 # NumPy: Mathematics Exercises, Practice, Solution

## NumPy Mathematics [41 exercises with solution]

[An editor is available at the bottom of the page to write and execute the scripts.] 1. Write a NumPy program to add, subtract, multiply, divide arguments element-wise. Go to the editor
Expected Output:
5.0
Subtract:
-3.0
Multiply:
4.0
Divide:
0.25
Click me to see the sample solution

2. Write a NumPy program to compute logarithm of the sum of exponentiations of the inputs, sum of exponentiations of the inputs in base-2. Go to the editor
Expected Output:
Logarithm of the sum of exponentiations:
-113.876491681
Logarithm of the sum of exponentiations of the inputs in base-2:
-113.599555228
Click me to see the sample solution

3. Write a NumPy program to get true division of the element-wise array inputs. Go to the editor
Expected Output:
Original array:
[0 1 2 3 4 5 6 7 8 9]
Division of the array inputs, element-wise:
[ 0. 0.33333333 0.66666667 1. 1.33333333 1.6666666
7 2. 2.33333333 2.66666667 3. ]
Click me to see the sample solution

4. Write a NumPy program to get the largest integer smaller or equal to the division of the inputs. Go to the editor
Expected Output:
Original array:
[1.0, 2.0, 3.0, 4.0]
Largest integer smaller or equal to the division of the inputs:
[ 0. 1. 2. 2.]
Click me to see the sample solution

5. Write a NumPy program to get the powers of an array values element-wise. Go to the editor
Note: First array elements raised to powers from second array
Expected Output:
Original array
[0 1 2 3 4 5 6]
First array elements raised to powers from second array, element-wise:
[ 0 1 8 27 64 125 216]
Click me to see the sample solution

6. Write a NumPy program to get the element-wise remainder of an array of division. Go to the editor
Sample Output:
Original array:
[0 1 2 3 4 5 6]
Element-wise remainder of division:
[0 1 2 3 4 0 1]
Click me to see the sample solution

7. Write a NumPy program to calculate the absolute value element-wise. Go to the editor
Sample output:
Original array:
[ -10.2 122.2 0.2]
Element-wise absolute value:
[ 10.2 122.2 0.2]
Click me to see the sample solution

8. Write a NumPy program to round array elements to the given number of decimals. Go to the editor
Sample Output:
[ 1. 2. 2.]
[ 0.3 0.5 0.6]
[ 0. 2. 2. 4. 4.]
Click me to see the sample solution

9. Write a NumPy program to round elements of the array to the nearest integer. Go to the editor
Sample Output:
Original array:
[-0.7 -1.5 -1.7 0.3 1.5 1.8 2. ]
Round elements of the array to the nearest integer:
[-1. -2. -2. 0. 2. 2. 2.]
Click me to see the sample solution

10. Write a NumPy program to get the floor, ceiling and truncated values of the elements of a numpy array. Go to the editor
Sample Output:
Original array:
[-1.6 -1.5 -0.3 0.1 1.4 1.8 2. ]
Floor values of the above array elements:
[-2. -2. -1. 0. 1. 1. 2.]
Ceil values of the above array elements:
[-1. -1. -0. 1. 2. 2. 2.]
Truncated values of the above array elements:
[-1. -1. -0. 0. 1. 1. 2.]
Click me to see the sample solution

11. Write a NumPy program to multiply a 5x3 matrix by a 3x2 matrix and create a real matrix product. Go to the editor
Sample output:
First array:
[[ 0.44349753 0.81043761 0.00771825]
[ 0.64004088 0.86774612 0.19944667]
[ 0.61520091 0.24796788 0.93798297]
[ 0.22156999 0.61318856 0.82348994]
[ 0.91324026 0.13411297 0.00622696]]
Second array:
[[ 0.73873542 0.06448186]
[ 0.90974982 0.06409165]
[ 0.22321268 0.39147412]]
Dot product of two arrays:
[[ 1.06664562 0.08356133]
[ 1.30677176 0.17496452]
[ 0.88942914 0.42275803]
[ 0.90534318 0.37596252]
[ 0.79804212 0.06992065]]
Click me to see the sample solution

12. Write a NumPy program to multiply a matrix by another matrix of complex numbers and create a new matrix of complex numbers. Go to the editor
Sample output:
First array:
[ 1.+2.j 3.+4.j]
Second array:
[ 5.+6.j 7.+8.j]
Product of above two arrays:
(70-8j)
Click me to see the sample solution

13. Write a NumPy program to create an inner product of two arrays. Go to the editor
Sample Output:
Array x:
[[[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]]
[[12 13 14 15]
[16 17 18 19]
[20 21 22 23]]]
Array y:
[0 1 2 3]
Inner of x and y arrays:
[[ 14 38 62]
[ 86 110 134]]
Click me to see the sample solution

