code: def irfft(x, n=None, axis=-1, overwrite_x=False):
      """
      Return inverse discrete Fourier transform of real sequence x.
  
      The contents of `x` are interpreted as the output of the `rfft`
      function.
  
      Parameters
      ----------
      x : array_like
          Transformed data to invert.
      n : int, optional
          Length of the inverse Fourier transform.
          If n < x.shape[axis], x is truncated.
          If n > x.shape[axis], x is zero-padded.
          The default results in n = x.shape[axis].
      axis : int, optional
          Axis along which the ifft's are computed; the default is over
          the last axis (i.e., axis=-1).
      overwrite_x : bool, optional
          If True, the contents of `x` can be destroyed; the default is False.
  
      Returns
      -------
      irfft : ndarray of floats
          The inverse discrete Fourier transform.
  
      See Also
      --------
      rfft, ifft, scipy.fft.irfft
  
      Notes
      -----
      The returned real array contains::
  
          [y(0),y(1),...,y(n-1)]
  
      where for n is even::
  
          y(j) = 1/n (sum[k=1..n/2-1] (x[2*k-1]+sqrt(-1)*x[2*k])
                                       * exp(sqrt(-1)*j*k* 2*pi/n)
                      + c.c. + x[0] + (-1)**(j) x[n-1])
  
      and for n is odd::
  
          y(j) = 1/n (sum[k=1..(n-1)/2] (x[2*k-1]+sqrt(-1)*x[2*k])
                                       * exp(sqrt(-1)*j*k* 2*pi/n)
                      + c.c. + x[0])
  
      c.c. denotes complex conjugate of preceding expression.
  
      For details on input parameters, see `rfft`.
  
      To process (conjugate-symmetric) frequency-domain data with a complex
      datatype, consider using the newer function `scipy.fft.irfft`.
  
      Examples
      --------
      >>> from scipy.fftpack import rfft, irfft
      >>> a = [1.0, 2.0, 3.0, 4.0, 5.0]
      >>> irfft(a)
      array([ 2.6       , -3.16405192,  1.24398433, -1.14955713,  1.46962473])
      >>> irfft(rfft(a))
      array([1., 2., 3., 4., 5.])
  
      """
      return _pocketfft.irfft_fftpack(x, n, axis, None, overwrite_x)
  
file_path: scipy/scipy/fftpack/_basic.py
imports: from scipy.fft import _pocketfft
  from ._helper import _good_shape
label_desc: Use image node_id 4 for calling a global function with example usage: irfft(x, n, axis, overwrite_x) and returns: _pocketfft