10-Nov-2026 15:27:23 slow_fourier_transform_test(): MATLAB/Octave version 11.3.0 slow_fourier_transform() implements a set of "slow" Fourier transforms. c8mat_sft_test(): c8mat_sftf() computes the forward slow Fourier transform. c8mat_sftb() computes the backward slow Fourier transform. The data has dimension N1 = 10 by N2 = 4 The data X: Col: 1 2 3 4 Row --- 1: 0.727280 -1.891111 0.882033 0.622926 -0.462508 0.210549 1.046823 -0.210143 2: -0.534563 -2.167520 0.085583 -0.035196 -0.834339 -0.134881 -0.816747 -0.844852 3: -0.055386 1.443669 -0.200420 1.718624 -0.714486 -0.011578 0.617400 1.169517 4: -0.308102 -0.896144 0.039585 1.926840 0.381335 0.417488 1.109213 -0.499305 5: -0.337530 -1.465512 0.456861 0.215421 0.074971 -0.051239 -0.142774 0.935842 6: -2.663872 -1.767314 0.049063 0.802607 -1.872558 2.292072 0.593713 -0.033274 7: -0.662983 0.054248 2.535387 0.367586 0.865240 -0.192007 -2.249069 0.077391 8: 0.682323 0.437387 -0.295283 0.400734 0.462156 0.479352 0.093951 -0.600456 9: -0.762650 0.225848 0.235582 1.399775 0.185869 0.366772 -1.605827 0.576851 10: -0.173070 0.650769 1.109272 0.758982 1.308190 -2.297945 0.478439 0.019024 The Fourier coefficients Y: Col: 1 2 3 4 Row --- 1: -0.671901 4.471797 -11.070126 -0.681723 -8.717468 -13.065991 4.105279 -12.226805 2: 4.643686 -5.488754 10.758875 4.325143 6.541954 -7.549785 1.733719 9.345593 3: -0.564314 -11.563264 0.312900 -2.341846 -11.956056 -1.043212 2.727243 -5.844499 4: 13.679406 -11.657258 8.819177 2.631396 3.395227 1.937082 7.397877 0.365388 5: -0.273365 2.166225 0.621583 -16.663677 -4.473674 2.044280 14.117125 0.717807 6: 1.539527 6.655060 5.439670 9.256791 3.281108 -3.302313 -2.636240 -4.169684 7: -5.091518 9.823852 0.265446 -8.156519 -6.455775 2.521814 -4.244374 0.222490 8: 5.668748 0.549612 -7.713534 -5.200974 4.974321 -1.948294 -2.099587 -1.181031 9: -1.899034 -4.767046 3.517823 -6.508666 -2.613482 -2.146492 -6.368155 -10.127024 10: 4.905048 -2.868009 -7.384614 0.675572 -0.617002 1.619451 5.495692 3.529067 The recovered data: Col: 1 2 3 4 Row --- 1: 0.727280 -1.891111 0.882033 0.622926 -0.462508 0.210549 1.046823 -0.210143 2: -0.534563 -2.167520 0.085583 -0.035196 -0.834339 -0.134881 -0.816747 -0.844852 3: -0.055386 1.443669 -0.200420 1.718624 -0.714486 -0.011578 0.617400 1.169517 4: -0.308102 -0.896144 0.039585 1.926840 0.381335 0.417488 1.109213 -0.499305 5: -0.337530 -1.465512 0.456861 0.215421 0.074971 -0.051239 -0.142774 0.935842 6: -2.663872 -1.767314 0.049063 0.802607 -1.872558 2.292072 0.593713 -0.033274 7: -0.662983 0.054248 2.535387 0.367586 0.865240 -0.192007 -2.249069 0.077391 8: 0.682323 0.437387 -0.295283 0.400734 0.462156 0.479352 0.093951 -0.600456 9: -0.762650 0.225848 0.235582 1.399775 0.185869 0.366772 -1.605827 0.576851 10: -0.173070 0.650769 1.109272 0.758982 1.308190 -2.297945 0.478439 0.019024 c8vec_sft_test(): c8vec_sftf() computes the forward slow Fourier transform. c8vec_sftb() computes the backward slow Fourier transform. The number of data values, N = 36 The original data: 1 0.57912+0.27608i 2 -0.21375-1.8756i 3 1.8231-0.53245i 4 1.2848-0.98439i 5 0.25539-1.1521i 6 1.7478+0.59602i 7 0.56427-1.3003i 8 -1.2929+0.21677i ...... .............. .............. 36 0.5127-0.44777i The Fourier coefficients: 1 2.2327-6.7868i 2 15.3404-10.835i 3 -5.0543+1.7978i 4 6.9648+9.206i 5 -0.19166-1.9966i 6 -8.3506+2.086i 7 10.4287+3.21419i 8 2.2136-4.6117i ...... .............. .............. 36 5.9277-4.7984i The retrieved data: 1 0.57912+0.27608i 2 -0.21375-1.8756i 3 1.8231-0.53245i 4 1.2848-0.98439i 5 0.25539-1.1521i 6 1.7478+0.59602i 7 0.56427-1.3003i 8 -1.2929+0.21677i ...... .............. .............. 36 0.5127-0.44777i r8vec_sct_test(): r8vec_sct() does a forward or backward slow cosine transform. The number of data items is N = 256 The original data: 1 2.138896 2 4.688543 3 3.459706 4 4.772934 5 4.072498 6 2.197434 7 0.765797 8 0.089222 ...... .............. 256 1.649720 The cosine coefficients: 1 1280.706235 2 -34.820384 3 48.881541 4 15.748777 5 1.228283 6 7.484446 7 5.187651 8 -35.318047 ...... .............. 256 123.211147 The retrieved data: 1 2.138896 2 4.688543 3 3.459706 4 4.772934 5 4.072498 6 2.197434 7 0.765797 8 0.089222 ...... .............. 