Top 30 analogous words or synonyms for kabsch
Article | Example |
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Kabsch algorithm | If singular value decomposition (SVD) routines are available, the optimal rotation, "U", can be calculated using the following simple algorithm. |
Kabsch algorithm | The Kabsch algorithm, named after Wolfgang Kabsch, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful in graphics, cheminformatics to compare molecular structures, and also bioinformatics for comparing protein structures (in particular, see root-mean-square deviation (bioinformatics)). |
Kabsch algorithm | The algorithm only computes the rotation matrix, but it also requires the computation of a translation vector. When both the translation and rotation are actually performed, the algorithm is sometimes called partial Procrustes superimposition (see also orthogonal Procrustes problem). |
Kabsch algorithm | The algorithm starts with two sets of paired points, "P" and "Q". Each set of points can be represented as an "N"×3 matrix. The first row is the coordinates of the first point, the second row is the coordinates of the second point, the "N"th row is the coordinates of the "N"th point. |
Kabsch algorithm | The second step consists of calculating a cross-covariance matrix "A". In matrix notation, |
Kabsch algorithm | This SVD algorithm is described in more detail at http://cnx.org/content/m11608/latest/ |
Kabsch algorithm | A Python script is available at https://github.com/charnley/rmsd |
Kabsch algorithm | The algorithm works in three steps: a translation, the computation of a covariance matrix, and the computation of the optimal rotation matrix. |
Kabsch algorithm | Both sets of coordinates must be translated first, so that their centroid coincides with the origin of the coordinate system. This is done by subtracting from the point coordinates the coordinates of the respective centroid. |
Kabsch algorithm | Next, decide whether we need to correct our rotation matrix to ensure a right-handed coordinate system |