18-May-2023 19:31:18 r8cb_test(): MATLAB version Test r8cb(). r8cb_det_test() r8cb_det() computes the determinant of a matrix that has been factored by R8CB_NP_FA. Matrix order N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The compact band 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 R8CB_DET computes the determinant = 6.000000 R8GE_DET computes the determinant = 6.000000 DET computes the determinant = 6.000000 r8cb_dif2_test(): r8cb_dif2() sets the second difference matrix as an R8CB matrix; Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 1 The R8CB zero 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 R8CB_INDICATOR_TEST R8CB_INDICATOR computes the indicator matrix in R8CB format; Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The R8CB indicator matrix: Col: 1 2 3 4 5 Row --- 1 101 102 103 104 2 201 202 203 204 205 3 301 302 303 304 305 4 402 403 404 405 5 503 504 505 6 604 605 7 705 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 8 806 807 808 809 810 R8CB_ML_TEST R8CB_ML computes A*x or A'*X for an R8CB matrix A after A has been factored by R8CB_FA. Matrix order 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 R8CB_MTV_TEST R8CB_MTV computes b=A'*x, where A is an R8CB matrix; Matrix rows M = 8 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8CB 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 6 64 65 7 75 Col: 6 7 8 Row --- 5 56 6 66 67 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: 146 2: 320 3: 582 4: 932 5: 1370 6: 1896 7: 1637 8: 1250 R8CB_MV_TEST R8CB_MV computes b=A*x, where A is an R8CB matrix; Matrix rows M = 8 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8CB 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 6 64 65 7 75 Col: 6 7 8 Row --- 5 56 6 66 67 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: 35 2: 134 3: 330 4: 614 5: 986 6: 1446 7: 1994 8: 1829 R8CB_NP_FA_TEST R8CB_NP_FA factors an R8CB matrix with no pivoting; Matrix order 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 R8CB_NP_SL_TEST R8CB_NP_SL solves a linear system factored by R8CB_NP_FA. Matrix order 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 R8CB_PRINT_TEST R8CB_PRINT prints an R8CB matrix; Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The R8CB matrix: Col: 1 2 3 4 5 Row --- 1 101 102 103 104 2 201 202 203 204 205 3 301 302 303 304 305 4 402 403 404 405 5 503 504 505 6 604 605 7 705 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 8 806 807 808 809 810 R8CB_PRINT_SOME_TEST R8CB_PRINT_SOME prints some of an R8CB matrix; Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 Rows 3-6, Cols 3-6: Col: 3 4 5 6 Row --- 3 303 304 305 306 4 403 404 405 406 5 503 504 505 506 6 604 605 606 R8CB_RANDOM_TEST R8CB_RANDOM randomizes an R8CB matrix; Matrix order M = 8 Matrix order N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The R8CB random matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.561695 0.109957 0.401306 2 0.956318 0.415307 0.043829 0.754673 0.0945448 3 0.829509 0.0661187 0.633966 0.797287 0.0136169 4 0.257578 0.0617272 0.00183837 0.859097 5 0.449539 0.897504 0.840847 6 0.350752 0.123104 7 0.00751236 Col: 6 7 8 9 10 Row --- 3 0.260303 4 0.912484 0.692066 5 0.113664 0.561662 0.597917 6 0.351629 0.861216 0.188955 0.185314 7 0.822887 0.453794 0.761492 0.574366 0.617205 8 0.267132 0.911977 0.396988 0.367027 0.361529 R8CB_TO_R8GE_TEST R8CB_TO_R8GE converts an R8CB matrix to R8GE format; Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The R8CB matrix: Col: 1 2 3 4 5 Row --- 1 101 102 103 104 2 201 202 203 204 205 3 301 302 303 304 305 4 402 403 404 405 5 503 504 505 6 604 605 7 705 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 8 806 807 808 809 810 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 101 102 103 104 0 2 201 202 203 204 205 3 301 302 303 304 305 4 0 402 403 404 405 5 0 0 503 504 505 6 0 0 0 604 605 7 0 0 0 0 705 8 0 0 0 0 0 Col: 6 7 8 9 10 Row --- 1 0 0 0 0 0 2 0 0 0 0 0 3 306 0 0 0 0 4 406 407 0 0 0 5 506 507 508 0 0 6 606 607 608 609 0 7 706 707 708 709 710 8 806 807 808 809 810 R8CB_TO_R8VEC_TEST R8CB_TO_R8VEC converts an R8CB matrix to an R8VEC. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8CB 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 11.000000 3 1 3 21.000000 4 1 4 31.000000 1 2 5 12.000000 2 2 6 22.000000 3 2 7 32.000000 4 2 8 42.000000 1 3 9 23.000000 2 3 10 33.000000 3 3 11 43.000000 4 3 12 53.000000 1 4 13 34.000000 2 4 14 44.000000 3 4 15 54.000000 4 4 16 0.000000 1 5 17 45.000000 2 5 18 55.000000 3 5 19 0.000000 4 5 20 0.000000 1 6 21 56.000000 2 6 22 0.000000 3 6 23 0.000000 4 6 24 0.000000 1 7 25 0.000000 2 7 26 0.000000 3 7 27 0.000000 4 7 28 0.000000 1 8 29 0.000000 2 8 30 0.000000 3 8 31 0.000000 4 8 32 0.000000 The recovered R8CB 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 R8CB_ZEROS_TEST R8CB_ZEROS zeros an R8CB matrix; Matrix rows M = 8 Matrix columns N = 10 Lower bandwidth ML = 2 Upper bandwidth MU = 3 The R8CB zero matrix: Col: 1 2 3 4 5 Row --- 1 0 0 0 0 2 0 0 0 0 0 3 0 0 0 0 0 4 0 0 0 0 5 0 0 0 6 0 0 7 0 Col: 6 7 8 9 10 Row --- 3 0 4 0 0 5 0 0 0 6 0 0 0 0 7 0 0 0 0 0 8 0 0 0 0 0 R8VEC_TO_R8CB_TEST R8VEC_TO_R8CB converts an R8VEC to an R8CB matrix. Matrix rows M = 5 Matrix columns N = 8 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8CB 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 11.000000 3 1 3 21.000000 4 1 4 31.000000 1 2 5 12.000000 2 2 6 22.000000 3 2 7 32.000000 4 2 8 42.000000 1 3 9 23.000000 2 3 10 33.000000 3 3 11 43.000000 4 3 12 53.000000 1 4 13 34.000000 2 4 14 44.000000 3 4 15 54.000000 4 4 16 0.000000 1 5 17 45.000000 2 5 18 55.000000 3 5 19 0.000000 4 5 20 0.000000 1 6 21 56.000000 2 6 22 0.000000 3 6 23 0.000000 4 6 24 0.000000 1 7 25 0.000000 2 7 26 0.000000 3 7 27 0.000000 4 7 28 0.000000 1 8 29 0.000000 2 8 30 0.000000 3 8 31 0.000000 4 8 32 0.000000 The recovered R8CB 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 r8cb_test(): Normal end of execution. 18-May-2023 19:31:19