📄 vfft.dat
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./vfft Verify Fast Fourier Transform PackageVerify the computed FFT of the AP series x[j]=jj = 0..7Performing Complex FFT of AP series (IM part being set to 0)It took 0.00 sec to perform Complex Fourier transformVerifying the Re part of the transform ...Verifying the Im part of the transform ...Two (4,1) elements of matrices with values 2.44929e-16 and 0differ the most, although the deviation 2.44929e-16 is smallVerifying the power spectrum ...Performing FFT of a REAL AP sequenceIt took 0.00 sec to perform "Real" Fourier transformCheck out that "Real" and Complex FFT give identical resultsDoneVerify the computed FFT of the AP series x[j]=jj = 0..1023Performing Complex FFT of AP series (IM part being set to 0)It took 0.02 sec to perform Complex Fourier transformVerifying the Re part of the transform ...Verifying the Im part of the transform ...Two (512,1) elements of matrices with values 3.1351e-14 and 0differ the most, although the deviation 3.1351e-14 is smallVerifying the power spectrum ...Performing FFT of a REAL AP sequenceIt took 0.02 sec to perform "Real" Fourier transformCheck out that "Real" and Complex FFT give identical resultsDoneVerify the computed FFT for x[j] = W^(-l*j)j = 0..1023, l=1Performing Complex FFTIt took 0.02 sec to perform Complex Fourier transformVerifying the Re part of the transform ...Two (869,1) elements of matrices with values 0 and 3.87654e-06differ the most, although the deviation 3.87654e-06 is smallVerifying the Im part of the transform ...Two (897,1) elements of matrices with values 0 and -3.21196e-14differ the most, although the deviation 3.21196e-14 is smallVerifying the power spectrum ...Two (869,1) elements of matrices with values 0 and 3.87654e-06differ the most, although the deviation 3.87654e-06 is smallDoneVerify the computed FFT of the truncated AP sequence x[j]=jj = 0..7, with N=16Performing Complex FFT (with IM part being set to 0)It took 0.00 sec to perform Complex Fourier transformSource Vector 0.0000 1.0000 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 Computed cos transform 28.0000 -9.1371 -4.0000 2.3801 -4.0000 3.2768 -4.0000 3.4802 -4.0000 3.4802 -4.0000 3.2768 -4.0000 2.3801 -4.0000 -9.1371 Computed sin transform 0.0000 -20.1094 9.6569 -5.9864 4.0000 -2.6727 1.6569 -0.7956 0.0000 0.7956 -1.6569 2.6727 -4.0000 5.9864 -9.6569 20.1094 Verifying the Re part of the transform ...Verifying the Im part of the transform ...Two (8,1) elements of matrices with values 2.44929e-16 and 0differ the most, although the deviation 2.44929e-16 is smallVerifying the power spectrum ...Performing FFT of a REAL AP sequenceIt took 0.00 sec to perform "Real" Fourier transformCheck out that "Real" and Complex FFT give identical resultsCheck out the functions returning the half of the transformDoneVerify the computed FFT of the truncated AP sequence x[j]=jj = 0..511, with N=1024Performing Complex FFT (with IM part being set to 0)It took 0.02 sec to perform Complex Fourier transformVerifying the Re part of the transform ...Verifying the Im part of the transform ...Two (512,1) elements of matrices with values 1.56755e-14 and 0differ the most, although the deviation 1.56755e-14 is smallVerifying the power spectrum ...Performing FFT of a REAL AP sequenceIt took 0.01 sec to perform "Real" Fourier transformCheck out that "Real" and Complex FFT give identical resultsCheck out the functions returning the half of the transformDoneVerify the sin/cos transform for the following example r*exp( -r/a ) <=== sin-transform ===> 2a^3 k/(1 + (ak)^2)^2 r*exp( -r/a ) <=== cos-transform ===> a^2 (1-(ak)^2)/(1 + (ak)^2)^2Parameter a is 4.000000No. of grids 512Grid mesh in the r-space dr = 0.039Grid mesh in the k-space dk = 0.157Check out the inquires to FFT package about N, dr, dk, cutoffsIt took 0.01 sec to perform Sine transformIt took 0.02 sec to perform Cosine transformComparison of two Matrices: Computed and Exact sin-transformMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.312458 occured at the point (1,1) Matrix 1 element is 10.6476 Matrix 2 element is 10.3351 Absolute error v2[i]-v1[i] -0.312458 Relative error -0.0297824||Matrix 1|| 26.1276||Matrix 2|| 23.5973||Matrix1-Matrix2|| 4.69511||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.189089Comparison of two Matrices: Computed and Exact cos-transformMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.649606 occured at the point (0,1) Matrix 1 element is 15.3504 Matrix 2 element is 16 Absolute error v2[i]-v1[i] 0.649606 Relative error 0.0414416||Matrix 1|| 34.543||Matrix 2|| 33.8396||Matrix1-Matrix2|| 