我如何知道在 numpy 中实现 function 时是否需要使用 np.dot() 或 * 运算符？

Question

I would like to implement the following mathematical formulas to calculate a cost function J in numpy:

    [1] 𝐴=𝜎(𝑤.𝑇𝑋+𝑏)=(𝑎(1),𝑎(2),...,𝑎(𝑚−1),𝑎(𝑚))

    [2] 𝐽=−1/𝑚 ∑𝑚𝑖=1(𝑦(𝑖)log(𝑎(𝑖))+(1−𝑦(𝑖))log(1−𝑎(𝑖)))

Therefore given:

• w, b, X, Y

I already found a solution, but I do not understand why it works that way:

 A = sigmoid(np.dot(w.T,X)+b)
 cost = -(1/m) * np.sum((Y*np.log(A))+(1-Y)*np.log(1-A))

My question is: How do I know when to use np.dot for Multiplication and when to use * Operator? For example, why is w.TX (from formula 1) impelemted by np.dot(wT,X) and not by wT *X?

How do I know to use np.dot() and when to use * Operator when implemening a function in numpy?

Answer 1

yes its confusing but you should use the np.dot() function when you want to perform matrix multiplication because it follows the standard rules for matrix multiplication and the * operator when you want to perform element-wise multiplication because it multiplies the corresponding elements of two arrays, regardless of their shape.

NOTE:using * operator, it's faster than using np.dot() especially when you have large matrices.