Sympy-numpy集成存在-在哪里记录? [英] Sympy-numpy integration exists - where is it documented?

问题描述

我只是偶然发现我可以将sympy表达式与numpy数组混合使用:

I just accidentally discovered that I can mix sympy expressions up with numpy arrays:

>>> import numpy as np
>>> import sympy as sym
>>> x, y, z = sym.symbols('x y z')
>>> np.ones(5)*x
array([1.0*x, 1.0*x, 1.0*x, 1.0*x, 1.0*x], dtype=object)
# I was expecting this to throw an error!

# sum works and collects terms etc. as I would expect
>>> np.sum(np.array([x+0.1,y,z+y]))
x + 2*y + z + 0.1
# dot works too
>>> np.dot(np.array([x,y,z]),np.array([z,y,x]))
2*x*z + y**2
>>> np.dot(np.array([x,y,z]),np.array([1,2,3]))
x + 2*y + 3*z

这对我来说非常有用，因为我在同一程序中同时进行了数值和符号计算.但是，我很好奇这种方法的缺陷和局限性，例如，似乎在包含Sympy对象的Numpy数组上都不支持np.sin和sym.sin，因为它们都给出了错误.

This is quite useful for me, because I'm doing both numerical and symbolic calculations in the same program. However, I'm curious about the pitfalls and limitations of this approach --- it seems for example that neither np.sin nor sym.sin are supported on Numpy arrays containing Sympy objects, since both give an error.

但是，这种numpy-sympy集成似乎在任何地方都没有记录.这些库是如何实现的只是偶然的情况，还是故意的功能?如果是后者，则什么时候设计使用它?什么时候使用sympy.Matrix或其他解决方案更好?使用这种类型的数组时，我是否可以期望保持numpy的速度，或者一旦涉及sympy符号，它是否会立即回到Python循环?

However, this numpy-sympy integration doesn't appear to be documented anywhere. Is it just an accident of how these libraries are implemented, or is it a deliberate feature? If the latter, when is it designed to be used, and when would it be better to use sympy.Matrix or other solutions? Can I expect to keep some of numpy's speed when working with arrays of this kind, or will it just drop back to Python loops as soon as a sympy symbol is involved?

简而言之，我很高兴发现此功能存在，但是我想了解更多！

In short I'm pleased to find this feature exists, but I would like to know more about it!

推荐答案

这只是NumPy对对象数组的支持.它不特定于SymPy. NumPy检查操作数，发现不是所有的操作数都是标量.其中涉及一些对象.因此，它将调用该对象的__mul__或__rmul__，并将结果放入对象数组中.例如:mpmath对象，

This is just NumPy's support for arrays of objects. It is not specific to SymPy. NumPy examines the operands and finds not all of them are scalars; there are some objects involved. So it calls that object's __mul__ or __rmul__, and puts the result into an array of objects. For example: mpmath objects,

>>> import mpmath as mp
>>> np.ones(5) * mp.mpf('1.23')
array([mpf('1.23'), mpf('1.23'), mpf('1.23'), mpf('1.23'), mpf('1.23')],
      dtype=object)

或列表:

>>> np.array([[2], 3])*5
array([list([2, 2, 2, 2, 2]), 15], dtype=object)
>>> np.array([2, 3])*[[1, 1], [2]]
array([list([1, 1, 1, 1]), list([2, 2, 2])], dtype=object)

使用这种数组时，我能否期望保持numpy的速度?

Can I expect to keep some of numpy's speed when working with arrays of this kind,

不.与Python列表相比，NumPy对象数组没有性能优势；访问元素的开销可能比列表中要大. 在Python中存储Python对象列表与固定长度的Numpy数组

No. NumPy object arrays have no performance benefits over Python lists; there is probably more overhead in accessing elements than would be in a list. Storing Python objects in a Python list vs. a fixed-length Numpy array

如果有更具体的数据结构，则没有理由使用此类数组.

There is no reason to use such arrays if a more specific data structure is available.

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