Python vector._check_vector函数代码示例

    def set_ang_vel(self, otherframe, value):
        """Define the angular velocity vector in a ReferenceFrame.

        Defines the angular velocity of this ReferenceFrame, in another.
        Angular velocity can be defined with respect to multiple different
        ReferenceFrames. Care must be taken to not create loops which are
        inconsistent.

        Parameters
        ==========

        otherframe : ReferenceFrame
            A ReferenceFrame to define the angular velocity in
        value : Vector
            The Vector representing angular velocity

        Examples
        ========

        >>> from sympy.physics.vector import ReferenceFrame, Vector
        >>> N = ReferenceFrame('N')
        >>> A = ReferenceFrame('A')
        >>> V = 10 * N.x
        >>> A.set_ang_vel(N, V)
        >>> A.ang_vel_in(N)
        10*N.x

        """

        if value == 0:
            value = Vector(0)
        value = _check_vector(value)
        _check_frame(otherframe)
        self._ang_vel_dict.update({otherframe: value})
        otherframe._ang_vel_dict.update({self: -value})

    def __and__(self, other):
        """The inner product operator for a Dyadic and a Dyadic or Vector.

        Parameters
        ==========

        other : Dyadic or Vector
            The other Dyadic or Vector to take the inner product with

        Examples
        ========

        >>> from sympy.physics.vector import ReferenceFrame, outer
        >>> N = ReferenceFrame('N')
        >>> D1 = outer(N.x, N.y)
        >>> D2 = outer(N.y, N.y)
        >>> D1.dot(D2)
        (N.x|N.y)
        >>> D1.dot(N.y)
        N.x

        """
        from sympy.physics.vector.vector import Vector, _check_vector
        if isinstance(other, Dyadic):
            other = _check_dyadic(other)
            ol = Dyadic(0)
            for i, v in enumerate(self.args):
                for i2, v2 in enumerate(other.args):
                    ol += v[0] * v2[0] * (v[2] & v2[1]) * (v[1] | v2[2])
        else:
            other = _check_vector(other)
            ol = Vector(0)
            for i, v in enumerate(self.args):
                ol += v[0] * v[1] * (v[2] & other)
        return ol

    def __rand__(self, other):
        """The inner product operator for a Vector or Dyadic, and a Dyadic

        This is for: Vector dot Dyadic

        Parameters
        ==========

        other : Vector
            The vector we are dotting with

        Examples
        ========

        >>> from sympy.physics.vector import ReferenceFrame, dot, outer
        >>> N = ReferenceFrame('N')
        >>> d = outer(N.x, N.x)
        >>> dot(N.x, d)
        N.x

        """

        from sympy.physics.vector.vector import Vector, _check_vector
        other = _check_vector(other)
        ol = Vector(0)
        for i, v in enumerate(self.args):
            ol += v[0] * v[2] * (v[1] & other)
        return ol

    def __xor__(self, other):
        """For a cross product in the form: Dyadic x Vector.

        Parameters
        ==========

        other : Vector
            The Vector that we are crossing this Dyadic with

        Examples
        ========

        >>> from sympy.physics.vector import ReferenceFrame, outer, cross
        >>> N = ReferenceFrame('N')
        >>> d = outer(N.x, N.x)
        >>> cross(d, N.y)
        (N.x|N.z)

        """

        from sympy.physics.vector.vector import _check_vector
        other = _check_vector(other)
        ol = Dyadic(0)
        for i, v in enumerate(self.args):
            ol += v[0] * (v[1] | (v[2] ^ other))
        return ol

    def set_vel(self, frame, value):
        """Sets the velocity Vector of this Point in a ReferenceFrame.

        Parameters
        ==========

        value : Vector
            The vector value of this point's velocity in the frame
        frame : ReferenceFrame
            The frame in which this point's velocity is defined

        Examples
        ========

        >>> from sympy.physics.vector import Point, ReferenceFrame
        >>> N = ReferenceFrame('N')
        >>> p1 = Point('p1')
        >>> p1.set_vel(N, 10 * N.x)
        >>> p1.vel(N)
        10*N.x

        """

        if value == 0:
            value = Vector(0)
        value = _check_vector(value)
        _check_frame(frame)
        self._vel_dict.update({frame: value})

    def set_pos(self, otherpoint, value):
        """Used to set the position of this point w.r.t. another point.

