SparseMatrixBase.h

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// 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 Gael Guennebaud <g.gael@free.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_SPARSEMATRIXBASE_H
#define EIGEN_SPARSEMATRIXBASE_H

template<typename Derived> class SparseMatrixBase
{
  public:

    typedef typename ei_traits<Derived>::Scalar Scalar;
//     typedef typename Derived::InnerIterator InnerIterator;

    enum {

      RowsAtCompileTime = ei_traits<Derived>::RowsAtCompileTime,
      ColsAtCompileTime = ei_traits<Derived>::ColsAtCompileTime,
      SizeAtCompileTime = (ei_size_at_compile_time<ei_traits<Derived>::RowsAtCompileTime,
                                                   ei_traits<Derived>::ColsAtCompileTime>::ret),
      MaxRowsAtCompileTime = RowsAtCompileTime,
      MaxColsAtCompileTime = ColsAtCompileTime,

      MaxSizeAtCompileTime = (ei_size_at_compile_time<MaxRowsAtCompileTime,
                                                      MaxColsAtCompileTime>::ret),

      IsVectorAtCompileTime = RowsAtCompileTime == 1 || ColsAtCompileTime == 1,
      Flags = ei_traits<Derived>::Flags,
      CoeffReadCost = ei_traits<Derived>::CoeffReadCost,
      IsRowMajor = Flags&RowMajorBit ? 1 : 0
    };

    typedef typename ei_meta_if<NumTraits<Scalar>::IsComplex,
                        const SparseCwiseUnaryOp<ei_scalar_conjugate_op<Scalar>, Derived>,
                        const Derived&
                     >::ret ConjugateReturnType;
    typedef CwiseUnaryOp<ei_scalar_real_op<Scalar>, Derived> RealReturnType;
    typedef CwiseUnaryOp<ei_scalar_imag_op<Scalar>, Derived> ImagReturnType;
    typedef SparseTranspose</*NestByValue<*/typename ei_cleantype<ConjugateReturnType>::type> /*>*/
            AdjointReturnType;

#ifndef EIGEN_PARSED_BY_DOXYGEN

    typedef typename NumTraits<Scalar>::Real RealScalar;

    typedef Matrix<Scalar,EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime),
                          EIGEN_ENUM_MAX(RowsAtCompileTime,ColsAtCompileTime)> SquareMatrixType;

    inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
    inline Derived& derived() { return *static_cast<Derived*>(this); }
    inline Derived& const_cast_derived() const
    { return *static_cast<Derived*>(const_cast<SparseMatrixBase*>(this)); }
#endif // not EIGEN_PARSED_BY_DOXYGEN

    inline int rows() const { return derived().rows(); }
    inline int cols() const { return derived().cols(); }
    inline int size() const { return rows() * cols(); }
    inline int nonZeros() const { return derived().nonZeros(); }
    inline bool isVector() const { return rows()==1 || cols()==1; }
    int outerSize() const { return (int(Flags)&RowMajorBit) ? this->rows() : this->cols(); }
    int innerSize() const { return (int(Flags)&RowMajorBit) ? this->cols() : this->rows(); }

    bool isRValue() const { return m_isRValue; }
    Derived& markAsRValue() { m_isRValue = true; return derived(); }

    SparseMatrixBase() : m_isRValue(false) { /* TODO check flags */ }

    inline Derived& operator=(const Derived& other)
    {
//       std::cout << "Derived& operator=(const Derived& other)\n";
//       if (other.isRValue())
//         derived().swap(other.const_cast_derived());
//       else
        this->operator=<Derived>(other);
      return derived();
    }


    template<typename OtherDerived>
    inline void assignGeneric(const OtherDerived& other)
    {
//       std::cout << "Derived& operator=(const MatrixBase<OtherDerived>& other)\n";
      //const bool transpose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
      ei_assert(( ((ei_traits<Derived>::SupportedAccessPatterns&OuterRandomAccessPattern)==OuterRandomAccessPattern) ||
                  (!((Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit)))) &&
                  "the transpose operation is supposed to be handled in SparseMatrix::operator=");

      const int outerSize = other.outerSize();
      //typedef typename ei_meta_if<transpose, LinkedVectorMatrix<Scalar,Flags&RowMajorBit>, Derived>::ret TempType;
      // thanks to shallow copies, we always eval to a tempary
      Derived temp(other.rows(), other.cols());

