29-Mar-2019 18:09:56 test_mat_test MATLAB version. Test test_mat. 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 Legendre zeros 1: -0.57735 2: 0.57735 Legendre zeros 1: -0.774597 2: 0 3: 0.774597 Legendre zeros 1: -0.861136 2: -0.339981 3: 0.339981 4: 0.861136 Legendre zeros 1: -0.90618 2: -0.538469 3: 0 4: 0.538469 5: 0.90618 Legendre zeros 1: -0.93247 2: -0.661209 3: -0.238619 4: 0.238619 5: 0.661209 6: 0.93247 Legendre zeros 1: -0.949108 2: -0.741531 3: -0.405845 4: 0 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 0.00390625 2 0.0585938 0.527344 0.394531 0.0195312 3 0.0195312 0.394531 0.527344 0.0585938 4 0.00390625 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 2: 0.25 3: 0.0625 4: 0.015625 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 0.00390625 2 0.0585938 0.527344 0.394531 0.0195312 3 0.0195312 0.394531 0.527344 0.0585938 4 0.00390625 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 2: 0.25 3: 0.0625 4: 0.015625 Frobenius norm of A*X-X*LAMBDA is 0 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 1.1547 0 4 0 0 0.866025 1.11803 Frobenius norm of A-L*L' is 2.18689e-15 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 2: -2 3: 1 Frobenius norm of X'*A is 0 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 2: -2 3: 1 Frobenius norm of A*x is 0 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 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_CONDITION Compute the L1 condition number of an example of each test matrix Title N COND COND AEGERTER 5 24 24 BAB 5 8.46751 8.46751 BAUER 6 8.52877e+06 8.52877e+06 BIS 5 42.9756 42.9756 BIW 5 59.9171 59.9171 BODEWIG 3 10.4366 10.4366 BOOTHROYD 5 1.002e+06 1.002e+06 COMBIN 3 5.4822 5.4822 COMPANION 5 66.4264 66.4264 CONEX1 4 68.0622 68.0622 CONEX2 3 17.7034 17.7034 CONEX3 5 80 80 CONEX4 4 4488 4488 DAUB2 4 2 2 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 7.5998 7.5998 DOWNSHIFT 5 1 1 EXCHANGE 5 1 1 FIBONACCI2 5 15 15 GFPP 5 12.2633 12.2633 GIVENS 5 50 50 HANKEL_N 5 5.8368 5.8368 HARMAN 8 77.069 77.069 HARTLEY 5 5 5 IDENTITY 5 1 1 ILL3 3 216775 216775 JORDAN 5 2.08956 2.08956 KERSHAW 4 49 49 LIETZKE 5 38 38 MAXIJ 5 100 100 MINIJ 5 60 60 ORTH_SYMM 5 4.39765 4.39765 OTO 5 18 18 PASCAL1 5 100 100 PASCAL3 5 18951.2 18951.2 PEI 5 3.69745 3.69745 RODMAN 5 11.0697 11.0697 RUTIS1 4 15 15 RUTIS2 4 11.44 