JMath/JMatrix2D.hh

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#ifndef __JMATRIX2D__
#define __JMATRIX2D__

#include <limits>
#include <cmath>
#include <ostream>
#include <iomanip>

#include "JIO/JSerialisable.hh"
#include "JLang/JEquals.hh"
#include "JLang/JManip.hh"
#include "JMath/JMath.hh"


/**
 * \author mdejong
 */

namespace JMATH {}
namespace JPP { using namespace JMATH; }

namespace JMATH {

  using JIO::JReader;
  using JIO::JWriter;
  using JLANG::JEquals;
  

  /**
   * 2 x 2 matrix
   */
  class JMatrix2D :
    public JMath  <JMatrix2D>,
    public JEquals<JMatrix2D>
  {
  public:

    using JMath<JMatrix2D>::mul;


    /**
     * Default constructor.
     */
    JMatrix2D() :
      a00(0.0), a01(0.0),
      a10(0.0), a11(0.0)
    {}


    /**
     * Contructor.
     *
     * \param   __a00   (0,0)
     * \param   __a01   (0,1)
     * \param   __a10   (1,0)
     * \param   __a11   (1,1)
     */
    JMatrix2D(const double __a00, const double __a01,
              const double __a10, const double __a11) :
      a00(__a00), a01(__a01),
      a10(__a10), a11(__a11)
    {}


    /**
     * Get reference to unique instance of this class object.
     *
     * \return          zero matrix
     */
    static const JMatrix2D& getInstance()
    {
      static JMatrix2D matrix;

      return matrix;
    }


    /**
     * Set to identity matrix.
     *
     * \return          this matrix
     */
    JMatrix2D& setIdentity()
    {
      a00 = 1.0;  a01 = 0.0;
      a10 = 0.0;  a11 = 1.0;

      return *this;
    }


    /**
     * Get reference to unique instance of this class object.
     *
     * \return          identity matrix
     */
    static const JMatrix2D& getIdentity()
    {
      static JMatrix2D matrix(JMatrix2D().setIdentity());

      return matrix;
    }


    /**
     * Set matrix.
     *
     * \param  A        matrix
     */
    void set(const JMatrix2D& A)
    {
      static_cast<JMatrix2D&>(*this) = A;
    }


    /**
     * Set matrix to the null matrix.
     *
     * \return          this matrix
     */
    JMatrix2D& reset()
    {
      *this = JMatrix2D();
      
      return *this;
    }

    
    /**
     * Transpose.
     *
     * \return          this matrix
     */
    JMatrix2D& transpose()
    {
      using std::swap;

      swap(a10, a01);
      
      return *this;
    }


    /**
     * Negate matrix.
     *
     * \return          -this matrix
     */
    JMatrix2D& negate()
    {
      a00 = -a00;  a01 = -a01;
      a10 = -a10;  a11 = -a11;

      return *this;
    }


    /**
     * Matrix addition.
     *
     * \param  A        matrix
     * \return          this matrix + A
     */
    JMatrix2D& add(const JMatrix2D& A)
    {
      a00 += A.a00;  a01 += A.a01;
      a10 += A.a10;  a11 += A.a11;

      return *this;
    }


    /**
     * Matrix subtraction.
     *
     * \param  A        matrix
     * \return          this matrix - A
     */
    JMatrix2D& sub(const JMatrix2D& A)
    {
      a00 -= A.a00;  a01 -= A.a01;
      a10 -= A.a10;  a11 -= A.a11;

      return *this;
    }


    /**
     * Scale matrix.
     *
     * \param  factor   factor
     * \return          this matrix * factor
     */
    JMatrix2D& mul(const double factor)
    {
      a00 *= factor; a01 *= factor;
      a10 *= factor; a11 *= factor;

      return *this;
    }


    /**
     * Scale matrix.
     *
     * \param  factor   factor
     * \return          this matrix / factor
     */
    JMatrix2D& div(const double factor)
    {
      a00 /= factor; a01 /= factor;
      a10 /= factor; a11 /= factor;

      return *this;
    }


    /**
     * Matrix multiplication.
     *
     * \param  A        matrix
     * \param  B        matrix
     * \return          this matrix
     */
    JMatrix2D& mul(const JMatrix2D& A, 
                   const JMatrix2D& B)
    {
      a00 = A.a00 * B.a00  +  A.a01 * B.a10;
      a01 = A.a00 * B.a01  +  A.a01 * B.a11;
      
      a10 = A.a10 * B.a00  +  A.a11 * B.a10;
      a11 = A.a10 * B.a01  +  A.a11 * B.a11;
      
      return *this;
    }
    

    /**
     * Equality.
     *
     * \param  A        matrix
     * \param  eps      numerical precision
     * \return          true if matrices identical; else false
     */
    bool equals(const JMatrix2D& A,
                const double     eps = std::numeric_limits<double>::min()) const
    {
      return (fabs(a00 - A.a00) <= eps  &&
              fabs(a01 - A.a01) <= eps  &&
              fabs(a10 - A.a10) <= eps  &&
              fabs(a11 - A.a11) <= eps);
    }


    /**
     * Test identity.
     *
     * \param  eps      numerical precision
     * \return          true if identity matrix; else false
     */
    bool isIdentity(const double eps = std::numeric_limits<double>::min()) const
    {
      return equals(getIdentity(), eps);
    }


    /**
     * Get determinant of matrix.
     *
     * \return         determinant of matrix
     */
    double getDeterminant() const
    {
      return a00 * a11 - a01 * a10;
    }


    /**
     * Transform.
     *
     * \param  __x      x value
     * \param  __y      y value
     */
    void transform(double& __x, double& __y) const
    {
      const double x = a00 * __x  +  a01 * __y;
      const double y = a10 * __x  +  a11 * __y;

      __x = x;
      __y = y;
    }


    /**
     * Read matrix from input.
     *
     * \param  in       reader
     * \param  matrix   matrix
     * \return          reader
     */
    friend inline JReader& operator>>(JReader& in, JMatrix2D& matrix)
    {
      in >> matrix.a00;  in >> matrix.a01;
      in >> matrix.a10;  in >> matrix.a11;

      return in;
    }


    /**
     * Write matrix to output.
     *
     * \param  out      writer
     * \param  matrix   matrix
     * \return          writer
     */
    friend inline JWriter& operator<<(JWriter& out, const JMatrix2D& matrix)
    {
      out << matrix.a00;  out << matrix.a01;
      out << matrix.a10;  out << matrix.a11;

      return out;
    }


    /**
     * Print ASCII formatted output.
     *
     * \param  out      output stream
     * \param  A        matrix
     * \return          output stream
     */
    friend inline std::ostream& operator<<(std::ostream& out, const JMatrix2D& A)
    {
      using namespace std;

      const JFormat format(out, getFormat<JMatrix2D>(JFormat_t(10, 3, std::ios::fixed | std::ios::showpos)));

      out << format << A.a00 << ' ' << format << A.a01 << endl;
      out << format << A.a10 << ' ' << format << A.a11 << endl;

      return out;
    }


    double a00, a01;
    double a10, a11;
  };
}

#endif