📄 vsvd.dat
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2 | 19.49 3 | 18.49 4 | 17.49 5 | 16.49 6 | 15.49 7 | 14.49 8 | 13.49 9 | 12.49 10 | 11.49 11 | 3.464 12 | 4.472 13 | 10.49 14 | 5.477 15 | 6.481 16 | 7.483 17 | 8.485 18 | 9.487 19 | 2.449 20 | 1.414 Doneright factor V follows Matrix 1:20x1:20 is not engaged | 1 | 2 | 3 | 4 | 5 | 6 |------------------------------------------------------------------------------- 1 | -1 0 0 0 0 0 2 | 0 -1 8.733e-07 3.631e-07 2.226e-07 2.17e-07 3 | 0 9.606e-07 1 4.574e-06 -9.265e-07 2.435e-07 4 | 0 -2.576e-07 5.031e-06 -1 1.709e-06 -7.874e-07 5 | 0 2.822e-07 1.263e-06 1.713e-06 1 -2.022e-06 6 | 0 -2.161e-07 2.623e-07 7.707e-07 -2.071e-06 -1 7 | 0 1.253e-07 -9.179e-08 5.592e-09 -3.293e-07 1.787e-07 8 | 0 6.207e-08 -9.77e-08 -6.128e-08 4.345e-07 1.018e-06 9 | 0 1.075e-07 1.252e-07 -5.056e-08 -1.534e-07 5.333e-07 10 | 0 -1.147e-08 9.892e-09 -8.341e-09 8.645e-08 2.383e-07 11 | 0 1.235e-07 9.021e-08 -1.972e-07 -7.138e-08 2.493e-07 12 | 0 4.29e-08 3.784e-08 4.01e-09 4.182e-08 1.049e-07 13 | 0 1.411e-08 6.802e-08 4.786e-08 -4.339e-08 -4.655e-08 14 | 0 7.549e-09 3.531e-08 7.561e-08 6.757e-08 -5.275e-08 15 | 0 2.235e-09 -5.335e-09 -1.194e-07 1.168e-08 2.061e-07 16 | 0 -3.959e-08 -1.39e-09 -1.57e-08 -7.327e-08 5.843e-09 17 | 0 -7.109e-09 -2.587e-08 -1.794e-08 -3.977e-09 8.712e-08 18 | 0 4.421e-08 1.081e-07 -1.485e-07 -1.527e-07 1.571e-07 19 | 0 0 0 0 0 0 20 | 0 0 0 0 0 0 | 7 | 8 | 9 | 10 | 11 | 12 |------------------------------------------------------------------------------- 1 | 0 0 0 0 0 0 2 | 8.372e-08 -9.309e-08 1.186e-07 -2.382e-08 1.438e-08 -1.895e-08 3 | 2.497e-07 6.421e-09 -1.498e-07 -1.138e-09 -9.71e-08 3.628e-08 4 | 8.699e-08 4.349e-09 -1.606e-09 -6.296e-10 -6.377e-08 4.847e-08 5 | 1.416e-07 4.805e-07 6.316e-08 1.552e-07 2.383e-08 -2.962e-08 6 | 2.541e-07 -9.759e-07 6.023e-07 -2.318e-07 9.485e-08 2.37e-08 7 | 1 5.184e-07 -7.591e-07 -1.321e-07 -4.625e-08 -6.943e-08 8 | 3.69e-07 -1 5.759e-08 9.817e-07 -1.118e-07 6.008e-09 9 | 6.579e-07 7.437e-08 1 -3.081e-07 -6.81e-08 -5.932e-08 10 | -2.191e-07 -9.217e-07 -1.444e-07 -1 -6.705e-08 5.446e-09 11 | 2.392e-07 -4.343e-07 -1.277e-07 2.377e-07 -4.575e-08 -8.325e-08 12 | 4.749e-08 2.203e-07 -3.073e-08 -4.633e-07 -3.498e-08 8.268e-09 13 | -2.35e-08 8.759e-08 -1.892e-08 -2.106e-07 1.601e-08 7.95e-09 14 | -3.1e-08 1.872e-07 5.452e-08 4.202e-08 -1.141e-07 -8.244e-08 15 | 6.716e-08 -1.977e-07 -1.687e-08 -4.409e-08 -6.138e-08 2.814e-07 16 | 1.015e-08 -6.073e-09 1.122e-07 -4.952e-08 1.24e-07 -5.649e-07 17 | 1.054e-07 -6.554e-08 7.516e-08 -8.275e-08 9.987e-07 1 18 | 1.382e-07 -3.202e-08 1.087e-07 -1.805e-07 1 -8.85e-07 19 | 0 0 0 0 0 0 20 | 0 0 0 0 0 0 | 13 | 14 | 15 | 16 | 17 | 18 |------------------------------------------------------------------------------- 1 | 0 0 0 0 0 0 2 | 9.101e-08 2.642e-08 1.238e-08 8.276e-09 4.795e-09 -3.74e-08 3 | -7.475e-08 2.302e-08 -9.278e-09 -4.053e-08 -5.093e-08 2.96e-08 4 | -1.164e-07 -1.122e-07 5.952e-08 2.598e-08 1.008e-08 1.171e-08 5 | 6.31e-08 1.399e-08 1.713e-08 -6.629e-08 3.286e-08 1.453e-08 6 | 7.262e-08 2.28e-08 -9.427e-08 -9.596e-09 -2.287e-08 -8.782e-08 7 | -2.033e-07 -5.151e-08 3.428e-08 2.055e-08 6.664e-08 4.036e-08 8 | -3.465e-07 -1.261e-08 2.3e-07 1.227e-07 -5.424e-08 -1.082e-07 9 | 4.946e-08 5.458e-08 -6.14e-08 6.928e-09 9.743e-08 -6.766e-08 10 | 2.56e-07 6.695e-08 3.678e-08 1.97e-08 -1.303e-07 3.79e-07 11 | 1 -4.445e-08 -2.748e-08 -1.376e-07 4.027e-08 -2.889e-07 12 | -4.329e-07 2.456e-09 -3.241e-08 -1.383e-08 3.099e-07 -1 13 | -1.472e-07 2.693e-07 -2.565e-07 1.077e-07 1 9.315e-08 14 | 8.94e-08 -6.006e-08 5.375e-07 1 -1.792e-07 1.449e-07 15 | 1.638e-07 4.652e-07 -1 6.158e-07 -2.732e-07 5.461e-08 16 | -4.486e-09 -1 -5.555e-07 -1.692e-07 2.7e-07 -1.2e-07 17 | 3.161e-08 -8.017e-07 2.84e-07 1.869e-07 