numerics/example/DenseMatrix/cxx_main.cpp

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// @HEADER
// *****************************************************************************
//                    Teuchos: Common Tools Package
//
// Copyright 2004 NTESS and the Teuchos contributors.
// SPDX-License-Identifier: BSD-3-Clause
// *****************************************************************************
// @HEADER

#include "Teuchos_SerialDenseMatrix.hpp"
#include "Teuchos_SerialDenseVector.hpp"
#include "Teuchos_SerialDenseSolver.hpp"
#include "Teuchos_RCP.hpp"
#include "Teuchos_Version.hpp"

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::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 );
  // Create a double-precision vector:
  Teuchos::SerialDenseVector<int,double> x(3), y(3);

  // 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, 2);
  TEUCHOS_ASSERT_EQUALITY(cols, 3);
  TEUCHOS_ASSERT_EQUALITY(stride, 3);

  // 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
  x = 1.0;                        // every entry of vector is 1.0
  y = 1.0;

  // Basic matrix arithmetic can be performed:
  double d;
  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
  d = x.dot( y );                // Vector dot product
  (void)d; // Not used!

  // The pointer to the array of matrix values can be obtained:
  double *My_Array=0, *My_Column=0;
  My_Array = My_Matrix.values();   // pointer to matrix values
  My_Column = My_Matrix[2];        // pointer to third column values
  (void)My_Array; // Not used!
  (void)My_Column; // Not used!

  // 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
  (void)norm_one; // Not used!
  (void)norm_inf; // Not used!
  (void)norm_fro; // Not used!

  // 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;
  }

  // A matrix can be factored and solved using Teuchos::SerialDenseSolver.
  Teuchos::SerialDenseSolver<int,double> My_Solver;
  Teuchos::SerialDenseMatrix<int,double> X(3,1), B(3,1);
  X.putScalar(1.0);
  B.multiply( Teuchos::NO_TRANS, Teuchos::NO_TRANS, 1.0, My_Matrix, X, 0.0 );
  X.putScalar(0.0);  // Make sure the computed answer is correct.

  int info = 0;
  My_Solver.setMatrix( Teuchos::rcp( &My_Matrix, false ) );
  My_Solver.setVectors( Teuchos::rcp( &X, false ), Teuchos::rcp( &B, false ) );
  info = My_Solver.factor();
  if (info != 0)
    std::cout << "Teuchos::SerialDenseSolver::factor() returned : " << info << std::endl;
  info = My_Solver.solve();
  if (info != 0)
    std::cout << "Teuchos::SerialDenseSolver::solve() returned : " << info << std::endl;

  // A matrix can be sent to the output stream:
  std::cout<< std::endl << printMat(My_Matrix) << std::endl;
  std::cout<< printMat(X) << std::endl;

  return 0;
}