fix to fft, implement fft2, rfft, and irfft for mlx (#20781)

keras/src/backend/mlx/math.py

@@ -54,24 +54,56 @@ def extract_sequences(x, sequence_length, sequence_stride):
     return x.reshape(*batch_shape, frames, sequence_length)
 
 
+def _get_complex_tensor_from_tuple(x):
+    if not isinstance(x, (tuple, list)) or len(x) != 2:
+        raise ValueError(
+            "Input `x` should be a tuple of two tensors - real and imaginary."
+            f"Received: x={x}"
+        )
+    real, imag = x
+    real = convert_to_tensor(real)
+    imag = convert_to_tensor(imag)
+    # Check shapes.
+    if real.shape != imag.shape:
+        raise ValueError(
+            "Input `x` should be a tuple of two tensors - real and imaginary."
+            "Both the real and imaginary parts should have the same shape. "
+            f"Received: x[0].shape = {real.shape}, x[1].shape = {imag.shape}"
+        )
+    # Ensure dtype is float.
+    if not mx.issubdtype(real.dtype, mx.floating) or not mx.issubdtype(
+        imag.dtype, mx.floating
+    ):
+        raise ValueError(
+            "At least one tensor in input `x` is not of type float."
+            f"Received: x={x}."
+        )
+    complex_input = mx.add(real, 1j * imag)
+    return complex_input
+
+
 def fft(x):
-    x = convert_to_tensor(x)
-    return mx.fft(x)
+    x = _get_complex_tensor_from_tuple(x)
+    complex_output = mx.fft.fft(x)
+    return mx.real(complex_output), mx.imag(complex_output)
 
 
 def fft2(x):
-    # TODO: https://ml-explore.github.io/mlx/build/html/python/fft.html#fft
-    raise NotImplementedError("fft not yet implemented in mlx")
+    x = _get_complex_tensor_from_tuple(x)
+    complex_output = mx.fft.fft2(x)
+    return mx.real(complex_output), mx.imag(complex_output)
 
 
 def rfft(x, fft_length=None):
-    # TODO: https://ml-explore.github.io/mlx/build/html/python/fft.html#fft
-    raise NotImplementedError("fft not yet implemented in mlx")
+    x = convert_to_tensor(x)
+    complex_output = mx.fft.rfft(x, n=fft_length)
+    return mx.real(complex_output), mx.imag(complex_output)
 
 
 def irfft(x, fft_length=None):
-    # TODO: https://ml-explore.github.io/mlx/build/html/python/fft.html#fft
-    raise NotImplementedError("fft not yet implemented in mlx")
+    x = _get_complex_tensor_from_tuple(x)
+    real_output = mx.fft.irfft(x, n=fft_length)
+    return real_output
 
 
 def stft(