Tue Nov 10 15:38:18 2026 slow_fourier_transform_test(): numpy version: 1.26.4 python version: 3.10.12 Test slow_fourier_transform(). c8mat_print_test c8mat_print prints an C8MAT. Here is a C8MAT: Col: 0 1 2 Row 0 : 10 1i 10 2i 10 3i 1 : 20 1i 20 2i 20 3i 2 : 30 1i 30 2i 30 3i 3 : 40 1i 40 2i 40 3i c8mat_print_some_test c8mat_print_some prints some of an C8MAT. Here is a C8MAT: Col: 3 4 5 Row 0 : 10 4i 10 5i 10 6i 1 : 20 4i 20 5i 20 6i 2 : 30 4i 30 5i 30 6i c8mat_uniform_01_test(): c8mat_uniform_01() computes a random C8MAT. 0 <= X <= 1 Random C8MAT: Col: 0 1 2 Row 0 : -0.495919 0.297669i -0.910914 -0.362339i -0.424071 -0.374313i 1 : 0.508454 -0.172843i 0.368479 0.159464i 0.595589 0.0750693i 2 : 0.293366 -0.891756i 0.552271 -0.515912i 0.816649 -0.0682234i 3 : 0.580695 0.267174i -0.19256 0.133087i 0.675515 0.690603i 4 : -0.394017 0.637742i 0.874906 -0.432088i 0.390558 0.769807i c8vec_indicator_test c8vec_indicator returns the indicator vector. The indicator vector: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 5 6 -6 6 7 -7 7 8 -8 8 9 -9 9 10 -10 c8vec_print_test c8vec_print prints an C8VEC. Here is a C8VEC: 0 1 2 1 3 4 2 5 6 3 7 8 c8vec_print_part_test c8vec_print_part prints part of a C8VEC. Part of the C8VEC: 0 1 -1 1 2 -2 2 3 -3 3 4 -4 4 5 -5 5 6 -6 6 7 -7 7 8 -8 ...... .............. .............. 99 100 -100 c8vec_uniform_01_test(): c8vec_uniform_01() computes pseudorandom complex values in the unit circle. 0 ( 0.108385, 0.711902 ) 1 ( -0.096607, -0.579189 ) 2 ( 0.151128, -0.014249 ) 3 ( -0.125836, 0.970322 ) 4 ( -0.182991, -0.360006 ) 5 ( 0.238356, -0.445463 ) 6 ( 0.570885, -0.706469 ) 7 ( 0.684274, -0.226706 ) 8 ( 0.290409, 0.429470 ) 9 ( -0.127034, -0.477655 ) i4_modp_test i4_modp factors a number into a multiple M and a positive remainder R. Number Divisor Multiple Remainder 107 50 2 7 107 -50 -2 7 -107 50 -3 43 -107 -50 3 43 Repeat using Python % Operator: 107 50 2 7 107 -50 -3 -43 -107 50 -3 43 -107 -50 2 -7 i4_wrap_test i4_wrap forces an integer to lie within given limits. ILO = 4 IHI = 8 I i4_wrap(I) -10 5 -9 6 -8 7 -7 8 -6 4 -5 5 -4 6 -3 7 -2 8 -1 4 0 5 1 6 2 7 3 8 4 4 5 5 6 6 7 7 8 8 9 4 10 5 11 6 12 7 13 8 14 4 15 5 16 6 17 7 18 8 19 4 20 5 r8vec_indicator1_test r8vec_indicator1 returns the 1-based indicator matrix. The 1-based indicator vector: 0: 1 1: 2 2: 3 3: 4 4: 5 5: 6 6: 7 7: 8 8: 9 9: 10 r8vec_print_part_test r8vec_print_part prints part of an R8VEC. Lines 10:20 of the vector: 10: 11 11: 12 12: 13 13: 14 14: 15 15: 16 16: 17 17: 18 18: 19 19: 20 20: 21 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 Row 1 : -0.789448 0.235497i -0.123337 -0.331836i -0.540585 0.0538967i 2 : 0.488804 -0.111634i -0.107814 -0.20349i -0.203566 0.763969i 3 : -0.931369 0.300881i 0.708985 0.369453i 0.500878 0.720014i 4 : -0.0832552 -0.487306i -0.367643 0.0743554i 0.87791 0.241993i 5 : 0.384629 0.373263i -0.895738 0.202749i -0.415225 0.330923i 6 : 0.548596 -0.697817i 0.785089 -0.512005i -0.165539 -0.657261i 7 : -0.922409 0.00467828i -0.443661 0.663039i 0.641163 -0.189198i 8 : 0.133186 0.564105i -0.253142 0.823933i 0.563211 -0.392473i 9 : 0.07005 0.0923385i 0.884582 0.201478i 0.571269 0.554336i The Fourier coefficients Y: Col: 1 2 3 Row 1 : -3.15246 -0.593573i 5.50724 -0.737998i -1.42258 -4.86425i 2 : -3.65025 