11.44 RUTIS3 4 6 6 RUTIS5 4 62608 62608 SUMMATION 5 10 10 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 2599.9 2599.9 UPSHIFT 5 1 1 WILK03 3 2.6e+10 2.6e+10 WILK04 4 2.45892e+16 2.45889e+16 WILK05 5 7.93703e+06 7.93703e+06 WILSON 4 4488 4488 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 -9.5162e-16 17 AEGERTER 5 -25 -25 9.4 ANTICIRCULANT 3 -235.484 -235.484 11 ANTICIRCULANT 4 1407.78 1407.78 13 ANTICIRCULANT 5 7148.67 7148.67 14 ANTIHADAMARD 5 1 1 3.3 ANTISYMM_RANDOM 5 2.41902e-16 2.9 ANTISYMM_RANDOM 6 0.097353 3.3 BAB 5 -1980.11 -1980.11 14 BAUER 6 1 1 1.9e+02 BERNSTEIN 5 96 96 25 BIMARKOV_RANDOM 5 -8.62803e-05 1.4 BIS 5 -177.02 -177.02 11 BIW 5 0.0547223 0.0547223 2.4 BODEWIG 4 568 568 13 BOOTHROYD 5 1 1 8.9e+02 BORDERBAND 5 -0.328125 -0.328125 2.8 CARRY 5 1.65382e-08 1.65382e-08 1.4 CAUCHY 5 38.7671 38.7671 6.8e+02 CHEBY_DIFF1 5 -2.8387e-14 13 CHEBY_DIFF1 6 -3.94228e-13 21 CHEBY_T 5 64 64 13 CHEBY_U 5 1024 1024 22 CHEBY_VAN1 5 18 4.3 CHEBY_VAN2 2 -2 -2 2 CHEBY_VAN2 3 -1.41421 -1.41421 2 CHEBY_VAN2 4 1 1 2.1 CHEBY_VAN2 5 0.707107 0.707107 2.2 CHEBY_VAN3 5 13.9754 13.9754 3.9 CHEBY_VAN2 6 -0.5 -0.5 2.3 CHEBY_VAN2 7 -0.353553 -0.353553 2.4 CHEBY_VAN2 8 0.25 0.25 2.5 CHEBY_VAN2 9 0.176777 0.176777 2.6 CHEBY_VAN2 10 -0.125 -0.125 2.7 CHOW 5 -70.5488 -70.5488 2e+02 CIRCULANT 5 7148.67 7148.67 14 CIRCULANT2 3 18 18 6.5 CIRCULANT2 4 -160 -160 11 CIRCULANT2 5 1875 1875 17 CLEMENT1 5 0 0 6.3 CLEMENT1 6 -225 -225 8.4 CLEMENT2 5 0 0 9 CLEMENT2 6 -178.154 -178.154 10 COMBIN 5 1257.33 1257.33 21 COMPANION 5 -2.81582 -2.81582 6.7 COMPLEX_I 2 1 1 1.4 CONEX1 4 -2.81582 -2.81582 8.1 CONEX2 3 -0.355137 -0.355137 2.6 CONEX3 5 -1 -1 3.9 CONEX4 4 -1 -1 31 CONFERENCE 6 -125 -125 5.5 CREATION 5 0 0 5.5 DAUB2 4 1 1 2 DAUB4 8 -1 -1 2.8 DAUB6 12 1 1 3.5 DAUB8 16 -1 -1 4 DAUB10 20 1 1 4.5 DAUB12 24 -1 -1 4.9 DIAGONAL 5 22.1228 22.1228 6.4 DIF1 5 0 0 2.8 DIF1 6 1 1 3.2 DIF1CYCLIC 5 0 0 3.2 DIF2 5 6 6 5.3 DIF2CYCLIC 5 0 0 5.5 DORR 5 -6.33817e+10 -6.33817e+10 5.3e+02 DOWNSHIFT 5 1 1 2.2 EBERLEIN 5 0 -9.28955e-13 18 EULERIAN 5 1 1 77 EXCHANGE 5 1 1 2.2 FIBONACCI1 5 0 3.92256e-43 95 FIBONACCI2 5 -1 -1 3 FIBONACCI3 5 8 8 3.6 FIEDLER 7 1332.21 1332.21 30 FORSYTHE 5 1975.68 1975.68 11 FORSYTHE 6 9031.06 9031.06 12 FOURIER_COSINE 5 1 1 2.2 FOURIER_SINE 5 1 1 2.2 FRANK 5 1 1 12 GEAR 4 -2.44929e-16 0 2.8 GEAR 5 2 2 3.2 