Minimum value in each row and each column of a matrix - Python - python

Can someone please help me out? I am trying to get the minimum value of each row and of each column of this matrix
matrix =[[12,34,28,16],
[13,32,36,12],
[15,32,32,14],
[11,33,36,10]]
So for example: I would want my program to print out that 12 is the minimum value of row 1 and so on.

Let's repeat the task statement: "get the minimum value of each row and of each column of this matrix".
Okay, so, if the matrix has n rows, you should get n minimum values, one for each row. Sounds interesting, doesn't it? So, the code'll look like this:
result1 = [<something> for row in matrix]
Well, what do you need to do with each row? Right, find the minimum value, which is super easy:
result1 = [min(row) for row in matrix]
As a result, you'll get a list of n values, just as expected.
Wait, by now we've only found the minimums for each row, but not for each column, so let's do this as well!
Given that you're using Python 3.x, you can do some pretty amazing stuff. For example, you can loop over columns easily:
result2 = [min(column) for column in zip(*matrix)] # notice the asterisk!
The asterisk in zip(*matrix) makes each row of matrix a separate argument of zip's, like this:
zip(matrix[0], matrix[1], matrix[2], matrix[3])
This doesn't look very readable and is dependent on the number of rows in matrix (basically, you'll have to hard-code them), and the asterisk lets you write much cleaner code.
zip returns tuples, and the ith tuple contains the ith values of all the rows, so these tuples are actually the columns of the given matrix.
Now, you may find this code a bit ugly, you may want to write the same thing in a more concise way. Sure enough, you can use some functional programming magic:
result1 = list(map(min, matrix))
result2 = list(map(min, zip(*matrix)))
These two approaches are absolutely equivalent.

Use numpy.
>>> import numpy as np
>>> matrix =[[12,34,28,16],
... [13,32,36,12],
... [15,32,32,14],
... [11,33,36,10]]
>>> np.min(matrix, axis=1) # computes minimum in each row
array([12, 12, 14, 10])
>>> np.min(matrix, axis=0) # computes minimum in each column
array([11, 32, 28, 10])

Related

How to get specific index of np.array of np.arrays fast

At the most basic I have the following dataframe:
a = {'possibility' : np.array([1,2,3])}
b = {'possibility' : np.array([4,5,6])}
df = pd.DataFrame([a,b])
This gives me a dataframe of size 2x1:
like so:
row 1: np.array([1,2,3])
row 2: np.array([4,5,6])
I have another vector of length 2. Like so:
[1,2]
These represent the index I want from each row.
So if I have [1,2] I want: from row 1: 2, and from row 2: 6.
Ideally, my output is [2,6] in a vector form, of length 2.
Is this possible? I can easily run through a for loop, but am looking for FAST approaches, ideally vectors approaches since it is already in pandas/numpy.
For actual use case approximations, I am looking to make this work in the 300k-400k row ranges. And need to run it in optimization problems (hence the fast part)
You could transform to a multi-dimensional numpy array and take_along_axis:
v = np.array([1,2])
a = np.vstack(df['possibility'])
np.take_along_axis(a.T, v[None], axis=0)[0]
output: array([2, 6])

Creating a matrix with at most one value in every row and column

From a matrix filled with values (see picture), I want to obtain a matrix with at most one value for every row and column. If there is more than one value, the maximum should be kept and the other set to 0. I know I can do that with np.max and np.argmax, but I'm wondering if there is some clever way to do it that I'm not aware of.
Here's the solution I have for now:
tmp = np.zeros_like(matrix)
for x in np.argmax(matrix, axis=0): # get max on x axis
for y in np.argmax(matrix, axis=1): # get max on y axis
tmp[x][y] = matrix[x][y]
matrix = tmp
The sparse structure may be used for efficiency, however right now I see a contradiction between at most one value for every row and column and your current implementation which may leave more than one value per row/column.
Either you need an order to prefer rows over columns or to go along an absolute sorting of all matrix values.
Just an idea which produces for sure at most one entry per row and column would be to, firstly select the maxima of rows, and secondly select from this intermediate matrix the maxima of columns:
import numpy as np
rows=5
cols=5
matrix=np.random.rand(rows, cols)
rowmax=np.argmax(matrix, 1)
rowmax_matrix=np.zeros((rows, cols))
for ri, rm in enumerate(rowmax):
rowmax_matrix[ri,rm]=matrix[ri, rm]
colrowmax=np.argmax(rowmax_matrix, 0)
colrowmax_matrix=np.zeros((rows, cols))
for ci, cm in enumerate(colrowmax):
colrowmax_matrix[cm, ci]=rowmax_matrix[cm, ci]
This is probably not the final answer, but may help to formulate the desired algorithm precisely.

