Given two 2D arrays
b. You can perform standard matrix multiplication with the operation
np.matmul(a, b) if the array a has shape
(x, y) and array be has shape
(y, z) for some integers
Problem Formulation: Given a two-dimensional NumPy array (=matrix)
a with shape
(x, y) and a two-dimensional array
b with shape
(y, z). In other words, the number of columns of
a is the same as the number of rows of
b. How to multiply
b using standard matrix multiplication?
Solution: Use the
np.matmul(a, b) function that takes two NumPy arrays as input and returns the result of the multiplication of both arrays. The arrays must be compatible in shape.
Let’s dive into some examples!
Matrix Multiplication of a 2×2 with a 2×2 matrix
import numpy as np a = np.array([[1, 1], [1, 0]]) b = np.array([[2, 0], [0, 2]]) c = np.matmul(a, b) print(a.shape) # (2, 2) print(b.shape) # (2, 2) print(c) ''' [[2 2] [2 0]] '''
Matrix Multiplication of a 2×3 and a 3×2 Matrix
import numpy as np a = np.array([[1, 1, 1], [1, 0, 1]]) b = np.array([[2, 0], [0, 2], [0, 0]]) c = np.matmul(a, b) print(a.shape) # (2, 3) print(b.shape) # (3, 2) print(c) ''' [[2 2] [2 0]] '''
NumPy Puzzle: Matrix Multiplication
import numpy as np # graphics data a = [[1, 1], [1, 0]] # stretch vectors b = [[2, 0], [0, 2]] c = np.matmul(a, b) print(c[0, 1])
What is the output of this puzzle?
Numpy is a popular Python library for data science focusing on arrays, vectors, and matrices.
This puzzle shows an important application domain of matrix multiplication: Computer Graphics.
We create two matrices a and b. The first matrix a is the data matrix (e.g. consisting of two column vectors
(1,0)). The second matrix b is the transformation matrix that transforms the input data. In our setting, the transformation matrix simply stretches the column vectors.
More precisely, the two column vectors
(1,0) are stretched by factor 2 to
(2,0). The resulting matrix is therefore
[[2,2],[2,0]]. We access the first row and second column.
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