Trabalho inversa de uma matriz

**Renancr** Dom 3 Abr 2011 - 19:44

Fazer um programa que calcule a inversa de uma matriz e depois calcular a matriz pela inversa para obter a matriz identidade.

**Renancr** Dom 3 Abr 2011 - 19:52

Programa matriz inversa >> identidade

Versão Final long Float melhores resultados

Código:: #include <iostream> #include <cstdlib> #include <iomanip> using namespace std; const int lin=3, col=3; float determinantOfMinor( int theRowHeightY, int theColumnWidthX, const long float theMatrix [/*Y=*/lin] [/*X=*/col] ); float determinant( const long float theMatrix [/*Y=*/lin] [/*X=*/col] ); bool inverse( const long float theMatrix [/*Y=*/lin] [/*X=*/col], long float theOutput [/*Y=*/lin] [/*X=*/col] ); void matrixMultiply( const long float theMatrixA [/*Y=*/lin] [/*X=*/col], const long float theMatrixB [/*Y=*/lin] [/*X=*/col],long float theOutput [/*Y=*/lin] [/*X=*/col]); void printMatrix( const long float theMatrix [/*Y=*/lin] [/*X=*/col], int indicate); void main() { long float matriz[lin][col], inversa[lin][col], identidade[lin][col], determinante; int l, c, op, chk=0, chk2=0, chk3=0; for(l=0; l<lin; l++) for(c=0; c<col; c++) { matriz[l][c]=0; inversa[l][c]=0; identidade[l][c]=0; } do{ do{ system("cls"); cout<< "1- Inserir valor na matriz\n"; cout<< "2- Mostrar a matriz\n"; if(chk!=0) { cout<< "3- Calcular a inversa\n"; if(chk2!=0) { cout<< "4- Mostrar a inversa\n"; cout<< "5- Verificar se a matriz * inversa = identidade\n"; } } cout<< "6- Sair\n"; cout<< "\n\n\tDigite a opcao desejada\n\t"; cin>> op; if(op < 1 || op > 6) { system("cls"); cout<< "Opcao invalida tente novamente\n\n"; system("pause"); } }while(op < 1 || op > 6); if(op == 1) { system("cls"); for(l=0; l<3; l++) { system("cls"); for(c=0; c<3; c++) { cout<< "Digite o valor da matriz linha " << l+1 << " coluna " << c+1 << ".\n"; cin>> matriz[l][c]; } } chk=1; } else if(op == 2) { system("cls"); printMatrix(matriz, 1); system("pause"); } else if(op == 3) { if(chk==0) { system("cls"); cout<< "A matriz nao foi preenchida\n\n"; system("pause"); } else { determinante = determinant(matriz); if(determinante != 0) { inverse( matriz, inversa); chk3=1; } else { system("cls"); cout<< "\n\n\tEsta matriz nao possui inversa\n\n"; system("pause"); } chk2=1; } } else if(op == 4) { if(chk==0 || chk2 == 0) { system("cls"); cout<< "\n\n\nA matriz nao foi preenchida ou a inversa nao foi calculada\n\n"; system("pause"); } else { system("cls"); printMatrix(inversa, 1); system("pause"); } } else if(op == 5) { if(chk3 == 0) { system("cls"); cout<< "\n\n\n\tA