big huge changes, so i dont remember everything.

* renaming, e.g. LU ---> FullPivLU
* split tests framework: more robust, e.g. dont generate empty tests if a number is skipped
* make all remaining tests use that splitting, as needed.
* Fix 4x4 inversion (see stable branch)
* Transform::inverse() and geo_transform test : adapt to new inverse() API, it was also trying to instantiate inverse() for 3x4 matrices.
* CMakeLists: more robust regexp to parse the version number
* misc fixes in unit tests

1 files changed, 429 insertions, 0 deletions

diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h
new file mode 100644
index 000000000..07ec343a5
--- /dev/null
+++ b/Eigen/src/QR/FullPivHouseholderQR.h
@@ -0,0 +1,429 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 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/>.
+
+#ifndef EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+#define EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H
+
+/** \ingroup QR_Module
+  * \nonstableyet
+  *
+  * \class FullPivHouseholderQR
+  *
+  * \brief Householder rank-revealing QR decomposition of a matrix with full pivoting
+  *
+  * \param MatrixType the type of the matrix of which we are computing the QR decomposition
+  *
+  * This class performs a rank-revealing QR decomposition using Householder transformations.
+  *
+  * This decomposition performs a very prudent full pivoting in order to be rank-revealing and achieve optimal
+  * numerical stability. The trade-off is that it is slower than HouseholderQR and ColPivHouseholderQR.
+  *
+  * \sa MatrixBase::fullPivHouseholderQr()
+  */
+template<typename MatrixType> class FullPivHouseholderQR
+{
+  public:
+
+    enum {
+      RowsAtCompileTime = MatrixType::RowsAtCompileTime,
+      ColsAtCompileTime = MatrixType::ColsAtCompileTime,
+      Options = MatrixType::Options,
+      DiagSizeAtCompileTime = EIGEN_ENUM_MIN(ColsAtCompileTime,RowsAtCompileTime)
+    };
+
+    typedef typename MatrixType::Scalar Scalar;
+    typedef typename MatrixType::RealScalar RealScalar;
+    typedef Matrix<Scalar, RowsAtCompileTime, RowsAtCompileTime> MatrixQType;
+    typedef Matrix<Scalar, DiagSizeAtCompileTime, 1> HCoeffsType;
+    typedef Matrix<int, 1, ColsAtCompileTime> IntRowVectorType;
+    typedef Matrix<int, RowsAtCompileTime, 1> IntColVectorType;
+    typedef Matrix<Scalar, 1, ColsAtCompileTime> RowVectorType;
+    typedef Matrix<Scalar, RowsAtCompileTime, 1> ColVectorType;
+
+    /** \brief Default Constructor.
+      *
+      * The default constructor is useful in cases in which the user intends to
+      * perform decompositions via FullPivHouseholderQR::compute(const MatrixType&).
+      */
+    FullPivHouseholderQR() : m_isInitialized(false) {}
+
+    FullPivHouseholderQR(const MatrixType& matrix)
+      : m_isInitialized(false)
+    {
+      compute(matrix);
+    }
+
+    /** This method finds a solution x to the equation Ax=b, where A is the matrix of which
+      * *this is the QR decomposition, if any exists.
+      *
+      * \returns \c true if a solution exists, \c false if no solution exists.
+      *
+      * \param b the right-hand-side of the equation to solve.
+      *
+      * \param result a pointer to the vector/matrix in which to store the solution, if any exists.
+      *          Resized if necessary, so that result->rows()==A.cols() and result->cols()==b.cols().
+      *          If no solution exists, *result is left with undefined coefficients.
+      *
+      * \note The case where b is a matrix is not yet implemented. Also, this
+      *       code is space inefficient.
