get rid of overwrite_x kwarg in mkl_fft, instead utilize out kwarg

Author: Vahid Tavanashad

README.md

@@ -53,11 +53,11 @@ While using these interfaces is the easiest way to leverage `mk_fft`, one can al
 
 ### complex-to-complex (c2c) transforms:
 
-`fft(x, n=None, axis=-1, overwrite_x=False, fwd_scale=1.0, out=None)` - 1D FFT, similar to `scipy.fft.fft`
+`fft(x, n=None, axis=-1, fwd_scale=1.0, out=None)` - 1D FFT, similar to `numpy.fft.fft`
 
-`fft2(x, s=None, axes=(-2, -1), overwrite_x=False, fwd_scale=1.0, out=None)` - 2D FFT, similar to `scipy.fft.fft2`
+`fft2(x, s=None, axes=(-2, -1), fwd_scale=1.0, out=None)` - 2D FFT, similar to `numpy.fft.fft2`
 
-`fftn(x, s=None, axes=None, overwrite_x=False, fwd_scale=1.0, out=None)` - ND FFT, similar to `scipy.fft.fftn`
+`fftn(x, s=None, axes=None, fwd_scale=1.0, out=None)` - ND FFT, similar to `numpy.fft.fftn`
 
 and similar inverse FFT (`ifft*`) functions.
 

mkl_fft/_fft_utils.py

@@ -262,23 +262,43 @@ def _iter_fftnd(
     axes=None,
     out=None,
     direction=+1,
-    overwrite_x=False,
-    scale_function=lambda n, ind: 1.0,
+    scale_function=lambda ind: 1.0,
 ):
     a = np.asarray(a)
     s, axes = _init_nd_shape_and_axes(a, s, axes)
-    ovwr = overwrite_x
-    for ii in reversed(range(len(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
+    # everywhere except when the size changes after the first FFT.
+    size_changes = [axis for axis, n in axes_and_s[1:] if a.shape[axis] != n]
+
+    # If there are any size changes, we cannot use out
+    res = None if size_changes else out
+    for ind, (axis, n) in enumerate(axes_and_s):
+        if axis in size_changes:
+            if axis == size_changes[-1]:
+                # Last size change, so any output should now be OK
+                # (an error will be raised if not), and if no output is
+                # required, we want a freshly allocated array of the right size.
+                res = out
+            elif res is not None and n < res.shape[axis]:
+                # For an intermediate step where we return fewer elements, we
+                # can use a smaller view of the previous array.
+                res = res[(slice(None),) * axis + (slice(n),)]
+            else:
+                # If we need more elements, we cannot use res.
+                res = None
         a = _c2c_fft1d_impl(
             a,
-            n=s[ii],
-            axis=axes[ii],
-            overwrite_x=ovwr,
+            n=n,
+            axis=axis,
             direction=direction,
-            fsc=scale_function(s[ii], ii),
-            out=out,
+            fsc=scale_function(ind),
+            out=res,
         )
-        ovwr = True
+        # Default output for next iteration.
+        res = a
     return a
 
 
@@ -360,7 +380,6 @@ def _c2c_fftnd_impl(
     x,
     s=None,
     axes=None,
-    overwrite_x=False,
     direction=+1,
     fsc=1.0,
     out=None,
@@ -385,7 +404,6 @@ def _c2c_fftnd_impl(
     if _direct:
         return _direct_fftnd(
             x,
-            overwrite_x=overwrite_x,
             direction=direction,
             fsc=fsc,
             out=out,
@@ -403,11 +421,7 @@ def _c2c_fftnd_impl(
                 x,
                 axes,
                 _direct_fftnd,
-                {
-                    "overwrite_x": overwrite_x,
-                    "direction": direction,
-                    "fsc": fsc,
-                },
+                {"direction": direction, "fsc": fsc},
                 res,
             )
         else:
@@ -418,97 +432,122 @@ def _c2c_fftnd_impl(
                 axes=axes,
                 out=out,
                 direction=direction,
-                overwrite_x=overwrite_x,
-                scale_function=lambda n, i: fsc if i == 0 else 1.0,
+                scale_function=lambda i: fsc if i == 0 else 1.0,
             )
 