5.23555i -0.596675 4.95467i 0.971891 0.963688i 3 : 0.250834 -2.06723i -0.412593 1.81092i -4.69087 7.31543i 4 : 4.26656 -3.19905i 2.07931 3.94691i 6.46379 -0.804059i 5 : 1.169 2.10257i -2.35321 2.686i 0.839273 -3.78674i 6 : 2.68852 2.97992i 0.625612 -0.235062i 4.12381 -2.39562i 7 : -4.94225 -6.3433i 2.43329 3.70952i -1.52308 -2.53789i 8 : 0.428785 3.83362i -3.69174 -0.5714i -4.61246 -2.64033i 9 : -0.995822 -2.19492i -2.04055 -0.392582i -0.689823 2.94261i The recovered data: Col: 1 2 3 Row 1 : -0.789448 0.235497i -0.123337 -0.331836i -0.540585 0.0538967i 2 : 0.488804 -0.111634i -0.107814 -0.20349i -0.203566 0.763969i 3 : -0.931369 0.300881i 0.708985 0.369453i 0.500878 0.720014i 4 : -0.0832552 -0.487306i -0.367643 0.0743554i 0.87791 0.241993i 5 : 0.384629 0.373263i -0.895738 0.202749i -0.415225 0.330923i 6 : 0.548596 -0.697817i 0.785089 -0.512005i -0.165539 -0.657261i 7 : -0.922409 0.00467828i -0.443661 0.663039i 0.641163 -0.189198i 8 : 0.133186 0.564105i -0.253142 0.823933i 0.563211 -0.392473i 9 : 0.07005 0.0923385i 0.884582 0.201478i 0.571269 0.554336i 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: 0 -0.122938 0.705072 1 0.624226 -0.164457 2 0.52846 -0.159197 3 0.633373 -0.153293 4 0.522989 0.584862 5 -0.618667 0.181677 6 -0.449586 0.137172 7 0.0848834 -0.0917938 ...... .............. .............. 35 -0.925606 0.356196 The Fourier coefficients: 0 -0.756476 3.20708 1 2.44862 1.78711 2 2.29508 5.78993 3 2.18315 4.1965 4 1.83194 -0.524822 5 0.933539 -1.4143 6 2.41467 3.92758 7 -5.96878 1.52808 ...... .............. .............. 35 -2.11786 1.09428 The retrieved data: 0 -0.122938 0.705072 1 0.624226 -0.164457 2 0.52846 -0.159197 3 0.633373 -0.153293 4 0.522989 0.584862 5 -0.618667 0.181677 6 -0.449586 0.137172 7 0.0848834 -0.0917938 ...... .............. .............. 35 -0.925606 0.356196 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: 0.63054 2: 2.3298 3: 3.44195 4: 3.74092 5: 3.0116 6: 0.57619 7: 1.77623 8: 4.72251 9: 3.44601 10: 3.5244 The cosine coefficients: 1: -29.6199 2: 76.6851 3: -59.4702 4: -17.049 5: 39.2929 6: -39.7297 7: 7.41352 8: 25.7892 9: -2.51868 10: -18.1007 The retrieved data: 1: 0.63054 2: 2.3298 3: 3.44195 4: 3.74092 5: 3.0116 6: 0.57619 7: 1.77623 8: 4.72251 9: 3.44601 10: 3.5244 r8vec_sft_test(): r8vec_sft_n_test(): r8vec_sftf() computes the forward slow Fourier transform. r8vec_sftb() computes the backward slow Fourier transform. The number of data values, N = 35 The original data: 0 4.29462 1 0.8728 2 1.74477 3 4.77238 4 3.86992 5 1.3772 6 3.77843 7 4.81614 ...... .............. 34 3.26293 A (cosine) coefficients: 0 2.41554 0 0.11939 1 0.278465 2 -0.551925 3 0.00675136 4 0.451331 5 0.117638 6 -0.505604 7 0.463391 8 0.0194586 9 0.615603 10 0.438208 11 0.330454 12 0.364471 13 -0.13016 14 0.105456 15 -0.293457 16 0.0496125 B (sine) coefficients: 0 0.680062 1 0.411539 2 -0.412347 3 0.222761 4 0.0398348 5 -0.0515481 6 -0.125478 7 -0.651996 8 -0.283197 9 0.0192966 10 -0.0950597 11 -0.0252391 12 0.160077 13 -0.436096 14 -0.130037 15 -0.166684 16 -0.0281616 The retrieved data: 0 4.29462 1 0.8728 2 1.74477 3 4.77238 4 3.86992 5 1.3772 6 3.77843 7 4.81614 ...... .............. 34 3.26293 r8vec_sft_n_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: 0 3.07696 1 0.845082 2 1.19683 3 3.85383 4 3.14852 5 4.00693 6 2.18795 7 0.00425041 ...... .............. 