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Vectorize list returning python function into numpy nd-array [duplicate]

numpy.vectorize takes a function f:a->b and turns it into g:a[]->b[].
This works fine when a and b are scalars, but I can't think of a reason why it wouldn't work with b as an ndarray or list, i.e. f:a->b[] and g:a[]->b[][]
For example:
import numpy as np
def f(x):
return x * np.array([1,1,1,1,1], dtype=np.float32)
g = np.vectorize(f, otypes=[np.ndarray])
a = np.arange(4)
print(g(a))
This yields:
array([[ 0. 0. 0. 0. 0.],
[ 1. 1. 1. 1. 1.],
[ 2. 2. 2. 2. 2.],
[ 3. 3. 3. 3. 3.]], dtype=object)
Ok, so that gives the right values, but the wrong dtype. And even worse:
g(a).shape
yields:
(4,)
So this array is pretty much useless. I know I can convert it doing:
np.array(map(list, a), dtype=np.float32)
to give me what I want:
array([[ 0., 0., 0., 0., 0.],
[ 1., 1., 1., 1., 1.],
[ 2., 2., 2., 2., 2.],
[ 3., 3., 3., 3., 3.]], dtype=float32)
but that is neither efficient nor pythonic. Can any of you guys find a cleaner way to do this?

np.vectorize is just a convenience function. It doesn't actually make code run any faster. If it isn't convenient to use np.vectorize, simply write your own function that works as you wish.
The purpose of np.vectorize is to transform functions which are not numpy-aware (e.g. take floats as input and return floats as output) into functions that can operate on (and return) numpy arrays.
Your function f is already numpy-aware -- it uses a numpy array in its definition and returns a numpy array. So np.vectorize is not a good fit for your use case.
The solution therefore is just to roll your own function f that works the way you desire.

A new parameter signature in 1.12.0 does exactly what you what.
def f(x):
return x * np.array([1,1,1,1,1], dtype=np.float32)
g = np.vectorize(f, signature='()->(n)')
Then g(np.arange(4)).shape will give (4L, 5L).
Here the signature of f is specified. The (n) is the shape of the return value, and the () is the shape of the parameter which is scalar. And the parameters can be arrays too. For more complex signatures, see Generalized Universal Function API.

import numpy as np
def f(x):
return x * np.array([1,1,1,1,1], dtype=np.float32)
g = np.vectorize(f, otypes=[np.ndarray])
a = np.arange(4)
b = g(a)
b = np.array(b.tolist())
print(b)#b.shape = (4,5)
c = np.ones((2,3,4))
d = g(c)
d = np.array(d.tolist())
print(d)#d.shape = (2,3,4,5)
This should fix the problem and it will work regardless of what size your input is. "map" only works for one dimentional inputs. Using ".tolist()" and creating a new ndarray solves the problem more completely and nicely(I believe). Hope this helps.

You want to vectorize the function
import numpy as np
def f(x):
return x * np.array([1,1,1,1,1], dtype=np.float32)
Assuming that you want to get single np.float32 arrays as result, you have to specify this as otype. In your question you specified however otypes=[np.ndarray] which means you want every element to be an np.ndarray. Thus, you correctly get a result of dtype=object.
The correct call would be
np.vectorize(f, signature='()->(n)', otypes=[np.float32])
For such a simple function it is however better to leverage numpy's ufunctions; np.vectorize just loops over it. So in your case just rewrite your function as
def f(x):
return np.multiply.outer(x, np.array([1,1,1,1,1], dtype=np.float32))
This is faster and produces less obscure errors (note however, that the results dtype will depend on x if you pass a complex or quad precision number, so will be the result).

I've written a function, it seems fits to your need.
def amap(func, *args):
'''array version of build-in map
amap(function, sequence[, sequence, ...]) -> array
Examples
--------
>>> amap(lambda x: x**2, 1)
array(1)
>>> amap(lambda x: x**2, [1, 2])
array([1, 4])
>>> amap(lambda x,y: y**2 + x**2, 1, [1, 2])
array([2, 5])
>>> amap(lambda x: (x, x), 1)
array([1, 1])
>>> amap(lambda x,y: [x**2, y**2], [1,2], [3,4])
array([[1, 9], [4, 16]])
'''
args = np.broadcast(None, *args)
res = np.array([func(*arg[1:]) for arg in args])
shape = args.shape + res.shape[1:]
return res.reshape(shape)
Let try
def f(x):
return x * np.array([1,1,1,1,1], dtype=np.float32)
amap(f, np.arange(4))
Outputs
array([[ 0., 0., 0., 0., 0.],
[ 1., 1., 1., 1., 1.],
[ 2., 2., 2., 2., 2.],
[ 3., 3., 3., 3., 3.]], dtype=float32)
You may also wrap it with lambda or partial for convenience
g = lambda x:amap(f, x)
g(np.arange(4))
Note the docstring of vectorize says
The vectorize function is provided primarily for convenience, not for
performance. The implementation is essentially a for loop.
Thus we would expect the amap here have similar performance as vectorize. I didn't check it, Any performance test are welcome.
If the performance is really important, you should consider something else, e.g. direct array calculation with reshape and broadcast to avoid loop in pure python (both vectorize and amap are the later case).