+      *
+      * Example: \include FullPivHouseholderQR_solve.cpp
+      * Output: \verbinclude FullPivHouseholderQR_solve.out
+      */
+    template<typename OtherDerived, typename ResultType>
+    bool solve(const MatrixBase<OtherDerived>& b, ResultType *result) const;
+
+    MatrixQType matrixQ(void) const;
+
+    /** \returns a reference to the matrix where the Householder QR decomposition is stored
+      */
+    const MatrixType& matrixQR() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_qr;
+    }
+
+    FullPivHouseholderQR& compute(const MatrixType& matrix);
+
+    const IntRowVectorType& colsPermutation() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_cols_permutation;
+    }
+
+    const IntColVectorType& rowsTranspositions() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_rows_transpositions;
+    }
+
+    /** \returns the absolute value of the determinant of the matrix of which
+      * *this is the QR decomposition. It has only linear complexity
+      * (that is, O(n) where n is the dimension of the square matrix)
+      * as the QR decomposition has already been computed.
+      *
+      * \note This is only for square matrices.
+      *
+      * \warning a determinant can be very big or small, so for matrices
+      * of large enough dimension, there is a risk of overflow/underflow.
+      * One way to work around that is to use logAbsDeterminant() instead.
+      *
+      * \sa logAbsDeterminant(), MatrixBase::determinant()
+      */
+    typename MatrixType::RealScalar absDeterminant() const;
+
+    /** \returns the natural log of the absolute value of the determinant of the matrix of which
+      * *this is the QR decomposition. It has only linear complexity
+      * (that is, O(n) where n is the dimension of the square matrix)
+      * as the QR decomposition has already been computed.
+      *
+      * \note This is only for square matrices.
+      *
+      * \note This method is useful to work around the risk of overflow/underflow that's inherent
+      * to determinant computation.
+      *
+      * \sa absDeterminant(), MatrixBase::determinant()
+      */
+    typename MatrixType::RealScalar logAbsDeterminant() const;
+
+    /** \returns the rank of the matrix of which *this is the QR decomposition.
+      *
+      * \note This is computed at the time of the construction of the QR decomposition. This
+      *       method does not perform any further computation.
+      */
+    inline int rank() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_rank;
+    }
+
+    /** \returns the dimension of the kernel of the matrix of which *this is the QR decomposition.
+      *
+      * \note Since the rank is computed at the time of the construction of the QR decomposition, this
+      *       method almost does not perform any further computation.
+      */
+    inline int dimensionOfKernel() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_qr.cols() - m_rank;
+    }
+
+    /** \returns true if the matrix of which *this is the QR decomposition represents an injective
+      *          linear map, i.e. has trivial kernel; false otherwise.
+      *
+      * \note Since the rank is computed at the time of the construction of the QR decomposition, this
+      *       method almost does not perform any further computation.
+      */
+    inline bool isInjective() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_rank == m_qr.cols();
+    }
+
+    /** \returns true if the matrix of which *this is the QR decomposition represents a surjective
+      *          linear map; false otherwise.
+      *
+      * \note Since the rank is computed at the time of the construction of the QR decomposition, this
+      *       method almost does not perform any further computation.
+      */
+    inline bool isSurjective() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return m_rank == m_qr.rows();
+    }
+
+    /** \returns true if the matrix of which *this is the QR decomposition is invertible.
+      *
+      * \note Since the rank is computed at the time of the construction of the QR decomposition, this
+      *       method almost does not perform any further computation.
+      */
+    inline bool isInvertible() const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      return isInjective() && isSurjective();
+    }
+
+    /** Computes the inverse of the matrix of which *this is the QR decomposition.
+      *
+      * \param result a pointer to the matrix into which to store the inverse. Resized if needed.
+      *
+      * \note If this matrix is not invertible, *result is left with undefined coefficients.
+      *       Use isInvertible() to first determine whether this matrix is invertible.
+      *
+      * \sa inverse()
+      */
+    inline void computeInverse(MatrixType *result) const
+    {
+      ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+      ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the inverse of a non-square matrix!");
+      solve(MatrixType::Identity(m_qr.rows(), m_qr.cols()), result);
+    }
+
+    /** \returns the inverse of the matrix of which *this is the QR decomposition.