3.01891||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.0882996Comparison of two Matrices: Computed cos-transform with DC component removed, and exact resultMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.651867 occured at the point (0,1) Matrix 1 element is 15.3481 Matrix 2 element is 16 Absolute error v2[i]-v1[i] 0.651867 Relative error 0.0415889||Matrix 1|| 34.9727||Matrix 2|| 33.8396||Matrix1-Matrix2|| 3.01892||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.0877554It took 0.02 sec to perform Inverse sine transformIt took 0.01 sec to perform Inverse cosine transformComparison of two Matrices: Computed inverse sin-transform vs the original functionMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 5.96046e-08 occured at the point (221,1) Matrix 1 element is 0.997371 Matrix 2 element is 0.997371 Absolute error v2[i]-v1[i] 5.96046e-08 Relative error 5.97618e-08||Matrix 1|| 392.97||Matrix 2|| 392.97||Matrix1-Matrix2|| 1.12206e-05||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 2.85533e-08Comparison of two Matrices: Computed inverse cos-transform vs the original functionMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.767671 occured at the point (58,1) Matrix 1 element is 2.05355 Matrix 2 element is 1.28588 Absolute error v2[i]-v1[i] -0.767671 Relative error -0.459761||Matrix 1|| 785.94||Matrix 2|| 392.97||Matrix1-Matrix2|| 392.97||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.707107Comparison of two Matrices: Computed inverse cos-transform with DC component removed,and the original functionMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.135816 occured at the point (55,1) Matrix 1 element is 1.11981 Matrix 2 element is 1.25562 Absolute error v2[i]-v1[i] 0.135816 Relative error 0.11435||Matrix 1|| 324.137||Matrix 2|| 392.97||Matrix1-Matrix2|| 69.4601||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.194622DoneVerify the sin/cos transform for the following example exp( -r^2/4a ) <=== cos-transform ===> sqrt(a*pi) exp(-a*k^2)Parameter a is 4.00No. of grids 512Grid mesh in the r-space dr = 0.039Grid mesh in the k-space dk = 0.157Check out the inquires to FFT package about N, dr, dk, cutoffsIt took 0.02 sec to perform Cosine transformComparison of two Matrices: Computed and Exact cos-transformMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.0195313 occured at the point (18,1) Matrix 1 element is 0.0195313 Matrix 2 element is 4.5914e-14 Absolute error v2[i]-v1[i] -0.0195313 Relative error -2||Matrix 1|| 21.7725||Matrix 2|| 11.7725||Matrix1-Matrix2|| 10||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.624616Comparison of two Matrices: Computed with DC removed, and Exact cos-transformMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 2.23517e-08 occured at the point (350,1) Matrix 1 element is -2.23517e-08 Matrix 2 element is 0 Absolute error v2[i]-v1[i] 2.23517e-08 Relative error 0.223517||Matrix 1|| 11.7725||Matrix 2|| 11.7725||Matrix1-Matrix2|| 3.91315e-06||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 3.32399e-07It took 0.02 sec to perform Inverse cosine transformComparison of two Matrices: Computed inverse cos-transform vs the original functionMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 0.177245 occured at the point (2,1) Matrix 1 element is 1.17686 Matrix 2 element is 0.999619 Absolute error v2[i]-v1[i] -0.177245 Relative error -0.162873||Matrix 1|| 181.999||Matrix 2|| 91.2496||Matrix1-Matrix2|| 90.7496||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 0.704198Comparison of two Matrices: Computed inverse with DC removed vs the originalMatrix 0:511x1:1 is not engagedMatrix 0:511x1:1 is not engagedMaximal discrepancy 3.57628e-07 occured at the point (0,1) Matrix 1 element is 1 Matrix 2 element is 1 Absolute error v2[i]-v1[i] 3.57628e-07 Relative error 3.57628e-07||Matrix 1|| 91.2496||Matrix 2|| 91.2496||Matrix1-Matrix2|| 6.16255e-06||Matrix1-Matrix2||/sqrt(||Matrix1|| ||Matrix2||) 6.75351e-08Donecheck speed of different kind of transformsj = 0..2047 for 100 times Performing Complex FFT It took 4.28 sec to perform Complex Fourier transform Performing FFT of a REAL sequenceIt took 3.48 sec to perform "Real" Fourier transform Performing Complex FFT of a half sequence padded by zerosIt took 3.86 sec to perform Complex Fourier transform Performing FFT of a REAL half-sequence padded by zerosIt took 3.38 sec to perform "Real" Fourier transform Performing FFT of a REAL padded half-sequence and getting halfIt took 3.24 sec to perform "Real" Fourier transformDoneCompilation finished at Fri Dec 25 23:27:07⌨️ 快捷键说明
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