numpy.vectorize of function that returns an array

Question

I am trying to vectorize a function which has 2 inputs, and outputs a np.array, of shape =(4,). The function looks like this:

def f(a, b):
    return np.array([a+b, a-b, a, b])

I was able to vectorize the function, using the signature parameter, however it only works if I exclude one of the parameters using the excluded argument of np.vectorize:

This works:

vec = np.vectorize(f, signature='()->(n)', excluded=[1])
x = np.arange(5)
y = 3
vec(x, y)

>> output:
array([[ 3, -3,  0,  3],
       [ 4, -2,  1,  3],
       [ 5, -1,  2,  3],
       [ 6,  0,  3,  3],
       [ 7,  1,  4,  3]])

However if I take out the excluded argument, things don't go as planned.

This does not work:

vec = np.vectorize(f, signature='()->(n)')
x = np.arange(5)
y = 3
vec(x, y)

>> Error:
TypeError: wrong number of positional arguments: expected 1, got 2

How can I make the vectorized function able to receive an array/list of input values for either one (or both) of the input parameters?

The expected output would be a vec function which would enable calling it with multiple inputs for either one of the input parameters.

hpaulj · Accepted Answer · 2019-03-26 02:39:30Z

5

In [237]: f1 = np.vectorize(f, signature='(),()->(n)')                          
In [238]: f1(np.arange(5),3)                                                    
Out[238]: 
array([[ 3, -3,  0,  3],
       [ 4, -2,  1,  3],
       [ 5, -1,  2,  3],
       [ 6,  0,  3,  3],
       [ 7,  1,  4,  3]])

In [241]: f1(np.arange(5),np.ones((4,5))).shape                                 
Out[241]: (4, 5, 4)
In [242]: f1(np.arange(5),np.ones((1,5))).shape                                 
Out[242]: (1, 5, 4)

frompyfunc returns a object dtype array:

In [336]: f2 = np.frompyfunc(f,2,1)                                             
In [337]: f2(np.arange(5), 3)                                                   
Out[337]: 
array([array([ 3, -3,  0,  3]), array([ 4, -2,  1,  3]),
       array([ 5, -1,  2,  3]), array([6, 0, 3, 3]), array([7, 1, 4, 3])],
      dtype=object)
In [338]: _.shape                                                               
Out[338]: (5,)

np.vectorize, without the signature, uses frompyfunc, but adds its own dtype conversion.

In [340]: f1(np.arange(5), np.arange(3)) 
ValueError: shape mismatch: objects cannot be broadcast to a single shape

This fails for the same reason the following addition fails:

In [341]: np.arange(5)+np.arange(3)                                             
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-341-fb1c4f4372da> in <module>
----> 1 np.arange(5)+np.arange(3)

ValueError: operands could not be broadcast together with shapes (5,) (3,)

To get a (5,3) result we need to make the first argument (5,1) shape:

In [342]: np.arange(5)[:,None]+np.arange(3)                                     
Out[342]: 
array([[0, 1, 2],
       [1, 2, 3],
       [2, 3, 4],
       [3, 4, 5],
       [4, 5, 6]])

edited Mar 26, 2019 at 2:39

answered Mar 25, 2019 at 1:34

hpaulj

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6 Comments

Paul Panzer Over a year ago

Rather monosyllabic by your standards ;-)

hpaulj Over a year ago

@PaulPanzer, I have mixed feels about this signature method. It's an interesting idea, but it runs even slower than the regular vectorize.

Patricio P Over a year ago

@hpaulj, I would expect another behavior... perhaps vectorize is not the function I should be using? For the case of f1(x, y), where x has n elements, and y has m elements, I would expect to be returned an array of dimensions n x m, where each element is f(x_i, y_j) for 0<i<n, 0<j<m. Then each element of this array would itself be a 4-item vector, as output by f(a,b)

Patricio P Over a year ago

@hpaulj not sure why we need to pass a 2-dim array as the second parameter. I would expect to call f1(np.arange(5),np.arange(3)) and get a shape (3, 5, 4)

hpaulj Over a year ago

The (4,5,4) array is a (n, m, 4) array. I just added a frompyfunc example that creates a (n,m) object dtype array, where each element is 4 element array.

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