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Pseudo-Vandermonde matrix of given degrees.

Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
points `(x, y)`. The pseudo-Vandermonde matrix is defined by

.. math:: V[..., deg[1]*i + j] = He_i(x) * He_j(y),

where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of
`V` index the points `(x, y)` and the last index encodes the degrees of
the HermiteE polynomials.(more...)

        def hermevander2d(x, y, deg) :
    """Pseudo-Vandermonde matrix of given degrees.

    Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
    points `(x, y)`. The pseudo-Vandermonde matrix is defined by

    .. math:: V[..., deg[1]*i + j] = He_i(x) * He_j(y),

    where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of
    `V` index the points `(x, y)` and the last index encodes the degrees of
    the HermiteE polynomials.

    If ``V = hermevander2d(x, y, [xdeg, ydeg])``, then the columns of `V`
    correspond to the elements of a 2-D coefficient array `c` of shape
    (xdeg + 1, ydeg + 1) in the order

    .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...

    and ``np.dot(V, c.flat)`` and ``hermeval2d(x, y, 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 2-D HermiteE
    series of the same degrees and sample points.

    Parameters
    ----------
    x, y : 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].

    Returns
    -------
    vander2d : ndarray
        The shape of the returned matrix is ``x.shape + (order,)``, where
        :math:`order = (deg[0]+1)*(deg([1]+1)`.  The dtype will be the same
        as the converted `x` and `y`.

    See Also
    --------
    hermevander, hermevander3d. hermeval2d, hermeval3d

    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]:
        raise ValueError("degrees must be non-negative integers")
    degx, degy = ideg
    x, y = np.array((x, y), copy=0) + 0.0

    vx = hermevander(x, degx)
    vy = hermevander(y, degy)
    v = vx[..., None]*vy[..., None,:]
    return v.reshape(v.shape[:-2] + (-1,))
        


src/n/u/nupic-linux64-HEAD/lib64/python2.6/site-packages/numpy/polynomial/tests/test_hermite_e.py   nupic-linux64(Download)
    def test_hermevander2d(self) :
        # also tests hermeval2d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3))
        van = herme.hermevander2d(x1, x2, [1, 2])
 
        # check shape
        van = herme.hermevander2d([x1], [x2], [1, 2])
        assert_(van.shape == (1, 5, 6))
 

src/n/u/numpy-1.8.1/numpy/polynomial/tests/test_hermite_e.py   numpy(Download)
    def test_hermevander2d(self) :
        # also tests hermeval2d for non-square coefficient array
        x1, x2, x3 = self.x
        c = np.random.random((2, 3))
        van = herme.hermevander2d(x1, x2, [1, 2])
 
        # check shape
        van = herme.hermevander2d([x1], [x2], [1, 2])
        assert_(van.shape == (1, 5, 6))