Tue May 20 22:27:33 2025 r8cbb_test(): python version: 3.10.12 numpy version: 1.26.4 Test r8cbb(). R8CBB_ADD_TEST R8CBB_ADD adds a value to elements of an R8CBB matrix. Matrix order N = 5 Matrix suborder N1 = 3 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 0 Matrix before additions: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 15 1 : 21 22 0 0 25 2 : 0 32 33 0 35 3 : 0 0 43 14 41 4 : 51 52 53 54 55 The matrix after additions: Col: 0 1 2 3 4 Row 0 : 100 0 0 0 215 1 : 21 122 0 0 225 2 : 0 32 133 0 235 3 : 0 0 43 214 41 4 : 51 52 53 454 55 R8CBB_DIF2_TEST R8CBB_DIF2 sets up an R8CBB second difference matrix. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB second difference matrix: Col: 0 1 2 3 4 Row 0 : 2 -1 0 0 0 1 : -1 2 -1 0 0 2 : 0 -1 2 -1 0 3 : 0 0 -1 2 -1 4 : 0 0 0 -1 2 5 : 0 0 0 0 -1 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : -1 0 0 0 0 5 : 2 -1 0 0 0 6 : -1 2 -1 0 0 7 : 0 -1 2 0 0 8 : 0 0 0 0 0 9 : 0 0 0 -1 2 r8cbb_fa_test(): r8cbb_fa() factors an R8CBB matrix, with no pivoting. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix: Col: 0 1 2 3 4 Row 0 : 0.671682 0.166413 0 0 0 1 : 0.525759 0.982627 0.25297 0 0 2 : 0 0.58825 0.641423 0.995587 0 3 : 0 0 0.878897 0.506077 0.273298 4 : 0 0 0 0.861972 0.20557 5 : 0 0 0 0 0.905971 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.630748 0.0991532 0.740828 0.478885 0.031987 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0.869454 1 : 0 0 0 0 0.0531338 2 : 0 0 0 0 0.0389409 3 : 0 0 0 0 0.447628 4 : 0.0428 0 0 0 0.295694 5 : 0.487133 0.668581 0 0 0.188621 6 : 0.13477 0.505861 0.777454 0 0.350379 7 : 0 0.939185 0.814184 0.961945 0.739599 8 : 0 0 0 0.893087 0.692198 9 : 0.183189 0.414365 0.0828607 0.344976 0.390014 The factored matrix: Col: 0 1 2 3 4 Row 0 : 0.671682 0.166413 0 0 0 1 : -0.782751 0.852367 0.25297 0 0 2 : 0 -0.690137 0.466838 0.995587 0 3 : 0 0 -1.88266 -1.36827 0.273298 4 : 0 0 0 0.62997 0.37774 5 : 0 0 0 0 -2.3984 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.630748 0.0991532 0.740828 0.478885 0.031987 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 -1.49647 1 : 0 0 0 0 0.815407 2 : 0 0 0 0 -0.267199 3 : 0 0 0 0 -0.348755 4 : 0.0428 0 0 0 -0.13279 5 : 0.384482 0.668581 0 0 0.752832 6 : -0.350525 0.271506 0.777454 0 -0.650702 7 : 0 -3.45916 -1.87516 -1.39969 -0.15779 8 : 0 0 0 -0.130991 0.692198 9 : 0.183189 0.414365 0.0828607 -0.843693 -1.00137 The right hand side vector: 0: 18.3566 1: 11.819 2: 15.4226 3: 10.6892 4: 10.8204 5: 15.4788 6: 16.3488 7: 27.2136 8: 32.6502 9: 16.7945 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8cbb_get_test() r8cbb_get() gets a value of an element of an R8CBB matrix. Matrix order N = 5 Matrix suborder N1 = 3 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 0 The R8CBB matrix to be queried: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 15 1 : 21 22 0 0 25 2 : 0 32 33 0 35 3 : 0 0 43 14 41 4 : 51 52 53 54 55 A( 0 , 0 ) = 0.0 A( 1 , 2 ) = 0.0 A( 3 , 0 ) = 0.0 A( 4 , 1 ) = 52.0 A( 1 , 2 ) = 0.0 A( 1 , 3 ) = 0.0 A( 0 , 3 ) = 0.0 A( 1 , 2 ) = 0.0 A( 1 , 2 ) = 0.0 A( 0 , 1 ) = 0.0 R8CBB_INDICATOR_TEST R8CBB_INDICATOR sets up an R8CBB indicator matrix. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The compact border-banded matrix: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 201 202 203 0 0 2 : 0 302 303 304 0 3 : 0 0 403 404 405 4 : 0 0 0 504 505 5 : 0 0 0 0 605 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 1001 1002 1003 1004 1005 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 110 1 : 0 0 0 0 210 2 : 0 0 0 0 310 3 : 0 0 0 0 410 4 : 506 0 0 0 510 5 : 606 607 0 0 610 6 : 706 707 708 0 710 7 : 0 807 808 109 810 8 : 0 0 908 209 901 9 : 1006 1007 1008 1009 1010 R8CBB_MTV_TEST R8CBB_MTV computes b=A'*x, where A is an R8CBB matrix. Matrix order N = 8 Matrix suborder N1 = 6 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix A: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 21 22 23 0 0 2 : 0 32 33 34 0 3 : 0 0 43 44 45 4 : 0 0 0 54 55 5 : 0 0 0 0 65 6 : 0 0 0 0 0 7 : 81 82 83 84 85 Col: 5 6 7 Row 0 : 0 0 18 1 : 0 0 28 2 : 0 0 38 3 : 0 0 48 4 : 56 0 58 5 : 66 17 68 6 : 76 27 71 7 : 86 87 88 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 The product b=A'*x: 0: 1187 1: 1300 2: 1492 3: 1738 4: 2050 5: 1896 6: 2292 7: 2328 R8CBB_MV_TEST R8CBB_MV computes b=A*x, where A is an R8CBB matrix. Matrix order N = 8 Matrix suborder N1 = 6 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix A: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 21 22 23 0 0 2 : 0 32 33 34 0 3 : 0 0 43 44 45 4 : 0 0 0 54 55 5 : 0 0 0 0 65 6 : 0 0 0 0 0 7 : 81 82 83 84 85 Col: 5 6 7 Row 0 : 0 0 18 1 : 0 0 28 2 : 0 0 38 3 : 0 0 48 4 : 56 0 58 5 : 66 17 68 6 : 76 27 71 7 : 86 87 88 The vector x: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 The product b=A*x: 0: 263 1: 547 2: 862 3: 1243 4: 1690 5: 1734 6: 2724 7: 3084 r8cbb_print_test(): r8cbb_print() prints an R8CBB matrix Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix: Col: 0 1 2 3 4 Row 0 : 0.813992 0.604794 0 0 0 1 : 0.64699 0.617098 0.169387 0 0 2 : 0 0.773735 0.919704 0.924542 0 3 : 0 0 0.757263 0.445662 0.0451934 4 : 0 0 0 0.524215 0.615293 5 : 0 0 0 0 0.257414 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.267095 0.0218197 0.606534 0.0576453 0.116713 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0.443204 1 : 0 0 0 0 0.0291393 2 : 0 0 0 0 0.240414 3 : 0 0 0 0 0.217701 4 : 0.371639 0 0 0 0.756966 5 : 0.441193 0.970094 0 0 0.525296 6 : 0.564694 0.95883 0.848477 0 0.245183 7 : 0 0.404898 0.508716 0.883795 0.168913 8 : 0 0 0 0.302835 0.124026 9 : 0.402007 0.209598 0.164492 0.138167 0.290995 r8cbb_print_some_test(): r8cbb_print_some() prints some of an R8CBB matrix Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 Rows 1-10, Cols 9-10 Col: 9 Row 1 : 0.0873659 2 : 0.982575 3 : 0.935897 4 : 0.766862 5 : 0.64665 6 : 0.621091 7 : 0.321805 8 : 0.470444 9 : 0.77514 r8cbb_random_test(): r8cbb_random() generates a random R8CBB matrix Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix: Col: 0 1 2 3 4 Row 0 : 0.629093 0.792922 0 0 0 1 : 0.899152 0.821729 0.243297 0 0 2 : 0 0.168938 0.508273 0.47075 0 3 : 0 0 0.205146 0.499249 0.419686 4 : 0 0 0 0.900607 0.774491 5 : 0 0 0 0 0.254708 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.132456 0.37759 0.617422 0.847996 0.791055 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0.200223 1 : 0 0 0 0 0.501054 2 : 0 0 0 0 0.947009 3 : 0 0 0 0 0.0608349 4 : 0.086054 0 0 0 0.655721 5 : 0.960641 0.0815257 0 0 0.158877 6 : 0.298338 0.853261 0.626484 0 0.658764 7 : 0 0.328078 0.536638 0.532369 0.361969 8 : 0 0 0 0.854911 0.348466 9 : 0.913603 0.168164 0.999896 0.625879 0.352077 R8CBB_SET_TEST R8CBB_SET sets the value of an element of an R8CBB matrix. Matrix order N = 5 Matrix suborder N1 = 4 