      temp.startFill(std::max(this->rows(),this->cols())*2);
      for (int j=0; j<outerSize; ++j)
      {
        for (typename OtherDerived::InnerIterator it(other.derived(), j); it; ++it)
        {
          Scalar v = it.value();
          if (v!=Scalar(0))
          {
            if (OtherDerived::Flags & RowMajorBit) temp.fill(j,it.index()) = v;
            else temp.fill(it.index(),j) = v;
          }
        }
      }
      temp.endFill();

      derived() = temp.markAsRValue();
    }


    template<typename OtherDerived>
    inline Derived& operator=(const SparseMatrixBase<OtherDerived>& other)
    {
//       std::cout << typeid(OtherDerived).name() << "\n";
//       std::cout << Flags << " " << OtherDerived::Flags << "\n";
      const bool transpose = (Flags & RowMajorBit) != (OtherDerived::Flags & RowMajorBit);
//       std::cout << "eval transpose = " << transpose << "\n";
      const int outerSize = (int(OtherDerived::Flags) & RowMajorBit) ? other.rows() : other.cols();
      if ((!transpose) && other.isRValue())
      {
        // eval without temporary
        derived().resize(other.rows(), other.cols());
        derived().startFill(std::max(this->rows(),this->cols())*2);
        for (int j=0; j<outerSize; ++j)
        {
          for (typename OtherDerived::InnerIterator it(other.derived(), j); it; ++it)
          {
            Scalar v = it.value();
            if (v!=Scalar(0))
            {
              if (IsRowMajor) derived().fill(j,it.index()) = v;
              else derived().fill(it.index(),j) = v;
            }
          }
        }
        derived().endFill();
      }
      else
      {
        assignGeneric(other.derived());
      }
      return derived();
    }

    template<typename Lhs, typename Rhs>
    inline Derived& operator=(const SparseProduct<Lhs,Rhs,SparseTimeSparseProduct>& product);

    friend std::ostream & operator << (std::ostream & s, const SparseMatrixBase& m)
    {
      if (Flags&RowMajorBit)
      {
        for (int row=0; row<m.outerSize(); ++row)
        {
          int col = 0;
          for (typename Derived::InnerIterator it(m.derived(), row); it; ++it)
          {
            for ( ; col<it.index(); ++col)
              s << "0 ";
            s << it.value() << " ";
            ++col;
          }
          for ( ; col<m.cols(); ++col)
            s << "0 ";
          s << std::endl;
        }
      }
      else
      {
        if (m.cols() == 1) {
          int row = 0;
          for (typename Derived::InnerIterator it(m.derived(), 0); it; ++it)
          {
            for ( ; row<it.index(); ++row)
              s << "0" << std::endl;
            s << it.value() << std::endl;
            ++row;
          }
          for ( ; row<m.rows(); ++row)
            s << "0" << std::endl;
        }
        else
        {
          SparseMatrix<Scalar, RowMajorBit> trans = m.derived();
          s << trans;
        }
      }
      return s;
    }

    const SparseCwiseUnaryOp<ei_scalar_opposite_op<typename ei_traits<Derived>::Scalar>,Derived> operator-() const;

    template<typename OtherDerived>
    const SparseCwiseBinaryOp<ei_scalar_sum_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
    operator+(const SparseMatrixBase<OtherDerived> &other) const;

    template<typename OtherDerived>
    const SparseCwiseBinaryOp<ei_scalar_difference_op<typename ei_traits<Derived>::Scalar>, Derived, OtherDerived>
    operator-(const SparseMatrixBase<OtherDerived> &other) const;

    template<typename OtherDerived>
    Derived& operator+=(const SparseMatrixBase<OtherDerived>& other);
    template<typename OtherDerived>
    Derived& operator-=(const SparseMatrixBase<OtherDerived>& other);

//     template<typename Lhs,typename Rhs>
//     Derived& operator+=(const Flagged<Product<Lhs,Rhs,CacheFriendlyProduct>, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit>& other);

    Derived& operator*=(const Scalar& other);
    Derived& operator/=(const Scalar& other);

    const SparseCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<Derived>::Scalar>, Derived>
    operator*(const Scalar& scalar) const;
    const SparseCwiseUnaryOp<ei_scalar_quotient1_op<typename ei_traits<Derived>::Scalar>, Derived>
    operator/(const Scalar& scalar) const;

    inline friend const SparseCwiseUnaryOp<ei_scalar_multiple_op<typename ei_traits<Derived>::Scalar>, Derived>
    operator*(const Scalar& scalar, const SparseMatrixBase& matrix)
    { return matrix*scalar; }


    template<typename OtherDerived>
    const typename SparseProductReturnType<Derived,OtherDerived>::Type
    operator*(const SparseMatrixBase<OtherDerived> &other) const;
    
