Pythonista way of extracting elements from an array - python

I'm writing a few Python lines of code doing the following:
I have two arrays a and b, b contains (non strictly) increasing integers.
I want to extract from a the values for which the values of b is a multiple of 20 but I don't want duplicates, in the sense that if b has values : ...,40,40,41,... I only want the first value in a corresponding the 40 not the second one.
That's why a[b%20==0] does not work.
I've been using:
factors = [20*i for i in xrange(1,int(b[-1]/20 +1))]
sample = numpy.array([a[numpy.nonzero(b==factor)[0][0]] for factor in factors])
but it is both slow and fairly inelegant.
Is there a Pythonista 'cute' way of doing it?

a[(b % 20 == 0) & np.r_[True, np.diff(b) > 0]]
The b % 20 == 0 part gives a binary mask that selects all the elements of b that are a factor of 20. The np.r_[True, np.diff(b) > 0] part creates a binary mask that selects only the elements that differ from the previous element (we explicitly add a True at the beginning, as the first element does not have a previous element). Add the masks together and voila!

Let's say we create a boolean array wich marks the unique values on b:
c = np.zeros(b.shape, dtype=np.bool)
c[np.unique(b, return_index = True)[1]] = True
Now you can do:
a[np.logical_and(b % 20 == 0, c)]

If your b is sorted, using diff should be a bit faster than using unique:
import numpy
a = numpy.random.random_integers(0, 1000, 1000)
b = numpy.random.random_integers(0, 1000, 1000)
b.sort()
subset = a[(numpy.diff(b) != 0) * (b[:-1]%20 == 0)]

Related

How to select list elements based on crteria from other lists

I am new to Python, coming from SciLab (an open source MatLab ersatz), which I am using as a toolbox for my analyses (test data analysis, reliability, acoustics, ...); I am definitely not a computer science lad.
I have data in the form of lists of same length (vectors of same size in SciLab).
I use some of them as parameter in order to select data from another one; e.g.
t_v = [1:10]; // a parameter vector
p_v = [20:29]; another parameter vector
res_v(t_v > 5 & p_v < 28); // are the res_v vector elements of which "corresponding" p_v and t_v values comply with my criteria; i can use it for analyses.
This is very direct and simple in SciLab; I did not find the way to achieve the same with Python, either "Pythonically" or simply translated.
Any idea that could help me, please?
Have a nice day,
Patrick.
You could use numpy arrays. It's easy:
import numpy as np
par1 = np.array([1,1,5,5,5,1,1])
par2 = np.array([-1,1,1,-1,1,1,1])
data = np.array([1,2,3,4,5,6,7])
print(par1)
print(par2)
print(data)
bool_filter = (par1[:]>1) & (par2[:]<0)
# example to do it directly in the array
filtered_data = data[ par1[:]>1 ]
print( filtered_data )
#filtering with the two parameters
filtered_data_twice = data[ bool_filter==True ]
print( filtered_data_twice )
output:
[1 1 5 5 5 1 1]
[-1 1 1 -1 1 1 1]
[1 2 3 4 5 6 7]
[3 4 5]
[4]
Note that it does not keep the same number of elements.
Here's my modified solution according to your last comment.
t_v = list(range(1,10))
p_v = list(range(20,29))
res_v = list(range(30,39))
def first_idex_greater_than(search_number, lst):
for count, number in enumerate(lst):
if number > search_number:
return count
def first_idex_lower_than(search_number, lst):
for count, number in enumerate(lst[::-1]):
if number < search_number:
return len(lst) - count # since I searched lst from top to bottom,
# I need to also reverse count
t_v_index = first_idex_greater_than(5, t_v)
p_v_index = first_idex_lower_than(28, p_v)
print(res_v[min(t_v_index, p_v_index):max(t_v_index, p_v_index)])
It returns an array [35, 36, 37].
I'm sure you can optimize it better according to your needs.
The problem statement is not clearly defined, but this is what I interpret to be a likely solution.
import pandas as pd
tv = list(range(1, 11))
pv = list(range(20, 30))
res = list(range(30, 40))
df = pd.DataFrame({'tv': tv, 'pv': pv, 'res': res})
print(df)
def criteria(row, col1, a, col2, b):
if (row[col1] > a) & (row[col2] < b):
return True
else:
return False
df['select'] = df.apply(lambda row: criteria(row, 'tv', 5, 'pv', 28), axis=1)
selected_res = df.loc[df['select']]['res'].tolist()
print(selected_res)
# ... or another way ..
print(df.loc[(df.tv > 5) & (df.pv < 28)]['res'])
This produces a dataframe where each column is the original lists, and applies a selection criteria, based on columns tv and pv to identify the rows in which the criteria, applied dependently to the 2 lists, is satisfied (or not), and then creates a new column of booleans identifying the rows where the criteria is either True or False.
[35, 36, 37]
5 35
6 36
7 37

How to eliminate data that consist dual three consecutive numbers in python?