inversa ainda nao foi calculada\n\n\n"; system("pause"); } else { system("cls"); matrixMultiply(matriz, inversa, identidade); printMatrix(matriz, 1); printMatrix(inversa, 1); printMatrix(identidade, 2); system("pause"); } } }while(op != 6); } float determinantOfMinor( int theRowHeightY, int theColumnWidthX, const long float theMatrix [/*Y=*/lin] [/*X=*/col] ) { int x1 = theColumnWidthX == 0 ? 1 : 0; /* always either 0 or 1 */ int x2 = theColumnWidthX == 2 ? 1 : 2; /* always either 1 or 2 */ int y1 = theRowHeightY == 0 ? 1 : 0; /* always either 0 or 1 */ int y2 = theRowHeightY == 2 ? 1 : 2; /* always either 1 or 2 */ return ( theMatrix [y1] [x1] * theMatrix [y2] [x2] ) - ( theMatrix [y1] [x2] * theMatrix [y2] [x1] ); } float determinant( const long float theMatrix [/*Y=*/lin] [/*X=*/col] ) { return ( theMatrix [0] [0] * determinantOfMinor( 0, 0, theMatrix ) ) - ( theMatrix [0] [1] * determinantOfMinor( 0, 1, theMatrix ) ) + ( theMatrix [0] [2] * determinantOfMinor( 0, 2, theMatrix ) ); } bool inverse( const long float theMatrix [/*Y=*/lin] [/*X=*/col], long float theOutput [/*Y=*/lin] [/*X=*/col] ) { float det = determinant( theMatrix ); /* Arbitrary for now. This should be something nicer... */ if ( abs(det) < 1e-2 ) { memset( theOutput, 0, sizeof theOutput ); return false; } float oneOverDeterminant = 1.0 / det; for ( int y = 0; y < 3; y ++ ) for ( int x = 0; x < 3; x ++ ) { /* Rule is inverse = 1/det * minor of the TRANSPOSE matrix. * * Note (y,x) becomes (x,y) INTENTIONALLY here! */ theOutput [y] [x] = determinantOfMinor( x, y, theMatrix ) * oneOverDeterminant; /* (y0,x1) (y1,x0) (y1,x2) and (y2,x1) all need to be negated. */ if( 1 == ((x + y) % 2) ) theOutput [y] [x] = - theOutput [y] [x]; } return true; } void matrixMultiply( const long float theMatrixA [/*Y=*/lin] [/*X=*/col], const long float theMatrixB [/*Y=*/lin] [/*X=*/col], long float theOutput [/*Y=*/lin] [/*X=*/col]) { for ( int y = 0; y < 3; y ++ ) for ( int x = 0; x < 3; x ++ ) { theOutput [y] [x] = 0; for ( int i = 0; i < 3; i ++ ) theOutput [y] [x] += theMatrixA [y] [i] * theMatrixB [i] [x]; } } void printMatrix( const long float theMatrix [/*Y=*/lin] [/*X=*/col], int indicate) { if(indicate == 1) { for ( int y = 0; y < 3; y ++ ) { cout << "[ "; for ( int x = 0; x < 3; x ++ ) cout << setprecision(4) << theMatrix [y] [x] << " "; cout << "]" << endl; } cout << endl; } else { for ( int y = 0; y < 3; y ++ ) { cout << "[ "; for ( int x = 0; x < 3; x ++ ) cout << setprecision(1) << theMatrix [y] [x] << " "; cout << "]" << endl; } cout << endl; } }

