symmetric_matrix.h

/* Copyright (C) 2003-2005  Martin Förg
 
 * This library 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 2.1 of the License, or (at your option) any later version.
 * 
 * This library 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 for more details.
 * 
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 * Contact:
 *   martin.o.foerg@googlemail.com
 *
 */
 
#ifndef symmetric_matrix_h
#define symmetric_matrix_h
 
#include "types.h"
#include "indices.h"
#include "matrix.h"
#include "_memory.h"
 
namespace fmatvec {
 
  template <class AT> class Matrix<Symmetric,Ref,Ref,AT> {
 
    protected:
 
 
      Memory<AT> memory;
      AT *ele;
      int n{0};
      int lda{0};
 
      friend class Matrix<General,Ref,Ref,AT>;
 
      template <class Type, class Row, class Col> inline Matrix<Symmetric,Ref,Ref,AT>& copy(const Matrix<Type,Row,Col,AT> &A);
      inline Matrix<Symmetric,Ref,Ref,AT>& copy(const Matrix<Symmetric,Ref,Ref,AT> &A);
      inline Matrix<Symmetric,Ref,Ref,AT>& copy(const Matrix<SymmetricSparse,Ref,Ref,AT> &A);
 
      const AT* elePtr(int i, int j) const {
    return  j > i ? ele+i*lda+j : ele+i+j*lda; 
      }
 
      AT* elePtr(int i, int j) {
    return  j > i ? ele+i*lda+j : ele+i+j*lda; 
      }
 
 
    public:
 
      static constexpr bool isVector {false};
      using value_type = AT;
      using shape_type = Symmetric;
 
      explicit Matrix() : memory(), ele(nullptr) {
      }
 
      explicit Matrix(int n_, Noinit) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { }
      explicit Matrix(int n_, Init ini=INIT, const AT &a=AT()) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { init(a); }
      explicit Matrix(int n_, Eye ini, const AT &a=1) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { init(ini,a); }
      explicit Matrix(int m_, int n_, Noinit) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { }
      explicit Matrix(int m_, int n_, Init ini=INIT, const AT &a=AT()) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { init(a); }
      explicit Matrix(int m_, int n_, Eye ini, const AT &a=1) : memory(n_*n_), ele((AT*)memory.get()), n(n_), lda(n_) { init(ini,a); }
 
      Matrix(const Matrix<Symmetric,Ref,Ref,AT> &A) : memory(A.n*A.n), ele((AT*)memory.get()) , n(A.n), lda(n) {
        copy(A);
      }
 
      template<class Row>
      Matrix(const Matrix<Symmetric,Row,Row,AT> &A) : memory(A.size()*A.size()), ele((AT*)memory.get()), n(A.size()), lda(n) {
        copy(A);
      }
 
      template<class Type, class Row, class Col>
      explicit Matrix(const Matrix<Type,Row,Col,AT> &A) : memory(A.rows()*A.cols()), ele((AT*)memory.get()), n(A.cols()), lda(n) {
    FMATVEC_ASSERT(A.rows() == A.cols(), AT);
    copy(A);
      }
 
      explicit Matrix(int n_, AT* ele_) : memory(), ele(ele_), n(n_), lda(n_) { }
 
      ~Matrix() = default;
 
      Matrix<Symmetric,Ref,Ref,AT>& resize(int n_, Noinit) { 
    n = n_; lda = n;
    memory.resize(n*n);
    ele = (AT*)memory.get();
        return *this;
      }
 
      Matrix<Symmetric,Ref,Ref,AT>& resize(int n, Init ini=INIT, const AT &a=AT()) { return resize(n,Noinit()).init(a); }
 
      Matrix<Symmetric,Ref,Ref,AT>& resize(int n, Eye ini, const AT &a=1) { return resize(n,Noinit()).init(ini,a); }
 
      void resize(int n, int m) {
        if(n!=m)
          throw std::runtime_error("A symmetric matrix cannot have different dimensions for rows and columns.");
        resize(n);
      }
 
      inline Matrix<Symmetric,Ref,Ref,AT>& operator=(const Matrix<Symmetric,Ref,Ref,AT> &A) {
        FMATVEC_ASSERT(n == A.rows(), AT);
        return copy(A);
      }
 
      template<class Type, class Row, class Col>
      inline Matrix<Symmetric,Ref,Ref,AT>& operator=(const Matrix<Type,Row,Col,AT> &A) {
        FMATVEC_ASSERT(A.rows() == A.cols(), AT);
        FMATVEC_ASSERT(n == A.rows(), AT);
        return copy(A);
      }
 
