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

4 files changed, 105 insertions, 81 deletions

diff --git a/Eigen/src/LU/Determinant.h b/Eigen/src/LU/Determinant.h
index b587065ed..8870d9f20 100644
--- a/Eigen/src/LU/Determinant.h
+++ b/Eigen/src/LU/Determinant.h
@@ -53,7 +53,7 @@ template<typename Derived,
 {
   static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
   {
-    return m.partialLu().determinant();
+    return m.partialPivLu().determinant();
   }
 };
 
diff --git a/Eigen/src/LU/LU.h b/Eigen/src/LU/FullPivLU.h
index 4792aaf07..8743dac92 100644
--- a/Eigen/src/LU/LU.h
+++ b/Eigen/src/LU/FullPivLU.h
@@ -31,7 +31,7 @@ template<typename MatrixType> struct ei_lu_image_impl;
 
 /** \ingroup LU_Module
   *
-  * \class LU
+  * \class FullPivLU
   *
   * \brief LU decomposition of a matrix with complete pivoting, and related features
   *
@@ -54,12 +54,12 @@ template<typename MatrixType> struct ei_lu_image_impl;
   * permutationP(), permutationQ().
   *
   * As an exemple, here is how the original matrix can be retrieved:
-  * \include class_LU.cpp
-  * Output: \verbinclude class_LU.out
+  * \include class_FullPivLU.cpp
+  * Output: \verbinclude class_FullPivLU.out
   *
-  * \sa MatrixBase::lu(), MatrixBase::determinant(), MatrixBase::inverse()
+  * \sa MatrixBase::fullPivLu(), MatrixBase::determinant(), MatrixBase::inverse()
   */
-template<typename MatrixType> class LU
+template<typename MatrixType> class FullPivLU
 {
   public:
 
@@ -81,14 +81,14 @@ template<typename MatrixType> class LU
     * The default constructor is useful in cases in which the user intends to
     * perform decompositions via LU::compute(const MatrixType&).
     */
-    LU();
+    FullPivLU();
 
     /** Constructor.
       *
       * \param matrix the matrix of which to compute the LU decomposition.
       *               It is required to be nonzero.
       */
-    LU(const MatrixType& matrix);
+    FullPivLU(const MatrixType& matrix);
 
     /** Computes the LU decomposition of the given matrix.
       *
@@ -97,11 +97,11 @@ template<typename MatrixType> class LU
       *
       * \returns a reference to *this
       */
-    LU& compute(const MatrixType& matrix);
+    FullPivLU& compute(const MatrixType& matrix);
     
     /** \returns the LU decomposition matrix: the upper-triangular part is U, the
       * unit-lower-triangular part is L (at least for square matrices; in the non-square
-      * case, special care is needed, see the documentation of class LU).
+      * case, special care is needed, see the documentation of class FullPivLU).
       *
       * \sa matrixL(), matrixU()
       */
@@ -131,7 +131,7 @@ template<typename MatrixType> class LU
     
     /** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed,
       * representing the P permutation i.e. the permutation of the rows. For its precise meaning,
-      * see the examples given in the documentation of class LU.
+      * see the examples given in the documentation of class FullPivLU.
       *
       * \sa permutationQ()
       */
@@ -143,7 +143,7 @@ template<typename MatrixType> class LU
 
