Mon Aug 8 09:29:52 2022 haar_test(): Python version: 3.6.9 Test haar(). haar_1d_test(): haar_1d() computes the Haar transform of a vector. i U(i) H(U)(i) Hinv(H(U))(i) 0 0.948095 2.331405 0.948095 1 0.528896 0.552873 0.528896 2 0.771407 -0.241469 0.771407 3 0.294390 -0.038592 0.294390 4 0.970615 0.205597 0.970615 5 0.700692 0.058424 0.700692 6 0.780859 -0.159283 0.780859 7 0.773600 0.300334 0.773600 8 0.645950 0.296419 0.645950 9 0.056745 0.337302 0.056745 10 0.702764 0.190865 0.702764 11 0.318495 0.005133 0.318495 12 0.465509 0.416631 0.465509 13 0.751379 0.271719 0.751379 14 0.056427 -0.202141 0.056427 15 0.559794 -0.355934 0.559794 i U(i) H(U)(i) Hinv(H(U))(i) 0 1.000000 2.828427 1.000000 1 1.000000 0.000000 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 i U(i) H(U)(i) Hinv(H(U))(i) 0 1.000000 34.000000 1.000000 1 2.000000 -16.000000 2.000000 2 3.000000 -5.656854 3.000000 3 4.000000 -5.656854 4.000000 4 5.000000 -2.000000 5.000000 5 6.000000 -2.000000 6.000000 6 7.000000 -2.000000 7.000000 7 8.000000 -2.000000 8.000000 8 9.000000 -0.707107 9.000000 9 10.000000 -0.707107 10.000000 10 11.000000 -0.707107 11.000000 11 12.000000 -0.707107 12.000000 12 13.000000 -0.707107 13.000000 13 14.000000 -0.707107 14.000000 14 15.000000 -0.707107 15.000000 15 16.000000 -0.707107 16.000000 i U(i) H(U)(i) Hinv(H(U))(i) 0 25.000000 21.213203 25.000000 1 16.000000 16.970563 16.000000 2 9.000000 14.000000 9.000000 3 4.000000 -2.000000 4.000000 4 1.000000 6.363961 1.000000 5 0.000000 3.535534 0.000000 6 1.000000 0.707107 1.000000 7 4.000000 -2.121320 4.000000 i U(i) H(U)(i) Hinv(H(U))(i) 0 0.872066 3.868425 0.872066 1 0.232593 -0.467051 0.232593 2 0.432895 0.433862 0.432895 3 0.976289 -0.296608 0.976289 4 0.427656 -0.110645 0.427656 5 0.463712 -0.242747 0.463712 6 0.360567 0.008866 0.360567 7 0.027880 0.147867 0.027880 8 0.600321 0.436295 0.600321 9 0.937161 0.080458 0.937161 10 0.561241 0.162100 0.561241 11 0.133180 -0.640597 0.133180 12 0.484577 0.018574 0.484577 13 0.285322 -0.222032 0.285322 14 0.929943 0.540101 0.929943 15 0.304490 -0.108726 0.304490 16 0.261749 -0.152262 0.261749 17 0.131352 0.251460 0.131352 18 0.798201 0.421530 0.798201 19 0.189096 -0.232267 0.189096 20 0.289213 -0.297098 0.289213 21 0.262348 0.090606 0.262348 22 0.355619 -0.295292 0.355619 23 0.014730 0.088716 0.014730 24 0.003837 0.019580 0.003837 25 0.066225 -0.506325 0.066225 26 0.444276 0.356799 0.444276 27 0.216369 -0.717010 0.216369 28 0.872467 -0.072674 0.872467 29 0.487544 0.662301 0.487544 30 0.692902 -0.592831 0.692902 31 0.489676 -0.287326 0.489676 32 0.260388 0.452176 0.260388 33 0.755760 -0.384237 0.755760 34 0.850947 -0.025495 0.850947 35 0.126043 0.235245 0.126043 36 0.278371 -0.238182 0.278371 37 0.185605 0.302685 0.185605 38 0.643278 0.140895 0.643278 39 0.833348 0.442262 0.833348 40 0.623196 0.092205 0.623196 41 0.551172 0.430703 0.551172 42 0.073800 0.018996 0.073800 43 0.386969 0.241045 0.386969 44 0.371204 -0.044116 0.371204 45 0.043356 0.161155 0.043356 46 0.918229 0.272181 0.918229 47 0.930351 0.143702 0.930351 48 0.617936 -0.350281 0.617936 49 0.953968 0.512585 0.953968 50 0.858244 0.065596 0.858244 51 0.859008 -0.134399 0.859008 52 0.566370 0.050928 0.566370 53 0.976690 -0.221444 0.976690 54 0.109164 0.231823 0.109164 55 0.109295 -0.008571 0.109295 56 0.428767 -0.237610 0.428767 57 0.016323 -0.000540 0.016323 58 0.745100 -0.290140 0.745100 59 0.885652 -0.000093 0.885652 60 0.798422 0.291642 0.798422 61 0.105935 -0.099385 0.105935 62 0.790256 0.489662 0.790256 63 0.688754 0.071773 0.688754 64 0.429560 0.429560 0.429560 65 0.857457 0.857457 0.857457 66 0.860865 0.860865 0.860865 67 0.139897 0.139897 0.139897 68 0.348154 0.348154 0.348154 