14. Write a NumPy program to generate inner, outer, and cross products of matrices and vectors. Go to the editor
Expected Output:
Matrices and vectors.
x:
[ 1. 4. 0.]
y:
[ 2. 2. 1.]
Inner product of x and y:
10.0
Outer product of x and y:
[[ 2. 2. 1.]
[ 8. 8. 4.]
[ 0. 0. 0.]]
Cross product of x and y:
[ 4. -1. -6.]
Click me to see the sample solution

15. Write a NumPy program to generate a matrix product of two arrays. Go to the editor
Sample Output:
Matrices and vectors.
x:
[[1, 0], [1, 1]]
y:
[[3, 1], [2, 2]]
Matrix product of above two arrays:
[[3 1]
[5 3]]
Click me to see the sample solution

16. Write a NumPy program to find the roots of the following polynomials. Go to the editor
a) x2 - 4x + 7.
b) x4 - 11x3 + 9x2 + 11x ? 10
Sample output:
Roots of the first polynomial:
[ 1. 1.]
Roots of the second polynomial:
[ 11.04461946+0.j -0.87114210+0.j 0.91326132+0.4531004j
0.91326132-0.4531004j]
Click me to see the sample solution

17. Write a NumPy program to compute the following polynomial values. Go to the editor
Sample output:
Polynomial value when x = 2:
1
Polynomial value when x = 3:
-142
Click me to see the sample solution

18. Write a NumPy program to add one polynomial to another, subtract one polynomial from another, multiply one polynomial by another and divide one polynomial by another. Go to the editor
Sample output:
[ 40. 60. 80.]
Subtract one polynomial from another:
[-20. -20. -20.]
Multiply one polynomial by another:
[ 300. 1000. 2200. 2200. 1500.]
Divide one polynomial by another:
(array([ 0.6]), array([-8., -4.]))
Click me to see the sample solution

19. Write a NumPy program to calculate mean across dimension, in a 2D numpy array. Go to the editor
Sample output:
Original array:
[[10 30]
[20 60]]
Mean of each column:
[ 15. 45.]
Mean of each row:
[ 20. 40.]
Click me to see the sample solution

20. Write a NumPy program to create a random array with 1000 elements and compute the average, variance, standard deviation of the array elements. Go to the editor
Sample output:
Average of the array elements:
-0.0255137240796
Standard deviation of the array elements:
0.984398282476
Variance of the array elements:
0.969039978542
Click me to see the sample solution

21. Write a NumPy program to compute the trigonometric sine, cosine and tangent array of angles given in degrees. Go to the editor
Sample output:
sine: array of angles given in degrees
[ 0. 0.5 0.70710678 0.8660254 1. ]
cosine: array of angles given in degrees
[ 1.00000000e+00 8.66025404e-01 7.07106781e-01 5.00000000e-01
6.12323400e-17]
tangent: array of angles given in degrees
[ 0.00000000e+00 5.77350269e-01 1.00000000e+00 1.73205081e+00
1.63312394e+16]
Click me to see the sample solution

22. Write a NumPy program to calculate inverse sine, inverse cosine, and inverse tangent for all elements in a given array. Go to the editor
Sample output:
Inverse sine: [-1.57079633 0. 1.57079633]
Inverse cosine: [3.14159265 1.57079633 0. ]
Inverse tangent: [-0.78539816 0. 0.78539816]
Click me to see the sample solution

23. Write a NumPy program to convert angles from radians to degrees for all elements in a given array. Go to the editor
Input: [-np.pi, -np.pi/2, np.pi/2, np.pi]
Sample output:
[-180. -90. 90. 180.]
Click me to see the sample solution

24. Write a NumPy program to convert angles from degrees to radians for all elements in a given array. Go to the editor
Input: Input: [-180., -90., 90., 180.]
Sample output:
[-3.14159265 -1.57079633 1.57079633 3.14159265]
Click me to see the sample solution

25. Write a NumPy program to calculate hyperbolic sine, hyperbolic cosine, and hyperbolic tangent for all elements in a given array. Go to the editor
Input: Input: Input: [-1., 0, 1.]
Sample output:
[-1.17520119 0. 1.17520119]
[1.54308063 1. 1.54308063]
[-0.76159416 0. 0.76159416]
Click me to see the sample solution

26. Write a NumPy program to calculate round, floor, ceiling, truncated and round (to the given number of decimals) of the input, element-wise of a given array. Go to the editor
Sample output:
Original array:
[ 3.1 3.5 4.5 2.9 -3.1 -3.5 -5.9]
around: [ 3. 4. 4. 3. -3. -4. -6.]
floor: [ 3. 3. 4. 2. -4. -4. -6.]
ceil: [ 4. 4. 5. 3. -3. -3. -5.]
trunc: [ 3. 3. 4. 2. -3. -3. -5.]
round: [3.0, 4.0, 4.0, 3.0, -3.0, -4.0, -6.0]
Click me to see the sample solution

