07-Jan-2022 21:38:03 haar_test(): MATLAB/Octave version 9.8.0.1380330 (R2020a) Update 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 0.814724 2.437867 0.814724 2 0.905792 -0.279788 0.905792 3 0.126987 0.426244 0.126987 4 0.913376 0.235428 0.913376 5 0.632359 0.340076 0.632359 6 0.097540 -0.047740 0.097540 7 0.278498 0.397095 0.278498 8 0.546882 0.250188 0.546882 9 0.957507 -0.064395 0.957507 10 0.964889 -0.556061 0.964889 11 0.157613 0.378174 0.157613 12 0.970593 -0.189776 0.970593 13 0.957167 -0.005220 0.957167 14 0.485376 -0.574863 0.485376 15 0.800280 0.333607 0.800280 16 0.141886 0.465555 0.141886 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))|| = 3.31713e-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 : 0.825817 0.910648 0.123319 0.403912 2 : 0.538342 0.181847 0.183908 0.0964545 3 : 0.996135 0.263803 0.239953 0.131973 4 : 0.0781755 0.145539 0.417267 0.942051 5 : 0.442678 0.136069 0.0496544 0.956135 6 : 0.106653 0.869292 0.902716 0.575209 7 : 0.961898 0.579705 0.944787 0.0597795 8 : 0.00463422 0.54986 0.490864 0.23478 9 : 0.77491 0.144955 0.489253 0.353159 10 : 0.817303 0.853031 0.337719 0.821194 11 : 0.868695 0.622055 0.900054 0.0154034 12 : 0.0844358 0.350952 0.369247 0.0430238 13 : 0.399783 0.51325 0.111203 0.16899 14 : 0.25987 0.401808 0.780252 0.649115 15 : 0.800068 0.0759667 0.389739 0.731722 16 : 0.431414 0.239916 0.241691 0.647746 Transformed array V: Col: 1 2 3 4 Row 1 : 3.62897 0.178404 0.274378 0.0249218 2 : -0.0430086 0.031179 -0.1621 -0.0418305 3 : -0.244937 0.347296 0.388924 -0.293016 4 : 0.177282 0.315665 -0.021461 0.384545 5 : 0.012338 0.474163 -0.139054 0.0790773 6 : 0.0530244 -0.323727 -0.10359 -0.608135 7 : 0.334415 -0.00238381 0.217119 -0.550926 8 : -0.0684982 0.0821709 -0.414012 0.290404 9 : 0.446589 0.272026 -0.220663 -0.184023 10 : 0.0172645 0.715456 0.399848 0.316381 11 : -0.307356 0.0264944 0.534625 -0.616994 12 : 0.44761 0.250381 0.46371 0.314462 13 : -0.377231 -0.15343 0.332842 0.309784 14 : 0.55103 0.195223 0.256578 0.279214 15 : -0.317428 0.495162 0.0142354 -0.0944619 16 : 0.154407 -0.00965865 0.266302 0.0320356 Recovered array W: Col: 1 2 3 4 Row 1 : 0.825817 0.910648 0.123319 0.403912 2 : 0.538342 0.181847 0.183908 0.0964545 3 : 0.996135 0.263803 0.239953 0.131973 4 : 0.0781755 0.145539 0.417267 0.942051 5 : 0.442678 0.136069 0.0496544 0.956135 6 : 0.106653 0.869292 0.902716 0.575209 7 : 0.961898 0.579705 0.944787 0.0597795 8 : 0.00463422 0.54986 0.490864 0.23478 9 : 0.77491 0.144955 0.489253 0.353159 10 : 0.817303 0.853031 0.337719 0.821194 11 : 0.868695 0.622055 0.900054 0.0154034 12 : 0.0844358 0.350952 0.369247 0.0430238 13 : 0.399783 0.51325 0.111203 0.16899 14 : 0.25987 0.401808 0.780252 0.649115 15 : 0.800068 0.0759667 0.389739 0.731722 16 : 0.431414 0.239916 0.241691 0.647746 M = 37, N = 53, ||haar_2d_inverse(haar_2d(u))-u|| = 2.62791e-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. 07-Jan-2022 21:38:03