From 54458cb39d1081d0cfe6b77ed8e085d457a4c921 Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <4643818-rmlarsen1@users.noreply.gitlab.com>
Date: Mon, 9 Mar 2026 00:35:26 -0700
Subject: [PATCH] Remove random retry loops in tests (batch 3: geometry,
 sparse, umeyama)

libeigen/eigen!2262

Co-authored-by: Rasmus Munk Larsen <rmlarsen@gmail.com>
---
 test/geo_transformations.cpp | 20 ++++++------------
 test/sparse_product.cpp      |  8 ++++---
 test/umeyama.cpp             | 41 ++++--------------------------------
 3 files changed, 15 insertions(+), 54 deletions(-)

diff --git a/test/geo_transformations.cpp b/test/geo_transformations.cpp
index 68120d9d3..d10281a10 100644
--- a/test/geo_transformations.cpp
+++ b/test/geo_transformations.cpp
@@ -223,13 +223,10 @@ void transformations() {
   t4 *= aa3;
   VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
 
-  {
-    int guard = 0;
-    do {
-      v3 = Vector3::Random();
-      dont_over_optimize(v3);
-    } while (v3.cwiseAbs().minCoeff() < NumTraits<Scalar>::epsilon() && (++guard) < 100);
-    VERIFY(guard < 100);
+  v3 = Vector3::Random();
+  dont_over_optimize(v3);
+  for (int k = 0; k < 3; ++k) {
+    if (numext::abs(v3(k)) < NumTraits<Scalar>::epsilon()) v3(k) = NumTraits<Scalar>::epsilon();
   }
   Translation3 tv3(v3);
   Transform3 t5(tv3);
@@ -384,13 +381,8 @@ void transformations() {
   // test transform inversion
   t0.setIdentity();
   t0.translate(v0);
-  {
-    int guard = 0;
-    do {
-      t0.linear().setRandom();
-    } while (t0.linear().jacobiSvd().singularValues()(2) < test_precision<Scalar>() && (++guard) < 100);
-    VERIFY(guard < 100);
-  }
+  t0.linear().setRandom();
+  if (t0.linear().jacobiSvd().singularValues()(2) < test_precision<Scalar>()) t0.linear().setIdentity();
   Matrix4 t044 = Matrix4::Zero();
   t044(3, 3) = 1;
   t044.block(0, 0, t0.matrix().rows(), 4) = t0.matrix();
diff --git a/test/sparse_product.cpp b/test/sparse_product.cpp
index c006a8923..426a37557 100644
--- a/test/sparse_product.cpp
+++ b/test/sparse_product.cpp
@@ -301,9 +301,11 @@ void sparse_product() {
     SparseMatrixType mS(rows, rows);
     SparseMatrixType mA(rows, rows);
     initSparse<Scalar>(density, refA, mA);
-    do {
-      initSparse<Scalar>(density, refUp, mUp, ForceRealDiag | /*ForceNonZeroDiag|*/ MakeUpperTriangular);
-    } while (refUp.isZero());
+    initSparse<Scalar>(density, refUp, mUp, ForceRealDiag | /*ForceNonZeroDiag|*/ MakeUpperTriangular);
+    if (refUp.isZero()) {
+      refUp(0, 0) = Scalar(1);
+      mUp.coeffRef(0, 0) = Scalar(1);
+    }
     refLo = refUp.adjoint();
     mLo = mUp.adjoint();
     refS = refUp + refLo;
diff --git a/test/umeyama.cpp b/test/umeyama.cpp
index 2f6fe34ec..e329f91aa 100644
--- a/test/umeyama.cpp
+++ b/test/umeyama.cpp
@@ -13,6 +13,7 @@
 #include <Eigen/Geometry>
 
 #include <Eigen/LU>   // required for MatrixBase::determinant
+#include <Eigen/QR>   // required for HouseholderQR
 #include <Eigen/SVD>  // required for SVD
 
 using namespace Eigen;
@@ -23,43 +24,9 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixUnitary(int size) {
   typedef T Scalar;
   typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixType;
 
-  MatrixType Q;
-
-  int max_tries = 40;
-  bool is_unitary = false;
-
-  while (!is_unitary && max_tries > 0) {
-    // initialize random matrix
-    Q = MatrixType::Random(size, size);
-
-    // orthogonalize columns using the Gram-Schmidt algorithm
-    for (int col = 0; col < size; ++col) {
-      typename MatrixType::ColXpr colVec = Q.col(col);
-      for (int prevCol = 0; prevCol < col; ++prevCol) {
-        typename MatrixType::ColXpr prevColVec = Q.col(prevCol);
-        colVec -= colVec.dot(prevColVec) * prevColVec;
-      }
-      Q.col(col) = colVec.normalized();
-    }
-
-    // this additional orthogonalization is not necessary in theory but should enhance
-    // the numerical orthogonality of the matrix
-    for (int row = 0; row < size; ++row) {
-      typename MatrixType::RowXpr rowVec = Q.row(row);
-      for (int prevRow = 0; prevRow < row; ++prevRow) {
-        typename MatrixType::RowXpr prevRowVec = Q.row(prevRow);
-        rowVec -= rowVec.dot(prevRowVec) * prevRowVec;
-      }
-      Q.row(row) = rowVec.normalized();
-    }
-
-    // final check
-    is_unitary = Q.isUnitary();
-    --max_tries;
-  }
-
-  if (max_tries == 0) eigen_assert(false && "randMatrixUnitary: Could not construct unitary matrix!");
-
+  // The Q factor of the QR decomposition of a random matrix is a random unitary matrix.
+  // HouseholderQR is numerically stable and always succeeds, unlike Gram-Schmidt.
+  MatrixType Q = MatrixType::Random(size, size).householderQr().householderQ();
   return Q;
 }