17 April 2015 11:20:15.138 AM TEST_MAT_PRB FORTRAN77 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 0.0000000 Legendre zeros 1 -0.57735027 2 0.57735027 Legendre zeros 1 -0.77459667 2 0.0000000 3 0.77459667 Legendre zeros 1 -0.86113631 2 -0.33998104 3 0.33998104 4 0.86113631 Legendre zeros 1 -0.90617985 2 -0.53846931 3 0.0000000 4 0.53846931 5 0.90617985 Legendre zeros 1 -0.93246951 2 -0.66120939 3 -0.23861919 4 0.23861919 5 0.66120939 6 0.93246951 Legendre zeros 1 -0.94910791 2 -0.74153119 3 -0.40584515 4 0.0000000 5 0.40584515 6 0.74153119 7 0.94910791 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 0.195313E-01 3: 0.195313E-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: 1.00000 1.00000 1.00000 1.00000 2: 11.0000 3.00000 -1.00000 -3.00000 3: 11.0000 -3.00000 -1.00000 3.00000 4: 1.00000 -1.00000 1.00000 -1.00000 Eigenvalues LAM: 1 1.0000000 2 0.25000000 3 0.62500000E-01 4 0.15625000E-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 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 0.195313E-01 3: 0.195313E-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: 1.00000 6.00000 11.0000 6.00000 2: 1.00000 2.00000 -1.00000 -2.00000 3: 1.00000 -2.00000 -1.00000 2.00000 4: 1.00000 -6.00000 11.0000 -6.00000 Eigenvalues LAM: 1 1.0000000 2 0.25000000 3 0.62500000E-01 4 0.15625000E-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: 2.00000 1.00000 0.00000 0.00000 2: 1.00000 2.00000 1.00000 0.00000 3: 0.00000 1.00000 2.00000 1.00000 4: 0.00000 0.00000 1.00000 2.00000 Factor L: Col 1 2 3 4 Row 1: 1.41421 0.00000 0.00000 0.00000 2: 0.707107 1.22474 0.00000 0.00000 3: 0.00000 0.816497 1.15470 0.00000 4: 0.00000 0.00000 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: 1.00000 2.00000 3.00000 2: 4.00000 5.00000 6.00000 3: 7.00000 8.00000 9.00000 Vector X: 1 1.0000000 2 -2.0000000 3 1.0000000 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: 1.00000 2.00000 3.00000 2: 4.00000 5.00000 6.00000 3: 7.00000 8.00000 9.00000 Vector X: 1 1.0000000 2 -2.0000000 3 1.0000000 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 0.236629E-13 R8MAT_NORM_FRO_TEST R8MAT_NORM_FRO computes the Frobenius norm of an R8MAT; A: Col 1 2 3 4 Row 1: 1.00000 2.00000 3.00000 4.00000 2: 5.00000 6.00000 7.00000 8.00000 3: 9.00000 10.0000 11.0000 12.0000 4: 13.0000 14.0000 15.0000 16.0000 5: 17.0000 18.0000 19.0000 20.0000 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 24.0000 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 3 -5.48220 5.48220 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 2.00000 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 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 0.334284E-69 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 16.4063 16.4063 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 0.404187E-01 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 1.00000 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 -222.565 12.4995 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 