[Octave-bug-tracker] [bug #44061] U and V result matrises are not othogonal

[anonymous]

URL:
  <http://savannah.gnu.org/bugs/?44061>

                 Summary: U and V result matrises are not othogonal
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Wed 21 Jan 2015 04:23:36 PM UTC
                Category: Octave Function
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Svend H. Sørensen
        Originator Email: address@hidden
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 3.8.2
        Operating System: GNU/Linux

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Details:


octave:1> load "test_files/in/two_vars_neg_in.sparse"
octave:2> A = spconvert(two_vars_neg_in)
A =

Compressed Column Sparse (rows = 4, cols = 4, nnz = 8 [50%])

  (1, 1) -> -1
  (2, 1) -> -1
  (3, 1) ->  1
  (4, 1) ->  1
  (1, 2) -> -1
  (2, 2) ->  1
  (3, 2) -> -1
  (4, 2) ->  1

octave:3>  [U,S,V]= svds(A,rows(A),rows(A))
U =

  -0.50000   0.50000   1.00000   0.00000
   0.50000   0.50000   0.00000   1.00000
  -0.50000  -0.50000   0.00000   1.00000
   0.50000  -0.50000   1.00000   0.00000

S =

Diagonal Matrix

   2   0   0   0
   0   2   0   0
   0   0   0   0
   0   0   0   0

V =

  -0.00000  -1.00000   0.00000   0.00000
   1.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000

octave:4> #[U,S,V] = svd (full(A) )
octave:4> ss = diag(S)
ss =

   2
   2
   0
   0

octave:5> nnull=sum(ss(:)==0)
nnull =  2
octave:6> V'*V  ## this should result en the identity matrix but does not !!
ans =

   1.00000   0.00000   0.00000   0.00000
   0.00000   1.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000
   0.00000   0.00000   0.00000   0.00000



octave:7> U'*U  ## here again we expect to see the identity matrix 
ans =

   1.00000   0.00000   0.00000   0.00000
   0.00000   1.00000   0.00000   0.00000
   0.00000   0.00000   2.00000   0.00000
   0.00000   0.00000   0.00000   2.00000






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File Attachments:


-------------------------------------------------------
Date: Wed 21 Jan 2015 04:23:36 PM UTC  Name: two_vars_neg_in.sparse  Size:
121B   By: None

<http://savannah.gnu.org/bugs/download.php?file_id=32889>
-------------------------------------------------------
Date: Wed 21 Jan 2015 04:23:36 PM UTC  Name: svd-2-var.oct  Size: 178B   By:
None

<http://savannah.gnu.org/bugs/download.php?file_id=32890>

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