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CategoryMath: Fft
GPUYes

What does the ifft2 function do in MATLAB / RunMat?

ifft2(X) computes the two-dimensional inverse discrete Fourier transform (IDFT) of X. It undoes the effect of fft2 by applying ifft along the first dimension and then along the second dimension, preserving MATLAB’s column-major semantics.

How does the ifft2 function behave in MATLAB / RunMat?

  • ifft2(X) transforms along the first two dimensions whose sizes exceed one.
  • ifft2(X, M, N) zero-pads or truncates the spectrum to M rows and N columns before the inverse.
  • ifft2(X, SIZE) accepts a scalar or two-element vector describing the transform lengths.
  • ifft2(..., 'symmetric') discards tiny imaginary parts and returns a real matrix when the spectrum is conjugate-symmetric. 'nonsymmetric' keeps the complex result.
  • Higher-dimensional inputs are processed slice-by-slice across trailing dimensions.
  • Empty sizes and zero padding mirror MATLAB behaviour, producing empty outputs when any requested length is zero.

Examples of using the ifft2 function in MATLAB / RunMat

Reconstructing an image patch from its 2-D spectrum

F = [10  -2  0  -2;
     -4   0  0   0];
x = ifft2(F);

Expected output:

x =
    1.0000    2.0000
    3.0000    4.0000

Zero-padding before the inverse transform

F = fft2([1 0; 0 1], 4, 4);
spatial = ifft2(F, 4, 4);

spatial is a 4×4 matrix representing the zero-padded impulse response.

Supplying transform lengths with a size vector

Y = fft2(rand(3,4));
X = ifft2(Y, [5 2]);   % pad rows to 5, truncate columns to 2

Forcing a real-valued result with 'symmetric'

F = fft2([1 2; 3 4]);
realImage = ifft2(F, 'symmetric');

realImage equals the original matrix and has no residual imaginary values.

Running ifft2 on gpuArray inputs

G = gpuArray(fft2(peaks(64)));
spatial = ifft2(G);
result = gather(spatial);

When the provider exposes ifft_dim, both passes execute on the GPU. Otherwise RunMat gathers G and finishes on the host transparently.

Recovering each slice of a volume

spectra = fft2(rand(16, 16, 10));
volume = ifft2(spectra);

Every 16×16 slice along the third dimension is reconstructed independently.

GPU residency in RunMat (Do I need gpuArray?)

You usually do not need to call gpuArray manually. RunMat’s native acceleration layer keeps intermediate tensors on the GPU whenever the provider implements ifft_dim. If the provider lacks that hook (or detects an unsupported length), RunMat gathers the input once, executes the inverse transform on the CPU with rustfft, and returns a MATLAB-compatible result automatically.

FAQ

  1. Is ifft2(X) equivalent to ifft(ifft(X, [], 1), [], 2)?
    Yes. RunMat literally performs two sequential 1-D inverse transforms so the behaviour matches MATLAB exactly.

  2. How do zero-length sizes behave?
    Passing 0 for either transform length produces an output with zero elements along that dimension, just like MATLAB.

  3. Can I mix [] with explicit sizes (e.g., ifft2(X, [], 64))?
    Yes. [] leaves that dimension unchanged while the other argument controls padding or truncation.

  4. What does the 'symmetric' flag do?
    It tells RunMat to coerce the result to real values, assuming the spectrum is conjugate-symmetric. Imaginary parts are dropped.

  5. What happens when the input is real-valued?
    RunMat promotes the data to complex with zero imaginary parts before applying the inverse. The output can still be coerced to real with 'symmetric'.

  6. Will ifft2 run on the GPU automatically?
    Yes when the active provider exposes ifft_dim. Otherwise the runtime gathers to the host and evaluates the inverse using rustfft.

  7. Does ifft2 normalise the result?
    Yes. The builtin divides by the product of the transform lengths so that ifft2(fft2(X)) reproduces X.

  8. Can I pass gpuArray size vectors or symmetry flags?
    No. Length arguments must be host scalars or vectors, and the symmetry flag must be a host string, mirroring MATLAB’s restrictions.

  9. How are higher-dimensional arrays handled?
    Transformations are applied to every 2-D slice defined by the first two dimensions; trailing dimensions are preserved unchanged.

  10. Does 'nonsymmetric' change the result?
    It simply states the default behaviour (return complex outputs) but is accepted for MATLAB compatibility.

See Also

fft2, ifft, fft, gpuArray, gather

Source & Feedback

  • Full source: crates/runmat-runtime/src/builtins/math/fft/ifft2.rs
  • Found an issue? Open a ticket with a minimal reproduction.