Python - Divide each row by a vector - python

I have a 10x10 matrix and I want to divide each row of the matrix with the elements of a vector.
For eg:
Suppose I have a 3x3 matrix
1 1 1
2 2 2
3 3 3
and a vector [1, 2, 3]
Then this is the operation I wish to do:
1/1 1/2 1/3
2/1 2/1 2/3
3/1 3/2 3/3
i.e, divide the elements of a row by the elements of a vector(A python list)
I can do this using for loops. But, is there a better way to do this operation in python?

You should look into broadcasting in numpy. For your example this is the solution:
a = np.array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])
b = np.array([1, 2, 3]).reshape(1, 3)
c = a / b
print(c)
>>> [[1. 0.5 0.33333333]
[2. 1. 0.66666667]
[3. 1.5 1. ]]

The first source array should be created as a Numpy array:
a = np.array([
[ 1, 1, 1 ],
[ 2, 2, 2 ],
[ 3, 3, 3 ]])
You don't need to reshape the divisor array (it can be a 1-D array,
as in your source data sample):
v = np.array([1, 2, 3])
Just divide them:
result = a / v
and the result is:
array([[1. , 0.5 , 0.33333333],
[2. , 1. , 0.66666667],
[3. , 1.5 , 1. ]])

Related

Numpy: How to stack a single array into each row of a bigger array and turn it into a 2D array?

I have a numpy array named heartbeats with 100 rows. Each row has 5 elements.
I also have a single array named time_index with 5 elements.
I need to prepend the time index to each row of heartbeats.
heartbeats = np.array([
[-0.58, -0.57, -0.55, -0.39, -0.40],
[-0.31, -0.31, -0.32, -0.46, -0.46]
])
time_index = np.array([-2, -1, 0, 1, 2])
What I need:
array([-2, -0.58],
[-1, -0.57],
[0, -0.55],
[1, -0.39],
[2, -0.40],
[-2, -0.31],
[-1, -0.31],
[0, -0.32],
[1, -0.46],
[2, -0.46])
I only wrote two rows of heartbeats to illustrate.
Assuming you are using numpy, the exact output array you are looking for can be made by stacking a repeated version of time_index with the raveled version of heartbeats:
np.stack((np.tile(time_index, len(heartbeats)), heartbeats.ravel()), axis=-1)
Another approach, using broadcasting
In [13]: heartbeats = np.array([
...: [-0.58, -0.57, -0.55, -0.39, -0.40],
...: [-0.31, -0.31, -0.32, -0.46, -0.46]
...: ])
...: time_index = np.array([-2, -1, 0, 1, 2])
Make a target array:
In [14]: res = np.zeros(heartbeats.shape + (2,), heartbeats.dtype)
In [15]: res[:,:,1] = heartbeats # insert a (2,5) into a (2,5) slot
In [17]: res[:,:,0] = time_index[None] # insert a (5,) into a (2,5) slot
In [18]: res
Out[18]:
array([[[-2. , -0.58],
[-1. , -0.57],
[ 0. , -0.55],
[ 1. , -0.39],
[ 2. , -0.4 ]],
[[-2. , -0.31],
[-1. , -0.31],
[ 0. , -0.32],
[ 1. , -0.46],
[ 2. , -0.46]]])
and then reshape to 2d:
In [19]: res.reshape(-1,2)
Out[19]:
array([[-2. , -0.58],
[-1. , -0.57],
[ 0. , -0.55],
[ 1. , -0.39],
[ 2. , -0.4 ],
[-2. , -0.31],
[-1. , -0.31],
[ 0. , -0.32],
[ 1. , -0.46],
[ 2. , -0.46]])
[17] takes a (5,), expands it to (1,5), and then to (2,5) for the insert. Read up on broadcasting.
As an alternative way, you can repeat time_index by np.concatenate based on the specified times:
concatenated = np.concatenate([time_index] * heartbeats.shape[0])
# [-2 -1 0 1 2 -2 -1 0 1 2]
# result = np.dstack((concatenated, heartbeats.reshape(-1))).squeeze()
result = np.array([concatenated, heartbeats.reshape(-1)]).T
Using np.concatenate may be faster than np.tile. This solution is faster than Mad Physicist, but the fastest is using broadcasting as hpaulj's answer.

