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Python: Collapsing arrays of arrays into each other without for loops

Suppose I have multiple NxN 2D arrays stored into a list in Python 3. I want to collapse all the arrays into 1 array, with the same dimensions NxN, but such that each element of this new array contains a 1xN array of the corresponding values from the original arrays.
To give you some more context, each array in this list corresponds to the set of values at a given time. For each new time point, I am storing the updated version of that array into the list. Once that's done, I want to compute the standard deviation of the values at each (i,j) element in the array.
I tried using a for loop, but it takes far too long for my simulations because this is a set of 100,000 arrays. I was wondering if there were any numpy or vectorized functions that can help me perform this operation more efficiently. Thanks!

Lets say l is your list of arrays. You need to get std of corresponding elements of those arrays into a single array:
std_l = np.std(np.stack(l),axis=0)

how to populate a numpy 2D array with function returning a numpy 1D array

I have function predicton like
def predictions(degree):
some magic,
return an np.ndarray([0..100])
I want to call this function for a few values of degree and use it to populate a larger np.ndarray (n=2), filling each row with the outcome of the function predictions. It seems like a simple task but somehow I cant get it working. I tried with
for deg in [1,2,4,8,10]:
np.append(result, predictions(deg),axis=1)
with result being an np.empty(100). But that failed with Singleton array array(1) cannot be considered a valid collection.
I could not get fromfunction it only works on a coordinate tuple, and the irregular list of degrees is not covered in the docs.

Don't use np.ndarray until you are older and wiser! I couldn't even use it without rereading the docs.
arr1d = np.array([1,2,3,4,5])
is the correct way to construct a 1d array from a list of numbers.
Also don't use np.append. I won't even add the 'older and wiser' qualification. It doesn't work in-place; and is slow when used in a loop.
A good way of building a 2 array from 1d arrays is:
alist = []
for i in ....:
alist.append(<alist or 1d array>)
arr = np.array(alist)
provided all the sublists have the same size, arr should be a 2d array.
This is equivalent to building a 2d array from
np.array([[1,2,3], [4,5,6]])
that is a list of lists.
Or a list comprehension:
np.array([predictions(i) for i in range(10)])
Again, predictions must all return the same length arrays or lists.

append is in the boring section of numpy. here you know the shape in advance
len_predictions = 100
def predictions(degree):
return np.ones((len_predictions,))
degrees = [1,2,4,8,10]
result = np.empty((len(degrees), len_predictions))
for i, deg in enumerate(degrees):
result[i] = predictions(deg)
if you want to store the degree somehow, you can use custom dtypes

Numpy array of multiple indices replace with a different matrix

I have an array of 2d indices.
indices = [[2,4], [6,77], [102,554]]
Now, I have a different 4-dimensional array, arr, and I want to only extract an array (it is an array, since it is 4-dimensional) with corresponding index in the indices array. It is equivalent to the following code.
for i in range(len(indices)):
output[i] = arr[indices[i][0], indices[i][1]]
However, I realized that using explicit for-loop yields a slow result. Is there any built-in numpy API that I can utilized? At this point, I tried using np.choose, np.put, np.take, but did not succeed to yield what I wanted. Thank you!

We need to index into the first two axes with the two columns from indices (thinking of it as an array).
Thus, simply convert to array and index, like so -
indices_arr = np.array(indices)
out = arr[indices_arr[:,0], indices_arr[:,1]]
Or we could extract those directly without converting to array and then index -
d0,d1 = [i[0] for i in indices], [i[1] for i in indices]
out = arr[d0,d1]
Another way to extract the elements would be with conversion to tuple, like so -
out = arr[tuple(indices_arr.T)]
If indices is already an array, skip the conversion process and use indices in places where we had indices_arr.

