parameters: (x, y, z, deg)
return_statement: return pu._vander_nd_flat((polyvander, polyvander, polyvander), (x, y, z), deg)
docstring: Pseudo-Vandermonde matrix of given degrees.
  
      Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
      points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`,
      then The pseudo-Vandermonde matrix is defined by
  
      .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = x^i * y^j * z^k,
  
      where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`.  The leading
      indices of `V` index the points `(x, y, z)` and the last index encodes
      the powers of `x`, `y`, and `z`.
  
      If ``V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns
      of `V` correspond to the elements of a 3-D coefficient array `c` of
      shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order
  
      .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...
  
      and  ``np.dot(V, c.flat)`` and ``polyval3d(x, y, z, c)`` will be the
      same up to roundoff. This equivalence is useful both for least squares
      fitting and for the evaluation of a large number of 3-D polynomials
      of the same degrees and sample points.
  
      Parameters
      ----------
      x, y, z : array_like
          Arrays of point coordinates, all of the same shape. The dtypes will
          be converted to either float64 or complex128 depending on whether
          any of the elements are complex. Scalars are converted to 1-D
          arrays.
      deg : list of ints
          List of maximum degrees of the form [x_deg, y_deg, z_deg].
  
      Returns
      -------
      vander3d : ndarray
          The shape of the returned matrix is ``x.shape + (order,)``, where
          :math:`order = (deg[0]+1)*(deg([1]+1)*(deg[2]+1)`.  The dtype will
          be the same as the converted `x`, `y`, and `z`.
  
      See Also
      --------
      polyvander, polyvander3d, polyval2d, polyval3d
  
      Notes
      -----
  
      .. versionadded:: 1.7.0
docstring_summary: Pseudo-Vandermonde matrix of given degrees.
docstring_tokens: Pseudo - Vandermonde matrix of given degrees .
function: def polyvander3d(x, y, z, deg):
      """Pseudo-Vandermonde matrix of given degrees.
  
      Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
      points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`,
      then The pseudo-Vandermonde matrix is defined by
  
      .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = x^i * y^j * z^k,
  
      where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`.  The leading
      indices of `V` index the points `(x, y, z)` and the last index encodes
      the powers of `x`, `y`, and `z`.
  
      If ``V = polyvander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns
      of `V` correspond to the elements of a 3-D coefficient array `c` of
      shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order
  
      .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...
  
      and  ``np.dot(V, c.flat)`` and ``polyval3d(x, y, z, c)`` will be the
      same up to roundoff. This equivalence is useful both for least squares
      fitting and for the evaluation of a large number of 3-D polynomials
      of the same degrees and sample points.
  
      Parameters
      ----------
      x, y, z : array_like
          Arrays of point coordinates, all of the same shape. The dtypes will
          be converted to either float64 or complex128 depending on whether
          any of the elements are complex. Scalars are converted to 1-D
          arrays.
      deg : list of ints
          List of maximum degrees of the form [x_deg, y_deg, z_deg].
  
      Returns
      -------
      vander3d : ndarray
          The shape of the returned matrix is ``x.shape + (order,)``, where
          :math:`order = (deg[0]+1)*(deg([1]+1)*(deg[2]+1)`.  The dtype will
          be the same as the converted `x`, `y`, and `z`.
  
      See Also
      --------
      polyvander, polyvander3d, polyval2d, polyval3d
  
      Notes
      -----
  
      .. versionadded:: 1.7.0
  
      """
      return pu._vander_nd_flat((polyvander, polyvander, polyvander), (x, y, z), deg)
function_tokens: def polyvander3d ( x , y , z , deg ) : return pu . _vander_nd_flat ( ( polyvander , polyvander , polyvander ) , ( x , y , z ) , deg )