Mon Aug 22 13:00:13 2022 r8gb_test(): Python version: 3.6.9 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 : 0.886471 0.683195 0.914443 1 : 0.859525 0.290928 0.350646 0.534624 2 : 0.186449 0.705569 0.343282 0.662953 0.5053 3 : 0.975799 0.742356 0.377034 0.95301 0.0474585 4 : 0.362994 0.0463476 0.379646 0.930279 5 : 0.44464 0.741437 0.260106 6 : 0.371299 0.469046 7 : 0.8143 Col: 5 6 7 8 9 Row 3 : 0.579449 4 : 0.337924 0.720412 5 : 0.357968 0.165301 0.510526 6 : 0.143404 0.722186 0.414713 0.90974 7 : 0.432736 0.136864 0.316347 0.860253 0.59288 8 : 0.305916 0.616859 0.155586 0.658595 0.226095 9 : 0.336568 0.636662 0.936687 0.994928 r8gb_det() computes the determinant = -0.04706835919017237 np.linalg.det() computes the determinant = -0.04706835919017237 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 : 0.923511 0.663654 0.815242 1 : 0.416422 0.361312 0.847506 0.814828 2 : 0.468058 0.860135 0.425789 0.925122 3 : 0.151113 0.411799 0.126369 4 : 0.843225 0.032704 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 1.75636 1: 2.79045 2: 5.69511 3: 8.77035 4: 3.44436 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: 2.60327 2.60327 1: 5.14831 5.14831 2: 8.96318 8.96318 3: 10.5253 10.5253 4: 8.82348 8.82348 5: 11.6125 11.6125 6: 18.6505 18.6505 7: 18.056 18.056 8: 6.73266 6.73266 9: 15.3819 15.3819 A*x and (PLU)*x 0: 2.38595 2.38595 1: 1.80101 1.80101 2: 3.4739 3.4739 3: 5.89926 5.89926 4: 6.50409 6.50409 5: 10.2571 10.2571 6: 10.2748 10.2748 7: 11.6775 11.6775 8: 15.4119 15.4119 9: 13.6209 13.6209 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 : 0.679443 0.870673 0.876512 1 : 0.0711184 0.919643 0.300196 0.301634 2 : 0.0362897 0.650197 0.0798281 0.439496 3 : 0.15714 0.661707 0.152928 4 : 0.707666 0.805196 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 0.82168 1: 2.81883 2: 4.05606 3: 7.02791 4: 5.95618 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: 2.13622 2.13622 1: 3.8343 3.8343 2: 5.98378 5.98378 3: 6.73488 6.73488 4: 9.69759 9.69759 5: 13.7375 13.7375 6: 13.3595 13.3595 7: 12.9025 12.9025 8: 14.2072 14.2072 9: 13.7805 13.7805 A*x and (PLU)*x 0: 1.22163 1.22163 1: 2.36925 2.36925 2: 3.11643 3.11643 3: 10.1802 10.1802 4: 4.93956 4.93956 5: 11.584 11.584 6: 12.7314 12.7314 7: 14.4844 14.4844 8: 10.6493 10.6493 9: 19.6884 19.6884 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 : 0.244097 0.513864 0.334129 1 : 0.675961 0.172569 0.411145 0.904378 2 : 0.419813 0.672021 0.474142 0.866234 3 : 0.835857 0.0882743 0.83726 4 : 0.841417 0.63784 x: 0: 1 1: 2 2: 3 3: 4 4: 5 b=A*x: 0: 2.27421 1: 5.87205 2: 9.08343 3: 7.04697 4: 6.55487 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 : 0.580523 0.815666 0.322333 1 : 0.914508 0.452661 0.649949 0.621374 2 : 0.93557 0.782381 0.345104 0 3 : 0.696331 0.680401 0 4 : 0.543238 0 5 : 0.914058 Col: 5 6 7 8 9 Row 3 : 0.802156 4 : 0.737823 0.452322 5 : 0.33162 0.559153 0.54381 6 : 0 0.534532 0.590294 0 7 : 0.896677 0.700783 0.480134 0.985303 8 : 0 0.829089 0 9 : 0 0.658731 Nonzero entries = 28 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 : 0.519809 0.576966 0.970602 1 : 0.286463 0.139727 0.498937 0.743564 2 : 0.662769 0.977762 0.605488 0.724581 3 : 0.55836 0.598779 0.630555 4 : 0.200362 0.6148 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 : 0.427465 0.428342 0.692167 1 : 0.252688 0.643291 0.487794 0.249745 2 : 0.773679 0.0887466 0.172705 0.329118 3 : 0.214911 0.823652 0.564031 4 : 0.637279 0.735129 Solution to A*x=b: 0: 1 1: 2 2: 3 3: 4 4: 5 Right hand side of transposed system: 0: 0.932841 1: 4.03596 2: 2.79364 3: 7.49861 4: 6.91912 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. Mon Aug 22 13:00:13 2022