Sat Apr 22 17:42:13 2023 walsh_transform_test(): Python version: 3.8.10 Test walsh_transform(). ffwt_test(): ffwt() computes a fast Walsh transform. I X(I) Y=FFWT(X)/N Z=FFWT(Y)/N 0 0.696780 0.543240 0.696780 1 0.435450 -0.073295 0.435450 2 0.244244 -0.109889 0.244244 3 0.021006 -0.010686 0.021006 4 0.737007 -0.036371 0.737007 5 0.840541 0.045616 0.840541 6 0.011535 0.097463 0.011535 7 0.772998 0.110037 0.772998 8 0.914295 0.017588 0.914295 9 0.378355 0.069415 0.378355 10 0.925354 -0.096595 0.925354 11 0.644948 0.019115 0.644948 12 0.544374 0.110365 0.544374 13 0.679414 0.058330 0.679414 14 0.690325 -0.099803 0.690325 15 0.155216 0.052249 0.155216 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 0.899981 0.607723 0.899981 1 0.742656 0.074759 0.742656 2 0.627979 0.074959 0.627979 3 0.841795 0.020661 0.841795 4 0.620377 -0.102559 0.620377 5 0.960031 0.022495 0.960031 6 0.384601 -0.017731 0.384601 7 0.382434 0.141010 0.382434 8 0.483348 -0.045030 0.483348 9 0.541356 0.048695 0.541356 10 0.855848 0.107666 0.855848 11 0.034110 -0.018546 0.034110 12 0.916204 0.062130 0.916204 13 0.825910 -0.027006 0.825910 14 0.283639 -0.075522 0.283639 15 0.323292 0.026274 0.323292 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 0.294567 7.480375 0.467523 0.294567 1 0.841368 -0.052796 -0.003300 0.841368 2 0.341635 -0.454549 -0.056819 0.341635 3 0.152050 -0.903698 -0.112962 0.152050 4 0.277269 0.642250 0.160562 0.277269 5 0.201271 -1.127088 -0.281772 0.201271 6 0.763338 -0.148211 -0.037053 0.763338 7 0.842291 -0.547246 -0.136811 0.842291 8 0.044900 -0.546800 -0.273400 0.044900 9 0.596717 0.189584 0.094792 0.596717 10 0.540490 0.075998 0.037999 0.540490 11 0.249338 -0.078952 -0.039476 0.249338 12 0.393155 -0.551817 -0.275908 0.393155 13 0.500793 0.291152 0.145576 0.500793 14 0.718389 -0.107638 -0.053819 0.718389 15 0.722805 -0.004416 -0.002208 0.722805 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 0.288917 0.494145 0.288917 1 0.852922 0.047000 0.852922 2 0.697394 -0.039107 0.697394 3 0.330736 0.040454 0.330736 4 0.260052 -0.042063 0.260052 5 0.829432 0.053805 0.829432 6 0.709276 0.129609 0.709276 7 0.360436 -0.112924 0.360436 8 0.053422 -0.096675 0.053422 9 0.323190 -0.134436 0.323190 10 0.856388 0.049644 0.856388 11 0.873824 -0.051200 0.873824 12 0.240102 0.013355 0.240102 13 0.201738 -0.010456 0.201738 14 0.256220 0.021688 0.256220 15 0.772277 -0.073924 0.772277 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. Sat Apr 22 17:42:13 2023