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NumPy - 09 Unique, Set Logic, Linear Algebra
Unique and Set Logic in NumPy
Array Set Operations
| Method | Description |
|---|---|
unique(x) | Compute the sorted, unique elements in array x. |
intersect1d(x, y) | Compute the sorted, common elements in arrays x and y. |
union1d(x, y) | Compute the sorted union of elements from arrays x and y. |
in1d(x, y) | Compute a Boolean array indicating whether each element of x is contained in y. |
setdiff1d(x, y) | Set difference; elements in x that are not in y. |
setxor1d(x, y) | Set symmetric difference; elements that are in either x or y, but not in both. |
’numpy.unique'
The numpy.unique() function is the most commonly used method for extracting unique values from a 1D array. It sorts the array and removes any duplicates, returning the sorted, unique elements as an ndarray.
>>> import numpy as np
>>> arr = np.array([3, 1, 2, 3, 2, 4, 5, 1])
>>> unique_values = np.unique(arr)
>>> unique_values
Array([1 2 3 4 5])This is similar to Python’s sorted( set(...) ), but numpy.unique() is faster and returns an ndarray rather than a Python list.
’numpy.in1d'
The numpy.in1d() function is used to test whether each element of one array (x) is contained in another array (y). It returns a Boolean array, where each element corresponds to whether the corresponding element of x is present in y.
>>> import numpy as np
>>> arr1 = np.array([3, 1, 4, 2])
>>> arr2 = np.array([1, 2, 5])
>>> membership = np.in1d(arr1, arr2)
>>> membership
[ True True False True]In this example, numpy.in1d() checks each element of arr1 against arr2. The resulting Boolean array [True, True, False, True] indicates that 3 and 4 are not in arr2, while 1 and 2 are present.
Linear Algebra in NumPy
Linear algebra operations, such as matrix multiplication, decompositions, determinants, and other square matrix math, are crucial in many array libraries. When multiplying two 2D arrays with *, it performs an element-wise product. For matrix multiplication, you need to use the dot function. This function is available both as a method on arrays and as a function in the NumPy namespace.
Matrix Operations
| Function | Description |
|---|---|
diag | Return the diagonal (or off-diagonal) elements of a square matrix as a 1D array, or convert a 1D array into a square matrix with zeros on the off-diagonal. |
dot | Perform matrix multiplication. Equivalent to np.dot(x, y) or x.dot(y). |
trace | Compute the sum of the diagonal elements of a matrix. |
det | Compute the determinant of a square matrix. |
eig | Compute the eigenvalues and eigenvectors of a square matrix. |
inv | Compute the inverse of a square matrix. |
pinv | Compute the Moore-Penrose pseudoinverse of a matrix. |
qr | Compute the QR decomposition of a matrix. |
svd | Compute the Singular Value Decomposition (SVD) of a matrix. |
solve | Solve the linear system Ax = b for x, where A is a square matrix. |
lstsq | Compute the least-squares solution to the linear system Ax = b. |
These functions enable advanced matrix operations, making NumPy an essential tool for linear algebra and numerical analysis.