Matrix suborder N2 = 1 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The matrix after additions: Col: 0 1 2 3 4 Row 0 : 11 12 0 0 0 1 : 21 22 23 0 0 2 : 31 32 33 34 0 3 : 0 42 43 44 15 4 : 0 0 0 0 25 r8cbb_sl_test(): r8cbb_sl() solves a linear system factored by R8CBB_FA Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix: Col: 0 1 2 3 4 Row 0 : 0.446897 0.536051 0 0 0 1 : 0.782584 0.368027 0.240994 0 0 2 : 0 0.297958 0.918355 0.695007 0 3 : 0 0 0.10596 0.158393 0.102232 4 : 0 0 0 0.675647 0.00766195 5 : 0 0 0 0 0.857928 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.813772 0.63601 0.653725 0.267337 0.28685 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0.324233 1 : 0 0 0 0 0.717956 2 : 0 0 0 0 0.0118785 3 : 0 0 0 0 0.678602 4 : 0.0758204 0 0 0 0.143694 5 : 0.131512 0.49521 0 0 0.915288 6 : 0.839901 0.282538 0.456362 0 0.505164 7 : 0 0.41393 0.0919321 0.0690767 0.499279 8 : 0 0 0 0.891356 0.768317 9 : 0.687922 0.92784 0.435151 0.783282 0.744148 The factored matrix: Col: 0 1 2 3 4 Row 0 : 0.446897 0.536051 0 0 0 1 : -1.75115 -0.570678 0.240994 0 0 2 : 0 0.522111 1.04418 0.695007 0 3 : 0 0 -0.101477 0.0878657 0.102232 4 : 0 0 0 -7.68954 -0.778455 5 : 0 0 0 0 1.10209 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0.813772 0.63601 0.653725 0.267337 0.28685 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 -1.48208 1 : 0 0 0 0 0.630729 2 : 0 0 0 0 0.870424 3 : 0 0 0 0 -1.43764 4 : 0.0758204 0 0 0 -5.31264 5 : 0.215073 0.49521 0 0 11.4527 6 : -3.9052 -1.65135 0.456362 0 4.31415 7 : 0 0.250661 0.206324 -2.1794 -24.8557 8 : 0 0 0 1.68807 0.768317 9 : 0.687922 0.92784 0.435151 -0.0358212 0.497308 The right hand side vector: 0: 5.38302 1: 17.4434 2: 10.5416 3: 15.8981 4: 11.6201 5: 26.3127 6: 21.1661 7: 15.5164 8: 37.3595 9: 35.1452 Solution: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 R8CBB_TO_R8GE_TEST R8CBB_TO_R8GE converts an R8CBB matrix to R8GE format. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB matrix: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 201 202 203 0 0 2 : 0 302 303 304 0 3 : 0 0 403 404 405 4 : 0 0 0 504 505 5 : 0 0 0 0 605 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 1001 1002 1003 1004 1005 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 110 1 : 0 0 0 0 210 2 : 0 0 0 0 310 3 : 0 0 0 0 410 4 : 506 0 0 0 510 5 : 606 607 0 0 610 6 : 706 707 708 0 710 7 : 0 807 808 109 810 8 : 0 0 908 209 901 9 : 1006 1007 1008 1009 1010 The R8GE matrix: [[ 0. 0. 0. 0. 0. 0. 0. 0. 109. 110.] [ 201. 202. 203. 0. 0. 0. 0. 0. 209. 210.] [ 0. 302. 303. 304. 0. 0. 0. 0. 309. 310.] [ 0. 0. 403. 404. 405. 0. 0. 0. 409. 410.] [ 0. 0. 0. 504. 505. 506. 0. 0. 509. 510.] [ 0. 0. 0. 0. 605. 606. 607. 0. 609. 610.] [ 0. 0. 0. 0. 0. 706. 707. 708. 709. 710.] [ 0. 0. 0. 0. 0. 0. 807. 808. 809. 810.] [ 901. 902. 903. 904. 905. 906. 907. 908. 909. 910.] [1001. 1002. 1003. 1004. 1005. 1006. 1007. 1008. 1009. 1010.]] R8CBB_ZEROS_TEST R8CBB_ZEROS zeros an R8CBB matrix. Matrix order N = 10 Matrix suborder N1 = 8 Matrix suborder N2 = 2 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CBB zero matrix: Col: 0 1 2 3 4 Row 0 : 0 0 0 0 0 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 Col: 5 6 7 8 9 Row 0 : 0 0 0 0 0 1 : 0 0 0 0 0 2 : 0 0 0 0 0 3 : 0 0 0 0 0 4 : 0 0 0 0 0 5 : 0 0 0 0 0 6 : 0 0 0 0 0 7 : 0 0 0 0 0 8 : 0 0 0 0 0 9 : 0 0 0 0 0 r8cbb_test(): Normal end of execution. Tue May 20 22:27:33 2025