09-Sep-2022 10:10:09 haar_test(): MATLAB/Octave version 4.2.2 Test haar(). haar_test01(): HAAR_1D computes the Haar transform of a vector. HAAR_1D_INVERSE inverts the transform. i U(i) H(U)(i) Hinv(H(U))(i) 1 0.181318 2.020916 0.181318 2 0.454614 -0.319223 0.454614 3 0.028475 -0.480681 0.028475 4 0.357500 0.099955 0.357500 5 0.848979 0.124978 0.848979 6 0.697352 0.355591 0.697352 7 0.227237 0.382628 0.227237 8 0.607911 0.038119 0.607911 9 0.912001 -0.193250 0.912001 10 0.711375 -0.232655 0.711375 11 0.208077 0.107217 0.208077 12 0.650044 -0.269177 0.650044 13 0.697957 0.141864 0.697957 14 0.439553 -0.312518 0.439553 15 0.198957 0.182719 0.198957 16 0.862315 -0.469065 0.862315 i U(i) H(U)(i) Hinv(H(U))(i) 1 1.000000 2.828427 1.000000 2 1.000000 0.000000 1.000000 3 1.000000 0.000000 1.000000 4 1.000000 0.000000 1.000000 5 1.000000 0.000000 1.000000 6 1.000000 0.000000 1.000000 7 1.000000 0.000000 1.000000 8 1.000000 0.000000 1.000000 i U(i) H(U)(i) Hinv(H(U))(i) 1 1.000000 34.000000 1.000000 2 2.000000 -16.000000 2.000000 3 3.000000 -5.656854 3.000000 4 4.000000 -5.656854 4.000000 5 5.000000 -2.000000 5.000000 6 6.000000 -2.000000 6.000000 7 7.000000 -2.000000 7.000000 8 8.000000 -2.000000 8.000000 9 9.000000 -0.707107 9.000000 10 10.000000 -0.707107 10.000000 11 11.000000 -0.707107 11.000000 12 12.000000 -0.707107 12.000000 13 13.000000 -0.707107 13.000000 14 14.000000 -0.707107 14.000000 15 15.000000 -0.707107 15.000000 16 16.000000 -0.707107 16.000000 i U(i) H(U)(i) Hinv(H(U))(i) 1 25.000000 21.213203 25.000000 2 16.000000 16.970563 16.000000 3 9.000000 14.000000 9.000000 4 4.000000 -2.000000 4.000000 5 1.000000 6.363961 1.000000 6 0.000000 3.535534 0.000000 7 1.000000 0.707107 1.000000 8 4.000000 -2.121320 4.000000 For N = 99, |u-haar_1d_inverse(haar_1d(u))| = 3.10687e-15 haar_test02(): HAAR_2D computes the Haar transform of an array. HAAR_2D_INVERSE inverts the transform. Input array U: Col: 1 2 3 4 Row 1 : 0.0863978 0.215739 0.358801 0.115165 2 : 0.129128 0.843953 0.665134 0.635718 3 : 0.123442 0.844297 0.323626 0.737668 4 : 0.18965 0.554701 0.510069 0.022887 5 : 0.659831 0.0764895 0.583986 0.704358 6 : 0.0635278 0.442216 0.257628 0.388969 7 : 0.513151 0.251507 0.638573 0.371304 8 : 0.328054 0.891072 0.428436 0.749248 9 : 0.889474 0.168188 0.377536 0.383791 10 : 0.793358 0.292016 0.320406 0.145796 11 : 0.356524 0.27763 0.280918 0.25925 12 : 0.860212 0.417122 0.432911 0.718154 13 : 0.156411 0.168861 0.692768 0.176677 14 : 0.788116 0.58265 0.801371 0.684661 15 : 0.256108 0.434233 0.533315 0.563506 16 : 0.881202 0.849573 0.758713 0.0885042 Transformed array V: Col: 1 2 3 4 Row 1 : 3.63684 -0.0406266 -0.0416591 0.215408 2 : -0.210653 -0.278977 -0.67492 -0.200935 3 : -0.175358 0.0910211 -0.458338 0.162862 4 : -0.255156 0.233013 0.424523 -0.34201 5 : -0.0640766 -0.15436 0.0854678 0.0706797 6 : -0.248585 -0.122275 0.178908 -0.0700634 7 : -0.0580388 0.173813 0.247715 0.15271 8 : -0.0784097 -0.284129 0.120035 -0.00255159 9 : -0.529563 0.0551336 0.292742 0.107111 10 : 0.265775 -0.107816 -0.177902 -0.450613 11 : 0.308414 -0.145371 0.481015 0.00548434 12 : -0.220007 -0.10135 0.412331 0.294041 13 : 0.0945448 -0.11414 0.109972 -0.0904326 14 : -0.443383 -0.0114142 -0.182098 0.153455 15 : -0.587634 -0.151641 -0.108958 0.19969 16 : -0.2796 -0.456097 -0.104877 -0.3502 Recovered array W: Col: 1 2 3 4 Row 1 : 0.0863978 0.215739 0.358801 0.115165 2 : 0.129128 0.843953 0.665134 0.635718 3 : 0.123442 0.844297 0.323626 0.737668 4 : 0.18965 0.554701 0.510069 0.022887 5 : 0.659831 0.0764895 0.583986 0.704358 6 : 0.0635278 0.442216 0.257628 0.388969 7 : 0.513151 0.251507 0.638573 0.371304 8 : 0.328054 0.891072 0.428436 0.749248 9 : 0.889474 0.168188 0.377536 0.383791 10 : 0.793358 0.292016 0.320406 0.145796 11 : 0.356524 0.27763 0.280918 0.25925 12 : 0.860212 0.417122 0.432911 0.718154 13 : 0.156411 0.168861 0.692768 0.176677 14 : 0.788116 0.58265 0.801371 0.684661 15 : 0.256108 0.434233 0.533315 0.563506 16 : 0.881202 0.849573 0.758713 0.0885042 M = 37, N = 53, |haar_2d_inverse(haar_2d(u))-u| = 2.39123e-14 haar_test03(): HAAR_2D computes the Haar transform of an array. HAAR_2D_INVERSE inverts the transform. Apply this to a 128x128 matrix of 0 and 1 values which is actually a bit map of the Sierpinski triangle. Input array U: Col: 1 2 3 4 5 Row 1 : 1 1 1 1 1 2 : 1 0 1 0 1 3 : 1 1 0 0 1 4 : 1 0 0 0 1 5 : 1 1 1 1 0 6 : 1 0 1 0 0 7 : 1 1 0 0 0 8 : 1 0 0 0 0 9 : 1 1 1 1 1 10 : 1 0 1 0 1 Col: 6 7 8 9 10 Row 1 : 1 1 1 1 1 2 : 0 1 0 1 0 3 : 1 0 0 1 1 4 : 0 0 0 1 0 5 : 0 0 0 1 1 6 : 0 0 0 1 0 7 : 0 0 0 1 1 8 : 0 0 0 1 0 9 : 1 1 1 0 0 10 : 0 1 0 0 0 Transformed array V: Col: 1 2 3 4 5 Row 1 : 17.0859 5.69531 5.36959 2.6848 5.0625 2 : 5.69531 -5.69531 0 2.6848 0 3 : 5.36959 0 -3.79687 -3.79687 0 4 : 2.6848 2.6848 -3.79687 0 0 5 : 5.0625 0 0 0 -2.53125 6 : 2.53125 0 1.78986 1.78986 -2.53125 7 : 2.53125 2.53125 0 0 -2.53125 8 : 1.26562 1.26562 1.78986 0 -2.53125 9 : 4.77297 0 0 0 0 10 : 2.38649 0 0 0 1.19324 Col: 6 7 8 9 10 Row 1 : 2.53125 2.53125 1.26562 4.77297 2.38649 2 : 0 2.53125 1.26562 0 0 3 : 1.78986 0 1.78986 0 0 4 : 1.78986 0 0 0 0 5 : -2.53125 -2.53125 -2.53125 0 1.19324 6 : 0 -2.53125 0 0 1.19324 7 : -2.53125 0 0 0 1.19324 8 : 0 0 0 0 1.19324 9 : 0 0 0 -1.6875 -1.6875 10 : 1.19324 1.19324 1.19324 -1.6875 0 Recovered array W: Col: 1 2 3 4 5 Row 1 : 1 1 1 1 1 2 : 1 -4.71028e-16 1 -3.14018e-16 1 3 : 1 1 -7.08753e-16 -5.69976e-16 1 4 : 1 -5.49532e-16 -5.12492e-16 -3.73714e-16 1 5 : 1 1 1 1 -3.83407e-16 6 : 1 -3.92523e-16 1 -3.92523e-16 -2.4463e-16 7 : 1 1 -5.02968e-16 -4.47457e-16 -3.48713e-16 8 : 1 -5.49532e-16 -3.85211e-16 -3.297e-16 -2.79324e-16 9 : 1 1 1 1 1 10 : 1 -3.92523e-16 1 -3.14018e-16 1 Col: 6 7 8 9 10 Row 1 : 1 1 1 1 1 2 :-5.49532e-16 1 -3.14018e-16 1 -3.92523e-16 3 : 1 -6.53242e-16 -4.86709e-16 1 1 4 :-6.28037e-16 -4.56981e-16 -2.90447e-16 1 -4.71028e-16 5 :-3.44155e-16 -2.6565e-16 -1.6752e-16 1 1 6 :-2.05377e-16 -1.26873e-16 -2.87418e-17 1 -3.14018e-16 7 :-3.09461e-16 -2.30956e-16 -1.32825e-16 1 1 8 :-2.40072e-16 -1.61567e-16 -6.34363e-17 1 -4.71028e-16 9 : 1 1 1 -1.34016e-16 -1.61771e-16 10 :-4.71028e-16 1 -3.14018e-16 -1.62588e-17 -4.40144e-17 haar_test(): Normal end of execution. 09-Sep-2022 10:10:09