GEAR 6 -4 -4 3.5 GEAR 7 2 2 3.7 GEAR 8 4.89859e-16 0 4 GFPP 5 212.007 212.007 9.4 GIVENS 5 16 16 21 GK316 5 -25 -25 9.4 GK323 5 32 32 10 GK324 5 11.953 11.953 11 GRCAR 5 8 3.6 HADAMARD 5 0 4 HANKEL 5 -2823.88 15 HANKEL_N 5 3125 3125 15 HANOWA 6 1803.1 1803.1 8.7 HARMAN 8 0.000954779 0.000954779 5.1 HARTLEY 5 55.9017 55.9017 5 HARTLEY 6 -216 -216 6 HARTLEY 7 -907.493 -907.493 7 HARTLEY 8 -4096 -4096 8 HELMERT 5 1 1 2.2 HELMERT2 5 1 2.2 HERMITE 5 1024 1024 54 HERNDON 5 -0.04 -0.04 1.8 HILBERT 5 3.7493e-12 3.7493e-12 1.6 HOUSEHOLDER 5 -1 1 2.2 IDEM_RANDOM 5 0 3.41458e-71 1 IDENTITY 5 1 1 2.2 IJFACT1 5 7.16636e+09 7.16636e+09 3.7e+06 IJFACT2 5 1.4948e-21 1.4948e-21 0.56 ILL3 3 6 6 8.2e+02 INTEGRATION 6 1 1 4.2 INVOL 5 -1 -1 1.9e+03 INVOL_RANDOM 5 -1 2.2 JACOBI 5 0 0 1.5 JACOBI 6 -0.021645 -0.021645 1.7 JORDAN 6 498.456 498.456 7.3 KAHAN 5 -3.78564e-08 -3.78564e-08 0.72 KERSHAW 4 1 1 8.2 KERSHAWTRI 5 553.995 553.995 8.7 KMS 5 2304.83 2304.83 1e+02 LAGUERRE 5 0.00347222 0.00347222 6.9 LEGENDRE 5 16.4062 16.4062 6.8 LEHMER 5 0.065625 0.065625 3.3 LESLIE 4 0.605244 0.605244 1.8 LESP 5 -42300 -42300 22 LIETZKE 5 48 48 18 LIGHTS_OUT 25 -4.27094e-31 10 LINE_ADJ 5 0 0 2.8 LINE_ADJ 6 -1 -1 3.2 LINE_LOOP_ADJ 5 0 0 3.6 LOEWNER 5 -29.0825 21 LOTKIN 5 1.87465e-11 1.87465e-11 2.5 MARKOV_RANDOM 5 0.00488558 1.3 MAXIJ 5 5 5 20 MILNES 5 11.953 11.953 11 MINIJ 5 1 1 12 MOLER1 5 1 1 62 MOLER2 5 0 1.15439e-12 1e+05 MOLER3 5 1 1 8.7 MOLER4 4 1 1 2.8 NEUMANN 25 0 0.00132153 23 ONE 5 0 0 5 ORTEGA 5 -16.5253 -16.5253 2.4e+02 ORTH_RANDOM 5 1 1 2.2 ORTH_SYMM 5 1 1 2.2 OTO 5 6 6 5.3 PARTER 5 131.917 131.917 6.3 PASCAL1 5 1 1 9.9 PASCAL2 5 1 1 92 PASCAL3 5 1 1 1.2e+02 PDS_RANDOM 5 0.0404187 0.0404187 1.5 PEI 5 137.311 137.311 6 PERMUTATION_RANDOM 5 1 1 2.2 PLU 5 1.93261e+07 1.93261e+07 1.5e+02 POISSON 25 3.25655e+13 3.25655e+13 22 PROLATE 5 -5651.77 13 RECTANGLE_ADJ 25 0 0 8.9 REDHEFFER 5 -2 -2 3.7 REF_RANDOM 5 1 1 2.8 RIEMANN 5 96 8.8 RING_ADJ 1 1 1 1 RING_ADJ 2 -1 -1 1.4 RING_ADJ 3 2 2 2.4 RING_ADJ 4 0 0 2.8 RING_ADJ 5 2 2 3.2 RING_ADJ 6 -4 -4 3.5 RING_ADJ 7 2 2 3.7 RING_ADJ 8 0 0 4 RIS 5 4.12239 4.12239 3.2 RODMAN 5 -2175.88 -2175.88 13 ROSSER1 8 0 -10611.3 2.5e+03 ROUTH 5 7.85813 7.85813 5.2 RUTIS1 4 -375 -375 17 RUTIS2 4 100 100 11 RUTIS3 4 624 624 14 RUTIS4 5 216 216 59 RUTIS5 4 1 1 24 SCHUR_BLOCK 5 589.771 589.771 8.4 SKEW_CIRCULANT 