    // dense * sparse (return a dense object)
    template<typename OtherDerived> friend 
    const typename SparseProductReturnType<OtherDerived,Derived>::Type
    operator*(const MatrixBase<OtherDerived>& lhs, const Derived& rhs)
    { return typename SparseProductReturnType<OtherDerived,Derived>::Type(lhs.derived(),rhs); }
    
    template<typename OtherDerived>
    const typename SparseProductReturnType<Derived,OtherDerived>::Type
    operator*(const MatrixBase<OtherDerived> &other) const;

    template<typename OtherDerived>
    Derived& operator*=(const SparseMatrixBase<OtherDerived>& other);

    template<typename OtherDerived>
    typename ei_plain_matrix_type_column_major<OtherDerived>::type
    solveTriangular(const MatrixBase<OtherDerived>& other) const;

    template<typename OtherDerived>
    void solveTriangularInPlace(MatrixBase<OtherDerived>& other) const;

    template<typename OtherDerived> Scalar dot(const MatrixBase<OtherDerived>& other) const;
    template<typename OtherDerived> Scalar dot(const SparseMatrixBase<OtherDerived>& other) const;
    RealScalar squaredNorm() const;
    RealScalar norm()  const;
//     const PlainMatrixType normalized() const;
//     void normalize();

    SparseTranspose<Derived> transpose() { return derived(); }
    const SparseTranspose<Derived> transpose() const { return derived(); }
    // void transposeInPlace();
    const AdjointReturnType adjoint() const { return conjugate()/*.nestByValue()*/; }

    // sub-vector
    SparseInnerVectorSet<Derived,1> row(int i);
    const SparseInnerVectorSet<Derived,1> row(int i) const;
    SparseInnerVectorSet<Derived,1> col(int j);
    const SparseInnerVectorSet<Derived,1> col(int j) const;
    SparseInnerVectorSet<Derived,1> innerVector(int outer);
    const SparseInnerVectorSet<Derived,1> innerVector(int outer) const;
    
    // set of sub-vectors
    SparseInnerVectorSet<Derived,Dynamic> subrows(int start, int size);
    const SparseInnerVectorSet<Derived,Dynamic> subrows(int start, int size) const;
    SparseInnerVectorSet<Derived,Dynamic> subcols(int start, int size);
    const SparseInnerVectorSet<Derived,Dynamic> subcols(int start, int size) const;
    SparseInnerVectorSet<Derived,Dynamic> innerVectors(int outerStart, int outerSize);
    const SparseInnerVectorSet<Derived,Dynamic> innerVectors(int outerStart, int outerSize) const;

//     typename BlockReturnType<Derived>::Type block(int startRow, int startCol, int blockRows, int blockCols);
//     const typename BlockReturnType<Derived>::Type
//     block(int startRow, int startCol, int blockRows, int blockCols) const;
//
//     typename BlockReturnType<Derived>::SubVectorType segment(int start, int size);
//     const typename BlockReturnType<Derived>::SubVectorType segment(int start, int size) const;
//
//     typename BlockReturnType<Derived,Dynamic>::SubVectorType start(int size);
//     const typename BlockReturnType<Derived,Dynamic>::SubVectorType start(int size) const;
//
//     typename BlockReturnType<Derived,Dynamic>::SubVectorType end(int size);
//     const typename BlockReturnType<Derived,Dynamic>::SubVectorType end(int size) const;
//
//     typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols);
//     const typename BlockReturnType<Derived>::Type corner(CornerType type, int cRows, int cCols) const;
//
//     template<int BlockRows, int BlockCols>
//     typename BlockReturnType<Derived, BlockRows, BlockCols>::Type block(int startRow, int startCol);
//     template<int BlockRows, int BlockCols>
//     const typename BlockReturnType<Derived, BlockRows, BlockCols>::Type block(int startRow, int startCol) const;

//     template<int CRows, int CCols>
//     typename BlockReturnType<Derived, CRows, CCols>::Type corner(CornerType type);
//     template<int CRows, int CCols>
//     const typename BlockReturnType<Derived, CRows, CCols>::Type corner(CornerType type) const;

//     template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType start(void);
//     template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType start() const;

//     template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType end();
//     template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType end() const;

//     template<int Size> typename BlockReturnType<Derived,Size>::SubVectorType segment(int start);
//     template<int Size> const typename BlockReturnType<Derived,Size>::SubVectorType segment(int start) const;

//     DiagonalCoeffs<Derived> diagonal();
//     const DiagonalCoeffs<Derived> diagonal() const;

