3*n_col+1) + (5*(n_col+1)) + n_row ;
|
|
*/
|
|
size_t s, c, r, t ;
|
|
|
|
/* MAX (2*nnz, 4*n_col) */
|
|
s = t_mult (nnz, 2, ok) ; /* 2*nnz */
|
|
t = t_mult (n_col, 4, ok) ; /* 4*n_col */
|
|
s = MAX (s,t) ;
|
|
|
|
s = t_add (s, n_col, ok) ; /* bare minimum elbow room */
|
|
|
|
/* Col and Row arrays */
|
|
c = CCOLAMD_C (n_col, ok) ; /* size of column structures */
|
|
r = CCOLAMD_R (n_row, ok) ; /* size of row structures */
|
|
s = t_add (s, c, ok) ;
|
|
s = t_add (s, r, ok) ;
|
|
|
|
c = t_mult (n_col, 3, ok) ; /* 3*n_col + 1 */
|
|
c = t_add (c, 1, ok) ;
|
|
s = t_add (s, c, ok) ;
|
|
|
|
c = t_add (n_col, 1, ok) ; /* 5 * (n_col + 1) */
|
|
c = t_mult (c, 5, ok) ;
|
|
s = t_add (s, c, ok) ;
|
|
|
|
s = t_add (s, n_row, ok) ; /* n_row */
|
|
|
|
return (ok ? s : 0) ;
|
|
}
|
|
|
|
PUBLIC size_t CCOLAMD_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 */
|
|
)
|
|
{
|
|
size_t s ;
|
|
int ok = TRUE ;
|
|
if (nnz < 0 || n_row < 0 || n_col < 0)
|
|
{
|
|
return (0) ;
|
|
}
|
|
s = ccolamd_need (nnz, n_row, n_col, &ok) ; /* bare minimum needed */
|
|
s = t_add (s, nnz/5, &ok) ; /* extra elbow room */
|
|
ok = ok && (s < Int_MAX) ;
|
|
return (ok ? s : 0) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd_set_defaults ================================================= */
|
|
/* ========================================================================== */
|
|
|
|
/*
|
|
* The ccolamd_set_defaults routine sets the default values of the user-
|
|
* controllable parameters for ccolamd.
|
|
*/
|
|
|
|
PUBLIC void CCOLAMD_set_defaults
|
|
(
|
|
/* === Parameters ======================================================= */
|
|
|
|
double knobs [CCOLAMD_KNOBS] /* knob array */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int i ;
|
|
|
|
if (!knobs)
|
|
{
|
|
return ; /* no knobs to initialize */
|
|
}
|
|
for (i = 0 ; i < CCOLAMD_KNOBS ; i++)
|
|
{
|
|
knobs [i] = 0 ;
|
|
}
|
|
knobs [CCOLAMD_DENSE_ROW] = 10 ;
|
|
knobs [CCOLAMD_DENSE_COL] = 10 ;
|
|
knobs [CCOLAMD_AGGRESSIVE] = TRUE ; /* default: do aggressive absorption*/
|
|
knobs [CCOLAMD_LU] = FALSE ; /* default: order for Cholesky */
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === symamd =============================================================== */
|
|
/* ========================================================================== */
|
|
|
|
PUBLIC Int CSYMAMD_MAIN /* return TRUE if OK, FALSE otherwise */
|
|
(
|
|
/* === Parameters ======================================================= */
|
|
|
|
Int n, /* number of rows and columns of A */
|
|
Int A [ ], /* row indices of A */
|
|
Int p [ ], /* column pointers of A */
|
|
Int perm [ ], /* output permutation, size n+1 */
|
|
double knobs [CCOLAMD_KNOBS], /* parameters (uses defaults if NULL) */
|
|
Int stats [CCOLAMD_STATS], /* output statistics and error codes */
|
|
void * (*allocate) (size_t, size_t),/* pointer to calloc (ANSI C) or */
|
|
/* mxCalloc (for MATLAB mexFunction) */
|
|
void (*release) (void *), /* pointer to free (ANSI C) or */
|
|
/* mxFree (for MATLAB mexFunction) */
|
|
Int cmember [ ], /* constraint set */
|
|
Int stype /* stype of A */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
double cknobs [CCOLAMD_KNOBS] ;
|
|
double default_knobs [CCOLAMD_KNOBS] ;
|
|
|
|
Int *count ; /* length of each column of M, and col pointer*/
|
|
Int *mark ; /* mark array for finding duplicate entries */
|
|
Int *M ; /* row indices of matrix M */
|
|
size_t Mlen ; /* length of M */
|
|
Int n_row ; /* number of rows in M */
|
|
Int nnz ; /* number of entries in A */
|
|
Int i ; /* row index of A */
|
|
Int j ; /* column index of A */
|
|
Int k ; /* row index of M */
|
|
Int mnz ; /* number of nonzeros in M */
|
|
Int pp ; /* index into a column of A */
|
|
Int last_row ; /* last row seen in the current column */
|
|
Int length ; /* number of nonzeros in a column */
|
|
Int both ; /* TRUE if ordering A+A' */
|
|
Int upper ; /* TRUE if ordering triu(A)+triu(A)' */
|
|
Int lower ; /* TRUE if ordering tril(A)+tril(A)' */
|
|
|
|
#ifndef NDEBUG
|
|
ccolamd_get_debug ("csymamd") ;
|
|
#endif
|
|
|
|
both = (stype == 0) ;
|
|
upper = (stype > 0) ;
|
|
lower = (stype < 0) ;
|
|
|
|
/* === Check the input arguments ======================================== */
|
|
|
|
if (!stats)
|
|
{
|
|
DEBUG1 (("csymamd: stats not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
for (i = 0 ; i < CCOLAMD_STATS ; i++)
|
|
{
|
|
stats [i] = 0 ;
|
|
}
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_OK ;
|
|
stats [CCOLAMD_INFO1] = -1 ;
|
|
stats [CCOLAMD_INFO2] = -1 ;
|
|
|
|
if (!A)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ;
|
|
DEBUG1 (("csymamd: A not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (!p) /* p is not present */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ;
|
|
DEBUG1 (("csymamd: p not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (n < 0) /* n must be >= 0 */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ;
|
|
stats [CCOLAMD_INFO1] = n ;
|
|
DEBUG1 (("csymamd: n negative "ID" \n", n)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
nnz = p [n] ;
|
|
if (nnz < 0) /* nnz must be >= 0 */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ;
|
|
stats [CCOLAMD_INFO1] = nnz ;
|
|
DEBUG1 (("csymamd: number of entries negative "ID" \n", nnz)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (p [0] != 0)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ;
|
|
stats [CCOLAMD_INFO1] = p [0] ;
|
|
DEBUG1 (("csymamd: p[0] not zero "ID"\n", p [0])) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
/* === If no knobs, set default knobs =================================== */
|
|
|
|
if (!knobs)
|
|
{
|
|
CCOLAMD_set_defaults (default_knobs) ;
|
|
knobs = default_knobs ;
|
|
}
|
|
|
|
/* === Allocate count and mark ========================================== */
|
|
|
|
count = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
|
|
if (!count)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
|
|
DEBUG1 (("csymamd: allocate count (size "ID") failed\n", n+1)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
mark = (Int *) ((*allocate) (n+1, sizeof (Int))) ;
|
|
if (!mark)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
|
|
(*release) ((void *) count) ;
|
|
DEBUG1 (("csymamd: allocate mark (size "ID") failed\n", n+1)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
/* === Compute column counts of M, check if A is valid ================== */
|
|
|
|
stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
|
|
|
|
for (i = 0 ; i < n ; i++)
|
|
{
|
|
mark [i] = -1 ;
|
|
}
|
|
|
|
for (j = 0 ; j < n ; j++)
|
|
{
|
|
last_row = -1 ;
|
|
|
|
length = p [j+1] - p [j] ;
|
|
if (length < 0)
|
|
{
|
|
/* column pointers must be non-decreasing */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ;
|
|
stats [CCOLAMD_INFO1] = j ;
|
|
stats [CCOLAMD_INFO2] = length ;
|
|
(*release) ((void *) count) ;
|
|
(*release) ((void *) mark) ;
|
|
DEBUG1 (("csymamd: col "ID" negative length "ID"\n", j, length)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
for (pp = p [j] ; pp < p [j+1] ; pp++)
|
|
{
|
|
i = A [pp] ;
|
|
if (i < 0 || i >= n)
|
|
{
|
|
/* row index i, in column j, is out of bounds */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ;
|
|
stats [CCOLAMD_INFO1] = j ;
|
|
stats [CCOLAMD_INFO2] = i ;
|
|
stats [CCOLAMD_INFO3] = n ;
|
|
(*release) ((void *) count) ;
|
|
(*release) ((void *) mark) ;
|
|
DEBUG1 (("csymamd: row "ID" col "ID" out of bounds\n", i, j)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (i <= last_row || mark [i] == j)
|
|
{
|
|
/* row index is unsorted or repeated (or both), thus col */
|
|
/* is jumbled. This is a notice, not an error condition. */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ;
|
|
stats [CCOLAMD_INFO1] = j ;
|
|
stats [CCOLAMD_INFO2] = i ;
|
|
(stats [CCOLAMD_INFO3]) ++ ;
|
|
DEBUG1 (("csymamd: row "ID" col "ID" unsorted/dupl.\n", i, j)) ;
|
|
}
|
|
|
|
if (mark [i] != j)
|
|
{
|
|
if ((both && i != j) || (lower && i > j) || (upper && i < j))
|
|
{
|
|
/* row k of M will contain column indices i and j */
|
|
count [i]++ ;
|
|
count [j]++ ;
|
|
}
|
|
}
|
|
|
|
/* mark the row as having been seen in this column */
|
|
mark [i] = j ;
|
|
|
|
last_row = i ;
|
|
}
|
|
}
|
|
|
|
/* === Compute column pointers of M ===================================== */
|
|
|
|
/* use output permutation, perm, for column pointers of M */
|
|
perm [0] = 0 ;
|
|
for (j = 1 ; j <= n ; j++)
|
|
{
|
|
perm [j] = perm [j-1] + count [j-1] ;
|
|
}
|
|
for (j = 0 ; j < n ; j++)
|
|
{
|
|
count [j] = perm [j] ;
|
|
}
|
|
|
|
/* === Construct M ====================================================== */
|
|
|
|
mnz = perm [n] ;
|
|
n_row = mnz / 2 ;
|
|
Mlen = CCOLAMD_recommended (mnz, n_row, n) ;
|
|
M = (Int *) ((*allocate) (Mlen, sizeof (Int))) ;
|
|
DEBUG1 (("csymamd: M is "ID"-by-"ID" with "ID" entries, Mlen = %g\n",
|
|
n_row, n, mnz, (double) Mlen)) ;
|
|
|
|
if (!M)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_out_of_memory ;
|
|
(*release) ((void *) count) ;
|
|
(*release) ((void *) mark) ;
