Elementwise operations over tuples in Python - python

Are there any built-in functions that allow elementwise operations over tuples in Python 3? If not, what is the "pythonic" way to perform these operations?
Example: I want to take the percent difference between a and b and compare them to some threshold th.
>>> a = (1, 2, 4)
>>> b = (1.1, 2.1, 4.1)
>>> # compute pd = 100*abs(a-b)/a = (10.0, 5.0, 2.5)
>>> th = 3
>>> # test threshold: pd < th => (False, False, True)

There is no builtin way, but there is a pretty simple way:
[f(aItem, bItem) for aItem, bItem in zip(a, b)]
. . . where f is the function you want to apply elementwise. For your case:
[100*abs(aItem - bItem)/aItem < 3 for aItem, bItem in zip(a, b)]
If you find yourself doing this a lot, especially with long tuples, you might want to look at Numpy, which provides a full-featured system of vector operations in which many common vector functions (basic operations, trig functions, etc.) apply elementwise.

map function
>>> a = (1, 2, 4)
>>> b = (1.1, 2.1, 4.1)
>>> map(lambda a,b: 100*abs(a-b)/a < 3, a, b)
[False, False, True]
EDIT
of course instead of map, you can use list comprehensions, like BrenBarn did http://docs.python.org/tutorial/datastructures.html#nested-list-comprehensions
EDIT 2 zip removed, thanks for DSM to point it out that zip is not needed

Why not use NumPy?
import numpy as np
a = np.array([1,2,4])
b = np.array([1.1, 2.1, 4.1])
pd = 100*abs(a-b)/a # result: array([ 10. , 5. , 2.5])
th = 3
pd < th # result: array([False, False, True], dtype=bool)

I am not aware of an operation like that, perhaps some of the functional programming features of Python would work (map? reduce?), though putting together a list comprehension (or generator if the list is not needed) is relatively straight forward:
[100*abs(j-b[i])/j < 3 for i,j in enumerate(a)]
[False, False, True]
Thanks to #delnan for pointing out a very nice simplification for the original, more explicit/verbose version:
[True if 100*abs(j-b[i])/j < 3 else False for i,j in enumerate(a)]

def pctError(observed, expected):
return (observed-expected)/expected * 100.0
a = (1, 2, 4)
b = (1.1, 2.1, 4.1)
th = 3
pctErrors = map(lambda t:pctError(*t), zip(a,b))
# returns [-9.091, -4.76, -2.44]
map(lambda x: x < th, pctErrors)
[x < th for x in pctErrors]
# both return [True, True, True]
# or if you always need absolute % errors
map(lambda x: abs(x) < th, pctErrors)
[abs(x) < th for x in pctErrors]
# both return [False, False, True]

I would say the Pythonic way is with list comprehension:
When a = (1, 2, 4) and b = (1.1, 2.1, 4.1)
then, in one line:
TEST = [100*abs(a[i]-b[i])/a[i] > th for i in range(len(A))]

Related

Count all values of an array that are between 0 and 1

Is there an effective way to count all the values in a numpy array which are between 0 and 1?
I know this is easily countable with a for loop, but that seems pretty inefficient to me. I tried to play around with the count_nonzero() function but I couldn't make it work the way I wanted.
Greetings
One quick and easy method is to use the logical_and() function, which returns a boolean mask array. Then simply use the .sum() function to sum the True values.
Example:
import numpy as np
a = np.array([0, .1, .2, .3, 1, 2])
np.logical_and(a>0, a<1).sum()
Output:
>>> 3
Example 2:
Or, if you'd prefer a more 'low-level' (non-helper function) approach, the & logical operator can be used:
((a > 0) & (a < 1)).sum()
This might be one way. You can easily replace <= and >= with strict inequalities as per your wish.
>>> import numpy as np
>>> a = np.random.randn(3,3)
>>> a
array([[-2.17470114, 0.59575531, 0.06795138],
[-0.57380035, 0.05663369, 1.12636801],
[ 0.55363332, -0.04039947, 1.14837819]])
>>> inds1 = a >= 0
>>> inds2 = a <= 1
>>> inds = inds1 * inds2
>>> inds
array([[False, True, True],
[False, True, False],
[ True, False, False]])
>>> inds.sum()
4

How to compare two numpy arrays with some NaN values?

