amd_demo2.out 8.75 KB
AMD demo, with a jumbled version of the 24-by-24
Harwell/Boeing matrix, can_24:

AMD version 2.2.0, May 31, 2007: approximate minimum degree ordering
    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
    size of AMD integer: 4


Jumbled input matrix:  24-by-24, with 116 entries.
   Note that for a symmetric matrix such as this one, only the
   strictly lower or upper triangular parts would need to be
   passed to AMD, since AMD computes the ordering of A+A'.  The
   diagonal entries are also not needed, since AMD ignores them.
   This version of the matrix has jumbled columns and duplicate
   row indices.

Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
    row indices: 0 17 18 21 5 12 5 0 13

Column: 1, number of entries: 5, with row indices in Ai [9 ... 13]:
    row indices: 14 1 8 13 17

Column: 2, number of entries: 6, with row indices in Ai [14 ... 19]:
    row indices: 2 20 11 6 11 22

Column: 3, number of entries: 8, with row indices in Ai [20 ... 27]:
    row indices: 3 3 10 7 18 18 15 19

Column: 4, number of entries: 5, with row indices in Ai [28 ... 32]:
    row indices: 7 9 15 14 16

Column: 5, number of entries: 4, with row indices in Ai [33 ... 36]:
    row indices: 5 13 6 17

Column: 6, number of entries: 7, with row indices in Ai [37 ... 43]:
    row indices: 5 0 11 6 12 6 23

Column: 7, number of entries: 9, with row indices in Ai [44 ... 52]:
    row indices: 3 4 9 7 14 16 15 17 18

Column: 8, number of entries: 5, with row indices in Ai [53 ... 57]:
    row indices: 1 9 14 14 14

Column: 9, number of entries: 5, with row indices in Ai [58 ... 62]:
    row indices: 7 13 8 1 17

Column: 10, number of entries: 0, with row indices in Ai [63 ... 62]:
    row indices:

Column: 11, number of entries: 3, with row indices in Ai [63 ... 65]:
    row indices: 2 12 23

Column: 12, number of entries: 3, with row indices in Ai [66 ... 68]:
    row indices: 5 11 12

Column: 13, number of entries: 3, with row indices in Ai [69 ... 71]:
    row indices: 0 13 17

Column: 14, number of entries: 3, with row indices in Ai [72 ... 74]:
    row indices: 1 9 14

Column: 15, number of entries: 3, with row indices in Ai [75 ... 77]:
    row indices: 3 15 16

Column: 16, number of entries: 4, with row indices in Ai [78 ... 81]:
    row indices: 16 4 4 15

Column: 17, number of entries: 4, with row indices in Ai [82 ... 85]:
    row indices: 13 17 19 17

Column: 18, number of entries: 5, with row indices in Ai [86 ... 90]:
    row indices: 15 17 19 9 10

Column: 19, number of entries: 6, with row indices in Ai [91 ... 96]:
    row indices: 17 19 20 0 6 10

Column: 20, number of entries: 4, with row indices in Ai [97 ... 100]:
    row indices: 22 10 20 21

Column: 21, number of entries: 11, with row indices in Ai [101 ... 111]:
    row indices: 6 2 10 19 20 11 21 22 22 22 22

Column: 22, number of entries: 0, with row indices in Ai [112 ... 111]:
    row indices:

Column: 23, number of entries: 4, with row indices in Ai [112 ... 115]:
    row indices: 12 11 12 23

Plot of (jumbled) input matrix pattern:
     0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
 0:  X . . . . . X . . . . . . X . . . . . X . . . .
 1:  . X . . . . . . X X . . . . X . . . . . . . . .
 2:  . . X . . . . . . . . X . . . . . . . . . X . .
 3:  . . . X . . . X . . . . . . . X . . . . . . . .
 4:  . . . . . . . X . . . . . . . . X . . . . . . .
 5:  X . . . . X X . . . . . X . . . . . . . . . . .
 6:  . . X . . X X . . . . . . . . . . . . X . X . .
 7:  . . . X X . . X . X . . . . . . . . . . . . . .
 8:  . X . . . . . . . X . . . . . . . . . . . . . .
 9:  . . . . X . . X X . . . . . X . . . X . . . . .
10:  . . . X . . . . . . . . . . . . . . X X X X . .
11:  . . X . . . X . . . . . X . . . . . . . . X . X
12:  X . . . . . X . . . . X X . . . . . . . . . . X
13:  X X . . . X . . . X . . . X . . . X . . . . . .
14:  . X . . X . . X X . . . . . X . . . . . . . . .
15:  . . . X X . . X . . . . . . . X X . X . . . . .
16:  . . . . X . . X . . . . . . . X X . . . . . . .
17:  X X . . . X . X . X . . . X . . . X X X . . . .
18:  X . . X . . . X . . . . . . . . . . . . . . . .
19:  . . . X . . . . . . . . . . . . . X X X . X . .
20:  . . X . . . . . . . . . . . . . . . . X X X . .
21:  X . . . . . . . . . . . . . . . . . . . X X . .
22:  . . X . . . . . . . . . . . . . . . . . X X . .
23:  . . . . . . X . . . . X . . . . . . . . . . . X