|
|
DEBUG1 (("csymamd: allocate M (size %g) failed\n", (double) Mlen)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
k = 0 ;
|
|
|
|
if (stats [CCOLAMD_STATUS] == CCOLAMD_OK)
|
|
{
|
|
/* Matrix is OK */
|
|
for (j = 0 ; j < n ; j++)
|
|
{
|
|
ASSERT (p [j+1] - p [j] >= 0) ;
|
|
for (pp = p [j] ; pp < p [j+1] ; pp++)
|
|
{
|
|
i = A [pp] ;
|
|
ASSERT (i >= 0 && i < n) ;
|
|
if ((both && i != j) || (lower && i > j) || (upper && i < j))
|
|
{
|
|
/* row k of M contains column indices i and j */
|
|
M [count [i]++] = k ;
|
|
M [count [j]++] = k ;
|
|
k++ ;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{
|
|
/* Matrix is jumbled. Do not add duplicates to M. Unsorted cols OK. */
|
|
DEBUG1 (("csymamd: Duplicates in A.\n")) ;
|
|
for (i = 0 ; i < n ; i++)
|
|
{
|
|
mark [i] = -1 ;
|
|
}
|
|
for (j = 0 ; j < n ; j++)
|
|
{
|
|
ASSERT (p [j+1] - p [j] >= 0) ;
|
|
for (pp = p [j] ; pp < p [j+1] ; pp++)
|
|
{
|
|
i = A [pp] ;
|
|
ASSERT (i >= 0 && i < n) ;
|
|
if (mark [i] != j)
|
|
{
|
|
if ((both && i != j) || (lower && i > j) || (upper && i<j))
|
|
{
|
|
/* row k of M contains column indices i and j */
|
|
M [count [i]++] = k ;
|
|
M [count [j]++] = k ;
|
|
k++ ;
|
|
mark [i] = j ;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* count and mark no longer needed */
|
|
(*release) ((void *) mark) ;
|
|
(*release) ((void *) count) ;
|
|
ASSERT (k == n_row) ;
|
|
|
|
/* === Adjust the knobs for M =========================================== */
|
|
|
|
for (i = 0 ; i < CCOLAMD_KNOBS ; i++)
|
|
{
|
|
cknobs [i] = knobs [i] ;
|
|
}
|
|
|
|
/* there are no dense rows in M */
|
|
cknobs [CCOLAMD_DENSE_ROW] = -1 ;
|
|
cknobs [CCOLAMD_DENSE_COL] = knobs [CCOLAMD_DENSE_ROW] ;
|
|
|
|
/* ensure CCSYMAMD orders for Cholesky, not LU */
|
|
cknobs [CCOLAMD_LU] = FALSE ;
|
|
|
|
/* === Order the columns of M =========================================== */
|
|
|
|
(void) CCOLAMD_2 (n_row, n, (Int) Mlen, M, perm, cknobs, stats,
|
|
(Int *) NULL, (Int *) NULL, (Int *) NULL, (Int *) NULL,
|
|
(Int *) NULL, (Int *) NULL, (Int *) NULL, cmember) ;
|
|
|
|
/* === adjust statistics ================================================ */
|
|
|
|
/* a dense column in ccolamd means a dense row and col in csymamd */
|
|
stats [CCOLAMD_DENSE_ROW] = stats [CCOLAMD_DENSE_COL] ;
|
|
|
|
/* === Free M =========================================================== */
|
|
|
|
(*release) ((void *) M) ;
|
|
DEBUG1 (("csymamd: done.\n")) ;
|
|
return (TRUE) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd ============================================================== */
|
|
/* ========================================================================== */
|
|
|
|
/*
|
|
* 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.
|
|
*/
|
|
|
|
PUBLIC Int CCOLAMD_MAIN
|
|
(
|
|
/* === 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 [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */
|
|
Int stats [CCOLAMD_STATS], /* output statistics and error codes */
|
|
Int cmember [ ] /* constraint set of A */
|
|
)
|
|
{
|
|
return (CCOLAMD_2 (n_row, n_col, Alen, A, p, knobs, stats,
|
|
(Int *) NULL, (Int *) NULL, (Int *) NULL, (Int *) NULL,
|
|
(Int *) NULL, (Int *) NULL, (Int *) NULL, cmember)) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd2 ============================================================= */
|
|
/* ========================================================================== */
|
|
|
|
/* Identical to ccolamd, except that additional information about each frontal
|
|
* matrix is returned to the caller. Not intended to be directly called by
|
|
* the user.
|
|
*/
|
|
|
|
PUBLIC Int CCOLAMD_2 /* returns TRUE if successful, FALSE otherwise */
|
|
(
|
|
/* === 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 [CCOLAMD_KNOBS],/* parameters (uses defaults if NULL) */
|
|
Int stats [CCOLAMD_STATS], /* output statistics and error codes */
|
|
|
|
/* each Front array is of size n_col+1. */
|
|
Int Front_npivcol [ ], /* # pivot cols in each front */
|
|
Int Front_nrows [ ], /* # of rows in each front (incl. pivot rows) */
|
|
Int Front_ncols [ ], /* # of cols in each front (incl. pivot cols) */
|
|
Int Front_parent [ ], /* parent of each front */
|
|
Int Front_cols [ ], /* link list of pivot columns for each front */
|
|
Int *p_nfr, /* total number of frontal matrices */
|
|
Int InFront [ ], /* InFront [row] = f if the original row was
|
|
* absorbed into front f. EMPTY if the row was
|
|
* empty, dense, or not absorbed. This array
|
|
* has size n_row+1 */
|
|
Int cmember [ ] /* constraint set of A */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int i ; /* loop index */
|
|
Int nnz ; /* nonzeros in A */
|
|
size_t Row_size ; /* size of Row [ ], in integers */
|
|
size_t Col_size ; /* size of Col [ ], in integers */
|
|
size_t need ; /* minimum required length of A */
|
|
CColamd_Row *Row ; /* pointer into A of Row [0..n_row] array */
|
|
CColamd_Col *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 [CCOLAMD_KNOBS] ; /* default knobs array */
|
|
|
|
Int n_cset ; /* number of constraint sets */
|
|
Int *cset ; /* cset of A */
|
|
Int *cset_start ; /* pointer into cset */
|
|
Int *temp_cstart ; /* temp pointer to start of cset */
|
|
Int *csize ; /* temp pointer to cset size */
|
|
Int ap ; /* column index */
|
|
Int order_for_lu ; /* TRUE: order for LU, FALSE: for Cholesky */
|
|
|
|
Int ndense_row, nempty_row, parent, ndense_col,
|
|
nempty_col, k, col, nfr, *Front_child, *Front_sibling, *Front_stack,
|
|
*Front_order, *Front_size ;
|
|
Int nnewlyempty_col, nnewlyempty_row ;
|
|
Int aggressive ;
|
|
Int row ;
|
|
Int *dead_cols ;
|
|
Int set1 ;
|
|
Int set2 ;
|
|
Int cs ;
|
|
|
|
int ok ;
|
|
|
|
#ifndef NDEBUG
|
|
ccolamd_get_debug ("ccolamd") ;
|
|
#endif
|
|
|
|
/* === Check the input arguments ======================================== */
|
|
|
|
if (!stats)
|
|
{
|
|
DEBUG1 (("ccolamd: stats not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
for (i = 0 ; i < CCOLAMD_STATS ; i++)
|
|
{
|
|
stats [i] = 0 ;
|
|
}
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_OK ;
|
|
stats [CCOLAMD_INFO1] = -1 ;
|
|
stats [CCOLAMD_INFO2] = -1 ;
|
|
|
|
if (!A) /* A is not present */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_not_present ;
|
|
DEBUG1 (("ccolamd: A not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (!p) /* p is not present */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p_not_present ;
|
|
DEBUG1 (("ccolamd: p not present\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (n_row < 0) /* n_row must be >= 0 */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nrow_negative ;
|
|
stats [CCOLAMD_INFO1] = n_row ;
|
|
DEBUG1 (("ccolamd: nrow negative "ID"\n", n_row)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (n_col < 0) /* n_col must be >= 0 */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_ncol_negative ;
|
|
stats [CCOLAMD_INFO1] = n_col ;
|
|
DEBUG1 (("ccolamd: ncol negative "ID"\n", n_col)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
nnz = p [n_col] ;
|
|
if (nnz < 0) /* nnz must be >= 0 */
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_nnz_negative ;
|
|
stats [CCOLAMD_INFO1] = nnz ;
|
|
DEBUG1 (("ccolamd: number of entries negative "ID"\n", nnz)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (p [0] != 0)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_p0_nonzero ;
|
|
stats [CCOLAMD_INFO1] = p [0] ;
|
|
DEBUG1 (("ccolamd: p[0] not zero "ID"\n", p [0])) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
/* === If no knobs, set default knobs =================================== */
|
|
|
|
if (!knobs)
|
|
{
|
|
CCOLAMD_set_defaults (default_knobs) ;
|
|
knobs = default_knobs ;
|
|
}
|
|
|
|
aggressive = (knobs [CCOLAMD_AGGRESSIVE] != FALSE) ;
|
|
order_for_lu = (knobs [CCOLAMD_LU] != FALSE) ;
|
|
|
|
/* === Allocate workspace from array A ================================== */
|
|
|
|
ok = TRUE ;
|
|
Col_size = CCOLAMD_C (n_col, &ok) ;
|
|
Row_size = CCOLAMD_R (n_row, &ok) ;
|
|
|
|
/* min size of A is 2nnz+ncol. cset and cset_start are of size 2ncol+1 */
|
|
/* Each of the 5 fronts is of size n_col + 1. InFront is of size nrow. */
|
|
|
|
/*
|
|
need = MAX (2*nnz, 4*n_col) + n_col +
|
|
Col_size + Row_size +
|
|
(3*n_col+1) + (5*(n_col+1)) + n_row ;
|
|
*/
|
|
need = ccolamd_need (nnz, n_row, n_col, &ok) ;
|
|
|
|
if (!ok || need > (size_t) Alen || need > Int_MAX)
|
|
{
|
|
/* not enough space in array A to perform the ordering */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_A_too_small ;
|
|
stats [CCOLAMD_INFO1] = need ;
|
|
stats [CCOLAMD_INFO2] = Alen ;
|
|
DEBUG1 (("ccolamd: Need Alen >= "ID", given "ID"\n", need, Alen)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
/* since integer overflow has been check, the following cannot overflow: */
|
|
Alen -= Col_size + Row_size + (3*n_col + 1) + 5*(n_col+1) + n_row ;
|
|
|
|
/* Size of A is now Alen >= MAX (2*nnz, 4*n_col) + n_col. The ordering
|
|
* requires Alen >= 2*nnz + n_col, and the postorder requires
|
|
* Alen >= 5*n_col. */
|
|
|
|
ap = Alen ;