Here's my data
id
123246512378
632746378456
378256364036
159204652855
327445634589
I want to make data that consist of data that consist dual three consecutive numbers like 123246512378, 3274456|34589 is reduced
id
632746378456
378256364036
159204652855
First, turn df.id into a an array of single digit integers.
a = np.array(list(map(list, map(str, df.id))), dtype=int)
Then check to see if one digit is one less than the next digit... twice
first = a[:, :-2] == a[:, 1:-1] - 1
second = a[:, 1:-1] == a[:, 2:] - 1
Create a mask for when we have this happen more than once
mask = np.count_nonzero(first & second, axis=1) < 2
df[mask]
id
1 632746378456
2 378256364036
3 159204652855
Not sure if this is faster than #piRSquared as I'm not good enough with pandas to generate my own test data, but it seems like it should be:
def mask_cons(df):
a = np.array(list(map(list, df.id.astype(str))), dtype = float)
# same as piRSquared, but float
g_a = np.gradient(a, axis = 1)[:,1:-1]
# 3 consecutive values will give grad(a) = +/-1
mask = (np.abs(g_a) == 1).sum(1) > 1
# this assumes 4 consecutive values count as 2 instances of 3 consecutive values
# otherwise more complicated methods are needed (probably #jit)
return df[mask]

python: divide list into pequal parts and add samples in each part together

The following is my script. Each equal part has self.number samples, in0 is input sample. There is an error as follows:
pn[i] = pn[i] + d
IndexError: list index out of range
Is this the problem about the size of pn? How can I define a list with a certain size but no exact number in it?
for i in range(0,len(in0)/self.number):
pn = []
m = i*self.number
for d in in0[m: m + self.number]:
pn[i] += d
if pn[i] >= self.alpha:
out[i] = 1
elif pn[i] <= self.beta:
out[i] = 0
else:
if pn[i] >= self.noise:
out[i] = 1
else:
out[i] = 0
if pn[i] >= self.noise:
out[i] = 1
else:
out[i] = 0
There are a number of problems in the code as posted, however, the gist seems to be something that you'd want to do with numpy arrays instead of iterating over lists.
For example, the set of if/else cases that check if pn[i] >= some_value and then sets a corresponding entry into another list with the result (true/false) could be done as a one-liner with an array operation much faster than iterating over lists.
import numpy as np
# for example, assuming you have 9 numbers in your list
# and you want them divided into 3 sublists of 3 values each
# in0 is your original list, which for example might be:
in0 = [1.05, -0.45, -0.63, 0.07, -0.71, 0.72, -0.12, -1.56, -1.92]
# convert into array
in2 = np.array(in0)
# reshape to 3 rows, the -1 means that numpy will figure out
# what the second dimension must be.
in2 = in2.reshape((3,-1))
print(in2)
output:
[[ 1.05 -0.45 -0.63]
[ 0.07 -0.71 0.72]
[-0.12 -1.56 -1.92]]
With this 2-d array structure, element-wise summing is super easy. So is element-wise threshold checking. Plus 'vectorizing' these operations has big speed advantages if you are working with large data.
# add corresponding entries, we want to add the columns together,
# as each row should correspond to your sub-lists.
pn = in2.sum(axis=0) # you can sum row-wise or column-wise, or all elements
print(pn)
output: [ 1. -2.72 -1.83]
# it is also trivial to check the threshold conditions
# here I check each entry in pn against a scalar
alpha = 0.0
out1 = ( pn >= alpha )
print(out1)
output: [ True False False]
# you can easily convert booleans to 1/0
x = out1.astype('int') # or simply out1 * 1
print(x)
output: [1 0 0]
# if you have a list of element-wise thresholds
beta = np.array([0.0, 0.5, -2.0])
out2 = (pn >= beta)
print(out2)
output: [True False True]
I hope this helps. Using the correct data structures for your task can make the analysis much easier and faster. There is a wealth of documentation on numpy, which is the standard numeric library for python.
You initialize pn to an empty list just inside the for loop, never assign anything into it, and then attempt to access an index i. There is nothing at index i because there is nothing at any index in pn yet.
for i in range(0, len(in0) / self.number):
pn = []
m = i*self.number
for d in in0[m: m + self.number]:
pn[i] += d
If you are trying to add the value d to the pn list, you should do this instead:
pn.append(d)

