Thu Sep 13 20:11:56 2018 TEST_MAT_TEST Python version: 3.6.5 Test the TEST_MAT library. BVEC_NEXT_GRLEX_TEST Python version: 3.6.5 BVEC_NEXT_GRLEX computes binary vectors in GRLEX order. 0: 0 0 0 0 1: 0 0 0 1 2: 0 0 1 0 3: 0 1 0 0 4: 1 0 0 0 5: 0 0 1 1 6: 0 1 0 1 7: 0 1 1 0 8: 1 0 0 1 9: 1 0 1 0 10: 1 1 0 0 11: 0 1 1 1 12: 1 0 1 1 13: 1 1 0 1 14: 1 1 1 0 15: 1 1 1 1 16: 0 0 0 0 BVEC_NEXT_GRLEX_TEST: Normal end of execution. C8_I_TEST Python version: 3.6.5 C8_I returns the value of the imaginary unit. C1=C8_I ( ) = (0,1) C2= C1 * C1 = (-1,0) C8_I_TEST: Normal end of execution. C8_NORMAL_01_TEST Python version: 3.6.5 C8_NORMAL_01 computes pseudonormal complex values. The initial seed is 123456789 1 ( 1.679040, -0.472769 ) 2 ( -0.566060, -0.231124 ) 3 ( 1.212934, 0.535037 ) 4 ( 1.269381, 1.049543 ) 5 ( -1.666087, -1.865228 ) 6 ( -2.242464, 0.735809 ) 7 ( 0.039675, -1.350736 ) 8 ( 0.673068, 0.007775 ) 9 ( -0.275127, 0.374940 ) 10 ( 2.164005, 0.185600 ) C8_NORMAL_01_TEST: Normal end of execution. C8_UNIFORM_01_TEST Python version: 3.6.5 C8_UNIFORM_01 computes pseudorandom complex values in the unit circle. The initial seed is 123456789 0 ( 0.44986, -0.126667 ) 1 ( -0.843197, -0.34428 ) 2 ( 0.589627, 0.26009 ) 3 ( 0.39114, 0.3234 ) 4 ( -0.139466, -0.156136 ) 5 ( -0.236066, 0.0774593 ) 6 ( 0.0185993, -0.633214 ) 7 ( 0.89285, 0.0103136 ) 8 ( -0.560465, 0.763795 ) 9 ( 0.306357, 0.0262752 ) C8_UNIFORM_01_TEST: Normal end of execution. C8MAT_IDENTITY_TEST Python version: 3.6.5 C8MAT_IDENTITY returns the complex identity matrix. Identity matrix: Col: 0 1 2 3 Row 0 : 1 0i 0 0i 0 0i 0 0i 1 : 0 0i 1 0i 0 0i 0 0i 2 : 0 0i 0 0i 1 0i 0 0i 3 : 0 0i 0 0i 0 0i 1 0i C8MAT_IDENTITY_TEST: Normal end of execution. C8MAT_INDICATOR_TEST Python version: 3.6.5 C8MAT_INDICATOR returns the complex indicator matrix. Indicator matrix: Col: 0 1 2 Row 0 : 1 -1i 1 -2i 1 -3i 1 : 2 -1i 2 -2i 2 -3i 2 : 3 -1i 3 -2i 3 -3i 3 : 4 -1i 4 -2i 4 -3i 4 : 5 -1i 5 -2i 5 -3i C8MAT_INDICATOR_TEST: Normal end of execution. C8MAT_UNIFORM_01_TEST Python version: 3.6.5 C8MAT_UNIFORM_01 computes a random C8MAT. 0 <= X <= 1 Initial seed is 123456789 Random C8MAT: Col: 0 1 2 Row 0 : 0.44986 -0.126667i -0.236066 0.0774593i 0.500804 -0.779931i 1 : -0.843197 -0.34428i 0.0185993 -0.633214i 0.350471 0.0165551i 2 : 0.589627 0.26009i 0.89285 0.0103136i 0.434989 -0.266623i 3 : 0.39114 0.3234i -0.560465 0.763795i -0.200947 0.270711i 4 : -0.139466 -0.156136i 0.306357 0.0262752i -0.0974599 0.901881i C8MAT_UNIFORM_01_TEST: Normal end of execution. C8VEC_PRINT_TEST Python version: 3.6.5 C8VEC_PRINT prints an C8VEC. Here is a C8VEC: 0 1 2 1 3 4 2 5 6 3 7 8 C8VEC_PRINT_TEST: Normal end of execution. C8VEC_UNIFORM_01_TEST Python version: 3.6.5 C8VEC_UNIFORM_01 computes pseudorandom complex values in the unit circle. The initial seed is 123456789 0 ( 0.449860, -0.126667 ) 1 ( -0.843197, -0.344280 ) 2 ( 0.589627, 0.260090 ) 3 ( 0.391140, 0.323400 ) 4 ( -0.139466, -0.156136 ) 5 ( -0.236066, 0.077459 ) 6 ( 0.018599, -0.633214 ) 7 ( 0.892850, 0.010314 ) 8 ( -0.560465, 0.763795 ) 9 ( 0.306357, 0.026275 ) C8VEC_UNIFORM_01_TEST: Normal end of execution. C8VEC_UNITY_TEST Python version: 3.6.5 C8VEC_UNITY returns the N roots of unity. The N roots of unity: 0 1 0 1 0.866025 0.5 2 0.5 0.866025 3 6.12323e-17 1 4 -0.5 0.866025 5 -0.866025 0.5 6 -1 1.22465e-16 7 -0.866025 -0.5 8 -0.5 -0.866025 9 -1.83697e-16 -1 10 0.5 -0.866025 11 0.866025 -0.5 C8VEC_UNITY_TEST: Normal end of execution. COMPLETE_SYMMETRIC_POLY_TEST Python version: 3.6.5 COMPLETE_SYMMETRIC_POLY evaluates a complete symmetric polynomial in a given set of variables X. Variable vector X: 0: 1 1: 2 2: 3 3: 4 4: 5 N\R 0 1 2 3 4 5 0 1 0 0 0 0 0 1 1 1 1 1 1 1 2 1 3 7 15 31 63 3 1 6 25 90 301 966 4 1 10 65 350 1701 7770 5 1 15 140 1050 6951 42525 COMPLETE_SYMMETRIC_POLY_TEST: Normal end of execution. I4_FACTOR_TEST Python version: 3.6.5 I4_FACTOR factors an integer. The integer is 2516 Prime representation: I, FACTOR(I), POWER(I) 0 2 2 1 17 1 2 37 1 I4_FACTOR_TEST Normal end of execution. I4_IS_EVEN_TEST Python version: 3.6.5 I4_IS_EVEN reports whether an I4 is even. I I4_IS_EVEN(I) -2 True -1 False 0 True 1 False 2 True 3 False 4 True 5 False 6 True 7 False 8 True 9 False 10 True 11 False 12 True 13 False 14 True 15 False 16 True 17 False 18 True 19 False 20 True 21 False 22 True 23 False 24 True 25 False I4_IS_EVEN_TEST Normal end of execution. I4_IS_ODD_TEST Python version: 3.6.5 I4_IS_ODD reports whether an I4 is odd. I I4_IS_ODD(I) -2 False -1 True 0 False 1 True 2 False 3 True 4 False 5 True 6 False 7 True 8 False 9 True 10 False 11 True 12 False 13 True 14 False 15 True 16 False 17 True 18 False 19 True 20 False 21 True 22 False 23 True 24 False 25 True I4_IS_ODD_TEST Normal end of execution. I4_IS_PRIME_TEST Python version: 3.6.5 I4_IS_PRIME reports whether an I4 is prime. I I4_IS_PRIME(I) -2 False -1 False 0 False 1 False 2 True 3 True 4 False 5 True 6 False 7 True 8 False 9 False 10 False 11 True 12 False 13 True 14 False 15 False 16 False 17 