|
|
|
|
/* Front array workspace: 5*(n_col+1) + n_row */
|
|
if (!Front_npivcol || !Front_nrows || !Front_ncols || !Front_parent ||
|
|
!Front_cols || !Front_cols || !InFront)
|
|
{
|
|
Front_npivcol = &A [ap] ; ap += (n_col + 1) ;
|
|
Front_nrows = &A [ap] ; ap += (n_col + 1) ;
|
|
Front_ncols = &A [ap] ; ap += (n_col + 1) ;
|
|
Front_parent = &A [ap] ; ap += (n_col + 1) ;
|
|
Front_cols = &A [ap] ; ap += (n_col + 1) ;
|
|
InFront = &A [ap] ; ap += (n_row) ;
|
|
}
|
|
else
|
|
{
|
|
/* Fronts are present. Leave the additional space as elbow room. */
|
|
ap += 5*(n_col+1) + n_row ;
|
|
ap = Alen ;
|
|
}
|
|
|
|
/* Workspace for cset management: 3*n_col+1 */
|
|
/* cset_start is of size n_col + 1 */
|
|
cset_start = &A [ap] ;
|
|
ap += n_col + 1 ;
|
|
|
|
/* dead_col is of size n_col */
|
|
dead_cols = &A [ap] ;
|
|
ap += n_col ;
|
|
|
|
/* cset is of size n_col */
|
|
cset = &A [ap] ;
|
|
ap += n_col ;
|
|
|
|
/* Col is of size Col_size. The space is shared by temp_cstart and csize */
|
|
Col = (CColamd_Col *) &A [ap] ;
|
|
temp_cstart = (Int *) Col ; /* [ temp_cstart is of size n_col+1 */
|
|
csize = temp_cstart + (n_col+1) ; /* csize is of size n_col+1 */
|
|
ap += Col_size ;
|
|
ASSERT (Col_size >= 2*n_col+1) ;
|
|
|
|
/* Row is of size Row_size */
|
|
Row = (CColamd_Row *) &A [ap] ;
|
|
ap += Row_size ;
|
|
|
|
/* Initialize csize & dead_cols to zero */
|
|
for (i = 0 ; i < n_col ; i++)
|
|
{
|
|
csize [i] = 0 ;
|
|
dead_cols [i] = 0 ;
|
|
}
|
|
|
|
/* === Construct the constraint set ===================================== */
|
|
|
|
if (n_col == 0)
|
|
{
|
|
n_cset = 0 ;
|
|
}
|
|
else if (cmember == (Int *) NULL)
|
|
{
|
|
/* no constraint set; all columns belong to set zero */
|
|
n_cset = 1 ;
|
|
csize [0] = n_col ;
|
|
DEBUG1 (("no cmember present\n")) ;
|
|
}
|
|
else
|
|
{
|
|
n_cset = 0 ;
|
|
for (i = 0 ; i < n_col ; i++)
|
|
{
|
|
if (cmember [i] < 0 || cmember [i] > n_col)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_invalid_cmember ;
|
|
DEBUG1 (("ccolamd: malformed cmember \n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
n_cset = MAX (n_cset, cmember [i]) ;
|
|
csize [cmember [i]]++ ;
|
|
}
|
|
/* cset is zero based */
|
|
n_cset++ ;
|
|
}
|
|
|
|
ASSERT ((n_cset >= 0) && (n_cset <= n_col)) ;
|
|
|
|
cset_start [0] = temp_cstart [0] = 0 ;
|
|
for (i = 1 ; i <= n_cset ; i++)
|
|
{
|
|
cset_start [i] = cset_start [i-1] + csize [i-1] ;
|
|
DEBUG4 ((" cset_start ["ID"] = "ID" \n", i , cset_start [i])) ;
|
|
temp_cstart [i] = cset_start [i] ;
|
|
}
|
|
|
|
/* do in reverse order to encourage natural tie-breaking */
|
|
if (cmember == (Int *) NULL)
|
|
{
|
|
for (i = n_col-1 ; i >= 0 ; i--)
|
|
{
|
|
cset [temp_cstart [0]++] = i ;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
for (i = n_col-1 ; i >= 0 ; i--)
|
|
{
|
|
cset [temp_cstart [cmember [i]]++] = i ;
|
|
}
|
|
}
|
|
|
|
/* ] temp_cstart and csize are no longer used */
|
|
|
|
/* === Construct the row and column data structures ===================== */
|
|
|
|
if (!init_rows_cols (n_row, n_col, Row, Col, A, p, stats))
|
|
{
|
|
/* input matrix is invalid */
|
|
DEBUG1 (("ccolamd: Matrix invalid\n")) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
/* === Initialize front info ============================================ */
|
|
|
|
for (col = 0 ; col < n_col ; col++)
|
|
{
|
|
Front_npivcol [col] = 0 ;
|
|
Front_nrows [col] = 0 ;
|
|
Front_ncols [col] = 0 ;
|
|
Front_parent [col] = EMPTY ;
|
|
Front_cols [col] = EMPTY ;
|
|
}
|
|
|
|
/* === Initialize scores, kill dense rows/columns ======================= */
|
|
|
|
init_scoring (n_row, n_col, Row, Col, A, p, knobs,
|
|
&n_row2, &n_col2, &max_deg, cmember, n_cset, cset_start, dead_cols,
|
|
&ndense_row, &nempty_row, &nnewlyempty_row,
|
|
&ndense_col, &nempty_col, &nnewlyempty_col) ;
|
|
|
|
ASSERT (n_row2 == n_row - nempty_row - nnewlyempty_row - ndense_row) ;
|
|
ASSERT (n_col2 == n_col - nempty_col - nnewlyempty_col - ndense_col) ;
|
|
DEBUG1 (("# dense rows "ID" cols "ID"\n", ndense_row, ndense_col)) ;
|
|
|
|
/* === Order the supercolumns =========================================== */
|
|
|
|
ngarbage = find_ordering (n_row, n_col, Alen, Row, Col, A, p,
|
|
#ifndef NDEBUG
|
|
n_col2,
|
|
#endif
|
|
max_deg, 2*nnz, cset, cset_start,
|
|
#ifndef NDEBUG
|
|
n_cset,
|
|
#endif
|
|
cmember, Front_npivcol, Front_nrows, Front_ncols, Front_parent,
|
|
Front_cols, &nfr, aggressive, InFront, order_for_lu) ;
|
|
|
|
ASSERT (Alen >= 5*n_col) ;
|
|
|
|
/* === Postorder ======================================================== */
|
|
|
|
/* A is no longer needed, so use A [0..5*nfr-1] as workspace [ [ */
|
|
/* This step requires Alen >= 5*n_col */
|
|
Front_child = A ;
|
|
Front_sibling = Front_child + nfr ;
|
|
Front_stack = Front_sibling + nfr ;
|
|
Front_order = Front_stack + nfr ;
|
|
Front_size = Front_order + nfr ;
|
|
|
|
CCOLAMD_fsize (nfr, Front_size, Front_nrows, Front_ncols,
|
|
Front_parent, Front_npivcol) ;
|
|
|
|
CCOLAMD_postorder (nfr, Front_parent, Front_npivcol, Front_size,
|
|
Front_order, Front_child, Front_sibling, Front_stack, Front_cols,
|
|
cmember) ;
|
|
|
|
/* Front_size, Front_stack, Front_child, Front_sibling no longer needed ] */
|
|
|
|
/* use A [0..nfr-1] as workspace */
|
|
CCOLAMD_apply_order (Front_npivcol, Front_order, A, nfr, nfr) ;
|
|
CCOLAMD_apply_order (Front_nrows, Front_order, A, nfr, nfr) ;
|
|
CCOLAMD_apply_order (Front_ncols, Front_order, A, nfr, nfr) ;
|
|
CCOLAMD_apply_order (Front_parent, Front_order, A, nfr, nfr) ;
|
|
CCOLAMD_apply_order (Front_cols, Front_order, A, nfr, nfr) ;
|
|
|
|
/* fix the parent to refer to the new numbering */
|
|
for (i = 0 ; i < nfr ; i++)
|
|
{
|
|
parent = Front_parent [i] ;
|
|
if (parent != EMPTY)
|
|
{
|
|
Front_parent [i] = Front_order [parent] ;
|
|
}
|
|
}
|
|
|
|
/* fix InFront to refer to the new numbering */
|
|
for (row = 0 ; row < n_row ; row++)
|
|
{
|
|
i = InFront [row] ;
|
|
ASSERT (i >= EMPTY && i < nfr) ;
|
|
if (i != EMPTY)
|
|
{
|
|
InFront [row] = Front_order [i] ;
|
|
}
|
|
}
|
|
|
|
/* Front_order longer needed ] */
|
|
|
|
/* === Order the columns in the fronts ================================== */
|
|
|
|
/* use A [0..n_col-1] as inverse permutation */
|
|
for (i = 0 ; i < n_col ; i++)
|
|
{
|
|
A [i] = EMPTY ;
|
|
}
|
|
|
|
k = 0 ;
|
|
set1 = 0 ;
|
|
for (i = 0 ; i < nfr ; i++)
|
|
{
|
|
ASSERT (Front_npivcol [i] > 0) ;
|
|
|
|
set2 = CMEMBER (Front_cols [i]) ;
|
|
while (set1 < set2)
|
|
{
|
|
k += dead_cols [set1] ;
|
|
DEBUG3 (("Skip null/dense columns of set "ID"\n",set1)) ;
|
|
set1++ ;
|
|
}
|
|
set1 = set2 ;
|
|
|
|
for (col = Front_cols [i] ; col != EMPTY ; col = Col [col].nextcol)
|
|
{
|
|
ASSERT (col >= 0 && col < n_col) ;
|
|
DEBUG1 (("ccolamd output ordering: k "ID" col "ID"\n", k, col)) ;
|
|
p [k] = col ;
|
|
ASSERT (A [col] == EMPTY) ;
|
|
|
|
cs = CMEMBER (col) ;
|
|
ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ;
|
|
|
|
A [col] = k ;
|
|
k++ ;
|
|
}
|
|
}
|
|
|
|
/* === Order the "dense" and null columns =============================== */
|
|
|
|
if (n_col2 < n_col)
|
|
{
|
|
for (col = 0 ; col < n_col ; col++)
|
|
{
|
|
if (A [col] == EMPTY)
|
|
{
|
|
k = Col [col].shared2.order ;
|
|
cs = CMEMBER (col) ;
|
|
#ifndef NDEBUG
|
|
dead_cols [cs]-- ;
|
|
#endif
|
|
ASSERT (k >= cset_start [cs] && k < cset_start [cs+1]) ;
|
|
DEBUG1 (("ccolamd output ordering: k "ID" col "ID
|
|
" (dense or null col)\n", k, col)) ;
|
|
p [k] = col ;
|
|
A [col] = k ;
|
|
}
|
|
}
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
for (i = 0 ; i < n_cset ; i++)
|
|
{
|
|
ASSERT (dead_cols [i] == 0) ;
|
|
}
|
|
#endif
|
|
|
|
/* === Return statistics in stats ======================================= */
|
|
|
|
stats [CCOLAMD_DENSE_ROW] = ndense_row ;
|
|
stats [CCOLAMD_DENSE_COL] = nempty_row ;
|
|
stats [CCOLAMD_NEWLY_EMPTY_ROW] = nnewlyempty_row ;
|
|
stats [CCOLAMD_DENSE_COL] = ndense_col ;
|
|
stats [CCOLAMD_EMPTY_COL] = nempty_col ;
|
|
stats [CCOLAMD_NEWLY_EMPTY_COL] = nnewlyempty_col ;
|
|
ASSERT (ndense_col + nempty_col + nnewlyempty_col == n_col - n_col2) ;
|
|
if (p_nfr)
|
|
{
|
|
*p_nfr = nfr ;
|
|
}
|
|
stats [CCOLAMD_DEFRAG_COUNT] = ngarbage ;
|
|
DEBUG1 (("ccolamd: done.\n")) ;
|
|
return (TRUE) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === colamd_report ======================================================== */
|
|
/* ========================================================================== */
|
|
|
|
PUBLIC void CCOLAMD_report
|
|
(
|
|
Int stats [CCOLAMD_STATS]
|
|
)
|
|
{
|
|
print_report ("ccolamd", stats) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === symamd_report ======================================================== */
|
|
/* ========================================================================== */
|
|
|
|
PUBLIC void CSYMAMD_report
|
|
(
|
|
Int stats [CCOLAMD_STATS]
|
|
)
|
|
{
|
|
print_report ("csymamd", stats) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === 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 FALSE if the matrix is invalid,
|
|
TRUE otherwise. Not user-callable.
