On Monday, 23 May 2022 at 15:23:38 UTC+1 Jim Zhang wrote:
> Hello,
>
> I am new to Sympy. At times, I wish to get an analytical expression in
> terms of certain variables. In the following case, one is a Numpy array (T)
> and the other is a Sympy matrix (X). I know it is not a good idea to
> directly multiply them, so I convert T to a Sympy matrix first. However,
> it would take forever to get the result because of this large-sized matrix.
> Are there any more computationally efficient ways?
>
> Thanks in advance,
>
> Jim
>
>
> import numpy as np
> import sympy as sp
>
> T = np.random.rand(100, 6000)
> x = sp.symbols('x:'+str(6000))
> X = sp.Matrix(x)
> W = sp.Matrix(T)
> V = W * X
>
Jonathan already mentioned SymEngine which can be used here and is likely
to be faster for this particular operation. However I want to question your
approach here: is this operation genuinely representative of what you are
actually doing in your code?
I suspect that there is a much better way of doing what you want to do here
just using NumPy. If we make this smaller and show what these objects are
then maybe you can see what I mean:
...: import numpy as np
...: import sympy as sp
...:
...: T = np.random.rand(3, 3)
...: x = sp.symbols('x:3')
...: X = sp.Matrix(x)
...: W = sp.Matrix(T)
...: V = W * X
In [2]: T
Out[2]:
array([[0.02171629, 0.07314606, 0.20216258],
[0.5911101 , 0.02585039, 0.57907704],
[0.21691524, 0.21911551, 0.84199378]])
In [3]: V
Out[3]:
⎡0.0217162949338237⋅x₀ + 0.0731460590358582⋅x₁ + 0.202162579518612⋅x₂⎤
⎢ ⎥
⎢ 0.59111010291895⋅x₀ + 0.0258503861066768⋅x₁ + 0.579077042048328⋅x₂ ⎥
⎢ ⎥
⎣ 0.216915237539653⋅x₀ + 0.21911551409902⋅x₁ + 0.841993775366244⋅x₂ ⎦
The matrix V here is really just an inefficient way of representing the
original array T. Whatever operation you want to do with V can probably be
done much more efficiently with T. For example if you want to differentiate
with respect to x0 then that's really just extracting the first column of T
e.g.:
In [4]: V.diff(X[0])
Out[4]:
⎡0.0217162949338237⎤
⎢ ⎥
⎢ 0.59111010291895 ⎥
⎢ ⎥
⎣0.216915237539653 ⎦
In [5]: T[:,0]
Out[5]: array([0.02171629, 0.5911101 , 0.21691524])
Whatever it is you are trying to do with V can almost certainly be done
better in some other way e.g. by using SymPy to derive a formula and then
using NumPy to evaluate that formula.
--
Oscar
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