15-May-2025 07:45:19 haar_transform_test(): MATLAB/Octave version 6.4.0 Test haar_transform(). 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 0.444306 1.985539 0.444306 2 0.611966 -0.172755 0.611966 3 0.315991 0.348750 0.315991 4 0.933730 -0.194605 0.933730 5 0.084531 -0.096725 0.084531 6 0.552452 -0.022805 0.552452 7 0.292559 0.851514 0.292559 8 0.390035 0.245897 0.390035 9 0.960807 -0.118554 0.960807 10 0.832247 -0.436807 0.832247 11 0.000824 -0.330870 0.000824 12 0.089203 -0.068926 0.089203 13 0.463906 0.090906 0.463906 14 0.998745 -0.062494 0.998745 15 0.304466 -0.378188 0.304466 16 0.666390 -0.255919 0.666390 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))| = 3.54132e-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 : 0.00420995 0.721269 0.552839 0.794419 2 : 0.439119 0.227937 0.0556996 0.967371 3 : 0.0646773 0.805301 0.507093 0.252125 4 : 0.530597 0.687229 0.15665 0.183057 5 : 0.842465 0.619752 0.71537 0.0605978 6 : 0.191432 0.532066 0.623674 0.284934 7 : 0.994405 0.855524 0.174403 0.0266348 8 : 0.377847 0.0592598 0.267033 0.0864355 9 : 0.487013 0.607878 0.455619 0.209863 10 : 0.327313 0.463442 0.760116 0.854431 11 : 0.296222 0.347928 0.0698398 0.324441 12 : 0.455833 0.611002 0.253758 0.577075 13 : 0.913342 0.190479 0.879245 0.302104 14 : 0.498562 0.421708 0.0814739 0.621335 15 : 0.953716 0.226129 0.613849 0.35648 16 : 0.795838 0.550594 0.984987 0.834108 Transformed array V: Col: 1 2 3 4 Row 1 : 3.74839 0.276628 0.0433268 0.073581 2 : -0.333037 0.28456 -0.419361 0.066846 3 : 0.0420304 -0.392901 -0.43567 -0.561642 4 : -0.375151 0.0379542 -0.559104 -0.218001 5 : 0.144033 -0.491668 0.138374 -0.488545 6 : 0.257187 -0.307848 -0.203431 0.235165 7 : 0.307394 -0.220064 -0.0177198 0.257868 8 : -0.351863 0.10077 -0.0612048 -0.131157 9 : 0.135273 -0.0939618 -0.46412 0.335045 10 : 0.0253369 -0.271302 -0.291996 0.140688 11 : 0.214281 0.308072 0.281674 0.158016 12 : 0.445615 0.5534 -0.0898532 -0.0164148 13 : -0.228017 0.443074 0.00763258 0.170036 14 : -0.303787 0.00490273 0.0517318 0.0343579 15 : 0.234084 -0.104294 0.323005 0.558501 16 : -0.358982 0.241187 0.241172 0.0532448 Recovered array W: Col: 1 2 3 4 Row 1 : 0.00420995 0.721269 0.552839 0.794419 2 : 0.439119 0.227937 0.0556996 0.967371 3 : 0.0646773 0.805301 0.507093 0.252125 4 : 0.530597 0.687229 0.15665 0.183057 5 : 0.842465 0.619752 0.71537 0.0605978 6 : 0.191432 0.532066 0.623674 0.284934 7 : 0.994405 0.855524 0.174403 0.0266348 8 : 0.377847 0.0592598 0.267033 0.0864355 9 : 0.487013 0.607878 0.455619 0.209863 10 : 0.327313 0.463442 0.760116 0.854431 11 : 0.296222 0.347928 0.0698398 0.324441 12 : 0.455833 0.611002 0.253758 0.577075 13 : 0.913342 0.190479 0.879245 0.302104 14 : 0.498562 0.421708 0.0814739 0.621335 15 : 0.953716 0.226129 0.613849 0.35648 16 : 0.795838 0.550594 0.984987 0.834108 M = 37, N = 53, |haar_2d_inverse(haar_2d(u))-u| = 2.57466e-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_transform_test(): Normal end of execution. 15-May-2025 07:45:19