matrix.h

矩阵类

    */
    bool InsertSubMatrix( const Matrix &src, const unsigned dst_row, const unsigned dst_col );

    /**
    \brief  Zero the entire matrix.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.Zero();          // Set A back to zeros.
    result = A.PrintStdout();   // Print Matrix A. A = [0 0 0; 0 0 0; 0 0 0].
    \endcode
    
    \return true if successful, false otherwise.  
    */
    bool Zero();

    /**
    \brief  Zero all elements in a specified column.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.ZeroColumn(1);   // Set the second column of A back to zeros.
    result = A.PrintStdout();   // Print Matrix A. A = [1 0 3; 4 0 6; 7 0 9].
    \endcode
       
    \return true if successful, false otherwise.    
    */
    bool ZeroColumn( const unsigned col );

    /**
    \brief  Zero all elements in a specified row.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.ZeroRow(1);      // Set the second row of A back to zeros.
    result = A.PrintStdout();   // Print Matrix A. A = [1 2 3; 0 0 0; 7 8 9].
    \endcode
       
    \return true if successful, false otherwise.    
    */
    bool ZeroRow( const unsigned row );

    /**
    \brief  Fill the matrix with the given value.

    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.Fill(7);         // Fill the matrix with 7.0.
    result = A.PrintStdout();   // Print Matrix A. A = [7 7 7; 7 7 7; 7 7 7].
    \endcode

    \return true if successful, false otherwise.    
    */
    bool Fill( const double value );

    /**
    \brief  Fill the matrix column with the given value.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.FillColumn(1,7); // Fill the second column with 7.0.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 7 3; 4 7 6; 7 7 9].
    \endcode
    
    \return true if successful, false otherwise.    
    */
    bool FillColumn( const unsigned col, const double value );

    /**
    \brief  Fills the matrix row with the given value.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.FillRow(1,7);    // Fill the second row with 7.0.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 2 3; 7 7 7; 7 8 9].
    \endcode
    
    \return true if successful, false otherwise.    
    */
    bool FillRow( const unsigned row, const double value );

    /**
    \brief  Reverse the order of elements of a column.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.FlipColumn(1);   // Flip the second column.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 8 3; 4 5 6; 7 2 9].
    \endcode
       
    \return true if successful, false otherwise.    
    */
    bool FlipColumn( const unsigned col );

    /**
    \brief  Reverse the order of elements of a row.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.FlipRow(1);      // Flip the second row.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 2 3; 6 5 4; 7 8 9].
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool FlipRow( const unsigned row );

    /**
    \brief  Set the matrix to identity using the current dimensions.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();   // Print Matrix A.
    result = A.Identity();      // Set A to identity.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 0 0; 0 1 0; 0 0 1].
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Identity();

    /**   
    \brief  Set the matrix to identity using the specified dimension (nxn).
    
    \code
    Matrix A;
    bool result;
    result = A.Identity(3);     // Set A to identity, 3x3.
    cout << endl;
    result = A.PrintStdout();   // Print Matrix A. A = [1 0 0; 0 1 0; 0 0 1].
    \endcode    
    
    \return true if successful, false otherwise.        
    */
    bool Identity(const unsigned dimension);



  public: // Inplace Operations

    /**
    \brief  Transpose the matrix as an inplace operation.
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();         // Print Matrix A.
    result = A.Inplace_Transpose();   // Make A = transpose(A).
    cout << endl;
    result = A.PrintStdout();         // Print Matrix A. A = [1 4 7; 2 5 8; 3 6 9].
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_Transpose();
    bool Inplace_transpose() { return this->Inplace_Transpose(); }