Averaging out sections of a multiple row array in Python

I've got a 2-row array called C like this:
from numpy import *
A = [1,2,3,4,5]
B = [50,40,30,20,10]
C = vstack((A,B))
I want to take all the columns in C where the value in the first row falls between i and i+2, and average them. I can do this with just A no problem:
i = 0
A_avg = []
while(i<6):
selection = A[logical_and(A >= i, A < i+2)]
A_avg.append(mean(selection))
i += 2
then A_avg is:
[1.0,2.5,4.5]
I want to carry out the same process with my two-row array C, but I want to take the average of each row separately, while doing it in a way that's dictated by the first row. For example, for C, I want to end up with a 2 x 3 array that looks like:
[[1.0,2.5,4.5],
[50,35,15]]
Where the first row is A averaged in blocks between i and i+2 as before, and the second row is B averaged in the same blocks as A, regardless of the values it has. So the first entry is unchanged, the next two get averaged together, and the next two get averaged together, for each row separately. Anyone know of a clever way to do this? Many thanks!
I hope this is not too clever. TIL boolean indexing does not broadcast, so I had to manually do the broadcasting. Let me know if anything is unclear.
import numpy as np
A = [1,2,3,4,5]
B = [50,40,30,20,10]
C = np.vstack((A,B)) # float so that I can use np.nan
i = np.arange(0, 6, 2)[:, None]
selections = np.logical_and(A >= i, A < i+2)[None]
D, selections = np.broadcast_arrays(C[:, None], selections)
D = D.astype(float) # allows use of nan, and makes a copy to prevent repeated behavior
D[~selections] = np.nan # exclude these elements from mean
D = np.nanmean(D, axis=-1)
Then,
>>> D
array([[ 1. , 2.5, 4.5],
[ 50. , 35. , 15. ]])
Another way, using np.histogram to bin your data. This may be faster for large arrays, but is only useful for few rows, since a hist must be done with different weights for each row:
bins = np.arange(0, 7, 2) # include the end
n = np.histogram(A, bins)[0] # number of columns in each bin
a_mean = np.histogram(A, bins, weights=A)[0]/n
b_mean = np.histogram(A, bins, weights=B)[0]/n
D = np.vstack([a_mean, b_mean])

