parameters: (x, a, period=None, _cache=_cache)
return_statement: return convolve.convolve_z(tmp,omega_real,omega_imag,
                                 overwrite_x=overwrite_x)
docstring: Shift periodic sequence x by a: y(u) = x(u+a).
  
      If x_j and y_j are Fourier coefficients of periodic functions x
      and y, respectively, then::
  
            y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
  
      Parameters
      ----------
      x : array_like
          The array to take the pseudo-derivative from.
      a : float
          Defines the parameters of the sinh/sinh pseudo-differential
      period : float, optional
          The period of the sequences x and y. Default period is ``2*pi``.
docstring_summary: Shift periodic sequence x by a: y(u) = x(u+a).
docstring_tokens: Shift periodic sequence x by a : y ( u ) = x ( u + a ) .
function: def shift(x, a, period=None, _cache=_cache):
      """
      Shift periodic sequence x by a: y(u) = x(u+a).
  
      If x_j and y_j are Fourier coefficients of periodic functions x
      and y, respectively, then::
  
            y_j = exp(j*a*2*pi/period*sqrt(-1)) * x_f
  
      Parameters
      ----------
      x : array_like
          The array to take the pseudo-derivative from.
      a : float
          Defines the parameters of the sinh/sinh pseudo-differential
      period : float, optional
          The period of the sequences x and y. Default period is ``2*pi``.
      """
      tmp = asarray(x)
      if iscomplexobj(tmp):
          return shift(tmp.real,a,period)+1j*shift(tmp.imag,a,period)
      if period is not None:
          a = a*2*pi/period
      n = len(x)
      omega = _cache.get((n,a))
      if omega is None:
          if len(_cache) > 20:
              while _cache:
                  _cache.popitem()
  
          def kernel_real(k,a=a):
              return cos(a*k)
  
          def kernel_imag(k,a=a):
              return sin(a*k)
          omega_real = convolve.init_convolution_kernel(n,kernel_real,d=0,
                                                        zero_nyquist=0)
          omega_imag = convolve.init_convolution_kernel(n,kernel_imag,d=1,
                                                        zero_nyquist=0)
          _cache[(n,a)] = omega_real,omega_imag
      else:
          omega_real,omega_imag = omega
      overwrite_x = _datacopied(tmp, x)
      return convolve.convolve_z(tmp,omega_real,omega_imag,
                                 overwrite_x=overwrite_x)
function_tokens: def shift ( x , a , period = None , _cache = _cache ) : tmp = asarray ( x ) if iscomplexobj ( tmp ) : return shift ( tmp . real , a , period ) + 1j * shift ( tmp . imag , a , period ) if period is not None : a = a * 2 * pi / period n = len ( x ) omega = _cache . get ( ( n , a ) ) if omega is None : if len ( _cache ) > 20 : while _cache : _cache . popitem ( ) def kernel_real ( k , a = a ) : return cos ( a * k ) def kernel_imag ( k , a = a ) : return sin ( a * k ) omega_real = convolve . init_convolution_kernel ( n , kernel_real , d = 0 , zero_nyquist = 0 ) omega_imag = convolve . init_convolution_kernel ( n , kernel_imag , d = 1 , zero_nyquist = 0 ) _cache [ ( n , a ) ] = omega_real , omega_imag else : omega_real , omega_imag = omega overwrite_x = _datacopied ( tmp , x ) return convolve . convolve_z ( tmp , omega_real , omega_imag , overwrite_x = overwrite_x )