ex6

README.md

 # A Statistical Learning library for Humans
 This toolkit currently offers enrichment analysis, hierarchical enrichment analysis, novel PLS regression, shape alignment, connectivity clustering, clustering and hierarchical clustering as well as factor analysis methods.
 
-The fine grained data can be studied via a statistical tests that relates it to observables in a coarse grained journal file. The final p values can then FDR corrected by employing a novel q-value method.
+The fine grained data can be studied via a statistical tests that relates it to observables in a coarse grained journal file. The final p values can then be rank corrected by employing a novel q-value method.
 
 Visit the active code via :
 https://github.com/richardtjornhammar/impetuous
@@ -300,8 +300,72 @@ which will report that
 
 is affected or perhaps needs to be compensated for... now perhaps you thought this exercise was a tad tedious? Well you are correct. It is and you could just as well have copied the gene transcripts into [String-db](https://string-db.org/cgi/input?sessionId=beIptQQxF85j&input_page_active_form=multiple_identifiers) and gotten similar results out. But, then you wouldn't have gotten to use the hierarchical enrichment method I invented!
 
-These examples were meant as illustrations of some of the codes implemented in the impetuous-gfa package.
+# Example 6 : Absolute and relative coordinates
+
+In this example we will use the SVD based distance geometry method to go between absolute coordinates and relative coordinate distances. Absolute coordinates are float values describing the position of something in space. If you have several of these then the same information can be conveyed via the pairwise distance graph. Going from absolute coordinates to pairwise distances is simple and only requires you to calculate all the pairwise distances between your absolute coordinates. Going back to mutually orthogonal coordinates from the pariwise distances is trickier, but a solved problem. The [distance geometry](https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.8051) can be obtained with SVD and it is implemented in the impetuous clustering module under the name `distance_matrix_to_absolute_coordinates`. We start by defining coordinates. Now we can calculate the pair distance matrix and transforming it back by using the code below
+
+```
+import pandas as pd
+import numpy as np
+
+coordinates = np.array([[-23.7100 ,  24.1000 ,  85.4400],
+  [-22.5600 ,  23.7600 ,  85.6500],
+  [-21.5500 ,  24.6200 ,  85.3800],
+  [-22.2600 ,  22.4200 ,  86.1900],
+  [-23.2900 ,  21.5300 ,  86.4800],
+  [-20.9300 ,  22.0300 ,  86.4300],
+  [-20.7100 ,  20.7600 ,  86.9400],
+  [-21.7900 ,  19.9300 ,  87.1900],
+  [-23.0300 ,  20.3300 ,  86.9600],
+  [-24.1300 ,  19.4200 ,  87.2500],
+  [-23.7400 ,  18.0500 ,  87.0000],
+  [-24.4900 ,  19.4600 ,  88.7500],
+  [-23.3700 ,  19.8900 ,  89.5200],
+  [-24.8500 ,  18.0000 ,  89.0900],
+  [-23.9600 ,  17.4800 ,  90.0800],
+  [-24.6600 ,  17.2400 ,  87.7500],
+  [-24.0800 ,  15.8500 ,  88.0100],
+  [-23.9600 ,  15.1600 ,  86.7600],
+  [-23.3400 ,  13.7100 ,  87.1000],
+  [-21.9600 ,  13.8700 ,  87.6300],
+  [-24.1800 ,  13.0300 ,  88.1100],
+  [-23.2900 ,  12.8200 ,  85.7600],
+  [-23.1900 ,  11.2800 ,  86.2200],
+  [-21.8100 ,  11.0000 ,  86.7000],
+  [-24.1500 ,  11.0300 ,  87.3200],
+  [-23.5300 ,  10.3200 ,  84.9800],
+  [-23.5400 ,   8.9800 ,  85.4800],
+  [-23.8600 ,   8.0100 ,  84.3400],
+  [-23.9800 ,   6.5760 ,  84.8900],
+  [-23.2800 ,   6.4460 ,  86.1300],
+  [-23.3000 ,   5.7330 ,  83.7800],
+  [-22.7300 ,   4.5360 ,  84.3100],
+  [-22.2000 ,   6.7130 ,  83.3000],
+  [-22.7900 ,   8.0170 ,  83.3800],
+  [-21.8100 ,   6.4120 ,  81.9200],
+  [-20.8500 ,   5.5220 ,  81.5200],
+  [-20.8300 ,   5.5670 ,  80.1200],
+  [-21.7700 ,   6.4720 ,  79.7400],
+  [-22.3400 ,   6.9680 ,  80.8000],
+  [-20.0100 ,   4.6970 ,  82.1500],
+  [-19.1800 ,   3.9390 ,  81.4700] ]);
+
+if __name__=='__main__':
 
+    import impetuous.clustering as impc
+
+    distance_matrix = impc.absolute_coordinates_to_distance_matrix( coordinates )
+    ordered_coordinates = impc.distance_matrix_to_absolute_coordinates( distance_matrix , n_dimensions=3 )
+
+    print ( pd.DataFrame(ordered_coordinates).T )
+
+```
+
+You will notice that the largest variation is now aligned with the `X axis`, the second most variation aligned with the `Y axis` and the third most, aligned with the `Z axis`.
+
+# Notes
+
+These examples were meant as illustrations of some of the codes implemented in the impetuous-gfa package.
 
 # Manually updated code backups for this library :