True 18 False 19 True 20 False 21 False 22 False 23 True 24 False 25 False I4_IS_PRIME_TEST Normal end of execution. I4_LOG_10_TEST Python version: 3.6.5 I4_LOG_10: whole part of log base 10, X, I4_LOG_10 0 0 1 0 2 0 3 0 9 0 10 1 11 1 99 1 101 2 -1 0 -2 0 -3 0 -9 0 I4_LOG_10_TEST Normal end of execution. I4_MODP_TEST Python version: 3.6.5 I4_MODP factors a number into a multiple M and a positive remainder R. Number Divisor Multiple Remainder 107 50 2 7 107 -50 -2 7 -107 50 -3 43 -107 -50 3 43 Repeat using Python % Operator: 107 50 2 7 107 -50 -3 -43 -107 50 -3 43 -107 -50 2 -7 I4_MODP_TEST Normal end of execution. I4_RISE_TEST Python version: 3.6.5 I4_RISE evaluates the rising factorial Fall(I,N). M N Exact I4_RISE(M,N) 5 0 1 1 5 1 5 5 5 2 30 30 5 3 210 210 5 4 1680 1680 5 5 15120 15120 5 6 151200 151200 50 0 1 1 10 1 10 10 4000 1 4000 4000 10 2 110 110 18 3 6840 6840 4 4 840 840 98 3 970200 970200 1 7 5040 5040 I4_RISE_TEST Normal end of execution. I4_RISE_VALUES_TEST: Python version: 3.6.5 I4_RISE_VALUES returns values of the integer rising factorial. M N I4_RISE(M,N) 5 0 1 5 1 5 5 2 30 5 3 210 5 4 1680 5 5 15120 5 6 151200 50 0 1 10 1 10 4000 1 4000 10 2 110 18 3 6840 4 4 840 98 3 970200 1 7 5040 I4_RISE_VALUES_TEST: Normal end of execution. I4_SIGN_TEST Python version: 3.6.5 I4_SIGN returns the sign of an I4. I4 I4_SIGN(I4) -10 -1 -7 -1 0 1 5 1 9 1 I4_SIGN_TEST Normal end of execution. I4_UNIFORM_AB_TEST Python version: 3.6.5 I4_UNIFORM_AB computes pseudorandom values in an interval [A,B]. The lower endpoint A = -100 The upper endpoint B = 200 The initial seed is 123456789 1 -35 2 187 3 149 4 69 5 25 6 -81 7 -23 8 -67 9 -87 10 90 11 -82 12 35 13 20 14 127 15 139 16 -100 17 170 18 5 19 -72 20 -96 I4_UNIFORM_AB_TEST: Normal end of execution. I4_WRAP_TEST Python version: 3.6.5 I4_WRAP forces an integer to lie within given limits. ILO = 4 IHI = 8 I I4_WRAP(I) -10 5 -9 6 -8 7 -7 8 -6 4 -5 5 -4 6 -3 7 -2 8 -1 4 0 5 1 6 2 7 3 8 4 4 5 5 6 6 7 7 8 8 9 4 10 5 11 6 12 7 13 8 14 4 15 5 16 6 17 7 18 8 19 4 20 5 I4_WRAP_TEST Normal end of execution. I4MAT_PRINT_TEST: Python version: 3.6.5 Test I4MAT_PRINT, which prints an I4MAT. A 5 x 6 integer matrix: Col: 0 1 2 3 4 Row 0: 11 12 13 14 15 1: 21 22 23 24 25 2: 31 32 33 34 35 3: 41 42 43 44 45 4: 51 52 53 54 55 Col: 5 Row 0: 16 1: 26 2: 36 3: 46 4: 56 I4MAT_PRINT_TEST: Normal end of execution. I4MAT_PRINT_SOME_TEST Python version: 3.6.5 I4MAT_PRINT_SOME prints some of an I4MAT. Here is I4MAT, rows 0:2, cols 3:5: Col: 3 4 5 Row 0: 14 15 16 1: 24 25 26 2: 34 35 36 I4MAT_PRINT_SOME_TEST: Normal end of execution. I4VEC_INDICATOR0_TEST Python version: 3.6.5 I4VEC_INDICATOR0 returns an indicator vector. The indicator0 vector: 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 I4VEC_INDICATOR0_TEST Normal end of execution. I4VEC_PRINT_TEST Python version: 3.6.5 I4VEC_PRINT prints an I4VEC. Here is an I4VEC: 0 91 1 92 2 93 3 94 I4VEC_PRINT_TEST: Normal end of execution. LEGENDRE_SYMBOL_TEST Python version: 3.6.5 LEGENDRE_SYMBOL computes the Legendre symbol (Q/P) which records whether Q is a quadratic residue modulo the prime P. Legendre Symbols for P = 7 7 0 0 7 1 1 7 2 1 7 3 -1 7 4 1 7 5 -1 7 6 -1 7 7 0 Legendre Symbols for P = 11 11 0 0 11 1 1 11 2 -1 11 3 1 11 4 1 11 5 1 11 6 -1 11 7 -1 11 8 -1 11 9 1 11 10 -1 11 11 0 Legendre Symbols for P = 13 13 0 0 13 1 1 13 2 -1 13 3 1 13 4 1 13 5 -1 13 6 -1 13 7 -1 13 8 -1 13 9 1 13 10 1 13 11 -1 13 12 1 13 13 0 Legendre Symbols for P = 17 17 0 0 17 1 1 17 2 1 17 3 -1 17 4 1 17 5 -1 17 6 -1 17 7 -1 17 8 1 17 9 1 17 10 -1 17 11 -1 17 12 -1 17 13 1 17 14 -1 17 15 1 17 16 1 17 17 0 LEGENDRE_SYMBOL_TEST_TEST Normal end of execution. MERTENS_TEST Python version: 3.6.5 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 MERTENS_TEST Normal end of execution. MERTENS_VALUES_TEST: Python version: 3.6.5 MERTENS_VALUES stores values of the MERTENS function. N MERTENS(N) 1 1 2 0 3 -1 4 -1 5 -2 6 -1 7 -2 8 -2 9 -2 10 -1 11 -2 12 -2 100 1 1000 2 10000 -23 MERTENS_VALUES_TEST: Normal end of execution. MOEBIUS_TEST Python version: 3.6.5 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 MOEBIUS_TEST Normal end of execution. MOEBIUS_VALUES_TEST: Python version: 3.6.5 MOEBIUS_VALUES stores values of the MOEBIUS function. N MOEBIUS(N) 1 1 2 -1 3 -1 4 0 5 -1 6 1 7 -1 8 0 9 0 10 1 11 -1 12 0 13 -1 14 1 15 1 16 0 17 -1 18 0 19 -1 20 0 MOEBIUS_VALUES_TEST: Normal end of execution. PRIME_TEST Python version: 3.6.5 PRIME returns primes from a table. Number of primes stored is 1600 I Prime(I) 1 2 2 3 3 5 4 7 5 11 6 13 7 17 8 19 9 23 10 29 1590 13411 1591 13417 1592 13421 1593 13441 1594 13451 1595 13457 1596 13463 1597 13469 1598 13477 1599 13487 1600 13499 PRIME_TEST Normal end of execution. R8_CHOOSE_TEST Python version: 3.6.5 R8_CHOOSE evaluates C(N,K). N K CNK 0 0 1 1 0 1 1 1 1 2 0 1 2 1 2 2 2 1 3 0 1 3 1 3 3 2 3 3 3 1 4 0 1 4 1 4 4 2 6 4 3 4 4 4 1 5 0 1 5 1 5 5 2 10 5 3 10 5 4 5 5 5 1 R8_CHOOSE_TEST Normal end of execution. R8_FACTORIAL_TEST Python version: 