20 February 2018 8:09:43.810 AM TEST_MAT_TEST FORTRAN90 version Test the TEST_MAT library. BVEC_NEXT_GRLEX_TEST BVEC_NEXT_GRLEX computes binary vectors in GRLEX order. 0: 0000 1: 0001 2: 0010 3: 0100 4: 1000 5: 0011 6: 0101 7: 0110 8: 1001 9: 1010 10: 1100 11: 0111 12: 1011 13: 1101 14: 1110 15: 1111 16: 0000 LEGENDRE_ZEROS_TEST: LEGENDRE_ZEROS computes the zeros of the N-th Legendre polynomial. Legendre zeros 1 0.00000 Legendre zeros 1 -0.577350 2 0.577350 Legendre zeros 1 -0.774597 2 0.00000 3 0.774597 Legendre zeros 1 -0.861136 2 -0.339981 3 0.339981 4 0.861136 Legendre zeros 1 -0.906180 2 -0.538469 3 0.00000 4 0.538469 5 0.906180 Legendre zeros 1 -0.932470 2 -0.661209 3 -0.238619 4 0.238619 5 0.661209 6 0.932470 Legendre zeros 1 -0.949108 2 -0.741531 3 -0.405845 4 0.00000 5 0.405845 6 0.741531 7 0.949108 MERTENS_TEST MERTENS computes the Mertens function. N Exact MERTENS(N) 1 1 1 2 0 0 3 -1 -1 4 -1 -1 5 -2 -2 6 -1 -1 7 -2 -2 8 -2 -2 9 -2 -2 10 -1 -1 11 -2 -2 12 -2 -2 100 1 1 1000 2 2 10000 -23 -23 MOEBIUS_TEST MOEBIUS computes the Moebius function. N Exact MOEBIUS(N) 1 1 1 2 -1 -1 3 -1 -1 4 0 0 5 -1 -1 6 1 1 7 -1 -1 8 0 0 9 0 0 10 1 1 11 -1 -1 12 0 0 13 -1 -1 14 1 1 15 1 1 16 0 0 17 -1 -1 18 0 0 19 -1 -1 20 0 0 R8MAT_IS_EIGEN_LEFT_TEST: R8MAT_IS_EIGEN_LEFT tests the error in the left eigensystem A' * X - X * LAMBDA = 0 Matrix A: Col 1 2 3 4 Row 1 0.136719 0.605469 0.253906 0.390625E-02 2 0.585938E-01 0.527344 0.394531 0.195312E-01 3 0.195312E-01 0.394531 0.527344 0.585938E-01 4 0.390625E-02 0.253906 0.605469 0.136719 Eigenmatrix X: Col 1 2 3 4 Row 1 1. 1. 1. 1. 2 11. 3. -1. -3. 3 11. -3. -1. 3. 4 1. -1. 1. -1. Eigenvalues LAM: 1 1.00000 2 0.250000 3 0.625000E-01 4 0.156250E-01 Frobenius norm of A'*X-X*LAMBDA is 9.40908 R8MAT_IS_EIGEN_LEFT_TEST Normal end of execution. R8MAT_IS_EIGEN_RIGHT_TEST: R8MAT_IS_EIGEN_RIGHT tests the error in the right eigensystem A * X - X * LAMBDA = 0 Matrix A: Col 1 2 3 4 Row 1 0.136719 0.605469 0.253906 0.390625E-02 2 0.585938E-01 0.527344 0.394531 0.195312E-01 3 0.195312E-01 0.394531 0.527344 0.585938E-01 4 0.390625E-02 0.253906 0.605469 0.136719 Eigenmatrix X: Col 1 2 3 4 Row 1 1. 6. 11. 6. 2 1. 2. -1. -2. 3 1. -2. -1. 2. 4 1. -6. 11. -6. Eigenvalues LAM: 1 1.00000 2 0.250000 3 0.625000E-01 4 0.156250E-01 Frobenius norm of A*X-X*LAMBDA is 0.00000 R8MAT_IS_EIGEN_RIGHT_TEST Normal end of execution. R8MAT_IS_LLT_TEST: R8MAT_IS_LLT tests the error in a lower triangular Cholesky factorization A = L * L' by looking at A - L * L' Matrix A: Col 1 2 3 4 Row 1 2. 1. 0. 0. 2 1. 2. 1. 0. 3 0. 1. 2. 1. 4 0. 0. 1. 2. Factor L: Col 1 2 3 4 Row 1 1.41421 0. 0. 0. 2 0.707107 1.22474 0. 0. 3 0. 0.816497 1.15470 0. 4 0. 0. 0.866025 1.11803 Frobenius norm of A-L*L' is 0.218689E-14 R8MAT_IS_LLT_TEST Normal end of execution. R8MAT_IS_NULL_LEFT_TEST: R8MAT_IS_NULL_LEFT tests whether the M vector X is a left null vector of A, that is, x'*A=0. Matrix A: Col 1 2 3 Row 1 1. 2. 3. 2 4. 5. 6. 3 7. 8. 