06 October 2025 6:33:31.592 PM 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 0.447779 0.540687 0.345547 0.768962 0.255457 2 0.255457 0.447779 0.540687 0.345547 0.768962 3 0.768962 0.255457 0.447779 0.540687 0.345547 4 0.345547 0.768962 0.255457 0.447779 0.540687 5 0.540687 0.345547 0.768962 0.255457 0.447779 Computed determinant = 0.357908E-01 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 0.186896 0.668881E-01 0.974841 0.702421 0.312399 2 0.312399 0.186896 0.668881E-01 0.974841 0.702421 3 0.702421 0.312399 0.186896 0.668881E-01 0.974841 4 0.974841 0.702421 0.312399 0.186896 0.668881E-01 5 0.668881E-01 0.974841 0.702421 0.312399 0.186896 The eigenvalues: 1 0.398349 0.403395 2 0.398349 -0.403395 3 -1.05283 0.733699E-01 4 -1.05283 -0.733699E-01 5 2.24345 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 0.539657 0.569848 0.300706 0.538176 0.532284 2 0.532284 0.539657 0.569848 0.300706 0.538176 3 0.538176 0.532284 0.539657 0.569848 0.300706 4 0.300706 0.538176 0.532284 0.539657 0.569848 5 0.569848 0.300706 0.538176 0.532284 0.539657 R8CI_SL_TEST R8CI_SL solves a circulant system. Matrix order N = 10 The circulant matrix: Col: 1 2 3 4 5 Row --- 1 0.585027 0.657894 0.699050E-01 0.394555 0.719373 2 0.350515 0.585027 0.657894 0.699050E-01 0.394555 3 0.697157 0.350515 0.585027 0.657894 0.699050E-01 4 0.765212 0.697157 0.350515 0.585027 0.657894 5 0.725175 0.765212 0.697157 0.350515 0.585027 6 0.800915 0.725175 0.765212 0.697157 0.350515 7 0.719373 0.800915 0.725175 0.765212 0.697157 8 0.394555 0.719373 0.800915 0.725175 0.765212 9 0.699050E-01 0.394555 0.719373 0.800915 0.725175 10 0.657894 0.699050E-01 0.394555 0.719373 0.800915 Col: 6 7 8 9 10 Row --- 1 0.800915 0.725175 0.765212 0.697157 0.350515 2 0.719373 0.800915 0.725175 0.765212 0.697157 3 0.394555 0.719373 0.800915 0.725175 0.765212 4 0.699050E-01 0.394555 0.719373 0.800915 0.725175 5 0.657894 0.699050E-01 0.394555 0.719373 0.800915 6 0.585027 0.657894 0.699050E-01 0.394555 0.719373 7 0.350515 0.585027 0.657894 0.699050E-01 0.394555 8 0.697157 0.350515 0.585027 0.657894 0.699050E-01 9 0.765212 0.697157 0.350515 0.585027 0.657894 10 0.725175 0.765212 0.697157 0.350515 0.585027 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. 06 October 2025 6:33:31.592 PM