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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] = L_i(x)*L_j(y)*L_k(z),

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(more...)

        def lagvander3d(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] = L_i(x)*L_j(y)*L_k(z),

    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 degrees of the Laguerre polynomials.

    If ``V = lagvander3d(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 ``lagval3d(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 Laguerre
    series 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
    --------
    lagvander, lagvander3d. lagval2d, lagval3d

    Notes
    -----

    .. versionadded::1.7.0

    """
    ideg = [int(d) for d in deg]
    is_valid = [id == d and id >= 0 for id, d in zip(ideg, deg)]
    if is_valid != [1, 1, 1]:
        raise ValueError("degrees must be non-negative integers")
    degx, degy, degz = ideg
    x, y, z = np.array((x, y, z), copy=0) + 0.0

    vx = lagvander(x, degx)
    vy = lagvander(y, degy)
    vz = lagvander(z, degz)
    v = vx[..., None, None]*vy[..., None,:, None]*vz[..., None, None,:]
    return v.reshape(v.shape[:-3] + (-1,))
        


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_laguerre.py   nupic-linux64(Download)
    def test_lagvander3d(self) :
        # also tests lagval3d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3, 4))
        van = lag.lagvander3d(x1, x2, x3, [1, 2, 3])
 
        # check shape
        van = lag.lagvander3d([x1], [x2], [x3], [1, 2, 3])
        assert_(van.shape == (1, 5, 24))
 

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_laguerre.py   numpy(Download)
    def test_lagvander3d(self) :
        # also tests lagval3d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3, 4))
        van = lag.lagvander3d(x1, x2, x3, [1, 2, 3])
 
        # check shape
        van = lag.lagvander3d([x1], [x2], [x3], [1, 2, 3])
        assert_(van.shape == (1, 5, 24))