10 April 2023 6:45:15.521 AM r8sto_test(): FORTRAN90 version: Test r8sto(). R8STO_DIF2_TEST R8STO_DIF2 sets the second difference as an R8STO matrix. Matrix order N = 4 The R8STO matrix: Col: 1 2 3 4 Row --- 1 2.00000 -1.00000 0.00000 0.00000 2 -1.00000 2.00000 -1.00000 0.00000 3 0.00000 -1.00000 2.00000 -1.00000 4 0.00000 0.00000 -1.00000 2.00000 R8STO_INDICATOR_TEST R8STO_INDICATOR sets up an R8STO indicator matrix. Matrix order N = 4 The R8STO indicator matrix: Col: 1 2 3 4 Row --- 1 11.0000 12.0000 13.0000 14.0000 2 12.0000 11.0000 12.0000 13.0000 3 13.0000 12.0000 11.0000 12.0000 4 14.0000 13.0000 12.0000 11.0000 R8STO_INVERSE_TEST R8STO_INVERSE computes the inverse of a positive definite symmetric Toeplitz matrix. Matrix order N = 3 The symmetric Toeplitz matrix A: Col: 1 2 3 Row --- 1 4.00000 2.00000 0.800000 2 2.00000 4.00000 2.00000 3 0.800000 2.00000 4.00000 The inverse matrix B: Col: 1 2 3 Row --- 1 0.334821 -0.178571 0.223214E-01 2 -0.178571 0.428571 -0.178571 3 0.223214E-01 -0.178571 0.334821 The product C = A * B: Col: 1 2 3 Row --- 1 1.00000 0.364788E-16 -0.733540E-17 2 0.416334E-16 1.00000 0.00000 3 0.277556E-16 0.00000 1.00000 R8STO_MV_TEST R8STO_MV_TEST computes b=A*x, where A is an R8STO matrix. Matrix order N = 5 The symmetric Toeplitz matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 b=A*x: 1 8.94290 2 10.3886 3 11.3702 4 10.7449 5 8.94459 R8STO_PRINT_TEST R8STO_PRINT prints an R8STO matrix. Matrix order N = 5 The R8STO indicator matrix: Col: 1 2 3 4 5 Row --- 1 11.0000 12.0000 13.0000 14.0000 15.0000 2 12.0000 11.0000 12.0000 13.0000 14.0000 3 13.0000 12.0000 11.0000 12.0000 13.0000 4 14.0000 13.0000 12.0000 11.0000 12.0000 5 15.0000 14.0000 13.0000 12.0000 11.0000 R8STO_PRINT_SOME_TEST R8STO_PRINT_SOME prints some of an R8STO matrix. Matrix order N = 5 Rows 2:5, Cols 1:3 Col: 1 2 3 Row --- 2 12.0000 11.0000 12.0000 3 13.0000 12.0000 11.0000 4 14.0000 13.0000 12.0000 5 15.0000 14.0000 13.0000 R8STO_RANDOM_TEST R8STO_RANDOM_TEST randomizes an R8STO matrix. Matrix order N = 5 The symmetric Toeplitz matrix: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 R8STO_SL_TEST R8STO_SL solves a positive definite symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix A: Col: 1 2 3 Row --- 1 1.00000 0.500000 0.200000 2 0.500000 1.00000 0.500000 3 0.200000 0.500000 1.00000 The right hand side vector B: 1 4.00000 2 -1.00000 3 3.00000 The solution X: 1 6.33929 2 -6.71429 3 5.08929 The product vector B = A * X: 1 4.00000 2 -1.00000 3 3.00000 R8STO_TO_R8GE_TEST R8STO_TO_R8GE converts a matrix from R8STO to R8GE format. Matrix order N = 5 The matrix in R8STO format: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 The matrix in R8GE format: Col: 1 2 3 4 5 Row --- 1 0.218418 0.956318 0.829509 0.561695 0.415307 2 0.956318 0.218418 0.956318 0.829509 0.561695 3 0.829509 0.956318 0.218418 0.956318 0.829509 4 0.561695 0.829509 0.956318 0.218418 0.956318 5 0.415307 0.561695 0.829509 0.956318 0.218418 R8STO_YW_SL_TEST R8STO_YW_SL solves the Yule-Walker equations for a symmetric Toeplitz system. Matrix order N = 3 The symmetric Toeplitz matrix: Col: 1 2 3 Row --- 1 1.00000 0.500000 0.200000 2 0.500000 1.00000 0.500000 3 0.200000 0.500000 1.00000 The right hand side, B: 1 -0.500000 2 -0.200000 3 -0.100000 The computed solution, X: 1 -0.535714 2 0.857143E-01 3 -0.357143E-01 The product A*X: 1 -0.500000 2 -0.200000 3 -0.100000 R8STO_ZEROS_TEST R8STO_ZEROS zeros an R8STO matrix. Matrix order N = 4 The R8STO matrix: Col: 1 2 3 4 Row --- 1 0.00000 0.00000 0.00000 0.00000 2 0.00000 0.00000 0.00000 0.00000 3 0.00000 0.00000 0.00000 0.00000 4 0.00000 0.00000 0.00000 0.00000 r8sto_test(): Normal end of execution. 10 April 2023 6:45:15.521 AM