        Parameters
        ==========

        value : Vector
            The vector which defines the location of this point
        point : Point
            The other point which this point's location is defined relative to

        Examples
        ========

        >>> from sympy.physics.vector import Point, ReferenceFrame
        >>> N = ReferenceFrame('N')
        >>> p1 = Point('p1')
        >>> p2 = Point('p2')
        >>> p1.set_pos(p2, 10 * N.x)
        >>> p1.pos_from(p2)
        10*N.x

        """

        if value == 0:
            value = Vector(0)
        value = _check_vector(value)
        self._check_point(otherpoint)
        self._pos_dict.update({otherpoint: value})
        otherpoint._pos_dict.update({self: -value})

    def set_acc(self, frame, value):
        """Used to set the acceleration of this Point in a ReferenceFrame.

        Parameters
        ==========

        value : Vector
            The vector value of this point's acceleration in the frame
        frame : ReferenceFrame
            The frame in which this point's acceleration is defined

        Examples
        ========

        >>> from sympy.physics.vector import Point, ReferenceFrame
        >>> N = ReferenceFrame('N')
        >>> p1 = Point('p1')
        >>> p1.set_acc(N, 10 * N.x)
        >>> p1.acc(N)
        10*N.x

        """

        if value == 0:
            value = Vector(0)
        value = _check_vector(value)
        _check_frame(frame)
        self._acc_dict.update({frame: value})

    def locatenew(self, name, value):
        """Creates a new point with a position defined from this point.

        Parameters
        ==========

        name : str
            The name for the new point
        value : Vector
            The position of the new point relative to this point

        Examples
        ========

        >>> from sympy.physics.vector import ReferenceFrame, Point
        >>> N = ReferenceFrame('N')
        >>> P1 = Point('P1')
        >>> P2 = P1.locatenew('P2', 10 * N.x)

        """

        if not isinstance(name, str):
            raise TypeError('Must supply a valid name')
        if value == 0:
            value = Vector(0)
        value = _check_vector(value)
        p = Point(name)
        p.set_pos(self, value)
        self.set_pos(p, -value)
        return p

def curl(vect, frame):
    """
    Returns the curl of a vector field computed wrt the coordinate
    symbols of the given frame.

    Parameters
    ==========

    vect : Vector
        The vector operand

    frame : ReferenceFrame
        The reference frame to calculate the curl in

    Examples
    ========

    >>> from sympy.physics.vector import ReferenceFrame
    >>> from sympy.physics.vector import curl
    >>> R = ReferenceFrame('R')
    >>> v1 = R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
    >>> curl(v1, R)
    0
    >>> v2 = R[0]*R[1]*R[2]*R.x
    >>> curl(v2, R)
    R_x*R_y*R.y - R_x*R_z*R.z

    """

    _check_vector(vect)
    if vect == 0:
        return Vector(0)
    vect = express(vect, frame, variables=True)
    #A mechanical approach to avoid looping overheads
    vectx = vect.dot(frame.x)
    vecty = vect.dot(frame.y)
    vectz = vect.dot(frame.z)
    outvec = Vector(0)
    outvec += (diff(vectz, frame[1]) - diff(vecty, frame[2])) * frame.x
    outvec += (diff(vectx, frame[2]) - diff(vectz, frame[0])) * frame.y
    outvec += (diff(vecty, frame[0]) - diff(vectx, frame[1])) * frame.z
    return outvec

def divergence(vect, frame):
    """
    Returns the divergence of a vector field computed wrt the coordinate
    symbols of the given frame.

