Fixed some SVD issues.

Make the SVD's output unitary.
Improved unit tests.
Added an assert to the SVD ctor to check whether rows>=cols.

Eigen/src/SVD/SVD.h

@@ -83,11 +83,14 @@ template<typename _MatrixType> class SVD
       * \sa JacobiSVD()
       */
     SVD(Index rows, Index cols) : m_matU(rows, rows),
-                              m_matV(cols,cols),
-                              m_sigma(std::min(rows, cols)),
-                              m_workMatrix(rows, cols),
-                              m_rv1(cols),
-                              m_isInitialized(false) {}
+                                  m_matV(cols,cols),
+                                  m_sigma(std::min(rows, cols)),
+                                  m_workMatrix(rows, cols),
+                                  m_rv1(cols),
+                                  m_isInitialized(false)
+    {
+      ei_assert(rows >= cols && "SVD is only defined if rows>=cols.");
+    }
 
     SVD(const MatrixType& matrix) : m_matU(matrix.rows(), matrix.rows()),
                                     m_matV(matrix.cols(),matrix.cols()),

test/svd.cpp

@@ -95,6 +95,8 @@ template<typename MatrixType> void svd_verify_assert()
   VERIFY_RAISES_ASSERT(svd.computePositiveUnitary(&tmp,&tmp))
   VERIFY_RAISES_ASSERT(svd.computeRotationScaling(&tmp,&tmp))
   VERIFY_RAISES_ASSERT(svd.computeScalingRotation(&tmp,&tmp))
+
+  VERIFY_RAISES_ASSERT(SVD<MatrixXf>(10, 20))
 }
 
 void test_svd()
@@ -116,7 +118,4 @@ void test_svd()
   CALL_SUBTEST_2( svd_verify_assert<Matrix4d>() );
   CALL_SUBTEST_3( svd_verify_assert<MatrixXf>() );
   CALL_SUBTEST_4( svd_verify_assert<MatrixXd>() );
-
-  // Test problem size constructors
-  CALL_SUBTEST_9( SVD<MatrixXf>(10, 20) );
 }