◆ cfft2b()

Two-dimensional complex Fourier backward transform

Purpose: cfft2b 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.
c[k][j] = sum(sum(c[m1][l1]exp(2pi*i*(j*l1/l+k*m1/m)))) (i is imaginary unit)

(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)

This transform is normalized since a call to cfft2b followed by a call to cfft2f (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]	ldc	Leading dimension of two dimensional array c[][]. (ldc >= l)
[in,out]	c[][]	Array c[lc][ldc] (lc >= m) [in] The two dimensional sequence dat to be transformed. [out] Fourier backward transformed two dimensional sequence data.
[in]	wsave[]	Array wsave[lwsave] Work data. Its contents must be initialized with a call to cfft2i before the first call to cfft2f or cfft2b for a given transform length l and m.
[in]	lwsave	The length of the array wsave[]. (lwsave >= 2*(l + m) + ln(l)/ln(2) + ln(m)/ln(2) + 8)
[out]	work[]	Array work[lwork] Work array.
[in]	lwork	The length of the array work[]. (lwork >= 2lm)
[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 ldc had an illegal value (ldc < 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)