    /**
    \brief  Round the matrix elements to the specified presision. \n
    e.g. precision = 0    1.8    -> 2     (default)\n
    e.g. precision = 1,   1.45   -> 1.5   \n
    e.g. precision = 2    1.456  -> 1.46  \n
    e.g. precision = 3,   1.4566 -> 1.457 \n
    *
    \code
    Matrix A;
    A = "[1.09 2.08 3.07; 4.06 5.05 6.04; 7.03 8.02 9.01]";
    bool result;
    result = A.PrintStdout();     // Print Matrix A.
    result = A.Inplace_Round(1);  // Make A = round(A) to the 1st decimal place.
    cout << endl;
    result = A.PrintStdout();     // Print Matrix A. A = "[1.1 2.1 3.1; 4.1 5.1 6.0; 7.0 8.0 9.0]";
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_Round( const unsigned precision = 0 );
    bool Inplace_round( const unsigned precision = 0 ) { return this->Inplace_Round( precision ); }

    /**
    \brief  Round the matrix elements to the nearest integers towards minus infinity.
    
    \code
    Matrix A;
    A = "[1.9 2.8 3.7; -4.6 -5.5 -6.4; 7.3 8.2 9.1]";
    bool result;
    result = A.PrintStdout();     // Print Matrix A.
    result = A.Inplace_Floor();   // Make A = floor(A).
    cout << endl;
    result = A.PrintStdout();     // Print Matrix A. A = "[1 2 3; -5 -6 -7; 7 8 9]";
    \endcode    
       
    \return true if successful, false otherwise.    
    */
    bool Inplace_Floor();
    bool Inplace_floor() { return this->Inplace_Floor(); }

    /**
    \brief  Round the matrix elements to the nearest integers towards infinity.
    
    \code
    Matrix A;
    A = "[1.9 2.8 3.7; -4.6 -5.5 -6.4; 7.3 8.2 9.1]";
    bool result;
    result = A.PrintStdout();     // Print Matrix A.
    result = A.Inplace_Ceil();    // Make A = ceil(A).
    cout << endl;
    result = A.PrintStdout();     // Print Matrix A. A = "[2 3 4; -4 -5 -6; 8 9 10]";
    \endcode    
           
    \return true if successful, false otherwise.    
    */
    bool Inplace_Ceil();
    bool Inplace_ceil() { return this->Inplace_Ceil(); }

    /**
    \brief  Rounds the matrix elements of X to the nearest integers towards zero.
    
    \code
    Matrix A;
    A = "[1.9 2.8 3.7; -4.6 -5.5 -6.4; 7.3 8.2 9.1]";
    bool result;
    result = A.PrintStdout();     // Print Matrix A.
    result = A.Inplace_Fix();     // Make A = fix(A).
    cout << endl;
    result = A.PrintStdout();     // Print Matrix A. A = "[1 2 3; -4 -5 -6; 7 8 9]";
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_Fix();

    /** \brief  Add a scaler double (ie: M += 5).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();        // Print Matrix A.
    result = A.Inplace_AddScalar(1); // A += 1.
    cout << endl;
    result = A.PrintStdout();        // Print Matrix A. A = "[2 3 4; 5 6 7; 8 9 10]";
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_AddScalar( const double scalar );

    /**
    \brief  Subtract a scaler double (ie: M -= 5).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();             // Print Matrix A.
    result = A.Inplace_SubtractScalar(1); // A -= 1.
    cout << endl;
    result = A.PrintStdout();             // Print Matrix A. A = "[0 1 2; 3 4 5; 6 7 8]";
    \endcode    
       
    \return true if successful, false otherwise.    
    */
    bool Inplace_SubtractScalar( const double scalar );

    /**
    \brief  Multiply by scaler double (ie: M *= 5).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();              // Print Matrix A.
    result = A.Inplace_MultiplyScalar(5);  // A *= 5.
    cout << endl;
    result = A.PrintStdout();              // Print Matrix A. A = "[5 10 15; 20 25 30; 35 40 45]";
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_MultiplyScalar( const double scalar );

    /**
    \brief  Divide by scaler double (ie: M /= 5).
    
