Wed Oct 8 09:15:49 2025 walsh_transform_test(): python version: 3.10.12 numpy version: 1.26.4 Test walsh_transform(). ffwt_test(): ffwt() computes a fast Walsh transform. I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 0 0.476297 0.476021 0.476297 1 0.626165 0.049155 0.626165 2 0.267782 -0.014721 0.267782 3 0.630423 -0.010287 0.630423 4 0.950986 -0.093286 0.950986 5 0.733401 -0.027187 0.733401 6 0.340837 0.059718 0.340837 7 0.175513 0.111819 0.175513 8 0.356675 0.032562 0.356675 9 0.477930 0.000567 0.477930 10 0.107386 -0.043291 0.107386 11 0.783210 0.063355 0.783210 12 0.464825 -0.105492 0.464825 13 0.616441 -0.006435 0.616441 14 0.377726 0.042007 0.377726 15 0.230737 -0.058207 0.230737 I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 0 1.000000 8.500000 1.000000 1 2.000000 -4.000000 2.000000 2 3.000000 0.000000 3.000000 3 4.000000 -2.000000 4.000000 4 5.000000 0.000000 5.000000 5 6.000000 0.000000 6.000000 6 7.000000 0.000000 7.000000 7 8.000000 -1.000000 8.000000 8 9.000000 0.000000 9.000000 9 10.000000 0.000000 10.000000 10 11.000000 0.000000 11.000000 11 12.000000 0.000000 12.000000 12 13.000000 0.000000 13.000000 13 14.000000 0.000000 14.000000 14 15.000000 0.000000 15.000000 15 16.000000 -0.500000 16.000000 fwt_test(): fwt() computes a fast Walsh transform. I X(I) Y=FWT(X)/N Z=FWT(Y)/N 0 0.878040 0.565007 0.878040 1 0.351930 0.035868 0.351930 2 0.726871 0.133694 0.726871 3 0.696719 -0.071179 0.696719 4 0.680214 -0.019548 0.680214 5 0.535232 -0.039337 0.535232 6 0.666750 0.000927 0.666750 7 0.271242 0.009552 0.271242 8 0.546097 0.015238 0.546097 9 0.159260 0.015441 0.159260 10 0.301973 -0.000270 0.301973 11 0.289730 0.093581 0.289730 12 0.547701 0.046202 0.547701 13 0.897994 -0.044230 0.897994 14 0.758137 0.063878 0.758137 15 0.732217 0.073216 0.732217 I X(I) Y=FWT(X)/N Z=FWT(Y)/N 0 1.000000 8.500000 1.000000 1 2.000000 -4.000000 2.000000 2 3.000000 0.000000 3.000000 3 4.000000 -2.000000 4.000000 4 5.000000 0.000000 5.000000 5 6.000000 0.000000 6.000000 6 7.000000 0.000000 7.000000 7 8.000000 -1.000000 8.000000 8 9.000000 0.000000 9.000000 9 10.000000 0.000000 10.000000 10 11.000000 0.000000 11.000000 11 12.000000 0.000000 12.000000 12 13.000000 0.000000 13.000000 13 14.000000 0.000000 14.000000 14 15.000000 0.000000 15.000000 15 16.000000 -0.500000 16.000000 haar_test() haar() computes a Haar transform. hnorm() normalizes the transformed data. haar_inverse() computes an inverse Haar transform. I X(I) Y=HAAR(X) Z=HNORM(Y) W=haar_inverse(Z) 0 0.479499 8.623143 0.538946 0.479499 1 0.591866 -0.369464 -0.023091 0.591866 2 0.306440 0.233841 0.029230 0.306440 3 0.802536 -0.168375 -0.021047 0.802536 4 0.676469 -0.037610 -0.009402 0.676469 5 0.301162 0.008761 0.002190 0.301162 6 0.590851 0.191799 0.047950 0.590851 7 0.378018 0.060083 0.015021 0.378018 8 0.953583 -0.112367 -0.056183 0.953583 9 0.224298 -0.496096 -0.248048 0.224298 10 0.744184 0.375307 0.187654 0.744184 11 0.241899 0.212834 0.106417 0.241899 12 0.373271 0.729285 0.364643 0.373271 13 0.822940 0.502286 0.251143 0.822940 14 0.760510 -0.449670 -0.224835 0.760510 15 0.375618 0.384892 0.192446 0.375618 I X(I) Y=HAAR(X) Z=HNORM(Y) W=haar_inverse(Z) 0 1.000000 136.000000 8.500000 1.000000 1 2.000000 -64.000000 -4.000000 2.000000 2 3.000000 -16.000000 -2.000000 3.000000 3 4.000000 -16.000000 -2.000000 4.000000 4 5.000000 -4.000000 -1.000000 5.000000 5 6.000000 -4.000000 -1.000000 6.000000 6 7.000000 -4.000000 -1.000000 7.000000 7 8.000000 -4.000000 -1.000000 8.000000 8 9.000000 -1.000000 -0.500000 9.000000 9 10.000000 -1.000000 -0.500000 10.000000 10 11.000000 -1.000000 -0.500000 11.000000 11 12.000000 -1.000000 -0.500000 12.000000 12 13.000000 -1.000000 -0.500000 13.000000 13 14.000000 -1.000000 -0.500000 14.000000 14 15.000000 -1.000000 -0.500000 15.000000 15 16.000000 -1.000000 -0.500000 16.000000 walsh_test(): walsh() computes a fast Walsh transform. I X(I) Y=FWT(X)/N Z=FWT(Y)/N 0 0.113672 0.560859 0.113672 1 0.931366 0.105752 0.931366 2 0.761884 -0.075995 0.761884 3 0.206345 -0.087299 0.206345 4 0.892415 0.056881 0.892415 5 0.818636 -0.060091 0.818636 6 0.620315 0.078214 0.620315 7 0.988252 -0.055802 0.988252 8 0.458501 0.011955 0.458501 9 0.395016 -0.128395 0.395016 10 0.304239 -0.090347 0.304239 11 0.617457 -0.136521 0.617457 12 0.378291 -0.007694 0.378291 13 0.052558 0.011694 0.052558 14 0.507218 -0.013247 0.507218 15 0.927583 -0.056292 0.927583 I X(I) Y=FWT(X)/N Z=FWT(Y)/N 0 1.000000 8.500000 1.000000 1 2.000000 -4.000000 2.000000 2 3.000000 0.000000 3.000000 3 4.000000 -2.000000 4.000000 4 5.000000 0.000000 5.000000 5 6.000000 -0.000000 6.000000 6 7.000000 0.000000 7.000000 7 8.000000 -1.000000 8.000000 8 9.000000 0.000000 9.000000 9 10.000000 -0.000000 10.000000 10 11.000000 0.000000 11.000000 11 12.000000 -0.000000 12.000000 12 13.000000 0.000000 13.000000 13 14.000000 -0.000000 14.000000 14 15.000000 0.000000 15.000000 15 16.000000 -0.500000 16.000000 walsh_transform_test() Normal end of execution. Wed Oct 8 09:15:49 2025