int main(int argc, char* argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
#endif
// Creating an instance of the LAPACK class for double-precision routines looks like:
Teuchos::LAPACK<int, double> lapack;
// This instance provides the access to all the LAPACK routines.
Teuchos::SerialDenseMatrix<int, double> My_Matrix(4,4);
Teuchos::SerialDenseVector<int, double> My_Vector(4);
My_Matrix.random();
My_Vector.random();
// Perform an LU factorization of this matrix.
int ipiv[4], info;
char TRANS = 'N';
lapack.GETRF( 4, 4, My_Matrix.values(), My_Matrix.stride(), ipiv, &info );
// Solve the linear system.
lapack.GETRS( TRANS, 4, 1, My_Matrix.values(), My_Matrix.stride(),
ipiv, My_Vector.values(), My_Vector.stride(), &info );
// Print out the solution.
cout << My_Vector << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}
int main(int argc, char* argv[])
{
std::cout << Teuchos::Teuchos_Version() << std::endl << std::endl;
// Creating a double-precision matrix can be done in several ways:
// Create an empty matrix with no dimension
Teuchos::SerialSymDenseMatrix<int,double> Empty_Matrix;
// Create an empty 4x4 matrix
Teuchos::SerialSymDenseMatrix<int,double> My_Matrix( 4 );
// Basic copy of My_Matrix
Teuchos::SerialSymDenseMatrix<int,double> My_Copy1( My_Matrix ),
// (Deep) Copy of principle 3x3 submatrix of My_Matrix
My_Copy2( Teuchos::Copy, My_Matrix, 3 ),
// (Shallow) Copy of 3x3 submatrix of My_Matrix
My_Copy3( Teuchos::View, My_Matrix, 3, 1 );
// The matrix dimensions and strided storage information can be obtained:
int rows, cols, stride;
rows = My_Copy3.numRows(); // number of rows
cols = My_Copy3.numCols(); // number of columns
stride = My_Copy3.stride(); // storage stride
TEUCHOS_ASSERT_EQUALITY(rows, 3);
TEUCHOS_ASSERT_EQUALITY(cols, 3);
TEUCHOS_ASSERT_EQUALITY(stride, 4);
// Matrices can change dimension:
Empty_Matrix.shape( 3 ); // size non-dimensional matrices
My_Matrix.reshape( 3 ); // resize matrices and save values
// Filling matrices with numbers can be done in several ways:
My_Matrix.random(); // random numbers
My_Copy1.putScalar( 1.0 ); // every entry is 1.0
My_Copy1 = 1.0; // every entry is 1.0 (still)
My_Copy2(1,1) = 10.0; // individual element access
Empty_Matrix = My_Matrix; // copy My_Matrix to Empty_Matrix
// Basic matrix arithmetic can be performed:
Teuchos::SerialDenseMatrix<int,double> My_Prod( 4, 3 ), My_GenMatrix( 4, 3 );
My_GenMatrix = 1.0;
// Matrix multiplication ( My_Prod = 1.0*My_GenMatrix*My_Matrix )
My_Prod.multiply( Teuchos::RIGHT_SIDE, 1.0, My_Matrix, My_GenMatrix, 0.0 );
My_Copy2 += My_Matrix; // Matrix addition
My_Copy2 *= 0.5; // Matrix scaling
// Matrices can be compared:
// Check if the matrices are equal in dimension and values
if (Empty_Matrix == My_Matrix) {
std::cout<< "The matrices are the same!" <<std::endl;
}
// Check if the matrices are different in dimension or values
if (My_Copy2 != My_Matrix) {
std::cout<< "The matrices are different!" <<std::endl;
}
// The norm of a matrix can be computed:
double norm_one, norm_inf, norm_fro;
norm_one = My_Matrix.normOne(); // one norm
norm_inf = My_Matrix.normInf(); // infinity norm
norm_fro = My_Matrix.normFrobenius(); // frobenius norm
std::cout << std::endl << "|| My_Matrix ||_1 = " << norm_one << std::endl;
std::cout << "|| My_Matrix ||_Inf = " << norm_inf << std::endl;
std::cout << "|| My_Matrix ||_F = " << norm_fro << std::endl << std::endl;
// A matrix can be factored and solved using Teuchos::SerialDenseSolver.