9. Vector X: 1 1.00000 2 -2.00000 3 1.00000 Frobenius norm of X'*A is 0.00000 R8MAT_IS_NULL_RIGHT_TEST: R8MAT_IS_NULL_RIGHT tests whether the N vector X is a right null vector of A, that is, A*X=0. Matrix A: Col 1 2 3 Row 1 1. 2. 3. 2 4. 5. 6. 3 7. 8. 9. Vector X: 1 1.00000 2 -2.00000 3 1.00000 Frobenius norm of A*X is 0.00000 R8MAT_IS_SOLUTION_TEST: R8MAT_IS_SOLUTION tests whether X is the solution of A*X=B by computing the Frobenius norm of the residual. A is 3 by 10 X is 10 by 9 B is 3 by 9 Frobenius error in A*X-B is 0.00000 R8MAT_NORM_FRO_TEST R8MAT_NORM_FRO computes a Frobenius norm of an R8MAT. A: Col 1 2 3 4 Row 1 1. 2. 3. 4. 2 5. 6. 7. 8. 3 9. 10. 11. 12. 4 13. 14. 15. 16. 5 17. 18. 19. 20. Expected norm = 53.5724 Computed norm = 53.5724 TEST_ANALYZE Analyze a matrix. A123 Not (unit) upper triangular Not (unit) lower triangular No band matrix structure detected. Cyclic tridiagonal. Diagonality = 0.247033-322 Relative sparseness = 0.00000 Irreducible. Not property A. Not a permutation matrix Not symmetric Not antisymmetric Not a Tournament matrix Not a transition matrix Not persymmetric Not antipersymmetric Not centrosymmetric Not positive (semi)-definite symmetric Not circulant Not anticirculant Positive Not negative or nonpositive Not (strictly) row diagonally dominant. Not (strictly) column diagonally dominant. Matrix rows do not have unit Euclidean norm. Matrix columns do not all have unit Euclidean norm. Not row orthogonal Not column orthogonal Not orthogonal Integer matrix. Not a zero/one matrix Not row scalar Not column scalar Not diagonal scalar Not antidiagonal scalar (Hankel) Row sum is not constant Column sum is not constant Not magic, stochastic or biMarkov Not an adjacency matrix. Not (reduced) row echelon form Not normal. Not an M matrix Spectral norm = 16.1168 L1 norm = 18.0000 L2 norm = 16.8481 Loo norm = 24.0000 Frobenius norm = 16.8819 EISPACK norm = 45.0000 TEST_CONDITION Compute the L1 condition number of an example of each test matrix Title N COND COND AEGERTER 5 24.0000 24.0000 BAB 5 8.46751 8.46751 BAUER 6 0.852877E+07 0.852877E+07 BIS 5 42.9756 42.9756 BIW 5 59.9171 59.9171 BODEWIG 4 10.4366 10.4366 BOOTHROYD 5 0.100200E+07 0.100200E+07 COMBIN 5 11.9644 11.9644 COMPANION 5 14.5786 14.5786 CONEX1 4 68.0622 68.0622 CONEX2 3 17.7034 17.7034 CONEX3 5 80.0000 80.0000 CONEX4 4 4488.00 4488.00 DAUB2 4 2.00000 2.00000 DAUB4 8 2.79904 2.79904 DAUB6 12 3.44146 3.44146 DAUB8 16 3.47989 3.47989 DAUB10 20 4.00375 4.00375 DAUB12 24 4.80309 4.80309 DIAGONAL 5 7.39629 7.39629 DIF2 5 18.0000 18.0000 DOWNSHIFT 5 1.00000 1.00000 EXCHANGE 5 1.00000 1.00000 FIBONACCI2 5 15.0000 15.0000 GFPP 5 12.2633 12.2633 GIVENS 5 50.0000 50.0000 HANKEL_N 5 5.83680 5.83680 HARMAN 8 77.0690 77.0690 HARTLEY 5 5.00000 5.00000 IDENTITY 5 1.00000 1.00000 ILL3 3 216775. 