fix a bug for repeated axes in N-D c2c FFT

Author: Vahid Tavanashad

.github/workflows/build-with-clang.yml

@@ -13,7 +13,7 @@ jobs:
 
     strategy:
       matrix:
-        python: ["3.9", "3.10", "3.11", "3.12", "3.13"]
+        python: ["3.10", "3.11", "3.12", "3.13"]
         numpy_version: ["numpy'<2'", "numpy'>=2'"]
 
     env:

.github/workflows/build_pip.yaml

@@ -22,7 +22,7 @@ jobs:
 
     strategy:
       matrix:
-        python: ['3.9', '3.10', '3.11', '3.12', '3.13']
+        python: ['3.10', '3.11', '3.12', '3.13']
         use_pre: ["", "--pre"]
 
     steps:

CHANGELOG.md

@@ -16,6 +16,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Fixed
 * Fixed a bug for N-D FFTs when both `s` and `out` are given [gh-185](https://github.com/IntelPython/mkl_fft/pull/185)
+* Fixed a bug for a case when a repeated indices is passed for axes keyword in N-dimensional FFT [gh-215](https://github.com/IntelPython/mkl_fft/pull/215)
 
 ## [2.0.0] - 2025-06-03
 

mkl_fft/_fft_utils.py

@@ -44,23 +44,19 @@ def _check_norm(norm):
         )
 
 
-def _check_shapes_for_direct(xs, shape, axes):
+def _check_shapes_for_direct(s, shape, axes):
     if len(axes) > 7:  # Intel MKL supports up to 7D
         return False
-    if not (len(xs) == len(shape)):
-        # full-dimensional transform
+    if len(s) != len(shape):
+        # not a full-dimensional transform
         return False
-    if not (len(set(axes)) == len(axes)):
+    if len(set(axes)) != len(axes):
         # repeated axes
         return False
-    for xsi, ai in zip(xs, axes):
-        try:
-            sh_ai = shape[ai]
-        except IndexError:
-            raise ValueError("Invalid axis (%d) specified" % ai)
-
-        if not (xsi == sh_ai):
-            return False
+    new_shape = tuple(shape[ax] for ax in axes)
+    if tuple(s) != new_shape:
+        # trimming or padding is needed
+        return False
     return True
 
 
@@ -78,30 +74,6 @@ def _compute_fwd_scale(norm, n, shape):
         return np.sqrt(fsc)
 
 
-def _cook_nd_args(a, s=None, axes=None, invreal=False):
-    if s is None:
-        shapeless = True
-        if axes is None:
-            s = list(a.shape)
-        else:
-            try:
-                s = [a.shape[i] for i in axes]
-            except IndexError:
-                # fake s designed to trip the ValueError further down
-                s = range(len(axes) + 1)
-                pass
-    else:
-        shapeless = False
-    s = list(s)
-    if axes is None:
-        axes = list(range(-len(s), 0))
-    if len(s) != len(axes):
-        raise ValueError("Shape and axes have different lengths.")
-    if invreal and shapeless:
-        s[-1] = (a.shape[axes[-1]] - 1) * 2
-    return s, axes
-
-
 # copied from scipy.fft module
 # https://github.com/scipy/scipy/blob/main/scipy/fft/_pocketfft/helper.py
 def _datacopied(arr, original):
@@ -129,89 +101,7 @@ def _flat_to_multi(ind, shape):
     return m_ind
 
