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Praktikum fertig :)

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This commit is contained in:
Steffen Vogel 2011-04-28 16:28:53 +02:00
parent 1ac9396867
commit 4b6b2f5c46
6 changed files with 121 additions and 53 deletions
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BIN
versuch07/Debug/versuch07
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20
versuch07/src/Gauss.cpp
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@ -49,6 +49,24 @@ void Gauss::stufenform()
{
int dim = A->getDim();
/* Vertausche Zeilen um 0en in der Hauptdiagonale zu vermeiden */
for (int i = 0; i < dim; i++)
{
if (A->get(i, i) == 0) /* 0 gefunden! */
{
for (int j = 0; j < dim; j++)
{
if (i != j && A->get(j, i) != 0)
{
A->vertauscheZeile(i, j);
cout << "Zeile " << i + 1 << " und " << j + 1
<< " vertauscht!" << endl;
break;
}
}
}
}
for (int k = 0; k < dim; k++)
{
for (int l = k + 1; l < dim; l++)
@ -70,7 +88,7 @@ void Gauss::rueckwaertsEinsetzen()
{
int dim = A->getDim();
for (int i = dim-1; i >= 0; i--)
for (int i = dim - 1; i >= 0; i--)
{
double xi = b->get(i);

18
versuch07/src/LR.cpp
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@ -51,7 +51,22 @@ void LR::zerlege(QMatrix& A)
{
int dim = A.getDim();
// TODO Der PseudoCode funktioniert nur, wenn nicht durch 0 dividiert wird.
/* Vertausche Zeilen um 0en in der Hauptdiagonale zu vermeiden */
for (int i = 0; i < dim; i++)
{
if (A.get(i, i) == 0) /* 0 gefunden! */
{
for (int j = 0; j < dim; j++)
{
if (i != j && A.get(j, i) != 0) {
A.vertauscheZeile(i, j);
cout << "Zeile " << i+1 << " und " << j+1 << " vertauscht!" << endl;
break;
}
}
}
}
for (int i = 0; i < dim; i++)
{
for (int j = i + 1; j < dim; j++)
@ -91,7 +106,6 @@ void LR::erzeugeLundR(QMatrix& A)
}
}
}
}
//////////////////////////////////////////////////////////////////////////////

30
versuch07/src/QMatrix.cpp
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@ -94,18 +94,32 @@ int QMatrix::getDim() const
//////////////////////////////////////////////////////////////////////////////
// Transponiere die Matrix
void QMatrix::transponiere()
QMatrix QMatrix::transponiere()
{
double temp;
QMatrix mat(dim);
for (int i = 0; i < dim; i++)
{
for (int j = i + 1; j < dim; j++)
for (int j = 0; j < dim; j++)
{
temp = A[i * dim + j];
A[i * dim + j] = A[j * dim + i];
A[j * dim + i] = temp;
mat.set(i, j, A[j * dim + i]);
}
}
return mat;
}
//////////////////////////////////////////////////////////////////////////////
QMatrix QMatrix::vertauscheZeile(int i, int j)
{
double temp;
for (int k = 0; k < dim; k++)
{
temp = A[i * dim + k];
A[i * dim + k] = A[j * dim + k];
A[j * dim + k] = temp;
}
}
//////////////////////////////////////////////////////////////////////////////
@ -173,9 +187,7 @@ QMatrix QMatrix::adjunkte()
}
}
mat.transponiere();
return mat;
return mat.transponiere();
}
//////////////////////////////////////////////////////////////////////////////

3
versuch07/src/QMatrix.h
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@ -43,7 +43,8 @@ public:
int getDim() const;
// Hilfsmethoden für die Cramersche Regel
void transponiere();
QMatrix transponiere();
QMatrix vertauscheZeile(int i, int j);
QMatrix untermatrix(int i, int j);
QMatrix inverse();
QMatrix adjunkte();