|
|
*/
|
|
|
|
PRIVATE Int init_rows_cols /* returns TRUE if OK, or FALSE otherwise */
|
|
(
|
|
/* === Parameters ======================================================= */
|
|
|
|
Int n_row, /* number of rows of A */
|
|
Int n_col, /* number of columns of A */
|
|
CColamd_Row Row [ ], /* of size n_row+1 */
|
|
CColamd_Col 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 */
|
|
Int stats [CCOLAMD_STATS] /* colamd statistics */
|
|
)
|
|
{
|
|
/* === 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_row ; /* previous row */
|
|
|
|
/* === Initialize columns, and check column pointers ==================== */
|
|
|
|
for (col = 0 ; col < n_col ; col++)
|
|
{
|
|
Col [col].start = p [col] ;
|
|
Col [col].length = p [col+1] - p [col] ;
|
|
|
|
if (Col [col].length < 0)
|
|
{
|
|
/* column pointers must be non-decreasing */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_col_length_negative ;
|
|
stats [CCOLAMD_INFO1] = col ;
|
|
stats [CCOLAMD_INFO2] = Col [col].length ;
|
|
DEBUG1 (("ccolamd: col "ID" length "ID" < 0\n",
|
|
col, Col [col].length)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
Col [col].shared1.thickness = 1 ;
|
|
Col [col].shared2.score = 0 ;
|
|
Col [col].shared3.prev = EMPTY ;
|
|
Col [col].shared4.degree_next = EMPTY ;
|
|
Col [col].nextcol = EMPTY ;
|
|
Col [col].lastcol = col ;
|
|
}
|
|
|
|
/* p [0..n_col] no longer needed, used as "head" in subsequent routines */
|
|
|
|
/* === Scan columns, compute row degrees, and check row indices ========= */
|
|
|
|
stats [CCOLAMD_INFO3] = 0 ; /* number of duplicate or unsorted row indices*/
|
|
|
|
for (row = 0 ; row < n_row ; row++)
|
|
{
|
|
Row [row].length = 0 ;
|
|
Row [row].shared2.mark = -1 ;
|
|
Row [row].thickness = 1 ;
|
|
Row [row].front = EMPTY ;
|
|
}
|
|
|
|
for (col = 0 ; col < n_col ; col++)
|
|
{
|
|
DEBUG1 (("\nCcolamd input column "ID":\n", col)) ;
|
|
last_row = -1 ;
|
|
|
|
cp = &A [p [col]] ;
|
|
cp_end = &A [p [col+1]] ;
|
|
|
|
while (cp < cp_end)
|
|
{
|
|
row = *cp++ ;
|
|
DEBUG1 (("row: "ID"\n", row)) ;
|
|
|
|
/* make sure row indices within range */
|
|
if (row < 0 || row >= n_row)
|
|
{
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_ERROR_row_index_out_of_bounds ;
|
|
stats [CCOLAMD_INFO1] = col ;
|
|
stats [CCOLAMD_INFO2] = row ;
|
|
stats [CCOLAMD_INFO3] = n_row ;
|
|
DEBUG1 (("row "ID" col "ID" out of bounds\n", row, col)) ;
|
|
return (FALSE) ;
|
|
}
|
|
|
|
if (row <= last_row || Row [row].shared2.mark == col)
|
|
{
|
|
/* row index are unsorted or repeated (or both), thus col */
|
|
/* is jumbled. This is a notice, not an error condition. */
|
|
stats [CCOLAMD_STATUS] = CCOLAMD_OK_BUT_JUMBLED ;
|
|
stats [CCOLAMD_INFO1] = col ;
|
|
stats [CCOLAMD_INFO2] = row ;
|
|
(stats [CCOLAMD_INFO3]) ++ ;
|
|
DEBUG1 (("row "ID" col "ID" unsorted/duplicate\n", row, col)) ;
|
|
}
|
|
|
|
if (Row [row].shared2.mark != col)
|
|
{
|
|
Row [row].length++ ;
|
|
}
|
|
else
|
|
{
|
|
/* this is a repeated entry in the column, */
|
|
/* it will be removed */
|
|
Col [col].length-- ;
|
|
}
|
|
|
|
/* mark the row as having been seen in this column */
|
|
Row [row].shared2.mark = col ;
|
|
|
|
last_row = row ;
|
|
}
|
|
}
|
|
|
|
/* === 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 (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED)
|
|
{
|
|
/* 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 (stats [CCOLAMD_STATUS] == CCOLAMD_OK_BUT_JUMBLED)
|
|
{
|
|
DEBUG1 (("ccolamd: reconstructing column form, matrix jumbled\n")) ;
|
|
|
|
#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 ;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* === Done. Matrix is not (or no longer) jumbled ====================== */
|
|
|
|
|
|
return (TRUE) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === 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 */
|
|
CColamd_Row Row [ ], /* of size n_row+1 */
|
|
CColamd_Col Col [ ], /* of size n_col+1 */
|
|
Int A [ ], /* column form and row form of A */
|
|
Int head [ ], /* of size n_col+1 */
|
|
double knobs [CCOLAMD_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 */
|
|
Int cmember [ ],
|
|
Int n_cset,
|
|
Int cset_start [ ],
|
|
Int dead_cols [ ],
|
|
Int *p_ndense_row, /* number of dense rows */
|
|
Int *p_nempty_row, /* number of original empty rows */
|
|
Int *p_nnewlyempty_row, /* number of newly empty rows */
|
|
Int *p_ndense_col, /* number of dense cols (excl "empty" cols) */
|
|
Int *p_nempty_col, /* number of original empty cols */
|
|
Int *p_nnewlyempty_col /* number of newly empty cols */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int c ; /* a column index */
|
|
Int r, row ; /* a row index */
|
|
Int *cp ; /* a column pointer */
|
|
Int deg ; /* degree 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 max_deg ; /* maximum row degree */
|
|
Int s ; /* a cset index */
|
|
Int ndense_row ; /* number of dense rows */
|
|
Int nempty_row ; /* number of empty rows */
|
|
Int nnewlyempty_row ; /* number of newly empty rows */
|
|
Int ndense_col ; /* number of dense cols (excl "empty" cols) */
|
|
Int nempty_col ; /* number of original empty cols */
|
|
Int nnewlyempty_col ; /* number of newly empty cols */
|
|
Int ne ;
|
|
|
|
#ifndef NDEBUG
|
|
Int debug_count ; /* debug only. */
|
|
#endif
|
|
|
|
/* === Extract knobs ==================================================== */
|
|
|
|
/* Note: if knobs contains a NaN, this is undefined: */
|
|
if (knobs [CCOLAMD_DENSE_ROW] < 0)
|
|
{
|
|
/* only remove completely dense rows */
|
|
dense_row_count = n_col-1 ;
|
|
}
|
|
else
|
|
{
|
|
dense_row_count = DENSE_DEGREE (knobs [CCOLAMD_DENSE_ROW], n_col) ;
|
|
}
|
|
if (knobs [CCOLAMD_DENSE_COL] < 0)
|
|
{
|
|
/* only remove completely dense columns */
|
|
dense_col_count = n_row-1 ;
|
|
}
|
|
else
|
|
{
|
|
dense_col_count =
|
|
DENSE_DEGREE (knobs [CCOLAMD_DENSE_COL], MIN (n_row, n_col)) ;
|
|
}
|
|
|
|
DEBUG1 (("densecount: "ID" "ID"\n", dense_row_count, dense_col_count)) ;
|
|
max_deg = 0 ;
|
|
|
|
n_col2 = n_col ;
|
|
n_row2 = n_row ;
|
|
|
|
/* Set the head array for bookkeeping of dense and empty columns. */
|
|
/* This will be used as hash buckets later. */
|
|
for (s = 0 ; s < n_cset ; s++)
|
|
{
|
|
head [s] = cset_start [s+1] ;
|
|
}
|
|
|
|
ndense_col = 0 ;
|
|
nempty_col = 0 ;
|
|
nnewlyempty_col = 0 ;
|
|
ndense_row = 0 ;
|
|
nempty_row = 0 ;
|
|
nnewlyempty_row = 0 ;
|
|
|
|
/* === Kill empty columns =============================================== */
|
|
|
|
/* Put the empty columns at the end in their natural order, 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 of its cset */
|
|
Col [c].shared2.order = --head [CMEMBER (c)] ;
|
|
--n_col2 ;
|
|
dead_cols [CMEMBER (c)] ++ ;
|
|
nempty_col++ ;
|
|
KILL_PRINCIPAL_COL (c) ;
|
|
}
|
|
}
|
|
DEBUG1 (("ccolamd: null columns killed: "ID"\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 of its cset */
|
|
Col [c].shared2.order = --head [CMEMBER (c)] ;
|
|
--n_col2 ;
|
|
dead_cols [CMEMBER (c)] ++ ;
|
|
ndense_col++ ;
|
|
/* 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) ;
|
|
}
|
|
}
|
|
DEBUG1 (("Dense and null columns killed: "ID"\n", n_col - n_col2)) ;
|
|
|
|
/* === Kill dense and empty rows ======================================== */
|
|
|
|
/* Note that there can now be empty rows, since dense columns have
|
|
* been deleted. These are "newly" empty rows. */
|
|
|
|
ne = 0 ;
|
|
for (r = 0 ; r < n_row ; r++)
|
|
{
|
|
deg = Row [r].shared1.degree ;
|
|
ASSERT (deg >= 0 && deg <= n_col) ;
|
|
if (deg > dense_row_count)
|
|
{
|
|
/* There is at least one dense row. Continue ordering, but */
|
|
/* symbolic factorization will be redone after ccolamd is done.*/
|
|
ndense_row++ ;
|
|
}
|
|
if (deg == 0)
|
|
{
|
|
/* this is a newly empty row, or original empty row */
|
|
ne++ ;
|
|
}
|
|
if (deg > dense_row_count || deg == 0)
|
|
{
|
|
/* kill a dense or empty row */
|
|
KILL_ROW (r) ;
|
|
Row [r].thickness = 0 ;
|
|
--n_row2 ;
|
|
}
|
|
else
|
|
{
|
|
/* keep track of max degree of remaining rows */
|
|
max_deg = MAX (max_deg, deg) ;
|
|
}
|
|
}
|
|
nnewlyempty_row = ne - nempty_row ;
|
|
DEBUG1 (("ccolamd: Dense and null rows killed: "ID"\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 COLMMD 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) */
|
|
DEBUG1 (("Newly null killed: "ID"\n", c)) ;
|
|
Col [c].shared2.order = -- head [CMEMBER (c)] ;
|
|
--n_col2 ;
|
|
dead_cols [CMEMBER (c)] ++ ;
|
|
nnewlyempty_col++ ;
|
|
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 ;
|
|
}
|
|
}
|
|
DEBUG1 (("ccolamd: Dense, null, and newly-null columns killed: "ID"\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_count = 0 ;
|
|
#endif
|
|
|
|
/* clear the hash buckets */
|
|
for (c = 0 ; c <= n_col ; c++)
|
|
{
|
|
head [c] = EMPTY ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
debug_structures (n_row, n_col, Row, Col, A, cmember, cset_start) ;
|
|
#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 ;
|
|
*p_ndense_row = ndense_row ;
|
|
*p_nempty_row = nempty_row ; /* original empty rows */
|
|
*p_nnewlyempty_row = nnewlyempty_row ;
|
|
*p_ndense_col = ndense_col ;
|
|
*p_nempty_col = nempty_col ; /* original empty cols */
|
|
*p_nnewlyempty_col = nnewlyempty_col ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === 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 + n_col or larger */
|
|
CColamd_Row Row [ ], /* of size n_row+1 */
|
|
CColamd_Col Col [ ], /* of size n_col+1 */
|
|
Int A [ ], /* column form and row form of A */
|
|
Int head [ ], /* of size n_col+1 */
|
|
#ifndef NDEBUG
|
|
