Wed Oct 8 08:50:30 2025 r8gb_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8gb(). r8gb_det_test(): r8gb_det() computes the determinant of an R8GB matrix which has been factored by r8gb_fa. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 3 Upper bandwidth MU = 2 A random R8GB matrix: Col: 0 1 2 3 4 Row 0 : 0.76693 0.359447 0.0031444 1 : 0.109387 0.578805 0.815423 0.138705 2 : 0.933191 0.447189 0.0557802 0.496158 0.285392 3 : 0.23732 0.0415892 0.360228 0.818228 0.676274 4 : 0.121106 0.423507 0.891178 0.691044 5 : 0.588894 0.0708847 0.450191 6 : 0.791586 0.281044 7 : 0.442121 Col: 5 6 7 8 9 Row 3 : 0.404737 4 : 0.573467 0.543725 5 : 0.885107 0.844638 0.220248 6 : 0.888751 0.213594 0.663832 0.393344 7 : 0.847174 0.27572 0.40754 0.621411 0.151659 8 : 0.405799 0.188901 0.099189 0.202594 0.926156 9 : 0.750512 0.835323 0.79629 0.804387 r8gb_det() computes the determinant = -0.004248189622457356 np.linalg.det() computes the determinant = -0.004248189622457355 r8gb_dif2_test(): r8gb_dif2() returns an R8GB second difference matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8GB second difference matrix: Col: 0 1 2 3 4 Row 0 : 2 -1 1 : -1 2 -1 2 : -1 2 -1 3 : -1 2 -1 4 : -1 2 r8gb_fa_test(): r8gb_fa() computes the PLU factors of an R8GB matrix. Number of matrix rows M = 5 Number of matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The banded matrix: Col: 0 1 2 3 4 Row 0 : 0.71248 0.426578 0.351952 1 : 0.812745 0.470591 0.491606 0.674231 2 : 0.719315 0.306895 0.757567 0.0971564 3 : 0.38475 0.344561 0.170556 4 : 0.799495 0.764302 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 2.33797 1: 3.52571 2: 3.79485 3: 8.99688 4: 4.7952 Solution to Ax=b: 0: 1 1: 2 2: 3 3: 4 4: 5 r8gb_indicator_test(): r8gb_indicator() returns an R8GB indicator matrix. Matrix rows M = 10 Matrix columns N = 8 Lower bandwidth ML = 3 Upper bandwidth MU = 2 The R8GB indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 13 1 : 21 22 23 24 2 : 31 32 33 34 35 3 : 41 42 43 44 45 4 : 52 53 54 55 5 : 63 64 65 6 : 74 75 7 : 85 Col: 5 6 7 Row 3 : 46 4 : 56 57 5 : 66 67 68 6 : 76 77 78 7 : 86 87 88 8 : 96 97 98 9 : 107 108 R8GB_ML_test R8GB_ML computes A*x or A*X where A has been factored by r8gb_fa(). Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 A*x and PLU*x 0: 1.59369 1.59369 1: 4.5896 4.5896 2: 5.43891 5.43891 3: 12.4714 12.4714 4: 9.25123 9.25123 5: 9.95863 9.95863 6: 18.2728 18.2728 7: 26.2441 26.2441 8: 21.3749 21.3749 9: 13.1618 13.1618 A*x and (PLU)*x 0: 1.53568 1.53568 1: 1.52014 1.52014 2: 3.62974 3.62974 3: 8.51335 8.51335 4: 8.60905 8.60905 5: 8.8092 8.8092 6: 10.0518 10.0518 7: 10.7825 10.7825 8: 7.28453 7.28453 9: 16.3262 16.3262 R8GB_MTV_test R8GB_MTV computes b=A*x, where A is an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The random R8GB matrix: Col: 0 1 2 3 4 Row 0 : 0.377369 0.830797 0.240257 1 : 0.122953 0.0194089 0.970056 0.67145 2 : 0.206551 0.284011 0.48709 0.00112684 3 : 0.879557 0.046154 0.151695 4 : 0.350845 0.760032 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 0.623276 1: 1.48927 2: 6.55063 3: 4.74301 4: 4.41032 R8GB_MU_test R8GB_MU computes A*x or A*X where A has been factored by R8GB_TRF. