Hi,
working offline with Edmond we have solved my problem.
The problem was that ROOT 4.0.8 was not able to
invert a matrix that ROOT 3.4.2 was able to invert.
My matrix had huge determinant (1E53) that caused problem
to ROOT 4.0.8 when determinant calculation was explicitly asked.
I used determinant computation just to catch singularity of
the matrix.
Edmond show me better ways of testing for singularity.
Reconditioning my matrix by dividing every element by the maximum
diagonal element make it more manageable for determinant
computation and now
both version of ROOT give identical results on this better behaved matrix.
For those interested this is the matrix that new ROOT has problem
to determine determinant:
Matrix 21x21 is as follows
| 0 | 1 | 2 | 3 | 4 |
------------------------------------------------------------------
0 | 833 475 474.7 154.2 490.4
1 | 475 947.1 538.4 155.1 560.1
2 | 474.7 538.4 1016 148.9 601.5
3 | 154.2 155.1 148.9 250.7 169.4
4 | 490.4 560.1 601.5 169.4 1314
5 | 489.2 556.5 596.4 155.1 771.8
6 | 481.1 549.4 588.4 155.1 760.9
7 | 475.5 532.8 552.2 159.7 571.6
8 | 476.5 543.4 584.3 156.6 772.7
9 | 394.4 461.4 504.8 70.02 661.3
10 | 474 537.3 575.8 152.8 742
11 | 460.4 525.7 564.5 146.2 755.7
12 | 276.7 319.8 353.9 22.09 478.5
13 | 0 16.61 52.61 0 171.2
14 | 101.4 149.6 182 0 292.6
15 | 246.4 277.8 299.4 77.6 370.5
16 | 0 0 0 0 58.85
17 | 0 0 0 0 39.23
18 | 0 0 0 0 42.14
19 | 17.77 43.23 65.38 0 133.9
20 | 970.8 1107 1191 315.2 1545
| 5 | 6 | 7 | 8 | 9 |
------------------------------------------------------------------
0 | 489.2 481.1 475.5 476.5 394.4
1 | 556.5 549.4 532.8 543.4 461.4
2 | 596.4 588.4 552.2 584.3 504.8
3 | 155.1 155.1 159.7 156.6 70.02
4 | 771.8 760.9 571.6 772.7 661.3
5 | 1365 781.8 567.4 792.9 703.6
6 | 781.8 1350 560.1 783.2 698.9
7 | 567.4 560.1 944.9 554.1 471.5
8 | 792.9 783.2 554.1 1342 711.2
9 | 703.6 698.9 471.5 711.2 1189
10 | 758.5 749.7 548.8 761.5 678.1
11 | 773.6 762.8 547.1 777.8 696.4
12 | 504.4 498.4 330.5 505.9 503.9
13 | 189.7 188.2 25.56 203.6 206
14 | 316.5 309.9 162.1 316.7 324.3
15 | 378.4 374.3 273.6 383.1 341.6
16 | 65.48 58.62 0 74.83 74.88
17 | 49.28 45.25 0 52.31 54.38
18 | 49.67 46.48 0 56.8 57.6
19 | 135 132.8 56.23 142.2 140.8
20 | 1581 1563 1131 1586 1409
| 10 | 11 | 12 | 13 | 14 |
------------------------------------------------------------------
0 | 474 460.4 276.7 0 101.4
1 | 537.3 525.7 319.8 16.61 149.6
2 | 575.8 564.5 353.9 52.61 182
3 | 152.8 146.2 22.09 0 0
4 | 742 755.7 478.5 171.2 292.6
5 | 758.5 773.6 504.4 189.7 316.5
6 | 749.7 762.8 498.4 188.2 309.9
7 | 548.8 547.1 330.5 25.56 162.1
8 | 761.5 777.8 505.9 203.6 316.7
9 | 678.1 696.4 503.9 206 324.3
10 | 1295 756.2 505.3 199 278.9
11 | 756.2 1304 508.8 201.4 319.3
12 | 505.3 508.8 844.5 176.1 315
13 | 199 201.4 176.1 319 171.6
14 | 278.9 319.3 315 171.6 530.7
15 | 382.5 375.3 317.3 120.6 230.8
16 | 67.16 75.5 78.26 68.94 77.3
17 | 45.89 55.56 51.24 49.8 57.54
18 | 46.73 57.49 55.5 51.34 60.05
19 | 127.7 144.1 142.4 101.3 149.8
20 | 1525 1548 1010 390.6 630
| 15 | 16 | 17 | 18 | 19 |
------------------------------------------------------------------
0 | 246.4 0 0 0 17.77
1 | 277.8 0 0 0 43.23
2 | 299.4 0 0 0 65.38
3 | 77.6 0 0 0 0
4 | 370.5 58.85 39.23 42.14 133.9
5 | 378.4 65.48 49.28 49.67 135
6 | 374.3 58.62 45.25 46.48 132.8
7 | 273.6 0 0 0 56.23
8 | 383.1 74.83 52.31 56.8 142.2
9 | 341.6 74.88 54.38 57.6 140.8
10 | 382.5 67.16 45.89 46.73 127.7
11 | 375.3 75.5 55.56 57.49 144.1
12 | 317.3 78.26 51.24 55.5 142.4
13 | 120.6 68.94 49.8 51.34 101.3
14 | 230.8 77.3 57.54 60.05 149.8
15 | 657.2 64.84 44.36 51 144
16 | 64.84 110.4 52.59 56 56.9
17 | 44.36 52.59 79.1 73.07 44.16
18 | 51 56 73.07 83.99 45.74
19 | 144 56.9 44.16 45.74 228.7
20 | 774 143.4 103.2 108 281.6
| 20 |
------------------------------------------------------------------
0 | 970.8
1 | 1107
2 | 1191
3 | 315.2
4 | 1545
5 | 1581
6 | 1563
7 | 1131
8 | 1586
9 | 1409
10 | 1525
11 | 1548
12 | 1010
13 | 390.6
14 | 630
15 | 774
16 | 143.4
17 | 103.2
18 | 108
19 | 281.6
20 | 3168
determinant
(as computed by ROOT 3)
136908227115674077978030740804195813377898749408313344.000000
Thanks
--
Nicolas Produit
INTEGRAL Science Data Center Phone: +41 22 950 91 40
16, Chemin d'Ecogia Fax: +41 22 950 91 33
CH-1290 Versoix www: http://isdc.unige.ch/~produit
Phone after 10 Dec 2004: +41 22 379 21 40
This archive was generated by hypermail 2b29 : Sun Jan 02 2005 - 05:50:10 MET