SymPy defines gradient only for scalar valued function.
Do you mean that gradient of vector valued function should return other
stuff like jacobian?
On Saturday, April 25, 2020 at 3:44:15 AM UTC+9, Alexander Lindsay wrote:
>
> I've been using the capabilities in sympy.vector for generating MMS
> solutions for verifying FEM in MOOSE. I'm curious whether sympy supports
> calculation of the gradient of a vector field (e.g. with the result being a
> tensor)? It doesn't appear to me that it does, but I'm hoping I overlooked
> something. Below is the sample code I'd like to be able to execute and the
> corresponding backtrace. If the ability to take the gradient of a vector
> doesn't exist, I'm curious whether it would be difficult to add? If it's
> not too much anticipated work, I'd be willing to take a stab at it.
>
> from sympy.vector import gradient, CoordSys3D
> R = CoordSys3D('R')
> u = R.x*R.y * (R.i + R.j)
> gradient(u)
>
> ---------------------------------------------------------------------------
> ValueError Traceback (most recent call last)
> <ipython-input-49-c095794df196> in <module>
> 5 u = R.x*R.y * (R.i + R.j)
> 6
> ----> 7 gradient(u)
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/operators.py
> in gradient(scalar_field, coord_sys, doit)
> 317
> 318 if doit:
> --> 319 return (vx * i + vy * j + vz * k).doit()
> 320 return vx * i + vy * j + vz * k
> 321 else:
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
> in doit(self, **hints)
> 169 """Calls .doit() on each term in the Dyadic"""
> 170 doit_components = [self.components[x].doit(**hints) * x
> --> 171 for x in self.components]
> 172 return self._add_func(*doit_components)
> 173
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
> in <listcomp>(.0)
> 169 """Calls .doit() on each term in the Dyadic"""
> 170 doit_components = [self.components[x].doit(**hints) * x
> --> 171 for x in self.components]
> 172 return self._add_func(*doit_components)
> 173
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/core/decorators.py
> in __sympifyit_wrapper(a, b)
> 89 if not hasattr(b, '_op_priority'):
> 90 b = sympify(b, strict=True)
> ---> 91 return func(a, b)
> 92 except SympifyError:
> 93 return retval
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/core/decorators.py
> in binary_op_wrapper(self, other)
> 127 if f is not None:
> 128 return f(self)
> --> 129 return func(self, other)
> 130 return binary_op_wrapper
> 131 return priority_decorator
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
> in __mul__(self, other)
> 34 @call_highest_priority('__rmul__')
> 35 def __mul__(self, other):
> ---> 36 return self._mul_func(self, other)
> 37
> 38 @_sympifyit('other', NotImplemented)
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/vector.py
> in __new__(cls, *args, **options)
> 412
> 413 def __new__(cls, *args, **options):
> --> 414 obj = BasisDependentMul.__new__(cls, *args, **options)
> 415 return obj
> 416
>
> ~/miniconda3/envs/moose-boost/lib/python3.7/site-packages/sympy/vector/basisdependent.py
> in __new__(cls, *args, **options)
> 257 # Make sure incompatible types weren't multiplied
> 258 if count > 1:
> --> 259 raise ValueError("Invalid multiplication")
> 260 elif count == 0:
> 261 return Mul(*args, **options)
>
> ValueError: Invalid multiplication
>
>
>
>
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