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 A*x and PLU*x 0: 4.99478 4.99478 1: 3.53983 3.53983 2: 5.96865 5.96865 3: 7.6952 7.6952 4: 9.99644 9.99644 5: 16.2192 16.2192 6: 15.3397 15.3397 7: 14.346 14.346 8: 9.31828 9.31828 9: 11.1173 11.1173 A*x and (PLU)*x 0: 1.14633 1.14633 1: 2.68182 2.68182 2: 6.18381 6.18381 3: 3.81155 3.81155 4: 9.5978 9.5978 5: 11.8341 11.8341 6: 11.9287 11.9287 7: 22.3245 22.3245 8: 18.4526 18.4526 9: 16.4227 16.4227 R8GB_MV_test R8GB_MV computes b=A*x, where A is an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The random R8GB matrix: Col: 0 1 2 3 4 Row 0 : 0.430881 0.220764 0.758409 1 : 0.11651 0.176506 0.506354 0.832337 2 : 0.0337602 0.678651 0.598517 0.988993 3 : 0.501545 0.642476 0.29958 4 : 0.632082 0.859634 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 3.14764 1: 5.31793 2: 9.44251 3: 5.57244 4: 6.8265 R8GB_NZ_NUM_test R8GB_NZ_NUM counts the nonzero entries in an R8GB matrix. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The R8GB matrix: Col: 0 1 2 3 4 Row 0 : 0.468615 0 0.525842 1 : 0.733244 0.357144 0.704248 0.904384 2 : 0.961276 0 0.448914 0.903793 3 : 0.795049 0.593386 0 4 : 0 0 5 : 0.465095 Col: 5 6 7 8 9 Row 3 : 0 4 : 0 0.943611 5 : 0.822374 0 0.699011 6 : 0 0 0.93495 0.840467 7 : 0.370725 0 0.760637 0.837408 8 : 0.726962 0 0 9 : 0.881991 0.512192 Nonzero entries = 23 R8GB_PRINT_test R8GB_PRINT prints an R8GB matrix. Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 3 The R8GB matrix: Col: 0 1 2 3 4 Row 0 : 101 102 103 104 1 : 201 202 203 204 205 2 : 302 303 304 305 3 : 403 404 405 4 : 504 505 5 : 605 Col: 5 6 7 8 9 Row 2 : 306 3 : 406 407 4 : 506 507 508 5 : 606 607 608 609 6 : 706 707 708 709 710 7 : 807 808 809 810 R8GB_PRINT_SOME_test R8GB_PRINT_SOME prints some of an R8GB matrix. Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 3 Rows(4-6), Cols (3-9) Col: 3 4 5 6 7 Row 4 : 504 505 506 507 508 5 : 605 606 607 608 6 : 706 707 708 Col: 8 9 Row 5 : 609 6 : 709 710 R8GB_RANDOM_test R8GB_RANDOM returns a random R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The random R8GB matrix: Col: 0 1 2 3 4 Row 0 : 0.651731 0.584778 0.249194 1 : 0.588762 0.333999 0.456041 0.761158 2 : 0.17635 0.306573 0.767934 0.920463 3 : 0.567477 0.626095 0.0297139 4 : 0.0306476 0.164408 R8GB_SL_test R8GB_SL solves a linear system factored by r8gb_fa. Number of matrix rows M = 5 Number of matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The banded matrix: Col: 0 1 2 3 4 Row 0 : 0.559815 0.018364 0.717725 1 : 0.835037 0.188568 0.788839 0.831861 2 : 0.079965 0.548394 0.624376 0.207664 3 : 0.645302 0.0802243 0.666349 4 : 0.417507 0.0708556 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 2.22989 1: 0.635394 2: 6.5218 3: 5.94528 4: 3.64267 Solution to Ax=b: 0: 1 1: 2 2: 3 3: 4 4: 5 R8GB_TO_R8GE_test R8GB_TO_R8GE copies an R8GB matrix to an R8GE matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB matrix: Col: 0 1 2 3 4 Row 0 : 11 12 1 : 21 22 23 2 : 31 32 33 34 3 : 42 43 44 45 4 : 53 54 55 Col: 5 6 7 Row 4 : 56 The R8GE matrix: [[11. 