Implement square root for real matrices via Schur.

1 files changed, 37 insertions, 6 deletions

diff --git a/unsupported/test/matrix_square_root.cpp b/unsupported/test/matrix_square_root.cpp
index cd2c6cfc4..56b86a288 100644
--- a/unsupported/test/matrix_square_root.cpp
+++ b/unsupported/test/matrix_square_root.cpp
@@ -25,16 +25,45 @@
 #include "main.h"
 #include <unsupported/Eigen/MatrixFunctions>
 
+template <typename MatrixType, int IsComplex = NumTraits<typename internal::traits<MatrixType>::Scalar>::IsComplex>
+struct generateTestMatrix;
+
+// for real matrices, make sure none of the eigenvalues are negative
+template <typename MatrixType>
+struct generateTestMatrix<MatrixType,0>
+{
+  static void run(MatrixType& result, typename MatrixType::Index size)
+  {
+    MatrixType mat = MatrixType::Random(size, size);
+    EigenSolver<MatrixType> es(mat);
+    typename EigenSolver<MatrixType>::EigenvalueType eivals = es.eigenvalues();
+    for (typename MatrixType::Index i = 0; i < size; ++i) {
+      if (eivals(i).imag() == 0 && eivals(i).real() < 0)
+	eivals(i) = -eivals(i);
+    }
+    result = (es.eigenvectors() * eivals.asDiagonal() * es.eigenvectors().inverse()).real();
+  }
+};
+
+// for complex matrices, any matrix is fine
+template <typename MatrixType>
+struct generateTestMatrix<MatrixType,1>
+{
+  static void run(MatrixType& result, typename MatrixType::Index size)
+  {
+    result = MatrixType::Random(size, size);
+  }
+};
+
 template<typename MatrixType>
 void testMatrixSqrt(const MatrixType& m)
 {
-  typedef typename MatrixType::Index Index;
-  const Index size = m.rows();
-  MatrixType A = MatrixType::Random(size, size);
+  MatrixType A;
+  generateTestMatrix<MatrixType>::run(A, m.rows());
   MatrixSquareRoot<MatrixType> msr(A);
-  MatrixType S;
-  msr.compute(S);
-  VERIFY_IS_APPROX(S*S, A);
+  MatrixType sqrtA;
+  msr.compute(sqrtA);
+  VERIFY_IS_APPROX(sqrtA * sqrtA, A);
 }
 
 void test_matrix_square_root()
@@ -42,5 +71,7 @@ void test_matrix_square_root()
   for (int i = 0; i < g_repeat; i++) {
     CALL_SUBTEST_1(testMatrixSqrt(Matrix3cf()));
     CALL_SUBTEST_2(testMatrixSqrt(MatrixXcd(12,12)));
+    CALL_SUBTEST_3(testMatrixSqrt(Matrix4f()));
+    CALL_SUBTEST_4(testMatrixSqrt(Matrix<double,Dynamic,Dynamic,RowMajor>(9, 9)));
   }
 }