21-Aug-2022 18:33:40 r8cbb_test(): MATLAB version 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: 1 2 3 4 5 Row --- 1 11 0 0 14 15 2 21 22 0 24 25 3 0 32 33 34 35 4 41 42 43 44 45 5 51 52 53 54 55 The R8BB matrix after additions: Col: 1 2 3 4 5 Row --- 1 111 0 0 214 215 2 21 122 0 224 225 3 0 32 133 234 235 4 41 42 43 44 445 5 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: 1 2 3 4 5 Row --- 1 2 -1 0 0 0 2 -1 2 -1 0 0 3 0 -1 2 -1 0 4 0 0 -1 2 -1 5 0 0 0 -1 2 6 0 0 0 0 -1 7 0 0 0 0 0 8 0 0 0 0 0 9 0 0 0 0 0 10 0 0 0 0 0 Col: 6 7 8 9 10 Row --- 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 -1 0 0 0 0 6 2 -1 0 0 0 7 -1 2 -1 0 0 8 0 -1 2 -1 0 9 0 0 -1 2 -1 10 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 0.956318 0.561695 0.0661187 0 0 3 0 0.415307 0.257578 0.043829 0 4 0 0 0.109957 0.633966 0.449539 5 0 0 0 0.0617272 0.401306 6 0 0 0 0 0.754673 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.123104 0.692066 2 0 0 0 0.00751236 0.561662 3 0 0 0 0.260303 0.861216 4 0 0 0 0.912484 0.453794 5 0.797287 0 0 0.113664 0.911977 6 0.00183837 0.350752 0 0.351629 0.597917 7 0.897504 0.0945448 0.859097 0.822887 0.188955 8 0 0.0136169 0.840847 0.267132 0.761492 9 0.825003 0.0618618 0.0882833 0.745303 0.899373 10 0.82466 0.710781 0.777994 0.308675 0.763537 The factored matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 -4.37838 -3.07021 0.0661187 0 0 3 0 0.13527 0.266522 0.043829 0 4 0 0 -0.412562 0.615884 0.449539 5 0 0 0 -0.100225 0.356251 6 0 0 0 0 -2.11838 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.125967 0.0710759 2 0 0 0 -0.181574 -0.853023 3 0 0 0 -0.39304 -2.27612 4 0 0 0 -1.90868 1.80997 5 0.797287 0 0 0.758046 -3.00525 6 -1.68711 0.350752 0 -0.376345 0.228679 7 0.531976 0.281136 0.859097 -2.63153 4.76017 8 0 -0.0484352 0.799237 -0.275079 -0.982712 9 0.825003 0.0618618 0.0882833 -0.366315 -0.539156 10 0.82466 0.710781 0.777994 -9.30432 7.85831 The right hand side vector: 1: 9.90604 2: 7.9623 3: 12.7335 4: 17.8637 5: 17.1799 6: 15.3835 7: 22.2151 8: 16.8412 9: 26.6284 10: 32.9193 Solution: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 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: 1 2 3 4 5 Row --- 1 11 0 0 14 15 2 21 22 0 24 25 3 0 32 33 34 35 4 41 42 43 44 45 5 51 52 53 54 55 A(2,5) = 25 A(5,3) = 53 A(3,1) = 0 A(2,1) = 21 A(1,4) = 14 A(1,3) = 0 A(3,4) = 34 A(4,1) = 41 A(5,2) = 52 A(1,1) = 11 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: 1 2 3 4 5 Row --- 1 101 102 0 0 0 2 201 202 203 0 0 3 0 302 303 304 0 4 0 0 403 404 405 5 0 0 0 504 505 6 0 0 0 0 605 7 0 0 0 0 0 8 0 0 0 0 0 9 901 902 903 904 905 10 1001 1002 1003 1004 1005 Col: 6 7 8 9 10 Row --- 1 0 0 0 109 110 2 0 0 0 209 210 3 0 0 0 309 310 4 0 0 0 409 410 5 506 0 0 509 510 6 606 607 0 609 610 7 706 707 708 709 710 8 0 807 808 809 810 9 906 907 908 909 910 10 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: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 0 32 33 34 0 4 0 0 43 44 45 5 0 0 0 54 55 6 0 0 0 0 65 7 71 72 73 74 75 8 81 82 83 84 85 Col: 6 7 8 Row --- 1 0 17 18 2 0 27 28 3 0 37 38 4 0 47 48 5 56 57 58 6 66 67 68 7 76 77 78 8 86 87 88 The vector x: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 The product b=A'*x: 1: 1198 2: 1312 3: 1492 4: 1738 5: 2050 6: 1896 7: 2292 8: 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: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 0 32 33 34 0 4 0 0 43 44 45 5 0 0 0 54 55 6 0 0 0 0 65 7 71 72 73 74 75 8 81 82 83 84 85 Col: 6 7 8 Row --- 1 0 17 18 2 0 27 28 3 0 37 38 4 0 47 48 5 56 57 58 6 66 67 68 7 76 77 78 8 86 87 88 The vector x: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 The product b=A*x: 1: 298 2: 547 3: 862 4: 1243 5: 1690 6: 1734 7: 2724 8: 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 0.956318 0.561695 0.0661187 0 0 3 0 0.415307 0.257578 0.043829 0 4 0 0 0.109957 0.633966 0.449539 5 0 0 0 0.0617272 0.401306 6 0 0 0 0 0.754673 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.123104 0.692066 2 0 0 0 0.00751236 0.561662 3 0 0 0 0.260303 0.861216 4 0 0 0 