22 August 2022 09:30:52 AM r8gb_test(): C version Test r8gb(). R8GB_DET_TEST R8GB_DET computes the determinant of an R8GB matrix. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 3 Upper bandwidth MU = 2 The banded matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.415307 0.633966 0 0 2 0.956318 0.0661187 0.0617272 0.00183837 0 3 0.829509 0.257578 0.449539 0.897504 0.840847 4 0.561695 0.109957 0.401306 0.350752 0.123104 5 0 0.043829 0.754673 0.0945448 0.00751236 6 0 0 0.797287 0.0136169 0.260303 7 0 0 0 0.859097 0.912484 8 0 0 0 0 0.113664 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 0.351629 0 0 0 0 5 0.822887 0.453794 0 0 0 6 0.267132 0.911977 0.185314 0 0 7 0.692066 0.597917 0.574366 0.21293 0 8 0.561662 0.188955 0.367027 0.714471 0.825003 9 0.861216 0.761492 0.617205 0.117707 0.82466 10 0 0.396988 0.361529 0.299329 0.0618618 R8GB_DET computes the determinant = 0.00240436 R8GE_DET computes the determinant = 0.00240436 R8GB_DIF2_TEST R8GB_DIF2 sets up 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. Matrix rows M = 5 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: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 Right hand side of transposed system: 0 2.131053 1 3.198821 2 1.086461 3 5.257800 4 5.462360 Solution to transposed system: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 R8GB_INDICATOR_TEST R8GB_INDICATOR returns an indicator matrix in R8GB format. Matrix rows M = 5 Matrix columns N = 5 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 R8GB_ML_TEST R8GB_ML computes A*x or A'*X where the R8GB matrix 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: 2.07579 2.07579 1: 5.3883 5.3883 2: 5.18076 5.18076 3: 8.02059 8.02059 4: 8.06762 8.06762 5: 12.7308 12.7308 6: 8.52067 8.52067 7: 15.4017 15.4017 8: 20.7578 20.7578 9: 13.7301 13.7301 A'*x and (PLU)'*x 0: 1.71194 1.71194 1: 2.49071 2.49071 2: 3.53774 3.53774 3: 7.10439 7.10439 4: 6.80503 6.80503 5: 14.9862 14.9862 6: 18.7469 18.7469 7: 7.88328 7.88328 8: 12.7733 12.7733 9: 2.65418 2.65418 R8GB_MTV_TEST R8GB_MTV computes A'*x, where A is an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Matrix A: 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 Vector x: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 b=A'*x: 0 2.131053 1 3.198821 2 1.086461 3 5.257800 4 5.462360 R8GB_MU_TEST R8GB_MU computes A*x or A'*X where the R8GB matrix 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: 2.07579 2.07579 1: 5.3883 5.3883 2: 5.18076 5.18076 3: 8.02059 8.02059 4: 8.06762 8.06762 5: 12.7308 12.7308 6: 8.52067 8.52067 7: 15.4017 15.4017 8: 20.7578 20.7578 9: 13.7301 13.7301 A'*x and (PLU)'*x 0: 2.13105 2.13105 1: 3.19882 3.19882 2: 1.08646 1.08646 3: 5.2578 5.2578 4: 10.8474 10.8474 5: 7.97111 7.97111 6: 7.07787 7.07787 7: 16.4896 16.4896 8: 21.0736 21.0736 9: 17.8173 17.8173 R8GB_MV_TEST R8GB_MV computes A*x, where A is an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Matrix A: 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 Vector x: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 b=A*x: 0 2.075793 1 5.388305 2 5.180761 3 5.916078 4 1.614417 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 banded 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(4-6), Cols (3-9) Col: 3 4 5 6 7 Row --- 4 403 404 405 406 407 5 504 505 506 507 6 605 606 607 Col: 8 9 Row --- 5 508 6 608 609 R8GB_RANDOM_TEST R8GB_RANDOM sets up a random R8GB matrix . Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The random R8GB matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.561695 2 0.956318 0.415307 0.109957 3 0.829509 0.0661187 0.043829 0.449539 4 0.257578 0.633966 0.401306 0.797287 5 0.0617272 0.754673 0.00183837 R8GB_SL_TEST R8GB_SL solves a linear system factored by R8GB_FA. Matrix rows M = 5 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: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 Right hand side of transposed system: 0 2.131053 1 3.198821 2 1.086461 3 5.257800 4 5.462360 Solution to transposed system: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 R8GB_TO_R8GE_TEST R8GB_TO_R8GE copies an R8GB matrix to R8GE format. 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 R8GB_TO_R8VEC_TEST R8GB_TO_R8VEC converts an R8GB matrix to R8VEC format. 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 R8VEC vector: 0 0.000000 1 0.000000 2 0.000000 3 11.000000 4 21.000000 5 31.000000 6 0.000000 7 0.000000 8 12.000000 9 22.000000 10 32.000000 11 42.000000 12 0.000000 13 0.000000 14 23.000000 15 33.000000 16 43.000000 17 53.000000 18 0.000000 19 0.000000 20 34.000000 21 44.000000 22 54.000000 23 0.000000 24 0.000000 25 0.000000 26 45.000000 27 55.000000 28 0.000000 29 0.000000 30 0.000000 31 0.000000 32 56.000000 33 0.000000 34 0.000000 35 0.000000 36 0.000000 37 0.000000 38 0.000000 39 0.000000 40 0.000000 41 0.000000 42 0.000000 43 0.000000 44 0.000000 45 0.000000 46 0.000000 47 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 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 5 6.000000 6 7.000000 7 8.000000 8 9.000000 9 10.000000 Solution to transposed system: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 5 6.000000 6 7.000000 7 8.000000 8 9.000000 9 10.000000 R8GB_TRS_TEST R8GB_TRS solves a linear system factored by R8GB_TRF. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 5 6.000000 6 7.000000 7 8.000000 8 9.000000 9 10.000000 Solution to transposed system: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 5 6.000000 6 7.000000 7 8.000000 8 9.000000 9 10.000000 R8GB_ZEROS_TEST R8GB_ZEROS zeros an R8GB matrix . Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GB zero matrix: Col: 1 2 3 4 5 Row --- 1 0 0 2 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 r8gb_test(): Normal end of execution. 22 August 2022 09:30:52 AM