Finding percentage change with Numpy

I'm writing a function to find the percentage change using Numpy and function calls. So far what I got is:
def change(a,b):
answer = (np.subtract(a[b+1], a[b])) / a[b+1] * 100
return answer
print(change(a,0))
"a" is the array I have made and b will be the index/numbers I am trying to calculate.
For example:
My Array is
[[1,2,3,5,7]
[1,4,5,6,7]
[5,8,9,10,32]
[3,5,6,13,11]]
How would I calculate the percentage change between 1 to 2 (=0.5) or 1 to 4(=0.75) or 5,7 etc..
Note: I know how mathematically to get the change, I'm not sure how to do this in python/ numpy.
If I understand correctly, that you're trying to find percent change in each row, then you can do:
>>> np.diff(a) / a[:,1:] * 100
Which gives you:
array([[ 50. , 33.33333333, 40. , 28.57142857],
[ 75. , 20. , 16.66666667, 14.28571429],
[ 37.5 , 11.11111111, 10. , 68.75 ],
[ 40. , 16.66666667, 53.84615385, -18.18181818]])
I know you have asked this question with Numpy in mind and got answers above:
import numpy as np
np.diff(a) / a[:,1:]
I attempt to solve this with Pandas. For those who would have the same question but using Pandas instead of Numpy
import pandas as pd
data = [[1,2,3,4,5],
[1,4,5,6,7],
[5,8,9,10,32],
[3,5,6,13,11]]
df = pd.DataFrame(data)
df_change = df.rolling(1,axis=1).sum().pct_change(axis=1)
print(df_change)
I suggest to simply shift the array. The computation basically becomes a one-liner.
import numpy as np
arr = np.array(
[
[1, 2, 3, 5, 7],
[1, 4, 5, 6, 7],
[5, 8, 9, 10, 32],
[3, 5, 6, 13, 11],
]
)
# Percentage change from row to row
pct_chg_row = arr[1:] / arr[:-1] - 1
[[ 0. 1. 0.66666667 0.2 0. ]
[ 4. 1. 0.8 0.66666667 3.57142857]
[-0.4 -0.375 -0.33333333 0.3 -0.65625 ]]
# Percentage change from column to column
pct_chg_col = arr[:, 1::] / arr[:, 0:-1] - 1
[[ 1. 0.5 0.66666667 0.4 ]
[ 3. 0.25 0.2 0.16666667]
[ 0.6 0.125 0.11111111 2.2 ]
[ 0.66666667 0.2 1.16666667 -0.15384615]]
You could easily generalize the task, so that you are not limited to compute the change from one row/column to another, but be able to compute the change for n rows/columns.
n = 2
pct_chg_row_generalized = arr[n:] / arr[:-n] - 1
[[4. 3. 2. 1. 3.57142857]
[2. 0.25 0.2 1.16666667 0.57142857]]
pct_chg_col_generalized = arr[:, n:] / arr[:, :-n] - 1
[[2. 1.5 1.33333333]
[4. 0.5 0.4 ]
[0.8 0.25 2.55555556]
[1. 1.6 0.83333333]]
If the output array must have the same shape as the input array, you need to make sure to insert the appropriate number of np.nan.
out_row = np.full_like(arr, np.nan, dtype=float)
out_row[n:] = arr[n:] / arr[:-n] - 1
[[ nan nan nan nan nan]
[ nan nan nan nan nan]
[4. 3. 2. 1. 3.57142857]
[2. 0.25 0.2 1.16666667 0.57142857]]
out_col = np.full_like(arr, np.nan, dtype=float)
out_col[:, n:] = arr[:, n:] / arr[:, :-n] - 1
[[ nan nan 2. 1.5 1.33333333]
[ nan nan 4. 0.5 0.4 ]
[ nan nan 0.8 0.25 2.55555556]
[ nan nan 1. 1.6 0.83333333]]
Finally, a small function for the general 2D case might look like this:
def np_pct_chg(arr: np.ndarray, n: int = 1, axis: int = 0) -> np.ndarray:
out = np.full_like(arr, np.nan, dtype=float)
if axis == 0:
out[n:] = arr[n:] / arr[:-n] - 1
elif axis == 1:
out[:, n:] = arr[:, n:] / arr[:, :-n] - 1
return out
The accepted answer is close but incorrect if you're trying to take % difference from left to right.
You should get the following percent difference:
1,2,3,5,7 --> 100%, 50%, 66.66%, 40%
check for yourself: https://www.calculatorsoup.com/calculators/algebra/percent-change-calculator.php
Going by what Josmoor98 said, you can use np.diff(a) / a[:,:-1] * 100 to get the percent difference from left to right, which will give you the correct answer.
array([[100. , 50. , 66.66666667, 40. ],
[300. , 25. , 20. , 16.66666667],
[ 60. , 12.5 , 11.11111111, 220. ],
[ 66.66666667, 20. , 116.66666667, -15.38461538]])
import numpy as np
a = np.array([[1,2,3,5,7],
[1,4,5,6,7],
[5,8,9,10,32],
[3,5,6,13,11]])
np.array([(i[:-1]/i[1:]) for i in a])
Combine all your arrays.
Then make a data frame from them.
df = pd.df(data=array you made)
Use the pct_change() function on dataframe. It will calculate the % change for all rows in dataframe.