Plot of symmetric matrix to be ordered by amd_order:
     0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
 0:  X . . . . X X . . . . . X X . . . X X X . X . .
 1:  . X . . . . . . X X . . . X X . . X . . . . . .
 2:  . . X . . . X . . . . X . . . . . . . . X X X .
 3:  . . . X . . . X . . X . . . . X . . X X . . . .
 4:  . . . . X . . X . X . . . . X X X . . . . . . .
 5:  X . . . . X X . . . . . X X . . . X . . . . . .
 6:  X . X . . X X . . . . X X . . . . . . X . X . X
 7:  . . . X X . . X . X . . . . X X X X X . . . . .
 8:  . X . . . . . . X X . . . . X . . . . . . . . .
 9:  . X . . X . . X X X . . . X X . . X X . . . . .
10:  . . . X . . . . . . X . . . . . . . X X X X . .
11:  . . X . . . X . . . . X X . . . . . . . . X . X
12:  X . . . . X X . . . . X X . . . . . . . . . . X
13:  X X . . . X . . . X . . . X . . . X . . . . . .
14:  . X . . X . . X X X . . . . X . . . . . . . . .
15:  . . . X X . . X . . . . . . . X X . X . . . . .
16:  . . . . X . . X . . . . . . . X X . . . . . . .
17:  X X . . . X . X . X . . . X . . . X X X . . . .
18:  X . . X . . . X . X X . . . . X . X X X . . . .
19:  X . . X . . X . . . X . . . . . . X X X X X . .
20:  . . X . . . . . . . X . . . . . . . . X X X X .
21:  X . X . . . X . . . X X . . . . . . . X X X X .
22:  . . X . . . . . . . . . . . . . . . . . X X X .
23:  . . . . . . X . . . . X X . . . . . . . . . . X
return value from amd_order: 1 (should be 1)

AMD version 2.2.0, May 31, 2007, results:
    status: OK, but jumbled
    n, dimension of A:                                  24
    nz, number of nonzeros in A:                        102
    symmetry of A:                                      0.4000
    number of nonzeros on diagonal:                     17
    nonzeros in pattern of A+A' (excl. diagonal):       136
    # dense rows/columns of A+A':                       0
    memory used, in bytes:                              2080
    # 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:
 22 20 10 23 12  5 16  8 14  4 15  7  1  9 13 17  0  2  3  6 11 18 21 19

Inverse permutation vector:
 16 12 17 18  9  5 19 11  7 13  2 20  4 14  8 10  6 15 21 23  1 22  0  3


Plot of (symmetrized) permuted matrix pattern:
     0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3
 0:  X X . . . . . . . . . . . . . . . X . . . . X .
 1:  X X X . . . . . . . . . . . . . . X . . . . X X
 2:  . X X . . . . . . . . . . . . . . . X . . X X X
 3:  . . . X X . . . . . . . . . . . . . . X X . . .
 4:  . . . X X X . . . . . . . . . . X . . X X . . .
 5:  . . . . X X . . . . . . . . X X X . . X . . . .
 6:  . . . . . . X . . X X X . . . . . . . . . . . .
 7:  . . . . . . . X X . . . X X . . . . . . . . . .
 8:  . . . . . . . X X X . X X X . . . . . . . . . .
 9:  . . . . . . X . X X X X . X . . . . . . . . . .
10:  . . . . . . X . . X X X . . . . . . X . . X . .
11:  . . . . . . X . X X X X . X . X . . X . . X . .
12:  . . . . . . . X X . . . X X X X . . . . . . . .
13:  . . . . . . . X X X . X X X X X . . . . . X . .
14:  . . . . . X . . . . . . X X X X X . . . . . . .
15:  . . . . . X . . . . . X X X X X X . . . . X . X
16:  . . . . X X . . . . . . . . X X X . . X . X X X
17:  X X . . . . . . . . . . . . . . . X . X X . X .
18:  . . X . . . . . . . X X . . . . . . X . . X . X
19:  . . . X X X . . . . . . . . . . X X . X X . X X
20:  . . . X X . . . . . . . . . . . . X . X X . X .
21:  . . X . . . . . . . X X . X . X X . X . . X . X
22:  X X X . . . . . . . . . . . . . X X . X X . X X
23:  . X X . . . . . . . . . . . . X X . X X . X X X