11 April 2023 8:53:00.100 AM r8ci_test(): FORTRAN90 version: Test r8ci(). R8CI_DET_TEST R8CI_DET finds the determinant 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 second difference matrix: Col: 1 2 3 4 5 Row --- 1 2.00000 -1.00000 0.00000 0.00000 -1.00000 2 -1.00000 2.00000 -1.00000 0.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 0.00000 4 0.00000 0.00000 -1.00000 2.00000 -1.00000 5 -1.00000 0.00000 0.00000 -1.00000 2.00000 R8CI_EVAL_TEST R8CI_EVAL finds the eigenvalues of a real circulant system. 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 The eigenvalues: 1 -0.461343 -0.632919E-01 2 -0.461343 0.632919E-01 3 -0.483235 -0.671949 4 -0.483235 0.671949 5 2.98125 0.00000 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 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 R8CI_MTV_TEST R8CI_MTV computes b=A'*x, where A is an R8CI matrix Matrix order N = 5 The circulant matrix A: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 The vector x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 The product b=A'*x: 1 195.000 2 200.000 3 200.000 4 195.000 5 185.000 R8CI_MV_TEST R8CI_MV computes b=A*x, where A is an R8CI matrix Matrix order N = 5 The circulant matrix A: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 The vector x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 The product b=A*x: 1 205.000 2 195.000 3 190.000 4 190.000 5 195.000 R8CI_PRINT_TEST R8CI_PRINT prints an R8CI matrix. Matrix order N = 5 The R8CI matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 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 --- 2 102.000 103.000 104.000 3 101.000 102.000 103.000 4 110.000 101.000 102.000 5 109.000 110.000 101.000 6 108.000 109.000 110.000 R8CI_RANDOM_TEST R8CI_RANDOM sets a random 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 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 0.438290E-01 0.633966 0.218418 0.956318 0.829509 4 0.109957 0.438290E-01 0.633966 0.218418 0.956318 5 0.257578 0.109957 0.438290E-01 0.633966 0.218418 6 0.661187E-01 0.257578 0.109957 0.438290E-01 0.633966 7 0.415307 0.661187E-01 0.257578 0.109957 0.438290E-01 8 0.561695 0.415307 0.661187E-01 0.257578 0.109957 9 0.829509 0.561695 0.415307 0.661187E-01 0.257578 10 0.956318 0.829509 0.561695 0.415307 0.661187E-01 Col: 6 7 8 9 10 Row --- 1 0.661187E-01 0.257578 0.109957 0.438290E-01 0.633966 2 0.415307 0.661187E-01 0.257578 0.109957 0.438290E-01 3 0.561695 0.415307 0.661187E-01 0.257578 0.109957 4 0.829509 0.561695 0.415307 0.661187E-01 0.257578 5 0.956318 0.829509 0.561695 0.415307 0.661187E-01 6 0.218418 0.956318 0.829509 0.561695 0.415307 7 0.633966 0.218418 0.956318 0.829509 0.561695 8 0.438290E-01 0.633966 0.218418 0.956318 0.829509 9 0.109957 0.438290E-01 0.633966 0.218418 0.956318 10 0.257578 0.109957 0.438290E-01 0.633966 0.218418 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 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 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 The R8GE matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 15.0000 11.0000 12.0000 13.0000 14.0000 3 14.0000 15.0000 11.0000 12.0000 13.0000 4 13.0000 14.0000 15.0000 11.0000 12.0000 5 12.0000 13.0000 14.0000 15.0000 11.0000 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 0.00000 0.00000 0.00000 0.00000 0.00000 2 0.00000 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 0.00000 r8ci_test(): Normal end of execution. 11 April 2023 8:53:00.100 AM