◆ rfftmb()

One-dimensional real Fourier backward transform (multiple sequences)

Purpose: rfftmb computes the one-dimensional Fourier transform of periodic sequences within a real array. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space.
When n is even:
r[l*jump+k] = r[l*jump] + (-1)^k r[l*jump+n-1] + Σr[l*jump+2j-1]cos(2πjk/n) + Σr[l*jump+2j]sin(2πjk/n) (Σ for j = 1 to n/2-1) (l = 0 to lot-1, k = 0 to n-1)

When n is odd:
r[l*jump+k] = r[l*jump] + Σr[l*jump+2j-1]cos(2πjk/n) + Σr[l*jump+2j]sin(2πjk/n) (Σ for j = 1 to (n-1)/2) (l = 0 to lot-1, k = 0 to n-1)

This transform is normalized since a call to rfftmb followed by a call to rfftmf (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc.

Parameters

[in]	lot	The 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	The length of the sequence to be transformed. (n >= 1) The transform is most efficient when n is a product of small primes.
[in]	inc	Integer increment between the locations, in array r[], of two consecutive elements within the sequence. (inc >= 1)
[in,out]	r[]	Array r[lr] [in] The sequences to be transformed. [out] The Fourier backward transformed sequences of data.
[in]	lr	The length of the array r[]. (lr >= (lot - 1)jump + inc(n - 1) + 1)
[in]	wsave[]	Array wsave[lwsave] Work data. Its contents must be initialized with a call to rfftmi before the first call to rfftmf or rfftmb for a given transform length n.
[in]	lwsave	The length of the array wsave[]. (lwsave >= n + ln(n)/ln(2) + 4)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= lot * n)
[out]	info	= 0: Successful exit = -1: The argument lot had an illegal value (lot < 1) = -2: The argument jump had an illegal value (jump < 1) = -3: The argument n had an illegal value (n < 1) = -4: The argument inc had an illegal value (inc < 1) = -6: The argument lr had an illegal value (lr not big enough) = -8: The argument lwsave had an illegal value (lwsave not big enough) = -10: The argument lwork had an illegal value (lwork not big enough)