Compare each column to a different value efficiently

I have a numpy array of 4000*6 (6 column). And I have a numpy column (1*6) of minimum values (made from another numpy array of 3000*6).
I want to find everything in the large array that is below those values. but each value to it's corresponding column.
I've tried the simple way, based on a one column solution I already had:
largearray=[float('nan') if x<min_values else x for x in largearray]
but sadly it didn't work :(.
I can do a for loop for each column and each value, but i was wondering if there is a faster more elegant solution.
Thanks
EDIT: I'll try to rephrase: I have 6 values, and 6 columns.
i want to find the values in each column that are lower then the corresponding one from the 6 values.
by array I mean a 2d array. sorry if it wasn't clear
sorry, i'm still thinking in Matlab a bit.
this my loop solution. It's on df, not numpy. still, is there a faster way?
a=0
for y in dfnames:
df[y]=[float('nan') if x<minvalues[a] else x for x in df[y]]
a=a+1
df is the large array or dataframe
dfnames are the column names i'm interested in.
minvalues are the minimum values for each column. I'm assuming that the order is the same. bad assumption, but works for now.
will appreciate any help making it better
I think you just need
result = largearray.copy()
result[result < min_values] = np.nan
That is, result is a copy of largearray but ay element less than the corresponding column of min_values is set to nan.
If you want to blank entire rows only when all entries in the row are less than the corresponding column of min_values, then you want:
result = largearray.copy()
result[np.all(result < min_values, axis=1)] = np.nan
I don't use numpy, so it may be not commont used solution, but such work:
largearray = numpy.array([[1,2,3], [3,4,5]])
minvalues =numpy.array([3,4,5])
largearray1=[(float('nan') if not numpy.all(numpy.less(x, min_values)) else x) for x in largearray]
result should be: [[1,2,3], 'nan']