    \code
    Matrix A;
    A = "[5 10 15; 20 25 30; 35 40 45]";
    bool result;
    result = A.PrintStdout();           // Print Matrix A.
    result = A.Inplace_DivideScalar(5); // A /= 5.
    cout << endl;
    result = A.PrintStdout();           // Print Matrix A. A = "[1 2 3; 4 5 6; 7 8 9]";
    \endcode    
       
    \return true if successful, false otherwise.    
    */
    bool Inplace_DivideScalar( const double scalar );

    /**
    \brief  Raise the matrix to a power scaler double (ie: M ^= 5).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();           // Print Matrix A.
    result = A.Inplace_PowerScalar(2);  // A = A.^2. Not A*A! Each element is raised.
    cout << endl;
    result = A.PrintStdout();           // Print Matrix A. A = "[1 4 9; 16 25 36; 49 64 81]";
    \endcode    
           
    \return true if successful, false otherwise.    
    */
    bool Inplace_PowerScalar( const double scalar );

    /**
    \brief  Add a scaler double (ie: M += (4+2i)).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();           // Print Matrix A.
    std::complex<double> cplx(4.0,2.0);
    result = A.Inplace_AddScalarComplex(cplx);  // A += (4+2i).
    cout << endl;
    result = A.PrintStdout();           // Print Matrix A. A = "[5+2i 6+2i 7+2i; 8+2i 9+2i 10+2i; 11+2i 12+2i 13+2i]";
    cout << "A(0,0) = " << A(0,0).real() << "+" << A(0,0).imag() << "i " << endl;
    \endcode    
               
    * \return true if successful, false otherwise.    
    */
    bool Inplace_AddScalarComplex( const std::complex<double> cplx );

    /**
    \brief  Subtract a scaler double (ie: M -= (5+2i)).
    
    \code
    Matrix A;
    A = "[1 2 3; 4 5 6; 7 8 9]";
    bool result;
    result = A.PrintStdout();           // Print Matrix A.
    std::complex<double> cplx(5.0,2.0);
    result = A.Inplace_SubtractScalarComplex(cplx);  // A -= (5+2i).
    cout << endl;
    result = A.PrintStdout();           // Print Matrix A. A = "[-4-2i -3-2i -2-2i; -1-2i 0-2i 1-2i; 2-2i 3-2i 4-2i]";
    cout << "A(0,0) = " << A(0,0).real() << "+" << A(0,0).imag() << "i " << endl;
    \endcode    
                   
    \return true if successful, false otherwise.    
    */
    bool Inplace_SubtractScalarComplex( const std::complex<double> cplx );

    /**
    \brief  Multiply by scaler double (ie: M *= (5+2i)).

    \code
    Matrix M;
    M = "[10 20]";
    std::complex<double> cplx(5,2);
    if( !M.Inplace_MultiplyScalarComplex(cplx) )
      return false;
    // M
    // 50+20i  100+40i
    \endcode
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_MultiplyScalarComplex( const std::complex<double> cplx );

    /**
    \brief  Divide by scaler double (ie: M /= (5+1i)).

    \code
    Matrix M;
    M = "[10+2i 20+4i]";
    std::complex<double> cplx(5,1);
    if( !M.Inplace_DivideScalarComplex(cplx) )
      return false;
    // M
    // 2  4
    \endcode
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_DivideScalarComplex( const std::complex<double> cplx );

    /**
    \brief  Raise the matrix to a power scaler double (ie: M ^= (5+2i)).

    \code
    Matrix M;
    M = "[2 3]";
    std::complex<double> cplx(5,2);
    if( !M.Inplace_PowerScalarComplex(cplx) )
      return false;
    // M
    // 5.87062319178566+31.4568876931598i    -142.459949032798+196.860770397691i
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_PowerScalarComplex( const std::complex<double> cplx );

    /**
    \brief  Compute the absolute value of each element in the matrix.

    \code
    Matrix A;
    A = "[-1 -2; -3 -4]";
    if( !A.Inplace_Abs() )
      return false;
    // A
    // 1 2
    // 3 4
    \endcode
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_Abs();

    /**
    \brief  Compute the value^2 of each element in the matrix.

    \code
    Matrix A;
    A = "[1 2; -3 -4]";
    if( !A.Inplace_Sqr() )
      return false;
    // A
    // 1 4
    // 9 16
    \endcode    
    
    \return true if successful, false otherwise.    
    */
    bool Inplace_Sqr();