23ws-LLMcoder/LLMcoder-GitHub-Python-Mix-Direct

1  dimensional case the coefficients may be thought of as stored in2        the columns of `c`.3    tensor : boolean, optional4        If True, the shape of the coefficient array is extended with ones5        on the right, one for each dimension of `x`. Scalars have dimension 06        for this action. The result is that every column of coefficients in7        `c` is evaluated for every element of `x`. If False, `x` is broadcast8        over the columns of `c` for the evaluation.  This keyword is useful9        when `c` is multidimensional. The default value is True.10 11        .. versionadded:: 1.7.012 13    Returns14    -------15    values : ndarray, algebra_like16        The shape of the return value is described above.17 18    See Also19    --------20    legval2d, leggrid2d, legval3d, leggrid3d21 22    Notes23    -----24    The evaluation uses Clenshaw recursion, aka synthetic division.25 26    """27    c = np.array(c, ndmin=1, copy=False)28    if c.dtype.char in '?bBhHiIlLqQpP':29        c = c.astype(np.double)30    if isinstance(x, (tuple, list)):31        x = np.asarray(x)32    if isinstance(x, np.ndarray) and tensor:33        c = c.reshape(c.shape + (1,)*x.ndim)34 35    if len(c) == 1:36        c0 = c[0]37        c1 = 038    elif len(c) == 2:39        c0 = c[0]40        c1 = c[1]41    else:42        nd = len(c)43        c0 = c[-2]44        c1 = c[-1]45        for i in range(3, len(c) + 1):46            tmp = c047            nd = nd - 148            c0 = c[-i] - (c1*(nd - 1))/nd49            c1 = tmp + (c1*x*(2*nd - 1))/nd50    return c0 + c1*x51 52 53def legval2d(x, y, c):54    """55    Evaluate a 2-D Legendre series at points (x, y).56 57    This function returns the values:58 59    .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * L_i(x) * L_j(y)60 61    The parameters `x` and `y` are converted to arrays only if they are62    tuples or a lists, otherwise they are treated as a scalars and they63    must have the same shape after conversion. In either case, either `x`64    and `y` or their elements must support multiplication and addition both65    with themselves and with the elements of `c`.66 67    If `c` is a 1-D array a one is implicitly appended to its s