在 sympy 表达式中使用矩阵乘法运算符

Question

I am trying to implement a function using a Sympy expression with multiple parameters. For example, I used the following code:

import sympy
a = sympy.symbols("a")
ad = sympy.symbols("ad")
x = sympy.symbols("x")
c = sympy.symbols("c")
f = (ad*a)*c + x
func = sympy.lambdify((a,ad,x,c),f)

And what I would like to evaluate is the following:

func(M_A,M_B,0,1)

When I use two matrices M_A and M_B , the function performs just an element-wise multiplication, but I need it to be a matrix multiplication for the objects a and ad . I do know that it is possible to do so when I define the variables using MatrixSymbol instead of symbols , but this is not possible in my case as I have implemented a scenario which uses diagonal matrices where element-wise or matrix multiplication would not make a difference. Further, it is also possible to do something like this with normal symbols

x_vars = [symbols("x"+i) for i in range(1,4)]
trans_mat = np.random.random([3,3])
y_vars = trans_mat.dot(x_vars)

which just does not seem to work when I am using MatrixSymbol .

So, I was thinking if I could just compute the expression and perform all the manipulations using the regular symbols and at the end replace all the multiplication operators with numpy.matmul . Please let me know if this is possible somehow, or any other suggestion which can help is also welcome.

Thanks!

Answer 1

Doing help(func) we can see the code produced by lambdify :

Help on function _lambdifygenerated:

_lambdifygenerated(a, ad, x, c)
    Created with lambdify. Signature:
    
    func(a, ad, x, c)
    
    Expression:
    
    a*ad*c + x
    
    Source code:
    
    def _lambdifygenerated(a, ad, x, c):
        return a*ad*c + x

That's a straightforward translation to python/numpy. Sounds like you want (a@ad)*c+x .