◆ cost1f()

One-dimensional cosine transform

Purpose: cost1f computes the one-dimensional Fourier transform of an even 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] = (1/2)r[0]/(n-1) + Σr[j]/(n-1) + (1/2)r[n-1]/(n-1) (Σ for j = 1 to n-2)

r[k] = r[0]/(n-1) + Σ2r[j]cos(πjk/(n-1))/(n-1) + (-1)^k r[n-1]/(n-1) (Σ for j = 1 to n-2) (k = 1 to n-2)

r[n-1] = (1/2)r[0]/(n-1) + Σr[j](-1)^k/(n-1) + (1/2)(-1)^(n-1) r[n-1]/(n-1) (Σ for j = 1 to n-2)

This transform is normalized since a call to cost1f followed by a call to cost1b (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc.

Parameters

[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 sequence of data.
[in]	lr	The length of the array r[]. (lr >= inc*(n - 1) + 1)
[in]	wsave[]	Array wsave[lwsave] Work data. Its contents must be initialized with a call to cost1i before the first call to cost1f or cost1b for a given transform length n.
[in]	lwsave	The length of the array wsave[]. (lwsave >= n/2 + n + ln(n)/ln(2) + 4)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= n - 1)
[out]	info	= 0: Successful exit = -1: The argument n had an illegal value (n < 1) = -2: The argument inc had an illegal value (inc < 1) = -4: The argument lr had an illegal value (lr not big enough) = -6: The argument lwsave had an illegal value (lwsave not big enough) = -8: The argument lwork had an illegal value (lwork not big enough)