def directional_derivative(field, direction_vector):
"""
Returns the directional derivative of a scalar or vector field computed
along a given vector in coordinate system which parameters are expressed.
Parameters
==========
field : Vector or Scalar
The scalar or vector field to compute the directional derivative of
direction_vector : Vector
The vector to calculated directional derivative along them.
Examples
========
>>> from sympy.vector import CoordSys3D, directional_derivative
>>> R = CoordSys3D('R')
>>> f1 = R.x*R.y*R.z
>>> v1 = 3*R.i + 4*R.j + R.k
>>> directional_derivative(f1, v1)
R.x*R.y + 4*R.x*R.z + 3*R.y*R.z
>>> f2 = 5*R.x**2*R.z
>>> directional_derivative(f2, v1)
5*R.x**2 + 30*R.x*R.z
"""
from sympy.vector.operators import _get_coord_sys_from_expr
coord_sys = _get_coord_sys_from_expr(field)
if len(coord_sys) > 0:
# TODO: This gets a random coordinate system in case of multiple ones:
coord_sys = next(iter(coord_sys))
field = express(field, coord_sys, variables=True)
i, j, k = coord_sys.base_vectors()
x, y, z = coord_sys.base_scalars()
out = Vector.dot(direction_vector, i) * diff(field, x)
out += Vector.dot(direction_vector, j) * diff(field, y)
out += Vector.dot(direction_vector, k) * diff(field, z)
if out == 0 and isinstance(field, Vector):
out = Vector.zero
return out
elif isinstance(field, Vector):
return Vector.zero
else:
return S.Zero
def directional_derivative(field, direction_vector):
"""
Returns the directional derivative of a scalar or vector field computed
along a given vector in coordinate system which parameters are expressed.
Parameters
==========
field : Vector or Scalar
The scalar or vector field to compute the directional derivative of
direction_vector : Vector
The vector to calculated directional derivative along them.
Examples
========
>>> from sympy.vector import CoordSys3D, directional_derivative
>>> R = CoordSys3D('R')
>>> f1 = R.x*R.y*R.z
>>> v1 = 3*R.i + 4*R.j + R.k
>>> directional_derivative(f1, v1)
R.x*R.y + 4*R.x*R.z + 3*R.y*R.z
>>> f2 = 5*R.x**2*R.z
>>> directional_derivative(f2, v1)
5*R.x**2 + 30*R.x*R.z
"""
from sympy.vector.operators import _get_coord_sys_from_expr
coord_sys = _get_coord_sys_from_expr(field)
if len(coord_sys) > 0:
# TODO: This gets a random coordinate system in case of multiple ones:
coord_sys = next(iter(coord_sys))
field = express(field, coord_sys, variables=True)
i, j, k = coord_sys.base_vectors()
x, y, z = coord_sys.base_scalars()
out = Vector.dot(direction_vector, i) * diff(field, x)
out += Vector.dot(direction_vector, j) * diff(field, y)
out += Vector.dot(direction_vector, k) * diff(field, z)
if out == 0 and isinstance(field, Vector):
out = Vector.zero
return out
elif isinstance(field, Vector):
return Vector.zero
else:
return S(0)
def directional_derivative(field, direction_vector):
"""
Returns the directional derivative of a scalar or vector field computed
along a given vector in coordinate system which parameters are expressed.
Parameters
==========
field : Vector or Scalar
The scalar or vector field to compute the directional derivative of
direction_vector : Vector
The vector to calculated directional derivative along them.
Examples
========
>>> from sympy.vector import CoordSys3D, directional_derivative
>>> R = CoordSys3D('R')
>>> f1 = R.x*R.y*R.z
>>> v1 = 3*R.i + 4*R.j + R.k
>>> directional_derivative(f1, v1)
R.x*R.y + 4*R.x*R.z + 3*R.y*R.z
>>> f2 = 5*R.x**2*R.z
>>> directional_derivative(f2, v1)
5*R.x**2 + 30*R.x*R.z
"""
from sympy.vector.operators import _get_coord_sys_from_expr
coord_sys = _get_coord_sys_from_expr(field)
if coord_sys is not None:
field = express(field, coord_sys, variables=True)
out = Vector.dot(direction_vector, coord_sys._i) * diff(
field, coord_sys._x)
out += Vector.dot(direction_vector, coord_sys._j) * diff(
field, coord_sys._y)
out += Vector.dot(direction_vector, coord_sys._k) * diff(
field, coord_sys._z)
if out == 0 and isinstance(field, Vector):
out = Vector.zero
return out
elif isinstance(field, Vector):
return Vector.zero
else:
return S(0)
def directional_derivative(field, direction_vector):
"""
Returns the directional derivative of a scalar or vector field computed
along a given vector in coordinate system which parameters are expressed.
Parameters
==========
field : Vector or Scalar
The scalar or vector field to compute the directional derivative of
direction_vector : Vector
The vector to calculated directional derivative along them.
Examples
========
>>> from sympy.vector import CoordSys3D, directional_derivative
>>> R = CoordSys3D('R')
>>> f1 = R.x*R.y*R.z
>>> v1 = 3*R.i + 4*R.j + R.k
>>> directional_derivative(f1, v1)
R.x*R.y + 4*R.x*R.z + 3*R.y*R.z
>>> f2 = 5*R.x**2*R.z
>>> directional_derivative(f2, v1)
5*R.x**2 + 30*R.x*R.z
"""
from sympy.vector.operators import _get_coord_sys_from_expr
coord_sys = _get_coord_sys_from_expr(field)
if coord_sys is not None:
field = express(field, coord_sys, variables=True)
out = Vector.dot(direction_vector, coord_sys._i) * diff(field, coord_sys._x)
out += Vector.dot(direction_vector, coord_sys._j) * diff(field, coord_sys._y)
out += Vector.dot(direction_vector, coord_sys._k) * diff(field, coord_sys._z)
if out == 0 and isinstance(field, Vector):
out = Vector.zero
return out
elif isinstance(field, Vector):
return Vector.zero
else:
return S(0)