Why Does Numpy Throw a 'Couldn't Broadcast' Error During Array Operations?

Broadcasting Errors in Numpy: Understanding the 'Couldn't Broadcast' Issue

In Numpy, numerical operations on arrays must adhere to specific broadcasting rules. When these rules are violated, the operation may fail, resulting in a "ValueError: operands could not be broadcast together" error.

Consider the case of an array X of shape (m,n) and a vector y of shape (n,1). Attempting element-wise multiplication of these arrays using the * operator will trigger this error.

Understanding Element-Wise Operations and Broadcasting

Element-wise operations in Numpy apply mathematical operations to corresponding elements of arrays. When the arrays have different shapes, broadcasting occurs, where one or both arrays are expanded in dimensions to make them compatible.

For example, in X*y, X is expanded in the second dimension (to become (m,n,1)), while y is expanded in the first dimension (to become (1,n,1)). However, this expansion conflicts with the dimensions of X and Y, as the first dimension of X is 97 while the second dimension of y is 2.

Alternative: Matrix Multiplication with dot

To perform matrix multiplication correctly between X and y (where y is a column vector), the dot product should be used. The dot product, denoted as X.dot(y), multiplies the corresponding elements of X and y and sums them, producing a vector of shape (m,1).

Conclusion

Understanding broadcasting rules is essential to avoid errors when performing numerical operations on arrays in Numpy. For matrix multiplication, using dot ensures correct operations without the risk of broadcasting errors.

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