Mercurial > octave-nkf
view liboctave/UMFPACK/AMD/Demo/amd_demo2.out @ 5164:57077d0ddc8e
[project @ 2005-02-25 19:55:24 by jwe]
| author | jwe |
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| date | Fri, 25 Feb 2005 19:55:28 +0000 |
| parents | |
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AMD demo, with a jumbled version of the 24-by-24 Harwell/Boeing matrix, can_24: 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 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, and must be fixed by amd_preprocess prior to ordering it with amd_order. 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 return value from amd_preprocess: 0 (should be 0) The column-oriented form of the sorted/transposed matrix R: Column: 0, number of entries: 4, with row indices in Ri [0 ... 3]: row indices: 0 6 13 19 Column: 1, number of entries: 4, with row indices in Ri [4 ... 7]: row indices: 1 8 9 14 Column: 2, number of entries: 3, with row indices in Ri [8 ... 10]: row indices: 2 11 21 Column: 3, number of entries: 3, with row indices in Ri [11 ... 13]: row indices: 3 7 15 Column: 4, number of entries: 2, with row indices in Ri [14 ... 15]: row indices: 7 16 Column: 5, number of entries: 4, with row indices in Ri [16 ... 19]: row indices: 0 5 6 12 Column: 6, number of entries: 5, with row indices in Ri [20 ... 24]: row indices: 2 5 6 19 21 Column: 7, number of entries: 4, with row indices in Ri [25 ... 28]: row indices: 3 4 7 9 Column: 8, number of entries: 2, with row indices in Ri [29 ... 30]: row indices: 1 9 Column: 9, number of entries: 5, with row indices in Ri [31 ... 35]: row indices: 4 7 8 14 18 Column: 10, number of entries: 5, with row indices in Ri [36 ... 40]: row indices: 3 18 19 20 21 Column: 11, number of entries: 5, with row indices in Ri [41 ... 45]: row indices: 2 6 12 21 23 Column: 12, number of entries: 5, with row indices in Ri [46 ... 50]: row indices: 0 6 11 12 23 Column: 13, number of entries: 6, with row indices in Ri [51 ... 56]: row indices: 0 1 5 9 13 17 Column: 14, number of entries: 5, with row indices in Ri [57 ... 61]: row indices: 1 4 7 8 14 Column: 15, number of entries: 6, with row indices in Ri [62 ... 67]: row indices: 3 4 7 15 16 18 Column: 16, number of entries: 4, with row indices in Ri [68 ... 71]: row indices: 4 7 15 16 Column: 17, number of entries: 9, with row indices in Ri [72 ... 80]: row indices: 0 1 5 7 9 13 17 18 19 Column: 18, number of entries: 3, with row indices in Ri [81 ... 83]: row indices: 0 3 7 Column: 19, number of entries: 5, with row indices in Ri [84 ... 88]: row indices: 3 17 18 19 21 Column: 20, number of entries: 4, with row indices in Ri [89 ... 92]: row indices: 2 19 20 21 Column: 21, number of entries: 3, with row indices in Ri [93 ... 95]: row indices: 0 20 21 Column: 22, number of entries: 3, with row indices in Ri [96 ... 98]: row indices: 2 20 21 Column: 23, number of entries: 3, with row indices in Ri [99 ... 101]: row indices: 6 11 23 Plot of the sorted/transposed matrix R: 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 . . 1: . X . . . . . . X . . . . X X . . X . . . . . . 2: . . X . . . X . . . . X . . . . . . . . X . X . 3: . . . X . . . X . . X . . . . X . . X X . . . . 4: . . . . . . . X . X . . . . X X X . . . . . . . 5: . . . . . X X . . . . . . X . . . X . . . . . . 6: X . . . . X X . . . . X X . . . . . . . . . . X 7: . . . X X . . X . X . . . . X X X X X . . . . . 8: . X . . . . . . . X . . . . X . . . . . . . . . 9: . X . . . . . X X . . . . X . . . X . . . . . . 10: . . . . . . . . . . . . . . . . . . . . . . . . 11: . . X . . . . . . . . . X . . . . . . . . . . X 12: . . . . . X . . . . . X X . . . . . . . . . . . 13: X . . . . . . . . . . . . X . . . X . . . . . . 14: . X . . . . . . . X . . . . X . . . . . . . . . 15: . . . X . . . . . . . . . . . X X . . . . . . . 16: . . . . X . . . . . . . . . . X X . . . . . . . 17: . . . . . . . . . . . . . X . . . X . X . . . . 18: . . . . . . . . . X X . . . . X . X . X . . . . 19: X . . . . . X . . . X . . . . . . X . X X . . . 20: . . . . . . . . . . X . . . . . . . . . X X X . 21: . . X . . . X . . . X X . . . . . . . X X X X . 22: . . . . . . . . . . . . . . . . . . . . . . . . 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: 0 (should be 0) amd: approximate minimum degree ordering, results: status: OK 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: 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 (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