def _check_orthogonality(equations):
"""
Helper method for _connect_to_cartesian. It checks if
set of transformation equations create orthogonal curvilinear
coordinate system
Parameters
==========
equations : Lambda
Lambda of transformation equations
"""
x1, x2, x3 = symbols("x1, x2, x3", cls=Dummy)
equations = equations(x1, x2, x3)
v1 = Matrix([diff(equations[0], x1),
diff(equations[1], x1), diff(equations[2], x1)])
v2 = Matrix([diff(equations[0], x2),
diff(equations[1], x2), diff(equations[2], x2)])
v3 = Matrix([diff(equations[0], x3),
diff(equations[1], x3), diff(equations[2], x3)])
if any(simplify(i[0] + i[1] + i[2]) == 0 for i in (v1, v2, v3)):
return False
else:
if simplify(v1.dot(v2)) == 0 and simplify(v2.dot(v3)) == 0 \
and simplify(v3.dot(v1)) == 0:
return True
else:
return False
def _check_orthogonality(self):
"""
Helper method for _connect_to_cartesian. It checks if
set of transformation equations create orthogonal curvilinear
coordinate system
Parameters
==========
equations : tuple
Tuple of transformation equations
"""
eq = self._transformation_equations()
v1 = Matrix([diff(eq[0], self.x), diff(eq[1], self.x), diff(eq[2], self.x)])
v2 = Matrix([diff(eq[0], self.y), diff(eq[1], self.y), diff(eq[2], self.y)])
v3 = Matrix([diff(eq[0], self.z), diff(eq[1], self.z), diff(eq[2], self.z)])
if any(simplify(i[0] + i[1] + i[2]) == 0 for i in (v1, v2, v3)):
return False
else:
if simplify(v1.dot(v2)) == 0 and simplify(v2.dot(v3)) == 0 and simplify(v3.dot(v1)) == 0:
return True
else:
return False
def _check_orthogonality(equations):
"""
Helper method for _connect_to_cartesian. It checks if
set of transformation equations create orthogonal curvilinear
coordinate system
Parameters
==========
equations : Lambda
Lambda of transformation equations
"""
x1, x2, x3 = symbols("x1, x2, x3", cls=Dummy)
equations = equations(x1, x2, x3)
v1 = Matrix([diff(equations[0], x1),
diff(equations[1], x1), diff(equations[2], x1)])
v2 = Matrix([diff(equations[0], x2),
diff(equations[1], x2), diff(equations[2], x2)])
v3 = Matrix([diff(equations[0], x3),
diff(equations[1], x3), diff(equations[2], x3)])
if any(simplify(i[0] + i[1] + i[2]) == 0 for i in (v1, v2, v3)):
return False
else:
if simplify(v1.dot(v2)) == 0 and simplify(v2.dot(v3)) == 0 \
and simplify(v3.dot(v1)) == 0:
return True
else:
return False
def _check_orthogonality(self):
"""
Helper method for _connect_to_cartesian. It checks if
set of transformation equations create orthogonal curvilinear
coordinate system
Parameters
==========
equations : tuple
Tuple of transformation equations
"""
eq = self._transformation_equations()
v1 = Matrix(
[diff(eq[0], self.x),
diff(eq[1], self.x),
diff(eq[2], self.x)])
v2 = Matrix(
[diff(eq[0], self.y),
diff(eq[1], self.y),
diff(eq[2], self.y)])
v3 = Matrix(
[diff(eq[0], self.z),
diff(eq[1], self.z),
diff(eq[2], self.z)])
if any(simplify(i[0] + i[1] + i[2]) == 0 for i in (v1, v2, v3)):
return False
else:
if simplify(v1.dot(v2)) == 0 and simplify(
v2.dot(v3)) == 0 and simplify(v3.dot(v1)) == 0:
return True
else:
return False