Wed Oct 8 07:29:18 2025 condition_test(): python version: 3.10.12 numpy version: 1.26.4 Test condition() combin_test(): combin() computes the COMBIN matrix. COMBIN matrix: Col: 0 1 2 3 Row 0 : 6.4 2.2 2.2 2.2 1 : 2.2 6.4 2.2 2.2 2 : 2.2 2.2 6.4 2.2 3 : 2.2 2.2 2.2 6.4 conex1_test() conex1() computes the CONEX1 matrix. CONEX1 matrix: Col: 0 1 2 3 Row 0 : 1 -1 -130.006 0 1 : 0 1 65.0031 -65.0031 2 : 0 1 66.0031 -66.0031 3 : 0 0 0 65.0031 conex2_test() conex2() computes the CONEX2 matrix. CONEX2 matrix: Col: 0 1 2 Row 0 : 1 0.991423 -2 1 : 0 0.0926112 -0.0926112 2 : 0 0 1 conex3_test conex3 computes the CONEX3 matrix. CONEX3 matrix: Col: 0 1 2 3 4 Row 0 : 1 0 0 0 0 1 : -1 1 0 0 0 2 : -1 -1 1 0 0 3 : -1 -1 -1 1 0 4 : -1 -1 -1 -1 -1 conex4_test conex4 computes the CONEX4 matrix. CONEX4 matrix: Col: 0 1 2 3 Row 0 : 7 10 8 7 1 : 6 8 10 9 2 : 5 7 9 10 3 : 5 7 6 5 kahan_test() kahan() computes the KAHAN matrix. KAHAN matrix: Col: 0 1 2 3 4 Row 0 : 0.65733 -0.495366 -0.495366 -0.495366 -0.495366 1 : 0 0.432083 -0.325619 -0.325619 -0.325619 2 : 0 0 0.284022 -0.214039 -0.214039 3 : 0 0 0 0.186696 -0.140695 4 : 0 0 0 0 0.122721 r8_sign_test(): 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 r8ge_fa_test01() r8ge_fa() computes the LU factors, r8ge_sl() solves a factored system. Matrix order N = 10 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution: 0: 1 1: 1 2: 1 3: 1 4: 1 5: 1 6: 1 7: 1 8: 1 9: 1 Solution of transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8ge_fa_test02() r8ge_fa() computes the LU factors, r8ge_sl() solves a factored system. Matrix order N = 5 The matrix: Col: 0 1 2 3 4 Row 0 : 0.736496 0.518778 0.760603 0.978573 0.706526 1 : 0.54646 0.868336 0.17252 0.855371 0.284758 2 : 0.86408 0.600701 0.930144 0.321443 0.58595 3 : 0.128653 0.583944 0.732032 0.909299 0.124131 4 : 0.73957 0.564549 0.201985 0.36123 0.516249 The compressed LU factors: Col: 0 1 2 3 4 Row 0 : 0.86408 0.600701 0.930144 0.321443 0.58595 1 : -0.632418 0.494506 0.593543 0.861439 0.0368887 2 : -0.852347 -0.0136942 -1.00198 -0.198792 -0.122244 3 : -0.14889 -0.987737 -0.0402512 0.700797 0.211509 4 : -0.855904 -0.101933 -0.653334 -0.182897 0.0521537 The pivot vector P: [2 3 3 3 4] Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 r8vec_max_abs_index_test(): r8vec_max_abs_index(): index of entry of maximum absolute value Input vector: 0: 2.64282 1: 6.24748 2: -3.85267 3: 6.22803 4: 8.03248 5: -4.83724 6: 2.73462 7: -4.47569 8: 5.52576 9: 8.34073 Maximum index: 9 r8vec_uniform_unit_test(): r8vec_uniform_unit() returns a random R8VEC on the surface of the unit M sphere. Vector: 0: -0.234128 1: -0.000924834 2: 0.816058 3: 0.384495 4: -0.362486 Vector: 0: 0.472545 1: -0.556866 2: 0.0729504 3: 0.522713 4: -0.433648 Vector: 0: -0.559489 1: -0.162119 2: 0.460704 3: 0.330314 4: -0.582524 Vector: 0: -0.692032 1: 0.660831 2: 0.0906903 3: 0.10075 4: -0.256942 Vector: 0: -0.560453 1: -0.78766 2: 0.109153 3: 0.222633 4: -0.0632828 cond_test() cond() is the condition number estimator built into Python. Matrix Order Condition Estimate Combinatorial 4 10 10 CONEX1 4 80601 80601 CONEX2 3 601.97 601.97 CONEX3 5 80 80 CONEX4 4 4488 4488 KAHAN 4 646.712 646.712 RANDOM 4 47.9367 47.9367 RANDOM 4 16.6398 16.6398 RANDOM 4 83.9544 83.9544 RANDOM 4 26.0912 26.0912 RANDOM 4 14.4464 14.4464 condition_hager_test() condition_hager() estimates the L1 condition number for a matrix in general storage. Matrix Order Condition Hager Combinatorial 4 10 10 CONEX1 4 80601 810.02 CONEX2 3 601.97 601.97 CONEX3 5 80 80 CONEX4 4 4488 4488 KAHAN 4 646.712 646.712 RANDOM 4 12.581 5.41581 RANDOM 4 25.6132 25.6132 RANDOM 4 191.749 191.749 RANDOM 4 105.289 105.289 RANDOM 4 32.2691 32.2691 condition_linpack_test(): condition_linpack() estimates the L1 condition number for a matrix in general storage. Matrix Order Condition Linpack Combinatorial 4 10 7 CONEX1 4 80601 565.586 CONEX2 3 601.97 7.50657 CONEX3 5 80 5 CONEX4 4 4488 3238.09 KAHAN 4 646.712 574.664 RANDOM 4 23.7564 19.9609 RANDOM 4 703.765 599.87 RANDOM 4 205.841 159.594 RANDOM 4 18.641 14.9233 RANDOM 4 22.2535 17.52 condition_sample1_test() condition_sample1() estimates the L1 condition number using sampling for a matrix in general storage. Matrix Samples Order Condition Estimate Combinatorial 10 4 10 7 Combinatorial 1000 4 10 8.39925 Combinatorial 100000 4 10 9.63855 CONEX1 10 4 80601 12.6014 CONEX1 1000 4 80601 36.9794 CONEX1 100000 4 80601 540.403 CONEX2 10 3 601.97 5.46652 CONEX2 1000 3 601.97 70.6156 CONEX2 100000 3 601.97 439.027 CONEX3 10 5 80 3.34874 CONEX3 1000 5 80 8.3661 CONEX3 100000 5 80 22.1776 CONEX4 10 4 4488 16.66 CONEX4 1000 4 4488 70.8347 CONEX4 100000 4 4488 331.73 KAHAN 10 4 646.712 4.91684 KAHAN 1000 4 646.712 29.6765 KAHAN 100000 4 646.712 214.258 RANDOM 10 4 172.54 4.64234 RANDOM 1000 4 172.54 20.1092 RANDOM 100000 4 172.54 90.6098 RANDOM 10 4 125.31 3.6692 RANDOM 1000 4 125.31 17.4145 RANDOM 100000 4 125.31 66.309 RANDOM 10 4 35.9786 6.75158 RANDOM 1000 4 35.9786 18.0179 RANDOM 100000 4 35.9786 32.3274 RANDOM 10 4 39.1939 5.02485 RANDOM 1000 4 39.1939 23.4465 RANDOM 100000 4 39.1939 37.379 RANDOM 10 4 20.552 6.1688 RANDOM 1000 4 20.552 13.9846 RANDOM 100000 4 20.552 19.5426 condition_test(): Normal end of execution. Wed Oct 8 07:30:14 2025