Int n_col2, /* Remaining columns to order */
|
|
#endif
|
|
Int max_deg, /* Maximum row degree */
|
|
Int pfree, /* index of first free slot (2*nnz on entry) */
|
|
Int cset [ ], /* constraint set of A */
|
|
Int cset_start [ ], /* pointer to the start of every cset */
|
|
#ifndef NDEBUG
|
|
Int n_cset, /* number of csets */
|
|
#endif
|
|
Int cmember [ ], /* col -> cset mapping */
|
|
Int Front_npivcol [ ],
|
|
Int Front_nrows [ ],
|
|
Int Front_ncols [ ],
|
|
Int Front_parent [ ],
|
|
Int Front_cols [ ],
|
|
Int *p_nfr, /* number of fronts */
|
|
Int aggressive,
|
|
Int InFront [ ],
|
|
Int order_for_lu
|
|
)
|
|
{
|
|
/* === 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 ; /* number of columns in pivot row */
|
|
Int pivot_row_length ; /* number 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" (no. 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 */
|
|
Int current_set ; /* consraint set that is being ordered */
|
|
Int score ; /* score of a column */
|
|
Int colstart ; /* pointer to first column in current cset */
|
|
Int colend ; /* pointer to last column in current cset */
|
|
Int deadcol ; /* number of dense & null columns in a cset */
|
|
|
|
#ifndef NDEBUG
|
|
Int debug_d ; /* debug loop counter */
|
|
Int debug_step = 0 ; /* debug loop counter */
|
|
Int cols_thickness = 0 ; /* the thickness of the columns in current */
|
|
/* cset degreelist and in pivot row pattern. */
|
|
#endif
|
|
|
|
Int pivot_row_thickness ; /* number of rows represented by pivot row */
|
|
Int nfr = 0 ; /* number of fronts */
|
|
Int child ;
|
|
|
|
/* === Initialization and clear mark ==================================== */
|
|
|
|
max_mark = Int_MAX - n_col ; /* Int_MAX defined in <limits.h> */
|
|
tag_mark = clear_mark (0, max_mark, n_row, Row) ;
|
|
min_score = 0 ;
|
|
ngarbage = 0 ;
|
|
current_set = -1 ;
|
|
deadcol = 0 ;
|
|
DEBUG1 (("ccolamd: Ordering, n_col2="ID"\n", n_col2)) ;
|
|
|
|
for (row = 0 ; row < n_row ; row++)
|
|
{
|
|
InFront [row] = EMPTY ;
|
|
}
|
|
|
|
/* === Order the columns ================================================ */
|
|
|
|
for (k = 0 ; k < n_col ; /* 'k' is incremented below */)
|
|
{
|
|
|
|
/* 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
|
|
|
|
/* Initialize the degree list with columns from next non-empty cset */
|
|
|
|
while ((k+deadcol) == cset_start [current_set+1])
|
|
{
|
|
current_set++ ;
|
|
DEBUG1 (("\n\n\n============ CSET: "ID"\n", current_set)) ;
|
|
k += deadcol ; /* jump to start of next cset */
|
|
deadcol = 0 ; /* reset dead column count */
|
|
|
|
ASSERT ((current_set == n_cset) == (k == n_col)) ;
|
|
|
|
/* return if all columns are ordered. */
|
|
if (k == n_col)
|
|
{
|
|
*p_nfr = nfr ;
|
|
return (ngarbage) ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
for (col = 0 ; col <= n_col ; col++)
|
|
{
|
|
ASSERT (head [col] == EMPTY) ;
|
|
}
|
|
#endif
|
|
|
|
min_score = n_col ;
|
|
colstart = cset_start [current_set] ;
|
|
colend = cset_start [current_set+1] ;
|
|
|
|
while (colstart < colend)
|
|
{
|
|
col = cset [colstart++] ;
|
|
|
|
if (COL_IS_DEAD(col))
|
|
{
|
|
DEBUG1 (("Column "ID" is dead\n", col)) ;
|
|
/* count dense and null columns */
|
|
if (Col [col].shared2.order != EMPTY)
|
|
{
|
|
deadcol++ ;
|
|
}
|
|
continue ;
|
|
}
|
|
|
|
/* only add principal columns in current set to degree lists */
|
|
ASSERT (CMEMBER (col) == current_set) ;
|
|
|
|
score = Col [col].shared2.score ;
|
|
DEBUG1 (("Column "ID" is alive, score "ID"\n", col, 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 [col].shared3.prev = EMPTY ;
|
|
Col [col].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 = col ;
|
|
}
|
|
head [score] = col ;
|
|
|
|
/* see if this score is less than current min */
|
|
min_score = MIN (min_score, score) ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("degree lists initialized \n")) ;
|
|
debug_deg_lists (n_row, n_col, Row, Col, head, min_score,
|
|
((cset_start [current_set+1]-cset_start [current_set])-deadcol),
|
|
max_deg) ;
|
|
#endif
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
if (debug_step % 100 == 0)
|
|
{
|
|
DEBUG2 (("\n... Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
|
|
}
|
|
else
|
|
{
|
|
DEBUG3 (("\n------Step k: "ID" out of n_col2: "ID"\n", k, n_col2)) ;
|
|
}
|
|
debug_step++ ;
|
|
DEBUG1 (("start of step k="ID": ", k)) ;
|
|
debug_deg_lists (n_row, n_col, Row, Col, head,
|
|
min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ;
|
|
debug_matrix (n_row, n_col, Row, Col, A) ;
|
|
#endif
|
|
|
|
/* === Select pivot column, and order it ============================ */
|
|
|
|
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)) ;
|
|
|
|
/* 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) ;
|
|
DEBUG3 (("Pivot col: "ID" thick "ID"\n", pivot_col,
|
|
pivot_col_thickness)) ;
|
|
|
|
/* === 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 Row [ ].shared2.mark array */
|
|
tag_mark = clear_mark (0, max_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 ;
|
|
pivot_row_thickness = 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++ ;
|
|
ASSERT (row >= 0 && row < n_row) ;
|
|
DEBUG4 (("Pivcol pattern "ID" "ID"\n", ROW_IS_ALIVE (row), row)) ;
|
|
/* skip if row is dead */
|
|
if (ROW_IS_ALIVE (row))
|
|
{
|
|
/* sum the thicknesses of all the rows */
|
|
pivot_row_thickness += Row [row].thickness ;
|
|
|
|
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 ;
|
|
DEBUG4 (("\t\t\tNew live col in pivrow: "ID"\n",col)) ;
|
|
}
|
|
#ifndef NDEBUG
|
|
if (col_thickness < 0 && COL_IS_ALIVE (col))
|
|
{
|
|
DEBUG4 (("\t\t\tOld live col in pivrow: "ID"\n",col)) ;
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
}
|
|
|
|
/* pivot_row_thickness is the number of rows in frontal matrix */
|
|
/* including both pivotal rows and nonpivotal rows */
|
|
|
|
/* 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++ ;
|
|
DEBUG3 (("Kill row in pivot col: "ID"\n", row)) ;
|
|
ASSERT (row >= 0 && row < n_row) ;
|
|
if (ROW_IS_ALIVE (row))
|
|
{
|
|
if (Row [row].front != EMPTY)
|
|
{
|
|
/* This row represents a frontal matrix. */
|
|
/* Row [row].front is a child of current front */
|
|
child = Row [row].front ;
|
|
Front_parent [child] = nfr ;
|
|
DEBUG1 (("Front "ID" => front "ID", normal\n", child, nfr));
|
|
}
|
|
else
|
|
{
|
|
/* This is an original row. Keep track of which front
|
|
* is its parent in the row-merge tree. */
|
|
InFront [row] = nfr ;
|
|
DEBUG1 (("Row "ID" => front "ID", normal\n", row, nfr)) ;
|
|
}
|
|
}
|
|
|
|
KILL_ROW (row) ;
|
|
Row [row].thickness = 0 ;
|
|
}
|
|
|
|
/* === 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] ;
|
|
DEBUG3 (("Pivotal row is "ID"\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 ====================================== */
|
|
|
|
DEBUG3 (("** Computing set differences phase. **\n")) ;
|
|
|
|
/* pivot row is currently dead - it will be revived later. */
|
|
|
|
DEBUG3 (("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) ;
|
|
DEBUG3 (("Col: "ID"\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 =========================== */
|
|
|
|
/* only columns in current_set will be in degree list */
|
|
if (CMEMBER (col) == current_set)
|
|
{
|
|
#ifndef NDEBUG
|
|
cols_thickness += col_thickness ;
|
|
#endif
|
|
cur_score = Col [col].shared2.score ;
|
|
prev_col = Col [col].shared3.prev ;
|
|
next_col = Col [col].shared4.degree_next ;
|
|
DEBUG3 ((" cur_score "ID" prev_col "ID" next_col "ID"\n",
|
|
cur_score, prev_col, next_col)) ;
|
|
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 && aggressive)
|
|
{
|
|
DEBUG3 (("aggressive absorption. Row: "ID"\n", row)) ;
|
|
|
|
if (Row [row].front != EMPTY)
|
|
{
|
|
/* Row [row].front is a child of current front. */
|
|
child = Row [row].front ;
|
|
Front_parent [child] = nfr ;
|
|
DEBUG1 (("Front "ID" => front "ID", aggressive\n",
|
|
child, nfr)) ;
|
|
}
|
|
else
|
|
{
|
|
/* this is an original row. Keep track of which front
|
|
* assembles it, for the row-merge tree */
|
|
InFront [row] = nfr ;
|
|
DEBUG1 (("Row "ID" => front "ID", aggressive\n",
|
|
row, nfr)) ;
|
|
}
|
|
|
|
KILL_ROW (row) ;
|
|
|
|
/* sum the thicknesses of all the rows */
|
|
pivot_row_thickness += Row [row].thickness ;
|
|
Row [row].thickness = 0 ;
|
|
}
|
|
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,
|
|
cset_start [current_set+1]-(k+deadcol)-(cols_thickness),
|
|
max_deg) ;
|
|
cols_thickness = 0 ;
|
|
#endif
|
|
|
|
/* === Add up set differences for each column ======================= */
|
|
|
|
DEBUG3 (("** 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 ;
|
|
|
|
DEBUG4 (("Adding set diffs for Col: "ID".\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))
|
|
{
|
|
DEBUG4 ((" Row "ID", dead\n", row)) ;
|
|
continue ;
|
|
}
|
|
DEBUG4 ((" Row "ID", set diff "ID"\n", row, row_mark-tag_mark));
|
|
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 && CMEMBER (col) == current_set)
|
|
{
|
|
DEBUG4 (("further mass elimination. Col: "ID"\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 ;
|
|
pivot_col_thickness += Col [col].shared1.thickness ;
|
|
/* add to column list of front */
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("Mass")) ;
|
|
dump_super (col, Col, n_col) ;
|
|
#endif
|
|
Col [Col [col].lastcol].nextcol = Front_cols [nfr] ;
|
|
Front_cols [nfr] = col ;
|
|
}
|
|
else
|
|
{
|
|
/* === Prepare for supercolumn detection ==================== */
|
|
|
|
DEBUG4 (("Preparing supercol detection for Col: "ID".\n", col));
|
|
|
|
/* save score so far */
|
|
Col [col].shared2.score = cur_score ;
|
