精通 NumPy 数组操作：数学计算的引擎

            import numpy as np

# 1D array
list_1d = [1, 2, 3, 4, 5]
arr_1d = np.array(list_1d)
print(arr_1d)

# 2D array
list_2d = [[1, 2, 3], [4, 5, 6]]
arr_2d = np.array(list_2d)
print(arr_2d)

            

              
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            # Array of zeros
arr_zeros = np.zeros((3, 4)) # Creates a 3x4 array filled with zeros
print(arr_zeros)

# Array of ones
arr_ones = np.ones((2, 3))  # Creates a 2x3 array filled with ones
print(arr_ones)

# Array with a specific value
arr_full = np.full((2, 2), 7) # Creates a 2x2 array filled with 7
print(arr_full)

# Identity matrix
arr_identity = np.eye(3)    # Creates a 3x3 identity matrix
print(arr_identity)

# Array with a range of values
arr_range = np.arange(0, 10, 2) # Creates an array from 0 to 10 (exclusive) with step 2
print(arr_range)

# Array with evenly spaced values
arr_linspace = np.linspace(0, 1, 5) # Creates 5 evenly spaced values between 0 and 1 (inclusive)
print(arr_linspace)

            

              
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            import numpy as np

arr1 = np.array([1, 2, 3])
arr2 = np.array([4, 5, 6])

# Addition
print(arr1 + arr2)  # Output: [5 7 9]

# Subtraction
print(arr1 - arr2)  # Output: [-3 -3 -3]

# Multiplication
print(arr1 * arr2)  # Output: [ 4 10 18]

# Division
print(arr1 / arr2)  # Output: [0.25 0.4  0.5 ]

# Modulo
print(arr1 % arr2)  # Output: [1 2 3]

# Exponentiation
print(arr1 ** 2)    # Output: [1 4 9] (operating on a single array)

            

              
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            import numpy as np

arr = np.array([1, 2, 3])
scalar = 5

print(arr + scalar)  # Output: [6 7 8]
print(arr * scalar)  # Output: [ 5 10 15]

            

              
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            import numpy as np

arr = np.array([0, np.pi/2, np.pi])

# Sine function
print(np.sin(arr))

# Exponential function
print(np.exp(arr))

# Square root
print(np.sqrt([1, 4, 9]))

# Logarithm
print(np.log([1, np.e, np.e**2]))

            

              
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            import numpy as np

arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Accessing an element (row 1, column 2)
print(arr_2d[1, 2])  # Output: 6

# Accessing a row
print(arr_2d[0, :])  # Output: [1 2 3] (all columns in row 0)

# Accessing a column
print(arr_2d[:, 1])  # Output: [2 5 8] (all rows in column 1)

            

              
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            import numpy as np

arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Slice a sub-array (rows 0 to 1, columns 1 to 2)
print(arr_2d[0:2, 1:3])
# Output:
# [[2 3]
#  [5 6]]

# Slice the first two rows
print(arr_2d[0:2, :])
# Output:
# [[1 2 3]
#  [4 5 6]]

            

              
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            import numpy as np

arr = np.array([10, 25, 8, 40, 15])

# Create a boolean array where elements are greater than 20
condition = arr > 20
print(condition) # Output: [False  True False  True False]

# Use the boolean array to select elements
print(arr[condition]) # Output: [25 40]

# Directly apply a condition
print(arr[arr % 2 == 0]) # Select even numbers: Output: [10  8 40]

            

              
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            import numpy as np

arr = np.array([1, 2, 3, 4, 5, 6])

# Select elements at specific indices
indices = np.array([1, 3, 5])
print(arr[indices]) # Output: [2 4 6]

arr_2d = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])

# Select specific rows and columns using fancy indexing
# Select elements at (0,1), (1,0), (2,2)
print(arr_2d[[0, 1, 2], [1, 0, 2]]) # Output: [2 4 9]

            

              
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            import numpy as np

# Array A (3x1)
arr_a = np.array([[1], [2], [3]])

# Array B (1x3)
arr_b = np.array([[4, 5, 6]])

# Broadcasting A and B
result = arr_a + arr_b
print(result)
# Output:
# [[5 6 7]
#  [6 7 8]
#  [7 8 9]]

# Here, arr_a (3x1) is broadcasted to 3x3 by repeating its columns.
# arr_b (1x3) is broadcasted to 3x3 by repeating its rows.

            

              
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            import numpy as np

arr = np.array([[1, 2, 3], [4, 5, 6]])

# Sum of all elements
print(np.sum(arr))  # Output: 21

# Sum along axis 0 (columns)
print(np.sum(arr, axis=0)) # Output: [5 7 9]

# Sum along axis 1 (rows)
print(np.sum(arr, axis=1)) # Output: [ 6 15]

            

              
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            import numpy as np

matrix1 = np.array([[1, 2], [3, 4]])
matrix2 = np.array([[5, 6], [7, 8]])

# Using the @ operator
result_at = matrix1 @ matrix2
print(result_at)

# Using np.dot()
result_dot = np.dot(matrix1, matrix2)
print(result_dot)

# Output for both:
# [[19 22]
#  [43 50]]

            

              
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            import numpy as np

matrix = np.array([[1, 2], [3, 4]])
inverse_matrix = np.linalg.inv(matrix)
print(inverse_matrix)
# Output:
# [[-2.   1. ]
#  [ 1.5 -0.5]]

            

              
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            import numpy as np

matrix = np.array([[1, 2], [3, 4]])
determinant = np.linalg.det(matrix)
print(determinant) # Output: -2.0

            

              
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            import numpy as np

matrix = np.array([[1, 2], [3, 4]])
eigenvalues, eigenvectors = np.linalg.eig(matrix)

print("Eigenvalues:", eigenvalues)
print("Eigenvectors:", eigenvectors)

            

              
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