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This article provides a detailed explanation of the einsum function in NumPy, focusing on its working principles and applications. einsum uses a concise subscript notation to efficiently perform multiplication, summation, and transposition on multidimensional arrays, avoiding the creation of temporary arrays and thus improving memory usage. Starting from basic concepts, the article uses code examples to explain the parsing rules of subscript strings and demonstrates how to implement common array operations such as matrix multiplication, dot products, and outer products with einsum. By comparing traditional NumPy operations, it highlights the advantages of einsum in performance and clarity, offering practical guidance for handling complex multidimensional data.

This article details a practical technique for quickly copying file lists as text in Windows Explorer. By analyzing the "Copy as Path" feature in Windows 7 and later versions, along with the operational steps involving the Shift key and right-click menu, it provides an efficient method for batch filename extraction. The article also discusses the limitations of this feature in Windows XP and briefly compares alternative command-line approaches, offering convenient technical references for daily file management.

This paper provides an in-depth analysis of the technical principles and implementation methods for statically linking shared library functions in the GCC compilation environment. By examining the fundamental differences between static and dynamic linking, it explains why directly statically linking shared library files is not feasible. The article details the mechanism of using the -static flag to force linking with static libraries, as well as the technical approach of mixed linking strategies through -Wl,-Bstatic and -Wl,-Bdynamic to achieve partial static linking. Alternative solutions using tools like statifier and Ermine are discussed, with practical code examples demonstrating common errors and solutions in the linking process.