216775. JORDAN 5 2.08956 2.08956 KERSHAW 4 49.0000 49.0000 LIETZKE 5 38.0000 38.0000 MAXIJ 5 100.000 100.000 MINIJ 5 60.0000 60.0000 ORTH_SYMM 5 4.39765 4.39765 OTO 5 18.0000 18.0000 PASCAL1 5 100.000 100.000 PASCAL3 5 14333.5 14333.5 PEI 5 4.90227 4.90227 RODMAN 5 5.85900 5.85900 RUTIS1 4 15.0000 15.0000 RUTIS2 4 11.4400 11.4400 RUTIS3 4 6.00000 6.00000 RUTIS5 4 62608.0 62608.0 SUMMATION 5 10.0000 10.0000 SWEET1 6 16.9669 16.9669 SWEET2 6 49.2227 49.2227 SWEET3 6 24.7785 24.7785 SWEET4 13 51.1709 51.1709 TRI_UPPER 5 2599.90 2599.90 UPSHIFT 5 1.00000 1.00000 WILK03 3 0.260000E+11 0.260000E+11 WILK04 4 0.245892E+17 0.285325E+17 WILK05 5 0.793703E+07 0.793703E+07 WILSON 4 4488.00 4488.00 TEST_DETERMINANT Compute the determinants of an example of each test matrix. Compare with the determinant routine, if available. Print the matrix Frobenius norm for an estimate of magnitude. Title N Determ Determ ||A|| A123 3 0.00000 0.666134E-15 16.8819 AEGERTER 5 -25.0000 -25.0000 9.43398 ANTICIRCULANT 3 -235.484 -235.484 10.9008 ANTICIRCULANT 4 1407.78 1407.78 12.6475 ANTICIRCULANT 5 7148.67 7148.67 14.2666 ANTIHADAMARD 5 1.00000 1.00000 3.31662 ANTISYMM_RANDOM 5 0.00000 2.87369 ANTISYMM_RANDOM 6 0.973530E-01 3.33451 BAB 5 -1980.11 -1980.11 14.3605 BAUER 6 1.00000 1.00000 185.855 BERNSTEIN 5 96.0000 96.0000 25.2784 BIMARKOV_RANDOM 5 -0.862803E-04 1.38793 BIS 5 -177.020 -177.020 11.0876 BIW 5 0.547223E-01 0.547223E-01 2.36051 BODEWIG 4 568.000 568.000 12.7279 BOOTHROYD 5 1.00000 1.00000 886.710 BORDERBAND 5 -0.328125 -0.328125 2.76699 CARRY 5 0.165382E-07 0.165382E-07 1.41391 CAUCHY 5 38.7671 38.7671 682.273 CHEBY_DIFF1 5 -0.213163E-13 13.4722 CHEBY_DIFF1 6 -0.511591E-12 20.7702 CHEBY_T 5 64.0000 64.0000 12.6886 CHEBY_U 5 1024.00 1024.00 22.4277 CHEBY_VAN1 5 18.0000 4.30116 CHEBY_VAN2 2 -2.00000 -2.00000 2.00000 CHEBY_VAN2 3 -1.41421 -1.41421 2.00000 CHEBY_VAN2 4 1.00000 1.00000 2.08167 CHEBY_VAN2 5 0.707107 0.707107 2.17945 CHEBY_VAN2 6 -0.500000 -0.500000 2.28035 CHEBY_VAN2 7 -0.353553 -0.353553 2.38048 CHEBY_VAN2 8 0.250000 0.250000 2.47848 CHEBY_VAN2 9 0.176777 0.176777 2.57391 CHEBY_VAN2 10 -0.125000 -0.125000 2.66667 CHEBY_VAN3 5 13.9754 13.9754 3.87298 CHOW 5 -70.5488 -70.5488 202.501 CIRCULANT 5 7148.67 7148.67 14.2666 CIRCULANT2 3 18.0000 18.0000 6.48074 CIRCULANT2 4 -160.000 -160.000 10.9545 CIRCULANT2 5 1875.00 1875.00 16.5831 CLEMENT1 5 0.00000 0.00000 6.32456 CLEMENT1 6 -225.000 -225.000 8.36660 CLEMENT2 5 0.00000 0.00000 8.97900 CLEMENT2 6 -178.154 -178.154 10.1600 COMBIN 5 1257.33 1257.33 20.7778 COMPANION 5 -2.81582 -2.81582 6.68633 COMPLEX_I 2 1.00000 1.00000 1.41421 CONEX1 4 -2.81582 -2.81582 8.12995 CONEX2 3 -0.355137 -0.355137 2.64876 CONEX3 5 -1.00000 -1.00000 3.87298 CONEX4 4 -1.00000 -1.00000 30.5450 CONFERENCE 6 -125.000 -125.000 5.47723 CREATION 5 0.00000 0.00000 5.47723 DAUB2 4 1.00000 1.00000 2.00000 DAUB4 8 -1.00000 -1.00000 2.82843 DAUB6 12 1.00000 1.00000 3.46410 DAUB8 16 -1.00000 -1.00000 4.00000 DAUB10 20 1.00000 1.00000 4.47214 DAUB12 24 -1.00000 -1.00000 4.89898 DIAGONAL 5 22.1228 22.1228 6.38020 DIF1 5 0.00000 0.00000 2.82843 DIF1 6 1.00000 1.00000 3.16228 DIF1CYCLIC 5 0.00000 0.00000 3.16228 DIF2 5 6.00000 