Re:[ROOT]problem matrix invertion

From: PRODUIT Nicolas (Nicolas.Produit@obs.unige.ch)
Date: Tue Dec 07 2004 - 17:32:46 MET


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



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