Is 3x3 Matrix inverse possible using SIMD instructions?

Question

Hi Guys,

I'm making use of an ARM Cortex-A8 based processor and I have several places where I calculate 3x3 Matrix inverse operations.

As the Cortex-a8 processor has a NEON SIMD processor I'm interested to use this co-processor for 3x3 matrix inverse, I saw several 4x4 implementations (Intel SSE and freevec) but no where did I see a 3x3 matrix inverse operation carried out using SIMD instructions. The method used by freevec is by splitting the 4x4 matrix into 4, 2x2 matrices, then carry out tiny operations on each and recombine the results in the end to get the inverse of 4x4 matrix. I don't see such an opportunity with 3x3 matrices.

Anyone out there has an idea how to carry out 3x3 matrix inversion using SIMD instructions, it will be very helpful to me?

Regards Vikram

Answer 1

You can expand the 3x3 matrix to 4x4 matrix by adding a 4th row and 4th column, both being (0 0 0 1). After inversion, the upper-left 3x3 submatrix will have the required inverse.

Answer 2

You could vectorize the analytic standard version for 3x3 matrices described in wikipedia. It should not be hard.