[Octave-bug-tracker] [bug #57145] backslash vs. pinv

[Muhali]

URL:
  <https://savannah.gnu.org/bugs/?57145>

                 Summary:  backslash vs. pinv
                 Project: GNU Octave
            Submitted by: muhali
            Submitted on: Wed 30 Oct 2019 09:34:39 AM PDT
                Category: None
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: None
                  Status: None
             Assigned to: None
         Originator Name: 
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 5.1.0
        Operating System: GNU/Linux

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Details:


A = magic(8);
A = A(:,1:6) ;
b = 260*ones(8,1) ;

x1 = A\b
x2 = pinv(A)*b

x3 = [3 4 0 0 1 0]' ;
norm(A*x1-b)
norm(A*x3-b)


There are two (possibly well known) issues here.

a) x1 differs from Matlab (which gives x3).

b) solution x3 is "closer" than solution x1.

The example comes from the Matlab pinv help. ML probably uses a
different/better optimization algorithm, so the difference should perhaps be
mentioned at least.





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