      inline Matrix<Symmetric,Ref,Ref,AT>& operator&=(Matrix<Symmetric,Ref,Ref,AT> &A) {
        n=A.n;
        memory = A.memory;
        ele = A.ele;
        lda = A.lda;
        return *this;
      }
 
      template<class Type, class Row, class Col>
        inline Matrix<Symmetric,Ref,Ref,AT>& operator<<=(const Matrix<Type,Row,Col,AT> &A) {
          FMATVEC_ASSERT(A.rows() == A.cols(), AT);
          if(n!=A.rows()) resize(A.rows(),NONINIT);
          return copy(A);
        }
 
      AT& operator()(int i, int j) {
    FMATVEC_ASSERT(i>=0, AT);
    FMATVEC_ASSERT(j>=0, AT);
    FMATVEC_ASSERT(i<n, AT);
    FMATVEC_ASSERT(j<n, AT);
    return e(i,j);
      }
 
      const AT& operator()(int i, int j) const {
    FMATVEC_ASSERT(i>=0, AT);
    FMATVEC_ASSERT(j>=0, AT);
    FMATVEC_ASSERT(i<n, AT);
    FMATVEC_ASSERT(j<n, AT);
 
    return e(i,j);
      }
 
      AT& ei(int i, int j) {
    return ele[i+j*lda];
      }
 
      const AT& ei(int i, int j) const {
    return ele[i+j*lda];
      }
 
      AT& ej(int i, int j) {
    return ele[i*lda+j];
      }
 
      const AT& ej(int i, int j) const {
    return ele[i*lda+j];
      }
 
      AT& e(int i, int j) {
    return j > i ? ej(i,j) : ei(i,j);
      }
 
      const AT& e(int i, int j) const {
    return j > i ? ej(i,j) : ei(i,j);
      }
 
      AT* operator()() {return ele;}
 
      const AT* operator()() const {return ele;}
 
      int size() const {return n;}
 
      int rows() const {return n;}
 
      int cols() const {return n;}
 
      int ldim() const {return lda;}
 
      CBLAS_ORDER blasOrder() const {
        return CblasColMajor;
      }
 
      CBLAS_UPLO blasUplo() const {
        return  CblasLower;
      }
 
      inline Matrix<Symmetric,Ref,Ref,AT>& init(const AT &val); 
      inline Matrix<Symmetric,Ref,Ref,AT>& init(Init, const AT &a=AT()) { return init(a); }
      inline Matrix<Symmetric,Ref,Ref,AT>& init(Eye, const AT &val=1);
      inline Matrix<Symmetric,Ref,Ref,AT>& init(Noinit, const AT &a=AT()) { return *this; }
 
      inline const Matrix<General,Ref,Ref,AT> operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const;
 
      inline const Matrix<Symmetric,Ref,Ref,AT> operator()(const Range<Var,Var> &I) const;
 
      template<class Type, class Row, class Col> inline void set(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A);
      template<class Type, class Row, class Col> inline void add(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A);
 
      template<class Row> inline void set(const Range<Var,Var> &I, const Matrix<Symmetric,Row,Row,AT> &A);
      template<class Row> inline void add(const Range<Var,Var> &I, const Matrix<Symmetric,Row,Row,AT> &A);
 
      inline const Matrix<General,Ref,Ref,AT> operator()(const Indices &I, const Indices &J) const;
 
      inline const Matrix<Symmetric,Ref,Ref,AT> operator()(const Indices &I) const;
 
      inline void ref(Matrix<Symmetric,Ref,Ref,AT> &A, const Range<Var,Var> &I);
 
      explicit inline operator std::vector<std::vector<AT>>() const;
 
      explicit Matrix(const std::vector<std::vector<AT>> &m);
 
//      /*! \brief Cast to AT.
//       *
//       * \return The AT representation of the matrix
//       * */
//      explicit operator AT() const {
//        FMATVEC_ASSERT(n==1, AT);
//        return e(0);
//      }
//
//      /*! \brief AT Constructor.
//       * Constructs and initializes a matrix with a AT object.
//       * \param x The AT the matrix will be initialized with.
//       * */
//      explicit Matrix(const AT &x) : memory(1), ele((AT*)memory.get()), n(1), lda(1) { ele[0] = x; }
 
      inline int nonZeroElements() const;
  };
 
  template <class AT>
    inline Matrix<Symmetric,Ref,Ref,AT>&  Matrix<Symmetric,Ref,Ref,AT>::init(const AT &val) {
 
