Cookbook for invert a matrix using owl library

data/cookbook/invert-matrix/01-owl.ml

@@ -0,0 +1,35 @@
+---
+packages: [owl]
+---
+
+(* Creates an Owl `float` matrix using random numbers drawn from a uniform distribution with `Owl.Mat.uniform`. It is very likely that it will be invertible, but we ensure it by checking that the determinant is not zero with `Owl.Linalg.D.det`. The dimensions of the matrix are defined by `m`. *)
+let rec create_invertible m =
+        let input = Owl.Mat.uniform m m in
+        match Owl.Linalg.D.det input with
+        | 0. -> create_invertible m 
+        | _  -> input 
+
+(* Define an input matrix that is invertible *)
+let input  = create_invertible 5 
+
+(* Calculates the inverse using `Owl.Mat.inv` *)
+let inverse = Owl.Mat.inv input
+
+(* Calculates the matrix product of input and inverse. It is used the operator `*@` available in `Owl.Mat` to perform the matrix product. *)
+let id_test = Owl.Mat.(input *@ inverse)
+
+(* `id_test` should be a diagonal matrix with ones. The non-diagonal elements should be reasonably close to zero (round-off effect). We can test this using the operator `=~`, also available in `Owl.Mat` *)
+let test_result input inverse = 
+        Owl.Mat.(input *@ inverse =~ eye 5);;
+
+let () = 
+    print_string "** Input matrix (random numbers)" ;
+    Owl.Mat.(input  |> print) ; flush_all() ;
+    print_string "\n** Inverse of input matrix" ;
+    Owl.Mat.(inverse |> print) ; flush_all() ;
+    print_string "\n** Product input and inverse =~ identity" ;
+    Owl.Mat.(id_test |> print) ; flush_all() ;
+    print_string "\n** Is the inverse correct?  " ;
+    test_result input inverse |> string_of_bool |> print_string ; 
+    print_endline ""
+