 
-# copied from scipy.fftpack.helper
-def _init_nd_shape_and_axes(x, shape, axes):
-    """Handle shape and axes arguments for n-dimensional transforms.
-    Returns the shape and axes in a standard form, taking into account negative
-    values and checking for various potential errors.
-    Parameters
-    ----------
-    x : array_like
-        The input array.
-    shape : int or array_like of ints or None
-        The shape of the result.  If both `shape` and `axes` (see below) are
-        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
-        not None, then `shape` is ``scipy.take(x.shape, axes, axis=0)``.
-        If `shape` is -1, the size of the corresponding dimension of `x` is
-        used.
-    axes : int or array_like of ints or None
-        Axes along which the calculation is computed.
-        The default is over all axes.
-        Negative indices are automatically converted to their positive
-        counterpart.
-    Returns
-    -------
-    shape : array
-        The shape of the result. It is a 1D integer array.
-    axes : array
-        The shape of the result. It is a 1D integer array.
-    """
-    x = np.asarray(x)
-    noshape = shape is None
-    noaxes = axes is None
-
-    if noaxes:
-        axes = np.arange(x.ndim, dtype=np.intc)
-    else:
-        axes = np.atleast_1d(axes)
-
-    if axes.size == 0:
-        axes = axes.astype(np.intc)
-
-    if not axes.ndim == 1:
-        raise ValueError("when given, axes values must be a scalar or vector")
-    if not np.issubdtype(axes.dtype, np.integer):
-        raise ValueError("when given, axes values must be integers")
-
-    axes = np.where(axes < 0, axes + x.ndim, axes)
-
-    if axes.size != 0 and (axes.max() >= x.ndim or axes.min() < 0):
-        raise ValueError("axes exceeds dimensionality of input")
-    if axes.size != 0 and np.unique(axes).shape != axes.shape:
-        raise ValueError("all axes must be unique")
-
-    if not noshape:
-        shape = np.atleast_1d(shape)
-    elif np.isscalar(x):
-        shape = np.array([], dtype=np.intc)
-    elif noaxes:
-        shape = np.array(x.shape, dtype=np.intc)
-    else:
-        shape = np.take(x.shape, axes)
-
-    if shape.size == 0:
-        shape = shape.astype(np.intc)
-
-    if shape.ndim != 1:
-        raise ValueError("when given, shape values must be a scalar or vector")
-    if not np.issubdtype(shape.dtype, np.integer):
-        raise ValueError("when given, shape values must be integers")
-    if axes.shape != shape.shape:
-        raise ValueError(
-            "when given, axes and shape arguments have to be of the same length"
-        )
-
-    shape = np.where(shape == -1, np.array(x.shape)[axes], shape)
-    if shape.size != 0 and (shape < 1).any():
-        raise ValueError(f"invalid number of data points ({shape}) specified")
-
-    return shape, axes
-
-
 def _iter_complementary(x, axes, func, kwargs, result):
-    if axes is None:
-        # s and axes are None, direct N-D FFT
-        return func(x, **kwargs, out=result)
     x_shape = x.shape
     nd = x.ndim
     r = list(range(nd))
@@ -260,9 +150,6 @@ def _iter_fftnd(
     direction=+1,
     scale_function=lambda ind: 1.0,
 ):
-    a = np.asarray(a)
-    s, axes = _init_nd_shape_and_axes(a, s, axes)
-
     # Combine the two, but in reverse, to end with the first axis given.
     axes_and_s = list(zip(axes, s))[::-1]
     # We try to use in-place calculations where possible, which is
@@ -309,13 +196,14 @@ def _output_dtype(dt):
 def _pad_array(arr, s, axes):
     """Pads array arr with zeros to attain shape s associated with axes"""
     arr_shape = arr.shape
+    new_shape = tuple(arr_shape[ax] for ax in axes)
+    if tuple(s) == new_shape:
+        return arr
+
     no_padding = True
     pad_widths = [(0, 0)] * len(arr_shape)
     for si, ai in zip(s, axes):
-        try:
-            shp_i = arr_shape[ai]
-        except IndexError:
-            raise ValueError(f"Invalid axis {ai} specified")
+        shp_i = arr_shape[ai]
         if si > shp_i:
             no_padding = False
             pad_widths[ai] = (0, si - shp_i)
@@ -345,14 +233,14 @@ def _trim_array(arr, s, axes):
     """
 
     arr_shape = arr.shape
+    new_shape = tuple(arr_shape[ax] for ax in axes)
+    if tuple(s) == new_shape:
+        return arr
+
     no_trim = True
     ind = [slice(None, None, None)] * len(arr_shape)
     for si, ai in zip(s, axes):
-        try:
-            shp_i = arr_shape[ai]
-        except IndexError:
-            raise ValueError(f"Invalid axis {ai} specified")
-        if si < shp_i:
+        if si < arr_shape[ai]:
             no_trim = False
             ind[ai] = slice(None, si, None)
     if no_trim:
@@ -383,16 +271,11 @@ def _c2c_fftnd_impl(
     if direction not in [-1, +1]:
         raise ValueError("Direction of FFT should +1 or -1")
 
