I followed https://askubuntu.com/a/1265802/124466 to install Intel MKL.

** Summary changed:

- Octave gives wrong results with MKL
+ Octave gives wrong results when diagonalizing large matrices with MKL

** Description changed:

  Octave gives wrong results when manipulating large matrices, when the
  package `intel-mkl` is installed, and BLAS, LAPACK are configured with
  `intel-mkl` (from default ubuntu repositories). With MKL, Octave seems
  to have a 2x speedup when diagonalize certain matrices, but the results
  are totally wrong (when the matrix is large, say 1000x1000).
  
  Code:
  ```
  for a = 1:500
-       for b = 1:500
-               c(a,b) = sin(a + b^2);
-       endfor
+  for b = 1:500
+   c(a,b) = sin(a + b^2);
+  endfor
  endfor
  
  g = eig(c);
  max(real(g))
  ```
- The correct result is `ans =  16.915`
+ The correct result is `ans =  16.915` (I checked this before installing 
intel-mkl, and also in Ubuntu 18.04 in the same computer, where intel-mkl was 
not installed)
  With MKL in Ubuntu 20.04, I get random numbers of order 10^5 - 10^6, which 
change every time the code is run.
- 
  
  lsb_release -rd
  Description:  Ubuntu 20.04 LTS
  Release:      20.04
  (It is Xubuntu 20.04)
  
  apt-cache policy octave
  octave:
-   Installed: 5.2.0-1
-   Candidate: 5.2.0-1
-   Version table:
-  *** 5.2.0-1 500
-         500 http://archive.ubuntu.com/ubuntu focal/universe amd64 Packages
-         100 /var/lib/dpkg/status
+   Installed: 5.2.0-1
+   Candidate: 5.2.0-1
+   Version table:
+  *** 5.2.0-1 500
+         500 http://archive.ubuntu.com/ubuntu focal/universe amd64 Packages
+         100 /var/lib/dpkg/status
  
  apt-cache policy intel-mkl
  intel-mkl:
-   Installed: 2020.0.166-1
-   Candidate: 2020.0.166-1
-   Version table:
-  *** 2020.0.166-1 500
-         500 http://archive.ubuntu.com/ubuntu focal/multiverse amd64 Packages
-         100 /var/lib/dpkg/status
+   Installed: 2020.0.166-1
+   Candidate: 2020.0.166-1
+   Version table:
+  *** 2020.0.166-1 500
+         500 http://archive.ubuntu.com/ubuntu focal/multiverse amd64 Packages
+         100 /var/lib/dpkg/status

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https://bugs.launchpad.net/bugs/1890984

Title:
  Octave gives wrong results when diagonalizing large matrices with MKL

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