Hello

I am working on a 241x241 double matrix and a 241 vector. I want to solve Ax=b, where b is unknown. The matrix is positive definite and is suitable for Cholesky.

In my Eigen code I write the following:

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VectorXd x= A.ldlt().solve(B)

I am using an ARM Cortex A9 and it takes 40ms to execute this code. Can someone verify that this is as quick as I can get? I expected quicker as my own written code also executes in 40ms. I was hoping that Eigen would be quicker than me.

I am using O3 optimisation with NEON supported and the -DNDEBUG flag set, although as the NEON for the A9 only supports single precision, I am not sure that this is in use.

Can I do anything else to make it quicker? I was hoping for around 20ms.

Indeed, NEON supports only single precision so you're loosing Eigen's SIMD capabilities. If your matrices are well conditioned you might try using float and/or Eigen's LLT factorization which has the advantage to leverage matrix-matrix operations instead of matrix-vector ones.

Using LLT, I got speeds of 13.9ms. I will need to check if this is good enough. I don't know yet the differences between LLT and LDLT But that 13.9ms is very good, better than I expected.

LDLT does numerical pivoting thus its superior numerical stability. LDLT can also handle indefinite matrices. If your matrices are positive definite, then LLT should be fine.

Just one more thing regarding Cholesky. Does anyone know if it supports complex numbers too? Will that be slower?

bobo01 wrote:Just one more thing regarding Cholesky. Does anyone know if it supports complex numbers too? Will that be slower?

Yes, it supports complex numbers. And yes, it will be slower.