5 -10310.4 -10310.4 14 SPLINE 5 -2566.72 -2566.72 21 STIRLING 5 1 1 68 STRIPE 5 2112 15 SUMMATION 5 1 1 3.9 SWEET1 6 -2.04682e+07 -2.04682e+07 70 SWEET2 6 9562.52 9562.52 30 SWEET3 6 -5.40561e+07 -5.40561e+07 73 SWEET4 13 -6.46348e+16 -6.46348e+16 1.2e+02 SYLVESTER 5 -222.565 12 SYLVESTER_KAC 5 0 0 7.7 SYLVESTER_KAC 6 -225 -225 10 SYMM_RANDOM 5 22.1228 22.1228 6.4 TOEPLITZ 5 -2823.88 15 TOEPLITZ_5DIAG 5 -747.438 13 TOEPLITZ_5S 25 -1.51735e+17 40 TOEPLITZ_PDS 5 0.0849362 3.4 TOURNAMENT_RANDOM 5 0 0 4.5 TRANSITION_RANDOM 5 0.00486764 1.3 TRENCH 5 -37.7411 7 TRI_UPPER 5 1 1 9.2 TRIS 5 6683.42 6683.42 13 TRIV 5 -700.369 -700.369 11 TRIW 5 1 1 9.4 UNITARY_RANDOM 5 1 1 3.2 UPSHIFT 5 1 1 2.2 VAND1 5 133985 133985 4.7e+02 VAND2 5 133985 133985 4.7e+02 WATHEN 96 7.49648e+292 3e+04 WILK03 3 9e-21 9e-21 1.4 WILK04 4 4.42923e-17 4.42923e-17 1.9 WILK05 5 3.7995e-15 3.79947e-15 1.5 WILK12 12 1 1 54 WILK20 20 1.4763e+25 1e+02 WILK21 21 -4.15825e+12 -4.15825e+12 28 WILSON 4 1 1 31 ZERO 5 0 0 0 ZIELKE 5 469.417 14 TEST_EIGEN_LEFT Compute the Frobenius norm of the left eigensystem 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 1.23231e-14 CARRY 5 5 1.41391 3.60025e-15 CHOW 5 5 202.501 4.90418e-13 DIAGONAL 5 5 6.3802 0 ROSSER1 8 8 2482.26 2.61994e-11 SYMM_RANDOM 5 5 6.3802 2.56137e-15 TEST_EIGEN_RIGHT Compute the Frobenius norm of the right eigensystem 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 1.33745e-14 BAB 5 5 14.3605 5.49271e-15 BODEWIG 4 4 12.7279 9.2479e-15 CARRY 5 5 1.41391 1.17914e-15 CHOW 5 5 202.501 2.98699e-13 COMBIN 5 5 20.7778 7.10543e-15 DIF2 5 5 5.2915 1.20319e-15 EXCHANGE 5 5 2.23607 0 IDEM_RANDOM 5 5 1.73205 7.32952e-16 IDENTITY 5 5 2.23607 0 ILL3 3 3 817.763 1.6229e-11 KERSHAW 4 4 8.24621 4.82333e-15 KMS 5 5 2.32288 3.2055e-08 LINE_ADJ 5 5 2.82843 1.13399e-15 LINE_LOOP_ADJ 5 5 3.60555 1.20042e-15 ONE 5 5 5 0 ORTEGA 5 5 244.268 4.15498e-13 OTO 5 5 5.2915 1.20319e-15 PDS_RANDOM 5 5 1.4623 5.54108e-16 PEI 5 5 6.04036 0 RODMAN 5 5 12.7897 0 ROSSER1 8 8 2482.26 2.61994e-11 RUTIS1 4 4 16.6132 0 RUTIS2 4 4 11.4018 0 RUTIS5 4 4 23.7697 1.41754e-14 SYLVESTER_KAC 5 5 7.74597 0 SYMM_RANDOM 5 5 6.3802 2.64499e-15 WILK12 12 12 53.591 1.01528e-07 WILSON 4 4 30.545 2.4263e-14 ZERO 5 5 0 0 TEST_INVERSE A = a test matrix of order N; B = inverse as computed by a routine. C = inverse as computed