I need to compare some numpy arrays which should have the same elements in the same order, excepting for some NaN values in the second one.
I need a function more or less like this:
def func( array1, array2 ):
if ???:
return True
else:
return False
Example:
x = np.array( [ 1, 2, 3, 4, 5 ] )
y = np.array( [ 11, 2, 3, 4, 5 ] )
z = np.array( [ 1, 2, np.nan, 4, 5] )
func( x, z ) # returns True
func( y, z ) # returns False
The arrays have always the same length and the NaN values are always in the third one (x and y have always numbers only). I can imagine there is a function or something already, but I just don't find it.
Any ideas?
You can use masked arrays, which have the behaviour you're asking for when combined with np.all:
zm = np.ma.masked_where(np.isnan(z), z)
np.all(x == zm) # returns True
np.all(y == zm) # returns False
Or you could just write out your logic explicitly, noting that numpy has to use | instead of or, and the difference in operator precedence that results:
def func(a, b):
return np.all((a == b) | np.isnan(a) | np.isnan(b))
You could use isclose to check for equality (or closeness to within a given tolerance -- this is particularly useful when comparing floats) and use isnan to check for NaNs in the second array.
Combine the two with bitwise-or (|), and use all to demand every pair is either close or contains a NaN to obtain the desired result:
In [62]: np.isclose(x,z)
Out[62]: array([ True, True, False, True, True], dtype=bool)
In [63]: np.isnan(z)
Out[63]: array([False, False, True, False, False], dtype=bool)
So you could use:
def func(a, b):
return (np.isclose(a, b) | np.isnan(b)).all()
In [67]: func(x, z)
Out[67]: True
In [68]: func(y, z)
Out[68]: False
What about:
from math import isnan
def fun(array1,array2):
return all(isnan(x) or isnan(y) or x == y for x,y in zip(array1,array2))
This function works in both directions (if there are NaNs in the first list, these are also ignored). If you do not want that (which is a bit odd since equality usually works bidirectional). You can define:
from math import isnan
def fun(array1,array2):
return all(isnan(y) or x == y for x,y in zip(array1,array2))
The code works as follows: we use zip to emit tuples of elements of both arrays. Next we check if either the element of the first list is NaN, or the second, or they are equal.
Given you want to write a really elegant function, you better also perform a length check:
from math import isnan
def fun(array1,array2):
return len(array1) == len(array2) and all(isnan(y) or x == y for x,y in zip(array1,array2))
numpy.islcose() now provides an argument equal_nan for this case!
>>> import numpy as np
>>> np.isclose([1.0, np.nan], [1.0, np.nan])
array([ True, False])
>>> np.isclose([1.0, np.nan], [1.0, np.nan], equal_nan=True)
array([ True, True])
docs https://numpy.org/doc/stable/reference/generated/numpy.isclose.html

Elementwise and in python list

I have two python lists A and B of equal length each containing only boolean values. Is it possible to get a third list C where C[i] = A[i] and B[i] for 0 <= i < len(A) without using loop?
I tried following
C = A and B
but probably it gives the list B
I also tried
C = A or B
which gives first list
I know it can easily be done using for loop in single line like C = [x and y for x, y in zip(A, B)].
I'd recommend you use numpy to use these kind of predicates over arrays. Now, I don't think you can avoid loops to achieve what you want, but... if you don't consider mapping or enumerating as a form of looping, you could do something like this (C1):
A = [True, True, True, True]
B = [False, False, True, True]
C = [x and y for x, y in zip(A, B)]
C1 = map(lambda (i,x): B[i] and x, enumerate(A))
C2 = [B[i] and x for i,x in enumerate(A)]
print C==C1==C2
You can do it without an explicit loop by using map, which performs the loop internally, at C speed. Of course, the actual and operation is still happening at Python speed, so I don't think it'll save much time (compared to doing essentially the same thing with Numpy, which can not only do the looping at C speed, it can do the and operation at C speed too. Of course, there's also the overhead of converting between native Python lists & Numpy arrays).
Demo:
from operator import and_
a = [0, 1, 0, 1]
b = [0, 0, 1, 1]
c = map(and_, a, b)
print c
output
[0, 0, 0, 1]
Note that the and_ function performs a bitwise and operation, but that should be ok since you're operating on boolean values.
Simple answer: you can't.
Except in the trivial way, which is by calling a function that does this for you, using a loop. If you want this kind of nice syntax you can use libraries as suggested: map, numpy, etc. Or you can write your own function.
If what you are looking for is syntactic convenience, Python does not allow overloading operators for built-in types such as list.
Oh, and you can use recursion, if that's "not a loop" for you.
Is it possible to get a third list C where C[i] = A[i] and B[i] for 0 <= i < len(A) without using loop?
Kind of:
class AndList(list):
def __init__(self, A, B):
self.A = A
self.B = B
def __getitem__(self, index):
return self.A[index] and self.B[index]
A = [False, False, True, True]
B = [False, True, False, True]
C = AndList(A, B)
print isinstance(C, list) and all(C[i] == (A[i] and B[i])
for i in range(len(A)))
Prints True.

