From 20440849794789eb9d9d29bc834296ce0e73b05c Mon Sep 17 00:00:00 2001
From: Antonio Sanchez <cantonios@google.com>
Date: Mon, 11 Jan 2021 11:30:01 -0800
Subject: [PATCH] Remove TODO from Transform::computeScaleRotation()

Upon investigation, `JacobiSVD` is significantly faster than `BDCSVD`
for small matrices (twice as fast for 2x2, 20% faster for 3x3,
1% faster for 10x10).  Since the majority of cases will be small,
let's stick with `JacobiSVD`.  See !361.
---
 Eigen/src/Geometry/Transform.h | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 7497b31ac..7d258c01d 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -1097,7 +1097,7 @@ template<typename Scalar, int Dim, int Mode, int Options>
 template<typename RotationMatrixType, typename ScalingMatrixType>
 EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
 {
-  // TODO: investigate BDCSVD implementation.
+  // Note that JacobiSVD is faster than BDCSVD for small matrices.
   JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
 
   Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant() < Scalar(0) ? Scalar(-1) : Scalar(1); // so x has absolute value 1
@@ -1127,7 +1127,7 @@ template<typename Scalar, int Dim, int Mode, int Options>
 template<typename ScalingMatrixType, typename RotationMatrixType>
 EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
 {
-  // TODO: investigate BDCSVD implementation.
+  // Note that JacobiSVD is faster than BDCSVD for small matrices.
   JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
 
   Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant() < Scalar(0) ? Scalar(-1) : Scalar(1); // so x has absolute value 1