6.00000 5.29150 DIF2CYCLIC 5 0.00000 0.00000 5.47723 DORR 5 -0.633817E+11 -0.633817E+11 533.003 DOWNSHIFT 5 1.00000 1.00000 2.23607 EBERLEIN 5 0.00000 -0.102318E-11 18.1002 EULERIAN 5 1.00000 1.00000 77.2981 EXCHANGE 5 1.00000 1.00000 2.23607 FIBONACCI1 5 0.00000 0.00000 95.3527 FIBONACCI2 5 -1.00000 -1.00000 3.00000 FIBONACCI3 5 8.00000 8.00000 3.60555 FIEDLER 7 1332.21 1332.21 30.1350 FORSYTHE 5 1975.68 1975.68 10.7723 FORSYTHE 6 9031.06 9031.06 11.7416 FOURIER_COSINE 5 1.00000 1.00000 2.23607 FOURIER_SINE 5 1.00000 1.00000 2.23607 FRANK 5 1.00000 1.00000 11.6190 GEAR 4 -0.244929E-15 -0.00000 2.82843 GEAR 5 2.00000 2.00000 3.16228 GEAR 6 -4.00000 -4.00000 3.46410 GEAR 7 2.00000 2.00000 3.74166 GEAR 8 0.489859E-15 0.00000 4.00000 GFPP 5 212.007 212.007 9.39618 GIVENS 5 16.0000 16.0000 20.6155 GK316 5 -25.0000 -25.0000 9.43398 GK323 5 32.0000 32.0000 10.0000 GK324 5 11.9530 11.9530 11.4577 GRCAR 5 8.00000 3.60555 HADAMARD 5 0.00000 4.00000 HANKEL 5 -2823.88 15.2126 HANKEL_N 5 3125.00 3125.00 15.0000 HANOWA 6 1803.10 1803.10 8.69327 HARMAN 8 0.954779E-03 0.954779E-03 5.05359 HARTLEY 5 55.9017 55.9017 5.00000 HARTLEY 6 -216.000 -216.000 6.00000 HARTLEY 7 -907.493 -907.493 7.00000 HARTLEY 8 -4096.00 -4096.00 8.00000 HELMERT 5 1.00000 1.00000 2.23607 HELMERT2 5 1.00000 2.23607 HERMITE 5 1024.00 1024.00 54.1941 HERNDON 5 -0.400000E-01 -0.400000E-01 1.77133 HILBERT 5 0.374930E-11 0.374930E-11 1.58091 HOUSEHOLDER 5 -1.00000 -1.00000 2.23607 IDEM_RANDOM 5 0.00000 0.00000 1.00000 IDENTITY 5 1.00000 1.00000 2.23607 IJFACT1 5 0.716636E+10 0.716636E+10 0.366559E+07 IJFACT2 5 0.149480E-20 0.149480E-20 0.557720 ILL3 3 6.00000 6.00000 817.763 INTEGRATION 6 1.00000 1.00000 4.19580 INVOL 5 -1.00000 -1.00000 1942.46 INVOL_RANDOM 5 -1.00000 2.23607 JACOBI 5 0.00000 0.00000 1.49071 JACOBI 6 -0.216450E-01 -0.216450E-01 1.65145 JORDAN 6 498.456 498.456 7.25072 KAHAN 5 -0.378564E-07 -0.378564E-07 0.715639 KERSHAW 4 1.00000 1.00000 8.24621 KERSHAWTRI 5 1.00000 553.995 8.73845 KMS 5 2304.83 2304.83 101.704 LAGUERRE 5 0.347222E-02 0.347222E-02 6.85376 LEGENDRE 5 16.4062 16.4062 6.80762 LEHMER 5 0.656250E-01 0.656250E-01 3.28041 LESLIE 4 0.605244 0.605244 1.78414 LESP 5 -42300.0 -42300.0 22.3487 LIETZKE 5 48.0000 48.0000 18.0278 LIGHTS_OUT 25 -0.325405E-29 10.2470 LINE_ADJ 5 0.00000 0.00000 2.82843 LINE_ADJ 6 -1.00000 -1.00000 3.16228 LINE_LOOP_ADJ 5 0.00000 -0.00000 3.60555 LOEWNER 5 -29.0825 20.5227 LOTKIN 5 0.187465E-10 0.187465E-10 2.45676 MARKOV_RANDOM 5 0.488558E-02 1.33584 MAXIJ 5 5.00000 5.00000 19.8746 MILNES 5 11.9530 11.9530 11.4577 MINIJ 5 1.00000 1.00000 12.4499 MOLER1 5 1.00000 1.00000 61.8850 MOLER2 5 0.00000 0.102538E-06 101035. MOLER3 5 1.00000 1.00000 8.66025 MOLER4 4 1.00000 1.00000 2.82843 NEUMANN 25 0.00000 0.124631E-02 23.2379 ONE 5 0.00000 -0.00000 5.00000 ORTEGA 5 -16.5253 -16.5253 244.268 ORTH_RANDOM 5 1.00000 1.00000 2.23607 ORTH_SYMM 5 1.00000 1.00000 2.23607 OTO 5 6.00000 6.00000 5.29150 PARTER 5 131.917 131.917 6.34077 PASCAL1 5 1.00000 