Division with numpy matrices that might result in nan

How can I divide two numpy matrices A and B in python when sometimes the two matrices will have 0 on the same cell?
Basically A[i,j]>=B[i,j] for all i, j. I need to calculate C=A/B. But sometimes A[i,j]==B[i,j]==0. And when this happens I need A[i,j]/B[i,j] to be defined as 0.
Is there a simple pythonic way other than going through all the indexes?
You can use the where argument for ufuncs like np.true_divide:
np.true_divide(A, B, where=(A!=0) | (B!=0))
In case you have no negative values (as stated in the comments) and A >= B for each element (as stated in the question) you can simplify this to:
np.true_divide(A, B, where=(A!=0))
because A[i, j] == 0 implies B[i, j] == 0.
For example:
import numpy as np
A = np.random.randint(0, 3, (4, 4))
B = np.random.randint(0, 3, (4, 4))
print(A)
print(B)
print(np.true_divide(A, B, where=(A!=0) | (B!=0)))
[[1 0 2 1]
[1 0 0 0]
[2 1 0 0]
[2 2 0 2]]
[[1 0 1 1]
[2 2 1 2]
[2 1 0 1]
[2 0 1 2]]
[[ 1. 0. 2. 1. ]
[ 0.5 0. 0. 0. ]
[ 1. 1. 0. 0. ]
[ 1. inf 0. 1. ]]
As alternative: Just replace nans after the division:
C = A / B # may print warnings, suppress them with np.seterrstate if you want
C[np.isnan(C)] = 0
You could use a mask with np.where to choose between such a case of A and B being both zeros and otherwise and put out 0 or an elementwise division respectively -
from __future__ import division # For Python 2.x
mask = (A == B) & (A==0)
C = np.where(mask, 0, A/B)
About the mask creation : (A==B) would be the mask of all elements that are equal between A and B and with (A==0) we have a mask of all elements that are zero in A. Thus, with a combined mask of (A == B) & (A==0), we have mask of places where both A and B are zeros. A more simpler version to do the same task and maybe easier to understand would be to check for zeros in both A and B and it would be :
mask = (A==0) & (B==0)
About the use of np.where, its syntax is :
C = np.where(mask, array1, array2)
i.e. we would select elements for assinging into C based on the mask. If the corresponding mask element is True, we pick the corresponding element from array1, else from array2. This is done on elementwise level and thus, we have the output C.
Sample run -
In [48]: A
Out[48]:
array([[4, 1, 4, 0, 3],
[0, 4, 1, 4, 3],
[1, 0, 0, 4, 0]])
In [49]: B
Out[49]:
array([[4, 2, 2, 1, 4],
[2, 1, 2, 4, 2],
[4, 0, 2, 0, 3]])
In [50]: mask = (A == B) & (A==0)
In [51]: np.where(mask, 0, A/B)
Out[51]:
array([[ 1. , 0.5 , 2. , 0. , 0.75],
[ 0. , 4. , 0.5 , 1. , 1.5 ],
[ 0.25, 0. , 0. , inf, 0. ]])