+      *
+      * \note If this matrix is not invertible, the returned matrix has undefined coefficients.
+      *       Use isInvertible() to first determine whether this matrix is invertible.
+      *
+      * \sa computeInverse()
+      */
+    inline MatrixType inverse() const
+    {
+      MatrixType result;
+      computeInverse(&result);
+      return result;
+    }
+
+  protected:
+    MatrixType m_qr;
+    HCoeffsType m_hCoeffs;
+    IntColVectorType m_rows_transpositions;
+    IntRowVectorType m_cols_permutation;
+    bool m_isInitialized;
+    RealScalar m_precision;
+    int m_rank;
+    int m_det_pq;
+};
+
+#ifndef EIGEN_HIDE_HEAVY_CODE
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const
+{
+  ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+  ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+  return ei_abs(m_qr.diagonal().prod());
+}
+
+template<typename MatrixType>
+typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDeterminant() const
+{
+  ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+  ei_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
+  return m_qr.diagonal().cwise().abs().cwise().log().sum();
+}
+
+template<typename MatrixType>
+FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
+{
+  int rows = matrix.rows();
+  int cols = matrix.cols();
+  int size = std::min(rows,cols);
+  m_rank = size;
+
+  m_qr = matrix;
+  m_hCoeffs.resize(size);
+
+  RowVectorType temp(cols);
+
+  m_precision = epsilon<Scalar>() * size;
+
+  m_rows_transpositions.resize(matrix.rows());
+  IntRowVectorType cols_transpositions(matrix.cols());
+  m_cols_permutation.resize(matrix.cols());
+  int number_of_transpositions = 0;
+
+  RealScalar biggest(0);
+
+  for (int k = 0; k < size; ++k)
+  {
+    int row_of_biggest_in_corner, col_of_biggest_in_corner;
+    RealScalar biggest_in_corner;
+
+    biggest_in_corner = m_qr.corner(Eigen::BottomRight, rows-k, cols-k)
+                            .cwise().abs()
+                            .maxCoeff(&row_of_biggest_in_corner, &col_of_biggest_in_corner);
+    row_of_biggest_in_corner += k;
+    col_of_biggest_in_corner += k;
+    if(k==0) biggest = biggest_in_corner;
+
+    // if the corner is negligible, then we have less than full rank, and we can finish early
+    if(ei_isMuchSmallerThan(biggest_in_corner, biggest, m_precision))
+    {
+      m_rank = k;
+      for(int i = k; i < size; i++)
+      {
+        m_rows_transpositions.coeffRef(i) = i;
+        cols_transpositions.coeffRef(i) = i;
+        m_hCoeffs.coeffRef(i) = Scalar(0);
+      }
+      break;
+    }
+
+    m_rows_transpositions.coeffRef(k) = row_of_biggest_in_corner;
+    cols_transpositions.coeffRef(k) = col_of_biggest_in_corner;
+    if(k != row_of_biggest_in_corner) {
+      m_qr.row(k).end(cols-k).swap(m_qr.row(row_of_biggest_in_corner).end(cols-k));
+      ++number_of_transpositions;
+    }
+    if(k != col_of_biggest_in_corner) {
+      m_qr.col(k).swap(m_qr.col(col_of_biggest_in_corner));
+      ++number_of_transpositions;
+    }
+
+    RealScalar beta;
+    m_qr.col(k).end(rows-k).makeHouseholderInPlace(&m_hCoeffs.coeffRef(k), &beta);
+    m_qr.coeffRef(k,k) = beta;
+
+    m_qr.corner(BottomRight, rows-k, cols-k-1)
+        .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), m_hCoeffs.coeffRef(k), &temp.coeffRef(k+1));
