>> amd_demo

 AMD Approximate minimum degree permutation.
     P = AMD (S) returns the approximate minimum degree permutation vector for
     the sparse matrix C = S+S'.  The Cholesky factorization of C (P,P), or
     S (P,P), tends to be sparser than that of C or S.  AMD tends to be faster
     than SYMMMD and SYMAMD, and tends to return better orderings than SYMMMD.
     S must be square. If S is full, amd (S) is equivalent to amd (sparse (S)).
 
     Usage:  P = amd (S) ;                   % finds the ordering
             [P, Info] = amd (S, Control) ;  % optional parameters & statistics
             Control = amd ;                 % returns default parameters
             amd ;                           % prints default parameters.
 
        Control (1); If S is n-by-n, then rows/columns with more than
            max (16, (Control (1))* sqrt(n)) entries in S+S' are considered
            "dense", and ignored during ordering.  They are placed last in the
            output permutation.  The default is 10.0 if Control is not present.
        Control (2): If nonzero, then aggressive absorption is performed.
            This is the default if Control is not present.
        Control (3): If nonzero, print statistics about the ordering.
 
        Info (1): status (0: ok, -1: out of memory, -2: matrix invalid)
        Info (2): n = size (A,1)
        Info (3): nnz (A)
        Info (4): the symmetry of the matrix S (0.0 means purely unsymmetric,
            1.0 means purely symmetric).  Computed as:
            B = tril (S, -1) + triu (S, 1) ; symmetry = nnz (B & B') / nnz (B);
        Info (5): nnz (diag (S))
        Info (6): nnz in S+S', excluding the diagonal (= nnz (B+B'))
        Info (7): number "dense" rows/columns in S+S'
        Info (8): the amount of memory used by AMD, in bytes
        Info (9): the number of memory compactions performed by AMD
 
     The following statistics are slight upper bounds because of the
     approximate degree in AMD.  The bounds are looser if "dense" rows/columns
     are ignored during ordering (Info (7) > 0).  The statistics are for a
     subsequent factorization of the matrix C (P,P).  The LU factorization
     statistics assume no pivoting.
 
        Info (10): the number of nonzeros in L, excluding the diagonal
        Info (11): the number of divide operations for LL', LDL', or LU
        Info (12): the number of multiply-subtract pairs for LL' or LDL'
        Info (13): the number of multiply-subtract pairs for LU
        Info (14): the max # of nonzeros in any column of L (incl. diagonal)
        Info (15:20): unused, reserved for future use
 
     An assembly tree post-ordering is performed, which is typically the same
     as an elimination tree post-ordering.  It is not always identical because
     of the approximate degree update used, and because "dense" rows/columns
     do not take part in the post-order.  It well-suited for a subsequent
     "chol", however.  If you require a precise elimination tree post-ordering,
     then do:
 
        P = amd (S) ;
        C = spones (S) + spones (S') ;  % skip this if S already symmetric
        [ignore, Q] = sparsfun ('symetree', C (P,P)) ;
        P = P (Q) ;
 
  --------------------------------------------------------------------------
  AMD Version 1.1 (Jan. 21, 2004), Copyright (c) 2004 by Timothy A. Davis,
  Patrick R. Amestoy, and Iain S. Duff.  See ../README for License.
  email: davis@cise.ufl.edu    CISE Department, Univ. of Florida.
  web: http://www.cise.ufl.edu/research/sparse/amd
  --------------------------------------------------------------------------
 
     Acknowledgements: This work was supported by the National Science
        Foundation, under grants ASC-9111263, DMS-9223088, and CCR-0203270.
 
     See also COLMMD, COLAMD, COLPERM, SYMAMD, SYMMMD, SYMRCM.

Matrix name:  HB/can_24
Matrix title: 1SYMMETRIC PATTERN FROM CANNES,LUCIEN MARRO,JUNE 1981.                  

If the next step fails, then you have
not yet compiled the AMD mexFunction.

amd:  approximate minimum degree ordering, parameters:
    dense row parameter: 10
    (rows with more than max (10 * sqrt (n), 16) entries are
    considered "dense", and placed last in output permutation)
    aggressive absorption:  yes

    input matrix A is 24-by-24
    input matrix A has 160 nonzero entries

amd:  approximate minimum degree ordering, results:
    status: OK
    n, dimension of A:                                  24
    nz, number of nonzeros in A:                        160
    symmetry of A:                                      1.0000
    number of nonzeros on diagonal:                     24
    nonzeros in pattern of A+A' (excl. diagonal):       136
    # dense rows/columns of A+A':                       0
    memory used, in bytes:                              1516
    # of memory compactions:                            0

    The following approximate statistics are for a subsequent
    factorization of A(P,P) + A(P,P)'.  They are slight upper
    bounds if there are no dense rows/columns in A+A', and become
    looser if dense rows/columns exist.

    nonzeros in L (excluding diagonal):                 97
    nonzeros in L (including diagonal):                 121
    # divide operations for LDL' or LU:                 97
    # multiply-subtract operations for LDL':            275
    # multiply-subtract operations for LU:              453
    max nz. in any column of L (incl. diagonal):        8

    chol flop count for real A, sqrt counted as 1 flop: 671
    LDL' flop count for real A:                         647
    LDL' flop count for complex A:                      3073
    LU flop count for real A (with no pivoting):        1003
    LU flop count for complex A (with no pivoting):     4497

Permutation vector:
 23 21 11 24 13  6 17  9 15  5 16  8  2 10 14 18  1  3  4  7 12 19 22 20

Analyze A(p,p) with MATLAB's symbfact routine:
predicted nonzeros:    120
predicted flops:       656
predicted height:      16
predicted front size:  7
number of nonzeros in L (including diagonal):      120
floating point operation count for chol (A (p,p)): 656

Results from AMD's approximate analysis:
number of nonzeros in L (including diagonal):      121
floating point operation count for chol (A (p,p)): 671

Note that the nonzero and flop counts from AMD are slight
upper bounds.  This is due to the approximate minimum degree
method used, in conjunction with "mass elimination".
See the discussion about mass elimination in amd.h and
amd_2.c for more details.
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