var_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 var_symmetric_matrix_h
#define var_symmetric_matrix_h
 
#include "types.h"
#include "range.h"
#include "indices.h"
 
namespace fmatvec {
 
  template <class AT> class Matrix<Symmetric,Var,Var,AT> {
 
    protected:
 
 
      int M{0};
 
      AT *ele;
 
      template <class Type, class Row, class Col> inline Matrix<Symmetric,Var,Var,AT>& copy(const Matrix<Type,Row,Col,AT> &A);
      template <class Row> inline Matrix<Symmetric,Var,Var,AT>& copy(const Matrix<Symmetric,Row,Row,AT> &A);
 
 
    public:
      static constexpr bool isVector {false};
      using value_type = AT;
      using shape_type = Symmetric;
 
      explicit Matrix() :  ele(nullptr) {
      }
 
      explicit Matrix(int m, Noinit) : M(m), ele(new AT[M*M]) { }
      explicit Matrix(int m, Init ini=INIT, const AT &a=AT()) : M(m), ele(new AT[M*M]) { init(a); }
      explicit Matrix(int m, Eye ini, const AT &a=1) : M(m), ele(new AT[M*M]) { init(ini,a); }
      explicit Matrix(int m, int n, Noinit) : M(m), ele(new AT[M*M]) { }
      explicit Matrix(int m, int n, Init ini=INIT, const AT &a=AT()) : M(m), ele(new AT[M*M]) { init(a); }
      explicit Matrix(int m, int n, Eye ini, const AT &a=1) : M(m), ele(new AT[M*M]) { init(ini,a); }
 
      // move
      Matrix(Matrix<Symmetric,Var,Var,AT> &&src)  noexcept {
        M=src.M;
        src.M=0;
        ele=src.ele;
        src.ele=nullptr;
      }
      Matrix<Symmetric,Var,Var,AT>& operator=(Matrix<Symmetric,Var,Var,AT> &&src)  noexcept {
        FMATVEC_ASSERT(M == src.M, AT);
        src.M=0;
        delete[]ele;
        ele=src.ele;
        src.ele=nullptr;
        return *this;
      }
 
      Matrix(const Matrix<Symmetric,Var,Var,AT> &A) : M(A.M), ele(new AT[M*M])  {
    copy(A);
      }
 
      template<class Row>
      Matrix(const Matrix<Symmetric,Row,Row,AT> &A) : M(A.size()), ele(new AT[M*M])  {
    copy(A);
      }
 
      template<class Type, class Row, class Col>
      explicit Matrix(const Matrix<Type,Row,Col,AT> &A) : M(A.rows()), ele(new AT[M*M])  {
    FMATVEC_ASSERT(A.rows() == A.cols(), AT); 
    copy(A);
      }
 
      ~Matrix() {
    delete[] ele;
      }
 
      Matrix<Symmetric,Var,Var,AT>& resize(int m, Noinit) { 
        delete[] ele;
        M = m;
        ele = new AT[M*M];
        return *this;
      }
 
      Matrix<Symmetric,Var,Var,AT>& resize(int m, Init ini=INIT, const AT &a=AT()) { return resize(m,Noinit()).init(a); }
 
      Matrix<Symmetric,Var,Var,AT>& resize(int m, Eye ini, const AT &a=1) { return resize(m,Noinit()).init(ini,a); }
 
      inline Matrix<Symmetric,Var,Var,AT>& operator=(const Matrix<Symmetric,Var,Var,AT> &A) {
        FMATVEC_ASSERT(M == A.M, AT);
        return copy(A);
      }
 
      template<class Type, class Row, class Col>
      inline Matrix<Symmetric,Var,Var,AT>& operator=(const Matrix<Type,Row,Col,AT> &A) {
        FMATVEC_ASSERT(A.rows() == A.cols(), AT);
        FMATVEC_ASSERT(M == A.rows(), AT);
        return copy(A);
      }
 
      template<class Type, class Row, class Col>
      inline Matrix<Symmetric,Var,Var,AT>& operator<<=(const Matrix<Type,Row,Col,AT> &A) {
        FMATVEC_ASSERT(A.rows() == A.cols(), AT);
        if(M!=A.rows()) resize(A.rows(),NONINIT);
        return copy(A);
      }
      // move
      inline Matrix<Symmetric,Var,Var,AT>& operator<<=(Matrix<Symmetric,Var,Var,AT> &&src) {
        FMATVEC_ASSERT(src.rows() == src.cols(), AT);
        M=src.M;
        src.M=0;
        delete[]ele;
        ele=src.ele;
        src.ele=nullptr;
        return *this;
      }
 
