How to determine which algorithm mldivide (A\b) uses

I have a sparse, banded matrix, A, for which I am solving the linear system Ax=b using A\b in Matlab.

The documentation for mldivide shows a flow chart that explains which solver it will use. However, I would like to automate the process of determining the best algorithm. Therefore, I would really just like to know which algorithm mldivide chooses for different inputs. Is there a way to get this information out?

Answer 1

[Grzegorz Knor]

For sparse matrices check function spparms :

spparms('spumoni',2)
sparse(rand(3))\rand(3,1)

On my computer it produces:

sp\: bandwidth = 2+1+2.
sp\: is A diagonal? no.
sp\: is band density (1) > bandden (0.5) to try banded solver? yes.
sp\: is LAPACK's banded solver successful? yes.

Answer 2

[the cyclist]

Look at the Algorithms section of this documentation page.

[Jonathan]

Yes, thanks, as I stated in my question, I already looked at that. However, what I what to know is if I can give mldivide various inputs and have it automatically tell me which algorithm it choses.

In other words, I want to automate this process.

Answer 3

[Jan]

I'm not sure if I understand your question. You explain:

 The documentation for mldivide shows a flow chart that explains which solver it will use.

Is this not a valid answer of your question already? Or are you looking for the name of the library function instead of the name of the solver? Matlab does not offer the source code for mldivide.

[Jonathan]

No, I want to automate the process. In other words, I give mldivide a matrix A, and it tells me which algorithm it will use.

Sorry, its not good for the job security of computer scientists, but its what I need to do...

[Jan]

The function mldivide willnot tell you, which algorithm is used. This is not the purpose of this command. You can write such a function by your own translating the flow chart of the documentation to a bunch of IF statements.

[Steven Lord]

Even if it DID tell you, for what purpose would you use that information?

Perhaps you would be better served by the LINSOLVE function, which allows you to specify various properties of the coefficient matrix for the system you're trying to solve. This can avoid some of the testing for those matrix properties (which for large matrices could be expensive.)