June 24 2002 11:17:07.974 AM FFTPACK_PRB A set of tests for FFTPACK. TEST01 For complex fast Fourier transforms, CFFTI initializes the transforms, CFFTF does a forward transforms; CFFTB does a backward transforms. The number of data items is N = 4096 The original data: 1 2.66674 2.79411 2 4.71589 3.47063 3 2.26311 0.314327 4 1.45949 4.32154 5 1.23554 3.63704 6 1.12323 0.190600 7 0.231875 4.15550 8 2.38322 0.927215 ...... .............. 4096 2.75656 1.38644 The FFT coefficients: 1 10123.7 10321.9 2 26.4347 78.7418 3 -75.5494 -49.0775 4 -84.3011 -89.4701 5 -89.9202 -107.519 6 159.588 -81.3343 7 23.5105 96.8781 8 -9.52498 13.8020 ...... .............. 4096 41.4269 48.4100 The retrieved data: 1 2.66674 2.79411 2 4.71589 3.47063 3 2.26311 0.314327 4 1.45950 4.32154 5 1.23554 3.63704 6 1.12323 0.190601 7 0.231875 4.15550 8 2.38322 0.927215 ...... .............. 4096 2.75656 1.38644 TEST02 For complex fast Fourier transforms of 2D data: CFFTF_2D computes the forward transform; CFFTB_2D computes the backward transform. Maximum error in CFFT2D calculation: 0.119605E-06 TEST03 For real fast cosine quarter wave transforms, COSQI initializes the transforms. COSQF does a forward transform; COSQB does a backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 13043.2 2 -4292.18 3 2429.45 4 -1924.28 5 1330.51 6 -1313.30 7 987.479 8 -752.542 ...... .............. 4096 -119.320 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522611 TEST04 For real slow quarter wave cosine transforms, RSQCTF does a forward transform; RSQCTB does a backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 2.49038 2 0.139931E-01 3 -0.137566E-01 4 -0.137146E-01 5 -0.107367E-01 6 -0.144464E-01 7 -0.142761E-01 8 0.140144E-01 ...... .............. 4096 -0.138860E-01 The retrieved data: 1 2.66665 2 2.79390 3 4.71608 4 3.47079 5 2.26304 6 0.313965 7 1.46000 8 4.32168 ...... .............. 4096 0.522515 TEST05 For real fast Fourier transforms, EZFFTI initializes the transforms. EZFFTF does a forward transform; EZFFTB does a backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The A0 coefficient: 2.49039 The A coefficients: 1 -0.274817E-01 2 -0.214702E-01 3 -0.286394E-01 4 0.566380E-03 5 0.168004E-01 6 -0.404785E-01 7 0.729359E-01 8 0.350856E-01 ...... .............. 2048 -0.226339E-01 The B coefficients: 1 0.399804E-01 2 0.210521E-02 3 -0.379842E-01 4 0.655784E-02 5 0.721754E-02 6 0.379599E-01 7 -0.114141E-01 8 0.329550E-01 ...... .............. 2048 0.00000 Retrieve data from FFT coeficients. The retrieved data: 1 2.66674 2 2.79409 3 4.71589 4 3.47062 5 2.26311 6 0.314352 7 1.45950 8 4.32151 ...... .............. 4096 0.522637 TEST06 For real fast Fourier transforms, EZFFTI initializes the transforms. EZFFTF does a forward transform; EZFFTB does a backward transform. The number of data items is N = 3087 which is not a multiple of two! The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 3087 1.48464 The A0 coefficient: 2.50046 The A coefficients: 1 -0.460916E-01 2 -0.486824E-01 3 0.164160E-01 4 0.364757E-01 5 0.357086E-02 6 0.945855E-02 7 -0.298771E-01 8 -0.416660E-01 ...... .............. 1543 0.598309E-02 The B coefficients: 1 0.194826E-01 2 -0.183413E-01 3 0.113155E-02 4 0.244454E-01 5 -0.797989E-01 6 0.355537E-01 7 0.230031E-01 8 0.823247E-01 ...... .............. 1543 0.328388E-01 The retrieved data: 1 2.66674 2 2.79410 3 4.71578 4 3.47063 5 2.26312 6 0.314410 7 1.45949 8 4.32149 ...... .............. 