    Parameters
    ==========

    vect : Vector
        The vector operand

    frame : ReferenceFrame
        The reference frame to calculate the divergence in

    Examples
    ========

    >>> from sympy.physics.vector import ReferenceFrame
    >>> from sympy.physics.vector import divergence
    >>> R = ReferenceFrame('R')
    >>> v1 = R[0]*R[1]*R[2] * (R.x+R.y+R.z)
    >>> divergence(v1, R)
    R_x*R_y + R_x*R_z + R_y*R_z
    >>> v2 = 2*R[1]*R[2]*R.y
    >>> divergence(v2, R)
    2*R_z

    """

    _check_vector(vect)
    if vect == 0:
        return S(0)
    vect = express(vect, frame, variables=True)
    vectx = vect.dot(frame.x)
    vecty = vect.dot(frame.y)
    vectz = vect.dot(frame.z)
    out = S(0)
    out += diff(vectx, frame[0])
    out += diff(vecty, frame[1])
    out += diff(vectz, frame[2])
    return out

#.........这里部分代码省略.........
            """DCM for simple axis 1,2,or 3 rotations. """
            if axis == 1:
                return Matrix([[1, 0, 0],
                    [0, cos(angle), -sin(angle)],
                    [0, sin(angle), cos(angle)]])
            elif axis == 2:
                return Matrix([[cos(angle), 0, sin(angle)],
                    [0, 1, 0],
                    [-sin(angle), 0, cos(angle)]])
            elif axis == 3:
                return Matrix([[cos(angle), -sin(angle), 0],
                    [sin(angle), cos(angle), 0],
                    [0, 0, 1]])

        approved_orders = ('123', '231', '312', '132', '213', '321', '121',
                           '131', '212', '232', '313', '323', '')
        rot_order = str(
            rot_order).upper()  # Now we need to make sure XYZ = 123
        rot_type = rot_type.upper()
        rot_order = [i.replace('X', '1') for i in rot_order]
        rot_order = [i.replace('Y', '2') for i in rot_order]
        rot_order = [i.replace('Z', '3') for i in rot_order]
        rot_order = ''.join(rot_order)
        if not rot_order in approved_orders:
            raise TypeError('The supplied order is not an approved type')
        parent_orient = []
        if rot_type == 'AXIS':
            if not rot_order == '':
                raise TypeError('Axis orientation takes no rotation order')
            if not (isinstance(amounts, (list, tuple)) & (len(amounts) == 2)):
                raise TypeError('Amounts are a list or tuple of length 2')
            theta = amounts[0]
            axis = amounts[1]
            axis = _check_vector(axis)
            if not axis.dt(parent) == 0:
                raise ValueError('Axis cannot be time-varying')
            axis = axis.express(parent).normalize()
            axis = axis.args[0][0]
            parent_orient = ((eye(3) - axis * axis.T) * cos(theta) +
                    Matrix([[0, -axis[2], axis[1]], [axis[2], 0, -axis[0]],
                        [-axis[1], axis[0], 0]]) * sin(theta) + axis * axis.T)
        elif rot_type == 'QUATERNION':
            if not rot_order == '':
                raise TypeError(
                    'Quaternion orientation takes no rotation order')
            if not (isinstance(amounts, (list, tuple)) & (len(amounts) == 4)):
                raise TypeError('Amounts are a list or tuple of length 4')
            q0, q1, q2, q3 = amounts
            parent_orient = (Matrix([[q0 ** 2 + q1 ** 2 - q2 ** 2 - q3 **
                2, 2 * (q1 * q2 - q0 * q3), 2 * (q0 * q2 + q1 * q3)],
                [2 * (q1 * q2 + q0 * q3), q0 ** 2 - q1 ** 2 + q2 ** 2 - q3 ** 2,
                2 * (q2 * q3 - q0 * q1)], [2 * (q1 * q3 - q0 * q2), 2 * (q0 *
                q1 + q2 * q3), q0 ** 2 - q1 ** 2 - q2 ** 2 + q3 ** 2]]))
        elif rot_type == 'BODY':
            if not (len(amounts) == 3 & len(rot_order) == 3):
                raise TypeError('Body orientation takes 3 values & 3 orders')
            a1 = int(rot_order[0])
            a2 = int(rot_order[1])
            a3 = int(rot_order[2])
            parent_orient = (_rot(a1, amounts[0]) * _rot(a2, amounts[1])
                    * _rot(a3, amounts[2]))
        elif rot_type == 'SPACE':
            if not (len(amounts) == 3 & len(rot_order) == 3):
                raise TypeError('Space orientation takes 3 values & 3 orders')
            a1 = int(rot_order[0])
            a2 = int(rot_order[1])

