Here's another piece of advice that covers a lot more than matrix inversion: don't solve math problems yourself in code if you can in any way avoid it.
Use a library instead, and use the most specific methods that are available: if there are specialized routines to solve Ax=b, use them, don't use the matrix inversion methods (which are probably also there), or even the LU decomposition ones, even if Real Math tells you that the result is equivalent - in numerical computation, mathematical equivalence is an entirely different entity than what "real" mathematicians concern themselves with.
Seriously. I don't care if you're a math PhD, I don't even care if you know a decent amount about numerical methods. Whatever code you're going to put together to do the job will be inferior to what a mature library can do, simply because the library has been put through many iterations and has had a lot more time to get patched up to handle all those special cases (usually related to finite precision or discretization) that Real Math doesn't have to worry about. And it will probably be vastly more optimized than anything you'll put together, because it's spent years of heavy use in some critical research environments.
The only time you should be writing your own math code (beyond simple arithmetic) is if no mature libraries are available to you. In which case you should allocate at the very least twice the amount of time it will take to research and implement the methods, and probably a lot more, because you're going to have a lot of fiddling to do.
Another reason would be (self-)education. There's no better way to gain a deeper understanding of a subject or learn the ins-and-outs of optimization than writing some code and then possibly trying to improve it. If you always blindly depend on third party libraries, you will remain ignorant and dumb.
Then, you can go on and use third party libraries in production while feeling satisfied that you know what's going on inside the library.
If you always blindly depend on third party libraries, you will remain ignorant and dumb.
Depends if your goal is to become an aeronautical engineer or an assembly language hacker, really. Neither one's "better" than the other, but the the former won't benefit much from understanding exactly how to optimize on SPARC vs x64... Nor will the latter need to worry about his compiler's stalling speed :-)
The other important reason to use a library is that if someone improves the algorithm someday, you can benefit for nothing more than installing and testing the new version of the library.
I remember this also being the case for Constraint Satisfaction Problem (CSP) algorithms in AI. If you can formulate your problem as a CSP and feed it to a library, you automatically benefit from future improvements in the field of CSP solvers.
Comments
Here's another piece of advice that covers a lot more than matrix inversion: don't solve math problems yourself in code if you can in any way avoid it.
Use a library instead, and use the most specific methods that are available: if there are specialized routines to solve Ax=b, use them, don't use the matrix inversion methods (which are probably also there), or even the LU decomposition ones, even if Real Math tells you that the result is equivalent - in numerical computation, mathematical equivalence is an entirely different entity than what "real" mathematicians concern themselves with.
Seriously. I don't care if you're a math PhD, I don't even care if you know a decent amount about numerical methods. Whatever code you're going to put together to do the job will be inferior to what a mature library can do, simply because the library has been put through many iterations and has had a lot more time to get patched up to handle all those special cases (usually related to finite precision or discretization) that Real Math doesn't have to worry about. And it will probably be vastly more optimized than anything you'll put together, because it's spent years of heavy use in some critical research environments.
The only time you should be writing your own math code (beyond simple arithmetic) is if no mature libraries are available to you. In which case you should allocate at the very least twice the amount of time it will take to research and implement the methods, and probably a lot more, because you're going to have a lot of fiddling to do.
Another reason would be (self-)education. There's no better way to gain a deeper understanding of a subject or learn the ins-and-outs of optimization than writing some code and then possibly trying to improve it. If you always blindly depend on third party libraries, you will remain ignorant and dumb.
Then, you can go on and use third party libraries in production while feeling satisfied that you know what's going on inside the library.
If you always blindly depend on third party libraries, you will remain ignorant and dumb.
Depends if your goal is to become an aeronautical engineer or an assembly language hacker, really. Neither one's "better" than the other, but the the former won't benefit much from understanding exactly how to optimize on SPARC vs x64... Nor will the latter need to worry about his compiler's stalling speed :-)
The other important reason to use a library is that if someone improves the algorithm someday, you can benefit for nothing more than installing and testing the new version of the library.
I remember this also being the case for Constraint Satisfaction Problem (CSP) algorithms in AI. If you can formulate your problem as a CSP and feed it to a library, you automatically benefit from future improvements in the field of CSP solvers.
What sort of keywords would one enter into a search engine to find such a library?
<<<linear algebra library>>> finds several good ones with Google.
[EDITED to add: That's if what you want is specifically linear algebra. <<<numerical library>>> does pretty well if your needs are more general.]