      for(int i=0; i<rows(); i++) 
        for(int j=i; j<cols(); j++) 
          ej(i,j) = val;
 
      return *this;
    }
 
  template <class AT>
    inline Matrix<Symmetric,Ref,Ref,AT>&  Matrix<Symmetric,Ref,Ref,AT>::init(Eye, const AT &val) {
 
      for(int i=0; i<size(); i++) {
        ej(i,i) = val;
        for(int j=i+1; j<size(); j++) {
          ej(i,j) = 0; 
        }
      }
      return *this;
    }
 
  template <class AT>
    inline const Matrix<General,Ref,Ref,AT> Matrix<Symmetric,Ref,Ref,AT>::operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const {
      FMATVEC_ASSERT(I.end()<n, AT);
      FMATVEC_ASSERT(J.end()<n, AT);
      Matrix<General,Ref,Ref,AT> A(I.size(),J.size(),NONINIT);
 
      for(int i=0; i<A.rows(); i++)
        for(int j=0; j<A.cols(); j++)
          A.e(i,j) = e(I.start()+i,J.start()+j);
 
      return A;
    }
 
  template <class AT> 
    inline const Matrix<Symmetric,Ref,Ref,AT> Matrix<Symmetric,Ref,Ref,AT>::operator()(const Range<Var,Var> &I) const {
      FMATVEC_ASSERT(I.end()<n, AT);
 
      Matrix<Symmetric,Ref,Ref,AT> A(I.size(),NONINIT);
 
      for(int i=0; i<A.rows(); i++)
        for(int j=i; j<A.cols(); j++)
          A.e(i,j) = e(I.start()+i,I.start()+j);
 
      return A;
    }
 
  template <class AT> template<class Type, class Row, class Col>
    inline void Matrix<Symmetric,Ref,Ref,AT>::set(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A) {
 
      if(I.start()>=J.start()) FMATVEC_ASSERT(I.start()>=J.end(), AT)
      else FMATVEC_ASSERT(J.start()>=I.end(), AT);
      FMATVEC_ASSERT(I.end()<rows(), AT);
      FMATVEC_ASSERT(J.end()<cols(), AT);
      FMATVEC_ASSERT(I.size()==A.rows(), AT);
      FMATVEC_ASSERT(J.size()==A.cols(), AT);
 
      for(int i=I.start(), ii=0; i<=I.end(); i++, ii++)
        for(int j=J.start(), jj=0; j<=J.end(); j++, jj++)
          e(i,j) = A.e(ii,jj);
    }
 
  template <class AT> template<class Type, class Row, class Col>
    inline void Matrix<Symmetric,Ref,Ref,AT>::add(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A) {
 
      if(I.start()>=J.start()) FMATVEC_ASSERT(I.start()>=J.end(), AT)
      else FMATVEC_ASSERT(J.start()>=I.end(), AT);
      FMATVEC_ASSERT(I.end()<rows(), AT);
      FMATVEC_ASSERT(J.end()<cols(), AT);
      FMATVEC_ASSERT(I.size()==A.rows(), AT);
      FMATVEC_ASSERT(J.size()==A.cols(), AT);
 
      for(int i=I.start(), ii=0; i<=I.end(); i++, ii++)
        for(int j=J.start(), jj=0; j<=J.end(); j++, jj++)
          e(i,j) += A.e(ii,jj);
    }
 
  template <class AT> template<class Row>
    inline void Matrix<Symmetric,Ref,Ref,AT>::set(const Range<Var,Var> &I, const Matrix<Symmetric,Row,Row,AT> &A) {
 
      FMATVEC_ASSERT(I.end()<size(), AT);
      FMATVEC_ASSERT(I.size()==A.size(), AT);
 
      for(int i=I.start(), ii=0; i<=I.end(); i++, ii++)
        for(int j=i, jj=ii; j<=I.end(); j++, jj++)
          e(i,j) = A.e(ii,jj);
    }
 
  template <class AT> template<class Row>
    inline void Matrix<Symmetric,Ref,Ref,AT>::add(const Range<Var,Var> &I, const Matrix<Symmetric,Row,Row,AT> &A) {
 
