26-Jan-2019 21:24:41 HAAR_TEST: MATLAB version 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 0.218418 1.639767 0.218418 2 0.956318 0.067684 0.956318 3 0.829509 0.607044 0.829509 4 0.561695 -0.270838 0.561695 5 0.415307 -0.108234 0.415307 6 0.066119 0.056946 0.066119 7 0.257578 0.083264 0.257578 8 0.109957 0.178427 0.109957 9 0.043829 -0.521774 0.043829 10 0.633966 0.189373 0.633966 11 0.061727 0.246913 0.061727 12 0.449539 0.104384 0.449539 13 0.401306 -0.417290 0.401306 14 0.754673 -0.274224 0.754673 15 0.797287 -0.249868 0.797287 16 0.001838 0.562467 0.001838 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))|| = 3.25011e-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 : 0.218418 0.897504 0.861216 0.825003 2 : 0.956318 0.350752 0.453794 0.82466 3 : 0.829509 0.0945448 0.911977 0.0618618 4 : 0.561695 0.0136169 0.597917 0.710781 5 : 0.415307 0.859097 0.188955 0.0882833 6 : 0.0661187 0.840847 0.761492 0.777994 7 : 0.257578 0.123104 0.396988 0.745303 8 : 0.109957 0.00751236 0.185314 0.308675 9 : 0.043829 0.260303 0.574366 0.899373 10 : 0.633966 0.912484 0.367027 0.763537 11 : 0.0617272 0.113664 0.617205 0.761731 12 : 0.449539 0.351629 0.361529 0.40697 13 : 0.401306 0.822887 0.21293 0.938749 14 : 0.754673 0.267132 0.714471 0.562088 15 : 0.797287 0.692066 0.117707 0.01782 16 : 0.00183837 0.561662 0.299329 0.501103 Transformed array V: Col: 1 2 3 4 Row 1 : 3.818 -0.386034 -0.107788 -0.277843 2 : 0.00752059 -0.138549 0.18837 0.283179 3 : 0.536878 -0.0974688 0.547781 0.197526 4 : -0.0148802 -0.505449 -0.0150938 -0.0590401 5 : 0.401441 0.0603724 -0.479618 -0.378976 6 : 0.465916 0.375694 -0.514575 0.196521 7 : 0.332723 0.104288 -0.19126 -0.187931 8 : 0.421356 -0.324784 0.184047 -0.166718 9 : 0.0765858 -0.211748 -0.642326 0.20354 10 : 0.0049084 0.241689 0.093443 0.481489 11 : -0.316363 0.576181 0.165469 0.0585867 12 : 0.322269 -0.13615 0.0160147 -0.112477 13 : -0.317895 -0.560556 0.031022 0.0357514 14 : -0.00542323 -0.437067 -0.0749236 -0.0495424 15 : 0.0274031 0.115707 -0.454561 -0.439101 16 : 0.0922587 0.562418 0.332522 0.15083 Recovered array W: Col: 1 2 3 4 Row 1 : 0.218418 0.897504 0.861216 0.825003 2 : 0.956318 0.350752 0.453794 0.82466 3 : 0.829509 0.0945448 0.911977 0.0618618 4 : 0.561695 0.0136169 0.597917 0.710781 5 : 0.415307 0.859097 0.188955 0.0882833 6 : 0.0661187 0.840847 0.761492 0.777994 7 : 0.257578 0.123104 0.396988 0.745303 8 : 0.109957 0.00751236 0.185314 0.308675 9 : 0.043829 0.260303 0.574366 0.899373 10 : 0.633966 0.912484 0.367027 0.763537 11 : 0.0617272 0.113664 0.617205 0.761731 12 : 0.449539 0.351629 0.361529 0.40697 13 : 0.401306 0.822887 0.21293 0.938749 14 : 0.754673 0.267132 0.714471 0.562088 15 : 0.797287 0.692066 0.117707 0.01782 16 : 0.00183837 0.561662 0.299329 0.501103 M = 37, N = 53, ||haar_2d_inverse(haar_2d(u))-u|| = 2.43737e-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. 26-Jan-2019 21:24:41