3.6.5 R8_FACTORIAL evaluates the factorial function. N Exact Computed 0 1 1 1 1 1 2 2 2 3 6 6 4 24 24 5 120 120 6 720 720 7 5040 5040 8 40320 40320 9 362880 362880 10 3628800 3628800 11 39916800 39916800 12 479001600 479001600 13 6227020800 6227020800 14 87178291200 87178291200 15 1307674368000 1307674368000 16 20922789888000 20922789888000 17 355687428096000 355687428096000 18 6402373705728000 6402373705728000 19 1.21645100408832e+17 1.21645100408832e+17 20 2.43290200817664e+18 2.43290200817664e+18 25 1.551121004333099e+25 1.551121004333099e+25 50 3.041409320171338e+64 3.041409320171338e+64 100 9.332621544394415e+157 9.33262154439441e+157 150 5.713383956445855e+262 5.71338395644585e+262 R8_FACTORIAL_TEST Normal end of execution. R8_MOP_TEST Python version: 3.6.5 R8_MOP evaluates (-1.0)^I4 as an R8. I4 R8_MOP(I4) -57 -1.0 92 1.0 66 1.0 12 1.0 -17 -1.0 -87 -1.0 -49 -1.0 -78 1.0 -92 1.0 27 -1.0 R8_MOP_TEST Normal end of execution. R8_NORMAL_01_TEST Python version: 3.6.5 R8_NORMAL_01 generates normally distributed random values. Using initial random number seed = 123456789 1.679040 -0.566060 1.212934 1.269381 -1.666087 -2.242464 0.039675 0.673068 -0.275127 2.164005 0.297785 2.044536 1.398819 -1.242985 -0.067084 -0.794396 -0.523768 -0.350567 0.131700 0.537380 R8_NORMAL_01_TEST Normal end of execution. R8_RISE_TEST Python version: 3.6.5 R8_RISE evaluates the rising factorial Rise(X,N). X N Exact Computed 5 4 1680 1680 5.25 4 1962.59765625 1962.59765625 5.5 4 2279.0625 2279.0625 5.75 4 2631.97265625 2631.97265625 6 4 3024 3024 7.5 0 1 1 7.5 1 7.5 7.5 7.5 2 63.75 63.75 7.5 3 605.625 605.625 7.5 4 6359.0625 6359.0625 7.5 5 73129.21875 73129.21875 7.5 6 914115.234375 914115.234375 7.5 7 12340555.6640625 12340555.6640625 7.5 8 178938057.1289063 178938057.1289062 7.5 9 2773539885.498047 2773539885.498047 R8_RISE_TEST Normal end of execution. R8_SIGN_TEST Python version: 3.6.5 R8_SIGN returns the sign of an R8. R8 R8_SIGN(R8) -1.2500 -1 -0.2500 -1 0.0000 1 0.5000 1 9.0000 1 R8_SIGN_TEST Normal end of execution. R8_UNIFORM_01_TEST Python version: 3.6.5 R8_UNIFORM_01 produces a sequence of random values. Using random seed 123456789 SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 Verify that the sequence can be restarted. Set the seed back to its original value, and see that we generate the same sequence. SEED R8_UNIFORM_01(SEED) 469049721 0.218418 2053676357 0.956318 1781357515 0.829509 1206231778 0.561695 891865166 0.415307 141988902 0.066119 553144097 0.257578 236130416 0.109957 94122056 0.043829 1361431000 0.633966 R8_UNIFORM_01_TEST Normal end of execution. R8_UNIFORM_AB_TEST Python version: 3.6.5 R8_UNIFORM_AB returns random values in a given range: [ A, B ] For this problem: A = 10.000000 B = 20.000000 12.184183 19.563176 18.295092 15.616954 14.153071 10.661187 12.575778 11.099568 10.438290 16.339657 R8_UNIFORM_AB_TEST Normal end of execution R8COL_SWAP_TEST Python version: 3.6.5 R8COL_SWAP swaps two columns of an R8COL. The array: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 Swap columns 0 and 2 The updated matrix: Col: 0 1 2 3 Row 0 : 13 12 11 14 1 : 23 22 21 24 2 : 33 32 31 34 R8COL_SWAP_TEST Normal end of execution. R8MAT_HOUSE_AXH_TEST Python version: 3.6.5 R8MAT_HOUSE_AXH multiplies a matrix A times a compact Householder matrix. Matrix A: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : 3.29509 -3.90043 -0.986937 -1.49248 -3.76896 3 : 0.616954 -4.56171 2.54673 -4.05455 -4.92488 4 : -0.846929 1.33966 2.97287 -4.86383 -2.39697 Compact vector V so column 3 of H*A is packed: 0: 0 1: 0 2: -0.788819 3: 0.399863 4: 0.466771 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 -0.244469 0.630839 0.736395 3 : 0 0 0.630839 0.680219 -0.373289 4 : 0 0 0.736395 -0.373289 0.56425 Indirect product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 Direct product A*H: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 0.573215 -7.49385 0.65837 1 : 4.56318 -2.42422 5.14095 1.11322 0.0678026 2 : 3.29509 -3.90043 -3.47568 -0.230898 -2.29629 3 : 0.616954 -4.56171 -6.80702 0.686997 0.610057 4 : -0.846929 1.33966 -5.56019 -0.538306 2.65233 H*A should pack column 3: Col: 0 1 2 3 4 Row 0 : -2.81582 -4.33881 -4.38273 -4.98162 3.59097 1 : 4.56318 -2.42422 -0.50461 3.97504 3.40847 2 : -1.04002 -0.937652 4.03706 -5.7746 -3.95052 3 : 2.81449 -6.06358 -4.44089e-16 -1.88388 -4.83284 4 : 1.71831 -0.41352 -4.44089e-16 -2.32995 -2.28953 R8MAT_HOUSE_AXH_TEST Normal end of execution. R8MAT_HOUSE_FORM_TEST Python version: 3.6.5 R8MAT_HOUSE_FORM forms a Householder matrix from its compact form. Compact vector form V: 0: 0 1: 0 2: 1 3: 2 4: 3 Householder matrix H: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : 0 1 0 0 0 2 : 0 0 0.857143 -0.285714 -0.428571 3 : 0 0 -0.285714 0.428571 -0.857143 4 : 0 0 -0.428571 -0.857143 -0.285714 R8MAT_HOUSE_FORM_TEST Normal end of execution. R8MAT_INDICATOR_TEST Python version: 3.6.5 R8MAT_INDICATOR creates an "indicator" R8MAT. The indicator matrix: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 