11 April 2023 8:34:23.056 AM r8gb_test(): FORTRAN90 version: Test r8gb(). R8GB_DET_TEST R8GB_DET computes the determinant for a general banded matrix. 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 0.661187E-01 0.617272E-01 0.183837E-02 3 0.829509 0.257578 0.449539 0.897504 0.840847 4 0.561695 0.109957 0.401306 0.350752 0.123104 5 0.438290E-01 0.754673 0.945448E-01 0.751236E-02 6 0.797287 0.136169E-01 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 0.212930 8 0.561662 0.188955 0.367027 0.714471 0.825003 9 0.861216 0.761492 0.617205 0.117707 0.824660 10 0.396988 0.361529 0.299329 0.618618E-01 R8GB_DET computes the determinant = 0.240436E-02 R8GE_DET computes the determinant = 0.240436E-02 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 2.00000 -1.00000 2 -1.00000 2.00000 -1.00000 3 -1.00000 2.00000 -1.00000 4 -1.00000 2.00000 -1.00000 5 -1.00000 2.00000 R8GB_FA_TEST R8GB_FA computes the PLU factors of a general banded 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 0.661187E-01 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.617272E-01 0.754673 4 0.438290E-01 0.449539 0.797287 5 0.401306 0.183837E-02 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 Right hand side of transposed system: 1 2.13105 2 3.19882 3 1.08646 4 5.25780 5 5.46236 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 R8GB_INDICATOR_TEST R8GB_INDICATOR computes the indicator matrix for a general band 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 11.0000 12.0000 13.0000 2 21.0000 22.0000 23.0000 24.0000 3 31.0000 32.0000 33.0000 34.0000 35.0000 4 41.0000 42.0000 43.0000 44.0000 45.0000 5 52.0000 53.0000 54.0000 55.0000 6 63.0000 64.0000 65.0000 7 74.0000 75.0000 8 85.0000 Col: 6 7 8 Row --- 4 46.0000 5 56.0000 57.0000 6 66.0000 67.0000 68.0000 7 76.0000 77.0000 78.0000 8 86.0000 87.0000 88.0000 9 96.0000 97.0000 98.0000 10 107.000 108.000 R8GB_ML_TEST R8GB_ML computes A*x or A'*X for a general banded matrix A 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 5.38830 5.38830 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 2.13105 2.13105 2 3.19882 3.19882 3 1.08646 1.08646 4 5.25780 5.25780 5 10.8474 10.8474 6 7.97111 7.97111 7 7.07787 7.07787 8 16.4896 16.4896 9 21.0736 21.0736 10 17.8173 17.8173 R8GB_MTV_TEST R8GB_MTV computes A'*x for an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 b=A'*x: 1 2.13105 2 3.19882 3 1.08646 4 5.25780 5 5.46236 R8GB_MU_TEST R8GB_MU computes A*x or A'*X for a general banded matrix A 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 5.38830 5.38830 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 2.13105 2.13105 2 3.19882 3.19882 3 1.08646 1.08646 4 5.25780 5.25780 5 10.8474 10.8474 6 7.97111 7.97111 7 7.07787 7.07787 8 16.4896 16.4896 9 21.0736 21.0736 10 17.8173 17.8173 R8GB_MV_TEST R8GB_MV computes A*x for an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 1 Upper bandwidth MU = 2 x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 b=A*x: 1 2.07579 2 5.38830 3 5.18076 4 5.91608 5 1.61442 R8GB_NZ_NUM_TEST R8GB_NZ_NUM counts the nonzero entries for a general banded 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 0.00000 0.829509 0.00000 2 0.956318 0.561695 0.00000 0.633966 