+    x = np.asarray(x)
     valid_dtypes = [np.complex64, np.complex128, np.float32, np.float64]
     # _direct_fftnd requires complex type, and full-dimensional transform
-    if isinstance(x, np.ndarray) and x.size != 0 and x.ndim > 1:
-        _direct = s is None and axes is None
-        if _direct:
-            _direct = x.ndim <= 7  # Intel MKL only supports FFT up to 7D
-        if not _direct:
-            xs, xa = _cook_nd_args(x, s, axes)
-            if _check_shapes_for_direct(xs, x.shape, xa):
-                _direct = True
+    if x.size != 0 and x.ndim > 1:
+        _direct = _check_shapes_for_direct(s, x.shape, axes)
         _direct = _direct and x.dtype in valid_dtypes
     else:
         _direct = False
@@ -405,14 +288,23 @@ def _c2c_fftnd_impl(
             out=out,
         )
     else:
-        if s is None and x.dtype in valid_dtypes:
-            x = np.asarray(x)
+        new_shape = tuple(x.shape[ax] for ax in axes)
+        if (
+            tuple(s) == new_shape
+            and x.dtype in valid_dtypes
+            and len(set(axes)) == len(axes)
+        ):
             if out is None:
                 res = np.empty_like(x, dtype=_output_dtype(x.dtype))
             else:
                 _validate_out_array(out, x, _output_dtype(x.dtype))
                 res = out
 
+            # MKL is capable of doing batch N-D FFT, it is not required to
+            # manually loop over the batches as done in _iter_complementary and
+            # it is the reason for bad performance mentioned in the gh-issue-#67
+            # TODO: implement a batch N-D FFT using MKL
+            # _iter_complementary performs batches of N-D FFT
             return _iter_complementary(
                 x,
                 axes,
@@ -434,14 +326,9 @@ def _c2c_fftnd_impl(
 
 def _r2c_fftnd_impl(x, s=None, axes=None, fsc=1.0, out=None):
     a = np.asarray(x)
-    no_trim = (s is None) and (axes is None)
-    s, axes = _cook_nd_args(a, s, axes)
-    axes = [ax + a.ndim if ax < 0 else ax for ax in axes]
     la = axes[-1]
-
     # trim array, so that rfft avoids doing unnecessary computations
-    if not no_trim:
-        a = _trim_array(a, s, axes)
+    a = _trim_array(a, s, axes)
 
     # last axis is not included since we calculate r2c FFT separately
     # and not in the loop
@@ -453,13 +340,11 @@ def _r2c_fftnd_impl(x, s=None, axes=None, fsc=1.0, out=None):
     a = _r2c_fft1d_impl(a, n=s[-1], axis=la, fsc=fsc, out=res)
     res = a
     if len(s) > 1:
-
         len_axes = len(axes)
         if len(set(axes)) == len_axes and len_axes == a.ndim and len_axes > 2:
-            if not no_trim:
-                ss = list(s)
-                ss[-1] = a.shape[la]
-                a = _pad_array(a, tuple(ss), axes)
+            ss = list(s)
+            ss[-1] = a.shape[la]
+            a = _pad_array(a, tuple(ss), axes)
             # a series of ND c2c FFTs along last axis
             ss, aa = _remove_axis(s, axes, -1)
             ind = [slice(None, None, 1)] * len(s)
@@ -494,17 +379,12 @@ def _r2c_fftnd_impl(x, s=None, axes=None, fsc=1.0, out=None):
 
 def _c2r_fftnd_impl(x, s=None, axes=None, fsc=1.0, out=None):
     a = np.asarray(x)
-    no_trim = (s is None) and (axes is None)
-    s, axes = _cook_nd_args(a, s, axes, invreal=True)
-    axes = [ax + a.ndim if ax < 0 else ax for ax in axes]
     la = axes[-1]
-    if not no_trim:
-        a = _trim_array(a, s, axes)
     if len(s) > 1:
         len_axes = len(axes)
         if len(set(axes)) == len_axes and len_axes == a.ndim and len_axes > 2:
-            if not no_trim:
-                a = _pad_array(a, s, axes)
+            a = _trim_array(a, s, axes)
+            a = _pad_array(a, s, axes)
             # a series of ND c2c FFTs along last axis
             # due to need to write into a, we must copy
             a = a if _datacopied(a, x) else a.copy()
@@ -521,8 +401,8 @@ def _c2r_fftnd_impl(x, s=None, axes=None, fsc=1.0, out=None):
                 tind = tuple(ind)
                 a_inp = a[tind]
                 # out has real dtype and cannot be used in intermediate steps
-                # ss and aa are reversed since np.irfftn uses forward order but
-                # np.ifftn uses reverse order see numpy-gh-28950
+                # ss and aa are reversed since np.fft.irfftn uses forward order
+                # but np.fft.ifftn uses reverse order see numpy-gh-28950
                 _ = _c2c_fftnd_impl(
                     a_inp, s=ss[::-1], axes=aa[::-1], out=a_inp, direction=-1
                 )