3087 1.48471 TEST07 EZFFTF can take the Fourier transform of a real vector of data. In this case, the vector is (1,1,1,...,1) and the transform should be (N,0,0,...,0), where N is the number of entries, 36 The maximum error in computation is 0.00000 TEST08 For real data, EZFFTF takes the fast Fourier transform forward. RSFTF computes the "slow" Fourier transform forward. The number of data values, N = 36 Fast Slow A coefficients: 0 2.07643 2.07643 1 0.269871 0.269871 2 0.556273 0.556273 3 -0.400940 -0.400939 4 -0.132558 -0.132558 5 0.374222 0.374222 6 -0.209030 -0.209029 7 -0.526619 -0.526619 8 -0.235116 -0.235116 9 -0.366338 -0.366339 10 0.160909 0.160909 11 0.650405 0.650406 12 0.178750 0.178751 13 -0.220436 -0.220435 14 -0.171850 -0.171851 15 -0.225756E-01 -0.225763E-01 16 0.316319 0.316318 17 0.408636 0.408634 18 -0.396105E-01 -0.396105E-01 B coefficients: 1 0.226408 0.226408 2 -0.445934E-01 -0.445932E-01 3 -0.571003E-01 -0.571006E-01 4 0.369893 0.369893 5 0.503471 0.503471 6 0.498154 0.498154 7 -0.553486E-01 -0.553489E-01 8 -0.229233 -0.229233 9 0.524417 0.524418 10 -0.422192E-01 -0.422187E-01 11 -0.611793E-01 -0.611781E-01 12 0.300000 0.299999 13 -0.439652 -0.439654 14 0.137160 0.137158 15 -0.397279 -0.397277 16 0.290930 0.290931 17 0.344359 0.344359 18 0.00000 -0.191935E-06 TEST09 EZFFTB can be used to recover a real data vector from a Fourier coefficient vector. In this test, the Fourier coefficient vector is: (1,0,0,...,0) and the recovered data vector should be (1,1,1,...,1). The maximum error in the computation was 0.00000 TEST10 RFFTF can compute the Fourier transform of a real vector of data. In this case, the vector is (1,1,1,...,1) and the transform should be (N,0,0,...,0), where N is the number of entries, N = 36 The maximum error in computation is 0.00000 TEST11 RFFTB can recover a real vector of data from Fourier coefficients. In this case, the coefficients are: (1,0,0,...,0) and the data should be: (1,1,1,...,1). The maximum error in computation is 0.00000 TEST12 For real slow Fourier transforms, RSFTF computes the forward transform. RSFTB computes the backward transform. The number of data values, N = 36 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 36 0.454505 A coefficients: 0 2.07643 1 0.269871 2 0.556273 3 -0.400939 4 -0.132558 5 0.374222 6 -0.209029 7 -0.526619 8 -0.235116 9 -0.366339 10 0.160909 11 0.650406 12 0.178751 13 -0.220435 14 -0.171851 15 -0.225763E-01 16 0.316318 17 0.408634 18 -0.396105E-01 B coefficients: 1 0.226408 2 -0.445932E-01 3 -0.571006E-01 4 0.369893 5 0.503471 6 0.498154 7 -0.553489E-01 8 -0.229233 9 0.524418 10 -0.422187E-01 11 -0.611781E-01 12 0.299999 13 -0.439654 14 0.137158 15 -0.397277 16 0.290931 17 0.344359 18 -0.191935E-06 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314330 7 1.45950 8 4.32154 ...... .............. 36 0.454511 TEST13 For real fast sine quarter wave transforms, SINQI initializes the transforms; SINQF does a forward transform; SINQB does a backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 12958.1 2 4503.34 3 2644.05 4 1842.79 5 1431.29 6 1101.79 7 786.754 8 854.813 ...... .............. 4096 -118.219 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314328 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 TEST14 For real slow quarter wave sine transforms, RSQSTF does a forward transform; RSQSTB does a backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 -1.59246 2 -0.199805E-01 3 -0.525083 4 -0.103600E-02 5 -0.312146 6 0.190251E-01 7 -0.208470 8 -0.327957E-02 ...... .............. 4096 0.226338E-01 The retrieved data: 1 2.66776 2 2.79350 3 4.71643 4 3.46988 5 2.26385 6 0.314189 7 1.45955 8 4.32122 ...... .............. 