colamd.c File Reference

A sparse matrix column ordering algorithm. More...

`#include "colamd.h"`
`#include <limits.h>`
`#include <stdio.h>`
`#include <assert.h>`
Include dependency graph for colamd.c:

## Macros

#define | NDEBUG
#define | PUBLIC
#define | PRIVATE static
#define | MAX(a, b) (((a) > (b)) ? (a) : (b))
#define | MIN(a, b) (((a) < (b)) ? (a) : (b))
#define | ONES_COMPLEMENT(r) (-(r)-1)
#define | TRUE (1)
#define | FALSE (0)
#define | EMPTY (-1)
#define | ALIVE (0)
#define | DEAD (-1)
#define | DEAD_PRINCIPAL (-1)
#define | DEAD_NON_PRINCIPAL (-2)
#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 ; }
#define | PRINTF printf
#define | INDEX(i) (i)
#define | DEBUG0(params) ;
#define | DEBUG1(params) ;
#define | DEBUG2(params) ;
#define | DEBUG3(params) ;
#define | DEBUG4(params) ;
#define | ASSERT(expression) ((void) 0)

## Functions

PRIVATE int | init_rows_cols (int n_row, int n_col, Colamd_Row Row[], Colamd_Col Col[], int A[], int p[], int stats[COLAMD_STATS])
PRIVATE void | init_scoring (int n_row, int n_col, Colamd_Row Row[], Colamd_Col Col[], int A[], int head[], double knobs[COLAMD_KNOBS], int *p_n_row2, int *p_n_col2, int *p_max_deg)
PRIVATE int | find_ordering (int n_row, int n_col, int Alen, Colamd_Row Row[], Colamd_Col Col[], int A[], int head[], int n_col2, int max_deg, int pfree)
PRIVATE void | order_children (int n_col, Colamd_Col Col[], int p[])
PRIVATE void | detect_super_cols (Colamd_Col Col[], int A[], int head[], int row_start, int row_length)
PRIVATE int | garbage_collection (int n_row, int n_col, Colamd_Row Row[], Colamd_Col Col[], int A[], int *pfree)
PRIVATE int | clear_mark (int n_row, Colamd_Row Row[])
PRIVATE void | print_report (char *method, int stats[COLAMD_STATS])
PUBLIC int | colamd_recommended (int nnz, int n_row, int n_col)
PUBLIC void | colamd_set_defaults (double knobs[COLAMD_KNOBS])
PUBLIC int | symamd (int n, int A[], int p[], int perm[], double knobs[COLAMD_KNOBS], int stats[COLAMD_STATS], void *(*allocate)(size_t, size_t), void(*release)(void *))
PUBLIC int | colamd (int n_row, int n_col, int Alen, int A[], int p[], double knobs[COLAMD_KNOBS], int stats[COLAMD_STATS])
PUBLIC void | colamd_report (int stats[COLAMD_STATS])
PUBLIC void | symamd_report (int stats[COLAMD_STATS])

## Detailed Description

Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)

All rights reserved.

The source code is distributed under BSD license, see the file License.txt at the top-level directory.

<

# pre>

# === colamd/symamd - a sparse matrix column ordering algorithm ============

colamd: an approximate minimum degree column ordering algorithm, for LU factorization of symmetric or unsymmetric matrices, QR factorization, least squares, interior point methods for linear programming problems, and other related problems.

symamd: an approximate minimum degree ordering algorithm for Cholesky factorization of symmetric matrices.

Purpose:

    Colamd computes a permutation Q such that the Cholesky factorization of
    (AQ)'(AQ) has less fill-in and requires fewer floating point operations
    than A'A.  This also provides a good ordering for sparse partial
    pivoting methods, P(AQ) = LU, where Q is computed prior to numerical
    factorization, and P is computed during numerical factorization via
    conventional partial pivoting with row interchanges.  Colamd is the
    column ordering method used in SuperLU, part of the ScaLAPACK library.
    It is also available as built-in function in MATLAB Version 6,
    available from MathWorks, Inc. (https://www.mathworks.com).  This
    routine can be used in place of colmmd in MATLAB.