     /** \returns a vector of integers, whose size is the number of columns of the matrix being
       * decomposed, representing the Q permutation i.e. the permutation of the columns.
-      * For its precise meaning, see the examples given in the documentation of class LU.
+      * For its precise meaning, see the examples given in the documentation of class FullPivLU.
       *
       * \sa permutationP()
       */
@@ -162,8 +162,8 @@ template<typename MatrixType> class LU
       *       For that, it uses the threshold value that you can control by calling
       *       setThreshold(const RealScalar&).
       *
-      * Example: \include LU_kernel.cpp
-      * Output: \verbinclude LU_kernel.out
+      * Example: \include FullPivLU_kernel.cpp
+      * Output: \verbinclude FullPivLU_kernel.out
       *
       * \sa image()
       */
@@ -187,8 +187,8 @@ template<typename MatrixType> class LU
       *       For that, it uses the threshold value that you can control by calling
       *       setThreshold(const RealScalar&).
       *
-      * Example: \include LU_image.cpp
-      * Output: \verbinclude LU_image.out
+      * Example: \include FullPivLU_image.cpp
+      * Output: \verbinclude FullPivLU_image.out
       *
       * \sa kernel()
       */
@@ -214,8 +214,8 @@ template<typename MatrixType> class LU
       * \note_about_arbitrary_choice_of_solution
       * \note_about_using_kernel_to_study_multiple_solutions
       *
-      * Example: \include LU_solve.cpp
-      * Output: \verbinclude LU_solve.out
+      * Example: \include FullPivLU_solve.cpp
+      * Output: \verbinclude FullPivLU_solve.out
       *
       * \sa TriangularView::solve(), kernel(), inverse()
       */
@@ -260,7 +260,7 @@ template<typename MatrixType> class LU
       *
       * If you want to come back to the default behavior, call setThreshold(Default_t)
       */
-    LU& setThreshold(const RealScalar& threshold)
+    FullPivLU& setThreshold(const RealScalar& threshold)
     {
       m_usePrescribedThreshold = true;
       m_prescribedThreshold = threshold;
@@ -274,7 +274,7 @@ template<typename MatrixType> class LU
       *
       * See the documentation of setThreshold(const RealScalar&).
       */
-    LU& setThreshold(Default_t)
+    FullPivLU& setThreshold(Default_t)
     {
       m_usePrescribedThreshold = false;
     }
@@ -383,20 +383,20 @@ template<typename MatrixType> class LU
 };
 
 template<typename MatrixType>
-LU<MatrixType>::LU()
+FullPivLU<MatrixType>::FullPivLU()
   : m_isInitialized(false), m_usePrescribedThreshold(false)
 {
 }
 
 template<typename MatrixType>
-LU<MatrixType>::LU(const MatrixType& matrix)
+FullPivLU<MatrixType>::FullPivLU(const MatrixType& matrix)
   : m_isInitialized(false), m_usePrescribedThreshold(false)
 {
   compute(matrix);
 }
 
 template<typename MatrixType>
-LU<MatrixType>& LU<MatrixType>::compute(const MatrixType& matrix)
+FullPivLU<MatrixType>& FullPivLU<MatrixType>::compute(const MatrixType& matrix)
 {
   m_isInitialized = true;
   m_lu = matrix;
@@ -483,7 +483,7 @@ LU<MatrixType>& LU<MatrixType>::compute(const MatrixType& matrix)
 }
 
 template<typename MatrixType>
-typename ei_traits<MatrixType>::Scalar LU<MatrixType>::determinant() const
+typename ei_traits<MatrixType>::Scalar FullPivLU<MatrixType>::determinant() const
 {
   ei_assert(m_isInitialized && "LU is not initialized.");
   ei_assert(m_lu.rows() == m_lu.cols() && "You can't take the determinant of a non-square matrix!");
@@ -511,7 +511,7 @@ struct ei_traits<ei_lu_kernel_impl<MatrixType> >
 template<typename MatrixType>
 struct ei_lu_kernel_impl : public ReturnByValue<ei_lu_kernel_impl<MatrixType> >
 {
-  typedef LU<MatrixType> LUType;
+  typedef FullPivLU<MatrixType> LUType;
   typedef typename MatrixType::Scalar Scalar;
   typedef typename MatrixType::RealScalar RealScalar;
   const LUType& m_lu;
@@ -615,7 +615,7 @@ struct ei_traits<ei_lu_image_impl<MatrixType> >
 template<typename MatrixType>
 struct ei_lu_image_impl : public ReturnByValue<ei_lu_image_impl<MatrixType> >
 {
-  typedef LU<MatrixType> LUType;
+  typedef FullPivLU<MatrixType> LUType;
   typedef typename MatrixType::RealScalar RealScalar;
   const LUType& m_lu;
   int m_rank, m_cols;
@@ -670,7 +670,7 @@ template<typename MatrixType, typename Rhs>
 struct ei_lu_solve_impl : public ReturnByValue<ei_lu_solve_impl<MatrixType, Rhs> >
 {
   typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
-  typedef LU<MatrixType> LUType;
+  typedef FullPivLU<MatrixType> LUType;
   const LUType& m_lu;
   const typename Rhs::Nested m_rhs;
   
@@ -739,15 +739,15 @@ struct ei_lu_solve_impl : public ReturnByValue<ei_lu_solve_impl<MatrixType, Rhs>
 
