example_main.cpp

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/**
\file     example_main.cpp
\brief    An example program using the Zenautics Matrix Class.
\author   Glenn D. MacGougan (GDM)
\date     2008-04-23
\version  0.02 Beta

\b License \b Information \n
Copyright (c) 2008, Glenn D. MacGougan, Zenautics Technologies Inc. \n
This file may be used, copied, modified and redistributed without restriction.
*/

#include <iostream>
#include <string>
#include <complex>
#include "Matrix.h"

using namespace Zenautics;
using namespace std;

#ifndef PI
#define PI  (3.1415926535897932384626433832795) 
#endif
 
int main( int argc, char* argv[] )                            
{  
  try
  {
    bool result = false;
    unsigned i;
    double re;
    double im;

    Matrix A;       // Create an empty matrix.
    Matrix B(2,2);  // Create a 2x2 matrix. 
    Matrix C;
    Matrix S;

    // Fill A from a matrix string.
    A = "[1 3; -2 4]"; 

    // Fill B with real data. A and B are now equal.
    B[0][0] = 1.0;
    B[0][1] = 3.0;
    B[1][0] = -2.0;
    B[1][1] = 4.0;

    // Output A to stdout.
    cout << "A =" << endl;
    A.PrintStdout();

    // Output B to stdout.
    cout << "B =" << endl;
    A.PrintStdout();

    // Output A to file.
    result = A.Print( "A.txt", 4 );

    // Load C from file.
    result = C.ReadFromFile( "A.txt" );

    // Save A to a binary file. 
    result = A.Save( "A.mtx" );

    // Load C from the binary file.
    result = C.ReadFromFile( "A.mtx" );

    // Add
    C = A+B;
    cout << "C = A+B;\nC = " << endl;
    C.PrintStdout();
    
    // Subtract
    C = A-B;
    cout << "C = A-B;\nC = " << endl;
    C.PrintStdout();

    // Multiply
    C = A*B;
    cout << "C = A*B;\nC = " << endl;
    C.PrintStdout();

    // Transpose
    C = A.Transpose();
    cout << "C = transpose(A);\nC = " << endl;
    C.PrintStdout();

    // Inversion
    C = A.Inverse();
    cout << "C = inverse(A);\nC = " << endl;
    C.PrintStdout();

    // Power
    C = A^3;
    cout << "C = A^3;\nC = " << endl;
    C.PrintStdout();

    // Determinant
    result = A.GetDeterminant(re,im); // im will be zero since A is real.
    cout << "determinant(A) = \n" << re << endl;

    // Trace
    A.GetTrace( re, im );// im will be zero since A is real.
    cout << "trace(A) = \n" << re << endl;

    // Identity
    C.Identity(12); // Set C to 12x12 Identity matrix;
    cout << "C = 12x12 Identity;\nC =" << endl;
    C.PrintStdout();

    // Make C = sqrt(-1) * I
    C *= -1.0; // multiply by a constant
    C.Inplace_sqrt();
    cout << "C = sqrt(-1) * 12x12 Identity;\nC =" << endl;
    C.PrintStdout();

    // Diagonal
    C = A.Diagonal();
    cout << "C = diagonal(A);\nC =" << endl;
    C.PrintStdout();
    
    // Tests
    cout << "A =" << endl;
    A.PrintStdout();
    if( A.isSquare() )
      cout << "A is a square matrix." << endl;
    else
      cout << "A is not a square matrix." << endl;

    if( A.isReal() )
      cout << "A is a real matrix." << endl;
    else
      cout << "A is a complex matrix." << endl;
    
    // Resize A to a 3x1 vector.
    A.Resize( 3 ); // Equivalently A.Resize(1,3) is a vector and is accessed the same way as below.
    A[0] = 1.0;
    A[1] = 2.0;
    A[2] = 3.0;

    // Output A to stdout.
    cout << "A =" << endl;
    A.PrintStdout();

    // Redimension B to a 3x3 matrix. The original data is maintained.
    B.Redim( 3, 3 );
    cout << "B =" << endl;
    B.PrintStdout();

    // Set A using complex values.
    complex<double> c1(1.0,1.0);
    complex<double> c2(-2.0,-2.0);
    complex<double> c3(3.0,3.0);
    A(0) = c1; // A is now a complex vector.
    A(1) = c2;
    A(2) = c3;

    cout << "A =" << endl;
    A.PrintStdout();

