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Figure 1 | BMC Research Notes

Figure 1

From: GPU-Q-J, a fast method for calculating root mean square deviation (RMSD) after optimal superposition

Figure 1

GPU-Q-J RMSD calculation procedure. The methodology used to calculate RMSDs on GPUs is shown. The Cartesian coordinates of the two proteins are reshuffled in 4-vectors. This allows the use of built-in dot product operations for the calculation of the covariance matrix R. Because we do not center the coordinates beforehand so that their barycenters are at the origin, a second term involving the mean values of the coordinates must be subtracted. By combining the two steps, we avoid an expensive extra fetch of coordinates. Optimized 4-vector summation is used to calculate the coordinate means. The values of the covariance matrix R are maintained as double precision but the 4 × 4 matrix passed to the cyclic-Jacobi routine is single precision. This compromise increases the accuracy in some degenerate cases without sacrificing speed, as the vast majority of calculations take place as 4-vector single precision operations. The final value of RMSD obtained is identical that obtained by the CPU methods to at least 2 decimal places.

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