Teuchos::SerialSpdDenseSolver<int,double> My_Solver;
Teuchos::SerialSymDenseMatrix<int,double> My_Matrix2( 3 );
My_Matrix2.random();
Teuchos::SerialDenseMatrix<int,double> X(3,1), B(3,1);
X = 1.0;
B.multiply( Teuchos::LEFT_SIDE, 1.0, My_Matrix2, X, 0.0 );
X = 0.0; // Make sure the computed answer is correct.
int info = 0;
My_Solver.setMatrix( Teuchos::rcp( &My_Matrix2, false ) );
My_Solver.setVectors( Teuchos::rcp( &X, false ), Teuchos::rcp( &B, false ) );
info = My_Solver.factor();
if (info != 0)
std::cout << "Teuchos::SerialSpdDenseSolver::factor() returned : " << info << std::endl;
info = My_Solver.solve();
if (info != 0)
std::cout << "Teuchos::SerialSpdDenseSolver::solve() returned : " << info << std::endl;
// A matrix triple-product can be computed: C = alpha*W'*A*W
double alpha=0.5;
Teuchos::SerialDenseMatrix<int,double> W(3,2);
Teuchos::SerialSymDenseMatrix<int,double> A1(2), A2(3);
A1(0,0) = 1.0, A1(1,1) = 2.0;
A2(0,0) = 1.0, A2(1,1) = 2.0, A2(2,2) = 3.00;
W = 1.0;
Teuchos::SerialSymDenseMatrix<int,double> C1(3), C2(2);
Teuchos::symMatTripleProduct<int,double>( Teuchos::NO_TRANS, alpha, A1, W, C1);
Teuchos::symMatTripleProduct<int,double>( Teuchos::TRANS, alpha, A2, W, C2 );
// A matrix can be sent to the output stream:
std::cout<< My_Matrix << std::endl;
std::cout<< X << std::endl;
return 0;
}
int main(int argc, char* argv[])
{
#ifdef HAVE_MPI
MPI_Init(&argc,&argv);
#endif
// Creating a double-precision matrix can be done in several ways:
// Create an empty matrix with no dimension
Teuchos::SerialDenseMatrix<int,double> Empty_Matrix;
// Create an empty 3x4 matrix
Teuchos::SerialDenseMatrix<int,double> My_Matrix( 3, 4 );
// Basic copy of My_Matrix
Teuchos::SerialDenseMatrix<int,double> My_Copy1( My_Matrix ),
// (Deep) Copy of principle 3x3 submatrix of My_Matrix
My_Copy2( Teuchos::Copy, My_Matrix, 3, 3 ),
// (Shallow) Copy of 2x3 submatrix of My_Matrix
My_Copy3( Teuchos::View, My_Matrix, 2, 3, 1, 1 );
// The matrix dimensions and strided storage information can be obtained:
int rows, cols, stride;
rows = My_Copy3.numRows(); // number of rows
cols = My_Copy3.numCols(); // number of columns
stride = My_Copy3.stride(); // storage stride
// Matrices can change dimension:
Empty_Matrix.shape( 3, 3 ); // size non-dimensional matrices
My_Matrix.reshape( 3, 3 ); // resize matrices and save values
// Filling matrices with numbers can be done in several ways:
My_Matrix.random(); // random numbers
My_Copy1.putScalar( 1.0 ); // every entry is 1.0
My_Copy2(1,1) = 10.0; // individual element access
Empty_Matrix = My_Matrix; // copy My_Matrix to Empty_Matrix
// Basic matrix arithmetic can be performed:
Teuchos::SerialDenseMatrix<int,double> My_Prod( 3, 2 );
// Matrix multiplication ( My_Prod = 1.0*My_Matrix*My_Copy^T )
My_Prod.multiply( Teuchos::NO_TRANS, Teuchos::TRANS,
1.0, My_Matrix, My_Copy3, 0.0 );
My_Copy2 += My_Matrix; // Matrix addition
My_Copy2.scale( 0.5 ); // Matrix scaling
// The pointer to the array of matrix values can be obtained:
double *My_Array, *My_Column;
My_Array = My_Matrix.values(); // pointer to matrix values
My_Column = My_Matrix[2]; // pointer to third column values
// The norm of a matrix can be computed:
double norm_one, norm_inf, norm_fro;
norm_one = My_Matrix.normOne(); // one norm
norm_inf = My_Matrix.normInf(); // infinity norm
norm_fro = My_Matrix.normFrobenius(); // frobenius norm
// Matrices can be compared:
// Check if the matrices are equal in dimension and values
if (Empty_Matrix == My_Matrix) {
cout<< "The matrices are the same!" <<endl;
}
// Check if the matrices are different in dimension or values
if (My_Copy2 != My_Matrix) {
cout<< "The matrices are different!" <<endl;
}
// A matrix can be sent to the output stream:
cout<< My_Matrix << endl;
#ifdef HAVE_MPI
MPI_Finalize();
#endif
return 0;
}
