◆ sinq1b()

One-dimensional quarter sine backward transform

Purpose: sinq1b computes the one-dimensional Fourier transform of a sequence which is a sine series with odd wave numbers. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space.
r[j] = Σr[k]sin(π(j+1)(2k+1)/(2n)) (Σ for k = 0 to n-1) (j = 0 to n-1)

This transform is normalized since a call to sinq1b followed by a call to sinq1f (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 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 backward 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 sinq1i before the first call to sinq1f or sinq1b 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 >= n)
[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)