0.486764E-02 1.32331 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 0.409317E-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 0.131825E-14 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 0.786804E-15 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 0.416439E-14 WILK12 12 12 53.5910 0.101528E-06 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. ||I-AB|| = Frobenius norm of I-A*B. ||I-AC|| = Frobenius norm of I-A*C. Title N ||A|| ||I-AB|| ||I-AC|| AEGERTER 5 9.43398 0.710890E-15 0.705075E-15 BAB 5 14.3605 0.951853E-15 0.964609E-15 BAUER 6 185.855 0.00000 0.879650E-10 BERNSTEIN 5 25.2784 0.00000 0.00000 BIS 5 11.0876 0.888178E-15 0.888178E-15 BIW 5 2.36051 0.101754E-14 0.393126E-14 BODEWIG 4 12.7279 0.708784E-15 0.866075E-15 BOOTHROYD 5 886.710 0.00000 0.511553E-10 BORDERBAND 5 2.76699 0.00000 0.00000 CARRY 5 1.41391 0.117630E-12 0.240612E-12 CAUCHY 5 682.273 0.942556E-13 0.175311E-12 CHEBY_T 5 12.6886 0.00000 0.00000 CHEBY_U 5 22.4277 0.00000 0.00000 CHEBY_VAN2 5 2.17945 0.591396E-15 0.474151E-15 CHEBY_VAN3 5 3.87298 0.754695E-15 0.886967E-15 CHOW 5 202.501 0.166606E-12 0.334083E-12 CIRCULANT --- NOT READY CIRCULANT2 5 16.5831 0.129402E-14 0.114595E-14 CLEMENT1 6 8.36660 0.00000 0.647646E-15 CLEMENT2 6 10.1600 0.110404E-14 0.513928E-15 COMBIN 5 20.7778 0.110466E-14 0.116670E-14 COMPANION 5 6.68633 0.166533E-15 0.732188E-15 COMPLEX_I 2 1.41421 0.00000 0.00000 CONEX1 4 8.12995 0.00000 0.00000 CONEX2 3 2.64876 0.00000 0.00000 CONEX3 5 3.87298 0.00000 0.00000 CONFERENCE 6 5.47723 0.00000 0.742465E-15 DAUB2 4 2.00000 0.888178E-15 0.00000 DAUB4 8 2.82843 0.210011E-14 0.396675E-15 DAUB6 12 3.46410 0.139744E-14 0.113170E-14 DAUB8 16 4.00000 0.464930E-14 0.176073E-14 DAUB10 20 4.47214 0.869739E-14 0.165358E-14 DAUB12 24 4.89898 0.195470E-13 0.224395E-14 DIAGONAL 5 6.38020 0.00000 0.00000 DIF1 6 3.16228 0.00000 0.00000 DIF2 5 5.29150 0.686635E-15 0.113951E-14 DORR 5 533.003 0.157817E-14 0.187187E-14 DOWNSHIFT 5 2.23607 0.00000 0.00000 EULERIAN 5 77.2981 0.00000 0.250443E-12 EXCHANGE 5 2.23607 0.00000 0.00000 FIBONACCI2 5 3.00000 0.00000 0.00000 FIBONACCI3 5 3.60555 0.00000 0.157009E-15 FIEDLER 7 30.1350 0.444956E-14 0.222153E-13 FORSYTHE 5 10.7723 0.607649E-16 0.234360E-15 FOURIER_COSINE 5 2.23607 0.101176E-14 0.108890E-14 FOURIER_SINE 5 2.23607 0.175717E-14 0.747084E-15 FRANK 5 11.6190 0.00000 0.347485E-13 GFPP 5 9.39618 0.223197E-13 0.325770E-15 GIVENS 5 20.6155 0.00000 0.00000 GK316 5 9.43398 0.710890E-15 0.705075E-15 GK323 5 10.0000 0.00000 0.00000 GK324 5 11.4577 0.134607E-14 0.244061E-14 HANKEL_N 6 21.0000 0.00000 0.680716E-15 HANOWA 8 11.1099 0.647366E-15 0.566105E-15 HARMAN 8 5.05359 0.954191E-06 0.709414E-14 HARTLEY 5 5.00000 0.275896E-14 0.901980E-15 HELMERT 5 2.23607 0.741186E-15 0.509651E-15 HELMERT2 5 2.23607 0.651343E-15 0.648880E-15 HERMITE 5 54.1941 0.00000 0.00000 HERNDON 5 1.77133 0.710890E-15 0.178578E-14 HILBERT 5 1.58091 0.727596E-11 0.201079E-10 HOUSEHOLDER 5 2.23607 