1.00000 9.94987 PASCAL2 5 1.00000 1.00000 92.4608 PASCAL3 5 1.00000 1.00000 124.742 PDS_RANDOM 5 0.909674E-05 0.404187E-01 1.46230 PEI 5 137.311 137.311 6.04036 PERMUTATION_RANDOM 5 -1.00000 1.00000 2.23607 PLU 5 0.193261E+08 0.193261E+08 152.462 POISSON 25 0.325655E+14 0.325655E+14 21.9089 PROLATE 5 -5651.77 12.5984 RECTANGLE_ADJ 25 0.00000 0.00000 8.94427 REDHEFFER 5 -2.00000 -2.00000 3.74166 REF_RANDOM 5 0.00000 0.00000 2.63560 REF_RANDOM 5 0.00000 1.00000 2.81894 RIEMANN 5 96.0000 8.83176 RING_ADJ 1 1.00000 1.00000 1.00000 RING_ADJ 2 -1.00000 -1.00000 1.41421 RING_ADJ 3 2.00000 2.00000 2.44949 RING_ADJ 4 0.00000 0.00000 2.82843 RING_ADJ 5 2.00000 2.00000 3.16228 RING_ADJ 6 -4.00000 -4.00000 3.46410 RING_ADJ 7 2.00000 2.00000 3.74166 RING_ADJ 8 0.00000 0.00000 4.00000 RIS 5 4.12239 4.12239 3.17039 RODMAN 5 -2175.88 -2175.88 12.7897 ROSSER1 8 0.00000 -9480.58 2482.26 ROUTH 5 7.85813 7.85813 5.15491 RUTIS1 4 -375.000 -375.000 16.6132 RUTIS2 4 100.000 100.000 11.4018 RUTIS3 4 624.000 624.000 14.1421 RUTIS4 5 216.000 216.000 59.1270 RUTIS5 4 1.00000 1.00000 23.7697 SCHUR_BLOCK 5 589.771 589.771 8.39978 SKEW_CIRCULANT 5 -10310.4 -10310.4 14.2666 SPLINE 5 -2566.72 -2566.72 20.8244 STIRLING 5 1.00000 1.00000 67.9191 STRIPE 5 2112.00 14.8324 SUMMATION 5 1.00000 1.00000 3.87298 SWEET1 6 -0.204682E+08 -0.204682E+08 70.1997 SWEET2 6 9562.52 9562.52 30.1433 SWEET3 6 -0.540561E+08 -0.540561E+08 73.4234 SWEET4 13 -0.646348E+17 -0.646348E+17 119.704 SYLVESTER 5 -89.6985 13.0548 SYLVESTER_KAC 5 0.00000 0.00000 7.74597 SYLVESTER_KAC 6 -225.000 -225.000 10.4881 SYMM_RANDOM 5 22.1228 22.1228 6.38020 TOEPLITZ 5 -2823.88 15.2126 TOEPLITZ_5DIAG 5 -747.438 12.8468 TOEPLITZ_5S 25 -0.151735E+18 40.3981 TOEPLITZ_PDS 5 0.849362E-01 3.41573 TOURNAMENT_RANDOM 5 0.00000 0.00000 4.47214 TRANSITION_RANDOM 5 0.736983E-04 1.10947 TRENCH 5 -37.7411 7.03032 TRI_UPPER 5 1.00000 1.00000 9.18086 TRIS 5 6683.42 6683.42 13.3888 TRIV 5 -700.369 -700.369 11.1204 TRIW 5 1.00000 1.00000 9.39629 UPSHIFT 5 1.00000 1.00000 2.23607 VAND1 5 133985. 133985. 466.164 VAND2 5 133985. 133985. 466.164 WATHEN 96 0.161186+269 29132.8 WILK03 3 0.900000E-20 0.900000E-20 1.39284 WILK04 4 0.442923E-16 0.442923E-16 1.89545 WILK05 5 0.379950E-14 0.379947E-14 1.51485 WILK12 12 1.00000 1.00000 53.5910 WILK20 20 0.147630E+26 102.362 WILK21 21 -0.415825E+13 -0.415825E+13 28.4605 WILSON 4 1.00000 1.00000 30.5450 ZERO 5 0.00000 0.00000 0.00000 ZIELKE 5 469.417 13.6953 TEST_EIGEN_LEFT Compute the Frobenius norm of the eigenvalue error: X * A - LAMBDA * X given K left eigenvectors X and eigenvalues LAMBDA. Title N K ||A|| ||X*A-LAMBDA*X|| A123 3 3 16.8819 0.123246E-13 CARRY 5 5 1.41391 0.357943E-14 CHOW 5 5 202.501 0.459018E-12 DIAGONAL 5 5 6.38020 0.00000 ROSSER1 8 8 2482.26 0.261994E-10 SYMM_RANDOM 5 5 6.38020 0.257279E-14 TEST_EIGEN_RIGHT Compute the Frobenius norm of the eigenvalue error: A * X - X * LAMBDA given K right eigenvectors X and eigenvalues LAMBDA. Title N K ||A|| ||A*X-X*Lambda|| A123 