35 1.6805 A (cosine) coefficients: 0 2.30207 0 0.338438 1 -0.299964 2 -0.38853 3 0.138752 4 -0.758651 5 -0.177774 6 -0.0716319 7 0.188725 8 1.10377 9 0.106296 10 0.224474 11 -0.0559637 12 0.346505 13 0.319735 14 0.216604 15 -0.430998 16 0.0228083 17 -0.0477025 B (sine) coefficients: 0 -0.271406 1 -0.125097 2 0.333655 3 0.0566155 4 -0.247384 5 -0.366246 6 0.358875 7 0.325596 8 -0.0504469 9 0.0147869 10 -0.372312 11 -0.337891 12 -0.0323995 13 -0.141505 14 0.37504 15 0.129643 16 -0.690645 17 1.83254e-15 The retrieved data: 0 3.07696 1 0.845082 2 1.19683 3 3.85383 4 3.14852 5 4.00693 6 2.18795 7 0.00425041 ...... .............. 35 1.6805 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: 0.902101 2: 4.14913 3: 3.82847 4: 1.54533 5: 1.62104 6: 2.33782 7: 2.27673 8: 3.43258 9: 3.29461 10: 1.744 The Hartley coefficients: 1: -0.537296 2: 1.24035 3: 0.22538 4: -0.255667 5: -0.828764 6: -0.0624182 7: 0.382766 8: 2.40822 9: 0.675026 10: -0.746222 The retrieved data: 1: 0.902101 2: 4.14913 3: 3.82847 4: 1.54533 5: 1.62104 6: 2.33782 7: 2.27673 8: 3.43258 9: 3.29461 10: 1.744 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: 4.83222 2: 3.10128 3: 2.49373 4: 0.461731 5: 2.45236 6: 2.00199 7: 0.333298 8: 4.70855 9: 1.40138 10: 0.0428828 The cosine coefficients: 1: 0.0361147 2: -0.0882454 3: 0.0460074 4: 0.0764333 5: 0.0733022 6: 0.00172073 7: -0.0149439 8: -0.0871779 9: -0.0330454 10: -0.00912987 The retrieved data: 1: 4.83222 2: 3.10128 3: 2.49373 4: 0.461731 5: 2.45236 6: 2.00199 7: 0.333298 8: 4.70855 9: 1.40138 10: 0.0428828 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: 4.90888 2: 0.773439 3: 3.59172 4: 3.48161 5: 1.45601 6: 3.37928 7: 0.836366 8: 2.06026 9: 0.0399945 10: 3.85693 The sine coefficients: 1: 0.181188 2: -0.561665 3: -0.0625155 4: -0.358371 5: -0.0790044 6: -0.0935526 7: -0.0978768 8: -0.212705 9: 0.049455 10: -0.0431849 The retrieved data: 1: 4.90888 2: 0.773439 3: 3.59172 4: 3.48161 5: 1.45601 6: 3.37928 7: 0.836366 8: 2.06026 9: 0.0399945 10: 3.85693 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: 3.95219 2: 3.88934 3: 1.34565 4: 2.77307 5: 0.301519 6: 4.49334 7: 0.883852 8: 3.90005 9: 2.23982 10: 0.141954 The sine coefficients: 1: -1.30883 2: 279.741 3: 59.53 4: 121.445 5: 40.1323 6: 153.513 7: -1.32936 8: 40.1059 9: -36.6772 10: 73.5126 The retrieved data: 1: 3.95219 2: 3.88934 3: 1.34565 4: 2.77307 5: 0.301519 6: 4.49334 7: 0.883852 8: 3.90005 9: 2.23982 10: 0.141954 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: 3.69163 2: 0.177884 3: 4.17994 4: 0.439998 5: 1.99349 6: 4.60661 7: 4.18551 8: 3.38233 9: 2.25861 10: 3.29526 I S(I) D(I) 0 3.942539 0.117091 1 3.423146 3.060609 2 2.370986 1.554643 3 6.191912 -1.328287 4 4.189123 -0.204260 5 2.338076 -1.542407 6 6.542174 -0.488054 7 3.495651 -1.243386 8 1.167396 0.063220 9 2.366304 -0.524492 10 1.638310 -1.496827 11 1.437555 -0.141315 12 4.852555 -0.081792 13 5.225200 -0.961861 14 4.819911 1.744995 15 2.355686 0.548153 16 5.469526 0.557013 17 2.696405 1.461779 The retrieved data: 1: 3.69163 2: 0.177884 3: 4.17994 4: 0.439998 5: 1.99349 6: 4.60661 7: 4.18551 8: 3.38233 9: 2.25861 10: 3.29526 slow_fourier_transform_test(): Normal end of execution. Tue Nov 10 15:38:19 2026