29-Jul-2021 09:03:17 qr_solve_test(): MATLAB/Octave version 9.9.0.1467703 (R2020b) Test qr_solve(). BACKSLASH_SOLVE_TEST MATLAB's backslash operator x=A\b solves a linear system A*x = b in the least squares sense. Compare a tabulated solution X1 to the backslash result X2. Number of problems = 6 Index M N ||B|| ||X1 - X2|| ||X1|| ||X2|| ||R1|| ||R2|| 1 5 3 6.205 2.861e-08 5.461 5.461 1.075 1.075 2 6 3 537.6 5.416e-05 194.8 194.8 5.222 5.222 [Warning: Rank deficient, rank = 2, tol = 2.470090e-14.] [> In backslash_solve_test (line 56) In qr_solve_test (line 27) In run (line 91) ] 3 5 3 40.37 0.1361 10.84 10.84 5.477e-07 0 4 3 5 232.1 10.37 7.416 12.75 0 1.954e-14 5 10 10 1 1461 1.534e+07 1.534e+07 1.507e-10 2.261e-10 6 10 10 1 5.118e-16 1 1 4.971e-16 2.554e-16 NORMAL_SOLVE_TEST NORMAL_SOLVE is a function with a simple interface which solves a linear system A*x = b in the least squares sense. Compare a tabulated solution X1 to the NORMAL_SOLVE result X2. NORMAL_SOLVE cannot be applied when N < M, or if the matrix does not have full column rank. Number of problems = 6 Index M N ||B|| ||X1 - X2|| ||X1|| ||X2|| ||R1|| ||R2|| 1 5 3 6.205 2.861e-08 5.461 5.461 1.075 1.075 2 6 3 537.6 5.416e-05 194.8 194.8 5.222 5.222 3 5 3 40.37 ------------ 10.84 ------------ 5.477e-07 ------------ 4 3 5 232.1 ------------ 7.416 ------------ 0 ------------ 5 10 10 1 ------------ 1.534e+07 ------------ 1.507e-10 ------------ 6 10 10 1 5.202e-16 1 1 4.971e-16 2.528e-16 QR_FACTOR_SOLVE_TEST QR_FACTOR_SOLVE is a function with a simple interface which solves a linear system A*x = b in the least squares sense. Compare a tabulated solution X1 to the QR_SOLVE result X2. Number of problems = 6 Index M N ||B|| ||X1 - X2|| ||X1|| ||X2|| ||R1|| ||R2|| 1 5 3 6.205 2.861e-08 5.461 5.461 1.075 1.075 2 6 3 537.6 5.416e-05 194.8 194.8 5.222 5.222 3 5 3 40.37 25.7 10.84 27.89 5.477e-07 2.842e-14 4 3 5 232.1 10.37 7.416 12.75 0 9.073e-14 5 10 10 1 2352 1.534e+07 1.534e+07 1.507e-10 9.97e-10 6 10 10 1 5.368e-16 1 1 4.971e-16 2.416e-16 SVD_SOLVE_TEST SVD_SOLVE is a function with a simple interface which solves a linear system A*x = b in the least squares sense. Compare a tabulated solution X1 to the SVD_SOLVE result X2. Number of problems = 6 Index M N ||B|| ||X1 - X2|| ||X1|| ||X2|| ||R1|| ||R2|| 1 5 3 6.205 2.861e-08 5.461 5.461 1.075 1.075 2 6 3 537.6 5.416e-05 194.8 194.8 5.222 5.222 3 5 3 40.37 5.092e-08 10.84 10.84 5.477e-07 3.28e-14 4 3 5 232.1 1.151e-13 7.416 7.416 0 8.233e-14 5 10 10 1 1958 1.534e+07 1.534e+07 1.507e-10 1.199e-09 6 10 10 1 8.684e-16 1 1 4.971e-16 7.437e-16 qr_solve_test(): Normal end of execution. 29-Jul-2021 09:03:17