Versão final usando double

Código:: #include <iostream> #include <cstdlib> using namespace std; const int lin=3, col=3; double determinantOfMinor( int theRowHeightY, int theColumnWidthX, const double theMatrix [/*Y=*/lin] [/*X=*/col] ); double determinant( const double theMatrix [/*Y=*/lin] [/*X=*/col] ); bool inverse( const double theMatrix [/*Y=*/lin] [/*X=*/col], double theOutput [/*Y=*/lin] [/*X=*/col] ); void matrixMultiply( const double theMatrixA [/*Y=*/lin] [/*X=*/col], const double theMatrixB [/*Y=*/lin] [/*X=*/col], double theOutput [/*Y=*/lin] [/*X=*/col]); void printMatrix( const double theMatrix [/*Y=*/lin] [/*X=*/col] ); void main() { double matriz[lin][col], inversa[lin][col], identidade[lin][col], determinante; int l, c, op, chk=0, chk2=0, chk3=0; for(l=0; l<lin; l++) for(c=0; c<col; c++) { matriz[l][c]=0; inversa[l][c]=0; identidade[l][c]=0; } do{ do{ system("cls"); cout<< "1- Inserir valor na matriz\n"; cout<< "2- Mostrar a matriz\n"; if(chk!=0) { cout<< "3- Calcular a inversa\n"; if(chk2!=0) { cout<< "4- Mostrar a inversa\n"; cout<< "5- Verificar se a matriz * inversa = identidade\n"; } } cout<< "6- Sair\n"; cout<< "\n\n\tDigite a opcao desejada\n\t"; cin>> op; if(op < 1 || op > 6) { system("cls"); cout<< "Opcao invalida tente novamente\n\n"; system("pause"); } }while(op < 1 || op > 6); if(op == 1) { system("cls"); for(l=0; l<3; l++) { system("cls"); for(c=0; c<3; c++) { cout<< "Digite o valor da matriz linha " << l+1 << " coluna " << c+1 << ".\n"; cin>> matriz[l][c]; } } chk=1; } else if(op == 2) { system("cls"); printMatrix(matriz); system("pause"); } else if(op == 3) { if(chk==0) { system("cls"); cout<< "A matriz nao foi preenchida\n\n"; system("pause"); } else { determinante = determinant(matriz); if(determinante != 0) { inverse( matriz, inversa); chk3=1; } else { system("cls"); cout<< "\n\n\tEsta matriz nao possui inversa\n\n"; system("pause"); } chk2=1; } } else if(op == 4) { if(chk==0 || chk2 == 0) { system("cls"); cout<< "\n\n\nA matriz nao foi preenchida ou a inversa nao foi calculada\n\n"; system("pause"); } else { system("cls"); printMatrix(inversa); system("pause"); } } else if(op == 5) { if(chk3 == 0) { system("cls"); cout<< "\n\n\n\tA inversa ainda nao foi calculada\n\n\n"; system("pause"); } else { system("cls"); matrixMultiply(matriz, inversa, identidade); printMatrix(matriz); printMatrix(inversa); printMatrix(identidade); system("pause"); } } }while(op != 6); } double determinantOfMinor( int theRowHeightY, int theColumnWidthX, const double theMatrix [/*Y=*/lin] [/*X=*/col] ) { int x1 = theColumnWidthX == 0 ? 1 : 0; /* always either 0 or 1 */ int x2 = theColumnWidthX == 2 ? 1 : 2; /* always either 1 or 2 */ int y1 = theRowHeightY == 0 ? 1 : 0; /* always either 0 or 1 */ int y2 = theRowHeightY == 2 ? 1 : 2; /* always either 1 or 2 */ return ( theMatrix [y1] [x1] * theMatrix [y2] [x2] ) - ( theMatrix [y1] [x2] * theMatrix [y2] [x1] ); } double determinant( const double theMatrix [/*Y=*/lin] [/*X=*/col] ) { return ( theMatrix [0] [0] * determinantOfMinor( 0, 0, theMatrix ) ) - ( theMatrix [0] [1] * determinantOfMinor( 0, 1, theMatrix ) ) + ( theMatrix [0] [2] * determinantOfMinor( 0, 2, theMatrix ) ); } bool inverse( const double theMatrix [/*Y=*/lin] [/*X=*/col], double theOutput [/*Y=*/lin] [/*X=*/col] ) { double det = determinant( theMatrix ); /* Arbitrary for now. This should be something nicer... */ if ( abs(det) < 1e-2 ) { memset( theOutput, 0, sizeof theOutput ); return false; } double oneOverDeterminant = 1.0 / det; for ( int y = 0; y < 3; y ++ ) for ( int x = 0; x < 3; x ++ ) { /* Rule is inverse = 1/det * minor of the TRANSPOSE matrix. * * Note (y,x) becomes (x,y) INTENTIONALLY here! */ theOutput [y] [x] = determinantOfMinor( x, y, theMatrix ) * oneOverDeterminant; /* (y0,x1) (y1,x0) (y1,x2) and (y2,x1) all need to be negated. */ if( 1 == ((x + y) % 2) ) theOutput [y] [x] = - theOutput [y] [x]; } return true; } void matrixMultiply( const double theMatrixA [/*Y=*/lin] [/*X=*/col], const double theMatrixB [/*Y=*/lin] [/*X=*/col], double theOutput [/*Y=*/lin] [/*X=*/col]) { for ( int y = 0; y < 3; y ++ ) for ( int x = 0; x < 3; x ++ ) { theOutput [y] [x] = 0; for ( int i = 0; i < 3; i ++ ) theOutput [y] [x] += theMatrixA [y] [i] * theMatrixB [i] [x]; } } void printMatrix( const double theMatrix [/*Y=*/lin] [/*X=*/col] ) { for ( int y = 0; y < 3; y ++ ) { cout << "[ "; for ( int x = 0; x < 3; x ++ ) cout << theMatrix [y] [x] << " "; cout << "]" << endl; } cout << endl; }

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