Find two disjoint pairs of pairs that sum to the same vector

This is a follow-up to Find two pairs of pairs that sum to the same value .
I have random 2d arrays which I make using
import numpy as np
from itertools import combinations
n = 50
A = np.random.randint(2, size=(m,n))
I would like to determine if the matrix has two disjoint pairs of pairs of columns which sum to the same column vector. I am looking for a fast method to do this. In the previous problem ((0,1), (0,2)) was acceptable as a pair of pairs of column indices but in this case it is not as 0 is in both pairs.
The accepted answer from the previous question is so cleverly optimised I can't see how to make this simple looking change unfortunately. (I am interested in columns rather than rows in this question but I can always just do A.transpose().)
Here is some code to show it testing all 4 by 4 arrays.
n = 4
nxn = np.arange(n*n).reshape(n, -1)
count = 0
for i in xrange(2**(n*n)):
A = (i >> nxn) %2
p = 1
for firstpair in combinations(range(n), 2):
for secondpair in combinations(range(n), 2):
if firstpair < secondpair and not set(firstpair) & set(secondpair):
if (np.array_equal(A[firstpair[0]] + A[firstpair[1]], A[secondpair[0]] + A[secondpair[1]] )):
if (p):
count +=1
p = 0
print count
This should output 3136.
Here is my solution, extended to do what I believe you want. It isn't entirely clear though; one may get an arbitrary number of row-pairs that sum to the same total; there may exist unique subsets of rows within them that sum to the same value. For instance:
Given this set of row-pairs that sum to the same total
[[19 19 30 30]
[11 16 11 16]]
There exists a unique subset of these rows that may still be counted as valid; but should it?
[[19 30]
[16 11]]
Anyway, I hope those details are easy to deal with, given the code below.
import numpy as np
n = 20
#also works for non-square A
A = np.random.randint(2, size=(n*6,n)).astype(np.int8)
##A = np.array( [[0, 0, 0], [1, 1, 1], [1, 1 ,1]], np.uint8)
##A = np.zeros((6,6))
#force the inclusion of some hits, to keep our algorithm on its toes
##A[0] = A[1]
def base_pack_lazy(a, base, dtype=np.uint64):
"""
pack the last axis of an array as minimal base representation
lazily yields packed columns of the original matrix
"""
a = np.ascontiguousarray( np.rollaxis(a, -1))
packing = int(np.dtype(dtype).itemsize * 8 / (float(base) / 2))
for columns in np.array_split(a, (len(a)-1)//packing+1):
R = np.zeros(a.shape[1:], dtype)
for col in columns:
R *= base
R += col
yield R
def unique_count(a):
"""returns counts of unique elements"""
unique, inverse = np.unique(a, return_inverse=True)
count = np.zeros(len(unique), np.int)
np.add.at(count, inverse, 1) #note; this scatter operation requires numpy 1.8; use a sparse matrix otherwise!
return unique, count, inverse
def voidview(arr):
"""view the last axis of an array as a void object. can be used as a faster form of lexsort"""
return np.ascontiguousarray(arr).view(np.dtype((np.void, arr.dtype.itemsize * arr.shape[-1]))).reshape(arr.shape[:-1])
def has_identical_row_sums_lazy(A, combinations_index):
"""
compute the existence of combinations of rows summing to the same vector,
given an nxm matrix A and an index matrix specifying all combinations
naively, we need to compute the sum of each row combination at least once, giving n^3 computations
however, this isnt strictly required; we can lazily consider the columns, giving an early exit opportunity
all nicely vectorized of course
"""
multiplicity, combinations = combinations_index.shape
#list of indices into combinations_index, denoting possibly interacting combinations
active_combinations = np.arange(combinations, dtype=np.uint32)
#keep all packed columns; we might need them later
columns = []
for packed_column in base_pack_lazy(A, base=multiplicity+1): #loop over packed cols
columns.append(packed_column)
#compute rowsums only for a fixed number of columns at a time.
#this is O(n^2) rather than O(n^3), and after considering the first column,
#we can typically already exclude almost all combinations
partial_rowsums = sum(packed_column[I[active_combinations]] for I in combinations_index)
#find duplicates in this column
unique, count, inverse = unique_count(partial_rowsums)
#prune those combinations which we can exclude as having different sums, based on columns inspected thus far
active_combinations = active_combinations[count[inverse] > 1]
#early exit; no pairs
if len(active_combinations)==0:
return False
"""
we now have a small set of relevant combinations, but we have lost the details of their particulars
to see which combinations of rows does sum to the same value, we do need to consider rows as a whole
we can simply apply the same mechanism, but for all columns at the same time,
but only for the selected subset of row combinations known to be relevant
"""
#construct full packed matrix
B = np.ascontiguousarray(np.vstack(columns).T)
#perform all relevant sums, over all columns
rowsums = sum(B[I[active_combinations]] for I in combinations_index)
#find the unique rowsums, by viewing rows as a void object
unique, count, inverse = unique_count(voidview(rowsums))
#if not, we did something wrong in deciding on active combinations
assert(np.all(count>1))
#loop over all sets of rows that sum to an identical unique value
for i in xrange(len(unique)):
#set of indexes into combinations_index;
#note that there may be more than two combinations that sum to the same value; we grab them all here
combinations_group = active_combinations[inverse==i]
#associated row-combinations
#array of shape=(mulitplicity,group_size)
row_combinations = combinations_index[:,combinations_group]
#if no duplicate rows involved, we have a match
if len(np.unique(row_combinations[:,[0,-1]])) == multiplicity*2:
print row_combinations
return True
#none of identical rowsums met uniqueness criteria
return False
def has_identical_triple_row_sums(A):
n = len(A)
idx = np.array( [(i,j,k)
for i in xrange(n)
for j in xrange(n)
for k in xrange(n)
if i<j and j<k], dtype=np.uint16)
idx = np.ascontiguousarray( idx.T)
return has_identical_row_sums_lazy(A, idx)
def has_identical_double_row_sums(A):
n = len(A)
idx = np.array(np.tril_indices(n,-1), dtype=np.int32)
return has_identical_row_sums_lazy(A, idx)
from time import clock
t = clock()
for i in xrange(1):
## print has_identical_double_row_sums(A)
print has_identical_triple_row_sums(A)
print clock()-t
Edit: code cleanup

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