0.100796E-14 0.113592E-14 IDENTITY 5 2.23607 0.00000 0.00000 ILL3 3 817.763 0.471661E-10 0.163698E-10 INTEGRATION 6 4.19580 0.841835E-15 0.555112E-16 INVOL 5 1942.46 0.727596E-11 0.840355E-10 JACOBI 6 1.65145 0.00000 0.736439E-15 JORDAN 6 7.25072 0.248253E-15 0.248253E-15 KAHAN 5 0.715639 0.421363E-14 0.748798E-15 KERSHAW 4 8.24621 0.00000 0.444089E-14 KERSHAWTRI 5 8.73845 0.482153E-15 0.372947E-15 KMS 5 101.704 0.194337E-13 0.219797E-13 LAGUERRE 5 6.85376 0.00000 0.173921E-13 LEGENDRE 5 6.80762 0.268032E-15 0.248253E-15 LEHMER 5 3.28041 0.141744E-14 0.220341E-14 LESP 5 22.3487 0.759974E-15 0.422830E-15 LIETZKE 5 18.0278 0.695553E-15 0.489906E-14 LINE_ADJ 6 3.16228 0.00000 0.00000 LOTKIN 5 2.45676 0.00000 0.288028E-10 MAXIJ 5 19.8746 0.00000 0.137775E-14 MILNES 5 11.4577 0.134607E-14 0.244061E-14 MINIJ 5 12.4499 0.00000 0.00000 MOLER1 5 61.8850 0.392428E-10 0.505038E-10 MOLER3 5 8.66025 0.00000 0.00000 ORTEGA 5 244.268 0.313937E-11 0.126134E-11 ORTH_SYMM 5 2.23607 0.220932E-14 0.115654E-14 OTO 5 5.29150 0.686635E-15 0.113951E-14 PARTER 5 6.34077 0.696142E-16 0.748746E-15 PASCAL1 5 9.94987 0.00000 0.00000 PASCAL2 5 92.4608 0.00000 0.00000 PASCAL3 5 124.742 0.572858E-13 0.325166E-12 PDS_RANDOM 5 1.46230 0.602445E-14 0.784616E-15 PEI 5 6.04036 0.200148E-15 0.122355E-14 PERMUTATION_RANDOM 5 2.23607 0.00000 0.00000 PLU 5 152.462 0.125663E-14 0.113274E-14 RIS 5 3.17039 0.837173E-16 0.735818E-15 RODMAN 5 12.7897 0.800593E-15 0.819196E-15 RUTIS1 4 16.6132 0.105471E-14 0.151741E-14 RUTIS2 4 11.4018 0.683824E-15 0.599455E-15 RUTIS3 4 14.1421 0.601660E-15 0.860331E-15 RUTIS4 5 59.1270 0.288694E-12 0.933214E-12 RUTIS5 4 23.7697 0.00000 0.480611E-11 SCHUR_BLOCK 5 8.39978 0.632925E-15 0.785046E-16 SPLINE 5 20.8244 0.139536E-14 0.759726E-15 STIRLING 5 67.9191 0.00000 0.376704E-13 SWEET1 6 70.1997 0.108864E-12 0.158877E-14 SWEET2 6 30.1433 0.343382E-13 0.662637E-14 SWEET3 6 73.4234 0.143445E-12 0.129962E-14 SWEET4 13 119.704 0.256668E-12 0.422388E-14 SUMMATION 5 3.87298 0.00000 0.00000 SYLVESTER_KAC 6 10.4881 0.00000 0.00000 SYMM_RANDOM 5 6.38020 0.686820E-14 0.124701E-14 TRI_UPPER 5 9.18086 0.419288E-13 0.615348E-14 TRIS 5 13.3888 0.708057E-15 0.485716E-15 TRIV 5 11.1204 0.984932E-15 0.132769E-14 TRIW 5 9.39629 0.00000 0.00000 UPSHIFT 5 2.23607 0.00000 0.00000 VAND1 5 466.164 0.538191E-14 0.899295E-14 VAND2 5 466.164 0.538191E-14 0.441062E-13 WILK03 3 1.39284 0.674350E-06 0.674350E-06 WILK04 4 1.89545 10.7174 0.482362E-04 WILK05 5 1.51485 0.122740E-08 0.742989E-09 WILK21 21 28.4605 0.382082E-14 0.155131E-14 WILSON 4 30.5450 0.00000 0.636941E-12 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. ||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 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 PASCAL2 5 5 92.4608 0.00000 PLU 5 5 152.462 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 Demonstrate functions which test 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_PRB Normal end of execution. 17 April 2015 11:20:15.174 AM