PyTorch gels函数解析：最小二乘估计及命名含义问询

Great question—this is one of those naming quirks that clicks once you dig into the linear algebra foundations powering PyTorch.

PyTorch's gels function inherits its name directly from the LAPACK (Linear Algebra Package) library, the backbone of most numerical linear algebra operations in frameworks like PyTorch, NumPy, and beyond.

In LAPACK, the gels family of functions (like sgels for single-precision floats, dgels for double-precision) is built to solve general linear least squares problems. The acronym breaks down to:

• General
• Equation
• Solver for Least Squares

The "general" here is critical—it means the solver handles both overdetermined systems (more equations than variables, where we calculate the best-fit least squares solution) and underdetermined systems (fewer equations than variables, where we find the minimum-norm solution). This flexibility makes it more versatile than specialized solvers that only handle one type of system.

Understanding this origin helps you use gels more intuitively:

• It signals the function uses QR/LQ factorization under the hood (the same stable method LAPACK relies on), giving you context about its performance and numerical behavior.
• The "general" label reminds you it’s not limited to basic least squares tasks—you can leverage it for a broader range of linear system scenarios.

内容的提问来源于stack exchange，提问作者user25004