What's the Difference Between NumPy Array Shapes (R, 1) and (R,)?

Difference Between NumPy Array Shapes (R, 1) and (R,)

In NumPy, arrays can have shapes that differ subtly, such as (R, 1) and (R,). These shapes may appear similar, but there are underlying differences in how they are interpreted and processed.

1. Understanding Array Structure

NumPy arrays consist of a data buffer and a view. The data buffer stores the raw data elements, while the view describes how to interpret the data. The shape is part of the view and specifies how many dimensions and elements the array has.

Shapes (R, 1) and (R,)

• (R, 1): This shape represents an array with R rows and 1 column. It behaves like a one-dimensional array but has an additional dimension of size 1.
• (R,): This shape represents an array with R rows only. It behaves like a true one-dimensional array without any additional dimensions.

2. Reasons for Different Shapes

NumPy has chosen to support both shapes for historical reasons and to provide flexibility in certain operations. Some operations expect or produce arrays with a particular shape, leading to different behavior depending on the input shape.

3. Implications for Matrix Multiplication

In your example, numpy.dot(M[:,0], numpy.ones((1, R))), the shapes can cause an issue. M[:,0] has shape (R,) while numpy.ones((1, R)) has shape (1, R), which leads to a misalignment error. To resolve this, you can explicitly reshape M[:,0] to (R, 1).

4. Best Practices

While there's no strict preference between (R, 1) and (R,), it's generally recommended to use (R, 1) when an array is logically one-dimensional but requires an extra dimension for certain operations. Be aware of the expected shapes in any functions you use to avoid errors.

Alternative Approaches

In your example, you can also consider the following alternatives to avoid reshaping:

• numpy.dot(M.T, numpy.ones((R, 1)))
• M.sum(axis=0).reshape((R, 1))

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