◆ _costmf()

One-dimensional cosine transform (multiple sequences)

Purpose: costmf 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	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-1 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 sequence to be transformed. [out] The Fourier forward 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 costmi before the first call to costmf or costmb for a given transform length n.
[in]	lwsave	The length of the array wsave[]. (lwsave >= 2*n + ln(n)/ln(2) + 4)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= lot*(n + 1))
[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)