Update Readme

Author: janbruedigam

README.md

@@ -2,9 +2,9 @@
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-A package for efficiently solving linear systems of equations based on graph properties. Any matrix representing an underlying real-world system can be represented by a graph, for example a mechanical system, checmical molecules, neural networks, ... The code of the package is currently used for the robotics simulator [Dojo.jl](https://github.com/dojo-sim/Dojo.jl)
+A package for efficiently solving linear systems of equations based on graph properties. Any matrix representing an underlying real-world system can be represented by a graph, for example a mechanical system, chemical molecules, neural networks, ... The code of the package is currently used for the robotics simulator [Dojo.jl](https://github.com/dojo-sim/Dojo.jl)
 
-By providing the adjacency matrix of a graph-based system, the `GraphBasedSystems` package can automatically exploit the existing sparsity when solving the linear system to speed up calculations. Currently, the LU and LDU decomposition/backsubstitution are implemented.
+By providing the adjacency matrix of a graph-based system, the `GraphBasedSystems` package can automatically exploit the existing sparsity when solving the linear system to speed up calculations. Currently, the LDU, LU, LDLt, and LLt decomposition/backsubstitution are implemented. LLt is currently slow due to memory allocations.
 
 ```julia
 using GraphBasedSystems
@@ -18,16 +18,10 @@ graph_matrix = [  # The adjacency matrix for the underlying graph
 
 dimensions = [2; 3; 0; 1] # The dimension of row/column
 
-system = System{Float64}(graph_matrix, dimensions) # The resulting linear system
+system = System{Float64}(graph_matrix, dimensions; symmetric=false) # The resulting linear system. Set symmetric=true for symmetric systems
 
-for entry in system.matrix_entries.nzval # Randomize all matrix entries
-    GraphBasedSystems.randomize!(entry)
-end
+randomize!(system) # Randomize all system entries
 system.matrix_entries[1,2].value = rand(2,3) # Directly set the value of a matrix entry
-
-for entry in system.vector_entries # Randomize all vector entries
-    GraphBasedSystems.randomize!(entry)
-end
 system.vector_entries[4].value = rand(1) # Directly set the value of a vector entry
 
 A = full_matrix(system) # Inspect the matrix