07-Jan-2022 23:02:09 matrix_analyze_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 2 Test matrix_analyze(). R8MAT_ANALYZE: Report properties of a matrix. Matrix title: "DIF2 Cyclic" Matrix dimensions (4,4) DIF2 Cyclic Col: 1 2 3 4 Row 1 : 2 -1 0 -1 2 : -1 2 -1 0 3 : 0 -1 2 -1 4 : -1 0 -1 2 Property Value Yes/No Error norm -------- ----- ------ ---------- Adjacency No Anticirculant No Antipersymmetric error 9.8 Antisymmetric error 5.7 Lower bandwidth 3 Upper bandwidth 3 Centrosymmetric Yes Circulant Yes Cyclic tridiagonal Yes Diagonal 0.71 Diagonally dominant Yes Diagonally dominant column Yes Diagonally dominant row Yes Hankel No Identity error 3.5 Integer error 0 Irreducible Yes L No [Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.850372e-17.] [> In r8mat_is_m (line 64) In r8mat_analyze (line 153) In matrix_analyze_test (line 31) In run (line 91) ] M Yes Negative No Normal error 0 Orthogonal error 16 Orthogonal column error 16 Orthogonal row error 16 Permutation No Persymmetric error 0 Positive No Property A Yes Row Echelon Form No Constant antidiagonal values No Constant column values No Constant diagonal values Yes Constant row values No Sparse 0.75 SPD Yes Square Yes Stochastic error 12 Constant column sum Yes Sum magic error 8.9 Sum weak magic error 0 Constant row sum Yes Symmetric error 0 Toeplitz Yes Tournament error 5.8 Transition error Inf Triangular lower No Triangular lower unit No Triangular upper No Triangular upper unit No Unit columns error 2.9 Unit row error 2.9 Zero/One No R8MAT_ANALYZE: Report properties of a matrix. Matrix title: "EXCHANGE" Matrix dimensions (5,4) EXCHANGE Col: 1 2 3 4 Row 1 : 0 0 0 1 2 : 0 0 1 0 3 : 0 1 0 0 4 : 1 0 0 0 5 : 0 0 0 0 Property Value Yes/No Error norm -------- ----- ------ ---------- Adjacency No Anticirculant No value = Inf Antipersymmetric error Inf Antisymmetric error Inf Lower bandwidth 3 Upper bandwidth 3 Centrosymmetric Yes Circulant No Cyclic tridiagonal No Diagonal 0.5 Diagonally dominant No Diagonally dominant column No Diagonally dominant row No Hankel Yes Identity error 2.8 Integer error 0 Irreducible No L No M No Negative No Normal error Inf Orthogonal error Inf Orthogonal column error 0 Orthogonal row error 1 Permutation No Persymmetric error Inf Positive Yes Property A Yes Row Echelon Form No Constant antidiagonal values Yes Constant column values No Constant diagonal values No Constant row values No Sparse 0.2 SPD No Square No Stochastic error 1 Constant column sum Yes Sum magic error 4.5 Sum weak magic error 3.5 Constant row sum No Symmetric error Inf Toeplitz No Tournament error 3.5 Transition error Inf Triangular lower No Triangular lower unit No Triangular upper No Triangular upper unit No Unit columns error 0 Unit row error 1 Zero/One Yes R8MAT_ANALYZE: Report properties of a matrix. Matrix title: "Identity" Matrix dimensions (4,4) Identity Col: 1 2 3 4 Row 1 : 1 0 0 0 2 : 0 1 0 0 3 : 0 0 1 0 4 : 0 0 0 1 Property Value Yes/No Error norm -------- ----- ------ ---------- Adjacency Yes Anticirculant No Antipersymmetric error 4 Antisymmetric error 2 Lower bandwidth 0 Upper bandwidth 0 Centrosymmetric Yes Circulant Yes Cyclic tridiagonal Yes Diagonal 0.14 Diagonally dominant Yes Diagonally dominant column Yes Diagonally dominant row Yes Hankel No Identity