NumPy Arrays: What's the Difference Between Shape (R, 1) and (R,) and How Does it Affect Matrix Multiplication?

What's the Difference Between Shape (R, 1) and (R,) in NumPy?

In NumPy, you may encounter arrays with shapes (R, 1) and (R,). While these shapes may appear similar, they represent different interpretations of the underlying data.

An array with shape (R, 1) is a 2D array with R rows and a single column. It's essentially a column vector, which can be thought of as a list of R elements. In contrast, an array with shape (R,) is a 1D array with R elements. It's effectively a list, with each element representing a scalar value.

Why Not Design NumPy to Favor (R, 1) for Easier Matrix Multiplication?

NumPy's design choice not to favor (R, 1) shapes for matrix multiplication stems from its inherent flexibility. Allowing for both shapes enables programmers to choose the most appropriate representation for their specific tasks. While (R, 1) shapes are more convenient for matrix multiplication, (R,) shapes may be preferable in other contexts, such as when working with vectors or lists of scalar values.

Better Ways to Perform Matrix Multiplication

Without explicitly reshaping the arrays, there are alternative approaches to perform matrix multiplication. For instance, using the np.expand_dims() function can achieve the desired shape transformation. Alternatively, you can take advantage of broadcasting, which NumPy automatically performs under certain conditions. For example, in the expression numpy.dot(M[:,0], numpy.ones((1, R))), broadcasting will automatically expand numpy.ones((1, R)) to numpy.ones((R, 1)).

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