27. Write a NumPy program to calculate cumulative sum of the elements along a given axis, sum over rows for each of the 3 columns and sum over columns for each of the 2 rows of a given 3x3 array. Go to the editor
Sample output:
Original array:
[[1 2 3]
[4 5 6]]
Cumulative sum of the elements along a given axis:
[ 1 3 6 10 15 21]
Sum over rows for each of the 3 columns:
[[1 2 3]
[5 7 9]]
Sum over columns for each of the 2 rows:
[[ 1 3 6]
[ 4 9 15]]
Click me to see the sample solution

28. Write a NumPy program to calculate cumulative product of the elements along a given axis, sum over rows for each of the 3 columns and product over columns for each of the 2 rows of a given 3x3 array. Go to the editor
Sample output:
Original array:
[[1 2 3]
[4 5 6]]
Cumulative product of the elements along a given axis:
[ 1 2 6 24 120 720]
Product over rows for each of the 3 columns:
[[ 1 2 3]
[ 4 10 18]]
Product over columns for each of the 2 rows:
[[ 1 2 6]
[ 4 20 120]]
Click me to see the sample solution

29. Write a NumPy program to calculate the difference between neighboring elements, element-wise of a given array. Go to the editor
Sample output:
Original array:
[1 3 5 7 0]
Difference between neighboring elements, element-wise of the said array.
[ 2 2 2 -7]
Click me to see the sample solution

30. Write a NumPy program to calculate the difference between neighboring elements, element-wise, and prepend [0, 0] and append to a given array. Go to the editor
Sample output:
Original array:
[1 3 5 7 0]
Difference between neighboring elements, element-wise, and prepend [0, 0] and append to the said array:
[ 0 0 2 2 2 -7 200]
Click me to see the sample solution

31. Write a NumPy program to compute ex, element-wise of a given array. Go to the editor
Sample output:
Original array:
[1. 2. 3. 4.]
e^x, element-wise of the said:
[ 2.7182817 7.389056 20.085537 54.59815 ]
Click me to see the sample solution

32. Write a NumPy program to calculate exp(x) - 1 for all elements in a given array. Go to the editor
Sample output:
Original array: [1. 2. 3. 4.] exp(x)-1 for all elements of the said array: [ 1.7182817 6.389056 19.085537 53.59815 ]
Click me to see the sample solution

33. Write a NumPy program to calculate 2p for all elements in a given array. Go to the editor
Sample output:
Original array:
[1. 2. 3. 4.]
2^p for all the elements of the said array:
[ 2. 4. 8. 16.]
Click me to see the sample solution

34. Write a NumPy program to compute natural, base 10, and base 2 logarithms for all elements in a given array. Go to the editor
Sample output:
Original array:
Original array:
[1. 2.71828183 7.3890561 ]
Natural log = [0. 1. 2.]
Common log = [0. 0.43429448 0.86858896]
Base 2 log = [0. 1.44269504 2.88539008]
Click me to see the sample solution

35. Write a NumPy program to compute the natural logarithm of one plus each element of a given array in floating-point accuracy. Go to the editor
Sample output:
Original array:
[1.e-099 1.e-100]
Natural logarithm of one plus each element:
[1.e-099 1.e-100]
Click me to see the sample solution

36. Write a NumPy program to check element-wise True/False of a given array where signbit is set. Go to the editor
Sample array: [-4, -3, -2, -1, 0, 1, 2, 3, 4]
Sample output:
Original array:
[-4 -3 -2 -1 0 1 2 3 4]
[ True True True True False False False False False]
Click me to see the sample solution

37. Write a NumPy program to change the sign of a given array to that of a given array, element-wise. Go to the editor
Sample output:
Original array:
[-1 0 1 2]
Sign of x1 to that of x2, element-wise:
[-1. 0. 1. 2.]
Click me to see the sample solution

38. Write a NumPy program to compute numerical negative value for all elements in a given array. Go to the editor
Sample output:
Original array:
[ 0 1 -1]
Numerical negative value for all elements of the said array:
[ 0 -1 1]
Click me to see the sample solution

39. Write a NumPy program to compute the reciprocal for all elements in a given array. Go to the editor
Sample output:
Original array:
[1. 2. 0.2 0.3]
Reciprocal for all elements of the said array:
[1. 0.5 5. 3.33333333]
Click me to see the sample solution

40. Write a NumPy program to compute xy, element-wise where x, y are two given arrays. Go to the editor
Sample output:
Array1:
[[1 2]
[3 4]]
Array1:
[[1 2]
[1 2]]
Result- x^y:
[[ 1 4]
[ 3 16]]
Click me to see the sample solution

41. Write a NumPy program to compute an element-wise indication of the sign for all elements in a given array. Go to the editor
Sample output:
Original array;
[ 1 3 5 0 -1 -7 0 5]
Element-wise indication of the sign for all elements of the said array:
[ 1 1 1 0 -1 -1 0 1]
Click me to see the sample solution

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## Python: Tips of the Day

While-else construct:

```i = 5

while i > 1:
print("Whil-ing away!")
i -= 1
if i == 3:
break
else:
print("Finished up!")
```