fixed_general_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 fixed_general_matrix_h
#define fixed_general_matrix_h
 
#include "types.h"
#include "range.h"
#include <vector>
#include <cstdlib>
#include <stdexcept>
 
namespace fmatvec {
 
  template <int M, int N, class AT> class Matrix<General,Fixed<M>,Fixed<N>,AT> {
 
    public:
      static constexpr bool isVector {false};
 
      using iterator = AT *;
      using const_iterator = const AT *;
      using value_type = AT;
      using shape_type = General;
 
 
    protected:
 
      AT ele[M][N];
 
      template <class Type, class Row, class Col> inline Matrix<General,Fixed<M>,Fixed<N>,AT>& copy(const Matrix<Type,Row,Col,AT> &A);
      template<class Row> inline Matrix<General,Fixed<M>,Fixed<N>,AT>& copy(const Matrix<Symmetric,Row,Row,AT> &A);
 
 
    public:
 
// Works with -std=gnu++0x only
//      template<class Ini=All<AT>>
//      Matrix(Ini ini=All<AT>()) {
//        init(ini);
//      }
//      template<class Ini=All<AT>>
//      Matrix(int m_, int n_, Ini ini=All<AT>()) {
//        init(ini);
//      }
 
      explicit Matrix(Noinit) { }
      explicit Matrix(Init ini=INIT, const AT &a=AT()) { init(a); }
      explicit Matrix(Eye ini, const AT &a=1) { init(ini,a); }
      explicit Matrix(int m, int n, Noinit) { FMATVEC_ASSERT(m==M && n==N, AT); }
      explicit Matrix(int m, int n, Init ini=INIT, const AT &a=AT()) { FMATVEC_ASSERT(m==M && n==N, AT); init(a); }
      explicit Matrix(int m, int n, Eye ini, const AT &a=1) { FMATVEC_ASSERT(m==M && n==N, AT); init(ini,a); }
 
      Matrix(const Matrix<General,Fixed<M>,Fixed<N>,AT> &A) = default;
 
      template<class Row, class Col>
      Matrix(const Matrix<General,Row,Col,AT> &A) {
    FMATVEC_ASSERT(A.rows() == M, AT); 
    FMATVEC_ASSERT(A.cols() == N, AT);
    copy(A);
      }
 
      template<class Type, class Row, class Col>
      explicit Matrix(const Matrix<Type,Row,Col,AT> &A) {
    FMATVEC_ASSERT(A.rows() == M, AT); 
    FMATVEC_ASSERT(A.cols() == N, AT);
    copy(A);
      }
 
      Matrix(const std::string &strs);
      Matrix(const char *strs);
 
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& operator=(const Matrix<General,Fixed<M>,Fixed<N>,AT> &A) = default;
 
      template <class Type, class Row, class Col>
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& operator=(const Matrix<Type,Row,Col,AT> &A) {
        FMATVEC_ASSERT(A.rows() == M, AT); 
        FMATVEC_ASSERT(A.cols() == N, AT);
        return copy(A);
      }
 
      template<class Type, class Row, class Col>
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& operator<<=(const Matrix<Type,Row,Col,AT> &A) { return operator=(A); }
 
      template <class AT2>
      operator Matrix<General,Fixed<M>,Fixed<N>,AT2>() const {
        Matrix<General,Fixed<M>,Fixed<N>,AT2> ret;
        for(size_t r=0; r<M; ++r)
          for(size_t c=0; c<N; ++c)
            ret(r,c) = (*this)(r,c);
        return ret;
      }
 
      iterator begin() { return &ele[0][0]; }
      iterator end() { return &ele[M-1][N]; }
      const_iterator begin() const { return &ele[0][0]; }
      const_iterator end() const { return &ele[M-1][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<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<M, AT);
    FMATVEC_ASSERT(j<N, AT);
 
    return e(i,j);
      }
 
      AT& e(int i, int j) {
    return ele[i][j];
      }
 
      const AT& e(int i, int j) const {
    return ele[i][j];
      }
 
      AT* operator()() {return &(ele[0][0]);}
 
      const AT* operator()() const {return &(ele[0][0]);}
 
      constexpr int rows() const {return M;}
 
      constexpr int cols() const {return N;}
 
      int ldim() const {return N;}
 
      void resize(int m, int n) {
        if(m!=M || n!=N)
          throw std::runtime_error("A fixed matrix cannot be resized.");
      }
 
