#10791: Fix and upgrade Gram-Schmidt
-------------------------------+--------------------------------------------
    Reporter:  rbeezer         |         Owner:  jason, was 
        Type:  defect          |        Status:  needs_work 
    Priority:  major           |     Milestone:  sage-4.8   
   Component:  linear algebra  |    Resolution:             
    Keywords:  sd32            |   Work_issues:             
    Upstream:  N/A             |      Reviewer:  Martin Raum
      Author:  Rob Beezer      |        Merged:             
Dependencies:                  |  
-------------------------------+--------------------------------------------
Changes (by jhpalmieri):

  * status:  needs_review => needs_work


Comment:

 There are errors on sage.math and on OS X 10.6.8, applied to Sage
 4.8.alpha3:
 {{{
 sage -t --long "devel/sage/sage/matrix/matrix2.pyx"
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8072:
     sage: G*G.transpose()
 Expected:
     [      1 0.?e-37 0.?e-35]
     [0.?e-37       1 0.?e-35]
     [0.?e-35 0.?e-35       1]
 Got:
     [      1 0.?e-18 0.?e-19]
     [0.?e-18       1 0.?e-18]
     [0.?e-19 0.?e-18       1]
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8087:
     sage: G
 Expected:
     [                         -0.3849001794597505?  -0.1924500897298753? -
 0.1924500897298753?*I   0.3849001794597505? + 0.7698003589195010?*I
 -0.1924500897298753?]
     [-0.06165497274852388? - 0.1387236886841787?*I  0.8188551068163327? -
 0.10018933071635130?*I  0.2003786614327026? + 0.05394810115495839?*I
 0.02119389688230508? + 0.5028733714801478?*I]
     [  0.3842387256410419? - 0.5694103019142261?*I  0.1416892863096208? -
 0.06139779741542298?*I  0.4633778333528464? - 0.01285039016180503?*I
 0.02658516588219101? - 0.5373044261814995?*I]
 Got:
     [                         -0.3849001794597505?  -0.1924500897298753? -
 0.1924500897298753?*I   0.3849001794597505? + 0.7698003589195010?*I
 -0.1924500897298753?]
     [-0.06165497274852388? - 0.1387236886841787?*I  0.8188551068163327? -
 0.10018933071635130?*I  0.2003786614327026? + 0.05394810115495839?*I
 0.02119389688230508? + 0.5028733714801478?*I]
     [  0.3842387256410419? - 0.5694103019142261?*I   0.1416892863096208? -
 0.0613977974154230?*I  0.4633778333528464? - 0.01285039016180503?*I
 0.02658516588219101? - 0.5373044261814995?*I]
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8091:
     sage: M
 Expected:
     [                        5.196152422706632?
 0                                          0]
     [-3.079201435678004? + 3.464101615137755?*I
 19.22286447225071? + 0.?e-37*I                                          0]
     [  4.426352063787131? - 8.66025403784439?*I -5.117362738127481? -
 3.502773139275513?*I             7.480012456446966? + 0.?e-35*I]
 Got:
     [                        5.196152422706632?
 0                                          0]
     [-3.079201435678004? + 3.464101615137755?*I
 19.22286447225071? + 0.?e-17*I                                          0]
     [  4.426352063787131? - 8.66025403784439?*I -5.117362738127481? -
 3.502773139275513?*I             7.480012456446966? + 0.?e-16*I]
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8095:
     sage: M*G-A
 Expected:
     [            0.?e-37 0.?e-37 + 0.?e-37*I 0.?e-37 + 0.?e-37*I
 0.?e-37]
     [0.?e-36 + 0.?e-36*I 0.?e-35 + 0.?e-36*I 0.?e-36 + 0.?e-36*I 0.?e-36 +
 0.?e-36*I]
     [0.?e-35 + 0.?e-35*I 0.?e-35 + 0.?e-35*I 0.?e-35 + 0.?e-35*I 0.?e-35 +
 0.?e-35*I]
 Got:
     [            0.?e-18 0.?e-18 + 0.?e-18*I 0.?e-18 + 0.?e-17*I
 0.?e-18]
     [0.?e-17 + 0.?e-17*I 0.?e-16 + 0.?e-17*I 0.?e-16 + 0.?e-17*I 0.?e-17 +
 0.?e-16*I]
     [0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 0.?e-16 + 0.?e-16*I 0.?e-16 +
 0.?e-16*I]
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8099:
     sage: G*G.conjugate().transpose()
 Expected:
     [1.000000000000000? + 0.?e-37*I            0.?e-37 + 0.?e-37*I
 0.?e-36 + 0.?e-36*I]
     [           0.?e-37 + 0.?e-37*I 1.000000000000000? + 0.?e-37*I
 0.?e-36 + 0.?e-36*I]
     [           0.?e-36 + 0.?e-36*I            0.?e-36 + 0.?e-36*I
 1.000000000000000? + 0.?e-35*I]
 Got:
     [1.000000000000000? + 0.?e-18*I            0.?e-18 + 0.?e-18*I
 0.?e-17 + 0.?e-16*I]
     [           0.?e-18 + 0.?e-18*I 1.000000000000000? + 0.?e-18*I
 0.?e-16 + 0.?e-17*I]
     [           0.?e-17 + 0.?e-16*I            0.?e-16 + 0.?e-17*I
 1.000000000000000? + 0.?e-16*I]
 **********************************************************************
 File
 "/Applications/sage_builds/sage-4.8.alpha3/devel/sage/sage/matrix/matrix2.pyx",
 line 8130:
     sage: G*G.transpose()
 Expected:
     [      1 0.?e-35]
     [0.?e-35       1]
 Got:
     [      1 0.?e-18]
     [0.?e-18       1]
 **********************************************************************
 1 items had failures:
    6 of  68 in __main__.example_97
 ***Test Failed*** 6 failures.
 For whitespace errors, see the file
 /Users/palmieri/.sage//tmp/matrix2_40831.py
          [37.9 s]

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t --long "devel/sage/sage/matrix/matrix2.pyx"
 Total time for all tests: 37.9 seconds
 }}}

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10791#comment:27>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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