      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);
      }
 
      AT& operator()(int i, int j) {
    FMATVEC_ASSERT(i>=0, AT);
    FMATVEC_ASSERT(j>=0, AT);
    FMATVEC_ASSERT(i<M, AT);
    FMATVEC_ASSERT(j<M, 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<M, AT);
    FMATVEC_ASSERT(j<M, AT);
 
    return e(i,j);
      }
 
      AT& ei(int i, int j) {
    return ele[i*M+j];
      }
 
      const AT& ei(int i, int j) const {
    return ele[i*M+j];
      }
 
      AT& ej(int i, int j) {
    return ele[i+j*M];
      }
 
      const AT& ej(int i, int j) const {
    return ele[i+j*M];
      }
 
       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;}
 
      constexpr int size() const {return M;}
 
      constexpr int rows() const {return M;}
 
      constexpr int cols() const {return M;}
 
      int ldim() const {return M;}
 
      CBLAS_ORDER blasOrder() const {
        return CblasRowMajor;
      }
 
      CBLAS_UPLO blasUplo() const {
        return CblasLower;
      }
 
      inline Matrix<Symmetric,Var,Var,AT>& init(const AT &val=AT()); 
      inline Matrix<Symmetric,Var,Var,AT>& init(Init, const AT &a=AT()) { return init(a); }
      inline Matrix<Symmetric,Var,Var,AT>& init(Eye eye, const AT &val=1);
      inline Matrix<Symmetric,Var,Var,AT>& init(Noinit, const AT &a=AT()) { return *this; }
 
      inline const Matrix<General,Var,Var,AT> operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const;
 
      inline const Matrix<Symmetric,Var,Var,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,Var,Var,AT> operator()(const Indices &I, const Indices &J) const;
 
      inline const Matrix<Symmetric,Var,Var,AT> operator()(const Indices &I) const;
 
      explicit inline operator std::vector<std::vector<AT>>() const;
 
      explicit Matrix(const std::vector<std::vector<AT>> &m);
 
      inline int nonZeroElements() const;
  };
 
  template <class AT>
    inline Matrix<Symmetric,Var,Var,AT>&  Matrix<Symmetric,Var,Var,AT>::init(const AT &val) {
 
      for(int i=0; i<M; i++) 
        for(int j=i; j<M; j++) 
          ej(i,j) = val;
 
      return *this;
    }
 
  template <class AT>
    inline Matrix<Symmetric,Var,Var,AT>&  Matrix<Symmetric,Var,Var,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,Var,Var,AT> Matrix<Symmetric,Var,Var,AT>::operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const {
      FMATVEC_ASSERT(I.end()<M, AT);
      FMATVEC_ASSERT(J.end()<M, AT);
      Matrix<General,Var,Var,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,Var,Var,AT> Matrix<Symmetric,Var,Var,AT>::operator()(const Range<Var,Var> &I) const {
      FMATVEC_ASSERT(I.end()<M, AT);
 
      Matrix<Symmetric,Var,Var,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,Var,Var,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,Var,Var,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,Var,Var,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,Var,Var,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,Var,Var,AT> Matrix<Symmetric,Var,Var,AT>::operator()(const Indices &I, const Indices &J) const {
      FMATVEC_ASSERT(I.max()<size(), AT);
      FMATVEC_ASSERT(J.max()<size(), AT);
 
      Matrix<General,Var,Var,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,Var,Var,AT> Matrix<Symmetric,Var,Var,AT>::operator()(const Indices &I) const {
      FMATVEC_ASSERT(I.max()<size(), AT);
 
      Matrix<Symmetric,Var,Var,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 Matrix<Symmetric,Var,Var,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>
    inline Matrix<Symmetric,Var,Var,AT>::Matrix(const std::vector<std::vector<AT>> &m) : M(static_cast<int>(m.size())), ele(new AT[M*M]) {
      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> template <class Type, class Row, class Col>
    inline Matrix<Symmetric,Var,Var,AT>& Matrix<Symmetric,Var,Var,AT>::copy(const Matrix<Type,Row,Col,AT> &A) {
      for(int i=0; i<M; i++) 
        for(int j=i; j<M; j++) 
          ej(i,j) = A.e(i,j);
      return *this;
    }
 
  template <class AT> template <class Row>
    inline Matrix<Symmetric,Var,Var,AT>& Matrix<Symmetric,Var,Var,AT>::copy(const Matrix<Symmetric,Row,Row,AT> &A) {
      for(int i=0; i<M; i++) 
        for(int j=i; j<M; j++) 
          ej(i,j) = A.ej(i,j);
      return *this;
    }
 
  template <class AT>
    inline int Matrix<Symmetric,Var,Var,AT>::nonZeroElements() const {
      int k = M;
      for (int j = 0; j < M; j++) {
        for (int i = j+1; i < M; i++) {
          if (fabs(e(i, j)) > 1e-16) {
            k+=2;
          }
        }
      }
      return k;
    }
 
 
}
 
#endif