+  }
+
+  for(int k = 0; k < matrix.cols(); ++k) m_cols_permutation.coeffRef(k) = k;
+  for(int k = 0; k < size; ++k)
+    std::swap(m_cols_permutation.coeffRef(k), m_cols_permutation.coeffRef(cols_transpositions.coeff(k)));
+
+  m_det_pq = (number_of_transpositions%2) ? -1 : 1;
+  m_isInitialized = true;
+
+  return *this;
+}
+
+template<typename MatrixType>
+template<typename OtherDerived, typename ResultType>
+bool FullPivHouseholderQR<MatrixType>::solve(
+  const MatrixBase<OtherDerived>& b,
+  ResultType *result
+) const
+{
+  ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+  result->resize(m_qr.cols(), b.cols());
+  if(m_rank==0)
+  {
+    if(b.squaredNorm() == RealScalar(0))
+    {
+      result->setZero();
+      return true;
+    }
+    else return false;
+  }
+
+  const int rows = m_qr.rows();
+  const int cols = b.cols();
+  ei_assert(b.rows() == rows);
+
+  typename OtherDerived::PlainMatrixType c(b);
+
+  Matrix<Scalar,1,MatrixType::ColsAtCompileTime> temp(cols);
+  for (int k = 0; k < m_rank; ++k)
+  {
+    int remainingSize = rows-k;
+    c.row(k).swap(c.row(m_rows_transpositions.coeff(k)));
+    c.corner(BottomRight, remainingSize, cols)
+     .applyHouseholderOnTheLeft(m_qr.col(k).end(remainingSize-1), m_hCoeffs.coeff(k), &temp.coeffRef(0));
+  }
+
+  if(!isSurjective())
+  {
+    // is c is in the image of R ?
+    RealScalar biggest_in_upper_part_of_c = c.corner(TopLeft, m_rank, c.cols()).cwise().abs().maxCoeff();
+    RealScalar biggest_in_lower_part_of_c = c.corner(BottomLeft, rows-m_rank, c.cols()).cwise().abs().maxCoeff();
+    if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision))
+      return false;
+  }
+  m_qr.corner(TopLeft, m_rank, m_rank)
+      .template triangularView<UpperTriangular>()
+      .solveInPlace(c.corner(TopLeft, m_rank, c.cols()));
+
+  for(int i = 0; i < m_rank; ++i) result->row(m_cols_permutation.coeff(i)) = c.row(i);
+  for(int i = m_rank; i < m_qr.cols(); ++i) result->row(m_cols_permutation.coeff(i)).setZero();
+  return true;
+}
+
+/** \returns the matrix Q */
+template<typename MatrixType>
+typename FullPivHouseholderQR<MatrixType>::MatrixQType FullPivHouseholderQR<MatrixType>::matrixQ() const
+{
+  ei_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
+  // compute the product H'_0 H'_1 ... H'_n-1,
+  // where H_k is the k-th Householder transformation I - h_k v_k v_k'
+  // and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
+  int rows = m_qr.rows();
+  int cols = m_qr.cols();
+  int size = std::min(rows,cols);
+  MatrixQType res = MatrixQType::Identity(rows, rows);
+  Matrix<Scalar,1,MatrixType::RowsAtCompileTime> temp(rows);
+  for (int k = size-1; k >= 0; k--)
+  {
+    res.block(k, k, rows-k, rows-k)
+       .applyHouseholderOnTheLeft(m_qr.col(k).end(rows-k-1), ei_conj(m_hCoeffs.coeff(k)), &temp.coeffRef(k));
+    res.row(k).swap(res.row(m_rows_transpositions.coeff(k)));
+  }
+  return res;
+}
+
+#endif // EIGEN_HIDE_HEAVY_CODE
+
+/** \return the full-pivoting Householder QR decomposition of \c *this.
+  *
+  * \sa class FullPivHouseholderQR
+  */
+template<typename Derived>
+const FullPivHouseholderQR<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::fullPivHouseholderQr() const
+{
+  return FullPivHouseholderQR<PlainMatrixType>(eval());
+}
+
+#endif // EIGEN_FULLPIVOTINGHOUSEHOLDERQR_H