The best way to solve this would be to use a 2-D NumPy array (in this case a column array) as an input to the original function, which will then generate a 2-D output with the results I believe you were expecting.
Here is what it might look like in code:
import numpy as np
def f(x):
return x*np.array([1, 1, 1, 1, 1], dtype=np.float32)
a = np.arange(4).reshape((4, 1))
b = f(a)
# b is a 2-D array with shape (4, 5)
print(b)
This is a much simpler and less error prone way to complete the operation. Rather than trying to transform the function with numpy.vectorize, this method relies on NumPy's natural ability to broadcast arrays. The trick is to make sure that at least one dimension has an equal length between the arrays.

subsetting affects .view(np.float64) behaviour

I'm trying to use some sklearn estimators for classifications on the coefficients of some fast fourier transform (technically Discrete Fourier Transform). I obtain a numpy array X_c as output of np.fft.fft(X) and I want to transform it into a real numpy array X_r, with each (complex) column of the original X_c transformed into two (real/float) columns in X_r, i.e the shape goes from (r, c) to (r, 2c). So I use .view(np.float64). and it works at first.
The problem is that if I first decide to keep only some coefficients of the original complex array with X_c2 = X_c[:, range(3)] and then to do the same thing as before instead of having the number of columns doubled, I obtain the number of ranks doubled (the imaginary part of each element is put in a new row below the original).
I really don't understand why this happens.
To make myself clearer, here is a toy example:
import numpy as np
# I create a complex array
X_c = np.arange(8, dtype = np.complex128).reshape(2, 4)
print(X_c.shape) # -> (2, 4)
# I use .view to transform it into something real and it works
# the way I want it.
X_r = X_c.view(np.float64)
print(X_r.shape) # -> (2, 8)
# Now I subset the array.
indices_coef = range(3)
X_c2 = X_c[:, indices_coef]
print(X_c2.shape) # -> (2, 3)
X_r2 = X_c2.view(np.float64)
# In the next line I obtain (4, 3), when I was expecting (2, 6)...
print(X_r2.shape) # -> (4, 3)
Does anyone see a reason for this difference of behavior?

I get a warning:
In [5]: X_c2 = X_c[:,range(3)]
In [6]: X_c2
Out[6]:
array([[ 0.+0.j, 1.+0.j, 2.+0.j],
[ 4.+0.j, 5.+0.j, 6.+0.j]])
In [7]: X_c2.view(np.float64)
/usr/local/bin/ipython3:1: DeprecationWarning: Changing the shape of non-C contiguous array by
descriptor assignment is deprecated. To maintain
the Fortran contiguity of a multidimensional Fortran
array, use 'a.T.view(...).T' instead
#!/usr/bin/python3
Out[7]:
array([[ 0., 1., 2.],
[ 0., 0., 0.],
[ 4., 5., 6.],
[ 0., 0., 0.]])
In [12]: X_c2.strides
Out[12]: (16, 32)
In [13]: X_c2.flags
Out[13]:
C_CONTIGUOUS : False
F_CONTIGUOUS : True
So this copy (or is a view?) is Fortran order. The recommended X_c2.T.view(float).T produces the same 4x3 array without the warning.
As your first view shows, a complex array has the same data layout as twice the number of floats.
I've seen funny shape behavior when trying to view a structured array. I'm wondering the complex dtype is behaving much like a dtype('f8,f8') array.
If I change your X_c2 so it is a copy, I get the expected behavior
In [19]: X_c3 = X_c[:,range(3)].copy()
In [20]: X_c3.flags
Out[20]:
C_CONTIGUOUS : True
F_CONTIGUOUS : False
OWNDATA : True
WRITEABLE : True
ALIGNED : True
UPDATEIFCOPY : False
In [21]: X_c3.strides
Out[21]: (48, 16)
In [22]: X_c3.view(float)
Out[22]:
array([[ 0., 0., 1., 0., 2., 0.],
[ 4., 0., 5., 0., 6., 0.]])
That's reassuring. But I'm puzzled as to why the [:, range(3)] indexing creates a F order view. That should be advance indexing.
And indeed, a true slice does not allow this view
In [28]: X_c[:,:3].view(np.float64)
---------------------------------------------------------------------------
ValueError: new type not compatible with array.
So the range indexing has created some sort of hybrid object.

