Introduction to Numpy - Mathematical Operation

Program 1

Mathematical Operation

Python 3.11 Ready

import numpy as np

''' Create two 1D NumPy arrays '''
arr1 = np.array([1, 2, 3, 4, 5])
arr2 = np.array([5, 4, 3, 2, 1])

''' Element-wise addition '''
add_result = np.add(arr1, arr2)
print("\nElement-wise addition:", add_result)

''' Element-wise subtraction '''
sub_result = np.subtract(arr1, arr2)
print("\nElement-wise subtraction:", sub_result)

''' Element-wise multiplication '''
mul_result = np.multiply(arr1, arr2)
print("\nElement-wise multiplication:", mul_result)

''' Element-wise division '''
div_result = np.divide(arr1, arr2)
print("\nElement-wise division:", div_result)

''' Element-wise power '''
pow_result = np.power(arr1, arr2)
print("\nElement-wise power:", pow_result)

''' Square root of each element '''
sqrt_result = np.sqrt(arr1)
print("\nSquare root:", sqrt_result)

''' Exponential of each element '''
exp_result = np.exp(arr1)
print("\nExponential:", exp_result)

''' Natural logarithm of each element '''
log_result = np.log(arr1)
print("\nNatural log:", log_result)

''' Logarithm base 10 of each element '''
log10_result = np.log10(arr1)
print("\nLog base 10:", log10_result)

''' Absolute value of each element '''
abs_result = np.abs(np.array([-1, -2, -3, 4, 5]))
print("\nAbsolute values:", abs_result)

''' Trigonometric sine of each element '''
sin_result = np.sin(arr1)
print("\nSine of elements:", sin_result)

''' Trigonometric cosine of each element '''
cos_result = np.cos(arr1)
print("\nCosine of elements:", cos_result)

''' Trigonometric tangent of each element '''
tan_result = np.tan(arr1)
print("\nTangent of elements:", tan_result)

''' Hyperbolic sine of each element '''
sinh_result = np.sinh(arr1)
print("\nHyperbolic sine:", sinh_result)

''' Hyperbolic cosine of each element '''
cosh_result = np.cosh(arr1)
print("\nHyperbolic cosine:", cosh_result)

''' Hyperbolic tangent of each element '''
tanh_result = np.tanh(arr1)
print("\nHyperbolic tangent:", tanh_result)

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

1 D Array

Program 2

Mathematical Operation

Python 3.11 Ready

import numpy as np

''' Create two 1D NumPy arrays '''
arr1 = np.array([1, 2, 3, 4, 5])
arr2 = np.array([5, 4, 3, 2, 1])

''' Floor of each element (round down to nearest integer) '''
arr3 = np.array([1.7, 2.3, 3.9, 4.5])
floor_result = np.floor(arr3)
print("\nFloor of elements:", floor_result)

''' Ceil of each element (round up to nearest integer) '''
ceil_result = np.ceil(arr3)
print("\nCeil of elements:", ceil_result)

''' Round each element to nearest integer '''
round_result = np.round(arr3)
print("\nRounded elements:", round_result)

''' Sum of all elements in the array '''
sum_result = np.sum(arr1)
print("\nSum of elements:", sum_result)

''' Product of all elements in the array '''
prod_result = np.prod(arr1)
print("\nProduct of elements:", prod_result)

''' Cumulative sum of array elements '''
cumsum_result = np.cumsum(arr1)
print("\nCumulative sum of elements:", cumsum_result)

''' Cumulative product of array elements '''
cumprod_result = np.cumprod(arr1)
print("\nCumulative product of elements:", cumprod_result)

''' Mean of all elements '''
mean_result = np.mean(arr1)
print("\nMean of elements:", mean_result)

''' Median of all elements '''
median_result = np.median(arr1)
print("\nMedian of elements:", median_result)

''' Variance of the elements '''
variance_result = np.var(arr1)
print("\nVariance of elements:", variance_result)

''' Standard deviation of the elements '''
std_result = np.std(arr1)
print("\nStandard deviation of elements:", std_result)

''' Maximum value in the array '''
max_result = np.max(arr1)
print("\nMaximum value:", max_result)

''' Minimum value in the array '''
min_result = np.min(arr1)
print("\nMinimum value:", min_result)

''' Dot product of two arrays '''
dot_result = np.dot(arr1, arr2)
print("\nDot product:", dot_result)

''' Modulus (remainder) of element-wise division '''
mod_result = np.mod(arr1, arr2)
print("\nModulus of elements:", mod_result)

''' Greatest common divisor (GCD) of elements '''
gcd_result = np.gcd(arr1, arr2)
print("\nGCD of elements:", gcd_result)

''' Least common multiple (LCM) of elements '''
lcm_result = np.lcm(arr1, arr2)
print("\nLCM of elements:", lcm_result)

''' Clip (limit) the values of the array '''
clipped_result = np.clip(arr1, 2, 4)
print("\nClipped array (values between 2 and 4):", clipped_result)

''' Remainder of division (modulo operation) '''
remainder_result = np.remainder(arr1, arr2)
print("\nRemainder of elements:", remainder_result)

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

1D Array

Program 3

Mathematical Operation

Python 3.11 Ready

import numpy as np

''' Create two 2D NumPy arrays '''
arr1 = np.array([[1, 2, 3], [4, 5, 6]])
arr2 = np.array([[6, 5, 4], [3, 2, 1]])

''' Element-wise addition '''
add_result = np.add(arr1, arr2)
print("\nElement-wise addition:\n", add_result)

''' Element-wise subtraction '''
sub_result = np.subtract(arr1, arr2)
print("\nElement-wise subtraction:\n", sub_result)

