* 4x4 inverse: revert to cofactors method

* inverse tests: use createRandomMatrixOfRank, use more strict precision
* tests: createRandomMatrixOfRank: support 1x1 matrices
* determinant: nest the xpr
* Minor: add comment

3 files changed, 19 insertions, 35 deletions

diff --git a/test/inverse.cpp b/test/inverse.cpp
index 59b791507..b80e139e0 100644
--- a/test/inverse.cpp
+++ b/test/inverse.cpp
@@ -38,18 +38,11 @@ template<typename MatrixType> void inverse(const MatrixType& m)
   typedef typename NumTraits<Scalar>::Real RealScalar;
   typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
 
-  MatrixType m1 = MatrixType::Random(rows, cols),
+  MatrixType m1(rows, cols),
              m2(rows, cols),
              mzero = MatrixType::Zero(rows, cols),
              identity = MatrixType::Identity(rows, rows);
-
-  if (ei_is_same_type<RealScalar,float>::ret)
-  {
-    // let's build a more stable to inverse matrix
-    MatrixType a = MatrixType::Random(rows,cols);
-    m1 += m1 * m1.adjoint() + a * a.adjoint();
-  }
-
+  createRandomMatrixOfRank(rows,rows,rows,m1);
   m2 = m1.inverse();
   VERIFY_IS_APPROX(m1, m2.inverse() );
 
diff --git a/test/main.h b/test/main.h
index 8bc71b3ae..06c17a9ae 100644
--- a/test/main.h
+++ b/test/main.h
@@ -353,13 +353,26 @@ void createRandomMatrixOfRank(int desired_rank, int rows, int cols, MatrixType&
   typedef Matrix<Scalar, Rows, Rows> MatrixAType;
   typedef Matrix<Scalar, Cols, Cols> MatrixBType;
 
+  if(desired_rank == 0)
+  {
+    m.setZero(rows,cols);
+    return;
+  }
+
+  if(desired_rank == 1)
+  {
+    m = VectorType::Random(rows) * VectorType::Random(cols).transpose();
+    return;
+  }
+
   MatrixAType a = MatrixAType::Random(rows,rows);
   MatrixType d = MatrixType::Identity(rows,cols);
   MatrixBType  b = MatrixBType::Random(cols,cols);
 
   // set the diagonal such that only desired_rank non-zero entries reamain
   const int diag_size = std::min(d.rows(),d.cols());
-  d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
+  if(diag_size != desired_rank)
+    d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
 
   HouseholderQR<MatrixAType> qra(a);
   HouseholderQR<MatrixBType> qrb(b);
diff --git a/test/prec_inverse_4x4.cpp b/test/prec_inverse_4x4.cpp
index 613535346..83b1a8a71 100644
--- a/test/prec_inverse_4x4.cpp
+++ b/test/prec_inverse_4x4.cpp
@@ -26,28 +26,6 @@
 #include <Eigen/LU>
 #include <algorithm>
 
-Matrix4f inverse(const Matrix4f& m)
-{
-  Matrix4f r;
-  r(0,0) = m.minor(0,0).determinant();
-  r(1,0) = -m.minor(0,1).determinant();
-  r(2,0) = m.minor(0,2).determinant();
-  r(3,0) = -m.minor(0,3).determinant();
-  r(0,2) = m.minor(2,0).determinant();
-  r(1,2) = -m.minor(2,1).determinant();
-  r(2,2) = m.minor(2,2).determinant();
-  r(3,2) = -m.minor(2,3).determinant();
-  r(0,1) = -m.minor(1,0).determinant();
-  r(1,1) = m.minor(1,1).determinant();
-  r(2,1) = -m.minor(1,2).determinant();
-  r(3,1) = m.minor(1,3).determinant();
-  r(0,3) = -m.minor(3,0).determinant();
-  r(1,3) = m.minor(3,1).determinant();
-  r(2,3) = -m.minor(3,2).determinant();
-  r(3,3) = m.minor(3,3).determinant();
-  return r / (m(0,0)*r(0,0) + m(1,0)*r(0,1) + m(2,0)*r(0,2) + m(3,0)*r(0,3));
-}
-
 template<typename MatrixType> void inverse_permutation_4x4()
 {
   typedef typename MatrixType::Scalar Scalar;
@@ -79,7 +57,7 @@ template<typename MatrixType> void inverse_general_4x4(int repeat)
     do {
       m = MatrixType::Random();
       absdet = ei_abs(m.determinant());
-    } while(absdet < 10 * epsilon<Scalar>());
+    } while(absdet < epsilon<Scalar>());
     MatrixType inv = m.inverse();
     double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / epsilon<Scalar>() );
     error_sum += error;
@@ -89,8 +67,8 @@ template<typename MatrixType> void inverse_general_4x4(int repeat)
   double error_avg = error_sum / repeat;
   EIGEN_DEBUG_VAR(error_avg);
   EIGEN_DEBUG_VAR(error_max);
-  VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.4 : 1.4) );
-  VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 160.0 : 75.) );
+  VERIFY(error_avg < (NumTraits<Scalar>::IsComplex ? 8.0 : 1.0));
+  VERIFY(error_max < (NumTraits<Scalar>::IsComplex ? 64.0 : 16.0));
 }
 
 void test_prec_inverse_4x4()