* add LU unit-test. Seems like we have very good numerical stability!

* some cleanup, and grant me a copyright line on the determinant test.
2026-04-10 11:34:33 +08:00 · 2008-08-09 19:26:14 +00:00
parent 4fa40367e9
commit d6e88f8155
5 changed files with 146 additions and 15 deletions
--- a/test/lu.cpp
+++ b/test/lu.cpp
@@ -0,0 +1,119 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2008 Benoit Jacob <jacob@math.jussieu.fr>
+//
+// Eigen is free software; you can redistribute it and/or
+// modify it under the terms of the GNU Lesser General Public
+// License as published by the Free Software Foundation; either
+// version 3 of the License, or (at your option) any later version.
+//
+// Alternatively, you can redistribute it and/or
+// modify it under the terms of the GNU General Public License as
+// published by the Free Software Foundation; either version 2 of
+// the License, or (at your option) any later version.
+//
+// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
+// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
+// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
+// GNU General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public
+// License and a copy of the GNU General Public License along with
+// Eigen. If not, see <http://www.gnu.org/licenses/>.
+
+#include "main.h"
+#include <Eigen/LU>
+
+template<typename Derived>
+void doSomeRankPreservingOperations(Eigen::MatrixBase<Derived>& m)
+{
+  for(int a = 0; a < 3*(m.rows()+m.cols()); a++)
+  {
+    double d = Eigen::ei_random<double>(-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
+  */
+  int rows = ei_random<int>(10,200), cols = ei_random<int>(10,200), cols2 = ei_random<int>(10,200);
+  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.setRandom();
+  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);
+  VERIFY(cols - rank == lu.dimensionOfKernel());
+  VERIFY(rank == lu.rank());
+  VERIFY(!lu.isInjective());
+  VERIFY(!lu.isInvertible());
+  VERIFY(lu.isSurjective() == (lu.rank() == rows));
+  VERIFY((m1 * lu.kernel()).isMuchSmallerThan(m1));
+  lu.computeKernel(&k);
+  VERIFY((m1 * k).isMuchSmallerThan(m1));
+  m2.setRandom();
+  m3 = m1*m2;
+  m2.setRandom();
+  lu.solve(m3, &m2);
+  VERIFY_IS_APPROX(m3, m1*m2);
+  m3.setRandom();
+  VERIFY(!lu.solve(m3, &m2));
+}
+
+template<typename MatrixType> void lu_invertible()
+{
+  /* this test covers the following files:
+     LU.h
+  */
+  int size = ei_random<int>(10,200);
+
+  MatrixType m1(size, size), m2(size, size), m3(size, size);
+  m1.setRandom();
+
+  LU<MatrixType> lu(m1);
+  VERIFY(0 == lu.dimensionOfKernel());
+  VERIFY(size == lu.rank());
+  VERIFY(lu.isInjective());
+  VERIFY(lu.isSurjective());
+  VERIFY(lu.isInvertible());
+  m3.setRandom();
+  lu.solve(m3, &m2);
+  VERIFY_IS_APPROX(m3, m1*m2);
+  VERIFY_IS_APPROX(m2, lu.inverse()*m3);
+  m3.setRandom();
+  VERIFY(lu.solve(m3, &m2));
+}
+
+void test_lu()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    CALL_SUBTEST( lu_non_invertible<MatrixXf>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXd>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXcf>() );
+    CALL_SUBTEST( lu_non_invertible<MatrixXcd>() );
+    CALL_SUBTEST( lu_invertible<MatrixXf>() );
+    CALL_SUBTEST( lu_invertible<MatrixXd>() );
+    CALL_SUBTEST( lu_invertible<MatrixXcf>() );
+    CALL_SUBTEST( lu_invertible<MatrixXcd>() );
+  }
+}