3 3 16.8819 0.133427E-13 BAB 5 5 14.3605 0.436701E-14 BODEWIG 4 4 12.7279 0.917346E-14 CARRY 5 5 1.41391 0.117642E-14 CHOW 5 5 202.501 0.252688E-12 COMBIN 5 5 20.7778 0.710543E-14 DIF2 5 5 5.29150 0.107099E-14 EXCHANGE 5 5 2.23607 0.00000 IDEM_RANDOM 5 5 1.73205 0.721290E-15 IDENTITY 5 5 2.23607 0.00000 ILL3 3 3 817.763 0.162356E-10 KERSHAW 4 4 8.24621 0.480549E-14 KMS 5 5 2.32288 0.320550E-07 LINE_ADJ 5 5 2.82843 0.899223E-15 LINE_LOOP_ADJ 5 5 3.60555 0.999459E-15 ONE 5 5 5.00000 0.00000 ORTEGA 5 5 244.268 0.345197E-12 OTO 5 5 5.29150 0.107099E-14 PDS_RANDOM 5 5 1.46230 0.974594 PEI 5 5 6.04036 0.00000 RODMAN 5 5 12.7897 0.00000 ROSSER1 8 8 2482.26 0.261994E-10 RUTIS1 4 4 16.6132 0.00000 RUTIS2 4 4 11.4018 0.00000 RUTIS5 4 4 23.7697 0.146286E-13 SYLVESTER_KAC 5 5 7.74597 0.00000 SYMM_RANDOM 5 5 6.38020 0.249712E-14 WILK12 12 12 53.5910 0.387684E-12 WILSON 4 4 30.5450 0.248731E-13 ZERO 5 5 0.00000 0.00000 TEST_INVERSE A = a test matrix of order N. B = inverse as computed by a routine. C = inverse as computed by R8MAT_INVERSE. ||A|| = Frobenius norm of A. ||C|| = Frobenius norm of C. ||I-AC|| = Frobenius norm of I-A*C. ||I-AB|| = Frobenius norm of I-A*B. Title N ||A|| ||C|| ||I-AC|| ||I-AB|| AEGERTER 5 9.4 1.8 0.71E-15 0.71E-15 BAB 5 14. 0.72 0.96E-15 0.95E-15 BAUER 6 0.19E+03 0.21E+05 0.88E-10 0.0 BERNSTEIN 5 25. 3.2 0.0 0.0 BIS 5 11. 3.9 0.89E-15 0.89E-15 BIW 5 2.4 26. 0.39E-14 0.10E-14 BODEWIG 4 13. 0.68 0.87E-15 0.71E-15 BOOTHROYD 5 0.89E+03 0.89E+03 0.51E-10 0.0 BORDERBAND 5 2.8 6.8 0.0 0.0 CARRY 5 1.4 0.31E+04 0.24E-12 0.12E-12 CAUCHY 5 0.68E+03 61. 0.18E-12 0.94E-13 CHEBY_T 5 13. 1.9 0.0 0.0 CHEBY_U 5 22. 1.2 0.0 0.0 CHEBY_VAN2 5 2.2 2.5 0.47E-15 0.59E-15 CHEBY_VAN3 5 3.9 1.3 0.89E-15 0.75E-15 CHOW 5 0.20E+03 0.27E+03 0.33E-12 0.17E-12 CIRCULANT 5 14. 0.41 0.85E-15 0.78E-15 CIRCULANT2 5 17. 0.64 0.11E-14 0.15E-14 CLEMENT1 6 8.4 1.5 0.65E-15 0.0 CLEMENT2 6 10. 2.7 0.51E-15 0.11E-14 COMBIN 5 21. 0.71 0.12E-14 0.11E-14 COMPANION 5 6.7 2.9 0.73E-15 0.17E-15 COMPLEX_I 2 1.4 1.4 0.0 0.0 CONEX1 4 8.1 6.4 0.0 0.0 CONEX2 3 2.6 4.3 0.0 0.0 CONEX3 5 3.9 11. 0.0 0.0 CONEX4 4 31. 99. 0.61E-12 0.0 CONFERENCE 6 5.5 1.1 0.74E-15 0.0 DAUB2 4 2.0 2.0 0.0 0.89E-15 DAUB4 8 2.8 2.8 0.40E-15 0.21E-14 DAUB6 12 3.5 3.5 0.11E-14 0.14E-14 DAUB8 16 4.0 4.0 0.18E-14 0.46E-14 DAUB10 20 4.5 4.5 0.17E-14 0.87E-14 DAUB12 24 4.9 4.9 0.22E-14 0.20E-13 DIAGONAL 5 6.4 2.1 0.0 0.0 DIF1 6 3.2 3.5 0.0 0.0 DIF2 5 5.3 3.9 0.11E-14 0.69E-15 DORR 5 0.53E+03 0.38E-01 0.19E-14 0.16E-14 DOWNSHIFT 5 2.2 2.2 0.0 0.0 EULERIAN 5 77. 0.78E+03 0.25E-12 0.0 EXCHANGE 5 2.2 2.2 0.0 0.0 FIBONACCI2 5 3.0 3.5 0.0 0.0 FIBONACCI3 5 3.6 1.6 0.16E-15 0.0 FIEDLER 7 30. 3.3 0.22E-13 0.44E-14 FORSYTHE 5 11. 0.52 0.23E-15 0.61E-16 FOURIER_COSINE 5 2.2 2.2 0.11E-14 0.10E-14 FOURIER_SINE 5 2.2 2.2 0.75E-15 0.18E-14 FRANK 5 12. 59. 0.35E-13 0.0 GFPP 5 9.4 1.0 0.33E-15 0.22E-13 GIVENS 5 21. 2.7 0.0 0.0 GK316 5 9.4 1.8 0.71E-15 0.71E-15 GK323 5 10. 2.3 0.0 0.0 GK324 5 11. 5.6 0.24E-14 0.13E-14 HANKEL_N 5 15. 