new unsupported module by Jitse Niesen: matrix exponential

2026-04-10 11:34:33 +08:00 · 2009-05-05 20:46:55 +00:00
parent 66f059b99d
commit 834eb5bfc8
6 changed files with 312 additions and 1 deletions
--- a/unsupported/test/matrixExponential.cpp
+++ b/unsupported/test/matrixExponential.cpp
@@ -0,0 +1,95 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra. Eigen itself is part of the KDE project.
+//
+// Copyright (C) 2009 Jitse Niesen <jitse@maths.leeds.ac.uk>
+//
+// 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 <Eigen/StdVector>
+#include "main.h"
+#include <unsupported/Eigen/MatrixFunctions>
+
+double binom(int n, int k) 
+{
+  double res = 1;
+  for (int i=0; i<k; i++)
+    res = res * (n-k+i+1) / (i+1);
+  return res;
+}
+
+void test2dRotation()
+{
+  Matrix2d A, B, C;
+  double angle;
+
+  for (int i=0; i<=20; i++) 
+  {
+    angle = pow(10, i / 5. - 2);
+    A << 0, angle, -angle, 0;
+    B << cos(angle), sin(angle), -sin(angle), cos(angle);
+    ei_matrix_exponential(A, &C);
+    VERIFY(C.isApprox(B, 1e-14));
+  }
+}
+
+void testPascal()
+{
+  for (int size=1; size<20; size++)
+  {
+    MatrixXd A(size,size), B(size,size), C(size,size);
+    A.setZero();
+    for (int i=0; i<size-1; i++)
+      A(i+1,i) = i+1;
+    B.setZero();
+    for (int i=0; i<size; i++)
+      for (int j=0; j<=i; j++)
+	B(i,j) = binom(i,j);
+    ei_matrix_exponential(A, &C);
+    VERIFY(C.isApprox(B, 1e-14));
+  }
+}
+
+template<typename MatrixType> void randomTest(const MatrixType& m)
+{
+  /* this test covers the following files:
+     Inverse.h
+  */
+  int rows = m.rows();
+  int cols = m.cols();
+  MatrixType m1(rows, cols), m2(rows, cols), m3(rows, cols),
+             identity = MatrixType::Identity(rows, rows);
+
+  for(int i = 0; i < g_repeat; i++) {
+    m1 = MatrixType::Random(rows, cols);
+    ei_matrix_exponential(m1, &m2);
+    ei_matrix_exponential(-m1, &m3);
+    VERIFY(identity.isApprox(m2 * m3, 1e-13));
+  }
+}
+
+void test_matrixExponential()
+{
+  CALL_SUBTEST(test2dRotation());
+  CALL_SUBTEST(testPascal());
+  CALL_SUBTEST(randomTest(Matrix2d()));
+  CALL_SUBTEST(randomTest(Matrix3d()));
+  CALL_SUBTEST(randomTest(Matrix4d()));
+  CALL_SUBTEST(randomTest(MatrixXd(8,8)));
+}