1.679e-08 4.861e-08 18 | 7.57e-08 8.651e-08 -1.568e-07 7.022e-09 -5.411e-08 -5.8e-08 19 | 0 0 0 0 0 0 20 | 0 0 0 0 0 0 | 19 | 20 |------------------------------------------------------------------------------- 1 | 0 0 2 | 0 0 3 | 0 0 4 | 0 0 5 | 0 0 6 | 0 0 7 | 0 0 8 | 0 0 9 | 0 0 10 | 0 0 11 | 0 0 12 | 0 0 13 | 0 0 14 | 0 0 15 | 0 0 16 | 0 0 17 | 0 0 18 | 0 0 19 | -1 0 20 | 0 -1 Done checking that U is orthogonal indeed, i.e., U'U=E and UU'=ETwo (4,4) elements of matrices with values 0.999999 and 1differ the most, although the deviation 7.15256e-07 is smallTwo (4,4) elements of matrices with values 0.999999 and 1differ the most, although the deviation 7.7486e-07 is small checking that V is orthogonal indeed, i.e., V'V=E and VV'=ETwo (4,4) elements of matrices with values 1 and 1differ the most, although the deviation 7.15256e-07 is smallTwo (4,4) elements of matrices with values 1 and 1differ the most, although the deviation 7.15256e-07 is small checking that U*Sig*V' is indeed AComparison of two Matrices: Original A and composed USigV'Matrix 1:21x1:20 is not engagedMatrix 1:21x1:20 is not engagedMaximal discrepancy 1.33514e-05 occured at the point (3,3) Matrix 1 element is 18 Matrix 2 element is 18 Absolute error v2[i]-v1[i] 1.33514e-05 Relative error 7.41746e-07||Matrix 1|| 420||Matrix 2|| 420||Matrix1-Matrix2|| 0.00037723||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 8.98168e-07DoneTest by W. Meier <wmeier@manu.com> to catch an obscure bug in QRexpect singular values to be1.4666e-024 1.828427 3.828427 4.366725 7.932951SVD-decompose matrix A and check if we can compose it backoriginal matrix follows Matrix 1:5x1:5 is not engaged | 1 | 2 | 3 | 4 | 5 |------------------------------------------------------------------------------- 1 | 1 2 0 0 0 2 | 0 2 3 0 0 3 | 0 0 0 4 0 4 | 0 0 0 4 5 5 | 0 0 0 0 5 Doneleft factor U follows Matrix 1:5x1:5 is not engaged | 1 | 2 | 3 | 4 | 5 |------------------------------------------------------------------------------- 1 | 2.047e-08 0.9239 0.3827 0 0 2 | -8.403e-09 -0.3827 0.9239 0 0 3 | 0.5774 -1.278e-08 0 0.7692 0.2738 4 | -0.5774 1.278e-08 0 0.1475 0.8031 5 | 0.5774 -1.278e-08 0 -0.6217 0.5293 DoneVector of Singular values follows Matrix 1:5x1:1 is not engaged | 1 |------------------------------------------------------------------------------- 1 | 1.413e-08 2 | 1.828 3 | 3.828 4 | 4.367 5 | 7.933 Doneright factor V follows Matrix 1:5x1:5 is not engaged | 1 | 2 | 3 | 4 | 5 |------------------------------------------------------------------------------- 1 | 0.8571 0.5053 0.09996 0 0 2 | -0.4286 0.592 0.6826 0 0 3 | 0.2857 -0.6279 0.724 0 0 4 | 0 0 0 0.8398 0.543 5 | 0 0 0 -0.543 0.8398 Done checking that U is orthogonal indeed, i.e., U'U=E and UU'=ETwo (2,2) elements of matrices with values 1 and 1differ the most, although the deviation 1.19209e-07 is smallTwo (2,2) elements of matrices with values 1 and 1differ the most, although the deviation 1.19209e-07 is small checking that V is orthogonal indeed, i.e., V'V=E and VV'=ETwo (2,2) elements of matrices with values 1 and 1differ the most, although the deviation 1.19209e-07 is smallTwo (3,3) elements of matrices with values 1 and 1differ the most, although the deviation 1.19209e-07 is small checking that U*Sig*V' is indeed AComparison of two Matrices: Original A and composed USigV'Matrix 1:5x1:5 is not engagedMatrix 1:5x1:5 is not engagedMaximal discrepancy 2.38419e-07 occured at the point (2,3) Matrix 1 element is 3 Matrix 2 element is 3 Absolute error v2[i]-v1[i] 2.38419e-07 Relative error 7.94729e-08||Matrix 1|| 26||Matrix 2|| 26||Matrix1-Matrix2|| 7.43272e-07||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 2.85874e-08DoneCompilation finished at Fri Dec 25 23:22:46⌨️ 快捷键说明
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