//     template<unsigned int Mode> Part<Derived, Mode> part();
//     template<unsigned int Mode> const Part<Derived, Mode> part() const;


//     static const ConstantReturnType Constant(int rows, int cols, const Scalar& value);
//     static const ConstantReturnType Constant(int size, const Scalar& value);
//     static const ConstantReturnType Constant(const Scalar& value);

//     template<typename CustomNullaryOp>
//     static const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr(int rows, int cols, const CustomNullaryOp& func);
//     template<typename CustomNullaryOp>
//     static const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr(int size, const CustomNullaryOp& func);
//     template<typename CustomNullaryOp>
//     static const CwiseNullaryOp<CustomNullaryOp, Derived> NullaryExpr(const CustomNullaryOp& func);

//     static const ConstantReturnType Zero(int rows, int cols);
//     static const ConstantReturnType Zero(int size);
//     static const ConstantReturnType Zero();
//     static const ConstantReturnType Ones(int rows, int cols);
//     static const ConstantReturnType Ones(int size);
//     static const ConstantReturnType Ones();
//     static const IdentityReturnType Identity();
//     static const IdentityReturnType Identity(int rows, int cols);
//     static const BasisReturnType Unit(int size, int i);
//     static const BasisReturnType Unit(int i);
//     static const BasisReturnType UnitX();
//     static const BasisReturnType UnitY();
//     static const BasisReturnType UnitZ();
//     static const BasisReturnType UnitW();

//     const DiagonalMatrix<Derived> asDiagonal() const;

//     Derived& setConstant(const Scalar& value);
//     Derived& setZero();
//     Derived& setOnes();
//     Derived& setRandom();
//     Derived& setIdentity();

      Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> toDense() const
      {
        Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime> res(rows(),cols());
        res.setZero();
        for (int j=0; j<outerSize(); ++j)
        {
          for (typename Derived::InnerIterator i(derived(),j); i; ++i)
            if(IsRowMajor)
              res.coeffRef(j,i.index()) = i.value();
            else
              res.coeffRef(i.index(),j) = i.value();
        }
        return res;
      }

    template<typename OtherDerived>
    bool isApprox(const SparseMatrixBase<OtherDerived>& other,
                  RealScalar prec = precision<Scalar>()) const
    { return toDense().isApprox(other.toDense(),prec); }

    template<typename OtherDerived>
    bool isApprox(const MatrixBase<OtherDerived>& other,
                  RealScalar prec = precision<Scalar>()) const
    { return toDense().isApprox(other,prec); }
//     bool isMuchSmallerThan(const RealScalar& other,
//                            RealScalar prec = precision<Scalar>()) const;
//     template<typename OtherDerived>
//     bool isMuchSmallerThan(const MatrixBase<OtherDerived>& other,
//                            RealScalar prec = precision<Scalar>()) const;

//     bool isApproxToConstant(const Scalar& value, RealScalar prec = precision<Scalar>()) const;
//     bool isZero(RealScalar prec = precision<Scalar>()) const;
//     bool isOnes(RealScalar prec = precision<Scalar>()) const;
//     bool isIdentity(RealScalar prec = precision<Scalar>()) const;
//     bool isDiagonal(RealScalar prec = precision<Scalar>()) const;

//     bool isUpperTriangular(RealScalar prec = precision<Scalar>()) const;
//     bool isLowerTriangular(RealScalar prec = precision<Scalar>()) const;

//     template<typename OtherDerived>
//     bool isOrthogonal(const MatrixBase<OtherDerived>& other,
//                       RealScalar prec = precision<Scalar>()) const;
//     bool isUnitary(RealScalar prec = precision<Scalar>()) const;

//     template<typename OtherDerived>
//     inline bool operator==(const MatrixBase<OtherDerived>& other) const
//     { return (cwise() == other).all(); }

//     template<typename OtherDerived>
//     inline bool operator!=(const MatrixBase<OtherDerived>& other) const
//     { return (cwise() != other).any(); }


    template<typename NewType>
    const SparseCwiseUnaryOp<ei_scalar_cast_op<typename ei_traits<Derived>::Scalar, NewType>, Derived> cast() const;

    EIGEN_STRONG_INLINE const typename ei_eval<Derived>::type eval() const
    { return typename ei_eval<Derived>::type(derived()); }

//     template<typename OtherDerived>
//     void swap(const MatrixBase<OtherDerived>& other);

    template<unsigned int Added>
    const SparseFlagged<Derived, Added, 0> marked() const;
//     const Flagged<Derived, 0, EvalBeforeNestingBit | EvalBeforeAssigningBit> lazy() const;

