Add an example for the resolution of a linear system.

examples/linear_system_resolution.rs

@@ -0,0 +1,39 @@
+#![cfg_attr(rustfmt, rustfmt_skip)]
+#[macro_use]
+extern crate approx; // for assert_relative_eq
+extern crate nalgebra as na;
+use na::{Matrix4, Matrix4x3, Vector4};
+
+fn main() {
+    let a = Matrix4::new(
+        1.0, 1.0,  2.0, -5.0,
+        2.0, 5.0, -1.0, -9.0,
+        2.0, 1.0, -1.0,  3.0,
+        1.0, 3.0,  2.0,  7.0,
+    );
+    let mut b = Vector4::new(3.0, -3.0, -11.0, -5.0);
+    let decomp = a.lu();
+    let x = decomp.solve(&b).expect("Linear resolution failed.");
+    assert_relative_eq!(a * x, b);
+
+    /*
+     * It is possible to perform the resolution in-place.
+     * This is particularly useful to avoid allocations when
+     * `b` is a `DVector` or a `DMatrix`.
+     */
+    assert!(decomp.solve_mut(&mut b), "Linear resolution failed.");
+    assert_relative_eq!(x, b);
+
+    /*
+     * It is possible to solve multiple systems
+     * simultaneously by using a matrix for `b`.
+     */
+    let b = Matrix4x3::new(
+         3.0,  2.0,  0.0,
+        -3.0,  0.0,  0.0,
+        -11.0, 5.0, -3.0,
+        -5.0,  10.0, 4.0,
+    );
+    let x = decomp.solve(&b).expect("Linear resolution failed.");
+    assert_relative_eq!(a * x, b);
+}