documenation start

.gitignore

@@ -0,0 +1 @@
+site

docs/kabsch.md

@@ -0,0 +1,36 @@
+# Kabsch Algorithm
+
+The Kabsch algorithm computes the optimal rotation matrix for two sets of points so that the RMSD (Root mean squared deviation) is minimal.
+
+## Functions
+
+### `rmsd(A, B)`
+
+Calculates the root mean square deviation of two matrices A and B using the following formula:
+
+: <math>
+\begin{align}
+\mathrm{RMSD}(\mathbf{v}, \mathbf{w}) & = \sqrt{\frac{1}{n}\sum_{i=1}^{n} \|v_i - w_i\|^2} \\
+& = \sqrt{\frac{1}{n}\sum_{i=1}^{n} 
+      (({v_i}_x - {w_i}_x)^2 + ({v_i}_y - {w_i}_y)^2 + ({v_i}_z - {w_i}_z)^2})
+\end{align}
+</math>
+
+### `calc_centroid(m)`
+
+Returns the centroid of a matrix m.
+
+### `translate_points(P, Q)`
+
+Translates two matrices P, Q so that their centroids are the origin of the coordinate system.
+
+### `kabsch(P,Q)`
+
+Calculates the optimal rotation matrix of two matrices P, Q.
+Using `translate_points` it shifts the matrices' centroids to the origin of the coordinate system, then computes the covariance matrix A:
+
+Next is the singular value decomposition of A:
+
+It's possible that the rotation matrix needs correction (basically flipping the sign of each element of the matrix):
+
+Finally the optimal rotation matrix U is calculated and returned together with the matrix P.