为什么当一个numpy数组里面有一个“ sympy.core.symbol.Symbol”时，它仍然是一个<class'numpy.ndarray'>？

由放弃幸福发布于 2020-08-11 02:07:50

当我声明一个符号和一个像这样的数组时

t  = symbols('t')
v1 = np.array([[1, 2, 3, 4, 5, ]])

print( type(v1) )

我在数组中放了一个符号

v2 = v1.dot(t)

print( type(v2) )

问题1：如果现在v2里面有一个符号，为什么它仍然是numpy.ndarray？

当我尝试集成此数组时，我无法做到

# I1 = integrate( v2 , t ) # this cannot be integrate because...

# AttributeError: 'ImmutableDenseNDimArray' object has no attribute 'as_poly'

那我就要做

v3 = smp.Matrix( v2 )

I2 = integrate( v3 , t )

问题2：

是否有另一种集成v2的方法，而无需在sympy Matrix中对其进行更改？

cvelit

2020-08-11 02:07:51

sympy and numpy are not integrated. sympy objects work in arrays to the extent that they can be treated as 'objects', and have the appropriate methods. Otherwise numpy does not do anything special with sympy objects.

In an isympy session:

In [200]: t                                                                                          
Out[200]: t

In [201]: tau                                                                                        
Out[201]: τ

An array with symbols will be object dtype. That's like a list, with references to those numbers and objects. It's not a special array dtype:

In [202]: arr = np.array([1,2,tau,t])                                                                

In [203]: arr                                                                                        
Out[203]: array([1, 2, tau, t], dtype=object)

np.dot works because the symbols can be added and multiplied:

In [204]: np.dot(arr,arr)                                                                            
Out[204]: 
 2    2    
t  + τ  + 5

In [205]: type(_)                                                                                    
Out[205]: sympy.core.add.Add

dot with two matching 1d arrays returns a "scalar", in this case a sympy object.

与具有匹配的数字大小列表的点相同：

In [206]: np.dot([1,2,3,4],arr)                                                                      
Out[206]: 4⋅t + 3⋅τ + 5

In [207]: type(_)                                                                                    
Out[207]: sympy.core.add.Add

But dot of the 3 element list with scalar tau produces an array:

In [208]: np.array([1,2,3]).dot(tau)                                                                 
Out[208]: array([tau, 2*tau, 3*tau], dtype=object)

（3,4）与（4，）的点产生一个（3，）数组：

In [210]: np.ones((3,4),int).dot(arr)                                                                
Out[210]: array([t + tau + 3, t + tau + 3, t + tau + 3], dtype=object)

sympy also does not "know" about numpy, so it shouldn't be surprising that integrate(ndarray, ...) does not work.

The error # AttributeError: 'ImmutableDenseNDimArray' object has no attribute 'as_poly' indicates that the array has been converted into an ImmutableDenseNDimArray sympy object. Without getting into details, that apparently is the wrong type of sympy object for this purpose.

With your v2:

In [220]: v2                                                                                         
Out[220]: array([[t, 2*t, 3*t, 4*t, 5*t]], dtype=object)
    
In [222]: Matrix(v2)                                                                                 
Out[222]: [t  2⋅t  3⋅t  4⋅t  5⋅t]

In [225]: type(_222)                                                                                 
Out[225]: sympy.matrices.dense.MutableDenseMatrix

In [227]: ImmutableDenseNDimArray(v2)                                                                
Out[227]: [[t  2⋅t  3⋅t  4⋅t  5⋅t]]

In [228]: type(_)                                                                                    
Out[228]: sympy.tensor.array.dense_ndim_array.ImmutableDenseNDimArray

Neither of these has an as_poly method, but integrate might be doing some further processing. numpy has one main class, ndarray, with a well known set of methods and attributes. sympy defines many more classes, so we (I) need to pay a lot more attention to the docs.

放弃幸福

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