Numpy 1D Arrays

This note covers vectors in Numpy using 1D arrays.

• Creation with np.array
• Indexing and slicing
• Element-wise operations
• Boolean filtering

Row and Column Vectors

When dealing with vectors, usually represented as 1D arrays, it’s useful to distinguish between column vectors (vertical) and row vectors (horizontal). Therefore, they’re usually treated as 2D arrays, because 2D arrays allow transposition and other operations to be performed on them.

arr = np.array([1,2,3,4,5]) # 1D array
> [1,2,3,4,5]
 
arr = arr.reshape(1, -1) # Using -1 for the axis automatically calculates the number of elements
arr.T
> [[1]
   [0]
   [1]
   [0]
   [1]]

1D Array Methods

Common ndarray methods and operations for 1D arrays:

Shape and Conversion

arr = np.array([1, 2, 3, 4, 5])
 
arr.shape        # (5,)
arr.ndim         # 1
arr.size         # 5
arr.dtype        # data type
arr.astype(float)
arr.tolist()     # [1, 2, 3, 4, 5]

Ordering and Rearranging

arr.sort()               # in place
np.sort(arr)             # returns sorted copy
arr.argsort()            # indices that sort arr
arr[::-1]                # reverse via slicing
np.flip(arr)             # reversed copy
np.concatenate((a, b))   # join arrays

Selection and Filtering

arr[2]                   # single index
arr[1:4]                 # slice
arr[[0, 2, 4]]           # index array
arr[arr > 2]             # boolean mask
np.where(arr % 2 == 0)   # matching indices

Statistics and Aggregation

arr.min()
arr.max()
arr.sum()
arr.mean()
arr.std()
arr.var()
arr.argmin()   # index of min
arr.argmax()   # index of max

Math and Linear Algebra Helpers

arr + 10
arr * 2
arr1 + arr2
arr1 * arr2             # element-wise product
np.dot(arr1, arr2)      # dot product
np.linalg.norm(arr)     # vector norm

Useful Transformations

arr.reshape(1, -1)   # row vector (2D)
arr.reshape(-1, 1)   # column vector (2D)
arr.flatten()        # 1D copy
arr.ravel()          # 1D view when possible