27-Jul-2022 16:29:37

toms923_test()
  MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2
  Test toms923().

test_pfaffian
Compute the Pfaffian of a test matrix using different methods
Pfaffian from LTL decomposition:

ans =

    0.2158

Pfaffian from Householder tridiagonalization:

ans =

    0.2158

Pfaffian from Hessenberg decomposition:

ans =

    0.2158

All of the results above should be the same
-------------------------------------------
Compare square of Pfaffian to determinant
Pfaffian squared: 

ans =

    0.0466

Determinant: 

ans =

    0.0466

Should again be identical
-------------------------
Compute the various decompositions
Error of A(P,P)-L*T*transpose(L):

ans =

   4.7063e-15

The error should be small (<1e-14)
Error of A-Q*T*transpose(Q):

ans =

   7.7677e-16

The error should be small (<1e-14)
----------------------------------

test_pfaffian_complex():
Compute the Pfaffian of a test matrix using different methods
Pfaffian from LTL decomposition:

ans =

  -0.3317 + 0.6483i

Pfaffian from Householder tridiagonalization:

ans =

  -0.3317 + 0.6483i

All of the results above should be the same
-------------------------------------------
Compare square of Pfaffian to determinant
Pfaffian squared: 

ans =

  -0.3103 - 0.4300i

Determinant: 

ans =

  -0.3103 - 0.4300i

Should again be identical
-------------------------
Compute the various decompositions
Error of A(P,P)-L*T*transpose(L):

ans =

   6.9104e-16

The error should be small (<1e-14)
Error of A-Q*T*transpose(Q):

ans =

   2.0379e-15

The error should be small (<1e-14)
----------------------------------

test_pfaffian_real():
Compute the Pfaffian of a test matrix using different methods
Pfaffian from LTL decomposition:

ans =

   -0.1850

Pfaffian from Householder tridiagonalization:

ans =

   -0.1850

Pfaffian from Hessenberg decomposition:

ans =

   -0.1850

All of the results above should be the same
-------------------------------------------
Compare square of Pfaffian to determinant
Pfaffian squared: 

ans =

    0.0342

Determinant: 

ans =

    0.0342

Should again be identical
-------------------------
Compute the various decompositions
Error of A(P,P)-L*T*transpose(L):

ans =

   9.7525e-16

The error should be small (<1e-14)
Error of A-Q*T*transpose(Q):

ans =

   8.7369e-16

The error should be small (<1e-14)
----------------------------------

toms923_test():
  Normal end of execution.

27-Jul-2022 16:29:38