12. 0. 0. 0. 0. 0. 0.] [21. 22. 23. 0. 0. 0. 0. 0.] [31. 32. 33. 34. 0. 0. 0. 0.] [ 0. 42. 43. 44. 45. 0. 0. 0.] [ 0. 0. 53. 54. 55. 56. 0. 0.]] R8GB_TO_r8st_test R8GB_TO_r8st copies a R8GB matrix to a r8st matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB matrix: Col: 0 1 2 3 4 Row 0 : 11 12 1 : 21 22 23 2 : 31 32 33 34 3 : 42 43 44 45 4 : 53 54 55 Col: 5 6 7 Row 4 : 56 Nonzeros NZ_NUM = 17 The r8st matrix: Col: 0 1 2 3 4 Row --- 1 0 11 12 0 0 2 0 21 22 23 0 3 0 31 32 33 34 4 0 0 42 43 44 Col: 5 6 7 Row --- 4 45 0 0 R8GB_TO_R8VEC_test R8GB_TO_R8VEC converts an R8GB matrix to an R8VEC. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 1 : 21 22 23 2 : 31 32 33 34 3 : 42 43 44 45 4 : 53 54 55 Col: 5 6 7 Row 4 : 56 1 1 1 0.000000 2 1 2 0.000000 3 1 3 0.000000 4 1 4 11.000000 5 1 5 21.000000 6 1 6 31.000000 1 2 7 0.000000 2 2 8 0.000000 3 2 9 12.000000 4 2 10 22.000000 5 2 11 32.000000 6 2 12 42.000000 1 3 13 0.000000 2 3 14 0.000000 3 3 15 23.000000 4 3 16 33.000000 5 3 17 43.000000 6 3 18 53.000000 1 4 19 0.000000 2 4 20 0.000000 3 4 21 34.000000 4 4 22 44.000000 5 4 23 54.000000 6 4 24 0.000000 1 5 25 0.000000 2 5 26 0.000000 3 5 27 45.000000 4 5 28 55.000000 5 5 29 0.000000 6 5 30 0.000000 1 6 31 0.000000 2 6 32 0.000000 3 6 33 56.000000 4 6 34 0.000000 5 6 35 0.000000 6 6 36 0.000000 1 7 37 0.000000 2 7 38 0.000000 3 7 39 0.000000 4 7 40 0.000000 5 7 41 0.000000 6 7 42 0.000000 1 8 43 0.000000 2 8 44 0.000000 3 8 45 0.000000 4 8 46 0.000000 5 8 47 0.000000 6 8 48 0.000000 R8GB_TRF_test R8GB_TRF computes the PLU factors of an R8GB matrix. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8GB_TRS_test R8GB_TRS solves a linear system factored by R8GB_TRS. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 Solution to transposed system: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8GB_ZEROS_test R8GB_ZEROS returns an R8GB zero matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 The R8GB zero matrix: Col: 0 1 2 3 4 Row 0 : 0 0 0 1 : 0 0 0 0 2 : 0 0 0 0 3 : 0 0 0 4 : 0 0 r8vec_to_r8gb_test() r8vec_to_r8gb() converts an R8VEC to an R8GB matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 1 : 21 22 23 2 : 31 32 33 34 3 : 42 43 44 45 4 : 53 54 55 Col: 5 6 7 Row 4 : 56 0 0 0 0 1 0 1 0 2 0 2 0 3 0 3 11 4 0 4 21 5 0 5 31 0 1 6 0 1 1 7 0 2 1 8 12 3 1 9 22 4 1 10 32 5 1 11 42 0 2 12 0 1 2 13 0 2 2 14 23 3 2 15 33 4 2 16 43 5 2 17 53 0 3 18 0 1 3 19 0 2 3 20 34 3 3 21 44 4 3 22 54 5 3 23 0 0 4 24 0 1 4 25 0 2 4 26 45 3 4 27 55 4 4 28 0 5 4 29 0 0 5 30 0 1 5 31 0 2 5 32 56 3 5 33 0 4 5 34 0 5 5 35 0 0 6 36 0 1 6 37 0 2 6 38 0 3 6 39 0 4 6 40 0 5 6 41 0 0 7 42 0 1 7 43 0 2 7 44 0 3 7 45 0 4 7 46 0 5 7 47 0 The recovered R8GB indicator matrix: Col: 0 1 2 3 4 Row 0 : 11 12 1 : 21 22 23 2 : 31 32 33 34 3 : 42 43 44 45 4 : 53 54 55 Col: 5 6 7 Row 4 : 56 r8gb_test(): Normal end of execution. Wed Oct 8 08:50:30 2025