/
amd_demo2.out
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amd_demo2.out
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AMD demo, with a jumbled version of the 24-by-24
Harwell/Boeing matrix, can_24:
AMD version 2.4.6, May 4, 2016: 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 2.4.6, May 4, 2016, 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