Wed Oct 8 07:49:34 2025 haar_transform_test(): python version: 3.10.12 numpy version: 1.26.4 Test haar_transform(). haar_1d_test(): haar_1d() computes the Haar transform of a vector. i U(i) H(U)(i) Hinv(H(U))(i) 0 0.506940 2.281157 0.506940 1 0.881783 0.103395 0.881783 2 0.890751 0.119251 0.890751 3 0.273725 0.460678 0.273725 4 0.603281 0.112123 0.603281 5 0.350882 -0.153790 0.350882 6 0.487846 -0.215541 0.487846 7 0.773896 -0.185719 0.773896 8 0.695475 -0.265054 0.695475 9 0.503613 0.436303 0.503613 10 0.951166 0.178473 0.951166 11 0.679005 -0.202268 0.679005 12 0.378914 0.135667 0.378914 13 0.198500 0.192447 0.198500 14 0.115826 0.127572 0.115826 15 0.833025 -0.507136 0.833025 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 0.457631 4.015249 0.457631 1 0.087221 -0.281035 0.087221 2 0.497311 -0.226814 0.497311 3 0.431235 -0.368608 0.431235 4 0.591703 -0.079250 0.591703 5 0.433178 0.091049 0.433178 6 0.317316 -0.471747 0.317316 7 0.439357 0.101731 0.439357 8 0.643986 -0.108950 0.643986 9 0.040691 -0.067060 0.040691 10 0.008723 -0.343092 0.008723 11 0.997739 0.158283 0.997739 12 0.431791 -0.140148 0.431791 13 0.797767 0.224026 0.797767 14 0.220602 0.288437 0.220602 15 0.430653 0.078726 0.430653 16 0.853800 -0.191847 0.853800 17 0.265511 0.134104 0.265511 18 0.057326 -0.160892 0.057326 19 0.456695 0.289151 0.456695 20 0.733803 0.302645 0.733803 21 0.655528 0.087460 0.655528 22 0.385220 0.347442 0.385220 23 0.829192 0.043448 0.829192 24 0.597725 0.161707 0.597725 25 0.829859 0.410642 0.829859 26 0.564580 -0.241124 0.564580 27 0.168120 0.246991 0.168120 28 0.056750 0.158258 0.056750 29 0.842995 -0.481588 0.842995 30 0.614875 0.366781 0.614875 31 0.197975 0.278453 0.197975 32 0.357966 0.261920 0.357966 33 0.412516 0.046723 0.412516 34 0.009311 0.112093 0.009311 35 0.437758 -0.086296 0.437758 36 0.826619 0.426594 0.826619 37 0.390997 -0.699340 0.390997 38 0.340980 -0.258784 0.340980 39 0.055353 -0.148529 0.055353 40 0.747564 0.415984 0.747564 41 0.349345 -0.282397 0.349345 42 0.946679 0.055348 0.946679 43 0.632477 -0.313936 0.632477 44 0.864368 -0.164144 0.864368 45 0.403835 0.280340 0.403835 46 0.429186 -0.555960 0.429186 47 0.345035 0.294793 0.345035 48 0.850038 -0.038573 0.850038 49 0.767435 -0.302958 0.767435 50 0.559392 0.308032 0.559392 51 0.741564 0.201969 0.741564 52 0.381467 0.281583 0.381467 53 0.188248 0.222175 0.188248 54 0.828630 0.325646 0.828630 55 0.704261 0.059504 0.704261 56 0.663272 0.058410 0.663272 57 0.912705 -0.128815 0.912705 58 0.343525 0.136627 0.343525 59 0.498890 0.087942 0.498890 60 0.508351 -0.176376 0.508351 61 0.867962 -0.109860 0.867962 62 0.273600 -0.254283 0.273600 63 0.545807 -0.192480 0.545807 64 0.924120 0.924120 0.924120 65 0.979996 0.979996 0.979996 66 0.948145 0.948145 0.948145 67 0.225744 0.225744 0.225744 68 0.480386 0.480386 0.480386 69 0.102014 0.102014 0.102014 70 0.712451 0.712451 0.712451 71 0.943384 0.943384 0.943384 72 0.457621 0.457621 0.457621 73 0.342511 0.342511 0.342511 74 0.964434 0.964434 0.964434 75 0.311644 0.311644 0.311644 76 0.699894 0.699894 0.699894 77 0.638317 0.638317 0.638317 78 0.692762 0.692762 0.692762 