Python: Elementwise comparison of same shaped arrays

I have n matrices of the same size and want to see how many cells are equal to each other across all matrices. Code:
import numpy as np
a = np.array([[1,2,3],[4,5,6],[7,8,9]])
b = np.array([[5,6,7], [4,2,6], [7, 8, 9]])
c = np.array([2,3,4],[4,5,6],[1,2,5])
#Intuition is below but is wrong
a == b == c
How do I get Python to return a value of 2 (cells 2,1 and 2,3 match in all 3 matrices) or an array of [[False, False, False], [True, False, True], [False, False, False]]?
You can do:
(a == b) & (b==c)
[[False False False]
[ True False True]
[False False False]]
For n items in, say, a list like x=[a, b, c, a, b, c], one could do:
r = x[0] == x[1]
for temp in x[2:]:
r &= x[0]==temp
The result in now in r.
If the structure is already in a 3D numpy array, one could also use:
np.amax(x,axis=2)==np.amin(x,axis=2)
The idea for the above line is that although it would be ideal to have an equal function with an axis argument, there isn't one so this line notes that if amin==amax along the axis, then all elements are equal.
If the different arrays to be compared aren't already in a 3D numpy array (or won't be in the future), looping the list is a fast and easy approach. Although I generally agree with avoiding Python loops for Numpy arrays, this seems like a case where it's easier and faster (see below) to use a Python loop since the loop is only along a single axis and it's easy to accumulate the comparisons in place. Here's a timing test:
def f0(x):
r = x[0] == x[1]
for y in x[2:]:
r &= x[0]==y
def f1(x): # from #Divakar
r = ~np.any(np.diff(np.dstack(x),axis=2),axis=2)
def f2(x):
x = np.dstack(x)
r = np.amax(x,axis=2)==np.amin(x,axis=2)
# speed test
for n, size, reps in ((1000, 3, 1000), (10, 1000, 100)):
x = [np.ones((size, size)) for i in range(n)]
print n, size, reps
print "f0: ",
print timeit("f0(x)", "from __main__ import x, f0, f1", number=reps)
print "f1: ",
print timeit("f1(x)", "from __main__ import x, f0, f1", number=reps)
print
1000 3 1000
f0: 1.14673900604 # loop
f1: 3.93413209915 # diff
f2: 3.93126702309 # min max
10 1000 100
f0: 2.42633581161 # loop
f1: 27.1066679955 # diff
f2: 25.9518558979 # min max
If arrays are already in a single 3D numpy array (eg, from using x = np.dstack(x) in the above) then modifying the above function defs appropriately and with the addition of the min==max approach gives:
def g0(x):
r = x[:,:,0] == x[:,:,1]
for iy in range(x[:,:,2:].shape[2]):
r &= x[:,:,0]==x[:,:,iy]
def g1(x): # from #Divakar
r = ~np.any(np.diff(x,axis=2),axis=2)
def g2(x):
r = np.amax(x,axis=2)==np.amin(x,axis=2)
which yields:
1000 3 1000
g0: 3.9761030674 # loop
g1: 0.0599548816681 # diff
g2: 0.0313589572906 # min max
10 1000 100
g0: 10.7617051601 # loop
g1: 10.881870985 # diff
g2: 9.66712999344 # min max
Note also that for a list of large arrays f0 = 2.4 and for a pre-built array g0, g1, g2 ~= 10., so that if the input arrays are large, than fastest approach by about 4x is to store them separately in a list. I find this a bit surprising and guess that this might be due to cache swapping (or bad code?), but I'm not sure anyone really cares so I'll stop this here.
Concatenate along the third axis with np.dstack and perfom differentiation with np.diff, so that the identical ones would show up as zeros. Then, check for cases where all are zeros with ~np.any. Thus, you would have a one-liner solution like so -
~np.any(np.diff(np.dstack((a,b,c)),axis=2),axis=2)
Sample run -
In [39]: a
Out[39]:
array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
In [40]: b
Out[40]:
array([[5, 6, 7],
[4, 2, 6],
[7, 8, 9]])
In [41]: c
Out[41]:
array([[2, 3, 4],
[4, 5, 6],
[1, 2, 5]])
In [42]: ~np.any(np.diff(np.dstack((a,b,c)),axis=2),axis=2)
Out[42]:
array([[False, False, False],
[ True, False, True],
[False, False, False]], dtype=bool)
Try this:
z1 = a == b
z2 = a == c
z = np.logical_and(z1,z2)
print "count:", np.sum(z)
You can do this in a single statement:
count = np.sum( np.logical_and(a == b, a == c) )