R8MAT_INDICATOR_TEST Normal end of execution. R8MAT_IS_ADJACENCY_TEST Python version: 3.6.5 R8MAT_IS_ADJACENCY reports whether a matrix is an adjacency matrix. Not square matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 Adjacency = False Not symmetric matrix: Col: 0 1 2 3 Row 0 : 1 0 1 0 1 : 0 1 0 0 2 : 1 0 1 0 3 : 0 0 1 1 T = 1 Adjacency = False Not zero/one matrix: Col: 0 1 2 3 Row 0 : 1 0 2 0 1 : 0 1 0 0 2 : 2 0 1 1 3 : 0 0 1 1 T = 0 Adjacency = False Adjacency matrix: Col: 0 1 2 3 Row 0 : 1 0 1 0 1 : 0 1 0 0 2 : 1 0 1 1 3 : 0 0 1 1 T = 0 Adjacency = True R8MAT_IS_ADJACENCY_TEST Normal end of execution. R8MAT_IS_ANTICIRCULANT_TEST Python version: 3.6.5 R8MAT_IS_ANTICIRCULANT reports whether a matrix is an anticirculant matrix. Circulant matrix: Col: 0 1 2 3 4 Row 0 : 0 1 2 3 4 1 : 4 0 1 2 3 2 : 3 4 0 1 2 3 : 2 3 4 0 1 Anticirculant = False Anticirculant matrix: Col: 0 1 2 3 4 Row 0 : 0 1 2 3 4 1 : 1 2 3 4 0 2 : 2 3 4 0 1 3 : 3 4 0 1 2 Anticirculant = True R8MAT_IS_ANTICIRCULANT_TEST Normal end of execution. R8MAT_IS_ANTISYMMETRIC_TEST Python version: 3.6.5 R8MAT_IS_ANTISYMMETRIC reports whether a matrix is antisymmetric. Not square matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 Antisymmetric = False Not antisymmetric matrix: Col: 0 1 2 3 Row 0 : 0 5 1 -2 1 : -5 0 3 0 2 : 1 -3 6 4 3 : 2 0 -4 0 Antisymmetric = False Antisymmetric matrix: Col: 0 1 2 3 Row 0 : 0 5 -1 -2 1 : -5 0 3 0 2 : 1 -3 0 4 3 : 2 0 -4 0 Antisymmetric = True R8MAT_IS_ANTISYMMETRIC_TEST Normal end of execution. R8MAT_IS_EIGEN_LEFT_TEST: Python version: 3.6.5 R8MAT_IS_EIGEN_LEFT tests the error in the left eigensystem A' * X - X * LAMBDA = 0 Matrix A: Col: 0 1 2 3 Row 0 : 0.136719 0.605469 0.253906 0.00390625 1 : 0.0585938 0.527344 0.394531 0.0195312 2 : 0.0195312 0.394531 0.527344 0.0585938 3 : 0.00390625 0.253906 0.605469 0.136719 Eigenmatrix X: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 11 3 -1 -3 2 : 11 -3 -1 3 3 : 1 -1 1 -1 Eigenvalues LAM: 0: 1 1: 0.25 2: 0.0625 3: 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: Python version: 3.6.5 R8MAT_IS_EIGEN_RIGHT tests the error in the right eigensystem A * X - X * LAMBDA = 0 Matrix A: Col: 0 1 2 3 Row 0 : 0.136719 0.605469 0.253906 0.00390625 1 : 0.0585938 0.527344 0.394531 0.0195312 2 : 0.0195312 0.394531 0.527344 0.0585938 3 : 0.00390625 0.253906 0.605469 0.136719 Eigenmatrix X: Col: 0 1 2 3 Row 0 : 1 6 11 6 1 : 1 2 -1 -2 2 : 1 -2 -1 2 3 : 1 -6 11 -6 Eigenvalues LAM: 0: 1 1: 0.25 2: 0.0625 3: 0.015625 Frobenius norm of A*X-X*LAMBDA is 0 R8MAT_IS_EIGEN_RIGHT_TEST Normal end of execution. R8MAT_IS_IDENTITY_TEST Python version: 3.6.5 R8MAT_IS_IDENTITY reports the Frobenius norm difference between a given matrix A and the identity matrix. Zero matrix: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 Difference is 2 Identity matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 Difference is 0 Almost identity matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1.001 0.002 0.003 2 : 0 0.002 1.004 0.006 3 : 0 0.003 0.006 1.009 Difference is 0.014 R8MAT_IS_IDENTITY_TEST Normal end of execution. R8MAT_IS_INTEGER_TEST Python version: 3.6.5 R8MAT_IS_INTEGER reports the Frobenius norm of the distance between a matrix A and the nearest integer matrix. MAXIJ matrix: Col: 0 1 2 3 Row 0 : 1 2 3 4 1 : 2 2 3 4 2 : 3 3 3 4 3 : 4 4 4 4 4 : 5 5 5 5 Frobenius norm = 0 INVOL matrix: Col: 0 1 2 3 Row 0 : -4 0.5 0.333333 0.25 1 : -120 20 15 12 2 : 240 -45 -36 -30 3 : -140 28 23.3333 20 Frobenius norm = 0.731247 R8MAT_IS_INTEGER_TEST Normal end of execution. R8MAT_IS_INVERSE_TEST: Python version: 3.6.5 R8MAT_IS_INVERSE tests the error in a matrix inverse: A * B - I = 0 B * A - I = 0 Matrix A: Col: 0 1 2 3 Row 0 : 2 1 3 4 1 : 1 -3 1 5 2 : 3 1 6 -2 3 : 4 5 -2 -1 Inverse matrix B: Col: 0 1 2 3 Row 0 : -0.244718 0.290493 0.139085 0.195423 1 : 0.290493 -0.272887 -0.100352 -0.00176056 2 : 0.139085 -0.100352 0.0792254 -0.103873 3 : 0.195423 -0.00176056 -0.103873 -0.0193662 Frobenius norm of error is 7.08784e-16 R8MAT_IS_INVERSE_TEST Normal end of execution. R8MAT_IS_LLT_TEST: Python version: 3.6.5 R8MAT_IS_LLT tests the error in a lower triangular Cholesky factorization ||A-L*L'||. Matrix A: Col: 0 1 2 3 Row 0 : 2 1 0 0 1 : 1 2 1 0 2 : 0 1 2 1 3 : 0 0 1 2 Factor L: Col: 0 1 2 3 Row 0 : 1.41421 0 0 0 1 : 0.707107 1.22474 0 0 2 : 0 0.816497 1.1547 0 3 : 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: Python version: 3.6.5 R8MAT_IS_NULL_LEFT tests whether the M vector X is a left null vector of A, that is, A'*x=0. Matrix A: Col: 0 1 2 Row 0 : 1 2 3 1 : 4 5 6 2 : 7 8 9 Vector X: 0: 1 1: -2 2: 1 Frobenius norm of A'*x is 0 R8MAT_IS_NULL_LEFT_TEST Normal end of execution. R8MAT_IS_NULL_RIGHT_TEST: Python version: 3.6.5 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: 0 1 2 Row 0 : 1 2 3 1 : 4 5 6 2 : 7 8 9 Vector X: 0: 1 1: -2 2: 1 Frobenius norm of A*x is 0 R8MAT_IS_NULL_RIGHT_TEST Normal end of execution. R8MAT_IS_ORTHOGONAL_TEST Python version: 3.6.5 R8MAT_IS_ORTHOGONAL reports