 
 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)
+
+    # last axis is not included since we calculate r2c FFT separately
+    # and not in the loop
+    axes_and_s = list(zip(axes, s))[-2::-1]
+    size_changes = [axis for axis, n in axes_and_s if a.shape[axis] != n]
+    res = None if size_changes else out
+
     # r2c along last axis
-    a = _r2c_fft1d_impl(a, n=s[-1], axis=la, fsc=fsc, out=out)
+    a = _r2c_fft1d_impl(a, n=s[-1], axis=la, fsc=fsc, out=res)
+    res = a
     if len(s) > 1:
-        if not no_trim:
-            ss = list(s)
-            ss[-1] = a.shape[la]
-            a = _pad_array(a, tuple(ss), axes)
+
         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)
             # a series of ND c2c FFTs along last axis
             ss, aa = _remove_axis(s, axes, -1)
-            ind = [
-                slice(None, None, 1),
-            ] * len(s)
+            ind = [slice(None, None, 1)] * len(s)
             for ii in range(a.shape[la]):
                 ind[la] = ii
                 tind = tuple(ind)
                 a_inp = a[tind]
-                res = out[tind] if out is not None else None
-                a_res = _c2c_fftnd_impl(
-                    a_inp, s=ss, axes=aa, overwrite_x=True, direction=1, out=res
-                )
-                if a_res is not a_inp:
-                    a[tind] = a_res  # copy in place
+                res = out[tind] if out is not None else a_inp
+                _ = _c2c_fftnd_impl(a_inp, s=ss, axes=aa, direction=1, out=res)
+            if out is not None:
+                a = out
         else:
+            # another size_changes check is needed if there are repeated axes
+            # of last axis, since since FFT changes the shape along last axis
+            size_changes = [
+                axis for axis, n in axes_and_s if a.shape[axis] != n
+            ]
+
             # a series of 1D c2c FFTs along all axes except last
-            for ii in range(len(axes) - 2, -1, -1):
-                a = _c2c_fft1d_impl(a, s[ii], axes[ii], overwrite_x=True)
+            for axis, n in axes_and_s:
+                if axis in size_changes:
+                    if axis == size_changes[-1]:
+                        res = out
+                    elif res is not None and n < res.shape[axis]:
+                        res = res[(slice(None),) * axis + (slice(n),)]
+                    else:
+                        res = None
+                a = _c2c_fft1d_impl(a, n, axis, out=res)
+                res = a
     return a
 
 
 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:
-        if not no_trim:
-            a = _pad_array(a, s, axes)
-        ovr_x = True if _datacopied(a, x) else False
         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 series of ND c2c FFTs along last axis
             # due to need to write into a, we must copy
-            if not ovr_x:
-                a = a.copy()
-                ovr_x = True
+            a = a if _datacopied(a, x) else a.copy()
             if not np.issubdtype(a.dtype, np.complexfloating):
                 # complex output will be copied to input, copy is needed
                 if a.dtype == np.float32:
                     a = a.astype(np.complex64)
                 else:
                     a = a.astype(np.complex128)
-                ovr_x = True
             ss, aa = _remove_axis(s, axes, -1)
-            ind = [
-                slice(None, None, 1),
-            ] * len(s)
+            ind = [slice(None, None, 1)] * len(s)
             for ii in range(a.shape[la]):
                 ind[la] = ii
                 tind = tuple(ind)
                 a_inp = a[tind]
                 # out has real dtype and cannot be used in intermediate steps
-                a_res = _c2c_fftnd_impl(
-                    a_inp, s=ss, axes=aa, overwrite_x=True, direction=-1
+                # ss and aa are reversed since np.irfftn uses forward order but
+                # np.ifftn uses reverse order see numpy-gh-28950
+                _ = _c2c_fftnd_impl(
+                    a_inp, s=ss[::-1], axes=aa[::-1], out=a_inp, direction=-1
                 )
-                if a_res is not a_inp:
-                    a[tind] = a_res  # copy in place
         else:
             # a series of 1D c2c FFTs along all axes except last
-            for ii in range(len(axes) - 1):
-                # out has real dtype and cannot be used in intermediate steps
-                a = _c2c_fft1d_impl(
-                    a, s[ii], axes[ii], overwrite_x=ovr_x, direction=-1
-                )
-                ovr_x = True
+            # forward order, see numpy-gh-28950
+            axes_and_s = list(zip(axes, s))[:-1]
+            size_changes = [
+                axis for axis, n in axes_and_s[1:] if a.shape[axis] != n
+            ]
+            # out has real dtype cannot be used for intermediate steps
+            res = None
+            for axis, n in axes_and_s:
+                if axis in size_changes:
+                    if res is not None and n < res.shape[axis]:
+                        # pylint: disable=unsubscriptable-object
+                        res = res[(slice(None),) * axis + (slice(n),)]
+                    else:
+                        res = None
+                a = _c2c_fft1d_impl(a, n, axis, out=res, direction=-1)
+                res = a
     # c2r along last axis
     a = _c2r_fft1d_impl(a, n=s[-1], axis=la, fsc=fsc, out=out)
     return a

mkl_fft/_mkl_fft.py

@@ -45,85 +45,57 @@
 ]
 
