Tue May 20 22:27:34 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 : 0.275015 0.395911 0.587878 1 : 0.807342 0.563955 0.630825 0.281805 2 : 0.607838 0.819784 0.163701 0.840821 0.943345 3 : 0.440325 0.98864 0.559259 0.484087 0.730353 4 : 0.00609185 0.941424 0.734054 0.238128 5 : 0.193127 0.785305 0.39712 6 : 0.160106 0.706492 7 : 0.146896 Col: 5 6 7 8 9 Row 3 : 0.108815 4 : 0.14681 0.298975 5 : 0.0680637 0.117561 0.988032 6 : 0.853483 0.542331 0.959726 0.822424 7 : 0.159281 0.638085 0.784246 0.180307 0.713601 8 : 0.264414 0.159199 0.148446 0.136349 0.761696 9 : 0.532113 0.749904 0.372461 0.735564 r8gb_det() computes the determinant = -0.005709130390718247 np.linalg.det() computes the determinant = -0.00570913039071824 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 : 0.0119934 0.980064 0.0931257 1 : 0.227586 0.274459 0.048778 0.601809 2 : 0.279493 0.258091 0.43386 0.78525 3 : 0.47679 0.23696 0.844713 4 : 0.658135 0.545238 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 0.467166 1: 2.36746 2: 2.87211 3: 6.74372 4: 8.46079 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: 3.87784 3.87784 1: 5.07887 5.07887 2: 5.62784 5.62784 3: 9.26875 9.26875 4: 10.5078 10.5078 5: 15.6883 15.6883 6: 16.3563 16.3563 7: 22.7164 22.7164 8: 12.091 12.091 9: 6.7938 6.7938 A*x and (PLU)*x 0: 1.30275 1.30275 1: 5.20066 5.20066 2: 1.84618 1.84618 3: 3.77083 3.77083 4: 9.93037 9.93037 5: 5.57633 5.57633 6: 15.0419 15.0419 7: 16.3758 16.3758 8: 24.8624 24.8624 9: 12.251 12.251 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 : 0.0296512 0.172346 0.612633 1 : 0.265009 0.34422 0.532208 0.844872 2 : 0.195643 0.0231694 0.613331 0.675194 3 : 0.951694 0.932027 0.881678 4 : 0.602058 0.809085 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 0.55967 1: 1.44771 2: 5.55334 3: 10.2681 4: 9.59772 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: 3.71469 3.71469 1: 5.13178 5.13178 2: 10.992 10.992 3: 7.56376 7.56376 4: 10.1728 10.1728 5: 7.23911 7.23911 6: 21.0277 21.0277 7: 15.4477 15.4477 8: 2.29133 2.29133 9: 9.11855 9.11855 A*x and (PLU)*x 0: 0.603405 0.603405 1: 2.21075 2.21075 2: 6.29181 6.29181 3: 8.32912 8.32912 4: 6.07595 6.07595 5: 5.90818 5.90818 6: 17.1012 17.1012 7: 4.70493 4.70493 8: 15.4538 15.4538 9: 18.756 18.756 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 : 0.291761 0.976726 0.0729504 1 : 0.85306 0.680093 0.513243 0.0266986 2 : 0.838169 0.714733 0.54692 0.999019 3 : 0.515551 0.989557 0.543446 4 : 0.137683 0.768777 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 2.46406 1: 3.85977 2: 11.0033 3: 8.22211 4: 4.39462 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 0 0.410903 1 : 0.419834 0.919356 0.784809 0.441331 2 : 0.446421 0.823054 0.483049 0 3 : 0.573366 0.968301 0.550297 4 : 0.402108 0 5 : 0.301853 Col: 5 6 7 8 9 Row 3 : 0.775264 4 : 0 0.4694 5 : 0.82962 0 0.946151 6 : 0.4004 0 0.366211 0.551272 7 : 0 0 0.810044 0 8 : 0.894002 0 0.611706 9 : 0.317053 0.460582 Nonzero entries = 25 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 : 0.314205 0.686978 0.523484 1 : 0.38032 0.985527 0.190816 0.597304 2 : 0.589037 0.811086 0.204913 0.958465 3 : 0.0630155 0.468674 0.976939 4 : 0.110858 0.0838561 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 : 0.857608 0.234543 0.435525 1 : 0.268194 0.802875 0.635226 0.689301 2 : 0.869137 0.895275 0.371646 0.10523 3 : 0.138659 0.958096 0.0600545 4 : 0.368874 0.617447 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 1.39399 1: 4.4477 2: 4.94644 3: 8.17029 4: 3.64314 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. Tue May 20 22:27:34 2025