the Frobenius norm difference between A'*A and the identity matrix. Random orthogonal matrix: Col: 0 1 2 3 Row 0 : -0.673118 0.24773 0.247806 -0.651256 1 : 0.22693 -0.629923 0.714709 -0.202215 2 : -0.486259 -0.730621 -0.477383 0.043016 3 : -0.508888 0.0895489 0.44709 0.730154 Frobenius error = 8.84049e-16 Summation matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 1 1 0 3 : 1 1 1 1 Frobenius error = 7.34847 R8MAT_IS_ORTHOGONAL_TEST Normal end of execution. R8MAT_IS_ORTHOGONAL_COLUMN_TEST Python version: 3.6.5 R8MAT_IS_ORTHOGONAL_COLUMN reports the Frobenius norm difference between A'*A and the MxM identity matrix. Random 4x4 orthogonal matrix: Col: 0 1 2 3 Row 0 : -0.673118 0.24773 0.247806 -0.651256 1 : 0.22693 -0.629923 0.714709 -0.202215 2 : -0.486259 -0.730621 -0.477383 0.043016 3 : -0.508888 0.0895489 0.44709 0.730154 Frobenius error = 8.84049e-16 3 columns of random 4x4 orthogonal matrix: Col: 0 1 2 Row 0 : -0.673118 0.24773 0.247806 1 : 0.22693 -0.629923 0.714709 2 : -0.486259 -0.730621 -0.477383 3 : -0.508888 0.0895489 0.44709 Frobenius error = 8.33823e-16 3 rows of random 4x4 orthogonal matrix: Col: 0 1 2 3 Row 0 : -0.673118 0.24773 0.247806 -0.651256 1 : 0.22693 -0.629923 0.714709 -0.202215 2 : -0.486259 -0.730621 -0.477383 0.043016 Frobenius error = 1 R8MAT_IS_ORTHOGONAL_COLUMN_TEST Normal end of execution. R8MAT_IS_ORTHOGONAL_ROW_TEST Python version: 3.6.5 R8MAT_IS_ORTHOGONAL_ROW reports the Frobenius norm difference between A*A' and the NxN identity matrix. Random 4x4 orthogonal matrix: Col: 0 1 2 3 Row 0 : -0.673118 0.24773 0.247806 -0.651256 1 : 0.22693 -0.629923 0.714709 -0.202215 2 : -0.486259 -0.730621 -0.477383 0.043016 3 : -0.508888 0.0895489 0.44709 0.730154 Frobenius error = 8.70893e-16 3 columns of random 4x4 orthogonal matrix: Col: 0 1 2 Row 0 : -0.673118 0.24773 0.247806 1 : 0.22693 -0.629923 0.714709 2 : -0.486259 -0.730621 -0.477383 3 : -0.508888 0.0895489 0.44709 Frobenius error = 1 3 rows of random 4x4 orthogonal matrix: Col: 0 1 2 3 Row 0 : -0.673118 0.24773 0.247806 -0.651256 1 : 0.22693 -0.629923 0.714709 -0.202215 2 : -0.486259 -0.730621 -0.477383 0.043016 Frobenius error = 7.72981e-16 R8MAT_IS_ORTHOGONAL_ROW_TEST Normal end of execution. R8MAT_IS_PERMUTATION_TEST Python version: 3.6.5 R8MAT_IS_PERMUTATION reports whether A is a permutation matrix. Zero matrix Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 Zero matrix is NOT a permutation matrix. Identity matrix Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 Identity matrix is a permutation matrix. 2 * Identity matrix Col: 0 1 2 3 Row 0 : 2 0 0 0 1 : 0 2 0 0 2 : 0 0 2 0 3 : 0 0 0 2 2 * Identity matrix is NOT a permutation matrix. M1 Col: 0 1 2 3 Row 0 : 0 0 1 0 1 : 0 0 0 1 2 : 1 0 0 0 3 : 0 1 0 0 M1 is a permutation matrix. M2 Col: 0 1 2 3 Row 0 : 0 0 1 0 1 : 0 1 0 1 2 : 1 0 0 0 3 : 0 0 0 0 M2 is NOT a permutation matrix. R8MAT_IS_PERMUTATION_TEST Normal end of execution. R8MAT_IS_PLU_TEST: Python version: 3.6.5 R8MAT_IS_PLU tests the error in the P*L*U factorization: A - P * L * U = 0 Matrix A: Col: 0 1 2 3 Row 0 : 5 7 6 5 1 : 7 10 8 7 2 : 6 8 10 9 3 : 5 7 9 10 Permutation P: Col: 0 1 2 3 Row 0 : 0 0 0 1 1 : 1 0 0 0 2 : 0 1 0 0 3 : 0 0 1 0 Lower triangular L: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0.857143 1 0 0 2 : 0.714286 0.25 1 0 3 : 0.714286 0.25 -0.2 1 Upper triangular U: Col: 0 1 2 3 Row 0 : 7 10 8 7 1 : 0 -0.571429 3.14286 3 2 : 0 0 2.5 4.25 3 : 0 0 0 0.1 Frobenius norm of A-P*L*U is 7.32411e-15 R8MAT_IS_PLU_TEST Normal end of execution. R8MAT_IS_SOLUTION_TEST: Python version: 3.6.5 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_IS_SOLUTION_TEST Normal end of execution. R8MAT_IS_SPARSE_TEST Python version: 3.6.5 R8MAT_IS_SPARSE reports whether a matrix is sparse. Zero matrix: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 Sparseness = 0 Identity-like matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 Sparseness = 0.25 Hardly sparse: Col: 0 1 2 3 Row 0 : 0 1 2 3 1 : 4 5 6 7 2 : 8 9 10 11 3 : 12 13 14 15 Sparseness = 0.9375 R8MAT_IS_SPARSE_TEST Normal end of execution. R8MAT_IS_SQUARE_TEST Python version: 3.6.5 R8MAT_IS_SQUARE reports whether a matrix is square. Not square matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 Square = False Square matrix: Col: 0 1 2 3 Row 0 : 1 0 1 0 1 : 0 1 0 0 2 : 1 0 1 0 3 : 0 0 1 1 Square = True R8MAT_IS_SQUARE_TEST Normal end of execution. R8MAT_IS_SYMMETRIC_TEST Python version: 3.6.5 R8MAT_IS_SYMMETRIC reports whether a matrix is symmetric. Not square matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 Symmetric = False Not symmetric matrix: Col: 0 1 2 3 Row 0 : 1 0 1 0 1 : 0 1 0 0 2 : 1 0 1 0 3 : 0 0 1 1 T = 1 Symmetric = False Symmetric matrix: Col: 0 1 2 3 Row 0 : 1 0 2 0 1 : 0 1 0 0 2 : 2 0 1 1 3 : 0 0 1 1 T = 0 Symmetric = True R8MAT_IS_SYMMETRIC_TEST Normal end of execution. R8MAT_IS_ZERO_ONE_TEST Python version: 3.6.5 R8MAT_IS_ZERO_ONE reports whether a matrix only has entries of 0 and 1. Zero matrix: Col: 0 1 2 3 Row 0 : 0 