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That occurs when computing the two-dimensional FFT. However, the size of the original array is modified to contain one or two additional rows, which are needed to store the values identically equal to zero. The values of the arguments used with the real two-dimensional FFT routines depend upon whether an in-place or out-of place transform is performed, and whether the results are stored in a full or partial result matrix, as shown in TABLE 16. TABLE 16 Relationships Between Values of Arguments for Real Two-Dimensional FFT Routines Full Result Matrix Partial Result Matrix In-Place Transform B unused B unused LDB unused LDB unused LDA must be even LDA must be even LDA 2*M LDA M+2 if M is evenLDA M+1 if M is odd A(1:2*M, 1:N) A(1:M+2, 1:N) if M is evenA(1:M+1, 1:N) if M is odd Out-of-Place Transform A unchanged A unchanged LDA M LDA M 2*LDB M 2*LDB M+2 if M is even2*LDB M+1 if M is odd B(1:2*M, 1:N) B(1:M+2, 1:N) if M is evenB(1:M+1, 1:N) if M is odd When computing the real two-dimensional FFT of an input sequence of M rows and N columns, the computed Fourier coefficients will be stored in a result matrix with 2*M rows and N columns when using the Full storage option. When using the Partial storage option, the Fourier coefficients will be stored in a result matrix with M+2 rows and N columns when M is even, or in a result matrix with M+1 rows and N columns when M CALL RFFT2F ('O', IS_FULL, M, N, AT, LDA, B, LDB, WT, LWORK) PRINT *, 'Transformed Out-of-Place, Full' DO I = 1, LDB_ACTUAL, N PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', $ (B(I,J), B(I+1,J), J = 1, N) END DO * B(M+3:LDB,1:N) = 0 * PRINT *, 'Transformed, last half clear:' * DO I = 1, LDB, N * PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', * $ (B(I,J), B(I+1,J), J = 1, N) * END DO CALL RFFT2B ('O', M, N, AT, LDA, B, LDB, WT, LWORK) PRINT *, 'Inverse: Scaled Output, Out-of-Place, Full' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J) / (M * N), J = 1, N) END DO PRINT * * * Example 2 * in-place, full * LDA must be at least 2*M * AT = INPUT IS_FULL = 'F' CALL RFFT2F ('I', IS_FULL, M, N, AT, LDA, 0, 0, WT, LWORK) PRINT *, 'Transformed In-Place, Full' DO I = 1, LDA, 2 PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', $ (AT(I,J), AT(I+1,J), J = 1, N) END DO CALL RFFT2B ('I', M, N, AT, LDA, 0, 0, WT, LWORK) PRINT *, 'Inverse: Scaled Output, In-Place, Full' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J) / (M * N), J = 1, N) END DO PRINT * DEALLOCATE(AT,WT,B) END SUBROUTINE my_system% f95 -dalign fft_ex16.f -xlic_lib=sunperf my_system% a.out Original Sequence 0.968 0.654 0.067 0.021 0.478 0.512 0.910 0.202 0.352 0.940 0.933 0.204 Transformed Out-of-Place, Full ( 6.241, 0.000) ( 1.173, 0.000) (LDB software updates and reviews: LDB QuickExecute, etc.
Where one row contains the real part of the complex coefficient and the next row contains the imaginary part of the complex coefficient. In CODE EXAMPLE 15, to better display the complex conjugate symmetry, the real and imaginary parts of each complex coefficient are displayed on one line. For example, the following output: Transformed Out-of-Place, Full ( 6.241, 0.000) ( 1.173, 0.000) ( -0.018, 1.169) ( 0.304, 0.111) represents the following values for the Fourier coefficients. Column 1 Column 2 Re(X0) Im(X0) Re(X0) Im(X0) Re(X1) Im(X1) Re(X1) Im(X1) The inverse transform is unnormalized and can be normalized by dividing each value by M*N. CODE EXAMPLE 16 RFFT2F and RFFT2B Example Showing In-Place and Out-of-Place Storage my_system% cat fft_ex16.f PROGRAM TESTFFT INTEGER M, N PARAMETER(M = 6, N = 2) CALL FFT(M,N) END SUBROUTINE FFT(M, N) CHARACTER*1 IS_FULL INTEGER I, J, M, N, ISTAT, LWORK, LDA, LDB, LDB_ACTUAL REAL RNUM, RAND EXTERNAL RFFT2F, RFFT2B, RFFT2I, RAND REAL, DIMENSION(:,:), ALLOCATABLE :: AT, B, INPUT REAL, DIMENSION(:), ALLOCATABLE :: WT LDA = 2*M LDB = 2*M LWORK = M+2*N+MAX(M,2*N)+30 ALLOCATE(AT(LDA,N), INPUT(LDA,N), WT(LWORK), B(LDB_ACTUAL,N)) CALL RFFT2I (M, N, WT) DO I = 1, N DO J = 1, M INPUT(J,I) = RAND(0) END DO END DO AT = INPUT * PRINT *, 'Original Sequence' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J), J = 1, N) END DO PRINT * * * Example 1 * Out-of-place, full * leading dimension of B (2*LDB) must be at least 2*M * IS_FULL = 'F' LDB =. Free ldb quickexecute download software at UpdateStar - LDB QuickExecute: A Comprehensive Review LDB QuickExecute by LDB Software is a powerful softwareLDB QuickExecute 3.0 Download - QuickExecute.exe