by Matlab's INV function. ||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 7.05994e-16 7.13729e-16 BAB 5 14 0.72 9.79779e-16 9.19858e-16 BAUER 6 1.9e+02 2.1e+04 1.23483e-10 0 BERNSTEIN 5 25 3.2 0 0 BIS 5 11 3.9 8.88178e-16 1.98603e-15 BIW 5 2.4 26 3.93126e-15 1.01754e-15 BODEWIG 4 13 0.68 9.98823e-16 7.25902e-16 BOOTHROYD 5 8.9e+02 8.9e+02 2.18559e-11 0 BORDERBAND 5 2.8 6.8 0 0 CARRY 5 1.4 3.1e+03 2.29097e-13 1.18547e-13 CAUCHY 5 6.8e+02 61 9.54396e-14 9.48647e-14 CHEBY_T 5 13 1.9 0 0 CHEBY_U 5 22 1.2 0 0 CHEBY_VAN2 5 2.2 2.5 4.6599e-16 6.04282e-16 CHEBY_VAN3 5 3.9 1.3 7.14387e-16 1.01199e-15 CHOW 5 2e+02 2.7e+02 1.30071e-13 2.59298e-13 CIRCULANT 5 14 0.41 8.57249e-16 7.29177e-16 CIRCULANT2 5 17 0.64 8.90791e-16 1.56583e-15 CLEMENT1 6 8.4 1.5 6.14783e-16 9.02024e-17 CLEMENT2 6 10 2.7 8.25906e-16 8.33717e-16 COMBIN 5 21 0.71 1.49154e-15 1.103e-15 COMPANION 5 6.7 2.9 8.65593e-16 1.29076e-16 COMPLEX_I 2 1.4 1.4 0 0 CONEX1 4 8.1 6.4 0 0 CONEX2 3 2.6 4.3 2.08719e-16 2.08719e-16 CONEX3 5 3.9 11 0 0 CONFERENCE 6 5.5 1.1 5.08193e-16 0 DAUB2 4 2 2 0 8.88178e-16 DAUB4 8 2.8 2.8 3.07157e-16 2.24342e-15 DAUB6 12 3.5 3.5 1.11711e-15 1.63024e-15 DAUB8 16 4 4 1.40228e-15 4.5719e-15 DAUB10 20 4.5 4.5 1.32402e-15 8.74086e-15 DAUB12 24 4.9 4.9 1.6905e-15 1.96031e-14 DIAGONAL 5 6.4 2.1 0 0 DIF1 6 3.2 3.5 0 0 DIF2 5 5.3 3.9 4.02446e-15 7.13054e-16 DORR 5 5.3e+02 0.038 1.88717e-15 1.60283e-15 DOWNSHIFT 5 2.2 2.2 0 0 EULERIAN 5 77 7.8e+02 0 0 EXCHANGE 5 2.2 2.2 0 0 FIBONACCI2 5 3 3.5 0 0 FIBONACCI3 5 3.6 1.6 1.57009e-16 0 FIEDLER 7 30 3.3 2.82918e-14 4.36161e-15 FORSYTHE 5 11 0.52 7.17395e-17 4.99274e-17 FOURIER_COSINE 5 2.2 2.2 7.33482e-16 1.19397e-15 FOURIER_SINE 5 2.2 2.2 9.4244e-16 1.98579e-15 FRANK 5 12 59 8.60706e-15 0 GFPP 5 9.4 1 4.88458e-16 2.9891e-14 GIVENS 5 21 2.7 2.50588e-15 0 GK316 5 9.4 1.8 7.05994e-16 7.13729e-16 GK323 5 10 2.3 0 0 GK324 5 11 5.6 4.00849e-15 1.40204e-15 HANKEL_N 6 21 0.51 3.15209e-16 2.3592e-16 HANOWA 6 8.7 0.71 4.95856e-16 5.62554e-16 HARMAN 8 5.1 15 6.65376e-15 1.13282e-14 HARTLEY 5 5 1 1.02254e-15 2.78177e-15 HELMERT 5 2.2 2.2 5.64063e-16 8.04975e-16 HELMERT2 5 2.2 2.2 8.49534e-16 6.08668e-16 HERMITE 5 54 1.8 0 0 HERNDON 5 1.8 9.4 1.021e-15 7.13729e-16 HILBERT 5 1.6 3e+05 1.54676e-11 6.68631e-12 HOUSEHOLDER 5 2.2 2.2 0 0 IDENTITY 5 2.2 2.2 0 0 ILL3 3 8.2e+02 3.4e+02 2.09427e-11 