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 0 4 : 0 0 0 0 Zero/one = True Identity matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 1 0 3 : 0 0 0 1 4 : 0 0 0 0 Zero/one = True Almost identity matrix: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1.001 0.002 0.003 2 : 0 0.002 1.004 0.006 3 : 0 0.003 0.006 1.009 4 : 0 0.004 0.008 0.012 Zero/one = False R8MAT_IS_ZERO_ONE_TEST Normal end of execution. R8MAT_MM_TEST Python version: 3.6.5 R8MAT_MM computes a matrix-matrix product C = A * B; A: Col: 0 1 2 Row 0 : 1 0 0 1 : 1 1 0 2 : 1 2 1 3 : 1 3 3 B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 0 1 2 3 2 : 0 0 1 3 C = A*B: Col: 0 1 2 3 Row 0 : 1 1 1 1 1 : 1 2 3 4 2 : 1 3 6 10 3 : 1 4 10 19 R8MAT_MM_TEST Normal end of execution. R8MAT_MTM_TEST Python version: 3.6.5 R8MAT_MTM computes a matrix-matrix product C = A' * B; A: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 B: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 1 1 0 0 2 : 1 2 1 0 C = A'*B: Col: 0 1 2 3 Row 0 : 3 3 1 0 1 : 3 5 2 0 2 : 1 2 1 0 3 : 0 0 0 0 R8MAT_MTM_TEST Normal end of execution. R8MAT_MTV_TEST Python version: 3.6.5 R8MAT_MTV computes a matrix-vector product b = A' * x; A: Col: 0 1 Row 0 : 1 1 1 : 2 1 2 : 3 1 3 : 4 1 X: 0: 1 1: 2 2: 3 3: 4 B = A'*X: 0: 30 1: 10 R8MAT_MTV_TEST Normal end of execution. R8MAT_MV_TEST Python version: 3.6.5 R8MAT_MV computes a matrix-vector product b = A * x; A: Col: 0 1 Row 0 : 1 1 1 : 2 1 2 : 3 1 3 : 4 1 X: 0: 1 1: 2 B = A*X: 0: 3 1: 4 2: 5 3: 6 R8MAT_MV_TEST Normal end of execution. R8MAT_PRINT_TEST Python version: 3.6.5 R8MAT_PRINT prints an R8MAT. Here is an R8MAT: Col: 0 1 2 3 4 Row 0 : 11 12 13 14 15 1 : 21 22 23 24 25 2 : 31 32 33 34 35 3 : 41 42 43 44 45 Col: 5 Row 0 : 16 1 : 26 2 : 36 3 : 46 R8MAT_PRINT_TEST: Normal end of execution. R8MAT_PRINT_SOME_TEST Python version: 3.6.5 R8MAT_PRINT_SOME prints some of an R8MAT. Here is an R8MAT: Col: 3 4 5 Row 0 : 14 15 16 1 : 24 25 26 2 : 34 35 36 R8MAT_PRINT_SOME_TEST: Normal end of execution. R8MAT_SUB_TEST Python version: 3.6.5 R8MAT_SUB computes C = A - B; A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 B: Col: 0 1 2 3 Row 0 : 11 21 31 41 1 : 12 22 32 42 2 : 13 23 33 43 3 : 14 24 34 44 C = A - B: Col: 0 1 2 3 Row 0 : 0 -9 -18 -27 1 : 9 0 -9 -18 2 : 18 9 0 -9 3 : 27 18 9 0 R8MAT_SUB_TEST Normal end of execution. R8MAT_TRANSPOSE_TEST Python version: 3.6.5 R8MAT_TRANSPOSE transposes an R8MAT. Matrix A: Col: 0 1 2 3 Row 0 : 11 12 13 14 1 : 21 22 23 24 2 : 31 32 33 34 3 : 41 42 43 44 4 : 51 52 53 54 Transposed matrix At: Col: 0 1 2 3 4 Row 0 : 11 21 31 41 51 1 : 12 22 32 42 52 2 : 13 23 33 43 53 3 : 14 24 34 44 54 R8MAT_TRANSPOSE_TEST Normal end of execution. R8MAT_UNIFORM_01_TEST Python version: 3.6.5 R8MAT_UNIFORM_01 computes a random R8MAT. 0 <= X <= 1 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.218418 0.0661187 0.0617272 0.00183837 1 : 0.956318 0.257578 0.449539 0.897504 2 : 0.829509 0.109957 0.401306 0.350752 3 : 0.561695 0.043829 0.754673 0.0945448 4 : 0.415307 0.633966 0.797287 0.0136169 R8MAT_UNIFORM_01_TEST: Normal end of execution. R8MAT_UNIFORM_AB_TEST Python version: 3.6.5 R8MAT_UNIFORM_AB computes a random R8MAT. -1 <= X <= 5 Initial seed is 123456789 Random R8MAT: Col: 0 1 2 3 Row 0 : 0.31051 -0.603288 -0.629637 -0.98897 1 : 4.73791 0.545467 1.69723 4.38502 2 : 3.97706 -0.340259 1.40784 1.10451 3 : 2.37017 -0.737026 3.52804 -0.432731 4 : 1.49184 2.80379 3.78372 -0.918299 R8MAT_UNIFORM_AB_TEST: Normal end of execution. R8POLY_PRINT_TEST Python version: 3.6.5 R8POLY_PRINT prints an R8POLY. The R8POLY: p(x) = 9 * x^5 + 0.78 * x^4 + 56 * x^2 - 3.4 * x + 12 R8POLY_PRINT_TEST: Normal end of execution. R8VEC_HOUSE_COLUMN_TEST Python version: 3.6.5 R8VEC_HOUSE_COLUMN returns the compact form of a Householder matrix that "packs" a column of a matrix. Matrix A: Col: 0 1 2 3 Row 0 : 1.09209 2.07654 0.219145 2.00653 1 : 4.78159 0.330594 3.16983 3.77337 2 : 4.14755 1.28789 0.308636 3.98643 3 : 2.80848 0.549784 2.24769 0.00919186 Working on column K = 0 Householder matrix H: Col: 0 1 2 3 Row 0 : -0.155781 -0.682069 -0.591626 -0.400615 1 : -0.682069 0.597486 -0.34914 -0.236418 2 : -0.591626 -0.34914 0.697156 -0.205068 3 : -0.400615 -0.236418 -0.205068 0.86114 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 :-8.88178e-16 -1.79845 1.1053 -0.508058 2 :-1.77636e-15 -0.558841 -1.48213 0.272729 3 :-8.88178e-16 -0.700714 1.03509 -2.50551 Working on column K = 1 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 -0.895014 -0.278112 -0.348717 2 : 0 -0.278112 0.959184 -0.0511776 3 : 0 -0.348717 -0.0511776 0.93583 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.59868e-15 2.00941 -0.938018 1.25258 2 :-1.41139e-15 7.63278e-17 -1.78201 0.531121 3 :-4.30552e-16 0 0.659083 -2.18152 Working on column K = 2 Householder matrix H: Col: 0 1 2 3 Row 0 : 1 0 0 0 1 : 0 1 0 0 2 : 0 0 -0.937906 0.346889 3 : 0 0 0.346889 0.937906 Product H*A: Col: 0 1 2 3 Row 0 : -7.01042 -1.53117 -3.27924 -5.24844 1 : 1.59868e-15 2.00941 -0.938018 1.25258 