Try using the take function of numpy arrays. Your code should be something like:
outputarray= np.take(arr,indices)

numpy arrays: filling and extracting data quickly

See important clarification at bottom of this question.
I am using numpy to speed up some processing of longitude/latitude coordinates. Unfortunately, my numpy "optimizations" made my code run about 5x more slowly than it ran without using numpy.
The bottleneck seems to be in filling the numpy array with my data, and then extracting out that data after I have done the mathematical transformations. To fill the array I basically have a loop like:
point_list = GetMyPoints() # returns a long list of ( lon, lat ) coordinate pairs
n = len( point_list )
point_buffer = numpy.empty( ( n, 2 ), numpy.float32 )
for point_index in xrange( 0, n ):
point_buffer[ point_index ] = point_list[ point_index ]
That loop, just filling in the numpy array before even operating on it, is extremely slow, much slower than the entire computation was without numpy. (That is, it's not just the slowness of the python loop itself, but apparently some huge overhead in actually transferring each small block of data from python to numpy.) There is similar slowness on the other end; after I have processed the numpy arrays, I access each modified coordinate pair in a loop, again as
some_python_tuple = point_buffer[ index ]
Again that loop to pull the data out is much slower than the entire original computation without numpy. So, how do I actually fill the numpy array and extract data from the numpy array in a way that doesn't defeat the purpose of using numpy in the first place?
I am reading the data from a shape file using a C library that hands me the data as a regular python list. I understand that if the library handed me the coordinates already in a numpy array there would be no "filling" of the numpy array necessary. But unfortunately the starting point for me with the data is as a regular python list. And more to the point, in general I want to understand how you quickly fill a numpy array with data from within python.
Clarification
The loop shown above is actually oversimplified. I wrote it that way in this question because I wanted to focus on the problem I was seeing of trying to fill a numpy array slowly in a loop. I now understand that doing that is just slow.
In my actual application what I have is a shape file of coordinate points, and I have an API to retrieve the points for a given object. There are something like 200,000 objects. So I repeatedly call a function GetShapeCoords( i ) to get the coords for object i. This returns a list of lists, where each sublist is a list of lon/lat pairs, and the reason it's a list of lists is that some of the objects are multi-part (i.e., multi-polygon). Then, in my original code, as I read in each object's points, I was doing a transformation on each point by calling a regular python function, and then plotting the transformed points using PIL. The whole thing took about 20 seconds to draw all 200,000 polygons. Not terrible, but much room for improvement. I noticed that at least half of those 20 seconds were spent doing the transformation logic, so I thought I'd do that in numpy. And my original implementation was just to read in the objects one at a time, and keep appending all the points from the sublists into one big numpy array, which I then could do the math stuff on in numpy.
So, I now understand that simply passing a whole python list to numpy is the right way to set up a big array. But in my case I only read one object at a time. So one thing I could do is keep appending points together in a big python list of lists of lists. And then when I've compiled some large number of objects' points in this way (say, 10000 objects), I could simply assign that monster list to numpy.
So my question now is three parts:
(a) Is it true that numpy can take that big, irregularly shaped, list of lists of lists, and slurp it okay and quickly?
(b) I then want to be able to transform all the points in the leaves of that monster tree. What is the expression to get numpy to, for instance, "go into each sublist, and then into each subsublist, and then for each coordinate pair you find in those subsublists multiply the first (lon coordinate) by 0.5"? Can I do that?
(c) Finally, I need to get those transformed coordinates back out in order to plot them.
Winston's answer below seems to give some hint at how I might do this all using itertools. What I want to do is pretty much like what Winston does, flattening the list out. But I can't quite just flatten it out. When I go to draw the data, I need to be able to know when one polygon stops and the next starts. So, I think I could make it work if there were a way to quickly mark the end of each polygon (i.e., each subsublist) with a special coordinate pair like (-1000, -1000) or something like that. Then I could flatten with itertools as in Winston's answer, and then do the transforms in numpy. Then I need to actually draw from point to point using PIL, and here I think I'd need to reassign the modified numpy array back to a python list, and then iterate through that list in a regular python loop to do the drawing. Does that seem like my best option short of just writing a C module to handle all the reading and drawing for me in one step?