convert 1d array to 2d array with nan values

suppose I have a series like this
S1 = Series([[1 , 2 , 3] , [4 , 5 , 6] , np.nan , [0] , [8 ,9 ]])
0 [1, 2, 3]
1 [4, 5, 6]
2 NaN
3 [0]
4 [8, 9]
then I will create a numpy array from this series
arr1d = S1.values # [[1, 2, 3] [4, 5, 6] nan [0] [8, 9]]
print(arr1d.shape) #(5L,)
print(arr1d.ndim) # 1
is it possible to create a 2d array from arr1d that looks like the following
arr2d = np.array([[1 , 2 , 3 ] , [4 , 5 , 6] ,
[np.nan , np.nan , np.nan] , [0 , np.nan , np.nan] , [8 , 9 , np.nan]])
this is how the 2d array looks like
[[ 1. 2. 3.]
[ 4. 5. 6.]
[ nan nan nan]
[ 0. nan nan]
[ 8. 9. nan]]
print(arr2d.ndim) # 2
print(arr2d.shape) # (5L, 3L)
the solution should work dynamically with any number of elements in arr1d this is just an example of how the data may look like
Not claiming efficiency but this should work:
from itertools import zip_longest
arr2d = np.array(list(zip_longest(*np.atleast_1d(*S1), fillvalue=np.nan))).T
print(arr2d)
print(arr2d.shape)
Output:
[[ 1. 2. 3.]
[ 4. 5. 6.]
[ nan nan nan]
[ 0. nan nan]
[ 8. 9. nan]]
(5, 3)

How to get euclidean distance on a 3x3x3 array in numpy

say I have a (3,3,3) array like this.
array([[[1, 1, 1],
[1, 1, 1],
[0, 0, 0]],
[[2, 2, 2],
[2, 2, 2],
[2, 2, 2]],
[[3, 3, 3],
[3, 3, 3],
[1, 1, 1]]])
How do I get the 9 values corresponding to euclidean distance between each vector of 3 values and the zeroth values?
Such as doing a numpy.linalg.norm([1,1,1] - [1,1,1]) 2 times, and then doing norm([0,0,0] - [0,0,0]), and then norm([2,2,2] - [1,1,1]) 2 times, norm([2,2,2] - [0,0,0]), then norm([3,3,3] - [1,1,1]) 2 times, and finally norm([1,1,1] - [0,0,0]).
Any good ways to vectorize this? I want to store the distances in a (3,3,1) matrix.
The result would be:
array([[[0. ],
[0. ],
[0. ]],
[[1.73],
[1.73],
[3.46]]
[[3.46],
[3.46],
[1.73]]])
keepdims argument is added in numpy 1.7, you can use it to keep the sum axis:
np.sum((x - [1, 1, 1])**2, axis=-1, keepdims=True)**0.5
the result is:
[[[ 0. ]
[ 0. ]
[ 0. ]]
[[ 1.73205081]
[ 1.73205081]
[ 1.73205081]]
[[ 3.46410162]
[ 3.46410162]
[ 0. ]]]
Edit
np.sum((x - x[0])**2, axis=-1, keepdims=True)**0.5
the result is:
array([[[ 0. ],
[ 0. ],
[ 0. ]],
[[ 1.73205081],
[ 1.73205081],
[ 3.46410162]],
[[ 3.46410162],
[ 3.46410162],
[ 1.73205081]]])
You might want to consider scipy.spatial.distance.cdist(), which efficiently computes distances between pairs of points in two collections of inputs (with a standard euclidean metric, among others). Here's example code:
import numpy as np
import scipy.spatial.distance as dist
i = np.array([[[1, 1, 1],
[1, 1, 1],
[0, 0, 0]],
[[2, 2, 2],
[2, 2, 2],
[2, 2, 2]],
[[3, 3, 3],
[3, 3, 3],
[1, 1, 1]]])
n,m,o = i.shape
# compute euclidean distances of each vector to the origin
# reshape input array to 2-D, as required by cdist
# only keep diagonal, as cdist computes all pairwise distances
# reshape result, adapting it to input array and required output
d = dist.cdist(i.reshape(n*m,o),i[0]).reshape(n,m,o).diagonal(axis1=2).reshape(n,m,1)
d holds:
array([[[ 0. ],
[ 0. ],
[ 0. ]],
[[ 1.73205081],
[ 1.73205081],
[ 3.46410162]],
[[ 3.46410162],
[ 3.46410162],
[ 1.73205081]]])
The big caveat of this approach is that we're calculating n*m*o distances, when we only need n*m (and that it involves an insane amount of reshaping).
I'm doing something similar that is to compute the the sum of squared distances (SSD) for each pair of frames in video volume. I think that it could be helpful for you.
video_volume is a a single 4d numpy array. This array should have dimensions
(time, rows, cols, 3) and dtype np.uint8.
Output is a square 2d numpy array of dtype float. output[i,j] should contain
the SSD between frames i and j.
video_volume = video_volume.astype(float)
size_t = video_volume.shape[0]
output = np.zeros((size_t, size_t), dtype = np.float)
for i in range(size_t):
for j in range(size_t):
output[i, j] = np.square(video_volume[i,:,:,:] - video_volume[j,:,:,:]).sum()

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