# NumPy: Mathematics Exercises, Practice, Solution

## NumPy Mathematics [41 exercises with solution]

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**1.** Write a NumPy program to add, subtract, multiply, divide arguments element-wise. Go to the editor

Expected Output:

Add:

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:

Add one polynomial to another:

[ 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[200] 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[200] 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 e^{x}, 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

**Getting rid of unwanted characters:**

You can get rid of whitespaces or any specific character using strip methods in Python. You can use either plain strip for both sides, lstrip for the left side and rstrip for the right side only.

str="+++Welcome python+++" str.strip() print(str)

Output:

+++Welcome python+++

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