amd_demo.out
7.41 KB
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AMD version 2.2, date: May 31, 2007
AMD demo, with 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
Input matrix: 24-by-24, with 160 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.
Column: 0, number of entries: 9, with row indices in Ai [0 ... 8]:
row indices: 0 5 6 12 13 17 18 19 21
Column: 1, number of entries: 6, with row indices in Ai [9 ... 14]:
row indices: 1 8 9 13 14 17
Column: 2, number of entries: 6, with row indices in Ai [15 ... 20]:
row indices: 2 6 11 20 21 22
Column: 3, number of entries: 6, with row indices in Ai [21 ... 26]:
row indices: 3 7 10 15 18 19
Column: 4, number of entries: 6, with row indices in Ai [27 ... 32]:
row indices: 4 7 9 14 15 16
Column: 5, number of entries: 6, with row indices in Ai [33 ... 38]:
row indices: 0 5 6 12 13 17
Column: 6, number of entries: 9, with row indices in Ai [39 ... 47]:
row indices: 0 2 5 6 11 12 19 21 23
Column: 7, number of entries: 9, with row indices in Ai [48 ... 56]:
row indices: 3 4 7 9 14 15 16 17 18
Column: 8, number of entries: 4, with row indices in Ai [57 ... 60]:
row indices: 1 8 9 14
Column: 9, number of entries: 9, with row indices in Ai [61 ... 69]:
row indices: 1 4 7 8 9 13 14 17 18
Column: 10, number of entries: 6, with row indices in Ai [70 ... 75]:
row indices: 3 10 18 19 20 21
Column: 11, number of entries: 6, with row indices in Ai [76 ... 81]:
row indices: 2 6 11 12 21 23
Column: 12, number of entries: 6, with row indices in Ai [82 ... 87]:
row indices: 0 5 6 11 12 23
Column: 13, number of entries: 6, with row indices in Ai [88 ... 93]:
row indices: 0 1 5 9 13 17
Column: 14, number of entries: 6, with row indices in Ai [94 ... 99]:
row indices: 1 4 7 8 9 14
Column: 15, number of entries: 6, with row indices in Ai [100 ... 105]:
row indices: 3 4 7 15 16 18
Column: 16, number of entries: 4, with row indices in Ai [106 ... 109]:
row indices: 4 7 15 16
Column: 17, number of entries: 9, with row indices in Ai [110 ... 118]:
row indices: 0 1 5 7 9 13 17 18 19
Column: 18, number of entries: 9, with row indices in Ai [119 ... 127]:
row indices: 0 3 7 9 10 15 17 18 19
Column: 19, number of entries: 9, with row indices in Ai [128 ... 136]:
row indices: 0 3 6 10 17 18 19 20 21
Column: 20, number of entries: 6, with row indices in Ai [137 ... 142]:
row indices: 2 10 19 20 21 22
Column: 21, number of entries: 9, with row indices in Ai [143 ... 151]:
row indices: 0 2 6 10 11 19 20 21 22
Column: 22, number of entries: 4, with row indices in Ai [152 ... 155]:
row indices: 2 20 21 22
Column: 23, number of entries: 4, with row indices in Ai [156 ... 159]:
row indices: 6 11 12 23
Plot of 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 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: 0 (should be 0)
AMD version 2.2.0, May 31, 2007, 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:
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 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