如何在numpy中将(n,)数组添加到(n,m)数组？

Question

Consider having two arrays:
A with shape (n,)
B with shape (n,m)

How can I add those two together so that A[i] is added to all m values of B[i] ?
Surely I could do it with for loops, but I want to learn how to properly use numpy.
So what's an elegant way to do it in numpy?

Example for (n,) + (n,m) :

A = [1,2]
B = [[1,2,3],[4,5,6]]
A + B should be [[2,3,4],[6,7,8]]

It would also be interesting how I could add the other way (n,) + (m,n) :

A = [1,2,3]
B = [[1,2,3],[3,4,5]]
A + B should be [[2,4,6],[4,6,8]]

Edit:
The shapes I meant aren't the same as I wrote down.
The first example is not (n,1)+(n,m) and the second example is not (n,1)+(m,n) .
Before this edit I confused (n,) with (n,1) . (and with (1,n) )

Answer 1

Numpy has a feature named broadcasting . See the docs

The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations. Subject to certain constraints, the smaller array is “broadcast” across the larger array so that they have compatible shapes. Broadcasting provides a means of vectorizing array operations so that looping occurs in C instead of Python. It does this without making needless copies of data and usually leads to efficient algorithm implementations. There are, however, cases where broadcasting is a bad idea because it leads to inefficient use of memory that slows computation.

You can add this two arrays, you should just change dims of array A

A = np.array([1,2,3]).reshape(1,3)
B = np.array([[1,2,3],[3,4,5]])  # this is already 2 dimensional

print(A + B)

Answer 2

It would literally be just A + B , but your inputs aren't the arrays you think they are.

Your inputs are nested lists, and converted to arrays, your A examples are 1D, not 2D. Your inputs should look like

A = numpy.array([[1],[2]])
B = numpy.array([[1,2,3],[4,5,6]])

Then A + B would work.

Answer 3

In [46]: A = [1,2]
    ...: B = [[1,2,3],[4,5,6]]
In [47]: A+B
Out[47]: [1, 2, [1, 2, 3], [4, 5, 6]]

Addition for lists is a join. But if you really mean you have arrays:

In [48]: AA = np.array(A); BB = np.array(B)
In [49]: AA+BB
Traceback (most recent call last):
  File "<ipython-input-49-14674959eb4e>", line 1, in <module>
    AA+BB
ValueError: operands could not be broadcast together with shapes (2,) (2,3) 

But by making the first (2,1) shape, that does work:

In [50]: AA[:,None]+BB
Out[50]: 
array([[2, 3, 4],
       [6, 7, 8]])

The 2nd case works without modification, adding a (3,) to (2,3). The first is automatically promoted to (1,3). Adding the lead dimension is automatic; trailing dimensions are your responsibility:

In [51]: A = np.array([1,2,3])
    ...: B = np.array([[1,2,3],[3,4,5]])
In [52]: A+B
Out[52]: 
array([[2, 4, 6],
       [4, 6, 8]])