Computing the three-dimensional FFT. However, the size of the original array is modified to contain one or two additional rows, which are needed to store the values identically equal to zero. The values of the arguments used with the real three-dimensional FFT routines depend upon whether an in-place or out-of place transform is performed, and whether the results are stored in a full or partial result matrix, as shown in TABLE 19. TABLE 19 Relationship Between Values of Arguments for Real Three-Dimensional FFT Routines Full Result Array Partial Result Array In-Place Transform B unused B unused LDB unused LDB unused LDA must be even LDA must be even LDA 2*M LDA M+2 if M is evenLDA M+1 if M is odd A(1:2*M, 1:N) A(1:M+2, 1:N) if M is evenA(1:M+1, 1:N) if M is odd Out-of-Place Transform A unchanged A unchanged LDA M LDA M LDB 2*M LDB M/2+1 if M is evenLDB (M-1)/2+1 if M is odd B(1:2*M, 1:N, 1:K) B(1:M+2, 1:N, 1:K) if M is evenB(1:M+1, 1:N, 1:K) if M is odd When computing the real 3D FFT of an input sequence of M rows, N columns, and K planes, the computed Fourier coefficients will be stored in a result matrix with 2*M rows, N columns for each value of K when using the Full storage option. When using the Partial storage option, the Fourier coefficients will be stored in a result matrix with M+2 rows and N columns for each value of K when M is even, or Quarter-wave transform VSINQF, VDSINQF M,N,X,XT,MDIMX,WSAVE Sine quarter-wave transform (Vector) SINQI, DSINQI N,WSAVE Initialize sine quarter-wave transform and inverse transform VSINQI, VDSINQI N,WSAVE Initialize sine quarter-wave transform and inverse transform (Vector) SINT, DSINT N,X,WSAVE Sine odd-wave transform VSINT, VDSINT M,N,X,XT,MDIMX,WSAVE Sine odd-wave transform (Vector) SINTI, DSINT N,WSAVE Initialize sine odd-wave transform VSINTI, VDSINTI N,WSAVE Initialize sine odd-wave transform (Vector) RFFT2B, DFFT2B PLACE,M,N,A,LDA,B,LDB,WORK,LWORK Inverse two-dimensional Fourier transform CFFT2B, ZFFT2B M,N,A,LDA,WORK,LWORK RFFT2F, DFFT2F PLACE,FULL,M,N,A,LDA,B,LDB,WORK,LWORK Two-dimensional Fourier transform CFFT2F, ZFFT2F M,N,A,LDA,WORK,LWORK RFFT2I, DFFT2I, CFFT2I, ZFFT2I M,N,WORK Initialize two-dimensional Fourier transform and inverse transform RFFT3B, DFFT3B PLACE,M,N,K,A,LDA,B,LDB,WORK,LWORK Inverse three-dimensional Fourier transform CFFT3B, ZFFT3B M,N,K,A,LDA,LD2A,WORK,LWORK RFFT3F, DFFT3F PLACE,FULL,M,N,K,A,LDA,B,LDB,WORK,LWORK Three-dimensional Fourier transform CFFT3F, ZFFT3F M,N,K,A,LDA,LD2A,WORK,LWORK RFFT3I, DFFT3I, CFFT3I, ZFFT3I M,N,K,WORK Initialize three-dimensional Fourier transform and inverse transform In addition to the FFT and VFFT routines listed in TABLE 8, the following routines are described in this manual. TABLE 9 Convolution and Correlation Routines Routine Arguments Function SCNVCOR, DCNVCOR, CCNVCOR, ZCNVCOR CNVCOR,FOUR,NX,X,IFX,INCX,NY,NPRE,M,Y,IFY,INC1Y,INC2Y,NZ,K,Z,IFZ,INC1Z,INC2Z,WORK,LWORK Convolution or correlation of two vectors SCNVCOR2, DCNVCOR2, CCNVCOR2, ZCNVCOR2 CNVCOR,METHOD,TRANSX,SCRATCHX,TRANSY,SCRATCHY,MX,NX,X,LDX,MY,NY,MPRE,NPRE,Y,LDY,MZ,NZ,Z,LDZ,WORKIN,LWORK Convolution or correlation of two matrices Calling FFT Routines FFT routines can be called using FORTRAN 77, Fortran 95, or C interfaces. 64-bit interfaces for compiling code that supports a 64-bit Solaris Operating Environment are also provided. Fortran Interface Conventions Sun Performance Library FORTRAN 77 and Fortran 95 interfaces use the following conventions: All arguments are passed by reference. The number of arguments to a routine is fixed. Types of arguments must match. Arrays are stored columnwise. Indices are based at one, following standard FortranDownload LDB QuickExecute 3.00 - soft32download.com
