Difference between numpy.array shape (R, 1) and (R,)

The difference between (R,) and (1,R) is literally the number of indices that you need to use. ones((1,R)) is a 2-D array that happens to have only one row. ones(R) is a vector. Generally if it doesn’t make sense for the variable to have more than one row/column, you should be using a vector, not a matrix with a singleton dimension.

For your specific case, there are a couple of options:

1) Just make the second argument a vector. The following works fine:

    np.dot(M[:,0], np.ones(R))

2) If you want matlab like matrix operations, use the class matrix instead of ndarray. All matricies are forced into being 2-D arrays, and operator * does matrix multiplication instead of element-wise (so you don’t need dot). In my experience, this is more trouble that it is worth, but it may be nice if you are used to matlab.

1) The reason not to prefer a shape of (R, 1) over (R,) is that it unnecessarily complicates things. Besides, why would it be preferable to have shape (R, 1) by default for a length-R vector instead of (1, R)? It’s better to keep it simple and be explicit when you require additional dimensions.

2) For your example, you are computing an outer product so you can do this without a reshape call by using np.outer:

np.outer(M[:,0], numpy.ones((1, R)))

For its base array class, 2d arrays are no more special than 1d or 3d ones. There are some operations that preserve the dimensions, some that reduce them, other combine or even expand them.

M=np.arange(9).reshape(3,3)
M[:,0].shape # (3,) selects one column, returns a 1d array
M[0,:].shape # same, one row, 1d array
M[:,[0]].shape # (3,1), index with a list (or array), returns 2d
M[:,[0,1]].shape # (3,2)

In [20]: np.dot(M[:,0].reshape(3,1),np.ones((1,3)))

Out[20]: 
array([[ 0.,  0.,  0.],
       [ 3.,  3.,  3.],
       [ 6.,  6.,  6.]])

In [21]: np.dot(M[:,[0]],np.ones((1,3)))
Out[21]: 
array([[ 0.,  0.,  0.],
       [ 3.,  3.,  3.],
       [ 6.,  6.,  6.]])

Other expressions that give the same array

np.dot(M[:,0][:,np.newaxis],np.ones((1,3)))
np.dot(np.atleast_2d(M[:,0]).T,np.ones((1,3)))
np.einsum('i,j',M[:,0],np.ones((3)))
M1=M[:,0]; R=np.ones((3)); np.dot(M1[:,None], R[None,:])

MATLAB started out with just 2D arrays. Newer versions allow more dimensions, but retain the lower bound of 2. But you still have to pay attention to the difference between a row matrix and column one, one with shape (1,3) v (3,1). How often have you written [1,2,3].'? I was going to write row vector and column vector, but with that 2d constraint, there aren’t any vectors in MATLAB – at least not in the mathematical sense of vector as being 1d.

Have you looked at np.atleast_2d (also _1d and _3d versions)?

In newer Python/numpy there’s a matmul operator

In [358]: M[:,0,np.newaxis]@np.ones((1,3))
Out[358]: 
array([[0., 0., 0.],
       [3., 3., 3.],
       [6., 6., 6.]])

In numpy element-wise multiplication is in a sense more basic than matrix multiplication. With the sum-of-products on a size 1 dimension, there’s no need to use dot/matmul:

In [360]: M[:,0,np.newaxis]*np.ones((1,3))
Out[360]: 
array([[0., 0., 0.],
       [3., 3., 3.],
       [6., 6., 6.]])

This uses broadcasting, a powerful feature that numpy has had all along. MATLAB only added it recently.

The shape is a tuple. If there is only 1 dimension the shape will be one number and just blank after a comma. For 2+ dimensions, there will be a number after all the commas.

# 1 dimension with 2 elements, shape = (2,). 
# Note there's nothing after the comma.
z=np.array([  # start dimension
    10,       # not a dimension
    20        # not a dimension
])            # end dimension
print(z.shape)

(2,)

# 2 dimensions, each with 1 element, shape = (2,1)
w=np.array([  # start outer dimension 
    [10],     # element is in an inner dimension
    [20]      # element is in an inner dimension
])            # end outer dimension
print(w.shape)

(2,1)

There are a lot of good answers here already. But for me it was hard to find some example, where the shape or array can break all the program.

So here is the one:

import numpy as np
a = np.array([1,2,3,4])
b = np.array([10,20,30,40])


from sklearn.linear_model import LinearRegression
regr = LinearRegression()
regr.fit(a,b)

This will fail with error:

ValueError: Expected 2D array, got 1D array instead

but if we add reshape to a:

a = np.array([1,2,3,4]).reshape(-1,1)

this works correctly!

The data structure of shape (n,) is called a rank 1 array. It doesn’t behave consistently as a row vector or a column vector which makes some of its operations and effects non intuitive. If you take the transpose of this (n,) data structure, it’ll look exactly same and the dot product will give you a number and not a matrix.
The vectors of shape (n,1) or (1,n) row or column vectors are much more intuitive and consistent.

To be clear, we are talking about:

• a NumPy array also known as numpy.ndarray
• the shape of an array known by numpy.ndarray.shape
• the question assumes some unknown numpy.ndarray with the shape (R,) where R should be understood as the length of its respective dimension

NumPy arrays have a shape. That .shape is represented by a tuple where each element in the tuple tells us the length of that dimension. To keep it simple, let’s stick to rows and columns. While the values of our numpy.ndarray will not change in the following examples, the shape will.

Let’s consider an array with the values 1, 2, 3, and 4.

Our examples will include the following .shape representations:

(4,)  # 1-dimensional array with length 4
(1,4) # 2-dimensional array with row length 1, column length 4
(4,1) # 2-dimensional array with row length 4, column length 1

We can think of this more abstractly with variables a and b.

(a,)  # 1-dimensional array with length a
(b,a) # 2-dimensional array with row length b, column length a
(a,b) # 2-dimensional array with row length a, column length b

For me, it is helpful to ‘manually’ build these out to get a better feel for what their dimensions mean.

>> # (4,)
>> one_dimensional_vector = np.array(
    [1, 2, 3, 4]
)

>> # (1,4)
>> row_vector = np.array(
    [
        [1, 2, 3, 4]
    ]
)

>> # (4,1)
>> column_vector = np.array(
    [
        [1], 
        [2], 
        [3], 
        [4]
    ]
)

So, the answer to the first question:

1. What’s the difference between shape (R, 1) and (R,)?

Answer: They have different dimensions. a is the length of the one dimension and b the length of another, .shape is (a, b) and (a,) respectively. b just happens to be 1. One way to think of this is if a = 1 then the row has length 1 thus it is a row vector. If b = 1 then the column has length 1 so the numpy.ndarray it represents is a column vector.

2. Are there better ways for the above example?

Answer: Let’s assume we have the array I used as example above with 1, 2, 3, and 4 as values. A convenient way to get (R,) to be (R, 1) is this:

>> one_dimensional_array = np.array([1,2,3,4])
>> one_dimensional_array.shape
(4,)
>> row_vector = one_dimensional_array[:, None]
>> row_vector.shape
(4, 1)

Resourses

1. NumPy — ndarrays — https://numpy.org/doc/stable/reference/arrays.ndarray.html
2. Cross Validated @unutbu — dimension trick — https://stats.stackexchange.com/a/285005