error 0 Integer error 0 Irreducible No L No M Yes Negative No Normal error 0 Orthogonal error 0 Orthogonal column error 0 Orthogonal row error 0 Permutation Yes Persymmetric error 0 Positive Yes Property A Yes Row Echelon Form Yes Constant antidiagonal values No Constant column values No Constant diagonal values Yes Constant row values No Sparse 0.25 SPD Yes Square Yes Stochastic error 0 Constant column sum Yes Sum magic error 4 Sum weak magic error 2.8 Constant row sum Yes Symmetric error 0 Toeplitz Yes Tournament error 3.2 Transition error 0 Triangular lower Yes Triangular lower unit Yes Triangular upper Yes Triangular upper unit Yes Unit columns error 0 Unit row error 0 Zero/One Yes R8MAT_ANALYZE: Report properties of a matrix. Matrix title: "RIS" Matrix dimensions (4,4) RIS Col: 1 2 3 4 Row 1 : 0.142857 0.2 0.333333 1 2 : 0.2 0.333333 1 -1 3 : 0.333333 1 -1 -0.333333 4 : 1 -1 -0.333333 -0.2 Property Value Yes/No Error norm -------- ----- ------ ---------- Adjacency No Anticirculant No Antipersymmetric error 4.3 Antisymmetric error 3.8 Lower bandwidth 3 Upper bandwidth 3 Centrosymmetric No Circulant No Cyclic tridiagonal No Diagonal 1 Diagonally dominant No Diagonally dominant column No Diagonally dominant row No Hankel Yes Identity error 3.6 Integer error 0.83 Irreducible Yes L No M No Negative No Normal error 0 Orthogonal error 2.4 Orthogonal column error 2.4 Orthogonal row error 2.4 Permutation No Persymmetric error 3.5 Positive No Property A No Row Echelon Form No Constant antidiagonal values Yes Constant column values No Constant diagonal values No Constant row values No Sparse 1 SPD Yes Square Yes Stochastic error 7.5 Constant column sum No Sum magic error 4.8 Sum weak magic error 3.4 Constant row sum No Symmetric error 0 Toeplitz No Tournament error 4 Transition error Inf Triangular lower No Triangular lower unit No Triangular upper No Triangular upper unit No Unit columns error 0.83 Unit row error 0.83 Zero/One No R8MAT_ANALYZE: Report properties of a matrix. Matrix title: "Chebyshev T Inverse" Matrix dimensions (4,4) Chebyshev T Inverse Col: 1 2 3 4 Row 1 : 1 0 0 0 2 : 0 1 0 0 3 : 0.5 0 0.5 0 4 : 0 0.75 0 0.25 Property Value Yes/No Error norm -------- ----- ------ ---------- Adjacency No Anticirculant No Antipersymmetric error 3.3 Antisymmetric error 1.8 Lower bandwidth 2 Upper bandwidth 0 Centrosymmetric No Circulant No Cyclic tridiagonal No Diagonal 0.29 Diagonally dominant No Diagonally dominant column Yes Diagonally dominant row No Hankel No Identity error 1.3 Integer error 0.79 Irreducible No L No M No Negative No Normal error 1.2 Orthogonal error 1.4 Orthogonal column error 1.4 Orthogonal row error 1.4 Permutation No Persymmetric error 1.3 Positive Yes Property A Yes Row Echelon Form No Constant antidiagonal values No Constant column values No Constant diagonal values No Constant row values No Sparse 0.38 SPD No Square Yes Stochastic error 0 Constant column sum No Sum magic error 3.8 Sum weak magic error 3.1 Constant row sum Yes Symmetric error 1.3 Toeplitz No Tournament error 3 Transition error 1.3 Triangular lower Yes Triangular lower unit No Triangular upper No Triangular upper unit No Unit columns error 0.94 Unit row error 0.36 Zero/One No matrix_analyze_test(): Normal end of execution. 07-Jan-2022 23:02:09