#.........这里部分代码省略.........
    Examples
    ========

    >>> from sympy.physics.vector import ReferenceFrame, get_motion_params, dynamicsymbols
    >>> from sympy import symbols
    >>> R = ReferenceFrame('R')
    >>> v1, v2, v3 = dynamicsymbols('v1 v2 v3')
    >>> v = v1*R.x + v2*R.y + v3*R.z
    >>> get_motion_params(R, position = v)
    (v1''*R.x + v2''*R.y + v3''*R.z, v1'*R.x + v2'*R.y + v3'*R.z, v1*R.x + v2*R.y + v3*R.z)
    >>> a, b, c = symbols('a b c')
    >>> v = a*R.x + b*R.y + c*R.z
    >>> get_motion_params(R, velocity = v)
    (0, a*R.x + b*R.y + c*R.z, a*t*R.x + b*t*R.y + c*t*R.z)
    >>> parameters = get_motion_params(R, acceleration = v)
    >>> parameters[1]
    a*t*R.x + b*t*R.y + c*t*R.z
    >>> parameters[2]
    a*t**2/2*R.x + b*t**2/2*R.y + c*t**2/2*R.z

    """

    ##Helper functions

    def _process_vector_differential(vectdiff, condition, \
                                     variable, ordinate, frame):
        """
        Helper function for get_motion methods. Finds derivative of vectdiff wrt
        variable, and its integral using the specified boundary condition at
        value of variable = ordinate.
        Returns a tuple of - (derivative, function and integral) wrt vectdiff

        """

        #Make sure boundary condition is independent of 'variable'
        if condition != 0:
            condition = express(condition, frame, variables=True)
        #Special case of vectdiff == 0
        if vectdiff == Vector(0):
            return (0, 0, condition)
        #Express vectdiff completely in condition's frame to give vectdiff1
        vectdiff1 = express(vectdiff, frame)
        #Find derivative of vectdiff
        vectdiff2 = time_derivative(vectdiff, frame)
        #Integrate and use boundary condition
        vectdiff0 = Vector(0)
        lims = (variable, ordinate, variable)
        for dim in frame:
            function1 = vectdiff1.dot(dim)
            abscissa = dim.dot(condition).subs({variable : ordinate})
            # Indefinite integral of 'function1' wrt 'variable', using
            # the given initial condition (ordinate, abscissa).
            vectdiff0 += (integrate(function1, lims) + abscissa) * dim
        #Return tuple
        return (vectdiff2, vectdiff, vectdiff0)

    ##Function body

    _check_frame(frame)
    #Decide mode of operation based on user's input
    if 'acceleration' in kwargs:
        mode = 2
    elif 'velocity' in kwargs:
        mode = 1
    else:
        mode = 0
    #All the possible parameters in kwargs
    #Not all are required for every case
    #If not specified, set to default values(may or may not be used in
    #calculations)
    conditions = ['acceleration', 'velocity', 'position',
                  'timevalue', 'timevalue1', 'timevalue2']
    for i, x in enumerate(conditions):
        if x not in kwargs:
            if i < 3:
                kwargs[x] = Vector(0)
            else:
                kwargs[x] = S(0)
        elif i < 3:
            _check_vector(kwargs[x])
        else:
            kwargs[x] = sympify(kwargs[x])
    if mode == 2:
        vel = _process_vector_differential(kwargs['acceleration'],
                                           kwargs['velocity'],
                                           dynamicsymbols._t,
                                           kwargs['timevalue2'], frame)[2]
        pos = _process_vector_differential(vel, kwargs['position'],
                                           dynamicsymbols._t,
                                           kwargs['timevalue1'], frame)[2]
        return (kwargs['acceleration'], vel, pos)
    elif mode == 1:
        return _process_vector_differential(kwargs['velocity'],
                                            kwargs['position'],
                                            dynamicsymbols._t,
                                            kwargs['timevalue1'], frame)
    else:
        vel = time_derivative(kwargs['position'], frame)
        acc = time_derivative(vel, frame)
        return (acc, vel, kwargs['position'])