|
|
|
/* add column to hash table, for supercolumn detection */
|
|
hash %= n_col + 1 ;
|
|
|
|
DEBUG4 ((" Hash = "ID", n_col = "ID".\n", hash, n_col)) ;
|
|
ASSERT (((Int) 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 ======================================== */
|
|
|
|
DEBUG3 (("** Supercolumn detection phase. **\n")) ;
|
|
|
|
detect_super_cols (
|
|
#ifndef NDEBUG
|
|
n_col, Row,
|
|
#endif
|
|
Col, A, head, pivot_row_start, pivot_row_length, cmember) ;
|
|
|
|
/* === Kill the pivotal column ====================================== */
|
|
|
|
DEBUG1 ((" KILLING column detect supercols "ID" \n", pivot_col)) ;
|
|
KILL_PRINCIPAL_COL (pivot_col) ;
|
|
|
|
/* add columns to column list of front */
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("Pivot")) ;
|
|
dump_super (pivot_col, Col, n_col) ;
|
|
#endif
|
|
Col [Col [pivot_col].lastcol].nextcol = Front_cols [nfr] ;
|
|
Front_cols [nfr] = pivot_col ;
|
|
|
|
/* === Clear mark =================================================== */
|
|
|
|
tag_mark = clear_mark (tag_mark+max_deg+1, max_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 ================ */
|
|
|
|
DEBUG3 (("** 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 ========================= */
|
|
|
|
if (CMEMBER (col) == current_set)
|
|
{
|
|
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) ;
|
|
}
|
|
else
|
|
{
|
|
Col [col].shared4.degree_next = EMPTY ;
|
|
Col [col].shared3.prev = EMPTY ;
|
|
}
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
debug_deg_lists (n_row, n_col, Row, Col, head,
|
|
min_score, cset_start [current_set+1]-(k+deadcol), max_deg) ;
|
|
#endif
|
|
|
|
/* frontal matrix can have more pivot cols than pivot rows for */
|
|
/* singular matrices. */
|
|
|
|
/* number of candidate pivot columns */
|
|
Front_npivcol [nfr] = pivot_col_thickness ;
|
|
|
|
/* all rows (not just size of contrib. block) */
|
|
Front_nrows [nfr] = pivot_row_thickness ;
|
|
|
|
/* all cols */
|
|
Front_ncols [nfr] = pivot_col_thickness + pivot_row_degree ;
|
|
|
|
Front_parent [nfr] = EMPTY ;
|
|
|
|
pivot_row_thickness -= pivot_col_thickness ;
|
|
DEBUG1 (("Front "ID" Pivot_row_thickness after pivot cols elim: "ID"\n",
|
|
nfr, pivot_row_thickness)) ;
|
|
pivot_row_thickness = MAX (0, pivot_row_thickness) ;
|
|
|
|
/* === Resurrect the new pivot row ================================== */
|
|
|
|
if ((pivot_row_degree > 0 && pivot_row_thickness > 0 && (order_for_lu))
|
|
|| (pivot_row_degree > 0 && (!order_for_lu)))
|
|
{
|
|
/* 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 ;
|
|
Row [pivot_row].thickness = pivot_row_thickness ;
|
|
Row [pivot_row].front = nfr ;
|
|
/* pivot row is no longer dead */
|
|
DEBUG1 (("Resurrect Pivot_row "ID" deg: "ID"\n",
|
|
pivot_row, pivot_row_degree)) ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("Front "ID" : "ID" "ID" "ID" ", nfr,
|
|
Front_npivcol [nfr], Front_nrows [nfr], Front_ncols [nfr])) ;
|
|
DEBUG1 ((" cols:[ ")) ;
|
|
debug_d = 0 ;
|
|
for (col = Front_cols [nfr] ; col != EMPTY ; col = Col [col].nextcol)
|
|
{
|
|
DEBUG1 ((" "ID, col)) ;
|
|
ASSERT (col >= 0 && col < n_col) ;
|
|
ASSERT (COL_IS_DEAD (col)) ;
|
|
debug_d++ ;
|
|
ASSERT (debug_d <= pivot_col_thickness) ;
|
|
}
|
|
ASSERT (debug_d == pivot_col_thickness) ;
|
|
DEBUG1 ((" ]\n ")) ;
|
|
#endif
|
|
nfr++ ; /* one more front */
|
|
}
|
|
|
|
/* === All principal columns have now been ordered ====================== */
|
|
|
|
*p_nfr = nfr ;
|
|
return (ngarbage) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === 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 */
|
|
CColamd_Row Row [ ], /* of size n_row+1 */
|
|
#endif
|
|
|
|
CColamd_Col 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 */
|
|
Int cmember [ ] /* col -> cset mapping */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int hash ; /* hash value 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, */
|
|
/* or if in different constraint sets */
|
|
if (Col [c].length != length ||
|
|
Col [c].shared2.score != Col [super_c].shared2.score
|
|
|| CMEMBER (c) != CMEMBER (super_c))
|
|
{
|
|
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" */
|
|
/* super columns should belong to the same constraint set */
|
|
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 ;
|
|
|
|
/* add c to end of list of super_c */
|
|
ASSERT (Col [super_c].lastcol >= 0) ;
|
|
ASSERT (Col [super_c].lastcol < n_col) ;
|
|
Col [Col [super_c].lastcol].nextcol = c ;
|
|
Col [super_c].lastcol = Col [c].lastcol ;
|
|
#ifndef NDEBUG
|
|
/* dump the supercolumn */
|
|
DEBUG1 (("Super")) ;
|
|
dump_super (super_c, Col, n_col) ;
|
|
#endif
|
|
}
|
|
}
|
|
|
|
/* === 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 */
|
|
CColamd_Row Row [ ], /* row info */
|
|
CColamd_Col 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 ;
|
|
DEBUG2 (("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_DEAD (r) || (Row [r].length == 0))
|
|
{
|
|
/* This row is already dead, or is of zero length. Cannot compact
|
|
* a row of zero length, so kill it. NOTE: in the current version,
|
|
* there are no zero-length live rows. Kill the row (for the first
|
|
* time, or again) just to be safe. */
|
|
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 tag_mark, /* new value of tag_mark */
|
|
Int max_mark, /* max allowed value of tag_mark */
|
|
|
|
Int n_row, /* number of rows in A */
|
|
CColamd_Row Row [ ] /* Row [0 ... n_row-1].shared2.mark is set to zero */
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int r ;
|
|
|
|
if (tag_mark <= 0 || tag_mark >= max_mark)
|
|
{
|
|
for (r = 0 ; r < n_row ; r++)
|
|
{
|
|
if (ROW_IS_ALIVE (r))
|
|
{
|
|
Row [r].shared2.mark = 0 ;
|
|
}
|
|
}
|
|
tag_mark = 1 ;
|
|
}
|
|
|
|
return (tag_mark) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === print_report ========================================================= */
|
|
/* ========================================================================== */
|
|
|
|
/* No printing occurs if NPRINT is defined at compile time. */
|
|
|
|
PRIVATE void print_report
|
|
(
|
|
char *method,
|
|
Int stats [CCOLAMD_STATS]
|
|
)
|
|
{
|
|
|
|
Int i1, i2, i3 ;
|
|
|
|
PRINTF (("\n%s version %d.%d, %s: ", method,
|
|
CCOLAMD_MAIN_VERSION, CCOLAMD_SUB_VERSION, CCOLAMD_DATE)) ;
|
|
|
|
if (!stats)
|
|
{
|
|
PRINTF (("No statistics available.\n")) ;
|
|
return ;
|
|
}
|
|
|
|
i1 = stats [CCOLAMD_INFO1] ;
|
|
i2 = stats [CCOLAMD_INFO2] ;
|
|
i3 = stats [CCOLAMD_INFO3] ;
|
|
|
|
if (stats [CCOLAMD_STATUS] >= 0)
|
|
{
|
|
PRINTF(("OK. ")) ;
|
|
}
|
|
else
|
|
{
|
|
PRINTF(("ERROR. ")) ;
|
|
}
|
|
|
|
switch (stats [CCOLAMD_STATUS])
|
|
{
|
|
|
|
case CCOLAMD_OK_BUT_JUMBLED:
|
|
|
|
PRINTF(("Matrix has unsorted or duplicate row indices.\n")) ;
|
|
|
|
PRINTF(("%s: duplicate or out-of-order row indices: "ID"\n",
|
|
method, i3)) ;
|
|
|
|
PRINTF(("%s: last seen duplicate or out-of-order row: "ID"\n",
|
|
method, INDEX (i2))) ;
|
|
|
|
PRINTF(("%s: last seen in column: "ID"",
|
|
method, INDEX (i1))) ;
|
|
|
|
/* no break - fall through to next case instead */
|
|
|
|
case CCOLAMD_OK:
|
|
|
|
PRINTF(("\n")) ;
|
|
|
|
PRINTF(("%s: number of dense or empty rows ignored: "ID"\n",
|
|
method, stats [CCOLAMD_DENSE_ROW])) ;
|
|
|
|
PRINTF(("%s: number of dense or empty columns ignored: "ID"\n",
|
|
method, stats [CCOLAMD_DENSE_COL])) ;
|
|
|
|
PRINTF(("%s: number of garbage collections performed: "ID"\n",
|
|
method, stats [CCOLAMD_DEFRAG_COUNT])) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_A_not_present:
|
|
|
|
PRINTF(("Array A (row indices of matrix) not present.\n")) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_p_not_present:
|
|
|
|
PRINTF(("Array p (column pointers for matrix) not present.\n")) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_nrow_negative:
|
|
|
|
PRINTF(("Invalid number of rows ("ID").\n", i1)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_ncol_negative:
|
|
|
|
PRINTF(("Invalid number of columns ("ID").\n", i1)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_nnz_negative:
|
|
|
|
PRINTF(("Invalid number of nonzero entries ("ID").\n", i1)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_p0_nonzero:
|
|
|
|
PRINTF(("Invalid column pointer, p [0] = "ID", must be 0.\n", i1)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_A_too_small:
|
|
|
|
PRINTF(("Array A too small.\n")) ;
|
|
PRINTF((" Need Alen >= "ID", but given only Alen = "ID".\n",
|
|
i1, i2)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_col_length_negative:
|
|
|
|
PRINTF(("Column "ID" has a negative number of entries ("ID").\n",
|
|
INDEX (i1), i2)) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_row_index_out_of_bounds:
|
|
|
|
PRINTF(("Row index (row "ID") out of bounds ("ID" to "ID") in"
|
|
"column "ID".\n", INDEX (i2), INDEX (0), INDEX (i3-1),
|
|
INDEX (i1))) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_out_of_memory:
|
|
|
|
PRINTF(("Out of memory.\n")) ;
|
|
break ;
|
|
|
|
case CCOLAMD_ERROR_invalid_cmember:
|
|
|
|
PRINTF(("cmember invalid\n")) ;
|
|
break ;
|
|
}
|
|
}
|
|
|
|
|
|
/* ========================================================================= */
|
|
/* === "Expert" routines =================================================== */
|
|
/* ========================================================================= */
|
|
|
|
/* The following routines are visible outside this routine, but are not meant
|
|
* to be called by the user. They are meant for a future version of UMFPACK,
|
|
* to replace UMFPACK internal routines with a similar name.