What does np.empty((0,shape)) in python mean?

How can the tuple with shape (0,2) be passed?
a = np.empty((0,2))
a
>>> array([], shape=(0, 2), dtype=float64)
Also what is the difference between tuple and list while passing the shape as a parameter in np.empty()?
arr = np.empty((2,2))
arr
>>> array([[ 0., 0.],
[ 0., 0.]])
arr1 = np.empty([2,2])
arr1
>>> array([[ 0., 0.],
[ 0., 0.]])
How both tuple and list gives same output?

Passing a tuple with 0, such as (0, 2) as shape parameter is allowed, but the resulting array is empty since it contains 0*2 = 0 elements. Written out in words, it's "zero rows with 2 elements in each row" where "2 elements in each row" is not of much consequence since there are no rows.
Such arrays arise when slicing goes wrong: for example,
b = np.ones((2, 2))
a = b[2:, :]
makes a an array of shape (0, 2) as there are no values of the first index that fall in the given slice. There is no reason to create such arrays intentionally.
There is no difference between np.empty([2, 2]) and np.empty((2, 2)), the array creation method, as many other NumPy methods, accepts a list instead of a tuple. It's still recommended to use tuples for shape parameters, because arr.shape is always a tuple.

Create a numpy array according to another array along with indices array

I have a numpy array(eg., a = np.array([ 8., 2.])), and another array which stores the indices I would like to get from the former array. (eg., b = np.array([ 0., 1., 1., 0., 0.]).
What I would like to do is to create another array from these 2 arrays, in this case, it should be: array([ 8., 2., 2., 8., 8.])
of course, I can always use a for loop to achieve this goal:
for i in range(5):
c[i] = a[b[i]]
I wonder if there is a more elegant method to create this array. Something like c = a[b[0:5]] (well, this apparently doesn't work)

Only integer arrays can be used for indexing, and you've created b as a float64 array. You can get what you're looking for if you explicitly convert to integer:
bi = np.array(b, dtype=int)
c = a[bi[0:5]]

How to assign a 1D numpy array of length x to an element of length y of a 2D Numpy Array?

I'm looking for a way to assign a 1D numpy-array consisting of x elements to a 2D numpy Array of shape (y,z).
Example:
A=np.array([[0],[0],[0]])
A[2]=np.array([0,2])
Which should result in
A=[[0],[0],[0,2]]
This works perfectly fine using a python list, but has been causing me huge trouble when trying to do it in numpy, usually resulting in the error message:
could not broadcast input array from shape (z) into shape (x)
This seems to occur as a result of the fact that numpy copies everything instead of modifying the array in place. I have only recently begun using numpy and would really be grateful if someone could help find a way to do this efficiently.

Actually the issue is that Numpy refuses to perform implicit copies or reshapes. For instance:
>>> A=np.array([[0],[0],[0]])
>>> A[2]=np.array([0,2])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ValueError: could not broadcast input array from shape (2) into shape (1)
Here A[2] is a subarray of A, of shape 1. 2 cells can't fit in 1, so we get shape error. The reverse situation is possible and known as broadcasting:
>>> A[0:2]=5
>>> A
array([[5],
[5],
[0]])
Here a single scalar has been broadcast to update the entire subarray. We can resize A to be able to fit the shape 2 entry:
>>> A.shape
(3, 1)
>>> A.resize((3,2))
>>> A.shape
(3, 2)
>>> A[2]=np.array([0,2])
>>> A
array([[5, 5],
[0, 0],
[0, 2]])
We can see that the resizing actually reorganized our cells. It still starts with 5 5 0 but the cells are no longer along a single column. This is because numpy doesn't copy unless asked to, either; all of our multicell slices in fact refer into the same original array. We can make a second matrix and copy the original into a single column there:
>>> B=np.zeros((A.shape[0]+1,A.shape[1]))
>>> B[:,0]=A.transpose()
>>> B
array([[ 5., 0.],
[ 5., 0.],
[ 0., 0.]])
The transpose is because the slice of B is 1-dimensional shape (3 long) rather than a 2-dimensional shape like A (which is 1 wide and 3 high). Numpy considers the 1-dimensional array to be a horisontal shape, so a 3 wide and 1 high matrix will fit. You could think of it like copying a range of cells in a spreadsheet.
Notably, the numbers thus placed in B are copies of what was in A. This is because we did a modification of B. Views can be used to manipulate sections of a matrix (including seeing it in another shape, like transpose() does), for instance:
>>> C=B[::-1,1]
>>> C
array([ 0., 0., 0.])
>>> C[:]=[1,2,3]
>>> B
array([[ 5., 3.],
[ 5., 2.],
[ 0., 1.]])