You describe your data as being "lists of lists of lists of coordinates". From this I'm guessing your extraction looks like this:
for x in points:
for y in x:
for Z in y:
# z is a tuple with GPS coordinates
Do this:
# initially, points is a list of lists of lists
points = itertools.chain.from_iterable(points)
# now points is an iterable producing lists
points = itertools.chain.from_iterable(points)
# now points is an iterable producing coordinates
points = itertools.chain.from_iterable(points)
# now points is an iterable producing individual floating points values
data = numpy.fromiter(points, float)
# data is a numpy array containing all the coordinates
data = data.reshape( data.size/2,2)
# data has now been reshaped to be an nx2 array
itertools and numpy.fromiter are both implemented in c and really efficient. As a result, this should do the transformation very quickly.
The second part of your question doesn't really indicate what you want do with the data. Indexing numpy array is slower then indexing python lists. You get speed by performing operations in mass on the data. Without knowing more about what you are doing with that data, its hard to suggest how to fix it.
UPDATE:
I've gone ahead and done everything using itertools and numpy. I am not responsible from any brain damage resulting from attempting to understand this code.
# firstly, we use imap to call GetMyPoints a bunch of times
objects = itertools.imap(GetMyPoints, xrange(100))
# next, we use itertools.chain to flatten it into all of the polygons
polygons = itertools.chain.from_iterable(objects)
# tee gives us two iterators over the polygons
polygons_a, polygons_b = itertools.tee(polygons)
# the lengths will be the length of each polygon
polygon_lengths = itertools.imap(len, polygons_a)
# for the actual points, we'll flatten the polygons into points
points = itertools.chain.from_iterable(polygons_b)
# then we'll flatten the points into values
values = itertools.chain.from_iterable(points)
# package all of that into a numpy array
all_points = numpy.fromiter(values, float)
# reshape the numpy array so we have two values for each coordinate
all_points = all_points.reshape(all_points.size // 2, 2)
# produce an iterator of lengths, but put a zero in front
polygon_positions = itertools.chain([0], polygon_lengths)
# produce another numpy array from this
# however, we take the cumulative sum
# so that each index will be the starting index of a polygon
polygon_positions = numpy.cumsum( numpy.fromiter(polygon_positions, int) )
# now for the transformation
# multiply the first coordinate of every point by *.5
all_points[:,0] *= .5
# now to get it out
# polygon_positions is all of the starting positions
# polygon_postions[1:] is the same, but shifted on forward,
# thus it gives us the end of each slice
# slice makes these all slice objects
slices = itertools.starmap(slice, itertools.izip(polygon_positions, polygon_positions[1:]))
# polygons produces an iterator which uses the slices to fetch
# each polygon
polygons = itertools.imap(all_points.__getitem__, slices)
# just iterate over the polygon normally
# each one will be a slice of the numpy array
for polygon in polygons:
draw_polygon(polygon)
You might find it best to deal with a single polygon at a time. Convert each polygon into a numpy array and do the vector operations on that. You'll probably get a significant speed advantage just doing that. Putting all of your data into numpy might be a little difficult.
This is more difficult then most numpy stuff because of your oddly shaped data. Numpy pretty much assumes a world of uniformly shaped data.

The point of using numpy arrays is to avoid as much as possible for loops. Writing for loops yourself will result in slow code, but with numpy arrays you can use predefined vectorized functions which are much faster (and easier!).
So for the conversion of a list to an array you can use:
point_buffer = np.array(point_list)
If the list contains elements like (lat, lon), then this will be converted to an array with two columns.
With that numpy array you can easily manipulate all elements at once. For example, to multiply the first element of each coordinate pair by 0.5 as in your question, you can do simply (assuming that the first elements are eg in the first column):
point_buffer[:,0] * 0.5