//     inline int stride(void) const { return derived().stride(); }

//     inline const NestByValue<Derived> nestByValue() const;


    ConjugateReturnType conjugate() const;
    const RealReturnType real() const;
    const ImagReturnType imag() const;

    template<typename CustomUnaryOp>
    const SparseCwiseUnaryOp<CustomUnaryOp, Derived> unaryExpr(const CustomUnaryOp& func = CustomUnaryOp()) const;

//     template<typename CustomBinaryOp, typename OtherDerived>
//     const CwiseBinaryOp<CustomBinaryOp, Derived, OtherDerived>
//     binaryExpr(const MatrixBase<OtherDerived> &other, const CustomBinaryOp& func = CustomBinaryOp()) const;


    Scalar sum() const;
//     Scalar trace() const;

//     typename ei_traits<Derived>::Scalar minCoeff() const;
//     typename ei_traits<Derived>::Scalar maxCoeff() const;

//     typename ei_traits<Derived>::Scalar minCoeff(int* row, int* col = 0) const;
//     typename ei_traits<Derived>::Scalar maxCoeff(int* row, int* col = 0) const;

//     template<typename BinaryOp>
//     typename ei_result_of<BinaryOp(typename ei_traits<Derived>::Scalar)>::type
//     redux(const BinaryOp& func) const;

//     template<typename Visitor>
//     void visit(Visitor& func) const;


    const SparseCwise<Derived> cwise() const;
    SparseCwise<Derived> cwise();

//     inline const WithFormat<Derived> format(const IOFormat& fmt) const;

    /*
    bool all(void) const;
    bool any(void) const;

    const PartialRedux<Derived,Horizontal> rowwise() const;
    const PartialRedux<Derived,Vertical> colwise() const;

    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random(int rows, int cols);
    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random(int size);
    static const CwiseNullaryOp<ei_scalar_random_op<Scalar>,Derived> Random();

    template<typename ThenDerived,typename ElseDerived>
    const Select<Derived,ThenDerived,ElseDerived>
    select(const MatrixBase<ThenDerived>& thenMatrix,
           const MatrixBase<ElseDerived>& elseMatrix) const;

    template<typename ThenDerived>
    inline const Select<Derived,ThenDerived, NestByValue<typename ThenDerived::ConstantReturnType> >
    select(const MatrixBase<ThenDerived>& thenMatrix, typename ThenDerived::Scalar elseScalar) const;

    template<typename ElseDerived>
    inline const Select<Derived, NestByValue<typename ElseDerived::ConstantReturnType>, ElseDerived >
    select(typename ElseDerived::Scalar thenScalar, const MatrixBase<ElseDerived>& elseMatrix) const;

    template<int p> RealScalar lpNorm() const;
    */


//     template<typename OtherDerived>
//     Scalar dot(const MatrixBase<OtherDerived>& other) const
//     {
//       EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
//       EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
//       EIGEN_STATIC_ASSERT((ei_is_same_type<Scalar, typename OtherDerived::Scalar>::ret),
//         YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
//
//       ei_assert(derived().size() == other.size());
//       // short version, but the assembly looks more complicated because
//       // of the CwiseBinaryOp iterator complexity
//       // return res = (derived().cwise() * other.derived().conjugate()).sum();
//
//       // optimized, generic version
//       typename Derived::InnerIterator i(derived(),0);
//       typename OtherDerived::InnerIterator j(other.derived(),0);
//       Scalar res = 0;
//       while (i && j)
//       {
//         if (i.index()==j.index())
//         {
// //           std::cerr << i.value() << " * " << j.value() << "\n";
//           res += i.value() * ei_conj(j.value());
//           ++i; ++j;
//         }
//         else if (i.index()<j.index())
//           ++i;
//         else
//           ++j;
//       }
//       return res;
//     }
//
//     Scalar sum() const
//     {
//       Scalar res = 0;
//       for (typename Derived::InnerIterator iter(*this,0); iter; ++iter)
//       {
//         res += iter.value();
//       }
//       return res;
//     }

    #ifdef EIGEN_TAUCS_SUPPORT
    taucs_ccs_matrix asTaucsMatrix();
    #endif

    #ifdef EIGEN_CHOLMOD_SUPPORT
    cholmod_sparse asCholmodMatrix();
    #endif

    #ifdef EIGEN_SUPERLU_SUPPORT
    SluMatrix asSluMatrix();
    #endif

  protected:

    bool m_isRValue;
};

#endif // EIGEN_SPARSEMATRIXBASE_H

---

vcglib
Author(s): Christian Bersch
autogenerated on Fri Jan 11 09:18:00 2013