     Symamd computes a permutation P of a symmetric matrix A such that the
    Cholesky factorization of PAP' has less fill-in and requires fewer
    floating point operations than A.  Symamd constructs a matrix M such
    that M'M has the same nonzero pattern of A, and then orders the columns
    of M using colmmd.  The column ordering of M is then returned as the
    row and column ordering P of A.

Authors:

    The authors of the code itself are Stefan I. Larimore and Timothy A.
    Davis (davis@cise.ufl.edu), University of Florida.  The algorithm was
    developed in collaboration with John Gilbert, Xerox PARC, and Esmond
    Ng, Oak Ridge National Laboratory.

Date:

    September 8, 2003.  Version 2.3.

Acknowledgements:

    This work was supported by the National Science Foundation, under
    grants DMS-9504974 and DMS-9803599.

Copyright and License:

    Copyright (c) 1998-2003 by the University of Florida.
    All Rights Reserved.

    THIS MATERIAL IS PROVIDED AS IS, WITH ABSOLUTELY NO WARRANTY
    EXPRESSED OR IMPLIED.  ANY USE IS AT YOUR OWN RISK.

    Permission is hereby granted to use, copy, modify, and/or distribute
    this program, provided that the Copyright, this License, and the
    Availability of the original version is retained on all copies and made
    accessible to the end-user of any code or package that includes COLAMD
    or any modified version of COLAMD.

Availability:

    The colamd/symamd library is available at

        https://web.archive.org/web/20141010162709/http://www.cise.ufl.edu/research/sparse/colamd/

    This is the https://web.archive.org/web/20040113022019/http://www.cise.ufl.edu/research/sparse/colamd/colamd.c
    file.  It requires the colamd.h file.  It is required by the colamdmex.c
    and symamdmex.c files, for the MATLAB interface to colamd and symamd.

See the ChangeLog file for changes since Version 1.0.

# === Description of user-callable routines ================================

## colamd_recommended:

    C syntax:

        #include "colamd.h"
        int colamd_recommended (int nnz, int n_row, int n_col) ;

        or as a C macro

        #include "colamd.h"
        Alen = COLAMD_RECOMMENDED (int nnz, int n_row, int n_col) ;

    Purpose:

        Returns recommended value of Alen for use by colamd.  Returns -1
        if any input argument is negative.  The use of this routine
        or macro is optional.  Note that the macro uses its arguments
        more than once, so be careful for side effects, if you pass
        expressions as arguments to COLAMD_RECOMMENDED.  Not needed for
        symamd, which dynamically allocates its own memory.

    Arguments (all input arguments):

        int nnz ;            Number of nonzeros in the matrix A.  This must
                     be the same value as p [n_col] in the call to
                     colamd - otherwise you will get a wrong value
                     of the recommended memory to use.

        int n_row ;          Number of rows in the matrix A.

        int n_col ;          Number of columns in the matrix A.

## colamd_set_defaults:

    C syntax:

        #include "colamd.h"
        colamd_set_defaults (double knobs [COLAMD_KNOBS]) ;

    Purpose:

        Sets the default parameters.  The use of this routine is optional.

    Arguments:

        double knobs [COLAMD_KNOBS] ;        Output only.

     Colamd: rows with more than (knobs [COLAMD_DENSE_ROW] * n_col)
     entries are removed prior to ordering.  Columns with more than
     (knobs [COLAMD_DENSE_COL] * n_row) entries are removed prior to
     ordering, and placed last in the output column ordering.

     Symamd: uses only knobs [COLAMD_DENSE_ROW], which is knobs [0].
     Rows and columns with more than (knobs [COLAMD_DENSE_ROW] * n)
     entries are removed prior to ordering, and placed last in the
     output ordering.

