Test that row-major output matrices give the same result.

This ensures that we don't make any assumptions about the output matrices being
column-major (even though this is the default).

We also add some more (weak) checks for similarity with a naive SVD.

tests/src/compare.h

@@ -15,7 +15,7 @@ void expect_equal_column_vectors(const Eigen::MatrixXd& left, const Eigen::Matri
 
     for (Eigen::Index i = 0; i < left.cols(); ++i) {
         for (Eigen::Index j = 0; j < left.rows(); ++j) {
-            EXPECT_TRUE(same_same(std::abs(left(j, i)), std::abs(right(j, i)), tol));
+            EXPECT_TRUE(same_same(std::abs(left(j, i)), std::abs(right(j, i)), tol)) << "(" << left(j, i) << " vs " << right(j, i) << ")" << std::endl;
         }
 
         double left_sum = std::abs(left.col(i).sum());

tests/src/irlba.cpp

@@ -49,10 +49,20 @@ TEST_P(IrlbaTester, Basic) {
     ASSERT_EQ(res.U.cols(), rank);
     ASSERT_EQ(res.D.size(), rank);
 
-    // Gives us singular values that are around about right. Unfortunately,
-    // the singular values don't converge enough for an exact comparison.
+    // Gives us singular values that are around about right. Unfortunately, the
+    // U and V values don't converge enough for a decent comparison; we'll
+    // limit this to the first column, as this seems to be the most accurate. 
     Eigen::BDCSVD svd(A, Eigen::ComputeThinU | Eigen::ComputeThinV);
     expect_equal_vectors(res.D, svd.singularValues().head(rank), 1e-6);
+    expect_equal_column_vectors(res.U.leftCols(1), svd.matrixU().leftCols(1), 1e-4);
+    expect_equal_column_vectors(res.V.leftCols(1), svd.matrixV().leftCols(1), 1e-4);
+
+    // Also gives the same results when the matrices are row-major.
+    typedef Eigen::Matrix<double, -1, -1, Eigen::RowMajor> RowEigenXd;
+    auto rmres = irlba::compute<RowEigenXd>(A, rank, opt);
+    expect_equal_matrix(res.U, rmres.U);
+    expect_equal_matrix(res.V, rmres.V);
+    expect_equal_vectors(res.D, rmres.D);
 
     // Also works with some custom initialization.
     auto init = create_random_vector(A.cols(), 1239);