- optimized determinant calculations for small matrices (size <= 4)

  (only 30 muls for size 4)
- rework the matrix inversion: now using cofactor technique for size<=3,
  so the ugly unrolling is only used for size 4 anymore, and even there
  I'm looking to get rid of it.

1 files changed, 78 insertions, 0 deletions

diff --git a/Eigen/src/LU/Determinant.h b/Eigen/src/LU/Determinant.h
new file mode 100644
index 000000000..16c33ec31
--- /dev/null
+++ b/Eigen/src/LU/Determinant.h
@@ -0,0 +1,78 @@
+// 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/>.
+
+#ifndef EIGEN_DETERMINANT_H
+#define EIGEN_DETERMINANT_H
+
+template<typename Derived>
+const typename Derived::Scalar ei_bruteforce_det3_helper
+(const MatrixBase<Derived>& matrix, int a, int b, int c)
+{
+  return matrix.coeff(0,a)
+         * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
+}
+
+template<typename Derived>
+const typename Derived::Scalar ei_bruteforce_det4_helper
+(const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
+{
+  return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
+       * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
+}
+
+template<typename Derived>
+const typename Derived::Scalar ei_bruteforce_det(const MatrixBase<Derived>& m)
+{
+  switch(Derived::RowsAtCompileTime)
+  {
+    case 1:
+      return m.coeff(0,0);
+    case 2:
+      return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
+    case 3:
+      return ei_bruteforce_det3_helper(m,0,1,2)
+           - ei_bruteforce_det3_helper(m,1,0,2)
+           + ei_bruteforce_det3_helper(m,2,0,1);
+    case 4:
+      // trick by Martin Costabel to compute 4x4 det with only 30 muls
+      return ei_bruteforce_det4_helper(m,0,1,2,3)
+           + ei_bruteforce_det4_helper(m,0,2,1,3)
+           + ei_bruteforce_det4_helper(m,0,3,1,2)
+           + ei_bruteforce_det4_helper(m,1,2,0,3)
+           + ei_bruteforce_det4_helper(m,1,3,0,2)
+           + ei_bruteforce_det4_helper(m,2,3,0,1);
+    default:
+      assert(false);
+  }
+}
+
+template<typename Derived>
+typename ei_traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
+{
+  assert(rows() == cols());
+  if(rows() <= 4) return ei_bruteforce_det(derived());
+  else assert(false); // unimplemented for now
+}
+
+#endif // EIGEN_DETERMINANT_H
\ No newline at end of file