     COLAMD_DENSE_ROW and COLAMD_DENSE_COL are defined as 0 and 1,
     respectively, in colamd.h.  Default values of these two knobs
     are both 0.5.  Currently, only knobs [0] and knobs [1] are
     used, but future versions may use more knobs.  If so, they will
     be properly set to their defaults by the future version of
     colamd_set_defaults, so that the code that calls colamd will
     not need to change, assuming that you either use
     colamd_set_defaults, or pass a (double *) NULL pointer as the
     knobs array to colamd or symamd.

## colamd:

    C syntax:

        #include "colamd.h"
        int colamd (int n_row, int n_col, int Alen, int *A, int *p,
             double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS]) ;

    Purpose:

        Computes a column ordering (Q) of A such that P(AQ)=LU or
        (AQ)'AQ=LL' have less fill-in and require fewer floating point
        operations than factorizing the unpermuted matrix A or A'A,
        respectively.

    Returns:

        TRUE (1) if successful, FALSE (0) otherwise.

    Arguments:

        int n_row ;          Input argument.

     Number of rows in the matrix A.
     Restriction:  n_row >= 0.
     Colamd returns FALSE if n_row is negative.

        int n_col ;          Input argument.

     Number of columns in the matrix A.
     Restriction:  n_col >= 0.
     Colamd returns FALSE if n_col is negative.

        int Alen ;           Input argument.

     Restriction (see note):
     Alen >= 2*nnz + 6*(n_col+1) + 4*(n_row+1) + n_col
     Colamd returns FALSE if these conditions are not met.

     Note:  this restriction makes an modest assumption regarding
     the size of the two typedef's structures in colamd.h.
     We do, however, guarantee that

             Alen >= colamd_recommended (nnz, n_row, n_col)

     or equivalently as a C preprocessor macro:

             Alen >= COLAMD_RECOMMENDED (nnz, n_row, n_col)

     will be sufficient.

        int A [Alen] ;       Input argument, undefined on output.

     A is an integer array of size Alen.  Alen must be at least as
     large as the bare minimum value given above, but this is very
     low, and can result in excessive run time.  For best
     performance, we recommend that Alen be greater than or equal to
     colamd_recommended (nnz, n_row, n_col), which adds
     nnz/5 to the bare minimum value given above.

     On input, the row indices of the entries in column c of the
     matrix are held in A [(p [c]) ... (p [c+1]-1)].  The row indices
     in a given column c need not be in ascending order, and
     duplicate row indices may be be present.  However, colamd will
     work a little faster if both of these conditions are met
     (Colamd puts the matrix into this format, if it finds that the
     the conditions are not met).

     The matrix is 0-based.  That is, rows are in the range 0 to
     n_row-1, and columns are in the range 0 to n_col-1.  Colamd
     returns FALSE if any row index is out of range.

     The contents of A are modified during ordering, and are
     undefined on output.

        int p [n_col+1] ;    Both input and output argument.

     p is an integer array of size n_col+1.  On input, it holds the
     "pointers" for the column form of the matrix A.  Column c of
     the matrix A is held in A [(p [c]) ... (p [c+1]-1)].  The first
     entry, p [0], must be zero, and p [c] <= p [c+1] must hold
     for all c in the range 0 to n_col-1.  The value p [n_col] is
     thus the total number of entries in the pattern of the matrix A.
     Colamd returns FALSE if these conditions are not met.

     On output, if colamd returns TRUE, the array p holds the column
     permutation (Q, for P(AQ)=LU or (AQ)'(AQ)=LL'), where p [0] is
     the first column index in the new ordering, and p [n_col-1] is
     the last.  That is, p [k] = j means that column j of A is the
     kth pivot column, in AQ, where k is in the range 0 to n_col-1
     (p [0] = j means that column j of A is the first column in AQ).

     If colamd returns FALSE, then no permutation is returned, and
     p is undefined on output.

        double knobs [COLAMD_KNOBS] ;        Input argument.

     See colamd_set_defaults for a description.

        int stats [COLAMD_STATS] ;           Output argument.