This will be faster:
numpy.array(point_buffer, dtype=numpy.float32)
Modifiy the array, not the list. It would obviously be better to avoid creating the list in the first place if possible.
Edit 1: profiling
Here is some test code that demonstrates just how efficiently numpy converts lists to arrays (it's good). And that my list-to-buffer idea is only comparable to what numpy does, not better.
import timeit
setup = '''
import numpy
import itertools
import struct
big_list = numpy.random.random((10000,2)).tolist()'''
old_way = '''
a = numpy.empty(( len(big_list), 2), numpy.float32)
for i,e in enumerate(big_list):
a[i] = e
'''
normal_way = '''
a = numpy.array(big_list, dtype=numpy.float32)
'''
iter_way = '''
chain = itertools.chain.from_iterable(big_list)
a = numpy.fromiter(chain, dtype=numpy.float32)
'''
my_way = '''
chain = itertools.chain.from_iterable(big_list)
buffer = struct.pack('f'*len(big_list)*2,*chain)
a = numpy.frombuffer(buffer, numpy.float32)
'''
for way in [old_way, normal_way, iter_way, my_way]:
print timeit.Timer(way, setup).timeit(1)
results:
0.22445492374
0.00450378469941
0.00523579114088
0.00451488946237
Edit 2: Regarding the hierarchical nature of the data
If i understand that the data is always a list of lists of lists (object - polygon - coordinate), then this is the approach I'd take: Reduce the data to the lowest dimension that creates a square array (2D in this case) and track the indices of the higher-level branches with a separate array. This is essentially an implementation of Winston's idea of using numpy.fromiter of a itertools chain object. The only added idea is the branch indexing.
import numpy, itertools
# heirarchical list of lists of coord pairs
polys = [numpy.random.random((n,2)).tolist() for n in [5,7,12,6]]
# get the indices of the polygons:
lengs = numpy.array([0]+[len(l) for l in polys])
p_idxs = numpy.add.accumulate(lengs)
# convert the flattend list to an array:
chain = itertools.chain.from_iterable
a = numpy.fromiter(chain(chain(polys)), dtype=numpy.float32).reshape(lengs.sum(), 2)
# transform the coords
a *= .5
# get a transformed polygon (using the indices)
def get_poly(n):
i0 = p_idxs[n]
i1 = p_idxs[n+1]
return a[i0:i1]
print 'poly2', get_poly(2)
print 'poly0', get_poly(0)

numpy: efficient execution of a complex reshape of an array

I am reading a vendor-provided large binary array into a 2D numpy array tempfid(M, N)
# load data
data=numpy.fromfile(file=dirname+'/fid', dtype=numpy.dtype('i4'))
# convert to complex data
fid=data[::2]+1j*data[1::2]
tempfid=fid.reshape(I*J*K, N)
and then I need to reshape it into a 4D array useful4d(N,I,J,K) using non-trivial mappings for the indices. I do this with a for loop along the following lines:
for idx in range(M):
i=f1(idx) # f1, f2, and f3 are functions involving / and % as well as some lookups
j=f2(idx)
k=f3(idx)
newfid[:,i,j,k] = tempfid[idx,:] #SLOW! CAN WE IMPROVE THIS?
Converting to complex takes 33% of the time while the copying of these slices M slices takes the remaining 66%. Calculating the indices is fast irrespective of whether I do this one by one in a loop as shown or by numpy.vectorizing the operation and applying it to an arange(M).
Is there a way to speed this up? Any help on more efficient slicing, copying (or not) etc appreciated.
EDIT:
As learned in the answer to question "What's the fastest way to convert an interleaved NumPy integer array to complex64?" the conversion to complex can be sped up by a factor of 6 if a view is used instead:
fid = data.astype(numpy.float32).view(numpy.complex64)

idx = numpy.arange(M)
i = numpy.vectorize(f1)(idx)
j = numpy.vectorize(f2)(idx)
k = numpy.vectorize(f3)(idx)
# you can index arrays with other arrays
# that lets you specify this operation in one line.
newfid[:, i,j,k] = tempfid.T
I've never used numpy's vectorize. Vectorize just means that numpy will call your python function multiple times. In order to get speed, you need use array operations like the one I showed here and you used to get complex numbers.
EDIT
The problem is that the dimension of size 128 was first in newfid, but last in tempfid. This is easily by using .T which takes the transpose.

How about this. Set us your indicies using the vectorized versions of f1,f2,f3 (not necessarily using np.vectorize, but perhaps just writing a function that takes an array and returns an array), then use np.ix_:
http://docs.scipy.org/doc/numpy/reference/generated/numpy.ix_.html
to get the index arrays. Then reshape tempfid to the same shape as newfid and then use the results of np.ix_ to set the values. For example:
tempfid = np.arange(10)
i = f1(idx) # i = [4,3,2,1,0]
j = f2(idx) # j = [1,0]
ii = np.ix_(i,j)
newfid = tempfid.reshape((5,2))[ii]
This maps the elements of tempfid onto a new shape with a different ordering.