code: def correlate(in1, in2, mode="full", method="auto"):
      r"""
      Cross-correlate two N-dimensional arrays.
  
      Cross-correlate `in1` and `in2`, with the output size determined by the
      `mode` argument.
  
      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 cross-correlation
             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.
      method : str {'auto', 'direct', 'fft'}, optional
          A string indicating which method to use to calculate the correlation.
  
          ``direct``
             The correlation is determined directly from sums, the definition of
             correlation.
          ``fft``
             The Fast Fourier Transform is used to perform the correlation more
             quickly (only available for numerical arrays.)
          ``auto``
             Automatically chooses direct or Fourier method based on an estimate
             of which is faster (default).  See `convolve` Notes for more detail.
  
             .. versionadded:: 0.19.0
  
      Returns
      -------
      correlate : array
          An N-dimensional array containing a subset of the discrete linear
          cross-correlation of `in1` with `in2`.
  
      See Also
      --------
      choose_conv_method : contains more documentation on `method`.
      correlation_lags : calculates the lag / displacement indices array for 1D
          cross-correlation.
  
      Notes
      -----
      The correlation z of two d-dimensional arrays x and y is defined as::
  
          z[...,k,...] = sum[..., i_l, ...] x[..., i_l,...] * conj(y[..., i_l - k,...])
  
      This way, if x and y are 1-D arrays and ``z = correlate(x, y, 'full')``
      then
  
      .. math::
  
            z[k] = (x * y)(k - N + 1)
                 = \sum_{l=0}^{||x||-1}x_l y_{l-k+N-1}^{*}
  
      for :math:`k = 0, 1, ..., ||x|| + ||y|| - 2`
  
      where :math:`||x||` is the length of ``x``, :math:`N = \max(||x||,||y||)`,
      and :math:`y_m` is 0 when m is outside the range of y.
  
      ``method='fft'`` only works for numerical arrays as it relies on
      `fftconvolve`. In certain cases (i.e., arrays of objects or when
      rounding integers can lose precision), ``method='direct'`` is always used.
  
      When using "same" mode with even-length inputs, the outputs of `correlate`
      and `correlate2d` differ: There is a 1-index offset between them.
  
      Examples
      --------
      Implement a matched filter using cross-correlation, to recover a signal
      that has passed through a noisy channel.
  
      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()
  
      >>> sig = np.repeat([0., 1., 1., 0., 1., 0., 0., 1.], 128)
      >>> sig_noise = sig + rng.standard_normal(len(sig))
      >>> corr = signal.correlate(sig_noise, np.ones(128), mode='same') / 128
  
      >>> clock = np.arange(64, len(sig), 128)
      >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, sharex=True)
      >>> ax_orig.plot(sig)
      >>> ax_orig.plot(clock, sig[clock], 'ro')
      >>> ax_orig.set_title('Original signal')
      >>> ax_noise.plot(sig_noise)
      >>> ax_noise.set_title('Signal with noise')
      >>> ax_corr.plot(corr)
      >>> ax_corr.plot(clock, corr[clock], 'ro')
      >>> ax_corr.axhline(0.5, ls=':')
      >>> ax_corr.set_title('Cross-correlated with rectangular pulse')
      >>> ax_orig.margins(0, 0.1)
      >>> fig.tight_layout()
      >>> plt.show()
  
      Compute the cross-correlation of a noisy signal with the original signal.
  
      >>> x = np.arange(128) / 128
      >>> sig = np.sin(2 * np.pi * x)
      >>> sig_noise = sig + rng.standard_normal(len(sig))
      >>> corr = signal.correlate(sig_noise, sig)
      >>> lags = signal.correlation_lags(len(sig), len(sig_noise))
      >>> corr /= np.max(corr)
  
      >>> fig, (ax_orig, ax_noise, ax_corr) = plt.subplots(3, 1, figsize=(4.8, 4.8))
      >>> ax_orig.plot(sig)
      >>> ax_orig.set_title('Original signal')
      >>> ax_orig.set_xlabel('Sample Number')
      >>> ax_noise.plot(sig_noise)
      >>> ax_noise.set_title('Signal with noise')
      >>> ax_noise.set_xlabel('Sample Number')
      >>> ax_corr.plot(lags, corr)
      >>> ax_corr.set_title('Cross-correlated signal')
      >>> ax_corr.set_xlabel('Lag')
      >>> ax_orig.margins(0, 0.1)
      >>> ax_noise.margins(0, 0.1)
      >>> ax_corr.margins(0, 0.1)
      >>> fig.tight_layout()
      >>> plt.show()
  
      """
      in1 = np.asarray(in1)
      in2 = np.asarray(in2)
  
      if in1.ndim == in2.ndim == 0:
          return in1 * in2.conj()
      elif in1.ndim != in2.ndim:
          raise ValueError(
              "in1 and in2 should have the same dimensionality"
          )
  
      # Don't use _valfrommode, since correlate should not accept numeric modes
      try:
          val = _modedict[mode]
      except KeyError as e:
          raise ValueError(
              "Acceptable mode flags are 'valid'," " 'same', or 'full'."
          ) from e
  
      # this either calls fftconvolve or this function with method=='direct'
      if method in ("fft", "auto"):
          return convolve(in1, _reverse_and_conj(in2), mode, method)
  
      elif method == "direct":
          # fastpath to faster numpy.correlate for 1d inputs when possible
          if _np_conv_ok(in1, in2, mode):
              return np.correlate(in1, in2, mode)
  
          # _correlateND is far slower when in2.size > in1.size, so swap them
          # and then undo the effect afterward if mode == 'full'.  Also, it fails
          # with 'valid' mode if in2 is larger than in1, so swap those, too.
          # Don't swap inputs for 'same' mode, since shape of in1 matters.
          swapped_inputs = (
              (mode == "full")
              and (in2.size > in1.size)
              or _inputs_swap_needed(mode, in1.shape, in2.shape)
          )
  
          if swapped_inputs:
              in1, in2 = in2, in1
  
          if mode == "valid":
              ps = [i - j + 1 for i, j in zip(in1.shape, in2.shape)]
              out = np.empty(ps, in1.dtype)
  
              z = sigtools._correlateND(in1, in2, out, val)
  
          else:
              ps = [i + j - 1 for i, j in zip(in1.shape, in2.shape)]
  
              # zero pad input
              in1zpadded = np.zeros(ps, in1.dtype)
              sc = tuple(slice(0, i) for i in in1.shape)
              in1zpadded[sc] = in1.copy()
  
              if mode == "full":
                  out = np.empty(ps, in1.dtype)
              elif mode == "same":
                  out = np.empty(in1.shape, in1.dtype)
  
              z = sigtools._correlateND(in1zpadded, in2, out, val)
  
          if swapped_inputs:
              # Reverse and conjugate to undo the effect of swapping inputs
              z = _reverse_and_conj(z)
  
          return z
  
      else:
          raise ValueError(
              "Acceptable method flags are 'auto',"
              " 'direct', or 'fft'."
          )
  
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 4 for calling a global function with example usage: correlate(in1, in2, mode, method) and returns: unknown, convolve, z, np