#11027: Schur matrix decomposition over RDF/CDF
------------------------------+---------------------------------------------
Reporter: rbeezer | Owner: jason, was
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-4.7
Component: linear algebra | Keywords:
Author: | Upstream: N/A
Reviewer: Martin Raum | Merged:
Work_issues: |
------------------------------+---------------------------------------------
Changes (by mraum):
* status: new => needs_work
* reviewer: => Martin Raum
Comment:
Some discussion is necessary: As a doctest I get
{{{
Expected:
[ 0.006 - 0.001*I 0.0425 + 0.1018*I -0.6446 + 0.2201*I 0.3981 +
0.6045*I]
[ 0.0875 - 0.005*I 0.1984 + 0.5537*I -0.5022 + 0.1944*I -0.3414 -
0.4896*I]
[ 0.3572 - 0.0159*I 0.2444 + 0.685*I 0.4499 - 0.1643*I 0.1983 +
0.2728*I]
[ 0.929 - 0.0377*I -0.111 - 0.317*I -0.1212 + 0.044*I -0.0466 -
0.0627*I]
Got:
[ 0.006 - 0.001*I 0.0283 + 0.1066*I -0.6784 + 0.0611*I 0.3686 +
0.6229*I]
[ 0.0875 - 0.005*I 0.1216 + 0.5755*I -0.534 + 0.0699*I -0.3175 -
0.5055*I]
[ 0.3572 - 0.0159*I 0.1494 + 0.7118*I 0.476 - 0.053*I 0.185 +
0.282*I]
[ 0.929 - 0.0377*I -0.067 - 0.3291*I -0.1282 + 0.0141*I -0.0435 -
0.0649*I]
**********************************************************************
File "/scratch/mraum/sagedev/devel/sage-
dev/sage/matrix/matrix_double_dense.pyx", line 1382:
sage: T.round(4)
Expected:
[ 30.7332 + 4648.5418*I -2342.252 + 767.2915*I -477.0197 -
1460.6287*I -532.7363 + 318.6099*I]
[ 0 -0.1841 - 159.0576*I 151.3315 +
0.458*I -15.2369 - 67.0242*I]
[ 0 0 -0.5239 +
11.158*I 6.2073 - 1.1208*I]
[ 0 0
0 -0.0252 - 0.6422*I]
Got:
[ 30.7332 + 4648.5418*I -2424.5875 + 443.008*I -117.3203 -
1532.0639*I -547.4078 + 292.6858*I]
[ 0 -0.1841 - 159.0576*I 150.4761 +
16.0737*I -21.0591 - 65.4288*I]
[ 0 0 -0.5239 +
11.158*I 5.8811 - 2.2803*I]
[ 0 0
0 -0.0252 - 0.6422*I]
}}}
Mathematica gives:
{{{
In[1]:= m = m = Table[Table[0.0 + i + 4 * j, {i, 0, 3}], {j, 0, 3}] +
Table[Table[(i + 4 * j)^3 * I, {i, 0, 3}], {j, 0, 3}]
Out[1]= {{0., 1. + 1. I, 2. + 8. I, 3. + 27. I},
> {4. + 64. I, 5. + 125. I, 6. + 216. I, 7. + 343. I},
> {8. + 512. I, 9. + 729. I, 10. + 1000. I, 11. + 1331. I},
> {12. + 1728. I, 13. + 2197. I, 14. + 2744. I, 15. + 3375. I}}
In[2]:= {matU, matT} = SchurDecomposition[m]
Out[2]= {{{0.0060036 - 0.000979619 I, -0.0373719 + 0.10381 I,
> -0.0166147 + 0.680909 I, 0.370437 + 0.621815 I},
> {0.0875304 - 0.00504818 I, -0.227102 + 0.542591 I,
> 0.0085438 + 0.538502 I, -0.318925 - 0.504541 I},
> {0.357191 - 0.0158906 I, -0.281727 + 0.670563 I,
> 0.0016419 - 0.478947 I, 0.185814 + 0.281457 I},
> {0.928988 - 0.0376762 I, 0.131963 - 0.308882 I,
> -0.000646133 + 0.128983 I, -0.0436872 - 0.064763 I}},
> {{30.7332 + 4648.54 I, -2246.55 - 1013.86 I, -1535.45 - 58.1104 I,
> -546.563 + 294.26 I}, {0. + 0. I, -0.184122 - 159.058 I,
> -56.6912 - 140.312 I, -54.6402 - 41.6996 I},
> {0. + 0. I, 0. + 0. I, -0.523917 + 11.158 I, 2.95198 + 5.57432 I},
> {0. + 0. I, 0. + 0. I, 0. + 0. I, -0.0251565 - 0.642223 I}}}
}}}
That is three different results, probably depending on the machine you run
it on.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11027#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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