From a1e6bc63805896dafe93c89581b77eb537034cc8 Mon Sep 17 00:00:00 2001
From: Jim Turner <git@turner.link>
Date: Wed, 5 May 2021 20:29:00 -0400
Subject: [PATCH 1/3] Fix LAPACK names in eigh_generalized docs

---
 lax/src/eigh.rs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lax/src/eigh.rs b/lax/src/eigh.rs
index 46a3b131..ad8963dc 100644
--- a/lax/src/eigh.rs
+++ b/lax/src/eigh.rs
@@ -14,7 +14,7 @@ pub trait Eigh_: Scalar {
         a: &mut [Self],
     ) -> Result<Vec<Self::Real>>;
 
-    /// Wraps `*syegv` for real and `*heegv` for complex
+    /// Wraps `*sygv` for real and `*hegv` for complex
     fn eigh_generalized(
         calc_eigenvec: bool,
         layout: MatrixLayout,

From 3c4df7604f034826b8c6a502ccae2bebd8a63ecc Mon Sep 17 00:00:00 2001
From: Jim Turner <git@turner.link>
Date: Wed, 5 May 2021 20:29:54 -0400
Subject: [PATCH 2/3] Add basic documentation for eigh

---
 ndarray-linalg/src/eigh.rs | 13 ++++++++++++-
 1 file changed, 12 insertions(+), 1 deletion(-)

diff --git a/ndarray-linalg/src/eigh.rs b/ndarray-linalg/src/eigh.rs
index 580c2b7e..850e6104 100644
--- a/ndarray-linalg/src/eigh.rs
+++ b/ndarray-linalg/src/eigh.rs
@@ -1,4 +1,15 @@
-//! Eigenvalue decomposition for Hermite matrices
+//! Eigendecomposition for Hermitian matrices.
+//!
+//! For a Hermitian matrix `A`, this solves the eigenvalue problem `A V = V D`
+//! for `D` and `V`, where `D` is the diagonal matrix of eigenvalues in
+//! ascending order and `V` is the orthonormal matrix of corresponding
+//! eigenvectors.
+//!
+//! For a pair of Hermitian matrices `A` and `B` where `B` is also positive
+//! definite, this solves the generalized eigenvalue problem `A V = B V D`,
+//! where `D` is the diagonal matrix of generalized eigenvalues in ascending
+//! order and `V` is the matrix of corresponding generalized eigenvectors. The
+//! matrix `V` is normalized such that `V^H B V = I`.
 
 use ndarray::*;
 

From ab4cc024cc32087eecae21a3d614670085fa4f55 Mon Sep 17 00:00:00 2001
From: Jim Turner <git@turner.link>
Date: Wed, 5 May 2021 23:42:43 -0400
Subject: [PATCH 3/3] Add example to eigh module

---
 ndarray-linalg/src/eigh.rs | 22 ++++++++++++++++++++++
 1 file changed, 22 insertions(+)

diff --git a/ndarray-linalg/src/eigh.rs b/ndarray-linalg/src/eigh.rs
index 850e6104..ec306ad6 100644
--- a/ndarray-linalg/src/eigh.rs
+++ b/ndarray-linalg/src/eigh.rs
@@ -10,6 +10,28 @@
 //! where `D` is the diagonal matrix of generalized eigenvalues in ascending
 //! order and `V` is the matrix of corresponding generalized eigenvectors. The
 //! matrix `V` is normalized such that `V^H B V = I`.
+//!
+//! # Example
+//!
+//! Find the eigendecomposition of a Hermitian (or real symmetric) matrix.
+//!
+//! ```
+//! use approx::assert_abs_diff_eq;
+//! use ndarray::{array, Array2};
+//! use ndarray_linalg::{Eigh, UPLO};
+//!
+//! let a: Array2<f64> = array![
+//!     [2., 1.],
+//!     [1., 2.],
+//! ];
+//! let (eigvals, eigvecs) = a.eigh(UPLO::Lower)?;
+//! assert_abs_diff_eq!(eigvals, array![1., 3.]);
+//! assert_abs_diff_eq!(
+//!     a.dot(&eigvecs),
+//!     eigvecs.dot(&Array2::from_diag(&eigvals)),
+//! );
+//! # Ok::<(), Box<dyn std::error::Error>>(())
+//! ```
 
 use ndarray::*;