* add Jacobi transformations

* add Jacobi (Hestenes) SVD decomposition for square matrices * add function for trivial Householder
2026-04-10 11:34:33 +08:00 · 2009-08-09 16:58:13 +02:00
parent 5f8d58f36a
commit 3ed83fa681
6 changed files with 303 additions and 0 deletions
--- a/Eigen/src/Jacobi/Jacobi.h
+++ b/Eigen/src/Jacobi/Jacobi.h
@@ -0,0 +1,91 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
+//
+// 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_JACOBI_H
+#define EIGEN_JACOBI_H
+
+template<typename Derived>
+void MatrixBase<Derived>::applyJacobiOnTheLeft(int p, int q, Scalar c, Scalar s)
+{
+  for(int i = 0; i < cols(); ++i)
+  {
+    Scalar tmp = coeff(p,i);
+    coeffRef(p,i) = c * tmp - s * coeff(q,i);
+    coeffRef(q,i) = s * tmp + c * coeff(q,i);
+  }
+}
+
+template<typename Derived>
+void MatrixBase<Derived>::applyJacobiOnTheRight(int p, int q, Scalar c, Scalar s)
+{
+  for(int i = 0; i < rows(); ++i)
+  {
+    Scalar tmp = coeff(i,p);
+    coeffRef(i,p) = c * tmp - s * coeff(i,q);
+    coeffRef(i,q) = s * tmp + c * coeff(i,q);
+  }
+}
+
+template<typename Scalar>
+bool ei_makeJacobi(Scalar x, Scalar y, Scalar z, Scalar max_coeff, Scalar *c, Scalar *s)
+{
+  if(ei_abs(y) < max_coeff * 0.5 * machine_epsilon<Scalar>())
+  {
+    *c = Scalar(1);
+    *s = Scalar(0);
+    return true;
+  }
+  else
+  {
+    Scalar tau = (z - x) / (2 * y);
+    Scalar w = ei_sqrt(1 + ei_abs2(tau));
+    Scalar t;
+    if(tau>0)
+      t = Scalar(1) / (tau + w);
+    else
+      t = Scalar(1) / (tau - w);
+    *c = Scalar(1) / ei_sqrt(1 + ei_abs2(t));
+    *s = *c * t;
+    return false;
+  }
+}
+
+template<typename Derived>
+inline bool MatrixBase<Derived>::makeJacobi(int p, int q, Scalar max_coeff, Scalar *c, Scalar *s)
+{
+  return ei_makeJacobi(coeff(p,p), coeff(p,q), coeff(q,q), max_coeff, c, s);
+}
+
+template<typename Derived>
+inline bool MatrixBase<Derived>::makeJacobiForAtA(int p, int q, Scalar max_coeff, Scalar *c, Scalar *s)
+{
+  return ei_makeJacobi(col(p).squaredNorm(),
+                       col(p).dot(col(q)),
+                       col(q).squaredNorm(),
+                       max_coeff,
+                       c,s);
+}
+
+
+#endif // EIGEN_JACOBI_H