Gaussian Elimination Compute Shadere

#pragma kernel GaussianElim

#define IDX(x,y,NumX) (x + y * NumX)

RWStructuredBuffer<float> AICMatrix;
uint2 resolution;

[numthreads(1024,1,1)]
void GaussianElim(uint3 id : SV_DispatchThreadID)
{
    uint x = id.x;

    for (uint pivot = 0; pivot < resolution.y; pivot++)
    {
        float pivotVal = AICMatrix[IDX(pivot, pivot, resolution.x)];
        DeviceMemoryBarrierWithGroupSync();
        if (x < resolution.x)
        {

            //If the pivot value is zero
            if (abs(pivotVal) < 0.0001f)
            {
                //Start by checking the row below
                uint notZeroPivot = pivot + 1;
                //Check all the remaining rows until the end of the matrix
                for (notZeroPivot; notZeroPivot < resolution.y; notZeroPivot++)
                {
                    //If a not zero pivot is found, break the loop
                    if (AICMatrix[IDX(pivot, notZeroPivot, resolution.x)] != 0)
                    {
                        break;
                    }
                }
                //Swap the values in the pivot'th, and notZeroPivot'th Row
                float temp = AICMatrix[IDX(x, pivot, resolution.x)];
                AICMatrix[IDX(x, pivot, resolution.x)] = AICMatrix[IDX(x, notZeroPivot, resolution.x)];
                AICMatrix[IDX(x, notZeroPivot, resolution.x)] = temp;

                //Reassign the pivot value
                pivotVal = AICMatrix[IDX(pivot, pivot, resolution.x)];
                //Otherwise, the answers to the system are zero
            }
            //Scale by the pivotValue
            AICMatrix[IDX(x, pivot, resolution.x)] /= pivotVal;
            if (pivot < (resolution.y - 1))
            {
                for (uint row = pivot + 1; row < resolution.y; row++)
                {
                    float elementToCancel = AICMatrix[IDX(pivot, row, resolution.x)];
                    AICMatrix[IDX(x, row, resolution.x)] += AICMatrix[IDX(x, pivot, resolution.x)] * -elementToCancel;
                }
            }
        }
    }
    DeviceMemoryBarrierWithGroupSync();
}