19-May-2023 10:47:14 r8ci_test() MATLAB version Test r8ci(). R8CI_DET_TEST R8CI_DET finds the determiannt of a real circulant system. 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 Computed determinant = 0.442848 R8CI_DIF2_TEST R8CI_DIF2 sets up an R8CI periodic second difference matrix. Matrix order N = 5 The R8CI periodic second difference 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 a real circulant system. 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: 1 -0.461343 + -0.0632919 i 2 -0.461343 + 0.0632919 i 3 -0.483235 + -0.671949 i 4 -0.483235 + 0.671949 i 5 2.98125 R8CI_INDICATOR_TEST R8CI_INDICATOR sets up a R8CI indicator matrix. Matrix order N = 5 The circulant 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 A: 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: 1: 1 2: 2 3: 3 4: 4 5: 5 The product b=A'*x: 1: 195 2: 200 3: 200 4: 195 5: 185 R8CI_MV_TEST R8CI_MV computes b=A*x where A is an R8CI indicator matrix. Matrix order N = 5 The R8CI matrix A: 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: 1: 1 2: 2 3: 3 4: 4 5: 5 The product b=A*x: 1: 205 2: 195 3: 190 4: 190 5: 195 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 2-6, Cols 3-5: Col: 3 4 5 Row --- 2 102 103 104 3 101 102 103 4 110 101 102 5 109 110 101 6 108 109 110 R8CI_RANDOM_TEST R8CI_RANDOM computes a random R8CI matrix. Matrix order N = 5 The random 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 R8CI_SL_TEST R8CI_SL solves a circulant system. 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: 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 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 zeros an R8CI matrix. Matrix order N = 5 The zero 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. 19-May-2023 10:47:14