test_Gauss.cpp

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// test_Gauss.cpp (c) adolfo@di-mare.com

#include "Gaussian_Elimination.h"
#include "rational.h"
#include "BUnit.h"

#undef Matriz_Repeat
#undef Matrix_Sparse
#undef Matrix_Dense

#define USE_Matrix_List

#if defined(USE_Matrix_Dense)
    #include "Matrix_Dense.h"
    typedef Mx::Matrix_Dense< rational<long> >  Rat_Matrix;
#endif
#if defined(USE_Matrix_List)
    #include "Matrix_List.h"
    typedef Mx::Matrix_List< rational<long> >  Rat_Matrix;
#endif
#if defined(USE_Matrix_Sparse)
    #include "Matrix_Sparse.h"
    typedef Mx::Matrix_Sparse< rational<long> > Rat_Matrix;
#endif
#if defined(USE_Matriz_Repeat)
    #include "Matriz_Repeat.h"
    typedef Matriz_Repeat< rational<long> > Rat_Matrix;
#endif

using namespace std;

/// Clase simple para probar \c Gauss().
class test_Gauss : public TestCase {
    Rat_Matrix ID; ///< Matriz identidad
    Rat_Matrix M1, M2, M3, M4;
    Rat_Matrix B1, B2, B3, B4;
public:
    void do_cout();
    void setUp();
    bool run();
private:
    void Ejecutor(const Rat_Matrix& M, const Rat_Matrix& B);
    void test_makeMatrix_long();
}; // test_Gauss

/// Inicializa los valores para \c test_Gauss.
void test_Gauss::setUp() {
    ID.reSize(3,3); // Matriz identidad
    B1.reSize( ID.rows(), 1 ); // B1 queda sincronizado con ID
    ID(0,0) = 1;   ID(0,1) = 0;   ID(0,2) = 0;     B1(0,0) = 10;
    ID(1,0) = 0;   ID(1,1) = 1;   ID(1,2) = 0;     B1(1,0) = 10;
    ID(2,0) = 0;   ID(2,1) = 0;   ID(2,2) = 1;     B1(2,0) = 10;

    M2.reSize(3,3); B2.reSize( M2.rows(), 1 );
    M2(0,0) = 14;  M2(0,1) = 21;  M2(0,2) =  7;    B2(0,0) = 1;
    M2(1,0) = -7;  M2(1,1) = 14;  M2(1,2) =  7;    B2(1,0) = 0;
    M2(2,0) =  7;  M2(2,1) = 35;  M2(2,2) = 14;    B2(2,0) = 14;

    M3.reSize(3,3); B3.reSize( M3.rows(), 1 );
    M3(0,0) =  0;  M3(0,1) = 0;   M3(0,2) = rational<long>(1,3);   B3(0,0) = 4;
    M3(1,0) =  0;  M3(1,1) = 0;   M3(1,2) = rational<long>(2,3);   B3(1,0) = 4;
    M3(2,0) =  0;  M3(2,1) = 0;   M3(2,2) = rational<long>(1,3);   B3(2,0) = 4;

    M4.reSize(3,3); B4.reSize( M4.rows(), 1 );
    M4(0,0) = 13;  M4(0,1) = 26;  M4(0,1) = 39;    B4(0,0) = 65;
    M4(1,0) = 52;  M4(1,1) = 65;  M4(1,1) = 78;    B4(1,0) = -91;
    M4(2,0) = 91;  M4(2,1) = 104; M4(2,2) = 130;   B4(2,0) = -26;
}
/// <code>cout << M;</code>
template <class MAT>
void print( std::ostream &COUT , MAT & V ) {
    for (unsigned i=0; i < V.rows(); ++i) {
        for (unsigned j=0; j < V.cols(); ++j) {
            COUT << ' ' << V(i,j);
        }
        COUT << '\n';
    }
}

#if 0

template <class MAT >
std::ostream& operator<< (std::ostream &COUT, const MAT& M) {
    print( COUT , M );
    return COUT;
}

/// Graba en \c cout el valor actual de las matrices de prueba.
void test_Gauss::do_cout() {
    cout << endl << endl << "=============" << endl;
    cout << "ID " << ID << endl << "......" << endl;
    cout << "B1 " << B1 << endl << "======" << endl;

    cout << endl << endl << "======" << endl;
    cout << "M2 " << M2 << endl << "======" << endl;
    cout << "B2 " << B2 << endl << "======" << endl;

    cout << endl << endl << "======" << endl;
    cout << "M3 " << M3 << endl << "======" << endl;
    cout << "B3 " << B3 << endl << "======" << endl;

    cout << endl << endl << "======" << endl;
    cout << "M4 " << M4 << endl << "======" << endl;
    cout << "B4 " << B4 << endl << "======" << endl;
}
#endif

