19-May-2023 17:06:31 r8gb_test(): MATLAB version 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: 1 2 3 4 5 Row --- 1 0.218418 0.415307 0.633966 2 0.956318 0.0661187 0.0617272 0.00183837 3 0.829509 0.257578 0.449539 0.897504 0.840847 4 0.561695 0.109957 0.401306 0.350752 0.123104 5 0.043829 0.754673 0.0945448 0.00751236 6 0.797287 0.0136169 0.260303 7 0.859097 0.912484 8 0.113664 Col: 6 7 8 9 10 Row --- 4 0.351629 5 0.822887 0.453794 6 0.267132 0.911977 0.185314 7 0.692066 0.597917 0.574366 0.21293 8 0.561662 0.188955 0.367027 0.714471 0.825003 9 0.861216 0.761492 0.617205 0.117707 0.82466 10 0.396988 0.361529 0.299329 0.0618618 R8GB_DET computes the determinant = 0.002404 R8GE_DET computes the determinant = 0.002404 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: 1 2 3 4 5 Row --- 1 2 -1 2 -1 2 -1 3 -1 2 -1 4 -1 2 -1 5 -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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0.0661187 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.0617272 0.754673 4 0.043829 0.449539 0.797287 5 0.401306 0.00183837 Solution to A*x=b: 1: 1 2: 2 3: 3 4: 4 5: 5 Right hand side of transposed system: 1: 2.13105 2: 3.19882 3: 1.08646 4: 5.2578 5: 5.46236 Solution to A'x=b: 1: 1 2: 2 3: 3 4: 4 5: 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: 1 2 3 4 5 Row --- 1 11 12 13 2 21 22 23 24 3 31 32 33 34 35 4 41 42 43 44 45 5 52 53 54 55 6 63 64 65 7 74 75 8 85 Col: 6 7 8 Row --- 4 46 5 56 57 6 66 67 68 7 76 77 78 8 86 87 88 9 96 97 98 10 107 108 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 1: 2.07579 2.07579 2: 5.3883 5.3883 3: 5.18076 5.18076 4: 8.02059 8.02059 5: 8.06762 8.06762 6: 12.7308 12.7308 7: 8.52067 8.52067 8: 15.4017 15.4017 9: 20.7578 20.7578 10: 13.7301 13.7301 A'*x and (PLU)'*x 1: 1.71194 1.71194 2: 2.49071 2.49071 3: 3.53774 3.53774 4: 7.10439 7.10439 5: 6.80503 6.80503 6: 14.9862 14.9862 7: 18.7469 18.7469 8: 7.88328 7.88328 9: 12.7733 12.7733 10: 2.65418 2.65418 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0.0661187 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.0617272 0.754673 4 0.043829 0.449539 0.797287 5 0.401306 0.00183837 x: 1: 1 2: 2 3: 3 4: 4 5: 5 b=A'*x: 1: 2.13105 2: 3.19882 3: 1.08646 4: 5.2578 5: 5.46236 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 1: 2.07579 2.07579 2: 5.3883 5.3883 3: 5.18076 5.18076 4: 8.02059 8.02059 5: 8.06762 8.06762 6: 12.7308 12.7308 7: 8.52067 8.52067 8: 15.4017 15.4017 9: 20.7578 20.7578 10: 13.7301 13.7301 A'*x and (PLU)'*x 1: 1.71194 1.71194 2: 2.49071 2.49071 3: 3.53774 3.53774 4: 7.10439 7.10439 5: 6.80503 6.80503 6: 14.9862 14.9862 7: 18.7469 18.7469 8: 7.88328 7.88328 9: 12.7733 12.7733 10: 2.65418 2.65418 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0.0661187 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.0617272 0.754673 4 0.043829 0.449539 0.797287 5 0.401306 0.00183837 x: 1: 1 2: 2 3: 3 4: 4 5: 5 b=A*x: 1: 2.07579 2: 5.3883 3: 5.18076 4: 5.91608 5: 1.61442 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: 1 2 3 4 5 Row --- 1 0 0.829509 0 2 0.956318 0.561695 0 0.633966 3 0.415307 0 0 0.754673 4 0 0.449539 0.797287 5 0.401306 0 6 0.897504 Col: 6 7 8 9 10 Row --- 4 0.350752 5 0 0.840847 6 0 0 0.912484 7 0.859097 0 0 0 8 0 0.351629 0.692066 0.453794 9 0.822887 0.561662 0.911977 10 0.861216 0.597917 Nonzero entries = 22 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: 1 2 3 4 5 Row --- 1 101 102 103 104 2 201 202 203 204 205 3 302 303 304 305 4 403 404 405 5 504 505 6 605 Col: 6 7 8 9 10 Row --- 3 306 4 406 407 5 506 507 508 6 606 607 608 609 7 706 707 708 709 710 8 807 808 809 810 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(5-7), Cols (4-10) Col: 4 5 6 7 8 Row --- 5 504 505 506 507 508 6 605 606 607 608 7 706 707 708 Col: 9 10 Row --- 6 609 7 709 710 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0.0661187 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.0617272 0.754673 4 0.043829 0.449539 0.797287 5 0.401306 0.00183837 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: 1 2 3 4 5 Row --- 1 0.218418 0.829509 0.0661187 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.0617272 0.754673 4 0.043829 0.449539 0.797287 5 0.401306 0.00183837 Solution to A*x=b: 1: 1 2: 2 3: 3 4: 4 5: 5 Right hand side of transposed system: 1: 2.13105 2: 3.19882 3: 1.08646 4: 5.2578 5: 5.46236 Solution to A'x=b: 1: 1 2: 2 3: 3 4: 4 5: 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: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 31 32 33 34 0 4 0 42 43 44 45 5 0 0 53 54 55 Col: 6 7 8 Row --- 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 56 0 0 R8GB_TO_R8S3_TEST R8GB_TO_R8S3 copies a R8GB matrix to a R8S3 matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 Nonzeros NZ_NUM = 17 The R8S3 matrix: Col: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 31 32 33 34 0 4 0 42 43 44 45 5 0 0 53 54 55 Col: 6 7 8 Row --- 5 56 0 0 R8GB_TO_R8SP_TEST R8GB_TO_R8SP copies an R8GB matrix to an R8SP matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 Nonzeros NZ_NUM = 17 The R8SP matrix: Col: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 31 32 33 34 0 4 0 42 43 44 45 5 0 0 53 54 55 Col: 6 7 8 Row --- 5 56 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: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 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 The recovered R8GB indicator matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 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: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 Solution to transposed system: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 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: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 10 Solution to transposed system: 1: 1 2: 2 3: 3 4: 4 5: 5 6: 6 7: 7 8: 8 9: 9 10: 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: 1 2 3 4 5 Row --- 1 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 5 0 0 r8ge_to_r8gb_test() R8GB_TO_R8GE copies a R8GB matrix to a R8GE matrix. R8GE_TO_R8GB copies a R8GE matrix to a R8GB matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11 12 0 0 0 2 21 22 23 0 0 3 31 32 33 34 0 4 0 42 43 44 45 5 0 0 53 54 55 Col: 6 7 8 Row --- 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 56 0 0 The recovered R8GB matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 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: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 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 The recovered R8GB indicator matrix: Col: 1 2 3 4 5 Row --- 1 11 12 2 21 22 23 3 31 32 33 34 4 42 43 44 45 5 53 54 55 Col: 6 7 8 Row --- 5 56 r8gb_test(): Normal end of execution. 19-May-2023 17:06:32