Lapack的行减少
我正在尝试编写一个函数，为代表性不足的方程组生成单个解（例如，描述该系统的矩阵比它的高更宽）。 为了做到这一点，我一直在 LAPACK 文档中寻找一种将矩阵行简化为其简化梯形形式的方法，类似于 Mathematica 和 TI 计算器中的函数 rref()。 我遇到的最接近的是 http:// /software.intel.com/en-us/forums/intel-math-kernel-library/topic/53107/ 这个小线程。 然而，该线程似乎暗示简单地采用“U”上三角矩阵（并将每行除以对角线）与矩阵的简化梯形形式相同，我不认为是这种情况。 我可以自己编写 rref() 代码，但我不相信我能够实现 LAPACK 闻名的性能。
1) 有没有更好的方法来简单地为代表性不足的系统提供任何一种特定的解决方案？
2）如果没有，LAPACK有没有办法对矩阵进行行归约？
谢谢！
I am trying to write a function that produces a single solution to an underrepresented system of equations (e.g. the matrix that describes the system is wider than it is tall). In order to do this, I have been looking in the LAPACK documentation for a way to row-reduce a matrix to it's reduced-echelon form, similar to the function rref() in both Mathematica and TI calculators. The closest I came across was http://software.intel.com/en-us/forums/intel-math-kernel-library/topic/53107/ this tiny thread. This thread, however, seems to imply that simply taking the "U" upper triangular matrix (and dividing each row by the diagonal) is the same as the reduced echelon form of a matrix, which I do not believe to be the case. I could code up rref() myself, but I do not believe I could achieve the performance LAPACK is famous for.
1) Is there a better way to simply get any one specific solution to an underrepresented system?
2) If not, is there a way for LAPACK to row-reduce a matrix?
Thanks!
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一种常用的方法是最小二乘解，请参阅 lapack 的 sgelsx
One often used method for this is the least square solution, see lapack's sgelsx