0.912484 0.453794 5 0.797287 0 0 0.113664 0.911977 6 0.00183837 0.350752 0 0.351629 0.597917 7 0.897504 0.0945448 0.859097 0.822887 0.188955 8 0 0.0136169 0.840847 0.267132 0.761492 9 0.825003 0.0618618 0.0882833 0.745303 0.899373 10 0.82466 0.710781 0.777994 0.308675 0.763537 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 10 Row --- 1 0.123104 0.692066 2 0.00751236 0.561662 3 0.260303 0.861216 4 0.912484 0.453794 5 0.113664 0.911977 6 0.351629 0.597917 7 0.822887 0.188955 8 0.267132 0.761492 9 0.745303 0.899373 10 0.308675 0.763537 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 0.956318 0.561695 0.0661187 0 0 3 0 0.415307 0.257578 0.043829 0 4 0 0 0.109957 0.633966 0.449539 5 0 0 0 0.0617272 0.401306 6 0 0 0 0 0.754673 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.123104 0.692066 2 0 0 0 0.00751236 0.561662 3 0 0 0 0.260303 0.861216 4 0 0 0 0.912484 0.453794 5 0.797287 0 0 0.113664 0.911977 6 0.00183837 0.350752 0 0.351629 0.597917 7 0.897504 0.0945448 0.859097 0.822887 0.188955 8 0 0.0136169 0.840847 0.267132 0.761492 9 0.825003 0.0618618 0.0882833 0.745303 0.899373 10 0.82466 0.710781 0.777994 0.308675 0.763537 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 R8BB matrix after additions: Col: 1 2 3 4 5 Row --- 1 11 12 0 0 15 2 21 22 23 0 25 3 31 32 33 34 35 4 0 42 43 44 45 5 51 52 53 54 55 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 0.956318 0.561695 0.0661187 0 0 3 0 0.415307 0.257578 0.043829 0 4 0 0 0.109957 0.633966 0.449539 5 0 0 0 0.0617272 0.401306 6 0 0 0 0 0.754673 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.123104 0.692066 2 0 0 0 0.00751236 0.561662 3 0 0 0 0.260303 0.861216 4 0 0 0 0.912484 0.453794 5 0.797287 0 0 0.113664 0.911977 6 0.00183837 0.350752 0 0.351629 0.597917 7 0.897504 0.0945448 0.859097 0.822887 0.188955 8 0 0.0136169 0.840847 0.267132 0.761492 9 0.825003 0.0618618 0.0882833 0.745303 0.899373 10 0.82466 0.710781 0.777994 0.308675 0.763537 The factored matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0 0 0 2 -4.37838 -3.07021 0.0661187 0 0 3 0 0.13527 0.266522 0.043829 0 4 0 0 -0.412562 0.615884 0.449539 5 0 0 0 -0.100225 0.356251 6 0 0 0 0 -2.11838 7 0 0 0 0 0 8 0 0 0 0 0 9 0.396988 0.574366 0.617205 0.21293 0.117707 10 0.185314 0.367027 0.361529 0.714471 0.299329 Col: 6 7 8 9 10 Row --- 1 0 0 0 0.125967 0.0710759 2 0 0 0 -0.181574 -0.853023 3 0 0 0 -0.39304 -2.27612 4 0 0 0 -1.90868 1.80997 5 0.797287 0 0 0.758046 -3.00525 6 -1.68711 0.350752 0 -0.376345 0.228679 7 0.531976 0.281136 0.859097 -2.63153 4.76017 8 0 -0.0484352 0.799237 -0.275079 -0.982712 9 0.825003 0.0618618 0.0882833 -0.366315 -0.539156 10 0.82466 0.710781 0.777994 -9.30432 7.85831 The right hand side vector: 1: 9.90604 2: 7.9623 3: 12.7335 4: 17.8637 5: 17.1799 6: 15.3835 7: 22.2151 8: 16.8412 9: 26.6284 10: 32.9193 Solution: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 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: 1 2 3 4 5 Row --- 1 101 102 0 0 0 2 201 202 203 0 0 3 0 302 303 304 0 4 0 0 403 404 405 5 0 0 0 504 505 6 0 0 0 0 605 7 0 0 0 0 0 8 0 0 0 0 0 9 901 902 903 904 905 10 1001 1002 1003 1004 1005 Col: 6 7 8 9 10 Row --- 1 0 0 0 109 110 2 0 0 0 209 210 3 0 0 0 309 310 4 0 0 0 409 410 5 506 0 0 509 510 6 606 607 0 609 610 7 706 707 708 709 710 8 0 807 808 809 810 9 906 907 908 909 910 10 1006 1007 1008 1009 1010 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 101 102 0 0 0 2 201 202 203 0 0 3 0 302 303 304 0 4 0 0 403 404 405 5 0 0 0 504 505 6 0 0 0 0 605 7 0 0 0 0 0 8 0 0 0 0 0 9 901 902 903 904 905 10 1001 1002 1003 1004 1005 Col: 6 7 8 9 10 Row --- 1 0 0 0 109 110 2 0 0 0 209 210 3 0 0 0 309 310 4 0 0 0 409 410 5 506 0 0 509 510 6 606 607 0 609 610 7 706 707 708 709 710 8 0 807 808 809 810 9 906 907 908 909 910 10 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: 1 2 3 4 5 Row --- 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 10 0 0 0 0 0 Col: 6 7 8 9 10 Row --- 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 10 0 0 0 0 0 r8cbb_test(): Normal end of execution. 21-Aug-2022 18:33:40