256 1.649720 r8vec_sft_test(): r8vec_sftf() computes the forward slow Fourier transform. r8vec_sftb() computes the backward slow Fourier transform. The number of data values, N = 36 The original data: 1 3.105005 2 2.196306 3 3.048821 4 3.079022 5 4.503743 6 4.563313 7 2.314006 8 2.500844 ...... .............. 36 2.546714 A (cosine) coefficients: 0 2.415721 1 0.405718 2 -0.079661 3 0.356402 4 -0.854493 5 -0.047922 6 0.106265 7 -0.200343 8 0.549183 9 0.040413 10 0.568355 11 0.115369 12 -0.334584 13 -0.152889 14 -0.070412 15 0.324013 16 -0.126097 17 -0.094188 18 0.184155 B (sine) coefficients: 1 0.172142 2 0.072830 3 0.540990 4 0.002512 5 -0.357144 6 0.152847 7 -0.049603 8 0.109781 9 0.412121 10 -0.244161 11 -0.377163 12 0.017071 13 -0.182331 14 -0.310633 15 0.152208 16 0.006198 17 0.038501 18 0.000000 The retrieved data: 1 3.105005 2 2.196306 3 3.048821 4 3.079022 5 4.503743 6 4.563313 7 2.314006 8 2.500844 ...... .............. 36 2.546714 r8vec_sht_test(): r8vec_sht() does a forward or backward slow Hartley transform. The number of data items is N = 17 The original data: 1 0.060233 2 3.517766 3 4.432627 4 4.697593 5 4.471414 6 1.186374 7 4.664369 8 1.970502 ...... .............. 17 4.200136 The Hartley coefficients: 1 12.406517 2 1.283620 3 0.302345 4 -0.956259 5 -2.284281 6 -1.280066 7 0.311708 8 -1.014358 ...... .............. 17 -1.299142 The retrieved data: 1 0.060233 2 3.517766 3 4.432627 4 4.697593 5 4.471414 6 1.186374 7 4.664369 8 1.970502 ...... .............. 17 4.200136 r8vec_sqct_test(): r8vec_sqctf() does a forward slow quarter wave cosine transform; r8vec_sqctb() does a backward slow quarter wave cosine transform. The number of data items is N = 256 The original data: 1 1.664404 2 0.002498 3 2.281139 4 0.456825 5 3.793990 6 1.864619 7 0.374484 8 0.536562 ...... .............. 256 0.358387 The cosine coefficients: 1 2.502515 2 0.034532 3 -0.099195 4 0.025490 5 -0.067068 6 -0.039981 7 -0.096024 8 0.075673 ...... .............. 256 -0.072132 The retrieved data: 1 1.664404 2 0.002498 3 2.281139 4 0.456825 5 3.793990 6 1.864619 7 0.374484 8 0.536562 ...... .............. 256 0.358387 r8vec_sqst_test(): r8vec_sqstf() does a forward slow quarter wave sine transform; r8vec_sqstb() does a backward slow quarter wave sine transform. The number of data items is N = 256 The original data: 1 3.567761 2 2.797109 3 4.874661 4 4.432913 5 4.185246 6 3.660702 7 1.976753 8 3.973993 ...... .............. 256 3.061504 The sine coefficients: 1 -1.570332 2 -0.082236 3 -0.515119 4 0.017925 5 -0.300089 6 -0.027263 7 -0.127382 8 -0.040359 ...... .............. 256 0.062706 The retrieved data: 1 3.567761 2 2.797109 3 4.874661 4 4.432913 5 4.185246 6 3.660702 7 1.976753 8 3.973993 ...... .............. 256 3.061504 r8vec_sst_test(): r8vec_sst() does a forward or backward slow sine transform. The number of data items is N = 256 The original data: 1 3.756305 2 1.490441 3 3.800044 4 0.774742 5 2.698331 6 0.940253 7 3.494639 8 0.187537 ...... .............. 256 4.841928 The sine coefficients: 1 816.973233 2 -10.571294 3 295.022975 4 -71.004236 5 211.529866 6 34.694545 7 126.518598 8 -23.611698 ...... .............. 256 40.799207 The retrieved data: 1 3.756305 2 1.490441 3 3.800044 4 0.774742 5 2.698331 6 0.940253 7 3.494639 8 0.187537 ...... .............. 256 4.841928 r8vec_swt_test(): r8vec_swtf() computes the forward slow wavelet transform. r8vec_swtb() computes the backward slow wavelet transform. The number of data values, N = 36 The original data: 1 4.119642 2 2.472514 3 1.667053 4 3.476319 5 2.614743 6 3.898640 7 2.940030 8 1.853168 ...... .............. 36 3.435503 I S(I) D(I) 1 3.981724 -1.453817 2 3.794680 1.371736 3 4.943272 0.690551 4 3.003506 -0.352143 5 4.900624 0.671286 6 5.266300 2.723475 7 2.004753 -1.665915 8 3.923740 2.029177 9 4.197714 -0.798057 10 2.096196 1.821927 11 3.831560 0.669699 12 4.979202 1.203927 13 3.649387 2.519835 14 2.991645 -0.021811 15 1.050546 0.977217 16 3.481907 0.730727 17 0.910778 -1.276716 18 3.582342 1.827351 The retrieved data: 1 4.119642 2 2.472514 3 1.667053 4 3.476319 5 2.614743 6 3.898640 7 2.940030 8 1.853168 ...... .............. 36 3.435503 slow_fourier_transform_test(): Normal end of execution. 10-Nov-2026 15:27:27