Numpy: Subtract array element by element

The title might be ambiguous, didn't know how else to word it.
I have gotten a bit far with my particle simulator in python using numpy and matplotlib, I have managed to implement coloumb, gravity and wind, now I just want to add temperature and pressure but I have a pre-optimization question (root of all evil). I want to see when particles crash:
Q: Is it in numpy possible to take the difference of an array with each of its own element based on a bool condition? I want to avoid looping.
Eg: (x - any element in x) < a
Should return something like
[True, True, False, True]
If element 0,1 and 3 in x meets the condition.
Edit:
The loop quivalent would be:
for i in len(x):
for j in in len(x):
#!= not so important
##earlier question I asked lets me figure that one out
if i!=j:
if x[j] - x[i] < a:
True
I notice numpy operations are far faster than if tests and this has helped me speed up things ALOT.
Here is a sample code if anyone wants to play with it.
#Simple circular box simulator, part of part_sim
#Restructure to import into gravity() or coloumb () or wind() or pressure()
#Or to use all forces: sim_full()
#Note: Implement crashing as backbone to all forces
import numpy as np
import matplotlib.pyplot as plt
N = 1000 #Number of particles
R = 8000 #Radius of box
r = np.random.randint(0,R/2,2*N).reshape(N,2)
v = np.random.randint(-200,200,r.shape)
v_limit = 10000 #Speedlimit
plt.ion()
line, = plt.plot([],'o')
plt.axis([-10000,10000,-10000,10000])
while True:
r_hit = np.sqrt(np.sum(r**2,axis=1))>R #Who let the dogs out, who, who?
r_nhit = ~r_hit
N_rhit = r_hit[r_hit].shape[0]
r[r_hit] = r[r_hit] - 0.1*v[r_hit] #Get the dogs back inside
r[r_nhit] = r[r_nhit] +0.1*v[r_nhit]
#Dogs should turn tail before they crash!
#---
#---crash code here....
#---crash end
#---
vmin, vmax = np.min(v), np.max(v)
#Give the particles a random kick when they hit the wall
v[r_hit] = -v[r_hit] + np.random.randint(vmin, vmax, (N_rhit,2))
#Slow down honey
v_abs = np.abs(v) > v_limit
#Hit the wall at too high v honey? You are getting a speed reduction
v[v_abs] *=0.5
line.set_ydata(r[:,1])
line.set_xdata(r[:,0])
plt.draw()
I plan to add colors to the datapoints above once I figure out how...such that high velocity particles can easily be distinguished in larger boxes.
Eg: x - any element in x < a Should return something like
[True, True, False, True]
If element 0,1 and 3 in x meets the condition. I notice numpy operations are far faster than if tests and this has helped me speed up things ALOT.
Yes, it's just m < a. For example:
>>> m = np.array((1, 3, 10, 5))
>>> a = 6
>>> m2 = m < a
>>> m2
array([ True, True, False, True], dtype=bool)
Now, to the question:
Q: Is it in numpy possible to take the difference of an array with each of its own element based on a bool condition? I want to avoid looping.
I'm not sure what you're asking for here, but it doesn't seem to match the example directly below it. Are you trying to, e.g., subtract 1 from each element that satisfies the predicate? In that case, you can rely on the fact that False==0 and True==1 and just subtract the boolean array:
>>> m3 = m - m2
>>> m3
>>> array([ 0, 2, 10, 4])
From your clarification, you want the equivalent of this pseudocode loop:
for i in len(x):
for j in in len(x):
#!= not so important
##earlier question I asked lets me figure that one out
if i!=j:
if x[j] - x[i] < a:
True