|
|
*/
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === CCOLAMD_apply_order ================================================== */
|
|
/* ========================================================================== */
|
|
|
|
/*
|
|
* Apply post-ordering of supernodal elimination tree.
|
|
*/
|
|
|
|
GLOBAL void CCOLAMD_apply_order
|
|
(
|
|
Int Front [ ], /* of size nn on input, size nfr on output */
|
|
const Int Order [ ], /* Order [i] = k, i in the range 0..nn-1,
|
|
* and k in the range 0..nfr-1, means that node
|
|
* i is the kth node in the postordered tree. */
|
|
Int Temp [ ], /* workspace of size nfr */
|
|
Int nn, /* nodes are numbered in the range 0..nn-1 */
|
|
Int nfr /* the number of nodes actually in use */
|
|
)
|
|
{
|
|
Int i, k ;
|
|
for (i = 0 ; i < nn ; i++)
|
|
{
|
|
k = Order [i] ;
|
|
ASSERT (k >= EMPTY && k < nfr) ;
|
|
if (k != EMPTY)
|
|
{
|
|
Temp [k] = Front [i] ;
|
|
}
|
|
}
|
|
|
|
for (k = 0 ; k < nfr ; k++)
|
|
{
|
|
Front [k] = Temp [k] ;
|
|
}
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === CCOLAMD_fsize ======================================================== */
|
|
/* ========================================================================== */
|
|
|
|
/* Determine the largest frontal matrix size for each subtree.
|
|
* Only required to sort the children of each
|
|
* node prior to postordering the column elimination tree. */
|
|
|
|
GLOBAL void CCOLAMD_fsize
|
|
(
|
|
Int nn,
|
|
Int Fsize [ ],
|
|
Int Fnrows [ ],
|
|
Int Fncols [ ],
|
|
Int Parent [ ],
|
|
Int Npiv [ ]
|
|
)
|
|
{
|
|
double dr, dc ;
|
|
Int j, parent, frsize, r, c ;
|
|
|
|
for (j = 0 ; j < nn ; j++)
|
|
{
|
|
Fsize [j] = EMPTY ;
|
|
}
|
|
|
|
/* ---------------------------------------------------------------------- */
|
|
/* find max front size for tree rooted at node j, for each front j */
|
|
/* ---------------------------------------------------------------------- */
|
|
|
|
DEBUG1 (("\n\n========================================FRONTS:\n")) ;
|
|
for (j = 0 ; j < nn ; j++)
|
|
{
|
|
if (Npiv [j] > 0)
|
|
{
|
|
/* this is a frontal matrix */
|
|
parent = Parent [j] ;
|
|
r = Fnrows [j] ;
|
|
c = Fncols [j] ;
|
|
/* avoid integer overflow */
|
|
dr = (double) r ;
|
|
dc = (double) c ;
|
|
frsize = (INT_OVERFLOW (dr * dc)) ? Int_MAX : (r * c) ;
|
|
DEBUG1 ((""ID" : npiv "ID" size "ID" parent "ID" ",
|
|
j, Npiv [j], frsize, parent)) ;
|
|
Fsize [j] = MAX (Fsize [j], frsize) ;
|
|
DEBUG1 (("Fsize [j = "ID"] = "ID"\n", j, Fsize [j])) ;
|
|
if (parent != EMPTY)
|
|
{
|
|
/* find the maximum frontsize of self and children */
|
|
ASSERT (Npiv [parent] > 0) ;
|
|
ASSERT (parent > j) ;
|
|
Fsize [parent] = MAX (Fsize [parent], Fsize [j]) ;
|
|
DEBUG1 (("Fsize [parent = "ID"] = "ID"\n",
|
|
parent, Fsize [parent]));
|
|
}
|
|
}
|
|
}
|
|
DEBUG1 (("fsize done\n")) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================= */
|
|
/* === CCOLAMD_postorder =================================================== */
|
|
/* ========================================================================= */
|
|
|
|
/* Perform a postordering (via depth-first search) of an assembly tree. */
|
|
|
|
GLOBAL void CCOLAMD_postorder
|
|
(
|
|
/* inputs, not modified on output: */
|
|
Int nn, /* nodes are in the range 0..nn-1 */
|
|
Int Parent [ ], /* Parent [j] is the parent of j, or EMPTY if root */
|
|
Int Nv [ ], /* Nv [j] > 0 number of pivots represented by node j,
|
|
* or zero if j is not a node. */
|
|
Int Fsize [ ], /* Fsize [j]: size of node j */
|
|
|
|
/* output, not defined on input: */
|
|
Int Order [ ], /* output post-order */
|
|
|
|
/* workspaces of size nn: */
|
|
Int Child [ ],
|
|
Int Sibling [ ],
|
|
Int Stack [ ],
|
|
Int Front_cols [ ],
|
|
|
|
/* input, not modified on output: */
|
|
Int cmember [ ]
|
|
)
|
|
{
|
|
Int i, j, k, parent, frsize, f, fprev, maxfrsize, bigfprev, bigf, fnext ;
|
|
|
|
for (j = 0 ; j < nn ; j++)
|
|
{
|
|
Child [j] = EMPTY ;
|
|
Sibling [j] = EMPTY ;
|
|
}
|
|
|
|
/* --------------------------------------------------------------------- */
|
|
/* place the children in link lists - bigger elements tend to be last */
|
|
/* --------------------------------------------------------------------- */
|
|
|
|
for (j = nn-1 ; j >= 0 ; j--)
|
|
{
|
|
if (Nv [j] > 0)
|
|
{
|
|
/* this is an element */
|
|
parent = Parent [j] ;
|
|
if (parent != EMPTY)
|
|
{
|
|
/* place the element in link list of the children its parent */
|
|
/* bigger elements will tend to be at the end of the list */
|
|
Sibling [j] = Child [parent] ;
|
|
if (CMEMBER (Front_cols[parent]) == CMEMBER (Front_cols[j]))
|
|
{
|
|
Child [parent] = j ;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
{
|
|
Int nels, ff, nchild ;
|
|
DEBUG1 (("\n\n================================ ccolamd_postorder:\n"));
|
|
nels = 0 ;
|
|
for (j = 0 ; j < nn ; j++)
|
|
{
|
|
if (Nv [j] > 0)
|
|
{
|
|
DEBUG1 ((""ID" : nels "ID" npiv "ID" size "ID
|
|
" parent "ID" maxfr "ID"\n", j, nels,
|
|
Nv [j], Fsize [j], Parent [j], Fsize [j])) ;
|
|
/* this is an element */
|
|
/* dump the link list of children */
|
|
nchild = 0 ;
|
|
DEBUG1 ((" Children: ")) ;
|
|
for (ff = Child [j] ; ff != EMPTY ; ff = Sibling [ff])
|
|
{
|
|
DEBUG1 ((ID" ", ff)) ;
|
|
nchild++ ;
|
|
ASSERT (nchild < nn) ;
|
|
}
|
|
DEBUG1 (("\n")) ;
|
|
parent = Parent [j] ;
|
|
nels++ ;
|
|
}
|
|
}
|
|
}
|
|
#endif
|
|
|
|
/* --------------------------------------------------------------------- */
|
|
/* place the largest child last in the list of children for each node */
|
|
/* --------------------------------------------------------------------- */
|
|
|
|
for (i = 0 ; i < nn ; i++)
|
|
{
|
|
if (Nv [i] > 0 && Child [i] != EMPTY)
|
|
{
|
|
|
|
#ifndef NDEBUG
|
|
Int nchild ;
|
|
DEBUG1 (("Before partial sort, element "ID"\n", i)) ;
|
|
nchild = 0 ;
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
DEBUG1 ((" f: "ID" size: "ID"\n", f, Fsize [f])) ;
|
|
nchild++ ;
|
|
}
|
|
#endif
|
|
|
|
/* find the biggest element in the child list */
|
|
fprev = EMPTY ;
|
|
maxfrsize = EMPTY ;
|
|
bigfprev = EMPTY ;
|
|
bigf = EMPTY ;
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
frsize = Fsize [f] ;
|
|
if (frsize >= maxfrsize)
|
|
{
|
|
/* this is the biggest seen so far */
|
|
maxfrsize = frsize ;
|
|
bigfprev = fprev ;
|
|
bigf = f ;
|
|
}
|
|
fprev = f ;
|
|
}
|
|
|
|
fnext = Sibling [bigf] ;
|
|
|
|
DEBUG1 (("bigf "ID" maxfrsize "ID" bigfprev "ID" fnext "ID
|
|
" fprev " ID"\n", bigf, maxfrsize, bigfprev, fnext, fprev)) ;
|
|
|
|
if (fnext != EMPTY)
|
|
{
|
|
/* if fnext is EMPTY then bigf is already at the end of list */
|
|
|
|
if (bigfprev == EMPTY)
|
|
{
|
|
/* delete bigf from the element of the list */
|
|
Child [i] = fnext ;
|
|
}
|
|
else
|
|
{
|
|
/* delete bigf from the middle of the list */
|
|
Sibling [bigfprev] = fnext ;
|
|
}
|
|
|
|
/* put bigf at the end of the list */
|
|
Sibling [bigf] = EMPTY ;
|
|
Sibling [fprev] = bigf ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("After partial sort, element "ID"\n", i)) ;
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
DEBUG1 ((" "ID" "ID"\n", f, Fsize [f])) ;
|
|
nchild-- ;
|
|
}
|
|
#endif
|
|
}
|
|
}
|
|
|
|
/* --------------------------------------------------------------------- */
|
|
/* postorder the assembly tree */
|
|
/* --------------------------------------------------------------------- */
|
|
|
|
for (i = 0 ; i < nn ; i++)
|
|
{
|
|
Order [i] = EMPTY ;
|
|
}
|
|
|
|
k = 0 ;
|
|
|
|
for (i = 0 ; i < nn ; i++)
|
|
{
|
|
if ((Parent [i] == EMPTY
|
|
|| (CMEMBER (Front_cols [Parent [i]]) != CMEMBER (Front_cols [i])))
|
|
&& Nv [i] > 0)
|
|
{
|
|
DEBUG1 (("Root of assembly tree "ID"\n", i)) ;
|
|
k = CCOLAMD_post_tree (i, k, Child, Sibling, Order, Stack) ;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/* ========================================================================= */
|
|
/* === CCOLAMD_post_tree =================================================== */
|
|
/* ========================================================================= */
|
|
|
|
/* Post-ordering of a supernodal column elimination tree. */
|
|
|
|
GLOBAL Int CCOLAMD_post_tree
|
|
(
|
|
Int root, /* root of the tree */
|
|
Int k, /* start numbering at k */
|
|
Int Child [ ], /* input argument of size nn, undefined on
|
|
* output. Child [i] is the head of a link
|
|
* list of all nodes that are children of node
|
|
* i in the tree. */
|
|
const Int Sibling [ ], /* input argument of size nn, not modified.