2 : 1.17439e-15 -7.15884e-17 1.89999 -1.25489 3 : -8.9341e-16 2.64773e-17 1.11022e-16 -1.86183 R8VEC_HOUSE_COLUMN_TEST Normal end of execution. R8VEC_NINT_TEST Python version: 3.6.5 R8VEC_NINT rounds an R8VEC. Vector A: 0: -2.81582 1: 4.56318 2: 3.29509 3: 0.616954 4: -0.846929 Rounded vector A: 0: -3 1: 5 2: 3 3: 1 4: -1 R8VEC_NINT_TEST: Normal end of execution. R8VEC_NORM_L2_TEST Python version: 3.6.5 R8VEC_NORM_L2 computes the L2 norm of an R8VEC. Input vector: 0: -5.63163 1: 9.12635 2: 6.59018 3: 1.23391 4: -1.69386 5: -8.67763 6: -4.84844 7: -7.80086 8: -9.12342 9: 2.67931 L2 norm = 20.3201 R8VEC_NORM_L2_TEST: Normal end of execution. R8VEC_PRINT_TEST Python version: 3.6.5 R8VEC_PRINT prints an R8VEC. Here is an R8VEC: 0: 123.456 1: 5e-06 2: -1e+06 3: 3.14159 R8VEC_PRINT_TEST: Normal end of execution. R8VEC_UNIFORM_01_TEST Python version: 3.6.5 R8VEC_UNIFORM_01 computes a random R8VEC. Initial seed is 123456789 Random R8VEC: 0: 0.218418 1: 0.956318 2: 0.829509 3: 0.561695 4: 0.415307 5: 0.0661187 6: 0.257578 7: 0.109957 8: 0.043829 9: 0.633966 R8VEC_UNIFORM_01_TEST: Normal end of execution. R8VEC_UNIFORM_AB_TEST Python version: 3.6.5 R8VEC_UNIFORM_AB computes a random R8VEC. -1 <= X <= 5 Initial seed is 123456789 Random R8VEC: 0: 0.31051 1: 4.73791 2: 3.97706 3: 2.37017 4: 1.49184 5: -0.603288 6: 0.545467 7: -0.340259 8: -0.737026 9: 2.80379 R8VEC_UNIFORM_AB_TEST: Normal end of execution. TIMESTAMP_TEST: Python version: 3.6.5 TIMESTAMP prints a timestamp of the current date and time. Thu Sep 13 20:11:57 2018 TIMESTAMP_TEST: Normal end of execution. TEST_CONDITION Python version: 3.6.5 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 4 10.4366 10.4366 BOOTHROYD 5 1.002e+06 1.002e+06 COMBIN 3 5.4822 5.4822 COMPANION 5 14.5786 14.5786 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 7.39629 7.39629 DIF2 5 18 18 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 14333.5 14333.5 PEI 5 4.90227 4.90227 RODMAN 5 5.859 5.859 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_CONDITION Normal end of execution. TEST_DETERMINANT Python version: 3.6.5 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 BAB 5 -1980.11 -1980.11 14 BAUER 6 1 1 1.9e+02 BERNSTEIN 5 96 96 25 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_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 CHEBY_VAN3 5 13.9754 13.9754 3.9 CHOW 5 -70.5488 -70.5488 2e+02 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 -2.81582 -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 5 -577.824 577.824 19 FORSYTHE 5 1975.68 1975.68 11 FORSYTHE 5 1975.68 1975.68 11 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 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 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 -7.16657e-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 5 1 1 4 INVOL 5 -1 -1 1.9e+03 JACOBI 5 0 0 1.5 JACOBI 6 -0.021645 -0.021645 1.7 JORDAN 5 -177.02 -177.02 6.6 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 LINE_ADJ 5 0 0 2.8 LINE_ADJ 6 -1 -1 3.2 LINE_LOOP_ADJ 5 0 0 3.6 LOTKIN 5 1.87465e-11 1.87465e-11 2.5 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 0.000890221 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 REDHEFFER 5 -2 -2 3.7 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 SPLINE 5 -2566.72 -2566.72 21 STIRLING 5 1 1 68 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_KAC 5 0 0 7.7 SYLVESTER_KAC 6 -225 -225 10 SYMM_RANDOM 5 22.1228 22.1228 6.4 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 UPSHIFT 5 1 1 2.2 VAND1 5 133985 133985 4.7e+02 VAND2 5 133985 133985 4.7e+02 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 WILK21 21 -4.15825e+12 -4.15825e+12 28 WILSON 4 1 1 31 ZERO 5 0 0 0 TEST_DETERMINANT Normal end of execution. TEST_EIGEN_LEFT Python version: 3.6.5 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 1.23246e-14 CARRY 5 5 1.41391 3.57943e-15 CHOW 5 5 202.501 4.61541e-13 DIAGONAL 5 5 6.3802 0 ROSSER1 8 8 2482.26 2.61994e-11 SYMM_RANDOM 5 5 6.3802 1.79855e-15 TEST_EIGEN_LEFT: Normal end of execution. TEST_EIGEN_RIGHT Python version: 3.6.5 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 1.33427e-14 BAB 5 5 14.3605 4.36701e-15 BODEWIG 4 4 12.7279 9.17346e-15 CARRY 5 5 1.41391 1.17642e-15 CHOW 5 5 202.501 2.40401e-13 COMBIN 5 5 20.7778 7.10543e-15 DIF2 5 5 5.2915 1.07099e-15 EXCHANGE 5 5 2.23607 0 IDEM_RANDOM 5 5 1.73205 5.23369e-16 IDENTITY 5 5 2.23607 0 ILL3 3 3 817.763 1.62356e-11 KERSHAW 4 4 8.24621 4.80549e-15 KMS 5 5 2.32288 3.2055e-08 LINE_ADJ 5 5 2.82843 8.99223e-16 LINE_LOOP_ADJ 5 5 3.60555 9.99459e-16 ONE 5 5 5 0 ORTEGA 5 5 244.268 3.45197e-13 OTO 5 5 5.2915 1.07099e-15 PDS_RANDOM 5 5 1.4623 3.88036e-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 1.46286e-14 SYLVESTER_KAC 5 5 7.74597 0 SYMM_RANDOM 5 5 6.3802 1.75168e-15 WILK12 12 12 53.591 1.01528e-07 WILSON 4 4 30.545 2.48731e-14 ZERO 5 5 0 0 TEST_EIGEN_RIGHT: Normal end of execution. TEST_INVERSE Python version: 3.6.5 A = a test matrix of order N B = inverse as computed by a routine. C = inverse as computed by the numpy.linalg.