8 April 2023 10:16:35.081 AM TOEPLITZ_TEST(): FORTRAN90 version Test TOEPLITZ(). TEST03 C8CI_SL solves a complex circulant system. Matrix order N = 4 The circulant matrix: Columns 1 2 3 4 Row --- 1 0.450 -0.127 -0.843 -0.344 0.590 0.260 0.391 0.323 2 0.391 0.323 0.450 -0.127 -0.843 -0.344 0.590 0.260 3 0.590 0.260 0.391 0.323 0.450 -0.127 -0.843 -0.344 4 -0.843 -0.344 0.590 0.260 0.391 0.323 0.450 -0.127 Solution: 1 1.00000 -1.00000 2 2.00000 -2.00000 3 3.00000 -3.00000 4 4.00000 -4.00000 TEST04 C8TO_SL solves a complex Toeplitz system. Matrix order N = 4 The Toeplitz matrix: Columns 1 2 3 4 Row --- 1 0.450 -0.127 -0.843 -0.344 0.590 0.260 0.391 0.323 2 -0.139 -0.156 0.450 -0.127 -0.843 -0.344 0.590 0.260 3 -0.236 0.775E-01-0.139 -0.156 0.450 -0.127 -0.843 -0.344 4 0.186E-01-0.633 -0.236 0.775E-01-0.139 -0.156 0.450 -0.127 Desired solution: 1 1.00000 -1.00000 2 2.00000 -2.00000 3 3.00000 -3.00000 4 4.00000 -4.00000 Right Hand Side: 1 3.35555 -0.838263 2 0.187223 -0.991121 3 -4.53014 0.546271 4 -0.525864 -2.38088 Solution: 1 1.00000 -1.00000 2 2.00000 -2.00000 3 3.00000 -3.00000 4 4.00000 -4.00000 Desired solution to transposed system: 1 1.00000 -1.00000 2 2.00000 -2.00000 3 3.00000 -3.00000 4 4.00000 -4.00000 Right Hand Side of transposed system: 1 -3.20229 -2.27654 2 -2.06232 0.549956 3 -1.73806 -1.12796 4 0.144314 -1.53617 Solution to transposed system: 1 1.00000 -1.00000 2 2.00000 -2.00000 3 3.00000 -3.00000 4 4.00000 -4.00000 TEST08 R8TO_SL solves a real Toeplitz system. Matrix order N = 4 The Toeplitz matrix: Columns 1 2 3 4 Row --- 1 0.218418 0.956318 0.829509 0.561695 2 0.415307 0.218418 0.956318 0.829509 3 0.661187E-01 0.415307 0.218418 0.956318 4 0.257578 0.661187E-01 0.415307 0.218418 Solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 Solution to transposed system: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 TEST09 For a real block Toeplitz matrix, R8BTO_MXV computes A * x. R8BTO_VXM computes x * A. The block Toeplitz matrix: Columns: 1 2 3 4 5 Row --- 1 1.00000 2.00000 3.00000 4.00000 5.00000 2 5.00000 5.00000 6.00000 6.00000 7.00000 3 7.00000 8.00000 1.00000 2.00000 3.00000 4 8.00000 8.00000 5.00000 5.00000 6.00000 5 9.00000 0.00000 7.00000 8.00000 1.00000 6 9.00000 9.00000 8.00000 8.00000 5.00000 Columns: 6 Row --- 1 6.00000 2 7.00000 3 4.00000 4 6.00000 5 2.00000 6 5.00000 The vector x: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 The product A*x: 1 91.0000 2 134.000 3 73.0000 4 125.000 5 79.0000 6 138.000 The product x*A: 1 163.000 2 122.000 3 121.000 4 130.000 5 87.0000 6 96.0000 TEST10 R8BTO_SL solves a block Toeplitz system. Matrix order N = 6 The block Toeplitz matrix: Columns: 1 2 3 4 5 Row --- 1 9.00000 1.00000 3.00000 4.00000 5.00000 2 2.00000 8.00000 6.00000 6.00000 7.00000 3 7.00000 8.00000 9.00000 1.00000 3.00000 4 8.00000 8.00000 2.00000 8.00000 6.00000 5 9.00000 0.00000 7.00000 8.00000 9.00000 6 9.00000 9.00000 8.00000 8.00000 2.00000 Columns: 6 Row --- 1 6.00000 2 7.00000 3 4.00000 4 6.00000 5 1.00000 6 8.00000 Right hand side: 1 97.0000 2 137.000 3 93.0000 4 128.000 5 113.000 6 141.000 Computed solution: 1 1.00000 2 2.00000 3 3.00000 4 4.00000 5 5.00000 6 6.00000 TOEPLITZ_TEST Normal end of execution. 8 April 2023 10:16:35.082 AM