      FMATVEC_ASSERT(I.end()<size(), AT);
      FMATVEC_ASSERT(I.size()==A.size(), AT);
 
      for(int i=I.start(), ii=0; i<=I.end(); i++, ii++)
        for(int j=i, jj=ii; j<=I.end(); j++, jj++)
          e(i,j) += A.e(ii,jj);
    }
 
  template <class AT>
    inline const Matrix<General,Ref,Ref,AT> Matrix<Symmetric,Ref,Ref,AT>::operator()(const Indices &I, const Indices &J) const {
      FMATVEC_ASSERT(I.max()<size(), AT);
      FMATVEC_ASSERT(J.max()<size(), AT);
 
      Matrix<General,Ref,Ref,AT> A(I.size(),J.size(),NONINIT);
 
      for(int i=0; i<A.rows(); i++)
        for(int j=0; j<A.cols(); j++)
      A.e(i,j) = e(I[i],J[j]);
 
      return A;
    }
 
  template <class AT>
    inline const Matrix<Symmetric,Ref,Ref,AT> Matrix<Symmetric,Ref,Ref,AT>::operator()(const Indices &I) const {
      FMATVEC_ASSERT(I.max()<size(), AT);
 
      Matrix<Symmetric,Ref,Ref,AT> A(I.size(),NONINIT);
 
      for(int i=0; i<A.rows(); i++)
        for(int j=0; j<A.cols(); j++)
      A.e(i,j) = e(I[i],I[j]);
 
      return A;
    }
 
  template <class AT>
    inline void Matrix<Symmetric,Ref,Ref,AT>::ref(Matrix<Symmetric,Ref,Ref,AT> &A, const Range<Var,Var> &I) {
      FMATVEC_ASSERT(I.end()<A.size(), AT);
      n=I.size();
      memory = A.memory;
      ele = A.elePtr(I.start(),I.start());
      lda = A.lda;
    }
 
  template <class AT>
    inline Matrix<Symmetric,Ref,Ref,AT>::operator std::vector<std::vector<AT>>() const {
      std::vector<std::vector<AT>> ret(rows(),std::vector<AT>(cols()));
      for(int r=0; r<rows(); r++) {
        for(int c=r; c<cols(); c++) {
          ret[r][c]=ej(r,c);
      if(c>r)
        ret[c][r]=ej(r,c);
    }
      }
      return ret;
    }
 
  template <class AT>
    Matrix<Symmetric,Ref,Ref,AT>::Matrix(const std::vector<std::vector<AT>> &m) : memory(m.size()*m.size()), ele((AT*)memory.get()), n(static_cast<int>(m.size())), lda(static_cast<int>(m.size())) {
      for(int r=0; r<rows(); r++) {
        if(static_cast<int>(m[r].size())!=cols())
          throw std::runtime_error("The rows of the input have different length.");
        for(int c=r; c<cols(); c++) {
          ej(r,c)=m[r][c];
          if(c>r && abs(m[r][c]-m[c][r])>abs(m[r][c]*1e-13+1e-13))
            throw std::runtime_error("The input is not symmetric.");
        }
      }
    }
 
  template <class AT>
    inline int Matrix<Symmetric,Ref,Ref,AT>::nonZeroElements() const {
      int k = n;
      for (int j = 0; j < n; j++) {
        for (int i = j+1; i < n; i++) {
          if (fabs(e(i, j)) > 1e-16) {
            k+=2;
          }
        }
      }
      return k;
    }
 
 
  template <class AT>
    inline Matrix<Symmetric,Ref,Ref,AT>& Matrix<Symmetric,Ref,Ref,AT>::copy(const Matrix<Symmetric,Ref,Ref,AT> &A) {
      for(int i=0; i<n; i++) 
        for(int j=i; j<n; j++) 
          ej(i,j) = A.ej(i,j);
      return *this;
    }
 
  template <class AT> template <class Type, class Row, class Col>
    inline Matrix<Symmetric,Ref,Ref,AT>& Matrix<Symmetric,Ref,Ref,AT>::copy(const Matrix<Type,Row,Col,AT> &A) {
      for(int i=0; i<n; i++) 
        for(int j=i; j<n; j++) 
          ej(i,j) = A.e(i,j);
      return *this;
    }
 
  template <class AT>
    inline Matrix<Symmetric,Ref,Ref,AT>& Matrix<Symmetric,Ref,Ref,AT>::copy(const Matrix<SymmetricSparse,Ref,Ref,AT> &A) {
      for(int i=0; i<n; i++) {
    for(int j=i; j<n; j++)
      ej(i,j) = 0;
        for(int j=A.Ip()[i]; j<A.Ip()[i+1]; j++)
          ej(i,A.Jp()[j]) = A()[j];
      }
      return *this;
  }
 
 
}
 
#endif