103
versuch07/src/main.cpp
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@ -6,12 +6,14 @@
// Inhalt: Hauptprogramm
//////////////////////////////////////////////////////////////////////////////
#include <iostream>
#include <cstdlib>
#include "QMatrix.h"
#include "Vektor.h"
#include "LR.h"
#include "Gauss.h"
#include "Cramer.h"
#include <iostream>
using namespace std;
@ -19,8 +21,6 @@ using namespace std;
void Eingabe(QMatrix& A, int n);
void Eingabe(Vektor& b, int n);
//////////////////////////////////////////////////////////////////////////////
/*
Die Benennung der Variablen entspricht, in diesem Versuch,
den mathematischen Bezeichnungen im Script.
@ -29,56 +29,79 @@ void Eingabe(Vektor& b, int n);
*/
//////////////////////////////////////////////////////////////////////////////
int main()
{
int dim = 3;
//cout << "Wieviele Gleichungen/Unbekannte hat ihr LGS?: "; cin >> dim;
QMatrix A(dim);
Vektor b(dim);
Vektor x(dim);
//Eingabe(A, dim);
//Eingabe(b, dim);
/* Beispiel Daten. Ergebnis (4, -2, -1) */
A.set(0, 0, 1);
A.set(0, 1, 2);
A.set(0, 2, 2);
A.set(1, 0, 2);
A.set(1, 1, 3);
A.set(1, 2, 1);
A.set(2, 0, 3);
A.set(2, 1, 4);
A.set(2, 2, 1);
char eingabe;
cout << "Wollen Sie selbst ein LGS angeben (j/n)? ";
cin >> eingabe;
if (eingabe == 'j')
{
cout << "Wieviele Gleichungen/Unbekannte hat ihr LGS?: ";
cin >> dim;
Eingabe(A, dim);
Eingabe(b, dim);
}
else
{
/* Beispiel Daten. Ergebnis (4, -2, -1) */
A.set(0, 0, 1);
A.set(0, 1, 2);
A.set(0, 2, 2);
A.set(1, 0, 2);
A.set(1, 1, 3);
A.set(1, 2, 1);
A.set(2, 0, 3);
A.set(2, 1, 4);
A.set(2, 2, 1);
b.set(0, -2);
b.set(1, 1);
b.set(2, 3);
b.set(0, -2);
b.set(1, 1);
b.set(2, 3);
/*A.set(0, 0, 3);
A.set(0, 1, 2);
A.set(0, 2, 1);
A.set(1, 0, 6);
A.set(1, 1, 6);
A.set(1, 2, 3);
A.set(2, 0, 9);
A.set(2, 1, 10);
A.set(2, 2, 6);
/*A.set(0, 0, 3);
A.set(0, 1, 2);
A.set(0, 2, 1);
A.set(1, 0, 6);
A.set(1, 1, 6);
A.set(1, 2, 3);
A.set(2, 0, 9);
A.set(2, 1, 10);
A.set(2, 2, 6);
b.set(0, 1);
b.set(1, 1);
b.set(2, 1);*/
b.set(0, 1);
b.set(1, 1);
b.set(2, 1);*/
}
cout << "A = " << endl << A;
cout << endl << "A = " << endl << A;
cout << "b = " << endl << b;
//cout << "Dim(A) = " << A.getDim() << endl;
//cout << "Det(A) = " << A.determinante() << endl;
//cout << "Adj(A) = " << endl << A.adjunkte() << endl;
//cout << "A^-1 = " << endl << A.inverse() << endl;
Cramer solver1(dim);
LR solver2(dim);
Gauss solver3(dim);
if (A.determinante() == 0)
{
cerr << "Fehler: Das LGS besitzt keine eindeutige Lösung (det(A) = 0)!"
<< endl;
exit(-1);
}
cout << "Wollen Sie weitere Eigenschaften der Koeffizientenmatrix berechnen (j/n)? ";
cin >> eingabe;
if (eingabe == 'j')
{
cout << "Dim(A) = " << A.getDim() << endl;
cout << "Det(A) = " << A.determinante() << endl;
cout << "Adj(A) = " << endl << A.adjunkte() << endl;
cout << "A^-1 = " << endl << A.inverse() << endl;
cout << "A^T = " << endl << A.transponiere() << endl;
}
Cramer solver1(dim);
LR solver2(dim);
Gauss solver3(dim);
cout << "x_cramer =" << endl << solver1.loese(A, b);
cout << "x_lr =" << endl << solver2.loese(A, b);