* introduced method createRandomMatrixOfRank (R = U*D*V where U,V unitary, D r-by-c diag. with rank non-zero values)

* switched lu/qr tests to be using createRandomMatrixOfRank
* removed unused methods doSomeRankPreservingOperations
* removed NOTE about doSomeRankPreservingOperations

test/lu.cpp

@@ -25,44 +25,16 @@
 #include "main.h"
 #include <Eigen/LU>
 
-template<typename Derived>
-void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
-{
-  typedef typename Derived::RealScalar RealScalar;
-  for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
-  {
-    RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
-    int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
-    int j;
-    do {
-      j = Eigen::ei_random<int>(0,m.rows()-1);
-    } while (i==j); // j is another one (must be different)
-    m.row(i) += d * m.row(j);
-
-    i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
-    do {
-      j = Eigen::ei_random<int>(0,m.cols()-1);
-    } while (i==j); // j is another one (must be different)
-    m.col(i) += d * m.col(j);
-  }
-}
-
 template<typename MatrixType> void lu_non_invertible()
 {
   /* this test covers the following files:
      LU.h
   */
-  // NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
   int rows = ei_random<int>(20,200), cols = ei_random<int>(20,200), cols2 = ei_random<int>(20,200);
   int rank = ei_random<int>(1, std::min(rows, cols)-1);
 
   MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
-  m1 = MatrixType::Random(rows,cols);
+  createRandomMatrixOfRank(rank, rows, cols, m1);
-  if(rows <= cols)
-    for(int i = rank; i < rows; i++) m1.row(i).setZero();
-  else
-    for(int i = rank; i < cols; i++) m1.col(i).setZero();
-  doSomeRankPreservingOperations(m1);
 
   LU<MatrixType> lu(m1);
   typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();

test/main.h

@@ -136,6 +136,7 @@ namespace Eigen
 #define EIGEN_INTERNAL_DEBUGGING
 #define EIGEN_NICE_RANDOM
 #include <Eigen/Array>
+#include <Eigen/QR> // required for createRandomMatrixOfRank
 
 
 #define VERIFY(a) do { if (!(a)) { \
@@ -225,6 +226,26 @@ inline bool test_ei_isMuchSmallerThan(const MatrixBase<Derived>& m,
   return m.isMuchSmallerThan(s, test_precision<typename ei_traits<Derived>::Scalar>());
 }
 
+template<typename Derived>
+void createRandomMatrixOfRank(int desired_rank, int rows, int cols, Eigen::MatrixBase<Derived>& m)
+{
+  typedef Derived MatrixType;
+  typedef MatrixType::Scalar Scalar;
+  typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType;
+
+  MatrixType a = MatrixType::Random(rows,rows);
+  MatrixType d = MatrixType::Identity(rows,cols);
+  MatrixType  b = MatrixType::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);
+
+  QR<MatrixType> qra(a);
+  QR<MatrixType> qrb(b);
+  m = (qra.matrixQ() * d * qrb.matrixQ()).lazy();
+}
+
 } // end namespace Eigen
 
 template<typename T> struct GetDifferentType;

test/qr.cpp

@@ -55,42 +55,14 @@ template<typename MatrixType> void qr(const MatrixType& m)
   VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint());
 }
 
-template<typename Derived>
-void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
-{
-  typedef typename Derived::RealScalar RealScalar;
-  for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
-  {
-    RealScalar d = Eigen::ei_random<RealScalar>(-1,1);
-    int i = Eigen::ei_random<int>(0,m.rows()-1); // i is a random row number
-    int j;
-    do {
-      j = Eigen::ei_random<int>(0,m.rows()-1);
-    } while (i==j); // j is another one (must be different)
-    m.row(i) += d * m.row(j);
-
-    i = Eigen::ei_random<int>(0,m.cols()-1); // i is a random column number
-    do {
-      j = Eigen::ei_random<int>(0,m.cols()-1);
-    } while (i==j); // j is another one (must be different)
-    m.col(i) += d * m.col(j);
-  }
-}
-
 template<typename MatrixType> void qr_non_invertible()
 {
   /* this test covers the following files: QR.h */
-  // NOTE there seems to be a problem with too small sizes -- could easily lie in the doSomeRankPreservingOperations function
   int rows = ei_random<int>(20,200), cols = ei_random<int>(20,rows), cols2 = ei_random<int>(20,rows);
   int rank = ei_random<int>(1, std::min(rows, cols)-1);
 
   MatrixType m1(rows, cols), m2(cols, cols2), m3(rows, cols2), k(1,1);
-  m1 = MatrixType::Random(rows,cols);
+  createRandomMatrixOfRank(rank, rows, cols, m1);
-  if(rows <= cols)
-    for(int i = rank; i < rows; i++) m1.row(i).setZero();
-  else
-    for(int i = rank; i < cols; i++) m1.col(i).setZero();
-  doSomeRankPreservingOperations(m1);
 
   QR<MatrixType> lu(m1);
 //   typename LU<MatrixType>::KernelResultType m1kernel = lu.kernel();