|
|
* If f is a node in the link list of the
|
|
* children of node i, then Sibling [f] is the
|
|
* next child of node i.
|
|
*/
|
|
Int Order [ ], /* output order, of size nn. Order [i] = k
|
|
* if node i is the kth node of the reordered
|
|
* tree. */
|
|
Int Stack [ ] /* workspace of size nn */
|
|
)
|
|
{
|
|
Int f, head, h, i ;
|
|
|
|
#if 0
|
|
/* --------------------------------------------------------------------- */
|
|
/* recursive version (Stack [ ] is not used): */
|
|
/* --------------------------------------------------------------------- */
|
|
|
|
/* this is simple, but can cause stack overflow if nn is large */
|
|
i = root ;
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
k = CCOLAMD_post_tree (f, k, Child, Sibling, Order, Stack, nn) ;
|
|
}
|
|
Order [i] = k++ ;
|
|
return (k) ;
|
|
#endif
|
|
|
|
/* --------------------------------------------------------------------- */
|
|
/* non-recursive version, using an explicit stack */
|
|
/* --------------------------------------------------------------------- */
|
|
|
|
/* push root on the stack */
|
|
head = 0 ;
|
|
Stack [0] = root ;
|
|
|
|
while (head >= 0)
|
|
{
|
|
/* get head of stack */
|
|
i = Stack [head] ;
|
|
DEBUG1 (("head of stack "ID" \n", i)) ;
|
|
|
|
if (Child [i] != EMPTY)
|
|
{
|
|
/* the children of i are not yet ordered */
|
|
/* push each child onto the stack in reverse order */
|
|
/* so that small ones at the head of the list get popped first */
|
|
/* and the biggest one at the end of the list gets popped last */
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
head++ ;
|
|
}
|
|
h = head ;
|
|
for (f = Child [i] ; f != EMPTY ; f = Sibling [f])
|
|
{
|
|
ASSERT (h > 0) ;
|
|
Stack [h--] = f ;
|
|
DEBUG1 (("push "ID" on stack\n", f)) ;
|
|
}
|
|
ASSERT (Stack [h] == i) ;
|
|
|
|
/* delete child list so that i gets ordered next time we see it */
|
|
Child [i] = EMPTY ;
|
|
}
|
|
else
|
|
{
|
|
/* the children of i (if there were any) are already ordered */
|
|
/* remove i from the stack and order it. Front i is kth front */
|
|
head-- ;
|
|
DEBUG1 (("pop "ID" order "ID"\n", i, k)) ;
|
|
Order [i] = k++ ;
|
|
}
|
|
|
|
#ifndef NDEBUG
|
|
DEBUG1 (("\nStack:")) ;
|
|
for (h = head ; h >= 0 ; h--)
|
|
{
|
|
Int j = Stack [h] ;
|
|
DEBUG1 ((" "ID, j)) ;
|
|
}
|
|
DEBUG1 (("\n\n")) ;
|
|
#endif
|
|
|
|
}
|
|
return (k) ;
|
|
}
|
|
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === CCOLAMD 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,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col Col [ ],
|
|
Int A [ ],
|
|
Int cmember [ ],
|
|
Int cset_start [ ]
|
|
)
|
|
{
|
|
/* === Local variables ================================================== */
|
|
|
|
Int i ;
|
|
Int c ;
|
|
Int *cp ;
|
|
Int *cp_end ;
|
|
Int len ;
|
|
Int score ;
|
|
Int r ;
|
|
Int *rp ;
|
|
Int *rp_end ;
|
|
Int deg ;
|
|
Int cs ;
|
|
|
|
/* === 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 ;
|
|
cs = CMEMBER (c) ;
|
|
ASSERT (i >= cset_start [cs] && i < cset_start [cs+1]) ;
|
|
}
|
|
}
|
|
|
|
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,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col 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 && ccolamd_debug <= 0)
|
|
{
|
|
return ;
|
|
}
|
|
have = 0 ;
|
|
DEBUG4 (("Degree lists: "ID"\n", min_score)) ;
|
|
for (deg = 0 ; deg <= n_col ; deg++)
|
|
{
|
|
col = head [deg] ;
|
|
if (col == EMPTY)
|
|
{
|
|
continue ;
|
|
}
|
|
DEBUG4 (("%d:", deg)) ;
|
|
ASSERT (Col [col].shared3.prev == EMPTY) ;
|
|
while (col != EMPTY)
|
|
{
|
|
DEBUG4 ((" "ID"", col)) ;
|
|
have += Col [col].shared1.thickness ;
|
|
ASSERT (COL_IS_ALIVE (col)) ;
|
|
col = Col [col].shared4.degree_next ;
|
|
}
|
|
DEBUG4 (("\n")) ;
|
|
}
|
|
DEBUG4 (("should "ID" have "ID"\n", should, have)) ;
|
|
ASSERT (should == have) ;
|
|
|
|
/* === Check the row degrees ============================================ */
|
|
|
|
if (n_row > 10000 && ccolamd_debug <= 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,
|
|
CColamd_Row 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 && ccolamd_debug <= 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,
|
|
CColamd_Row Row [ ],
|
|
CColamd_Col 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 (ccolamd_debug < 3)
|
|
{
|
|
return ;
|
|
}
|
|
DEBUG3 (("DUMP MATRIX:\n")) ;
|
|
for (r = 0 ; r < n_row ; r++)
|
|
{
|
|
DEBUG3 (("Row "ID" alive? "ID"\n", r, ROW_IS_ALIVE (r))) ;
|
|
if (ROW_IS_DEAD (r))
|
|
{
|
|
continue ;
|
|
}
|
|
|
|
DEBUG3 (("start "ID" length "ID" degree "ID"\nthickness "ID"\n",
|
|
Row [r].start, Row [r].length, Row [r].shared1.degree,
|
|
Row [r].thickness)) ;
|
|
|
|
rp = &A [Row [r].start] ;
|
|
rp_end = rp + Row [r].length ;
|
|
while (rp < rp_end)
|
|
{
|
|
c = *rp++ ;
|
|
DEBUG4 ((" "ID" col "ID"\n", COL_IS_ALIVE (c), c)) ;
|
|
}
|
|
}
|
|
|
|
for (c = 0 ; c < n_col ; c++)
|
|
{
|
|
DEBUG3 (("Col "ID" alive? "ID"\n", c, COL_IS_ALIVE (c))) ;
|
|
if (COL_IS_DEAD (c))
|
|
{
|
|
continue ;
|
|
}
|
|
DEBUG3 (("start "ID" length "ID" shared1 "ID" shared2 "ID"\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++ ;
|
|
DEBUG4 ((" "ID" row "ID"\n", ROW_IS_ALIVE (r), r)) ;
|
|
}
|
|
}
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === dump_super =========================================================== */
|
|
/* ========================================================================== */
|
|
|
|
PRIVATE void dump_super
|
|
(
|
|
Int super_c,
|
|
CColamd_Col Col [ ],
|
|
Int n_col
|
|
)
|
|
{
|
|
Int col, ncols ;
|
|
|
|
DEBUG1 ((" =[ ")) ;
|
|
ncols = 0 ;
|
|
for (col = super_c ; col != EMPTY ; col = Col [col].nextcol)
|
|
{
|
|
DEBUG1 ((" "ID, col)) ;
|
|
ASSERT (col >= 0 && col < n_col) ;
|
|
if (col != super_c)
|
|
{
|
|
ASSERT (COL_IS_DEAD (col)) ;
|
|
}
|
|
if (Col [col].nextcol == EMPTY)
|
|
{
|
|
ASSERT (col == Col [super_c].lastcol) ;
|
|
}
|
|
ncols++ ;
|
|
ASSERT (ncols <= Col [super_c].shared1.thickness) ;
|
|
}
|
|
ASSERT (ncols == Col [super_c].shared1.thickness) ;
|
|
DEBUG1 (("]\n")) ;
|
|
}
|
|
|
|
|
|
/* ========================================================================== */
|
|
/* === ccolamd_get_debug ==================================================== */
|
|
/* ========================================================================== */
|
|
|
|
PRIVATE void ccolamd_get_debug
|
|
(
|
|
char *method
|
|
)
|
|
{
|
|
FILE *debug_file ;
|
|
ccolamd_debug = 0 ; /* no debug printing */
|
|
|
|
/* Read debug info from the debug file. */
|
|
debug_file = fopen ("debug", "r") ;
|
|
if (debug_file)
|
|
{
|
|
(void) fscanf (debug_file, ""ID"", &ccolamd_debug) ;
|
|
(void) fclose (debug_file) ;
|
|
}
|
|
|
|
DEBUG0 ((":")) ;
|
|
DEBUG1 (("%s: debug version, D = "ID" (THIS WILL BE SLOW!)\n",
|
|
method, ccolamd_debug)) ;
|
|
DEBUG1 ((" Debug printing level: "ID"\n", ccolamd_debug)) ;
|
|
}
|
|
|
|
#endif
|