Tue Oct 19 17:05:48 2021 qr_solve_testS Python version: 3.6.9 Test the qr_solve library. lstsq_solve_test Python version: 3.6.9 The function x=np.linalg.lstsq(A,b) solves a linear system A*x = b in the least squares sense. Compare a tabulated solution X1 to the LSTSQ 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 2.93e-14 4 3 5 232.1 2.485e-14 7.416 7.416 0 8.71e-14 5 10 10 1 1332 1.534e+07 1.534e+07 1.2e-10 9.331e-10 6 10 10 1 5.042e-16 1 1 4.773e-16 6.92e-16 lstsq_solve_test Normal end of execution. normal_solve_test Python version: 3.6.9 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 ------------ 1.2e-10 ------------ 6 10 10 1 5.231e-16 1 1 4.773e-16 2.017e-16 normal_solve_test Normal end of execution. qr_solve_test Python version: 3.6.9 qr_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 20.96 10.84 23.6 5.477e-07 1.231e-14 4 3 5 232.1 10.37 7.416 12.75 0 3.553e-14 5 10 10 1 2290 1.534e+07 1.534e+07 1.2e-10 9.917e-10 6 10 10 1 5.93e-16 1 1 4.773e-16 3.295e-16 qr_solve_test Normal end of execution. svd_solve_test Python version: 3.6.9 svd_solve is a function with a simple interface which solves a linear system A*x = b in the least squares sense using the singular value decomposition (SVD). 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 5.092e-08 10.84 10.84 5.477e-07 7.105e-15 4 3 5 232.1 1.026e-13 7.416 7.416 0 2.693e-13 5 10 10 1 1997 1.534e+07 1.534e+07 1.2e-10 1.163e-09 6 10 10 1 8.163e-16 1 1 4.773e-16 6.186e-16 svd_solve_test Normal end of execution. qr_solve_tests Normal end of execution. Tue Oct 19 17:05:48 2021