[Octave-bug-tracker] [bug #54167] eigs called with user defined function gives incorrect results if B is not the identity matrix

[anonymous]

URL:
  <http://savannah.gnu.org/bugs/?54167>

                 Summary: eigs called with user defined function gives
incorrect results if B is not the identity matrix
                 Project: GNU Octave
            Submitted by: None
            Submitted on: Fri 22 Jun 2018 08:19:48 PM UTC
                Category: Libraries
                Severity: 3 - Normal
                Priority: 5 - Normal
              Item Group: Incorrect Result
                  Status: None
             Assigned to: None
         Originator Name: Octave user
        Originator Email: 
             Open/Closed: Open
         Discussion Lock: Any
                 Release: 4.4.0
        Operating System: Microsoft Windows

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Details:

If you run the code below, you get an error if B is not the identity matrix.


clear all;
rand("seed", 0);

tol = sqrt(eps);

for j=1:2
  for i=1:100
    A = rand(10, 10);
    if j == 1
      B = eye(columns(A));
    else
      B = rand(rows(A), columns(A));
    endif
    A *= A.';
    B *= B.';
    opts.isreal = 1;
    opts.issym = 1;
    [v, lambda] = eigs(A, B, 3, "sm");
    [v2, lambda2] = eigs(@(x) A \ x, columns(A), B, 3, "sm", opts);
    assert(lambda, lambda2, tol*max(max(abs(lambda))));
    for i=1:columns(v)
      assert(A * v(:, i), lambda(i,i) * B * v(:,i), tol * norm(A * v(:,i)));
    endfor
    for i=1:columns(v2)
      assert(A * v2(:, i), lambda2(i,i) * B * v2(:, i), tol * norm(A *
v2(:,i)));
    endfor
  endfor
endfor





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File Attachments:


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Date: Fri 22 Jun 2018 08:19:48 PM UTC  Name: eigs_test.m  Size: 694B   By:
None

<http://savannah.gnu.org/bugs/download.php?file_id=44417>

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