# 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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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