79 0.039494 0.039494 0.039494 80 0.600688 0.600688 0.600688 81 0.456379 0.456379 0.456379 82 0.419313 0.419313 0.419313 83 0.243129 0.243129 0.243129 84 0.038905 0.038905 0.038905 85 0.887938 0.887938 0.887938 86 0.337088 0.337088 0.337088 87 0.414032 0.414032 0.414032 88 0.608308 0.608308 0.608308 89 0.495774 0.495774 0.495774 90 0.242699 0.242699 0.242699 91 0.527246 0.527246 0.527246 92 0.819222 0.819222 0.819222 93 0.524314 0.524314 0.524314 94 0.077708 0.077708 0.077708 95 0.429298 0.429298 0.429298 96 0.951026 0.951026 0.951026 97 0.219659 0.219659 0.219659 98 0.253873 0.253873 0.253873 haar_2d_test(): haar_2d() computes the Haar transform of an array. haar_2d_inverse() inverts the transform. Input array U: [[0.31535288 0.7240111 0.44300756 0.56061011] [0.6155234 0.68293368 0.45883145 0.94668917] [0.40606824 0.52960411 0.9213906 0.32563204] [0.71103415 0.00398455 0.44859001 0.44726905] [0.58329616 0.59728938 0.01690157 0.44818929] [0.33635786 0.21694462 0.82040848 0.50171742] [0.17856975 0.35636205 0.47571015 0.10059458] [0.06211476 0.25611598 0.27531324 0.58452091] [0.89630802 0.60280597 0.42252495 0.50595866] [0.36198534 0.05061757 0.4340141 0.21647198] [0.37036559 0.30835529 0.7736502 0.08112841] [0.43468814 0.22634402 0.90759307 0.14708887] [0.89899556 0.24390888 0.52906703 0.98348091] [0.58260149 0.4607012 0.1404279 0.39925122] [0.47437776 0.03822741 0.15904396 0.2596267 ] [0.04251809 0.81837604 0.72308751 0.80710416]] Transformed array V: [[ 3.58145429 -0.23476953 0.20392524 0.11211678] [ 0.00628028 -0.06518371 -0.26011486 -0.1315868 ] [ 0.48262263 0.01286885 0.09345468 0.00957701] [-0.14511522 0.03613716 0.10948621 0.62124275] [ 0.23834665 0.10521836 -0.37461889 -0.42516202] [ 0.30795084 0.1324119 0.16872046 -0.06311089] [ 0.06036825 0.22561368 0.11826905 -0.46630778] [ 0.22901814 0.17733578 0.39481115 -0.18690169] [-0.2336974 0.05049091 -0.17062397 0.18512758] [ 0.20216792 -0.04614223 -0.41529273 0.2972188 ] [-0.08122959 0.5247857 -0.06670323 -0.37498939] [-0.02362739 0.17685818 0.00810446 0.34216162] [ 0.48242664 0.28585271 -0.00893286 -0.15048791] [-0.0644226 0.0769304 -0.07316691 -0.03399121] [ 0.37917561 -0.30874654 0.2665932 -0.09779528] [-0.51612076 0.26984328 0.60600415 -0.00828304]] Recovered array W: [[0.31535288 0.7240111 0.44300756 0.56061011] [0.6155234 0.68293368 0.45883145 0.94668917] [0.40606824 0.52960411 0.9213906 0.32563204] [0.71103415 0.00398455 0.44859001 0.44726905] [0.58329616 0.59728938 0.01690157 0.44818929] [0.33635786 0.21694462 0.82040848 0.50171742] [0.17856975 0.35636205 0.47571015 0.10059458] [0.06211476 0.25611598 0.27531324 0.58452091] [0.89630802 0.60280597 0.42252495 0.50595866] [0.36198534 0.05061757 0.4340141 0.21647198] [0.37036559 0.30835529 0.7736502 0.08112841] [0.43468814 0.22634402 0.90759307 0.14708887] [0.89899556 0.24390888 0.52906703 0.98348091] [0.58260149 0.4607012 0.1404279 0.39925122] [0.47437776 0.03822741 0.15904396 0.2596267 ] [0.04251809 0.81837604 0.72308751 0.80710416]] M = 37, N = 53, ||haar_2d_inverse(haar_2d(u))-u|| = 2.57949e-14 haar_transform_test(): Normal end of execution. Wed Oct 8 07:49:34 2025