[Octave-bug-tracker] [bug #60839] linsolve returns an incorrect solution with an inconsistent system

[anónimo]

URL:
  <https://savannah.gnu.org/bugs/?60839>

                 Summary: linsolve returns an incorrect solution with an
inconsistent system
                 Project: GNU Octave
            Submitted by: None
            Submitted on: dom 27 jun 2021 18:36:50 UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Jose Luis Nuñez Crespi
        Originator Email: joseluis.nunez@selenitas.es
             Open/Closed: Open
                 Release: 6.2.0
         Discussion Lock: Any
        Operating System: GNU/Linux

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Details:

I have written a set of libraries in Java to deal with complex numbers with
several mathematical functions and arithmetic capablities.

I use GNU Octave, Maxima and sometimes Wolfram to check the results returned
from my progrmas.

In one of the tests I use the following system that is inconsistent
+(1)x0+(-1)x1+(1)x2+(1)x3+(-1)x4 = -1
+(1)x0+(-1)x1+(-1)x2+(1)x3+(-1)x4 = -1
+(1)x0+(-1)x1+(-1)x2+(1)x3+(-1)x4 = 1
+(-1)x0+(-1)x1+(1)x2+(1)x3+(-1)x4 = 1
+(-1)x0+(-1)x1+(1)x2+(-1)x3+(-1)x4 = 1

But Octave returns the following result, and I think that is incorrect, maybe
the warnings invalidate the result returned... 

>> disp(Sol =
linsolve([1.000,-1.000,1.000,1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000;-1.000,-1.000,1.000,1.000,-1.000;-1.000,-1.000,1.000,-1.000,-1.000],[-1.000;-1.000;1.000;1.000;1.000]))
warning: matrix singular to machine precision
warning: called from
    linsolve at line 113 column 7

  -1.0000e+00
  -2.5000e-01
  -5.0000e-01
  -2.2204e-16
  -2.5000e-01
>>
rank([1.00,-1.00,1.00,1.00,-1.00;1.00,-1.00,-1.00,1.00,-1.00;1.00,-1.00,-1.00,1.00,-1.00;-1.00,-1.00,1.00,1.00,-1.00;-1.00,-1.00,1.00,-1.00,-1.00])
ans = 4
>>
rank([1.00,-1.00,1.00,1.00,-1.00;1.00,-1.00,-1.00,1.00,-1.00;1.00,-1.00,-1.00,1.00,1.00;-1.00,-1.00,1.00,1.00,1.00;-1.00,-1.00,1.00,-1.00,1.00])
ans = 5

The answer given from Maxima for the same system is

(%i1)   
expand(linsolve([+(1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(-1.000)*x3+(-1.000)*x4=1.000],[x0,x1,x2,x3,x4]));
(%o1)   []

And from my java program (https://github.com/ipserc/complexarith
TestSyseq1.java) 

#===============================================================#
I                                                               I
I                 LINEAR EQUATIONS SYSTEM TEST                  I
I                                                               I
#===============================================================#
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
:                        Equation System                        :
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
+(1.000)x0+(-1.000)x1+(1.000)x2+(1.000)x3+(-1.000)x4 = -1.000
+(1.000)x0+(-1.000)x1+(-1.000)x2+(1.000)x3+(-1.000)x4 = -1.000
+(1.000)x0+(-1.000)x1+(-1.000)x2+(1.000)x3+(-1.000)x4 = 1.000
+(-1.000)x0+(-1.000)x1+(1.000)x2+(1.000)x3+(-1.000)x4 = 1.000
+(-1.000)x0+(-1.000)x1+(1.000)x2+(-1.000)x3+(-1.000)x4 = 1.000
The system is INCONSISTENT
+---------------------------------------------------------------+
|                     System Solve Commands                     |
+---------------------------------------------------------------+
MComplex:new
MatrixComplex("1.000,-1.000,1.000,1.000,-1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000,1.000;-1.000,-1.000,1.000,1.000,-1.000,1.000;-1.000,-1.000,1.000,-1.000,-1.000,1.000")
MAXIMA:expand(linsolve([+(1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(-1.000)*x3+(-1.000)*x4=1.000],[x0,x1,x2,x3,x4]))
OCTAVE:disp(Sol =
linsolve([1.000,-1.000,1.000,1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000;1.000,-1.000,-1.000,1.000,-1.000;-1.000,-1.000,1.000,1.000,-1.000;-1.000,-1.000,1.000,-1.000,-1.000],[-1.000;-1.000;1.000;1.000;1.000]))
WOLFRAM:solve(+(1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=-1.000,+(1.000)*x0+(-1.000)*x1+(-1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(1.000)*x3+(-1.000)*x4=1.000,+(-1.000)*x0+(-1.000)*x1+(1.000)*x2+(-1.000)*x3+(-1.000)*x4=1.000,x0,x1,x2,x3,x4)
#===============================================================#
|                       System Solutions                        |
#===============================================================#
There are no solutions for an INCONSISTENT Equation System





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