linear-algebra - dtrtrs 和 dtrsm 的区别

Question

我正在寻找一些三角求解器，我遇到了两个求解器。BLAS 中的一个：dtrsm 和 LAPACK 中的另一个：dtrtrs。从外观上看，两者似乎都具有共同的功能，而 dtrsm 具有更多功能（在解决系统之前缩放右侧）。

我想知道
1）这些功能还有什么不同？
2）当执行相同的操作时，哪个更快？
3) 如果 (2) 的答案不明显，什么时候建议 dtrsm 优于 dtrtrs，反之亦然？

Answer 1

1. Besides scaling, dtrsm can also solve systems in which the triangular matrix is right-multiplied into the unknown matrix (i.e., it can solve XA = B as well as AX = B). On the other hand, dtrsm can silently fail if A is singular, whereas dtrtrs checks for this condition and reports an error.

2. In a "typical" LAPACK distribution, dtrtrs is just a wrapper that checks for singularity and then calls dtrsm. dtrsm is therefore slightly faster, but that difference is insignificant for matrices of any reasonable size.