code: def fftconvolve(in1, in2, mode="full", axes=None):
      """Convolve two N-dimensional arrays using FFT.
  
      Convolve `in1` and `in2` using the fast Fourier transform method, with
      the output size determined by the `mode` argument.
  
      This is generally much faster than `convolve` for large arrays (n > ~500),
      but can be slower when only a few output values are needed, and can only
      output float arrays (int or object array inputs will be cast to float).
  
      As of v0.19, `convolve` automatically chooses this method or the direct
      method based on an estimation of which is faster.
  
      Parameters
      ----------
      in1 : array_like
          First input.
      in2 : array_like
          Second input. Should have the same number of dimensions as `in1`.
      mode : str {'full', 'valid', 'same'}, optional
          A string indicating the size of the output:
  
          ``full``
             The output is the full discrete linear convolution
             of the inputs. (Default)
          ``valid``
             The output consists only of those elements that do not
             rely on the zero-padding. In 'valid' mode, either `in1` or `in2`
             must be at least as large as the other in every dimension.
          ``same``
             The output is the same size as `in1`, centered
             with respect to the 'full' output.
      axes : int or array_like of ints or None, optional
          Axes over which to compute the convolution.
          The default is over all axes.
  
      Returns
      -------
      out : array
          An N-dimensional array containing a subset of the discrete linear
          convolution of `in1` with `in2`.
  
      See Also
      --------
      convolve : Uses the direct convolution or FFT convolution algorithm
                 depending on which is faster.
      oaconvolve : Uses the overlap-add method to do convolution, which is
                   generally faster when the input arrays are large and
                   significantly different in size.
  
      Examples
      --------
      Autocorrelation of white noise is an impulse.
  
      >>> from scipy import signal
      >>> rng = np.random.default_rng()
      >>> sig = rng.standard_normal(1000)
      >>> autocorr = signal.fftconvolve(sig, sig[::-1], mode='full')
  
      >>> import matplotlib.pyplot as plt
      >>> fig, (ax_orig, ax_mag) = plt.subplots(2, 1)
      >>> ax_orig.plot(sig)
      >>> ax_orig.set_title('White noise')
      >>> ax_mag.plot(np.arange(-len(sig)+1,len(sig)), autocorr)
      >>> ax_mag.set_title('Autocorrelation')
      >>> fig.tight_layout()
      >>> fig.show()
  
      Gaussian blur implemented using FFT convolution.  Notice the dark borders
      around the image, due to the zero-padding beyond its boundaries.
      The `convolve2d` function allows for other types of image boundaries,
      but is far slower.
  
      >>> from scipy import misc
      >>> face = misc.face(gray=True)
      >>> kernel = np.outer(signal.windows.gaussian(70, 8),
      ...                   signal.windows.gaussian(70, 8))
      >>> blurred = signal.fftconvolve(face, kernel, mode='same')
  
      >>> fig, (ax_orig, ax_kernel, ax_blurred) = plt.subplots(3, 1,
      ...                                                      figsize=(6, 15))
      >>> ax_orig.imshow(face, cmap='gray')
      >>> ax_orig.set_title('Original')
      >>> ax_orig.set_axis_off()
      >>> ax_kernel.imshow(kernel, cmap='gray')
      >>> ax_kernel.set_title('Gaussian kernel')
      >>> ax_kernel.set_axis_off()
      >>> ax_blurred.imshow(blurred, cmap='gray')
      >>> ax_blurred.set_title('Blurred')
      >>> ax_blurred.set_axis_off()
      >>> fig.show()
  
      """
      in1 = np.asarray(in1)
      in2 = np.asarray(in2)
  
      if in1.ndim == in2.ndim == 0:  # scalar inputs
          return in1 * in2
      elif in1.ndim != in2.ndim:
          raise ValueError(
              "in1 and in2 should have the same dimensionality"
          )
      elif in1.size == 0 or in2.size == 0:  # empty arrays
          return np.array([])
  
      in1, in2, axes = _init_freq_conv_axes(
          in1, in2, mode, axes, sorted_axes=False
      )
  
      s1 = in1.shape
      s2 = in2.shape
  
      shape = [
          max((s1[i], s2[i])) if i not in axes else s1[i] + s2[i] - 1
          for i in range(in1.ndim)
      ]
  
      ret = _freq_domain_conv(in1, in2, axes, shape, calc_fast_len=True)
  
      return _apply_conv_mode(ret, s1, s2, mode, axes)
  
imports: import operator
  import math
  import timeit
  from scipy.spatial import cKDTree
  from .None import sigtools, dlti
  from ._upfirdn import upfirdn, _output_len, _upfirdn_modes
  from scipy import linalg, fft
  from scipy.fft._helper import _init_nd_shape_and_axes
  from scipy._lib._util import prod
  import numpy
  from scipy.special import lambertw
  from .windows import get_window
  from ._arraytools import axis_slice, axis_reverse, odd_ext, even_ext, const_ext
  from .filter_design import cheby1, _validate_sos
  from .fir_filter_design import firwin
  from ._sosfilt import _sosfilt
  import warnings
label_desc: Use image node_id 10 for calling a global function with example usage: fftconvolve(in1, in2, mode, axes) and returns: _apply_conv_mode, unknown, np