      CBLAS_TRANSPOSE blasTrans() const {
        return CblasNoTrans;
      }
 
      CBLAS_ORDER blasOrder() const {
        return CblasRowMajor;
      }
 
      inline const Matrix<General,Var,Var,AT> operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const;
      
      template <int M1, int M2, int N1, int N2>
      inline const Matrix<General,Fixed<M2-M1+1>,Fixed<N2-N1+1>,AT> operator()(const Range<Fixed<M1>,Fixed<M2>> &I, const Range<Fixed<N1>,Fixed<N2>> &J) const;
      template <int M1, int M2>
      inline const Matrix<General,Fixed<M2-M1+1>,Var,AT> operator()(const Range<Fixed<M1>,Fixed<M2>> &I, const Range<Var,Var > &J) const;
 
      template <int N1, int N2>
      inline const Matrix<General,Var,Fixed<N2-N1+1>,AT> operator()(const Range<Var,Var> &I, const Range<Fixed<N1>,Fixed<N2>> &J) const;
 
      inline const RowVector<Fixed<N>,AT> row(int i) const;
      inline const Vector<Fixed<M>,AT> col(int j) const;
 
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& init(const AT &val=AT()); 
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& init(Init, const AT &a=AT()) { return init(a); }
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& init(Eye, const AT &val=1);
      inline Matrix<General,Fixed<M>,Fixed<N>,AT>& init(Noinit, const AT &a=AT()) { return *this; }
 
      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(M==1, AT);
//        FMATVEC_ASSERT(N==1, AT);
//        return ele[0][0];
//      }
//
//      /*! \brief AT Constructor.
//       * Constructs and initializes a matrix with a AT object.
//       * \param v The AT the matrix will be initialized with.
//       * */
//      explicit Matrix(const AT &x) {
//        FMATVEC_ASSERT(M==1, AT);
//        FMATVEC_ASSERT(N==1, AT);
//        ele[0][0] = x;
//      }
 
      inline const Matrix<General,Fixed<N>,Fixed<M>,AT> T() const;
 
      template<class Row> inline void set(int j, const Vector<Row,AT> &x);
 
      template<class Col> inline void set(int i, const RowVector<Col,AT> &x);
 
      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 Row> inline void add(int j, const Vector<Row,AT> &x);
 
      template<class Col> inline void add(int i, const RowVector<Col,AT> &x);
 
      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 <int M, int N, class AT> 
    Matrix<General,Fixed<M>,Fixed<N>,AT>::Matrix(const std::string &strs) {
      std::istringstream iss(strs);
      iss>>*this;
 
      // check end of stream
      iss>>std::ws;
      if(!iss.eof())
        throw std::runtime_error("Input not fully read.");
    }
  template <int M, int N, class AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::Matrix(const char *strs) :
    Matrix<General,Fixed<M>,Fixed<N>,AT>::Matrix(std::string(strs)) {}
 
  template <int M, int N, class AT>
    inline Matrix<General,Fixed<M>,Fixed<N>,AT>& Matrix<General,Fixed<M>,Fixed<N>,AT>::init(const AT &val) {
       for(int i=0; i<M; i++) 
        for(int j=0; j<N; j++) 
          e(i,j) = val;
      return *this;
    }
 
  template <int M, int N, class AT>
    inline Matrix<General,Fixed<M>,Fixed<N>,AT>& Matrix<General,Fixed<M>,Fixed<N>,AT>::init(Eye, const AT &val) {
      for(int i=0; i<M; i++)
        for(int j=0; j<N; j++)
          e(i,j) = (i==j) ? val : 0;
      return *this;
    }
 
  template <int M, int N, class AT> 
    inline const Matrix<General,Var,Var,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::operator()(const Range<Var,Var> &I, const Range<Var,Var> &J) const {
      FMATVEC_ASSERT(I.end()<M, AT);
      FMATVEC_ASSERT(J.end()<N, 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 <int M, int N, class AT> template <int M1, int M2, int N1, int N2>
    inline const Matrix<General,Fixed<M2-M1+1>,Fixed<N2-N1+1>,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::operator()(const Range<Fixed<M1>,Fixed<M2>> &I, const Range<Fixed<N1>,Fixed<N2>> &J) const {
      FMATVEC_ASSERT(M2<M, AT);
      FMATVEC_ASSERT(N2<N, AT);
      Matrix<General,Fixed<M2-M1+1>,Fixed<N2-N1+1>,AT> A(NONINIT);
 
