Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341, USA.
J Comput Chem. 2010 May;31(7):1561-3. doi: 10.1002/jcc.21439.
Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 x 3 or 4 x 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton-Raphson quaternion-based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high-throughput analyses of molecular conformations.
找到能够最小化两个向量之间平方差之和的旋转矩阵是生物信息学和晶体学中的一个重要问题。传统的算法涉及到 3x3 或 4x4 矩阵的求逆或分解，这在某些情况下可能会非常耗费计算资源并且数值不稳定。在这里，我们提出了一种简单而强大的算法，使用牛顿-拉普森四元数方法和伴随矩阵来快速确定最佳旋转。我们的方法比传统的求逆/分解方法至少快一个数量级，对于分子构象的高通量分析应该特别有用。