3.87807e-12 INTEGRATION 6 4.2 7.7 5.63899e-17 8.03563e-16 INVOL 5 1.9e+03 1.9e+03 1.40631e-10 7.27597e-12 n = 6 JACOBI 6 1.7 6.5 5.39314e-16 2.09375e-16 JORDAN 5 6.6 0.84 2.22045e-16 2.22045e-16 KAHAN 5 0.72 4.3e+02 4.57319e-15 1.5034e-14 KERSHAW 4 8.2 8.2 8.1886e-15 0 KERSHAWTRI 5 8.7 0.69 3.72441e-16 4.8215e-16 KMS 5 1e+02 2.5 2.5596e-14 1.83291e-14 LAGUERRE 5 6.9 2e+02 0 0 LEGENDRE 5 6.8 1.9 2.48253e-16 2.68032e-16 LEHMER 5 3.3 7.7 3.62337e-15 1.58193e-15 LESP 5 22 0.32 3.58519e-16 7.29486e-16 LIETZKE 5 18 2.4 2.89391e-15 6.96106e-16 LINE_ADJ 6 3.2 3.5 0 0 LOTKIN 5 2.5 2.4e+05 4.62466e-11 2.66219e-12 MAXIJ 5 20 4.7 4.9641e-15 0 MILNES 5 11 5.6 4.00849e-15 1.40204e-15 MINIJ 5 12 5 0 0 MOLER1 5 62 2.8e+04 1.02992e-10 4.35208e-11 MOLER3 5 8.7 1.2e+02 0 0 ORTEGA 5 2.4e+02 91 1.33019e-12 3.09261e-12 ORTH_SYMM 5 2.2 2.2 8.54957e-16 1.98385e-15 OTO 5 5.3 3.9 4.02446e-15 7.13054e-16 PARTER 5 6.3 0.94 7.75379e-16 7.0839e-17 PASCAL1 5 9.9 9.9 0 0 PASCAL2 5 92 92 0 0 PASCAL3 5 1.2e+02 1.2e+02 1.02329e-13 5.31721e-14 PDS_RANDOM 5 1.5 5.7 5.76051e-16 4.92018e-15 PEI 5 6 0.85 4.49395e-16 1.66533e-16 PERMUTATION_RANDOM 5 2.2 2.2 0 0 PLU 5 1.5e+02 0.14 1.01775e-15 1.01435e-15 RIS 5 3.2 1.9 7.68292e-16 4.28968e-17 RODMAN 5 13 0.53 9.46229e-16 7.40375e-16 RUTIS1 4 17 1 1.48172e-15 1.11022e-15 RUTIS2 4 11 1.1 1.69269e-15 6.89434e-16 RUTIS3 4 14 0.58 7.69425e-16 5.92697e-16 RUTIS4 4 51 18 9.1547e-14 8.48665e-14 RUTIS5 4 24 1.9e+03 7.25127e-12 0 SCHUR_BLOCK 5 8.4 0.65 7.85046e-17 6.32925e-16 SPLINE 5 21 0.97 7.21639e-16 1.39426e-15 STIRLING 5 68 32 0 0 SUMMATION 5 3.9 3 0 0 SWEET1 6 70 0.26 1.49174e-15 1.08789e-13 SWEET2 6 30 1.4 3.4874e-15 3.41614e-14 SWEET3 6 73 0.34 1.06164e-15 1.43329e-13 SWEET4 13 1.2e+02 0.38 4.55608e-15 2.56799e-13 SYLVESTER_KAC 6 10 2.5 1.14439e-16 1.14439e-16 SYMM_RANDOM 5 6.4 2.1 1.16539e-15 4.10892e-15 TRI_UPPER 5 9.2 1.7e+02 2.64046e-14 4.12941e-14 TRIS 5 13 0.4 4.01159e-16 7.08272e-16 TRIV 5 11 1.1 6.77788e-16 1.024e-15 TRIW 5 9.4 4.6e+02 0 0 UNITARY_RANDOM 5 3.2 3.2 4.71297e-08 6.36075e-08 UPSHIFT 5 2.2 2.2 0 0 VAND1 5 4.7e+02 1.3 1.06502e-14 4.47315e-15 VAND2 5 4.7e+02 1.3 2.97877e-14 4.47315e-15 WILK03 3 1.4 1.8e+10 9.88368e-07 8.96394e-07 WILK04 4 1.9 1.2e+16 0.000474855 10.7174 WILK05 5 1.5 3.1e+06 1.1293e-09 1.2232e-09 WILK21 21 28 4.3 1.59108e-15 3.82389e-15 WILSON 4 31 99 2.77112e-13 