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 7.4e-16 7.1e-16 BAB 5 14 0.72 7.3e-16 9.5e-16 BAUER 6 1.9e+02 2.1e+04 6.2e-11 0 BERNSTEIN 5 25 3.2 0 0 BIS 5 11 3.9 8.9e-16 2e-15 BIW 5 2.4 26 1e-15 1e-15 BODEWIG 4 13 0.68 7.4e-16 7.1e-16 BOOTHROYD 5 8.9e+02 8.9e+02 6.1e-11 0 BORDERBAND 5 2.8 6.8 0 0 CARRY 5 1.4 3.1e+03 1e-12 1.2e-13 CAUCHY 5 6.8e+02 61 1e-13 9.4e-14 CHEBY_T 5 13 1.9 0 0 CHEBY_U 5 22 1.2 5.6e-16 0 CHEBY_VAN2 5 2.2 2.5 6.2e-16 5.9e-16 CHEBY_VAN3 5 3.9 1.3 7.1e-16 7.5e-16 CHOW 5 2e+02 2.7e+02 1.4e-13 2.6e-13 CLEMENT1 6 8.4 1.5 1.3e-16 0 CLEMENT2 6 10 2.7 1e-15 1.1e-15 COMBIN 5 21 0.71 1.1e-15 1.1e-15 COMPANION 5 6.7 2.9 3.3e-16 1.7e-16 COMPLEX_I 2 1.4 1.4 0 0 CONEX1 4 8.1 6.4 6.3e-17 0 CONEX2 3 2.6 4.3 0 0 CONEX3 5 3.9 11 0 0 CONEX4 4 31 99 4.4e-13 0 CONFERENCE 6 5.5 1.1 9.7e-16 0 DAUB2 4 2 2 0 8.9e-16 DAUB4 8 2.8 2.8 4.3e-16 2.1e-15 DAUB6 12 3.5 3.5 1.2e-15 1.4e-15 DAUB8 16 4 4 1.7e-15 4.6e-15 DAUB10 20 4.5 4.5 1.6e-15 8.7e-15 DAUB12 24 4.9 4.9 2.3e-15 2e-14 DIAGONAL 5 6.4 2.1 0 0 DIF1 6 3.2 3.5 0 0 DIF2 5 5.3 3.9 1.2e-15 6.9e-16 DORR 5 5.3e+02 0.038 1.9e-15 1.6e-15 DOWNSHIFT 5 2.2 2.2 0 0 EULERIAN 5 77 7.8e+02 5.5e-13 0 EXCHANGE 5 2.2 2.2 0 0 FIBONACCI2 5 3 3.5 0 0 FIBONACCI3 5 3.6 1.6 4.2e-16 0 FIEDLER 7 30 3.3 2.7e-14 4.4e-15 FORSYTHE 5 11 0.52 5.6e-17 6.1e-17 FOURIER_COSINE 5 2.2 2.2 1e-15 1e-15 FOURIER_SINE 5 2.2 2.2 8.3e-16 1.8e-15 FRANK 5 12 59 8.7e-15 0 GFPP 5 9.4 1 7.1e-16 2.2e-14 GIVENS 5 21 2.7 0 0 GK316 5 9.4 1.8 7.4e-16 7.1e-16 GK323 5 10 2.3 0 0 GK324 5 11 5.6 3.3e-15 1.3e-15 HANKEL_N 5 15 0.55 4.4e-16 0 HANOWA 6 8.7 0.71 3.8e-16 6.5e-16 HARMAN 8 5.1 15 5.8e-15 1.1e-14 HARTLEY 5 5 1 1e-15 2.8e-15 HELMERT 5 2.2 2.2 4.5e-16 8.2e-16 HELMERT2 5 2.2 2.2 7.7e-16 6.5e-16 HERMITE 5 54 1.8 3.2e-15 0 HERNDON 5 1.8 9.4 1.2e-15 7.1e-16 HILBERT 5 1.6 3e+05 1.6e-11 7.3e-12 HOUSEHOLDER 5 2.2 2.2 9.4e-16 1e-15 IDENTITY 5 2.2 2.2 0 0 ILL3 3 8.2e+02 3.4e+02 1.2e-11 0 INTEGRATION 5 4 7.5 0 7.6e-16 INVOL 5 1.9e+03 1.9e+03 1.2e-10 7.3e-12 JACOBI 6 1.7 6.5 2.2e-16 0 JORDAN 5 6.6 0.84 2.2e-16 2.2e-16 KAHAN 5 0.72 4.3e+02 1.8e-16 1.5e-14 KERSHAW 4 8.2 8.2 4.8e-15 0 KERSHAWTRI 5 8.7 0.69 1.3e-16 4.8e-16 KMS 5 1e+02 2.5 1.4e-14 1.9e-14 LAGUERRE 5 6.9 2e+02 1.7e-14 0 LEGENDRE 5 6.8 1.9 6.6e-16 2.7e-16 LEHMER 5 3.3 7.7 1.3e-15 1.4e-15 LESP 5 22 0.32 4e-16 7.6e-16 LIETZKE 5 18 2.4 2.6e-15 7e-16 LINE_ADJ 6 3.2 3.5 0 0 LOTKIN 5 2.5 2.4e+05 2.7e-11 0 MAXIJ 5 20 4.7 6e-15 0 MILNES 5 11 5.6 3.3e-15 1.3e-15 MINIJ 5 12 5 0 0 MOLER1 5 62 2.8e+04 6.2e-11 4.1e-11 MOLER3 5 8.7 1.2e+02 0 0 ORTEGA 5 2.4e+02 91 1.3e-12 3.1e-12 ORTH_SYMM 5 2.2 2.2 9.9e-16 2.2e-15 OTO 5 5.3 3.9 1.2e-15 6.9e-16 PARTER 5 6.3 0.94 6e-16 7e-17 PASCAL1 5 9.9 9.9 0 0 PASCAL2 5 92 92 0 0 PASCAL3 5 1.2e+02 1.2e+02 5e-14 5.7e-14 PDS_RANDOM 5 1.5 5.7 9.6e-16 3.3e-15 PEI 5 6 0.85 7.8e-16 2e-16 PERMUTATION_RANDOM 5 2.2 2.2 0 0 PLU 5 1.5e+02 0.14 9.7e-16 1.3e-15 RIS 5 3.2 1.9 6e-16 8.4e-17 RODMAN 5 13 0.53 9.1e-16 8e-16 RUTIS1 4 17 1 1.6e-15 1.1e-15 RUTIS2 4 11 1.1 3.4e-16 6.8e-16 RUTIS3 4 14 0.58 9e-16 6e-16 RUTIS4 4 51 18 7.3e-14 9.1e-14 RUTIS5 4 24 1.9e+03 5.4e-12 0 SCHUR_BLOCK 5 8.4 0.65 5.6e-17 6.3e-16 SPLINE 5 21 0.97 5.4e-16 1.4e-15 STIRLING 5 68 32 2.7e-14 0 SUMMATION 5 3.9 3 0 0 SWEET1 6 70 0.26 2.4e-15 1.1e-13 SWEET2 6 30 1.4 4.6e-15 3.4e-14 SWEET3 6 73 0.34 1.5e-15 1.4e-13 SWEET4 13 1.2e+02 0.38 3.3e-15 2.6e-13 SYLVESTER_KAC 6 10 2.5 2.2e-16 0 SYMM_RANDOM 5 6.4 2.1 1.5e-15 3.4e-15 TRI_UPPER 5 9.2 1.7e+02 4.2e-14 4.2e-14 TRIS 5 13 0.4 4.2e-16 7.1e-16 TRIV 5 11 1.1 3.5e-16 9.8e-16 TRIW 5 9.4 4.6e+02 0 0 UPSHIFT 5 2.2 2.2 0 0 VAND1 5 4.7e+02 1.3 7e-15 5.1e-15 VAND2 5 4.7e+02 1.3 7.4e-14 5.1e-15 WILK03 3 1.4 1.8e+10 7.7e-07 6.7e-07 WILK04 4 1.9 1.2e+16 4.8e-05 11 WILK05 5 1.5 3.1e+06 6.8e-10 1.2e-09 WILK21 21 28 4.3 1.6e-15 3.8e-15 WILSON 4 31 99 4.3e-13 0 TEST_INVERSE: Normal end of execution. TEST_LLT Python version: 3.6.5 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 5.25453e-15 TEST_LLT: Normal end of execution. TEST_NULL_LEFT Python version: 3.6.5 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 4.5e-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 2.23607 0 TEST_NULL_LEFT: Normal end of execution. TEST_NULL_RIGHT Python version: 3.6.5 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 6.5e-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_NULL_RIGHT: Normal end of execution. TEST_PLU Python version: 3.6.5 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|| 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 2.60787e-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_PLU: Normal end of execution. TEST_SOLUTION Python version: 3.6.5 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 BODEWIG 4 4 1 12.7279 0 DIF2 10 10 2 7.61577 0 FRANK 10 10 2 38.6652 0 POISSON 20 20 1 19.5448 0 WILK03 3 3 1 1.39284 6.7435e-07 WILK04 4 4 1 1.89545 3.95105e-05 WILSON 4 4 1 30.545 0 TEST_SOLUTION Normal end of execution. TEST_MAT_TEST: Normal end of execution. Thu Sep 13 20:11:57 2018