◆ rfft2b()

Two-dimensional real Fourier backward transform

Purpose: rfft2b computes the two-dimensional Fourier transform of a periodic sequence within a real array. This is referred to as the backward transform or Fourier synthesis, transforming the sequence from spectral to physical space.
r[k][j] = ΣΣc[m1][l1]exp(2πi(j*l1/l+k*m1/m)) (1st Σ for l1 = 0 to l-1, 2nd Σ for m1 = 0 to m-1) (j = 0 to l-1, k = 0 to m-1) (i is imaginary unit)

This transform is normalized since a call to rfft2b followed by a call to rfft2f (or vice-versa) reproduces the original array subject to algorithmic constraints, roundoff error, etc.

Parameters

[in]	l	The number of elements to be transformed in the first dimension of the two-dimensional data array. (l >= 1) The transform is most efficient when l is a product of small primes.
[in]	m	The number of elements to be transformed in the second dimension of the two-dimensional data array. (m >= 1) The transform is most efficient when m is a product of small primes.
[in]	ldr	Leading dimension of two dimensional array r[][]. (ldr >= l)
[in,out]	r[][]	Array r[lr][ldr] (lr >= m) [in] The two dimensional complex sequence data to be transformed (packed conjugate symmetric data as decsribed in the documentation of rfft2f). [out] The Fourier backward transformed two dimensional real sequence data.
[in]	wsave[]	Array wsave[lwsave] Work data. Its contents must be initialized with a call to rfft2i before the first call to rfft2f or rfft2b for a given transform length n.
[in]	lwsave	The length of the array wsave[]. (lwsave >= l+3m+ln(l)/ln(2)+2ln(m)/ln(2)+12)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= (l + 1)*m)
[out]	info	= 0: Successful exit = -1: The argument l had an illegal value (l < 1) = -2: The argument m had an illegal value (m < 1) = -3: The argument ldr had an illegal value (ldr < l) = -6: The argument lwsave had an illegal value (lwsave not big enough) = -8: The argument lwork had an illegal value (lwork not big enough)