rfft1b rfft1f rfft1i

rfft1f() def rfft1f ( n  , r  , wsave  , inc  = 1  ) One-dimensional real Fourier transform Purpose rfft1f computes the one-dimensional Fourier transform of a periodic sequence within a real array. This is referred to as the forward transform or Fourier analysis, transforming the sequence from physical to spectral space. r[0] = (1/n)Σr[j] (Σ for j = 0 to n-1) r[2k-1] = (2/n)Σr[j]cos(2πjk/n) (Σ for j = 0 to n-1) (k = 1 to nh) r[2k] = (2/n)Σr[j]sin(2πjk/n) (Σ for j = 0 to n-1) (k = 1 to nh) r[n-1] = (1/n)Σ(-1)^j r[j] (Σ for j = 0 to n-1) (only if n is even) (If n is even, nh = n/2-1. If n is odd, nh = (n-1)/2) This transform is normalized since a call to rfft1f followed by a call to rfft1b (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc. Returns info (int) = 0: Successful exit = -1: The argument n had an illegal value (n < 1) = -2: The argument r is invalid = -3: The argument wsave is invalid = -4: The argument inc had an illegal value (inc < 1) Parameters [in] n The length of the sequence to be transformed. (n >= 1) The transform is most efficient when n is a product of small primes. [in,out] r Numpy ndarray (1-dimensional, float, length inc*(n - 1) + 1) [in] The sequence to be transformed. [out] The Fourier forward transformed sequence of data. [in] wsave Numpy ndarray (1-dimensional, float, length n + ln(n)/ln(2) + 4) Work data. Its contents must be initialized with a call to rfft1i before the first call to rfft1f or rfft1b for a given transform length n. [in] inc (Optional) Integer increment between the locations, in array r, of two consecutive elements within the sequence. (inc >= 1) (default = 1) Reference FFTPACK 5.1 Example Program Compute the Fourier transform and backward transform of 5 random data sequence successively, and compare with the original data sequence. def TestRfft1(): # Initialization seed = 13 init_genrand(seed) n = 5 lwsave = n + int(log(n)/log(2)) + 4 wsave = np.empty(lwsave) info = rfft1i(n, wsave) if info != 0: print('Error during initialization: info =', info) return 1 # Generate test data inc = 1 lr = inc*(n - 1) + 1 r = np.empty(lr) rcopy = np.empty(lr) for i in range(n): k = inc*i r[k] = genrand_res53() rcopy[k] = r[k] # Forward transform info = rfft1f(n, r, wsave) if info != 0: print('Error in Rfft1f: info =', info) return 2 # Backward transform info = rfft1b(n, r, wsave) if info != 0: print('Error in Rfft1b: info =', info) return 3 # Check results diff = 0.0 for i in range(n): k = inc*i if abs(r[k] - rcopy[k]) > diff: diff = abs(r[k] - rcopy[k]) print(rcopy[k], r[k], abs(r[k] - rcopy[k])) print('diff(max) =', diff) Example Results >>> TestRfft1() 0.7777024105738202 0.7777024105738204 2.220446049250313e-16 0.2375412200349123 0.23754122003491207 2.220446049250313e-16 0.8242785326613685 0.8242785326613685 0.0 0.9657491980429997 0.9657491980429999 1.1102230246251565e-16 0.9726011139048933 0.9726011139048933 0.0 diff(max) = 2.220446049250313e-16