 /** \lu_module
   *
-  * \return the LU decomposition of \c *this.
+  * \return the full-pivoting LU decomposition of \c *this.
   *
-  * \sa class LU
+  * \sa class FullPivLU
   */
 template<typename Derived>
-inline const LU<typename MatrixBase<Derived>::PlainMatrixType>
-MatrixBase<Derived>::lu() const
+inline const FullPivLU<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::fullPivLu() const
 {
-  return LU<PlainMatrixType>(eval());
+  return FullPivLU<PlainMatrixType>(eval());
 }
 
 #endif // EIGEN_LU_H
diff --git a/Eigen/src/LU/Inverse.h b/Eigen/src/LU/Inverse.h
index a168d58cd..306b5f60a 100644
--- a/Eigen/src/LU/Inverse.h
+++ b/Eigen/src/LU/Inverse.h
@@ -34,7 +34,7 @@ struct ei_compute_inverse
 {
   static inline void run(const MatrixType& matrix, ResultType& result)
   {
-    result = matrix.partialLu().inverse();
+    result = matrix.partialPivLu().inverse();
   }
 };
 
@@ -232,22 +232,31 @@ struct ei_compute_inverse<MatrixType, ResultType, 4>
     typename MatrixType::PlainMatrixType matrix(_matrix);
 
     // let's extract from the 2 first colums a 2x2 block whose determinant is as big as possible.
-    int good_row0=0, good_row1=1;
-    RealScalar good_absdet(-1);
-    // this double for loop shouldn't be too costly: only 6 iterations
-    for(int row0=0; row0<4; ++row0) {
-      for(int row1=row0+1; row1<4; ++row1)
-      {
-        RealScalar absdet = ei_abs(matrix.coeff(row0,0)*matrix.coeff(row1,1)
-                                 - matrix.coeff(row0,1)*matrix.coeff(row1,0));
-        if(absdet > good_absdet)
-        {
-          good_absdet = absdet;
-          good_row0 = row0;
-          good_row1 = row1;
-        }
-      }
-    }
+    int good_row0, good_row1, good_i;
+    Matrix<RealScalar,6,1> absdet;
+
+    // any 2x2 block with determinant above this threshold will be considered good enough
+    RealScalar d = (matrix.col(0).squaredNorm()+matrix.col(1).squaredNorm()) * RealScalar(1e-2);
+    #define ei_inv_size4_helper_macro(i,row0,row1) \
+    absdet[i] = ei_abs(matrix.coeff(row0,0)*matrix.coeff(row1,1) \
+                                 - matrix.coeff(row0,1)*matrix.coeff(row1,0)); \
+    if(absdet[i] > d) { good_row0=row0; good_row1=row1; goto good; }
+    ei_inv_size4_helper_macro(0,0,1)
+    ei_inv_size4_helper_macro(1,0,2)
+    ei_inv_size4_helper_macro(2,0,3)
+    ei_inv_size4_helper_macro(3,1,2)
+    ei_inv_size4_helper_macro(4,1,3)
+    ei_inv_size4_helper_macro(5,2,3)
+
+    // no 2x2 block has determinant bigger than the threshold. So just take the one that
+    // has the biggest determinant
+    absdet.maxCoeff(&good_i);
+    good_row0 = good_i <= 2 ? 0 : good_i <= 4 ? 1 : 2;
+    good_row1 = good_i <= 2 ? good_i+1 : good_i <= 4 ? good_i-1 : 3;
+
+    // now good_row0 and good_row1 are correctly set
+    good:
+    
     // do row permutations to move this 2x2 block to the top
     matrix.row(0).swap(matrix.row(good_row0));
     matrix.row(1).swap(matrix.row(good_row1));
@@ -318,12 +327,12 @@ struct ei_inverse_impl : public ReturnByValue<ei_inverse_impl<MatrixType> >
   * \returns the matrix inverse of this matrix.
   *
   * For small fixed sizes up to 4x4, this method uses ad-hoc methods (cofactors up to 3x3, Euler's trick for 4x4).
-  * In the general case, this method uses class PartialLU.
+  * In the general case, this method uses class PartialPivLU.
   *
   * \note This matrix must be invertible, otherwise the result is undefined. If you need an
   * invertibility check, do the following:
   * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
-  * \li for the general case, use class LU.
+  * \li for the general case, use class FullPivLU.
   *
   * Example: \include MatrixBase_inverse.cpp
   * Output: \verbinclude MatrixBase_inverse.out
diff --git a/Eigen/src/LU/PartialLU.h b/Eigen/src/LU/PartialPivLU.h
index e8d21e5ad..647ada38f 100644
--- a/Eigen/src/LU/PartialLU.h
+++ b/Eigen/src/LU/PartialPivLU.h
@@ -30,7 +30,7 @@ template<typename MatrixType, typename Rhs> struct ei_partiallu_solve_impl;
 
