arrayop.py 文件源码

def derive_by_array(expr, dx):
    r"""
    Derivative by arrays. Supports both arrays and scalars.

    Given the array `A_{i_1, \ldots, i_N}` and the array `X_{j_1, \ldots, j_M}`
    this function will return a new array `B` defined by

    `B_{j_1,\ldots,j_M,i_1,\ldots,i_N} := \frac{\partial A_{i_1,\ldots,i_N}}{\partial X_{j_1,\ldots,j_M}}`

    Examples
    ========

    >>> from sympy import derive_by_array
    >>> from sympy.abc import x, y, z, t
    >>> from sympy import cos
    >>> derive_by_array(cos(x*t), x)
    -t*sin(t*x)
    >>> derive_by_array(cos(x*t), [x, y, z, t])
    [-t*sin(t*x), 0, 0, -x*sin(t*x)]
    >>> derive_by_array([x, y**2*z], [[x, y], [z, t]])
    [[[1, 0], [0, 2*y*z]], [[0, y**2], [0, 0]]]

    """
    from sympy.matrices import MatrixBase
    array_types = (collections.Iterable, MatrixBase, NDimArray)

    if isinstance(dx, array_types):
        dx = ImmutableDenseNDimArray(dx)
        for i in dx:
            if not i._diff_wrt:
                raise ValueError("cannot derive by this array")

    if isinstance(expr, array_types):
        expr = ImmutableDenseNDimArray(expr)
        if isinstance(dx, array_types):
            new_array = [[y.diff(x) for y in expr] for x in dx]
            return type(expr)(new_array, dx.shape + expr.shape)
        else:
            return expr.diff(dx)
    else:
        if isinstance(dx, array_types):
            return ImmutableDenseNDimArray([expr.diff(i) for i in dx], dx.shape)
        else:
            return diff(expr, dx)