Consider the following code in Python, where multiplying a pre-transposed matrix yields faster execution time compared to multiplying a non-transposed matrix:
import numpy as np
import time
# Generate random matrix
matrix_size = 1000
matrix = np.random.rand(matrix_size, matrix_size)
# Transpose the matrix
transposed_matrix = np.transpose(matrix)
# Multiply non-transposed matrix
start = time.time()
result1 = np.matmul(matrix, matrix)
end = time.time()
execution_time1 = end - start
# Multiply pre-transposed matrix
start = time.time()
result2 = np.matmul(transposed_matrix, transposed_matrix)
end = time.time()
execution_time2 = end - start
print("Execution time (non-transposed):", execution_time1)
print("Execution time (pre-transposed):", execution_time2)
Surprisingly, multiplying the pre-transposed matrix is faster. One might assume that the order of multiplication should not affect the performance significantly, but there seems to be a difference.
Why does processing a pre-transposed matrix result in faster execution time compared to a non-transposed matrix? Is there any underlying reason or optimization that explains this behavior?
from Why is performing matrix multiplication on a pre-transposed matrix faster than on a non-transposed matrix?
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