 /** \ingroup LU_Module
   *
-  * \class PartialLU
+  * \class PartialPivLU
   *
   * \brief LU decomposition of a matrix with partial pivoting, and related features
   *
@@ -46,10 +46,10 @@ template<typename MatrixType, typename Rhs> struct ei_partiallu_solve_impl;
   * matrix is invertible: it is your task to check that you only use this decomposition on invertible matrices.
   *
   * The guaranteed safe alternative, working for all matrices, is the full pivoting LU decomposition, provided
-  * by class LU.
+  * by class FullPivLU.
   *
   * This is \b not a rank-revealing LU decomposition. Many features are intentionally absent from this class,
-  * such as rank computation. If you need these features, use class LU.
+  * such as rank computation. If you need these features, use class FullPivLU.
   *
   * This LU decomposition is suitable to invert invertible matrices. It is what MatrixBase::inverse() uses
   * in the general case.
@@ -57,9 +57,9 @@ template<typename MatrixType, typename Rhs> struct ei_partiallu_solve_impl;
   *
   * The data of the LU decomposition can be directly accessed through the methods matrixLU(), permutationP().
   *
-  * \sa MatrixBase::partialLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class LU
+  * \sa MatrixBase::partialPivLu(), MatrixBase::determinant(), MatrixBase::inverse(), MatrixBase::computeInverse(), class FullPivLU
   */
-template<typename MatrixType> class PartialLU
+template<typename MatrixType> class PartialPivLU
 {
   public:
 
@@ -79,40 +79,40 @@ template<typename MatrixType> class PartialLU
     * \brief Default Constructor.
     *
     * The default constructor is useful in cases in which the user intends to
-    * perform decompositions via PartialLU::compute(const MatrixType&).
+    * perform decompositions via PartialPivLU::compute(const MatrixType&).
     */
-    PartialLU();
+    PartialPivLU();
 
     /** Constructor.
       *
       * \param matrix the matrix of which to compute the LU decomposition.
       *
       * \warning The matrix should have full rank (e.g. if it's square, it should be invertible).
-      * If you need to deal with non-full rank, use class LU instead.
+      * If you need to deal with non-full rank, use class FullPivLU instead.
       */
-    PartialLU(const MatrixType& matrix);
+    PartialPivLU(const MatrixType& matrix);
 
-    PartialLU& compute(const MatrixType& matrix);
+    PartialPivLU& compute(const MatrixType& matrix);
 
     /** \returns the LU decomposition matrix: the upper-triangular part is U, the
       * unit-lower-triangular part is L (at least for square matrices; in the non-square
-      * case, special care is needed, see the documentation of class LU).
+      * case, special care is needed, see the documentation of class FullPivLU).
       *
       * \sa matrixL(), matrixU()
       */
     inline const MatrixType& matrixLU() const
     {
-      ei_assert(m_isInitialized && "PartialLU is not initialized.");
+      ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
       return m_lu;
     }
 
     /** \returns a vector of integers, whose size is the number of rows of the matrix being decomposed,
       * representing the P permutation i.e. the permutation of the rows. For its precise meaning,
-      * see the examples given in the documentation of class LU.
+      * see the examples given in the documentation of class FullPivLU.
       */
     inline const IntColVectorType& permutationP() const
     {
-      ei_assert(m_isInitialized && "PartialLU is not initialized.");
+      ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
       return m_p;
     }
 