      for(int i=0; i<A.rows(); i++) 
        for(int j=0; j<A.cols(); j++)
          A.e(i,j) = e(M1+i,J.start()+j);
 
      return A;
    }
 
 template <int M, int N, class AT> template <int M1, int M2>
    inline const Matrix<General,Fixed<M2-M1+1>,Var,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::operator()(const Range<Fixed<M1>,Fixed<M2>> &I, const Range<Var,Var> &J) const {
      FMATVEC_ASSERT(M2<M, AT);
      FMATVEC_ASSERT(J.end()<N, AT);
      Matrix<General,Fixed<M2-M1+1>,Var,AT> A(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 <int M, int N, class AT> template <int N1, int N2>
    inline const Matrix<General,Var,Fixed<N2-N1+1>,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::operator()(const Range<Var,Var> &I, const Range<Fixed<N1>,Fixed<N2>> &J) const {
      FMATVEC_ASSERT(I.end()<M, AT);
      FMATVEC_ASSERT(N2<N, AT);
      Matrix<General,Var,Fixed<N2-N1+1>,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.start()+i,J.start()+j);
 
      return A;
    }
 
  template <int M, int N, class AT>
    inline const RowVector<Fixed<N>,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::row(int i) const {
 
      FMATVEC_ASSERT(i>=0, AT);
      FMATVEC_ASSERT(i<M, AT);
 
      RowVector<Fixed<N>,AT> x(NONINIT);
 
      for(int j=0; j<N; j++)
        x.e(j) = e(i,j);
 
      return x;
    }
 
  template <int M, int N, class AT>
    inline const Vector<Fixed<M>,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::col(int j) const {
 
      FMATVEC_ASSERT(j>=0, AT);
      FMATVEC_ASSERT(j<N, AT);
 
      Vector<Fixed<M>,AT> x(NONINIT);
 
      for(int i=0; i<M; i++)
        x.e(i) = e(i,j);
 
      return x;
    }
 
  template <int M, int N, class AT>
    inline const Matrix<General,Fixed<N>,Fixed<M>,AT> Matrix<General,Fixed<M>,Fixed<N>,AT>::T() const {
      Matrix<General,Fixed<N>,Fixed<M>,AT> A(NONINIT);
      for(int i=0; i<N; i++)
        for(int j=0; j<M; j++)
          A.e(i,j) = e(j,i);
      return A;
    }
 
  template <int M, int N, class AT> template <class Row>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::set(int j, const Vector<Row,AT> &x) {
      FMATVEC_ASSERT(j<cols(), AT);
      FMATVEC_ASSERT(rows()==x.size(), AT);
      for(int i=0; i<rows(); i++)
        e(i,j) = x.e(i);
    }
 
  template <int M, int N, class AT> template <class Col>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::set(int i, const RowVector<Col,AT> &x) {
      FMATVEC_ASSERT(i<rows(), AT);
      FMATVEC_ASSERT(cols()==x.size(), AT);
      for(int j=0; j<cols(); j++)
        e(i,j) = x.e(j);
    }
 
  template <int M, int N, class AT> template<class Type, class Row, class Col>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::set(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A) {
 
      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 <int M, int N, class AT> template <class Row>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::add(int j, const Vector<Row,AT> &x) {
      FMATVEC_ASSERT(j<cols(), AT);
      FMATVEC_ASSERT(rows()==x.size(), AT);
      for(int i=0; i<rows(); i++)
        e(i,j) += x.e(i);
    }
 
  template <int M, int N, class AT> template <class Col>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::add(int i, const RowVector<Col,AT> &x) {
      FMATVEC_ASSERT(i<rows(), AT);
      FMATVEC_ASSERT(cols()==x.size(), AT);
      for(int j=0; j<cols(); j++)
        e(i,j) += x.e(j);
    }
 
  template <int M, int N, class AT> template<class Type, class Row, class Col>
    inline void Matrix<General,Fixed<M>,Fixed<N>,AT>::add(const Range<Var,Var> &I, const Range<Var,Var> &J, const Matrix<Type,Row,Col,AT> &A) {
 
