* JacobiSVD:

- support complex numbers
 - big rewrite of the 2x2 kernel, much more robust
* Jacobi:
 - fix weirdness in initial design, e.g. applyJacobiOnTheRight actually did the inverse transformation
 - fully support complex numbers
 - fix logic to decide whether to vectorize
 - remove several clumsy methods

fix for complex numbers

test/CMakeLists.txt

@@ -126,6 +126,7 @@ ei_add_test(qr_fullpivoting)
 ei_add_test(eigensolver_selfadjoint " " "${GSL_LIBRARIES}")
 ei_add_test(eigensolver_generic " " "${GSL_LIBRARIES}")
 ei_add_test(svd)
+ei_add_test(jacobisvd ${EI_OFLAG})
 ei_add_test(geo_orthomethods)
 ei_add_test(geo_homogeneous)
 ei_add_test(geo_quaternion)

test/jacobisvd.cpp

@@ -0,0 +1,105 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// 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/>.
+
+#include "main.h"
+#include <Eigen/SVD>
+#include <Eigen/LU>
+
+template<typename MatrixType> void svd(const MatrixType& m, bool pickrandom = true)
+{
+  int rows = m.rows();
+  int cols = m.cols();
+
+  enum {
+    RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+    ColsAtCompileTime = MatrixType::ColsAtCompileTime
+  };
+    
+  typedef typename MatrixType::Scalar Scalar;
+  typedef typename NumTraits<Scalar>::Real RealScalar;
+  typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixUType;
+  typedef Matrix<Scalar, ColsAtCompileTime, ColsAtCompileTime> MatrixVType;
+  typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
+  typedef Matrix<Scalar, ColsAtCompileTime, 1> InputVectorType;
+  
+  MatrixType a;
+  if(pickrandom) a = MatrixType::Random(rows,cols);
+  else a = m;
+
+  JacobiSVD<MatrixType> svd(a);
+  MatrixType sigma = MatrixType::Zero(rows,cols);
+  sigma.diagonal() = svd.singularValues().template cast<Scalar>();
+  MatrixUType u = svd.matrixU();
+  MatrixVType v = svd.matrixV();
+  
+  VERIFY_IS_APPROX(a, u * sigma * v.adjoint());
+  VERIFY_IS_UNITARY(u);
+  VERIFY_IS_UNITARY(v);
+}
+
+template<typename MatrixType> void svd_verify_assert()
+{
+  MatrixType tmp;
+
+  SVD<MatrixType> svd;
+  //VERIFY_RAISES_ASSERT(svd.solve(tmp, &tmp))
+  VERIFY_RAISES_ASSERT(svd.matrixU())
+  VERIFY_RAISES_ASSERT(svd.singularValues())
+  VERIFY_RAISES_ASSERT(svd.matrixV())
+  /*VERIFY_RAISES_ASSERT(svd.computeUnitaryPositive(&tmp,&tmp))
+  VERIFY_RAISES_ASSERT(svd.computePositiveUnitary(&tmp,&tmp))
+  VERIFY_RAISES_ASSERT(svd.computeRotationScaling(&tmp,&tmp))
+  VERIFY_RAISES_ASSERT(svd.computeScalingRotation(&tmp,&tmp))*/
+}
+
+void test_jacobisvd()
+{
+  for(int i = 0; i < g_repeat; i++) {
+    Matrix2cd m;
+    m << 0, 1,
+         0, 1;
+    CALL_SUBTEST( svd(m, false) );
+    m << 1, 0,
+         1, 0;
+    CALL_SUBTEST( svd(m, false) );
+    Matrix2d n;
+    n << 1, 1,
+         1, -1;
+    CALL_SUBTEST( svd(n, false) );
+    CALL_SUBTEST( svd(Matrix3f()) );
+    CALL_SUBTEST( svd(Matrix4d()) );
+    CALL_SUBTEST( svd(MatrixXf(50,50)) );
+//    CALL_SUBTEST( svd(MatrixXd(14,7)) );
+    CALL_SUBTEST( svd(MatrixXcf(3,3)) );
+    CALL_SUBTEST( svd(MatrixXd(30,30)) );
+  }
+  CALL_SUBTEST( svd(MatrixXf(200,200)) );
+  CALL_SUBTEST( svd(MatrixXcd(100,100)) );
+  
+  CALL_SUBTEST( svd_verify_assert<Matrix3f>() );
+  CALL_SUBTEST( svd_verify_assert<Matrix3d>() );
+  CALL_SUBTEST( svd_verify_assert<MatrixXf>() );
+  CALL_SUBTEST( svd_verify_assert<MatrixXd>() );
+}