/// Método auxiliar que permite hace pruebas con todas las matrices
void test_Gauss::Ejecutor(const Rat_Matrix& M, const Rat_Matrix& B) {
    Rat_Matrix X;
    Rat_Matrix Bmod = B;
    if ( rational<long>(0) == Gaussian_Elimination(M, X, B) ) {
        fail_Msg("Matriz singular");
        return;
    }
    assertTrue(M*X == B); // La matriz sabe multiplicar

    assertTrue( check_ok( M ) );
    for (unsigned i=1; i<12; ++i) {
        for (unsigned j=0; j<B1.rows(); ++j) {
            Bmod(j,0) = rational<long>( B(j,0).num() * j, B(j,0).den() + j);
        }
        Gaussian_Elimination(M, X, Bmod);
        assertTrue( check_ok( X ) );
        assertTrue( check_ok( Bmod ) );
        assertTrue(M*X == Bmod);
    }
}

/// Ejecuta las pruebas para \c test_Gauss.
bool test_Gauss::run() {
    Rat_Matrix X;
    assertTrue(ID*B1 == B1);
    Ejecutor(ID, B1);
    assertTrue( rational<long>(0) == Gaussian_Elimination(M2, X, B2) ); // M2 es singular
    assertTrue( rational<long>(0) == Gaussian_Elimination(M3, X, B3) ); // M3 es singular
    Ejecutor(M4, B4);
    B4.swap( M4 );
    assertTrue( check_ok( M2 ) );
    test_makeMatrix_long();
    return wasSuccessful();
}

Rat_Matrix makeMatrix_long(const char **V , int rows , int cols);

/// Ejecuta las pruebas para \c makeMatrix_long().
void test_Gauss::test_makeMatrix_long() {
    {{ // test::makeMatrix_long()
        const char *M_val[3] = {
            " 0  1  2  3  4  5  6" ,
            "10 11 12 13 14 15 16" ,
            "20 21 22 23 24 25 26"
        };
        Rat_Matrix M = makeMatrix_long( M_val, 3, 7 );
        for (unsigned i=0; i<M.rows(); ++i) {
            for (unsigned j=0; j<M.cols(); ++j) {
                cout << M(i,j);
            }
            cout << endl;
        }
    }}
}

/** Retorna una matriz de enteros \c "M" construida en base a la hilera \c "V".
    \dontinclude test_Gauss.cpp
    \skipline    test::makeMatrix_long()
    \until       }}
    \see         std::test_Gauss<T>::test_makeMatrix_long()
*/
Rat_Matrix makeMatrix_long(const char **V , int rows , int cols) {
    Rat_Matrix M;
    if (V == 0 || rows<=0 || cols<=0) {
        return M;
    }
    if (*V == 0) {
        return M;
    }

    enum { SI_Digito,  NO_Digito };

    M.reSize(rows, cols);
    for ( int row=0; row<rows; ++row ) {
        const char* pCH = V[row];
        for ( ;*pCH;pCH++ ) { cout << *pCH; } cout << "**"<< endl; pCH = V[row];
        bool es_positivo = true;  // manejo del cambio de signo
        int  estado = NO_Digito;
        int  num = 0, col = 0;
        do {
            switch (estado) {
                case SI_Digito:
                    if (*pCH == '-') {
                        es_positivo = !es_positivo; // cambio de signo
                        ++pCH;
                    }
                    else if (*pCH == '+') {
                        ++pCH;
                    }
                    else if ( isdigit(*pCH) ) {     // Este es un autómata finito de 2 estados
                        num = num*10 + (*pCH-'0');  // - nunca pregunta por '(' porque se lo brinca
                        ++pCH;                      // - Tampoco le importa el ']'
                    }                               // - Sólo trabaja con los dígitos y los signos
                    else {
                        num = ( es_positivo ? num : -num );
                        M(row,col) = num;
                        num = 0; col++;
                        es_positivo = true;
                        estado = NO_Digito;
                    }
                    break;
                case NO_Digito:
                    if (*pCH == '-') {
                        es_positivo = false;
                        num = 0;
                        estado = SI_Digito;
                        ++pCH;
                    }
                    else if (*pCH == '+') {
                        es_positivo = true;
                        num = 0;
                        estado = SI_Digito;
                        ++pCH;
                    }
                    else if ( isdigit(*pCH) ) {
                        num = (*pCH-'0');
                        es_positivo = true;
                        estado = SI_Digito;
                        ++pCH;
                    }
                    else {
                        ++pCH;
                    break;
                }
            }
        } while (*pCH != 0);
    }
    return M;
}

/// Programa principal para probar el algoritmo \c Gauss().
int main() {
    cout << "1) Prueba directa con \"TestCase\"" << endl;
    test_Gauss test_Gauss_Instance;
    test_Gauss_Instance.setUp();
    test_Gauss_Instance.run();
    if ( true ) {
    //  test_Gauss_Instance.do_cout();
    }
    cout << test_Gauss_Instance.report();
}
// EOF: test_Gauss.cpp