    // Demonstrate A as a complex matrix.
    A.Resize(2,2);
    A(0,0) = c1; // Set a matrix element to a complex value.
    A(0,1) = c2;
    A(1,0) = c2;
    A(1,1) = 10.0; // Set a matrix element to a double value.    
    cout << "A =" << endl;
    A.PrintStdout();
    re = A(0,0).real();
    im = A(1,1).imag();

    A.Redim(3,3);   // Change the dimensions of A to 3x3 and retain previous data.    
    cout << "A =" << endl;
    A.PrintStdout();

    // Set a matrix using a complex matrix string.
    A = "[1-2i 2+i; 3-7i 4-2i]";    
    cout << "A =" << endl;
    A.PrintStdout();

    // Plot columns of the matrix.
    A = "[1 2 3 4 5 6 7 8 9 10; 1 4 9 16 25 36 49 64 81 100;]";
    A.Inplace_transpose();
    cout << "A =" << endl;
    A.PrintStdout();
    A.Plot(0,1,"testplot.bmp","testing plot", "X", "Y", "Y=X^2" );

    // Plot is also a friend function in Matrix.h
    Matrix X;
    Matrix Y1;
    Matrix Y2;
    X = A.Column(0);
    Y1 = X^2;
    Y2 = X^3;
    Plot( "testplot2.bmp", "testing plot", "X (m)", "Y (m)", X, Y1, "Y=X^2", "(m)", X, Y2, "Y=X^3", "(m)", false, MTX_BLUE, false, MTX_RED, false, false, false );

    // Set S to a vector.
    S.Resize(512);
    // Set A to a complex tone sinusoid.
    for( i = 0; i < S.GetNrRows(); i++ )
    { 
      complex<double> cplx( cos(i*2*PI/512.0), sin(i*2*PI/512.0) );
      S(i) = cplx;
    }
    // Using the member plotting function, plot the real and imaginary components of S.
    C.Inplace_colon( 1.0/512.0, 1.0/512.0, 1.0 ); // Set C as a column vector from 1.0/512.0:1.0/512.0:1.0.
    C.Concatonate( S.Real() ); // Concatonte the real part of A to make C = C | real(S)
    C.Concatonate( S.Imag() ); // C = C | real(S) | imag(S)
    // Use the member plotting function.
    C.Plot( 0, 1, 2, "testplot3.bmp", "The real and imaginary parts of a complex sinusoid", "time (s)", "amplitude", "real part", "(V)", "imag part", "(V)" ); 
    
    // Take the fft of S inplace
    S.Inplace_FFT();  // Perform an fft of the columns in S. S is now complex. 

    std::complex<double> cplxResult;
    cplxResult = S(1);   // Get a complex value from the matrix.
    re = S(1).real();    // or re = S[1];
    im = S(1).imag();

    // Output A to a the specified ASCII file name.
    S.Print( "S.txt", 6 );

    // Output A to a the specified ASCII file name.
    S.PrintDelimited( "S.csv", 6, ',' );

    // Output A to a compressed binary matrix file.
    result = S.Save("S.mtx");
      
    // Read real or complex data from an ascii comma delimited file.          
    result = S.ReadFromFile( "S.csv" );

    // Read data from an ascii white space delimited file.    
    result = S.ReadFromFile( "S.txt" );                     

    // Read data from a binary .mtx format file.
    result = S.ReadFromFile( "S.mtx");

    // Force an exception with invalid index usage.
    // Uncomment the following lines to demonstrate matrix exception handling.
    //cout << "Causing an intentional exception to be thrown." << endl;
    //double q = A(2000,1).real();   // This will cause an exception.  
    //double r = A[2000][1];         // This will cause an exception.  
    //double s = A[2000];            // This will cause an exception.  
    //double t = A(2000).real();     // This will cause an exception.      
  }                                                           
  catch( MatrixException& matrix_exception )
  {
    cout << matrix_exception << endl;
  }
  catch ( ... )
  {
    cout << "Caught unknown exception" << endl;
  }

  char anykey;
  cout << "You have successfully executed the Zenautics Matrix Project example progam.\n" << endl;
  cout << "Type something and hit enter: " << endl;
  cin >> anykey;
  return 0;
}                                   

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