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 5.2915 8.88178e-16 GIVENS 5 5 20.6155 4.23634e-15 KERSHAW 4 4 8.24621 2.57035e-15 LEHMER 5 5 3.28041 2.07704e-16 MINIJ 5 5 12.4499 0 MOLER1 5 5 61.885 6.15348e-15 MOLER3 5 5 8.66025 0 OTO 5 5 5.2915 7.36439e-16 PASCAL2 5 5 92.4608 0 WILSON 4 4 30.545 4.94517e-15 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. ||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 CHEBY_DIFF1 5 5 13.4722 3.74166 4.9e-16 CREATION 5 5 5.47723 1 0 DIF1 5 5 2.82843 1.73205 0 DIF1CYCLIC 5 5 3.16228 2.23607 0 DIF2CYCLIC 5 5 5.47723 2.23607 0 EBERLEIN 5 5 18.1002 2.23607 5.6e-16 FIBONACCI1 5 5 95.3527 1.73205 0 LAUCHLI 6 5 6.68163 3.59567 0 LINE_ADJ 7 7 3.4641 2 0 MOLER2 5 5 101035 263.82 0 ONE 5 5 5 1.41421 0 RING_ADJ 12 12 4.89898 3.4641 0 ROSSER1 8 8 2482.26 22.3607 0 ZERO 5 5 0 0 Inf 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 ARCHIMEDES 7 8 93.397 1.87697e+07 0 CHEBY_DIFF1 5 5 13.4722 2.23607 8.9e-16 CREATION 5 5 5.47723 1 0 DIF1 5 5 2.82843 1.73205 0 DIF1CYCLIC 5 5 3.16228 2.23607 0 DIF2CYCLIC 5 5 5.47723 2.23607 0 FIBONACCI1 5 5 95.3527 1.73205 0 HAMMING 5 31 8.94427 2.44949 0 LINE_ADJ 7 7 3.4641 2 0 MOLER2 5 5 101035 1016.3 0 NEUMANN 25 25 23.2379 5 0 ONE 5 5 5 1.41421 0 RING_ADJ 12 12 4.89898 3.4641 0 ROSSER1 8 8 2482.26 22.3607 0 ZERO 5 5 0 2.23607 0 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 6.8798e-15 BODEWIG 4 4 12.7279 4.1243e-15 BORDERBAND 5 5 2.76699 0 DIF2 5 5 5.2915 0 GFPP 5 5 9.39618 2.92964e-14 GIVENS 5 5 20.6155 0 KMS 5 5 101.704 2.60701e-13 LEHMER 5 5 3.28041 1.11022e-16 MAXIJ 5 5 19.8746 0 MINIJ 5 5 12.4499 0 MOLER1 5 5 61.885 6.15348e-15 MOLER3 5 5 8.66025 0 OTO 5 5 5.2915 0 PASCAL2 5 5 92.4608 0 PLU 5 5 152.462 0 VAND2 4 4 107.076 2.05727e-14 WILSON 4 4 30.545 7.32411e-15 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 16.881943 0.000000 BODEWIG 4 4 1 12.727922 0.000000 DIF2 10 10 2 7.615773 0.000000 FRANK 10 10 2 38.665230 0.000000 POISSON 20 20 1 19.544820 0.000000 WILK03 3 3 1 1.392839 0.000001 WILK04 4 4 1 1.895450 0.000056 WILSON 4 4 1 30.545049 0.000000 TEST_TYPE Demonstrate functions which test the type of a matrix. Title M N ||A|| ||Transition Error|| BODEWIG 4 4 12.7279 Inf SNAKES 101 101 5.92077 9.80522e-16 TRANSITION_RANDOM 5 5 1.32331 0 test_mat_test Normal end of execution. 29-Mar-2019 18:11:03