''' Element-wise multiplication '''
mul_result = np.multiply(arr1, arr2)
print("\nElement-wise multiplication:\n", mul_result)

''' Element-wise division '''
div_result = np.divide(arr1, arr2)
print("\nElement-wise division:\n", div_result)

''' Element-wise power '''
pow_result = np.power(arr1, arr2)
print("\nElement-wise power:\n", pow_result)

''' Square root of each element '''
sqrt_result = np.sqrt(arr1)
print("\nSquare root:\n", sqrt_result)

''' Exponential of each element '''
exp_result = np.exp(arr1)
print("\nExponential:\n", exp_result)

''' Natural logarithm of each element '''
log_result = np.log(arr1 + 1)  # Added 1 to avoid log(0)
print("\nNatural log:\n", log_result)

''' Logarithm base 10 of each element '''
log10_result = np.log10(arr1 + 1)  # Added 1 to avoid log10(0)
print("\nLog base 10:\n", log10_result)

''' Absolute value of each element '''
abs_result = np.abs(np.array([[-1, -2, -3], [4, -5, 6]]))
print("\nAbsolute values:\n", abs_result)

''' Trigonometric sine of each element '''
sin_result = np.sin(arr1)
print("\nSine of elements:\n", sin_result)

''' Trigonometric cosine of each element '''
cos_result = np.cos(arr1)
print("\nCosine of elements:\n", cos_result)

''' Trigonometric tangent of each element '''
tan_result = np.tan(arr1)
print("\nTangent of elements:\n", tan_result)

''' Hyperbolic sine of each element '''
sinh_result = np.sinh(arr1)
print("\nHyperbolic sine:\n", sinh_result)

''' Hyperbolic cosine of each element '''
cosh_result = np.cosh(arr1)
print("\nHyperbolic cosine:\n", cosh_result)

''' Hyperbolic tangent of each element '''
tanh_result = np.tanh(arr1)
print("\nHyperbolic tangent:\n", tanh_result)

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

2D Array

Program 4

Mathematical Operation

Python 3.11 Ready

import numpy as np

''' Create two 2D NumPy arrays '''
arr1 = np.array([[1, 2, 3, 8, 9], [4, 5, 6, 3, 1]])
arr2 = np.array([[6, 5, 4, 3, 2], [3, 2, 1, -1, -4]])

''' Floor of each element (round down to nearest integer) '''
arr3 = np.array([[1.7, 2.3, 3.9, 4.2, 4.9], [4.5, 5.6, 6.1, 7.8, 5.2]])
floor_result = np.floor(arr3)
print("\nFloor of elements:\n", floor_result)

''' Ceil of each element (round up to nearest integer) '''
ceil_result = np.ceil(arr3)
print("\nCeil of elements:\n", ceil_result)

''' Round each element to nearest integer '''
round_result = np.round(arr3)
print("\nRounded elements:\n", round_result)

''' Sum of all elements in the 2D array '''
sum_result = np.sum(arr1)
print("\nSum of elements:", sum_result)

''' Sum along each row '''
sum_along_rows = np.sum(arr1, axis=1)
print("\nSum along rows:", sum_along_rows)

''' Sum along each column '''
sum_along_cols = np.sum(arr1, axis=0)
print("\nSum along columns:", sum_along_cols)

''' Product of all elements in the 2D array '''
prod_result = np.prod(arr1)
print("\nProduct of elements:", prod_result)

''' Cumulative sum of elements '''
cumsum_result = np.cumsum(arr1)
print("\nCumulative sum of elements:", cumsum_result)

''' Mean of all elements in the array '''
mean_result = np.mean(arr1)
print("\nMean of elements:", mean_result)

''' Median of all elements in the array '''
median_result = np.median(arr1)
print("\nMedian of elements:", median_result)

''' Variance of the elements '''
variance_result = np.var(arr1)
print("\nVariance of elements:", variance_result)

''' Standard deviation of the elements '''
std_result = np.std(arr1)
print("\nStandard deviation of elements:", std_result)

''' Maximum value in the 2D array '''
max_result = np.max(arr1)
print("\nMaximum value:", max_result)

''' Minimum value in the 2D array '''
min_result = np.min(arr1)
print("\nMinimum value:", min_result)

''' Maximum value along each row '''
max_along_rows = np.max(arr1, axis=1)
print("\nMaximum value along rows:", max_along_rows)

''' Maximum value along each column '''
max_along_cols = np.max(arr1, axis=0)
print("\nMaximum value along columns:", max_along_cols)

''' Dot product of two 2D arrays (matrix multiplication) '''
dot_result = np.dot(arr1, arr2.T)
print("\nDot product (matrix multiplication):\n", dot_result)

''' Modulus (remainder) of element-wise division '''
mod_result = np.mod(arr1, arr2)
print("\nModulus of elements:\n", mod_result)

''' Greatest common divisor (GCD) of elements '''
gcd_result = np.gcd(arr1, arr2)
print("\nGCD of elements:\n", gcd_result)

''' Least common multiple (LCM) of elements '''
lcm_result = np.lcm(arr1, arr2)
print("\nLCM of elements:\n", lcm_result)

''' Clip (limit) the values of the array '''
clipped_result = np.clip(arr1, 2, 4)
print("\nClipped array (values between 2 and 4):\n", clipped_result)

''' Flatten the 2D array into a 1D array '''
flatten_result = arr1.flatten()
print("\nFlattened array:", flatten_result)

Click "Run Code" to execute script and render figures.

Mathematical Problem Formulation

2D Array

Ch. 7.4 Mathematical Operation

Mathematical Operation

Mathematical Problem Formulation

Mathematical Operation

Mathematical Problem Formulation

Mathematical Operation

Mathematical Problem Formulation

Mathematical Operation

Mathematical Problem Formulation