     Statistics on the ordering, and error status.
     See colamd.h for related definitions.
     Colamd returns FALSE if stats is not present.

     stats [0]:  number of dense or empty rows ignored.

     stats [1]:  number of dense or empty columns ignored (and
                     ordered last in the output permutation p)
                     Note that a row can become "empty" if it
                     contains only "dense" and/or "empty" columns,
                     and similarly a column can become "empty" if it
                     only contains "dense" and/or "empty" rows.

     stats [2]:  number of garbage collections performed.
                     This can be excessively high if Alen is close
                     to the minimum required value.

     stats [3]:  status code.  < 0 is an error code.
                 > 1 is a warning or notice.

             0       OK.  Each column of the input matrix contained
                     row indices in increasing order, with no
                     duplicates.

             1       OK, but columns of input matrix were jumbled
                     (unsorted columns or duplicate entries).  Colamd
                     had to do some extra work to sort the matrix
                     first and remove duplicate entries, but it
                     still was able to return a valid permutation
                     (return value of colamd was TRUE).

                             stats [4]: highest numbered column that
                                     is unsorted or has duplicate
                                     entries.
                             stats [5]: last seen duplicate or
                                     unsorted row index.
                             stats [6]: number of duplicate or
                                     unsorted row indices.

             -1      A is a null pointer

             -2      p is a null pointer

             -3      n_row is negative

                             stats [4]: n_row

             -4      n_col is negative

                             stats [4]: n_col

             -5      number of nonzeros in matrix is negative

                             stats [4]: number of nonzeros, p [n_col]

             -6      p [0] is nonzero

                             stats [4]: p [0]

             -7      A is too small

                             stats [4]: required size
                             stats [5]: actual size (Alen)

             -8      a column has a negative number of entries

                             stats [4]: column with < 0 entries
                             stats [5]: number of entries in col

             -9      a row index is out of bounds

                             stats [4]: column with bad row index
                             stats [5]: bad row index
                             stats [6]: n_row, # of rows of matrx

             -10     (unused; see symamd.c)

             -999    (unused; see symamd.c)

     Future versions may return more statistics in the stats array.

    Example:

        See http://www.cise.ufl.edu/research/sparse/colamd/example.c
        for a complete example.

        To order the columns of a 5-by-4 matrix with 11 nonzero entries in
        the following nonzero pattern

             x 0 x 0
     x 0 x x
     0 x x 0
     0 0 x x
     x x 0 0

        with default knobs and no output statistics, do the following:

     #include "colamd.h"
     #define ALEN COLAMD_RECOMMENDED (11, 5, 4)
     int A [ALEN] = {1, 2, 5, 3, 5, 1, 2, 3, 4, 2, 4} ;
     int p [ ] = {0, 3, 5, 9, 11} ;
     int stats [COLAMD_STATS] ;
     colamd (5, 4, ALEN, A, p, (double *) NULL, stats) ;

        The permutation is returned in the array p, and A is destroyed.

## symamd:

    C syntax:

        #include "colamd.h"
        int symamd (int n, int *A, int *p, int *perm,
             double knobs [COLAMD_KNOBS], int stats [COLAMD_STATS],
     void (*allocate) (size_t, size_t), void (*release) (void *)) ;

    Purpose:

         The symamd routine computes an ordering P of a symmetric sparse
        matrix A such that the Cholesky factorization PAP' = LL' remains
        sparse.  It is based on a column ordering of a matrix M constructed
        so that the nonzero pattern of M'M is the same as A.  The matrix A
        is assumed to be symmetric; only the strictly lower triangular part
        is accessed.  You must pass your selected memory allocator (usually
        calloc/free or mxCalloc/mxFree) to symamd, for it to allocate
        memory for the temporary matrix M.

    Returns:

        TRUE (1) if successful, FALSE (0) otherwise.

    Arguments:

        int n ;              Input argument.