0.55 0.69E-15 0.0 HANOWA 6 8.7 0.71 0.57E-15 0.65E-15 HARMAN 8 5.1 15. 0.71E-14 0.95E-06 HARTLEY 5 5.0 1.0 0.90E-15 0.28E-14 HELMERT 5 2.2 2.2 0.51E-15 0.74E-15 HELMERT2 5 2.2 2.2 0.65E-15 0.65E-15 HERMITE 5 54. 1.8 0.0 0.0 HERNDON 5 1.8 9.4 0.18E-14 0.71E-15 HILBERT 5 1.6 0.30E+06 0.20E-10 0.73E-11 HOUSEHOLDER 5 2.2 2.2 0.11E-14 0.10E-14 IDENTITY 5 2.2 2.2 0.0 0.0 ILL3 3 0.82E+03 0.34E+03 0.16E-10 0.47E-10 INTEGRATION 5 4.0 7.5 0.0 0.76E-15 INVOL 5 0.19E+04 0.19E+04 0.84E-10 0.73E-11 JACOBI 6 1.7 6.5 0.74E-15 0.0 JORDAN 5 6.6 0.84 0.22E-15 0.22E-15 KAHAN 5 0.72 0.43E+03 0.75E-15 0.42E-14 KERSHAW 4 8.2 8.2 0.44E-14 0.0 KERSHAWTRI 5 8.7 0.69 0.37E-15 0.48E-15 KMS 5 0.10E+03 2.5 0.22E-13 0.19E-13 LAGUERRE 5 6.9 0.20E+03 0.17E-13 0.0 LEGENDRE 5 6.8 1.9 0.25E-15 0.27E-15 LEHMER 5 3.3 7.7 0.22E-14 0.14E-14 LESP 5 22. 0.32 0.42E-15 0.76E-15 LIETZKE 5 18. 2.4 0.49E-14 0.70E-15 LINE_ADJ 6 3.2 3.5 0.0 0.0 LOTKIN 5 2.5 0.24E+06 0.29E-10 0.0 MAXIJ 5 20. 4.7 0.14E-14 0.0 MILNES 5 11. 5.6 0.24E-14 0.13E-14 MINIJ 5 12. 5.0 0.0 0.0 MOLER1 5 62. 0.28E+05 0.51E-10 0.39E-10 MOLER3 5 8.7 0.12E+03 0.0 0.0 ORTEGA 5 0.24E+03 91. 0.13E-11 0.31E-11 ORTH_SYMM 5 2.2 2.2 0.12E-14 0.22E-14 OTO 5 5.3 3.9 0.11E-14 0.69E-15 PARTER 5 6.3 0.94 0.75E-15 0.70E-16 PASCAL1 5 9.9 9.9 0.0 0.0 PASCAL2 5 92. 92. 0.0 0.0 PASCAL3 5 0.12E+03 0.12E+03 0.33E-12 0.57E-13 PDS_RANDOM 5 1.5 5.7 0.95E-15 0.16E+03 PEI 5 6.0 0.85 0.12E-14 0.20E-15 PERMUTATION_RANDOM 5 2.2 2.2 0.0 6.3 PLU 5 0.15E+03 0.14 0.11E-14 0.13E-14 RIS 5 3.2 1.9 0.74E-15 0.84E-16 RODMAN 5 13. 0.53 0.82E-15 0.80E-15 RUTIS1 4 17. 1.0 0.15E-14 0.11E-14 RUTIS2 4 11. 1.1 0.60E-15 0.68E-15 RUTIS3 4 14. 0.58 0.86E-15 0.60E-15 RUTIS4 5 59. 52. 0.93E-12 0.29E-12 RUTIS5 4 24. 0.19E+04 0.48E-11 0.0 SCHUR_BLOCK 5 8.4 0.65 0.79E-16 0.63E-15 SPLINE 5 21. 0.97 0.76E-15 0.14E-14 STIRLING 5 68. 32. 0.38E-13 0.0 SUMMATION 5 3.9 3.0 0.0 0.0 SWEET1 6 70. 0.26 0.16E-14 0.11E-12 SWEET2 6 30. 1.4 0.66E-14 0.34E-13 SWEET3 6 73. 0.34 0.13E-14 0.14E-12 SWEET4 13 0.12E+03 0.38 0.42E-14 0.26E-12 SYLVESTER_KAC 6 10. 2.5 0.0 0.0 SYMM_RANDOM 5 6.4 2.1 0.16E-14 0.43E-14 TRI_UPPER 5 9.2 0.17E+03 0.62E-14 0.42E-13 TRIS 5 13. 0.40 0.49E-15 0.71E-15 TRIV 5 11. 1.1 0.13E-14 0.98E-15 TRIW 5 9.4 0.46E+03 0.0 0.0 UPSHIFT 5 2.2 2.2 0.0 0.0 VAND1 5 0.47E+03 1.3 0.90E-14 0.54E-14 VAND2 5 0.47E+03 1.3 0.44E-13 0.54E-14 WILK03 3 1.4 0.18E+11 0.67E-06 0.67E-06 WILK04 4 1.9 0.12E+17 0.48E-04 11. WILK05 5 1.5 0.31E+07 0.74E-09 0.12E-08 WILK21 21 28. 4.3 0.16E-14 0.38E-14 WILSON 4 31. 99. 0.64E-12 0.0 TEST_LLT A = a test matrix of order M by M L is an M by N lower triangular Cholesky factor. ||A|| = Frobenius norm of A. ||A-LLT|| = Frobenius norm of A-L*L'. Title M N ||A|| ||A-LLT|| DIF2 5 5 5.29150 0.888178E-15 GIVENS 5 5 20.6155 0.423634E-14 KERSHAW 4 4 8.24621 0.257035E-14 LEHMER 5 5 3.28041 0.207704E-15 MINIJ 5 5 12.4499 0.00000 MOLER1 5 5 61.8850 0.00000 MOLER3 5 5 8.66025 0.00000 OTO 5 5 5.29150 0.736439E-15 PASCAL2 5 5 92.4608 0.00000 