finding the max of a column in an array

def maxvalues():
for n in range(1,15):
dummy=[]
for k in range(len(MotionsAndMoorings)):
dummy.append(MotionsAndMoorings[k][n])
max(dummy)
L = [x + [max(dummy)]] ## to be corrected (adding columns with value max(dummy))
## suggest code to add new row to L and for next function call, it should save values here.
i have an array of size (k x n) and i need to pick the max values of the first column in that array. Please suggest if there is a simpler way other than what i tried? and my main aim is to append it to L in columns rather than rows. If i just append, it is adding values at the end. I would like to this to be done in columns for row 0 in L, because i'll call this function again and add a new row to L and do the same. Please suggest.
General suggestions for your code
First of all it's not very handy to access globals in a function. It works but it's not considered good style. So instead of using:
def maxvalues():
do_something_with(MotionsAndMoorings)
you should do it with an argument:
def maxvalues(array):
do_something_with(array)
MotionsAndMoorings = something
maxvalues(MotionsAndMoorings) # pass it to the function.
The next strange this is you seem to exlude the first row of your array:
for n in range(1,15):
I think that's unintended. The first element of a list has the index 0 and not 1. So I guess you wanted to write:
for n in range(0,15):
or even better for arbitary lengths:
for n in range(len(array[0])): # I chose the first row length here not the number of columns
Alternatives to your iterations
But this would not be very intuitive because the max function already implements some very nice keyword (the key) so you don't need to iterate over the whole array:
import operator
column = 2
max(array, key=operator.itemgetter(column))[column]
this will return the row where the i-th element is maximal (you just define your wanted column as this element). But the maximum will return the whole row so you need to extract just the i-th element.
So to get a list of all your maximums for each column you could do:
[max(array, key=operator.itemgetter(column))[column] for column in range(len(array[0]))]
For your L I'm not sure what this is but for that you should probably also pass it as argument to the function:
def maxvalues(array, L): # another argument here
but since I don't know what x and L are supposed to be I'll not go further into that. But it looks like you want to make the columns of MotionsAndMoorings to rows and the rows to columns. If so you can just do it with:
dummy = [[MotionsAndMoorings[j][i] for j in range(len(MotionsAndMoorings))] for i in range(len(MotionsAndMoorings[0]))]
that's a list comprehension that converts a list like:
[[1, 2, 3], [4, 5, 6], [0, 2, 10], [0, 2, 10]]
to an "inverted" column/row list:
[[1, 4, 0, 0], [2, 5, 2, 2], [3, 6, 10, 10]]
Alternative packages
But like roadrunner66 already said sometimes it's easiest to use a library like numpy or pandas that already has very advanced and fast functions that do exactly what you want and are very easy to use.
For example you convert a python list to a numpy array simple by:
import numpy as np
Motions_numpy = np.array(MotionsAndMoorings)
you get the maximum of the columns by using:
maximums_columns = np.max(Motions_numpy, axis=0)
you don't even need to convert it to a np.array to use np.max or transpose it (make rows to columns and the colums to rows):
transposed = np.transpose(MotionsAndMoorings)
I hope this answer is not to unstructured. Some parts are suggestions to your function and some are alternatives. You should pick the parts that you need and if you have any trouble with it, just leave a comment or ask another question. :-)
An example with a random input array, showing that you can take the max in either axis easily with one command.
import numpy as np
aa= np.random.random([4,3])
print aa
print
print np.max(aa,axis=0)
print
print np.max(aa,axis=1)
Output:
[[ 0.51972266 0.35930957 0.60381998]
[ 0.34577217 0.27908173 0.52146593]
[ 0.12101346 0.52268843 0.41704152]
[ 0.24181773 0.40747905 0.14980534]]
[ 0.51972266 0.52268843 0.60381998]
[ 0.60381998 0.52146593 0.52268843 0.40747905]

Element-wise median and percentiles of arrays with Numeric Python

I am using Numeric Python. Unfortunately, NumPy is not an option. If I have multiple arrays, such as:
a=Numeric.array(([1,2,3],[4,5,6],[7,8,9]))
b=Numeric.array(([9,8,7],[6,5,4],[3,2,1]))
c=Numeric.array(([5,9,1],[5,4,7],[5,2,3]))
How do I return an array that represents the element-wise median of arrays a,b and c?...such as,
array(([5,8,3],[5,5,6],[5,2,3]))
And then looking at a more general situation: Given n number of arrays, how do I find the percentiles of each element? For example, return an array that represents the 30th percentile of 10 arrays. Thank you very much for your help!
Combine your stack of 2-D arrays into one 3-D array, d = Numeric.array([a, b, c]) and then sort on the third dimension. Afterwards, the successive 2-D planes will be rank order so you can extract planes for the low, high, quartiles, percentiles, or median.
Well, I'm not versed in Numeric, but I'll just start with a naive solution and see if we can make it any better.
To get the 30th percentile of list foo let x=0.3, sort the list, and pick the the element at foo[int(len(foo)*x)]
For your data, you want to put it in a matrix, transpose it, sort each row, and get the median of each row.
A matrix in Numeric (just like numpy) is an array with two dimensions.
I think that bar = Numeric.array(a,b,c) would make Array you want, and then you could get the nth column with 'bar[:,n]' if Numeric has the same slicing techniques as Numpy.
foo = sorted(bar[:,n])
foo[int(len(foo)*x)]
I hope that helps you.
Putting Raymond Hettinger's description into python:
a=Numeric.array(([1,2,3],[4,5,6],[7,8,9]))
b=Numeric.array(([9,8,7],[6,5,4],[3,2,1]))
c=Numeric.array(([5,9,1],[5,4,7],[5,2,3]))
d = Numeric.array([a, b, c])
d.sort(axis=0)
Since there are n=3 input matrii so the median would be that of the middle one, the one indexed by one,
print d[n//2]
[[5 8 3]
[5 5 6]
[5 2 3]]
And if you had 4 input matrii, you would have to get the mean-elements of d[1] and d[2].

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