             Number of rows and columns in the symmetrix matrix A.
     Restriction:  n >= 0.
     Symamd returns FALSE if n is negative.

        int A [nnz] ;        Input argument.

             A is an integer array of size nnz, where nnz = p [n].

     The row indices of the entries in column c of the matrix are
     held in A [(p [c]) ... (p [c+1]-1)].  The row indices in a
     given column c need not be in ascending order, and duplicate
     row indices may be present.  However, symamd 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.  Symamd
     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.
     Symamd returns FALSE if these conditions are not met.

     The contents of p are not modified.

        int perm [n+1] ;     Output argument.

     On output, if symamd 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 [COLAMD_KNOBS] ;        Input argument.

     See colamd_set_defaults for a description.

        int stats [COLAMD_STATS] ;           Output argument.

     Statistics on the ordering, and error status.
     See colamd.h for related definitions.
     Symamd 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).  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       OK.  Each column of the input matrix contained
                     row indices in increasing order, with no
                     duplicates.

             1       OK, but columns of input matrix were jumbled
                     (unsorted columns or duplicate entries).  Symamd
                     had to do some extra work to sort the matrix
                     first and remove duplicate entries, but it
                     still was able to return a valid permutation
                     (return value of symamd was TRUE).

                             stats [4]: highest numbered column that
                                     is unsorted or has duplicate
                                     entries.
                             stats [5]: last seen duplicate or
                                     unsorted row index.
                             stats [6]: number of duplicate or
                                     unsorted row indices.

             -1      A is a null pointer

             -2      p is a null pointer

             -3      (unused, see colamd.c)

             -4      n is negative

                             stats [4]: n

             -5      number of nonzeros in matrix is negative

                             stats [4]: # of nonzeros (p [n]).

             -6      p [0] is nonzero

                             stats [4]: p [0]

             -7      (unused)

             -8      a column has a negative number of entries

                             stats [4]: column with < 0 entries
                             stats [5]: number of entries in col

             -9      a row index is out of bounds

                             stats [4]: column with bad row index
                             stats [5]: bad row index
                             stats [6]: n_row, # of rows of matrx

             -10     out of memory (unable to allocate temporary
                     workspace for M or count arrays using the
                     "allocate" routine passed into symamd).

             -999    internal error.  colamd failed to order the
                     matrix M, when it should have succeeded.  This
                     indicates a bug.  If this (and *only* this)
                     error code occurs, please contact the authors.
                     Don't contact the authors if you get any other
                     error code.

     Future versions may return more statistics in the stats array.

        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.

## colamd_report:

    C syntax:

        #include "colamd.h"
        colamd_report (int stats [COLAMD_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 [COLAMD_STATS] ;   Input only.  Statistics from colamd.

## symamd_report:

    C syntax:

        #include "colamd.h"
        symamd_report (int stats [COLAMD_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 [COLAMD_STATS] ;   Input only.  Statistics from symamd.

## Macro Definition Documentation

#define ALIVE (0)

#define ASSERT | ( |  | expression | ) | ((void) 0)

#define COL_IS_ALIVE | ( |  | c | ) | (Col [c].start >= ALIVE)

#define COL_IS_DEAD | ( |  | c | ) | (Col [c].start < ALIVE)

#define COL_IS_DEAD_PRINCIPAL | ( |  | c | ) | (Col [c].start == DEAD_PRINCIPAL)

#define DEAD (-1)

#define DEAD_NON_PRINCIPAL (-2)

#define DEAD_PRINCIPAL (-1)

#define DEBUG0 | ( |  | params | ) | ;

#define DEBUG1 | ( |  | params | ) | ;

#define DEBUG2 | ( |  | params | ) | ;

#define DEBUG3 | ( |  | params | ) | ;

#define DEBUG4 | ( |  | params | ) | ;

#define EMPTY (-1)

#define FALSE (0)

#define INDEX | ( |  | i | ) | (i)

#define KILL_NON_PRINCIPAL_COL | ( |  | c | ) | { Col [c].start = DEAD_NON_PRINCIPAL ; }

