21 August 2022 10:23:08 PM r8ci_test(): C version Test r8ci(). R8CI_DET_TEST R8CI_DET finds the determinant of an R8CI matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.415307 0.218418 0.956318 0.829509 0.561695 3 0.561695 0.415307 0.218418 0.956318 0.829509 4 0.829509 0.561695 0.415307 0.218418 0.956318 5 0.956318 0.829509 0.561695 0.415307 0.218418 Computed determinant = 0.442848 R8CI_DIF2_TEST R8CI_DIF2 sets up an R8CI periodic second difference matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 2 -1 0 0 -1 2 -1 2 -1 0 0 3 0 -1 2 -1 0 4 0 0 -1 2 -1 5 -1 0 0 -1 2 R8CI_EVAL_TEST R8CI_EVAL finds the eigenvalues of an R8CI matrix. Matrix order N = 5 The circulant matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.415307 0.218418 0.956318 0.829509 0.561695 3 0.561695 0.415307 0.218418 0.956318 0.829509 4 0.829509 0.561695 0.415307 0.218418 0.956318 5 0.956318 0.829509 0.561695 0.415307 0.218418 The eigenvalues: 0: -0.461343 -0.063292 1: -0.461343 0.063292 2: -0.483235 -0.671949 3: -0.483235 0.671949 4: 2.981248 0.000000 R8CI_INDICATOR_TEST R8CI_INDICATOR sets up an R8CI indicator matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 R8CI_MTV_TEST R8CI_MTV computes b=A'*x, where A is an R8CI indicator matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 The vector x: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 The product b=A'*x: 0 195.000000 1 200.000000 2 200.000000 3 195.000000 4 185.000000 R8CI_MV_TEST R8CI_MV computes b=A*x, where A is an R8CI indicator matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 The vector x: 0 1.000000 1 2.000000 2 3.000000 3 4.000000 4 5.000000 The product b=A*x: 0 205.000000 1 195.000000 2 190.000000 3 190.000000 4 195.000000 R8CI_PRINT_TEST R8CI_PRINT prints an R8CI matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 R8CI_PRINT_SOME_TEST R8CI_PRINT_SOME prints some of an R8CI matrix. Matrix order N = 10 Rows 1-5, Cols 2-4: Col: 2 3 4 Row --- 1 102 103 104 2 101 102 103 3 110 101 102 4 109 110 101 5 108 109 110 R8CI_SL_TEST R8CI_SL solves a linear system with an R8CI matrix. Matrix order N = 10 The circulant matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.633966 0.218418 0.956318 0.829509 0.561695 3 0.043829 0.633966 0.218418 0.956318 0.829509 4 0.109957 0.043829 0.633966 0.218418 0.956318 5 0.257578 0.109957 0.043829 0.633966 0.218418 6 0.0661187 0.257578 0.109957 0.043829 0.633966 7 0.415307 0.0661187 0.257578 0.109957 0.043829 8 0.561695 0.415307 0.0661187 0.257578 0.109957 9 0.829509 0.561695 0.415307 0.0661187 0.257578 10 0.956318 0.829509 0.561695 0.415307 0.0661187 Col: 6 7 8 9 10 Row --- 1 0.0661187 0.257578 0.109957 0.043829 0.633966 2 0.415307 0.0661187 0.257578 0.109957 0.043829 3 0.561695 0.415307 0.0661187 0.257578 0.109957 4 0.829509 0.561695 0.415307 0.0661187 0.257578 5 0.956318 0.829509 0.561695 0.415307 0.0661187 6 0.218418 0.956318 0.829509 0.561695 0.415307 7 0.633966 0.218418 0.956318 0.829509 0.561695 8 0.043829 0.633966 0.218418 0.956318 0.829509 9 0.109957 0.043829 0.633966 0.218418 0.956318 10 0.257578 0.109957 0.043829 0.633966 0.218418 Solution to A*x=b: 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 A'*x=b: 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 R8CI_TO_R8GE_TEST R8CI_TO_R8GE converts an R8CI matrix to R8GE format. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11 12 13 14 15 2 15 11 12 13 14 3 14 15 11 12 13 4 13 14 15 11 12 5 12 13 14 15 11 R8CI_ZEROS_TEST R8CI_ZEROS sets up a zero R8CI matrix. Matrix order N = 5 The R8CI 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 r8ci_test(): Normal end of execution. 21 August 2022 10:23:08 PM