16-May-2025 09:56:10 toms923_test() MATLAB/Octave version 6.4.0 Test toms923(). test_pfaffian Compute the Pfaffian of a test matrix using different methods Pfaffian from LTL decomposition: ans = -0.1223 Pfaffian from Householder tridiagonalization: ans = -0.1223 Pfaffian from Hessenberg decomposition: ans = -0.1223 All of the results above should be the same ------------------------------------------- Compare square of Pfaffian to determinant Pfaffian squared: ans = 0.014966 Determinant: ans = 0.014966 Should again be identical ------------------------- Compute the various decompositions Error of A(P,P)-L*T*transpose(L): ans = 2.2218e-14 The error should be small (<1e-14) Error of A-Q*T*transpose(Q): ans = 8.1871e-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 = 0.4498 - 0.2821i Pfaffian from Householder tridiagonalization: ans = 0.4498 - 0.2821i All of the results above should be the same ------------------------------------------- Compare square of Pfaffian to determinant Pfaffian squared: ans = 0.1228 - 0.2538i Determinant: ans = 0.1228 - 0.2538i Should again be identical ------------------------- Compute the various decompositions Error of A(P,P)-L*T*transpose(L): ans = 1.0890e-15 The error should be small (<1e-14) Error of A-Q*T*transpose(Q): ans = 1.6544e-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 = 0.1283 Pfaffian from Householder tridiagonalization: ans = 0.1283 Pfaffian from Hessenberg decomposition: ans = 0.1283 All of the results above should be the same ------------------------------------------- Compare square of Pfaffian to determinant Pfaffian squared: ans = 0.016461 Determinant: ans = 0.016461 Should again be identical ------------------------- Compute the various decompositions Error of A(P,P)-L*T*transpose(L): ans = 4.6532e-16 The error should be small (<1e-14) Error of A-Q*T*transpose(Q): ans = 7.9873e-16 The error should be small (<1e-14) ---------------------------------- toms923_test(): Normal end of execution. 16-May-2025 09:56:10