#define KILL_PRINCIPAL_COL | ( |  | c | ) | { Col [c].start = DEAD_PRINCIPAL ; }

#define KILL_ROW | ( |  | r | ) | { Row [r].shared2.mark = DEAD ; }

#define MAX | ( |  | a,
|  |  | b
| ) |  | (((a) > (b)) ? (a) : (b))

#define MIN | ( |  | a,
|  |  | b
| ) |  | (((a) < (b)) ? (a) : (b))

#define NDEBUG

#define ONES_COMPLEMENT | ( |  | r | ) | (-(r)-1)

#define PRINTF printf

#define PRIVATE static

#define PUBLIC

#define ROW_IS_ALIVE | ( |  | r | ) | (Row [r].shared2.mark >= ALIVE)

#define ROW_IS_DEAD | ( |  | r | ) | ROW_IS_MARKED_DEAD (Row[r].shared2.mark)

#define ROW_IS_MARKED_DEAD | ( |  | row_mark | ) | (row_mark < ALIVE)

#define TRUE (1)

## Function Documentation

PRIVATE int clear_mark | ( | int | n_row,
|  | Colamd_Row | Row[]
| ) |  |

PUBLIC int colamd | ( | int | n_row,
|  | int | n_col,
|  | int | Alen,
|  | int | A[],
|  | int | p[],
|  | double | knobs[COLAMD_KNOBS],
|  | int | stats[COLAMD_STATS]
| ) |  |

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PUBLIC int colamd_recommended | ( | int | nnz,
|  | int | n_row,
|  | int | n_col
| ) |  |

PUBLIC void colamd_report | ( | int | stats[COLAMD_STATS] | ) |

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PUBLIC void colamd_set_defaults | ( | double | knobs[COLAMD_KNOBS] | ) |

PRIVATE void detect_super_cols | ( | Colamd_Col | Col[],
|  | int | A[],
|  | int | head[],
|  | int | row_start,
|  | int | row_length
| ) |  |

PRIVATE int find_ordering | ( | int | n_row,
|  | int | n_col,
|  | int | Alen,
|  | Colamd_Row | Row[],
|  | Colamd_Col | Col[],
|  | int | A[],
|  | int | head[],
|  | int | n_col2,
|  | int | max_deg,
|  | int | pfree
| ) |  |

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PRIVATE int garbage_collection | ( | int | n_row,
|  | int | n_col,
|  | Colamd_Row | Row[],
|  | Colamd_Col | Col[],
|  | int | A[],
|  | int * | pfree
| ) |  |

PRIVATE int init_rows_cols | ( | int | n_row,
|  | int | n_col,
|  | Colamd_Row | Row[],
|  | Colamd_Col | Col[],
|  | int | A[],
|  | int | p[],
|  | int | stats[COLAMD_STATS]
| ) |  |

PRIVATE void init_scoring | ( | int | n_row,
|  | int | n_col,
|  | Colamd_Row | Row[],
|  | Colamd_Col | Col[],
|  | int | A[],
|  | int | head[],
|  | double | knobs[COLAMD_KNOBS],
|  | int * | p_n_row2,
|  | int * | p_n_col2,
|  | int * | p_max_deg
| ) |  |

PRIVATE void order_children | ( | int | n_col,
|  | Colamd_Col | Col[],
|  | int | p[]
| ) |  |

PRIVATE void print_report | ( | char * | method,
|  | int | stats[COLAMD_STATS]
| ) |  |

PUBLIC int symamd | ( | int | n,
|  | int | A[],
|  | int | p[],
|  | int | perm[],
|  | double | knobs[COLAMD_KNOBS],
|  | int | stats[COLAMD_STATS],
|  | void *(*)(size_t, size_t) | allocate,
|  | void(*)(void *) | release
| ) |  |

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PUBLIC void symamd_report | ( | int | stats[COLAMD_STATS] | ) |

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