@@ -125,10 +125,10 @@ template<typename MatrixType> class PartialLU
       *
       * \returns the solution.
       *
-      * Example: \include PartialLU_solve.cpp
-      * Output: \verbinclude PartialLU_solve.out
+      * Example: \include PartialPivLU_solve.cpp
+      * Output: \verbinclude PartialPivLU_solve.out
       *
-      * Since this PartialLU class assumes anyway that the matrix A is invertible, the solution
+      * Since this PartialPivLU class assumes anyway that the matrix A is invertible, the solution
       * theoretically exists and is unique regardless of b.
       *
       * \note_about_checking_solutions
@@ -146,7 +146,7 @@ template<typename MatrixType> class PartialLU
     /** \returns the inverse of the matrix of which *this is the LU decomposition.
       *
       * \warning The matrix being decomposed here is assumed to be invertible. If you need to check for
-      *          invertibility, use class LU instead.
+      *          invertibility, use class FullPivLU instead.
       *
       * \sa MatrixBase::inverse(), LU::inverse()
       */
@@ -180,7 +180,7 @@ template<typename MatrixType> class PartialLU
 };
 
 template<typename MatrixType>
-PartialLU<MatrixType>::PartialLU()
+PartialPivLU<MatrixType>::PartialPivLU()
   : m_lu(),
     m_p(),
     m_det_p(0),
@@ -189,7 +189,7 @@ PartialLU<MatrixType>::PartialLU()
 }
 
 template<typename MatrixType>
-PartialLU<MatrixType>::PartialLU(const MatrixType& matrix)
+PartialPivLU<MatrixType>::PartialPivLU(const MatrixType& matrix)
   : m_lu(),
     m_p(),
     m_det_p(0),
@@ -378,12 +378,12 @@ void ei_partial_lu_inplace(MatrixType& lu, IntVector& row_transpositions, int& n
 }
 
 template<typename MatrixType>
-PartialLU<MatrixType>& PartialLU<MatrixType>::compute(const MatrixType& matrix)
+PartialPivLU<MatrixType>& PartialPivLU<MatrixType>::compute(const MatrixType& matrix)
 {
   m_lu = matrix;
   m_p.resize(matrix.rows());
 
-  ei_assert(matrix.rows() == matrix.cols() && "PartialLU is only for square (and moreover invertible) matrices");
+  ei_assert(matrix.rows() == matrix.cols() && "PartialPivLU is only for square (and moreover invertible) matrices");
   const int size = matrix.rows();
 
   IntColVectorType rows_transpositions(size);
@@ -401,9 +401,9 @@ PartialLU<MatrixType>& PartialLU<MatrixType>::compute(const MatrixType& matrix)
 }
 
 template<typename MatrixType>
-typename ei_traits<MatrixType>::Scalar PartialLU<MatrixType>::determinant() const
+typename ei_traits<MatrixType>::Scalar PartialPivLU<MatrixType>::determinant() const
 {
-  ei_assert(m_isInitialized && "PartialLU is not initialized.");
+  ei_assert(m_isInitialized && "PartialPivLU is not initialized.");
   return Scalar(m_det_p) * m_lu.diagonal().prod();
 }
 
@@ -424,7 +424,7 @@ template<typename MatrixType, typename Rhs>
 struct ei_partiallu_solve_impl : public ReturnByValue<ei_partiallu_solve_impl<MatrixType, Rhs> >
 {
   typedef typename ei_cleantype<typename Rhs::Nested>::type RhsNested;
-  typedef PartialLU<MatrixType> LUType;
+  typedef PartialPivLU<MatrixType> LUType;
   const LUType& m_lu;
   const typename Rhs::Nested m_rhs;
 
@@ -464,15 +464,30 @@ struct ei_partiallu_solve_impl : public ReturnByValue<ei_partiallu_solve_impl<Ma
 
 /** \lu_module
   *
-  * \return the LU decomposition of \c *this.
+  * \return the partial-pivoting LU decomposition of \c *this.
   *
-  * \sa class LU
+  * \sa class PartialPivLU
   */
 template<typename Derived>
-inline const PartialLU<typename MatrixBase<Derived>::PlainMatrixType>
-MatrixBase<Derived>::partialLu() const
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::partialPivLu() const
 {
-  return PartialLU<PlainMatrixType>(eval());
+  return PartialPivLU<PlainMatrixType>(eval());
+}
+
+/** \lu_module
+  *
+  * Synonym of partialPivLu().
+  *
+  * \return the partial-pivoting LU decomposition of \c *this.
+  *
+  * \sa class PartialPivLU
+  */
+template<typename Derived>
+inline const PartialPivLU<typename MatrixBase<Derived>::PlainMatrixType>
+MatrixBase<Derived>::lu() const
+{
+  return PartialPivLU<PlainMatrixType>(eval());
 }
 
 #endif // EIGEN_PARTIALLU_H