Of rows to be transformed N Number of columns to be transformed A Two-dimensional array A(LDA,N) containing the sequences to be transformed and the results of an in-place transform LDA Leading dimension of array containing data to be transformed WORK Work array initialized by xFFT2I LWORK Dimension of work array WORK Arguments for PLACE, FULL, B, and LDB are not used with the complex two-dimensional FFT routines, because the transformed sequence is stored in the original input array without any additional manipulations. Real two-dimensional FFT routines use the arguments shown in TABLE 15. TABLE 15 Arguments for Real Two-Dimensional FFT Routines Argument Definition PLACE `I' or `i' specifies that an in-place transform is performed.`O' or `o' specifies that an out-of-place transform is performed. FULL RFFT2F or DFFT2F only: `F' or `f' specifies that a full result matrix is generated.Any other character specifies that a partial result matrix is generated. M Number of rows to be transformed N Number of columns to be transformed A Two-dimensional array A(LDA,N) containing the sequences to be transformed and the results of an in-place transform LDA Leading dimension of array containing data to be transformed B Two-dimensional array B(2*LDB,N) that stores the results of an out-of-place transform LDB One half of the actual leading dimension of array that stores results of out-of-place transform WORK Work array initialized by xFFT2I LWORK Dimension of work array WORK Normalization The xFFT2 operations are unnormalized, so a call of xFFT2F followed by a call of xFFT2B will multiply theLDB QuickExecute - Download Review - Softpile
And the results of an in-place transform LDA Leading dimension of array containing data to be transformed, where LDA M LD2A Second dimension of array to be transformed, where LD2A N WORK Work array initialized by xFFT3I LWORK Dimension of work array WORK Arguments for PLACE, FULL, B, and LDB are not used with the complex three-dimensional FFT routines, because the transformed sequence is stored in the original input array without any additional manipulations. Real three-dimensional FFT routines use the arguments shown in TABLE 18. TABLE 18 Arguments for Real Three-Dimensional FFT Routines Argument Definition PLACE `I' or `i' specifies that an in-place transform is performed.`O' or `o' specifies that an out-of-place transform is performed. FULL RFFT3F or DFFT3F only: `F' or `f' specifies that a full result matrix is generated.Any other character specifies that a partial result matrix is generated. M Number of rows to be transformed N Number of columns to be transformed K Number of planes to be transformed A Three-dimensional array A(LDA,N,K) containing the sequences to be transformed and the results of an in-place transform LDA Leading dimension of array containing data to be transformed B Three-dimensional array B(2*LDB,N,K) that stores the results of an out-of-place transform LDB Leading dimension of array that stores results of out-of-place transform WORK Work array initialized by xFFT3I LWORK Dimension of work array WORK Normalization The xFFT3 operations are unnormalized, so a call of xFFT3F followed by a call of xFFT3B will multiply the input sequence by M*N*K. Data Storage. Free ldb quickexecute download software at UpdateStar - LDB QuickExecute: A Comprehensive Review LDB QuickExecute by LDB Software is a powerful softwareLdb Quickexecute Free Download - tags.topshareware.com