I think the confusion here is that this is the exact opposite of what you said: you don't want "the difference of an array with each of its own element based on a bool condition", but "a bool condition based on the difference of an array with each of its own elements". And even that only really gets you to a square matrix of len(m)*len(m) bools, but I think the part left over is that the "any".
At any rate, you're asking for an implicit cartesian product, comparing each element of m to each element of m.
You can easily reduce this from two loops to one (or, rather, implicitly vectorize one of them, gaining the usual numpy performance benefits). For each value, create a new array by subtracting that value from each element and comparing the result with a, and then join those up:
>>> a = -2
>>> comparisons = np.array([m - x < a for x in m])
>>> flattened = np.any(comparisons, 0)
>>> flattened
array([ True, True, False, True], dtype=bool)
But you can also turn this into a simple matrix operation pretty easily. Subtracting every element of m from every other element of m is just m - m.T. (You can make the product more explicit, but the way numpy handles adding row and column vectors, it isn't necessary.) And then you just compare every element of that to the scalar a, and reduce with any, and you're done:
>>> a = -2
>>> m = np.matrix((1, 3, 10, 5))
>>> subtractions = m - m.T
>>> subtractions
matrix([[ 0, 2, 9, 4],
[-2, 0, 7, 2],
[-9, -7, 0, -5],
[-4, -2, 5, 0]])
>>> comparisons = subtractions < a
>>> comparisons
matrix([[False, False, False, False],
[False, False, False, False],
[ True, True, False, True],
[ True, False, False, False]], dtype=bool)
>>> np.any(comparisons, 0)
matrix([[ True, True, False, True]], dtype=bool)
Or, putting it all together in one line:
>>> np.any((m - m.T) < a, 0)
matrix([[ True, True, True, True]], dtype=bool)
If you need m to be an array rather than a matrix, you can replace the subtraction line with m - np.matrix(m).T.
For higher dimensions, you actually do need to work in arrays, because you're trying to cartesian-product a 2D array with itself to get a 4D array, and numpy doesn't do 4D matrices. So, you can't use the simple "row vector - column vector = matrix" trick. But you can do it manually:
>>> m = np.array([[1,2], [3,4]]) # 2x2
>>> m4d = m.reshape(1, 1, 2, 2) # 1x1x2x2
>>> m4d
array([[[[1, 2],
[3, 4]]]])
>>> mt4d = m4d.T # 2x2x1x1
>>> mt4d
array([[[[1]],
[[3]]],
[[[2]],
[[4]]]])
>>> subtractions = m - mt4d # 2x2x2x2
>>> subtractions
array([[[[ 0, 1],
[ 2, 3]],
[[-2, -1],
[ 0, 1]]],
[[[-1, 0],
[ 1, 2]],
[[-3, -2],
[-1, 0]]]])
And from there, the remainder is the same as before. Putting it together into one line:
>>> np.any((m - m.reshape(1, 1, 2, 2).T) < a, 0)
(If you remember my original answer, I'd somehow blanked on reshape and was doing the same thing by multiplying m by a column vector of 1s, which obviously is a much stupider way to proceed.)
One last quick thought: If your algorithm really is "the bool result of (for any element y of m, x - y < a) for each element x of m", you don't actually need "for any element y", you can just use "for the maximal element y". So you can simplify from O(N^2) to O(N):
>>> (m - m.max()) < a
Or, if a is positive, that's always false, so you can simplify to O(1):
>>> np.zeros(m.shape, dtype=bool)
But I'm guessing your real algorithm is actually using abs(x - y), or something more complicated, which can't be simplified in this way.

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