Cost1b Cost1f Cost1i Costmb Costmf Costmi Sint1b Sint1f Sint1i Sintmb Sintmf Sintmi

Costmf() Sub Costmf ( Lot As  Long, Jump As  Long, N As  Long, R() As  Double, Wsave() As  Double, Info As  Long, Optional Inc As  Long = 1  ) One-dimensional cosine transform (multiple sequences) Purpose This routine computes the one-dimensional Fourier transform of multiple even sequences within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. R(l*jump) = (1/2)R(l*jump)/(N-1) + ΣR(l*jump+j)/(N-1) + (1/2)R(l*jump+N-1)/(N-1) (Σ for j = 1 to N-2) (l = 0 to lot-1) R(l*jump+k) = R(l*jump)/(N-1) + Σ2R(l*jump+j)cos(πjk/(N-1))/(N-1) + (-1)^k R(l*jump+N-1)/(N-1) (Σ for j = 1 to N-2) (l = 0 to lot-1, k = 1 to N-2) R(l*jump+N-1) = (1/2)R(l*jump)/(N-1) + ΣR(l*jump+j)(-1)^k/(N-1) + (1/2)(-1)^(N-1) R(l*jump+N-1)/(N-1) (Σ for j = 1 to N-2) (l = 0 to lot-1) This transform is normalized since a call to Costmf followed by a call to Costmb (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Parameters [in] Lot Number of sequences to be transformed. (Lot >= 1) [in] Jump Increment between the locations, in array R(), of the first elements of two consecutive sequences to be transformed. (Jump >= 1) [in] N Length of the sequence to be transformed. (N >= 1) (The transform is most efficient when N-1 is a product of small primes) [in,out] R() Array R(LR - 1) (LR >= (Lot - 1)*Jump + Inc*(N - 1) + 1) [in] The sequences to be transformed. [out] The Fourier forward transformed sequences of data. [in] Wsave() Array Wsave(LWsave - 1) (LWsave >= 2*N + ln(N)/ln(2) + 4) Work data. Its contents must be initialized with a call to Costmi before the first call to Costmf or Costmb for a given transform length N. [out] Info = 0: Successful exit. = -1: The argument Lot had an illegal value. (Lot < 1, or, Lot, Jump, N and Inc are inconsistent) = -2: The argument Jump had an illegal value. (Jump < 1) = -3: The argument N had an illegal value. (N < 1) = -4: The argument R() had an illegal value. (Array R() is not big enough) = -5: The argument Wsave() had an illegal value. (Array Wsave() is not big enough) = -7: The argument Inc had an illegal value. (Inc < 1) [in] Inc (Optional) Integer increment between the locations, in array R(), of two consecutive elements within the sequence. (Inc >= 1) (default = 1) Reference FFTPACK Example Program Compute the cosine transform and backward transform of 2 sequences of 5 random data successively, and compare with the original data sequences. Sub Ex_Costm() Const N = 5, Lot = 2, Jump = N Dim Wsave() As Double, R(Lot * N - 1) As Double, R0(Lot * N - 1) As Double Dim LWsave As Long, Info As Long, I As Long, J As Long, K As Long '-- Initialization LWsave = 2 * N + Log(N) / Log(2) + 4 ReDim Wsave(LWsave - 1) Call Costmi(N, Wsave, Info) If Info <> 0 Then GoTo Err '-- Generate test data For I = 0 To Lot * N - 1 R(I) = Rnd() R0(I) = R(I) Next '-- Forward transform Call Costmf(Lot, Jump, N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Backward transform Call Costmb(Lot, Jump, N, R(), Wsave(), Info) If Info <> 0 Then GoTo Err '-- Print result For J = 0 To Lot - 1 For I = 0 To N - 1 K = J * Jump + I Debug.Print R0(K), R(K), R(K) - R0(K) Next Debug.Print Next Exit Sub Err: Debug.Print "Error in Costmi/Costmf/Costmb: Info =", Info End Sub Example Results 0.116536915302277 0.116536915302277 0 0.999308347702026 0.999308347702026 1.11022302462516E-16 0.710308015346527 0.710308015346527 0 0.436867117881775 0.436867117881775 -1.11022302462516E-16 0.866015493869781 0.866015493869781 0 0.189593315124512 0.189593315124512 0 0.073291003704071 0.073291003704071 -5.55111512312578E-17 0.796404480934143 0.796404480934143 0 0.691944420337677 0.691944420337677 0 0.248183488845825 0.248183488845825 0