Cleanup of QZ module and added GE's calculation of eigenvalues as a test for QZ's calculation of eigenvalues

nalgebra-lapack/src/qz.rs

@@ -13,7 +13,11 @@ use na::{DefaultAllocator, Matrix, OMatrix, OVector, Scalar};
 
 use lapack;
 
-/// Generalized eigendecomposition of a pair of N*N square matrices.
+/// QZ decomposition of a pair of N*N square matrices.
+/// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
+/// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
+/// decomposed input matrix `a`  equals `VSL * S * VSL.transpose()` and
+/// decomposed input matrix `b`  equals `VSL * T * VSL.transpose()`.
 #[cfg_attr(feature = "serde-serialize", derive(Serialize, Deserialize))]
 #[cfg_attr(
     feature = "serde-serialize",
@@ -59,6 +63,11 @@ where
 {
     /// Attempts to compute the QZ decomposition of input square matrices `a` and `b`.
     ///
+    /// i.e retrieves the left and right matrices of Schur Vectors (VSL and VSR)
+    /// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
+    /// decomposed matrix `a`  equals `VSL * S * VSL.transpose()` and
+    /// decomposed matrix `b`  equals `VSL * T * VSL.transpose()`.
+    ///
     /// Panics if the method did not converge.
     pub fn new(a: OMatrix<T, D, D>, b: OMatrix<T, D, D>) -> Self {
         Self::try_new(a, b).expect("QZ decomposition: convergence failed.")
@@ -154,8 +163,8 @@ where
 
     /// Retrieves the left and right matrices of Schur Vectors (VSL and VSR)
     /// the upper-quasitriangular matrix `S` and upper triangular matrix `T` such that the
-    /// decomposed matrix `A`  equals `VSL * S * VSL.transpose()` and
+    /// decomposed input matrix `a`  equals `VSL * S * VSL.transpose()` and
-    /// decomposed matrix `B`  equals `VSL * T * VSL.transpose()`.
+    /// decomposed input matrix `b`  equals `VSL * T * VSL.transpose()`.
     pub fn unpack(
         self,
     ) -> (
@@ -167,8 +176,6 @@ where
         (self.vsl, self.s, self.t, self.vsr)
     }
 
-
-
     /// computes the generalized eigenvalues
     #[must_use]
     pub fn eigenvalues(&self) -> OVector<Complex<T>, D>

nalgebra-lapack/tests/linalg/qz.rs

@@ -1,7 +1,5 @@
-use na::{zero, DMatrix, SMatrix};
+use na::DMatrix;
-use nl::QZ;
+use nl::{GE, QZ};
-use num_complex::Complex;
-use simba::scalar::ComplexField;
 use std::cmp;
 
 use crate::proptest::*;
@@ -16,33 +14,28 @@ proptest! {
 
         let qz =  QZ::new(a.clone(), b.clone());
         let (vsl,s,t,vsr) = qz.clone().unpack();
-        //let eigenvalues = qz.eigenvalues();
+        let eigenvalues = qz.eigenvalues();
-        //let a_c = a.clone().map(|x| Complex::new(x, zero::<f64>()));
+
+        let ge = GE::new(a.clone(), b.clone());
+        let eigenvalues2 = ge.eigenvalues();
 
         prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a.clone(), epsilon = 1.0e-7));
         prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b.clone(), epsilon = 1.0e-7));
-        // spotty test that skips over the first eigenvalue which in some cases is extremely large relative to the other ones
+        prop_assert!(eigenvalues == eigenvalues2);
-        // and fails the condition
-        //for i in 1..n {
-        //   let b_c = b.clone().map(|x| eigenvalues[i]*Complex::new(x,zero::<f64>()));
-        //   prop_assert!(relative_eq!((&a_c  - &b_c).determinant().modulus(), 0.0, epsilon = 1.0e-6));
-        //}
     }
 
     #[test]
     fn qz_static(a in matrix4(), b in matrix4()) {
         let qz = QZ::new(a.clone(), b.clone());
+        let ge = GE::new(a.clone(), b.clone());
         let (vsl,s,t,vsr) = qz.unpack();
-        //let eigenvalues = qz.eigenvalues();
+        let eigenvalues = qz.eigenvalues();
-        //let a_c = a.clone().map(|x| Complex::new(x, zero::<f64>()));
+        let eigenvalues2 = ge.eigenvalues();
 
         prop_assert!(relative_eq!(&vsl * s * vsr.transpose(), a, epsilon = 1.0e-7));
         prop_assert!(relative_eq!(vsl * t * vsr.transpose(), b, epsilon = 1.0e-7));
 
-        //for i in 0..4 {
+        prop_assert!(eigenvalues == eigenvalues2);
-        //    let b_c = b.clone().map(|x| eigenvalues[i]*Complex::new(x,zero::<f64>()));
+
-        //    println!("{}",eigenvalues);
-        //    prop_assert!(relative_eq!((&a_c  - &b_c).determinant().modulus(), 0.0, epsilon = 1.0e-4))
-        //}
     }
 }