faster leftdivide given prior information

Hi,

Among other calculation in my code there is a part where i use :

c=A\b;

Where A is sparse diagonal matrix (~100k x 100k) .

I am not sure whether checking of the matrix A properties takes considerable time or not.

Given that i already know that A is diagonal, is it possible to speed up the computation and avoid checkups for choosing solver?

thanks in advance,

redi

Answer 1

[Steven Lord]

The linsolve or decomposition functions may be of interest to you. decomposition may be particularly beneficial if you're solving multiple systems with the same A matrix.

Though if you're certain A is a diagonal matrix, I'd probably try calling diag then using element-wise division between b and that diagonal (or if possible skipping creating A altogether and just create its diagonal as a vector instead.)

[Christine Tobler]

Note linsolve only supports dense matrices, so wouldn't be ideal here. In general, decomposition can be used to skip some input checking in A\b. But I agree for a diagonal matrix, the cheapest will be to just compute the diagonal vector d (as a column vector, e.g. by call d = diag(A)) and call d.\b instead.