3 0.415307 0.00000 0.00000 0.754673 4 0.00000 0.449539 0.797287 5 0.401306 0.00000 6 0.897504 Col: 6 7 8 9 10 Row --- 4 0.350752 5 0.00000 0.840847 6 0.00000 0.00000 0.912484 7 0.859097 0.00000 0.00000 0.00000 8 0.00000 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 a general banded 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 --- 1 101.000 102.000 103.000 104.000 2 201.000 202.000 203.000 204.000 205.000 3 302.000 303.000 304.000 305.000 4 403.000 404.000 405.000 5 504.000 505.000 6 605.000 Col: 6 7 8 9 10 Row --- 3 306.000 4 406.000 407.000 5 506.000 507.000 508.000 6 606.000 607.000 608.000 609.000 7 706.000 707.000 708.000 709.000 710.000 8 807.000 808.000 809.000 810.000 R8GB_PRINT_SOME_TEST R8GB_PRINT_SOME prints some of a general banded 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 --- 5 504.000 505.000 506.000 507.000 508.000 6 605.000 606.000 607.000 608.000 7 706.000 707.000 708.000 Col: 9 10 Row --- 6 609.000 7 709.000 710.000 R8GB_RANDOM_TEST R8GB_RANDOM returns 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 0.661187E-01 0.438290E-01 0.449539 4 0.257578 0.633966 0.401306 0.797287 5 0.617272E-01 0.754673 0.183837E-02 R8GB_SL_TEST R8GB_SL solves a linear system. that was 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 0.661187E-01 2 0.956318 0.561695 0.257578 0.633966 3 0.415307 0.109957 0.617272E-01 0.754673 4 0.438290E-01 0.449539 0.797287 5 0.401306 0.183837E-02 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 Right hand side of transposed system: 1 2.13105 2 3.19882 3 1.08646 4 5.25780 5 5.46236 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 R8GB_TO_R8GE_TEST R8GB_TO_R8GE copies a R8GB matrix to a 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 11.0000 12.0000 2 21.0000 22.0000 23.0000 3 31.0000 32.0000 33.0000 34.0000 4 42.0000 43.0000 44.0000 45.0000 5 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 5 56.0000 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 0.00000 0.00000 0.00000 2 21.0000 22.0000 23.0000 0.00000 0.00000 3 31.0000 32.0000 33.0000 34.0000 0.00000 4 0.00000 42.0000 43.0000 44.0000 45.0000 5 0.00000 0.00000 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 1 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 5 56.0000 0.00000 0.00000 R8GB_TO_R8VEC_TEST R8GB_TO_R8VEC converts an R8GB matrix to a real vector. 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 11.0000 12.0000 2 21.0000 22.0000 23.0000 3 31.0000 32.0000 33.0000 34.0000 4 42.0000 43.0000 44.0000 45.0000 5 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 5 56.0000 1 1 1 0.00000 2 1 2 0.00000 3 1 3 0.00000 4 1 4 11.0000 5 1 5 21.0000 6 1 6 31.0000 1 2 7 0.00000 2 2 8 0.00000 3 2 9 12.0000 4 2 10 22.0000 5 2 11 32.0000 6 2 12 42.0000 1 3 13 0.00000 2 3 14 0.00000 3 3 15 23.0000 4 3 16 33.0000 5 3 17 43.0000 6 3 18 53.0000 1 4 19 0.00000 2 4 20 0.00000 3 4 21 34.0000 4 4 22 44.0000 5 4 23 54.0000 6 4 24 0.00000 1 5 25 0.00000 2 5 26 0.00000 3 5 27 45.0000 4 5 28 55.0000 5 5 29 0.00000 6 5 30 0.00000 1 6 31 0.00000 2 6 32 0.00000 3 6 33 56.0000 4 6 34 0.00000 5 6 35 0.00000 6 6 36 0.00000 1 7 37 0.00000 2 7 38 0.00000 3 7 39 0.00000 4 7 40 0.00000 5 7 41 0.00000 6 7 42 0.00000 1 8 43 0.00000 2 8 44 0.00000 3 8 45 0.00000 4 8 46 0.00000 5 8 47 0.00000 6 8 48 0.00000 The recovered R8GB indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 2 21.0000 22.0000 23.0000 3 31.0000 32.0000 33.0000 34.0000 4 42.0000 43.0000 44.0000 45.0000 5 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 5 56.0000 R8GB_TRF_TEST R8GB_TRF computes the PLU factors for a general banded matrix. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 R8GB_TRS_TEST R8GB_TRS solves a general band matrix linear system that was factored by R8GB_TRF. Matrix rows M = 10 Matrix columns N = 10 Lower bandwidth ML = 1 Upper bandwidth MU = 2 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 7 7.00000 8 8.00000 9 9.00000 10 10.0000 R8GB_ZEROS_TEST R8GB_ZEROS returns a zero R8GB matrix. Matrix rows M = 10 Matrix columns N = 8 Lower bandwidth ML = 3 Upper bandwidth MU = 2 The R8GB zero matrix: Col: 1 2 3 4 5 Row --- 1 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 0.00000 5 0.00000 0.00000 0.00000 0.00000 6 0.00000 0.00000 0.00000 7 0.00000 0.00000 8 0.00000 Col: 6 7 8 Row --- 4 0.00000 5 0.00000 0.00000 6 0.00000 0.00000 0.00000 7 0.00000 0.00000 0.00000 8 0.00000 0.00000 0.00000 9 0.00000 0.00000 0.00000 10 0.00000 0.00000 R8GE_TO_R8GB_TEST R8GE_TO_R8GB converts an R8GE matrix to an R8GB matrix. Matrix rows M = 5 Matrix columns N = 5 Lower bandwidth ML = 2 Upper bandwidth MU = 1 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.661187E-01 0.617272E-01 0.183837E-02 0.859097 2 0.956318 0.257578 0.449539 0.897504 0.840847 3 0.829509 0.109957 0.401306 0.350752 0.123104 4 0.561695 0.438290E-01 0.754673 0.945448E-01 0.751236E-02 5 0.415307 0.633966 0.797287 0.136169E-01 0.260303 The R8GB matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.661187E-01 2 0.956318 0.257578 0.449539 3 0.829509 0.109957 0.401306 0.350752 4 0.438290E-01 0.754673 0.945448E-01 0.751236E-02 5 0.797287 0.136169E-01 0.260303 R8VEC_TO_R8GB_TEST R8VEC_TO_R8GB converts a real vector 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 11.0000 12.0000 2 21.0000 22.0000 23.0000 3 31.0000 32.0000 33.0000 34.0000 4 42.0000 43.0000 44.0000 45.0000 5 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 5 56.0000 1 1 1 0.00000 2 1 2 0.00000 3 1 3 0.00000 4 1 4 11.0000 5 1 5 21.0000 6 1 6 31.0000 1 2 7 0.00000 2 2 8 0.00000 3 2 9 12.0000 4 2 10 22.0000 5 2 11 32.0000 6 2 12 42.0000 1 3 13 0.00000 2 3 14 0.00000 3 3 15 23.0000 4 3 16 33.0000 5 3 17 43.0000 6 3 18 53.0000 1 4 19 0.00000 2 4 20 0.00000 3 4 21 34.0000 4 4 22 44.0000 5 4 23 54.0000 6 4 24 0.00000 1 5 25 0.00000 2 5 26 0.00000 3 5 27 45.0000 4 5 28 55.0000 5 5 29 0.00000 6 5 30 0.00000 1 6 31 0.00000 2 6 32 0.00000 3 6 33 56.0000 4 6 34 0.00000 5 6 35 0.00000 6 6 36 0.00000 1 7 37 0.00000 2 7 38 0.00000 3 7 39 0.00000 4 7 40 0.00000 5 7 41 0.00000 6 7 42 0.00000 1 8 43 0.00000 2 8 44 0.00000 3 8 45 0.00000 4 8 46 0.00000 5 8 47 0.00000 6 8 48 0.00000 The recovered R8GB indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 2 21.0000 22.0000 23.0000 3 31.0000 32.0000 33.0000 34.0000 4 42.0000 43.0000 44.0000 45.0000 5 53.0000 54.0000 55.0000 Col: 6 7 8 Row --- 5 56.0000 r8gb_test(): Normal end of execution. 11 April 2023 8:34:23.057 AM