11 March 2020 08:24:44 AM HAAR_TEST C++ version Test the HAAR library. TEST01 HAAR_1D computes the Haar transform of a vector. i U(i) H(U)(i) Hinv(H(U))(i) 0 0.218418 1.63977 0.218418 1 0.956318 0.0676837 0.956318 2 0.829509 0.607044 0.829509 3 0.561695 -0.270838 0.561695 4 0.415307 -0.108234 0.415307 5 0.0661187 0.0569456 0.0661187 6 0.257578 0.0832643 0.257578 7 0.109957 0.178427 0.109957 8 0.043829 -0.521774 0.043829 9 0.633966 0.189373 0.633966 10 0.0617272 0.246913 0.0617272 11 0.449539 0.104384 0.449539 12 0.401306 -0.41729 0.401306 13 0.754673 -0.274224 0.754673 14 0.797287 -0.249868 0.797287 15 0.00183837 0.562467 0.00183837 i U(i) H(U)(i) Hinv(H(U))(i) 0 1 2.82843 1 1 1 0 1 2 1 0 1 3 1 0 1 4 1 0 1 5 1 0 1 6 1 0 1 7 1 0 1 i U(i) H(U)(i) Hinv(H(U))(i) 0 1 34 1 1 2 -16 2 2 3 -5.65685 3 3 4 -5.65685 4 4 5 -2 5 5 6 -2 6 6 7 -2 7 7 8 -2 8 8 9 -0.707107 9 9 10 -0.707107 10 10 11 -0.707107 11 11 12 -0.707107 12 12 13 -0.707107 13 13 14 -0.707107 14 14 15 -0.707107 15 15 16 -0.707107 16 i U(i) H(U)(i) Hinv(H(U))(i) 0 25 21.2132 25 1 16 16.9706 16 2 9 14 9 3 4 -2 4 4 1 6.36396 1 5 0 3.53553 7.85046e-16 6 1 0.707107 1 7 4 -2.12132 4 For N = 99, ||u-haar_1d_inverse(haar_1d(u))|| = 3.33568e-15 TEST02 HAAR_2D computes the Haar transform of an array. HAAR_2D_INVERSE inverts the transform. Input array U: Col: 0 1 2 3 Row 0: 0.218418 0.897504 0.861216 0.825003 1: 0.956318 0.350752 0.453794 0.82466 2: 0.829509 0.0945448 0.911977 0.0618618 3: 0.561695 0.0136169 0.597917 0.710781 4: 0.415307 0.859097 0.188955 0.0882833 5: 0.0661187 0.840847 0.761492 0.777994 6: 0.257578 0.123104 0.396988 0.745303 7: 0.109957 0.00751236 0.185314 0.308675 8: 0.043829 0.260303 0.574366 0.899373 9: 0.633966 0.912484 0.367027 0.763537 10: 0.0617272 0.113664 0.617205 0.761731 11: 0.449539 0.351629 0.361529 0.40697 12: 0.401306 0.822887 0.21293 0.938749 13: 0.754673 0.267132 0.714471 0.562088 14: 0.797287 0.692066 0.117707 0.01782 15: 0.00183837 0.561662 0.299329 0.501103 Transformed array V: Col: 0 1 2 3 Row 0: 3.818 -0.386034 -0.107788 -0.277843 1: 0.00752059 -0.138549 0.18837 0.283179 2: 0.536878 -0.0974688 0.547781 0.197526 3: -0.0148802 -0.505449 -0.0150938 -0.0590401 4: 0.401441 0.0603724 -0.479618 -0.378976 5: 0.465916 0.375694 -0.514575 0.196521 6: 0.332723 0.104288 -0.19126 -0.187931 7: 0.421356 -0.324784 0.184047 -0.166718 8: 0.0765858 -0.211748 -0.642326 0.20354 9: 0.0049084 0.241689 0.093443 0.481489 10: -0.316363 0.576181 0.165469 0.0585867 11: 0.322269 -0.13615 0.0160147 -0.112477 12: -0.317895 -0.560556 0.031022 0.0357514 13: -0.00542323 -0.437067 -0.0749236 -0.0495424 14: 0.0274031 0.115707 -0.454561 -0.439101 15: 0.0922587 0.562418 0.332522 0.15083 Recovered array W: Col: 0 1 2 3 Row 0: 0.218418 0.897504 0.861216 0.825003 1: 0.956318 0.350752 0.453794 0.82466 2: 0.829509 0.0945448 0.911977 0.0618618 3: 0.561695 0.0136169 0.597917 0.710781 4: 0.415307 0.859097 0.188955 0.0882833 5: 0.0661187 0.840847 0.761492 0.777994 6: 0.257578 0.123104 0.396988 0.745303 7: 0.109957 0.00751236 0.185314 0.308675 8: 0.043829 0.260303 0.574366 0.899373 9: 0.633966 0.912484 0.367027 0.763537 10: 0.0617272 0.113664 0.617205 0.761731 11: 0.449539 0.351629 0.361529 0.40697 12: 0.401306 0.822887 0.21293 0.938749 13: 0.754673 0.267132 0.714471 0.562088 14: 0.797287 0.692066 0.117707 0.01782 15: 0.00183837 0.561662 0.299329 0.501103 M = 37, N = 53, ||haar_2d_inverse(haar_2d(u))-u|| = 2.54887e-14 HAAR_TEST Normal end of execution. 11 March 2020 08:24:44 AM