      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 <int M, int N, class AT>
    inline Matrix<General,Fixed<M>,Fixed<N>,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=0; c<cols(); c++)
          ret[r][c]=e(r,c);
      }
      return ret;
    }
 
  template <int M, int N, class AT>
    inline Matrix<General,Fixed<M>,Fixed<N>,AT>::Matrix(const std::vector<std::vector<AT>> &m) {
      if(m.size() != M)
        throw std::runtime_error("The input has "+std::to_string(m.size())+" rows but "+std::to_string(M)+" rows are required.");
      if((m.empty()?0:m[0].size()) != N)
        throw std::runtime_error("The input has "+std::to_string((m.empty()?0:m[0].size()))+" columne but "+std::to_string(N)+" columns are required.");
      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=0; c<cols(); c++)
          e(r,c)=m[r][c];
      }
    }
 
 
  template <int M, int N, class AT> template <class Type, class Row, class Col>
    inline Matrix<General,Fixed<M>,Fixed<N>,AT>& Matrix<General,Fixed<M>,Fixed<N>,AT>::copy(const Matrix<Type,Row,Col,AT> &A) {
      for(int i=0; i<M; i++) 
        for(int j=0; j<N; j++)
          e(i,j) = A.e(i,j);
      return *this;
    }
 
  template<int M, int N, class AT> template<class Row>
    inline Matrix<General,Fixed<M>,Fixed<N>,AT>& Matrix<General,Fixed<M>,Fixed<N>,AT>::copy(const Matrix<Symmetric,Row,Row,AT> &A) {
      for(int i=0; i<A.size(); i++) {
        e(i,i) = A.ej(i,i);
        for(int j=i+1; j<A.size(); j++)
          e(i,j) = e(j,i) = A.ej(i,j);
      }
      return *this;
    }
 
 
  template<int M, class AT>
  class Matrix<Rotation,Fixed<M>,Fixed<M>,AT> : public Matrix<General,Fixed<M>,Fixed<M>,AT> {
    public:
      using value_type = AT;
      using shape_type = Rotation;
      // Constructors are not inherited. Hence we must redefine all ctors here.
 
      Matrix(Noinit ini) { }
      Matrix(Init ini=INIT, const AT &a=0) { this->init(a); }
      Matrix(Eye ini, const AT &a=1) { this->init(ini,a); }
 
      Matrix(int m, int n) { }
      Matrix(int m, int n, Noinit ini) { }
      Matrix(int m, int n, Init ini, const AT &a=0) { this->init(a); }
      Matrix(int m, int n, Eye ini, const AT &a=1) { this->init(ini,a); }
 
      Matrix(const Matrix<Rotation,Fixed<M>,Fixed<M>,AT> &A) = default;
 
      explicit Matrix(const Matrix<General,Fixed<M>,Fixed<M>,AT> &A) : Matrix<General,Fixed<M>,Fixed<M>,AT>(A) { }
 
      template<class Row>
      explicit Matrix(const Matrix<Symmetric,Row,Row,AT> &A) : Matrix<General,Fixed<M>,Fixed<M>,AT>(A) { }
 
      template<class Type, class Row, class Col>
      explicit Matrix(const Matrix<Type,Row,Col,AT> &A) : Matrix<General,Fixed<M>,Fixed<M>,AT>(A) { }
 
      explicit Matrix(const std::vector<std::vector<AT>> &m) : Matrix<General,Fixed<M>,Fixed<M>,AT>(m) { }
 
      inline const Matrix<Rotation,Fixed<M>,Fixed<M>,AT> T() const;
 
      using Matrix<General,Fixed<M>,Fixed<M>,AT>::e;
 
      // TODO: we should add some overloaded member functions here which capitalize the special
      // properties of rotation matrices, link "RotMat inv() { return trans(*this); }"
  };
 
  template <int M, class AT>
    inline const Matrix<Rotation,Fixed<M>,Fixed<M>,AT> Matrix<Rotation,Fixed<M>,Fixed<M>,AT>::T() const {
      Matrix<Rotation,Fixed<M>,Fixed<M>,AT> A(NONINIT);
      for(int i=0; i<M; i++)
        for(int j=0; j<M; j++)
          A.e(i,j) = e(j,i);
      return A;
    }
 
}
 
#endif