 
-def fft(x, n=None, axis=-1, out=None, overwrite_x=False, fwd_scale=1.0):
+def fft(x, n=None, axis=-1, fwd_scale=1.0, out=None):
     return _c2c_fft1d_impl(
-        x,
-        n=n,
-        axis=axis,
-        out=out,
-        overwrite_x=overwrite_x,
-        direction=+1,
-        fsc=fwd_scale,
+        x, n=n, axis=axis, out=out, direction=+1, fsc=fwd_scale
     )
 
 
-def ifft(x, n=None, axis=-1, out=None, overwrite_x=False, fwd_scale=1.0):
+def ifft(x, n=None, axis=-1, fwd_scale=1.0, out=None):
     return _c2c_fft1d_impl(
-        x,
-        n=n,
-        axis=axis,
-        out=out,
-        overwrite_x=overwrite_x,
-        direction=-1,
-        fsc=fwd_scale,
+        x, n=n, axis=axis, out=out, direction=-1, fsc=fwd_scale
     )
 
 
-def fft2(x, s=None, axes=(-2, -1), out=None, overwrite_x=False, fwd_scale=1.0):
-    return fftn(
-        x, s=s, axes=axes, out=out, overwrite_x=overwrite_x, fwd_scale=fwd_scale
-    )
+def fft2(x, s=None, axes=(-2, -1), fwd_scale=1.0, out=None):
+    return fftn(x, s=s, axes=axes, out=out, fwd_scale=fwd_scale)
 
 
-def ifft2(x, s=None, axes=(-2, -1), out=None, overwrite_x=False, fwd_scale=1.0):
-    return ifftn(
-        x, s=s, axes=axes, out=out, overwrite_x=overwrite_x, fwd_scale=fwd_scale
-    )
+def ifft2(x, s=None, axes=(-2, -1), fwd_scale=1.0, out=None):
+    return ifftn(x, s=s, axes=axes, out=out, fwd_scale=fwd_scale)
 
 
-def fftn(x, s=None, axes=None, out=None, overwrite_x=False, fwd_scale=1.0):
+def fftn(x, s=None, axes=None, fwd_scale=1.0, out=None):
     return _c2c_fftnd_impl(
-        x,
-        s=s,
-        axes=axes,
-        out=out,
-        overwrite_x=overwrite_x,
-        direction=+1,
-        fsc=fwd_scale,
+        x, s=s, axes=axes, out=out, direction=+1, fsc=fwd_scale
     )
 
 
-def ifftn(x, s=None, axes=None, out=None, overwrite_x=False, fwd_scale=1.0):
+def ifftn(x, s=None, axes=None, fwd_scale=1.0, out=None):
     return _c2c_fftnd_impl(
-        x,
-        s=s,
-        axes=axes,
-        out=out,
-        overwrite_x=overwrite_x,
-        direction=-1,
-        fsc=fwd_scale,
+        x, s=s, axes=axes, out=out, direction=-1, fsc=fwd_scale
     )
 
 
-def rfft(x, n=None, axis=-1, out=None, fwd_scale=1.0):
+def rfft(x, n=None, axis=-1, fwd_scale=1.0, out=None):
     return _r2c_fft1d_impl(x, n=n, axis=axis, out=out, fsc=fwd_scale)
 
 
-def irfft(x, n=None, axis=-1, out=None, fwd_scale=1.0):
+def irfft(x, n=None, axis=-1, fwd_scale=1.0, out=None):
     return _c2r_fft1d_impl(x, n=n, axis=axis, out=out, fsc=fwd_scale)
 
 
-def rfft2(x, s=None, axes=(-2, -1), out=None, fwd_scale=1.0):
+def rfft2(x, s=None, axes=(-2, -1), fwd_scale=1.0, out=None):
     return rfftn(x, s=s, axes=axes, out=out, fwd_scale=fwd_scale)
 
 
-def irfft2(x, s=None, axes=(-2, -1), out=None, fwd_scale=1.0):
+def irfft2(x, s=None, axes=(-2, -1), fwd_scale=1.0, out=None):
     return irfftn(x, s=s, axes=axes, out=out, fwd_scale=fwd_scale)
 
 
-def rfftn(x, s=None, axes=None, out=None, fwd_scale=1.0):
+def rfftn(x, s=None, axes=None, fwd_scale=1.0, out=None):
     return _r2c_fftnd_impl(x, s=s, axes=axes, out=out, fsc=fwd_scale)
 
 
-def irfftn(x, s=None, axes=None, out=None, fwd_scale=1.0):
+def irfftn(x, s=None, axes=None, fwd_scale=1.0, out=None):
     return _c2r_fftnd_impl(x, s=s, axes=axes, out=out, fsc=fwd_scale)