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That occurs when computing the two-dimensional FFT. However, the size of the original array is modified to contain one or two additional rows, which are needed to store the values identically equal to zero. The values of the arguments used with the real two-dimensional FFT routines depend upon whether an in-place or out-of place transform is performed, and whether the results are stored in a full or partial result matrix, as shown in TABLE 16. TABLE 16 Relationships Between Values of Arguments for Real Two-Dimensional FFT Routines Full Result Matrix Partial Result Matrix In-Place Transform B unused B unused LDB unused LDB unused LDA must be even LDA must be even LDA 2*M LDA M+2 if M is evenLDA M+1 if M is odd A(1:2*M, 1:N) A(1:M+2, 1:N) if M is evenA(1:M+1, 1:N) if M is odd Out-of-Place Transform A unchanged A unchanged LDA M LDA M 2*LDB M 2*LDB M+2 if M is even2*LDB M+1 if M is odd B(1:2*M, 1:N) B(1:M+2, 1:N) if M is evenB(1:M+1, 1:N) if M is odd When computing the real two-dimensional FFT of an input sequence of M rows and N columns, the computed Fourier coefficients will be stored in a result matrix with 2*M rows and N columns when using the Full storage option. When using the Partial storage option, the Fourier coefficients will be stored in a result matrix with M+2 rows and N columns when M is even, or in a result matrix with M+1 rows and N columns when
2025-04-01M CALL RFFT2F ('O', IS_FULL, M, N, AT, LDA, B, LDB, WT, LWORK) PRINT *, 'Transformed Out-of-Place, Full' DO I = 1, LDB_ACTUAL, N PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', $ (B(I,J), B(I+1,J), J = 1, N) END DO * B(M+3:LDB,1:N) = 0 * PRINT *, 'Transformed, last half clear:' * DO I = 1, LDB, N * PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', * $ (B(I,J), B(I+1,J), J = 1, N) * END DO CALL RFFT2B ('O', M, N, AT, LDA, B, LDB, WT, LWORK) PRINT *, 'Inverse: Scaled Output, Out-of-Place, Full' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J) / (M * N), J = 1, N) END DO PRINT * * * Example 2 * in-place, full * LDA must be at least 2*M * AT = INPUT IS_FULL = 'F' CALL RFFT2F ('I', IS_FULL, M, N, AT, LDA, 0, 0, WT, LWORK) PRINT *, 'Transformed In-Place, Full' DO I = 1, LDA, 2 PRINT '(100('' ('', F8.3, '','', F8.3, '')'' :))', $ (AT(I,J), AT(I+1,J), J = 1, N) END DO CALL RFFT2B ('I', M, N, AT, LDA, 0, 0, WT, LWORK) PRINT *, 'Inverse: Scaled Output, In-Place, Full' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J) / (M * N), J = 1, N) END DO PRINT * DEALLOCATE(AT,WT,B) END SUBROUTINE my_system% f95 -dalign fft_ex16.f -xlic_lib=sunperf my_system% a.out Original Sequence 0.968 0.654 0.067 0.021 0.478 0.512 0.910 0.202 0.352 0.940 0.933 0.204 Transformed Out-of-Place, Full ( 6.241, 0.000) ( 1.173, 0.000) (
2025-04-08Where one row contains the real part of the complex coefficient and the next row contains the imaginary part of the complex coefficient. In CODE EXAMPLE 15, to better display the complex conjugate symmetry, the real and imaginary parts of each complex coefficient are displayed on one line. For example, the following output: Transformed Out-of-Place, Full ( 6.241, 0.000) ( 1.173, 0.000) ( -0.018, 1.169) ( 0.304, 0.111) represents the following values for the Fourier coefficients. Column 1 Column 2 Re(X0) Im(X0) Re(X0) Im(X0) Re(X1) Im(X1) Re(X1) Im(X1) The inverse transform is unnormalized and can be normalized by dividing each value by M*N. CODE EXAMPLE 16 RFFT2F and RFFT2B Example Showing In-Place and Out-of-Place Storage my_system% cat fft_ex16.f PROGRAM TESTFFT INTEGER M, N PARAMETER(M = 6, N = 2) CALL FFT(M,N) END SUBROUTINE FFT(M, N) CHARACTER*1 IS_FULL INTEGER I, J, M, N, ISTAT, LWORK, LDA, LDB, LDB_ACTUAL REAL RNUM, RAND EXTERNAL RFFT2F, RFFT2B, RFFT2I, RAND REAL, DIMENSION(:,:), ALLOCATABLE :: AT, B, INPUT REAL, DIMENSION(:), ALLOCATABLE :: WT LDA = 2*M LDB = 2*M LWORK = M+2*N+MAX(M,2*N)+30 ALLOCATE(AT(LDA,N), INPUT(LDA,N), WT(LWORK), B(LDB_ACTUAL,N)) CALL RFFT2I (M, N, WT) DO I = 1, N DO J = 1, M INPUT(J,I) = RAND(0) END DO END DO AT = INPUT * PRINT *, 'Original Sequence' DO I = 1, M PRINT '(100(F8.3))', (AT(I,J), J = 1, N) END DO PRINT * * * Example 1 * Out-of-place, full * leading dimension of B (2*LDB) must be at least 2*M * IS_FULL = 'F' LDB =
2025-04-04