69 0.005496 0.005496 0.005496 70 0.194044 0.194044 0.194044 71 0.717116 0.717116 0.717116 72 0.843900 0.843900 0.843900 73 0.961965 0.961965 0.961965 74 0.438009 0.438009 0.438009 75 0.068890 0.068890 0.068890 76 0.469933 0.469933 0.469933 77 0.871391 0.871391 0.871391 78 0.420360 0.420360 0.420360 79 0.331962 0.331962 0.331962 80 0.873789 0.873789 0.873789 81 0.735435 0.735435 0.735435 82 0.783119 0.783119 0.783119 83 0.236458 0.236458 0.236458 84 0.453323 0.453323 0.453323 85 0.892811 0.892811 0.892811 86 0.416171 0.416171 0.416171 87 0.595137 0.595137 0.595137 88 0.862675 0.862675 0.862675 89 0.841151 0.841151 0.841151 90 0.427337 0.427337 0.427337 91 0.787845 0.787845 0.787845 92 0.108168 0.108168 0.108168 93 0.793407 0.793407 0.793407 94 0.026574 0.026574 0.026574 95 0.428190 0.428190 0.428190 96 0.279706 0.279706 0.279706 97 0.002639 0.002639 0.002639 98 0.325377 0.325377 0.325377 haar_2d_test(): haar_2d() computes the Haar transform of an array. haar_2d_inverse() inverts the transform. Input array U: [[0.91259746 0.43197678 0.95681235 0.68889793] [0.78540183 0.27723113 0.88304545 0.11850615] [0.91982355 0.75183605 0.54743697 0.8764304 ] [0.65188035 0.69612612 0.31386742 0.96713789] [0.63509717 0.92222293 0.26578452 0.18791495] [0.75989331 0.36760562 0.11327487 0.32670595] [0.68980575 0.72536155 0.45324604 0.18253825] [0.80515271 0.06326242 0.60516467 0.06337444] [0.57241677 0.20237701 0.59516158 0.21344765] [0.35243701 0.72634473 0.74049032 0.51874897] [0.22058133 0.86056599 0.39517513 0.007198 ] [0.13086311 0.82287924 0.87110042 0.29568577] [0.85972189 0.65324984 0.47113595 0.75608667] [0.2919344 0.96560769 0.55163994 0.63804179] [0.85963989 0.63202515 0.7300991 0.38121423] [0.63792657 0.30791349 0.18990361 0.46478693]] Transformed array V: [[ 4.35772665e+00 5.15213063e-01 1.19958431e-01 3.52956304e-01] [ 1.28626600e-01 1.96071052e-01 5.60288730e-01 -9.58783238e-02] [ 6.38623966e-01 -4.76529699e-01 7.52591744e-02 -1.56686676e-01] [-3.29768811e-01 -1.36763881e-01 -3.56573830e-01 4.66049519e-01] [-1.67517421e-01 -1.38712015e-01 3.05841232e-01 7.12310246e-01] [-2.35162795e-03 2.02969928e-01 -2.12546599e-01 -3.35189662e-01] [ 7.93437681e-02 -1.70000835e-01 4.69565864e-01 -1.27256773e-01] [ 2.45977300e-01 -7.94729364e-02 -3.62331792e-01 -1.57456463e-01] [ 3.27425779e-01 -1.28063189e-01 -1.37750097e-02 -2.48312434e-01] [ 1.64938025e-01 6.39192955e-02 1.06116638e-01 1.62138518e-01] [ 1.56815012e-01 1.47114455e-01 -3.39706725e-01 1.45650321e-01] [ 1.81725504e-01 2.04886665e-01 -3.88723047e-01 -1.35541219e-01] [-2.66797760e-01 5.18458085e-02 3.71973743e-01 7.99862939e-02] [-2.25216375e-01 3.15305290e-01 2.60157328e-02 -9.37187630e-02] [ 1.03580725e-01 7.70353087e-02 4.40072676e-01 -9.92744376e-02] [ 3.54418814e-01 3.15377406e-02 -5.11991680e-02 3.11884096e-01]] Recovered array W: [[0.91259746 0.43197678 0.95681235 0.68889793] [0.78540183 0.27723113 0.88304545 0.11850615] [0.91982355 0.75183605 0.54743697 0.8764304 ] [0.65188035 0.69612612 0.31386742 0.96713789] [0.63509717 0.92222293 0.26578452 0.18791495] [0.75989331 0.36760562 0.11327487 0.32670595] [0.68980575 0.72536155 0.45324604 0.18253825] [0.80515271 0.06326242 0.60516467 0.06337444] [0.57241677 0.20237701 0.59516158 0.21344765] [0.35243701 0.72634473 0.74049032 0.51874897] [0.22058133 0.86056599 0.39517513 0.007198 ] [0.13086311 0.82287924 0.87110042 0.29568577] [0.85972189 0.65324984 0.47113595 0.75608667] [0.2919344 0.96560769 0.55163994 0.63804179] [0.85963989 0.63202515 0.7300991 0.38121423] [0.63792657 0.30791349 0.18990361 0.46478693]] M = 37, N = 53, ||haar_2d_inverse(haar_2d(u))-u|| = 2.50369e-14 haar_test(): Normal end of execution. Mon Aug 8 09:29:53 2022