WILSON 4 4 30.5450 0.525453E-14 TEST_NULL_LEFT A = a test matrix of order M by N x = an M vector, candidate for a left null vector. ||A|| = Frobenius norm of A. ||x|| = L2 norm of x. ||x'*A||/||x|| = L2 norm of x'A over L2 norm of x. Title M N ||A|| ||x|| ||x'*A||/||x|| A123 3 3 16.8819 2.44949 0.00000 CHEBY_DIFF1 5 5 13.4722 3.74166 0.445079E-15 CREATION 5 5 5.47723 1.00000 0.00000 DIF1 5 5 2.82843 1.73205 0.00000 DIF1CYCLIC 5 5 3.16228 2.23607 0.00000 DIF2CYCLIC 5 5 5.47723 2.23607 0.00000 EBERLEIN 5 5 18.1002 2.23607 0.561733E-15 FIBONACCI1 5 5 95.3527 1.73205 0.00000 LAUCHLI 6 5 6.68163 3.59567 0.00000 LINE_ADJ 7 7 3.46410 2.00000 0.00000 MOLER2 5 5 101035. 263.820 0.00000 ONE 5 5 5.00000 1.41421 0.00000 RING_ADJ 12 12 4.89898 3.46410 0.00000 ROSSER1 8 8 2482.26 22.3607 0.00000 ZERO 5 5 0.00000 2.23607 0.00000 TEST_NULL_RIGHT A = a test matrix of order M by N x = an N vector, candidate for a right null vector. ||A|| = Frobenius norm of A. ||x|| = L2 norm of x. ||A*x||/||x|| = L2 norm of A*x over L2 norm of x. Title M N ||A|| ||x|| ||A*x||/||x|| A123 3 3 16.8819 2.44949 0.00000 ARCHIMEDES 7 8 93.3970 0.187697E+08 0.00000 CHEBY_DIFF1 5 5 13.4722 2.23607 0.649741E-15 CREATION 5 5 5.47723 1.00000 0.00000 DIF1 5 5 2.82843 1.73205 0.00000 DIF1CYCLIC 5 5 3.16228 2.23607 0.00000 DIF2CYCLIC 5 5 5.47723 2.23607 0.00000 FIBONACCI1 5 5 95.3527 1.73205 0.00000 HAMMING 5 31 8.94427 2.44949 0.00000 LINE_ADJ 7 7 3.46410 2.00000 0.00000 MOLER2 5 5 101035. 1016.30 0.00000 NEUMANN 25 25 23.2379 5.00000 0.00000 ONE 5 5 5.00000 1.41421 0.00000 RING_ADJ 12 12 4.89898 3.46410 0.00000 ROSSER1 8 8 2482.26 22.3607 0.00000 ZERO 5 5 0.00000 2.23607 0.00000 TEST_PLU A = a test matrix of order M by N P, L, U are the PLU factors. ||A|| = Frobenius norm of A. ||A-PLU|| = Frobenius norm of A-P*L*U. Title M N ||A|| ||A-PLU|| A123 3 3 16.8819 0.687980E-14 BODEWIG 4 4 12.7279 0.412430E-14 BORDERBAND 5 5 2.76699 0.00000 DIF2 5 5 5.29150 0.00000 GFPP 5 5 9.39618 0.292964E-13 GIVENS 5 5 20.6155 0.00000 KMS 5 5 101.704 0.260787E-12 LEHMER 5 5 3.28041 0.111022E-15 MAXIJ 5 5 19.8746 0.00000 MINIJ 5 5 12.4499 0.00000 MOLER1 5 5 61.8850 0.00000 MOLER3 5 5 8.66025 0.00000 OTO 5 5 5.29150 0.00000 PLU 5 5 152.462 0.00000 PASCAL2 5 5 92.4608 0.00000 VAND2 4 4 107.076 0.164856E-13 WILSON 4 4 30.5450 0.732411E-14 TEST_SOLUTION Compute the Frobenius norm of the solution error: A * X - B given MxN matrix A, NxK solution X, MxK right hand side B. Title M N K ||A|| ||A*X-B|| A123 3 3 1 16.8819 0.00000 BODEWIG 4 4 1 12.7279 0.00000 DIF2 10 10 2 7.61577 0.00000 FRANK 10 10 2 38.6652 0.00000 POISSON 20 20 1 19.5448 0.00000 WILK03 3 3 1 1.39284 0.674350E-06 WILK04 4 4 1 1.89545 0.129463E+17 WILSON 4 4 1 30.5450 0.00000 TEST_TYPE Test functions that query the type of a matrix. Title M N ||A|| ||Transition Error|| BODEWIG 4 4 12.7279 0.100000E+31 SNAKES 101 101 5.92077 0.980522E-15 TRANSITION_RANDOM 5 5 1.32331 0.00000 TEST_MAT_TEST Normal end of execution. 20 February 2018 8:09:43.825 AM