4096 0.522714 TEST15 For real fast sine transforms, RSINTI initializes the transforms. RSINT does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 13048.6 2 163.673 3 4302.47 4 8.36138 5 2557.59 6 -155.859 7 1708.13 8 27.0501 ...... .............. 4096 -116.151 The retrieved data: 1 2.67961 2 2.79449 3 4.72027 4 3.47134 5 2.26568 6 0.314478 7 1.46089 8 4.32199 ...... .............. 4096 0.535344 TEST16 For double precision fast sine transforms, DSINTI initializes the transforms. DSINT does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 13048.6 2 163.673 3 4302.43 4 8.36150 5 2557.56 6 -155.860 7 1708.09 8 27.0505 ...... .............. 4096 -116.192 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 TEST17 For real slow sine transforms, RSST does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 13048.5 2 163.677 3 4302.43 4 8.36126 5 2557.56 6 -155.857 7 1708.09 8 27.0490 ...... .............. 4096 -116.183 The retrieved data: 1 2.66662 2 2.79407 3 4.71606 4 3.47045 5 2.26362 6 0.313664 7 1.45980 8 4.32156 ...... .............. 4096 0.522607 TEST18 For double precision slow sine transforms, DSST does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The sine coefficients: 1 13048.6 2 163.673 3 4302.43 4 8.36150 5 2557.56 6 -155.860 7 1708.09 8 27.0505 ...... .............. 4096 -116.192 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 TEST19 For real fast cosine transforms, RCOSTI initializes the transforms. RCOST does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 20398.0 2 112.511 3 -110.896 4 -114.423 5 -86.2141 6 -120.584 7 -115.347 8 112.540 ...... .............. 4096 -187.554 The retrieved data: 1 2.66846 2 2.79384 3 4.71590 4 3.47044 5 2.26314 6 0.314356 7 1.45942 8 4.32146 ...... .............. 4096 0.520892 TEST20 For double precision fast cosine transforms, DCOSTI initializes the transforms. DCOST does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 20398.0 2 112.511 3 -110.895 4 -114.423 5 -86.2157 6 -120.585 7 -115.346 8 112.541 ...... .............. 4096 -187.560 The retrieved data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 TEST21 For real slow cosine transforms, RSCT does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 10200.6 2 114.657 3 -107.698 4 -112.279 5 -83.0259 6 -118.440 7 -112.159 8 114.684 ...... .............. 4096 -92.7095 The retrieved data: 1 2.66572 2 2.79273 3 4.71357 4 3.46893 5 2.26200 6 0.314170 7 1.45878 8 4.31943 ...... .............. 4096 0.522359 TEST22 For double precision slow cosine transforms, DSCT does a forward or backward transform. The number of data items is N = 4096 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 4096 0.522610 The cosine coefficients: 1 10200.6 2 114.655 3 -107.705 4 -112.279 5 -83.0263 6 -118.441 7 -112.157 8 114.685 ...... .............. 4096 -92.7081 The retrieved data: 1 2.66544 2 2.79274 3 4.71359 4 3.46894 5 2.26201 6 0.314173 7 1.45878 8 4.31943 ...... .............. 4096 0.522355 TEST23 For real slow Hartley transforms, RSHT does a forward or backward transform. The number of data items is N = 17 The original data: 1 2.66674 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314327 7 1.45949 8 4.32154 ...... .............. 17 3.13227 The Hartley coefficients: 1 9.46431 2 2.14782 3 1.11323 4 -0.154454 5 0.246043 6 -0.379701 7 -1.30123 8 -1.64563 ...... .............. 17 0.278515 The retrieved data: 1 2.66675 2 2.79411 3 4.71589 4 3.47063 5 2.26311 6 0.314326 7 1.45949 8 4.32154 ...... .............. 17 3.13227 FFTPACK_PRB Normal end of execution.