qr.cpp

This tutorial shows how the QR factorization of matrices from ViennaCL or Boost.uBLAS can be computed.

// Activate ublas support in ViennaCL
#define VIENNACL_WITH_UBLAS

//
// Include necessary system headers
//
#include <iostream>

//
// ViennaCL includes
//
#include "viennacl/matrix.hpp"
#include "viennacl/linalg/prod.hpp"
#include "viennacl/linalg/qr.hpp"

//
// Boost includes
//
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>

A helper function comparing two matrices and returning the maximum entry-wise relative error encountered.

template<typename MatrixType>
double check(MatrixType const & qr, MatrixType const & ref)
{
  bool do_break = false;
  double max_error = 0;
  for (std::size_t i=0; i<ref.size1(); ++i)
  {
    for (std::size_t j=0; j<ref.size2(); ++j)
    {
      if (qr(i,j) != 0.0 && ref(i,j) != 0.0)
      {
        double rel_err = fabs(qr(i,j) - ref(i,j)) / fabs(ref(i,j) );

        if (rel_err > max_error)
          max_error = rel_err;
      }


      /* Uncomment the following if you also want to check for NaNs.
      if (qr(i,j) != qr(i,j))
      {
        std::cout << "!!!" << std::endl;
        std::cout << "!!! NaN detected at i=" << i << " and j=" << j << std::endl;
        std::cout << "!!!" << std::endl;
        do_break = true;
        break;
      }*/
    }
    if (do_break)
      break;
  }
  return max_error;
}

We set up a random matrix using Boost.uBLAS and use it to initialize a ViennaCL matrix. Then we compute the QR factorization directly for the uBLAS matrix as well as the ViennaCL matrix.

int main (int, const char **)
{
  typedef double               ScalarType;     //feel free to change this to 'double' if supported by your hardware
  typedef boost::numeric::ublas::matrix<ScalarType>              MatrixType;
  typedef viennacl::matrix<ScalarType, viennacl::column_major>   VCLMatrixType;

  std::size_t rows = 113;   // number of rows in the matrix
  std::size_t cols = 54;    // number of columns

Create uBLAS matrices with some random input data.

MatrixType ublas_A(rows, cols);
MatrixType Q(rows, rows);
MatrixType R(rows, cols);

// Some random data with a bit of extra weight on the diagonal
for (std::size_t i=0; i<rows; ++i)
{
  for (std::size_t j=0; j<cols; ++j)
  {
    ublas_A(i,j) = ScalarType(-1.0) + ScalarType((i+1)*(j+1))
                   + ScalarType( (rand() % 1000) - 500.0) / ScalarType(1000.0);

    if (i == j)
      ublas_A(i,j) += ScalarType(10.0);

    R(i,j) = 0.0;
  }

  for (std::size_t j=0; j<rows; ++j)
    Q(i,j) = ScalarType(0.0);
}

// keep initial input matrix for comparison
MatrixType ublas_A_backup(ublas_A);

Setup the matrix in ViennaCL and copy the data from the uBLAS matrix:

VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());

viennacl::copy(ublas_A, vcl_A);

QR Factorization with Boost.uBLAS Matrices

Compute QR factorization of A. A is overwritten with Householder vectors. Coefficients are returned and a block size of 3 is used. Note that at the moment the number of columns of A must be divisible by the block size

std::cout << "--- Boost.uBLAS ---" << std::endl;
std::vector<ScalarType> ublas_betas = viennacl::linalg::inplace_qr(ublas_A);  //computes the QR factorization

Let us check for the correct result:

viennacl::linalg::recoverQ(ublas_A, ublas_betas, Q, R);
MatrixType ublas_QR = prod(Q, R);
double ublas_error = check(ublas_QR, ublas_A_backup);
std::cout << "Maximum relative error (ublas): " << ublas_error << std::endl;

QR Factorization with Boost.uBLAS Matrices

We now compute the QR factorization from a ViennaCL matrix. Internally it uses Boost.uBLAS for the panel factorization.

std::cout << "--- Hybrid (default) ---" << std::endl;
viennacl::copy(ublas_A_backup, vcl_A);
std::vector<ScalarType> hybrid_betas = viennacl::linalg::inplace_qr(vcl_A);

Let us check for the correct result:

viennacl::copy(vcl_A, ublas_A);
Q.clear(); R.clear();
viennacl::linalg::recoverQ(ublas_A, hybrid_betas, Q, R);
double hybrid_error = check(ublas_QR, ublas_A_backup);
std::cout << "Maximum relative error (hybrid): " << hybrid_error << std::endl;

That's it. Print a success message and exit.

  std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;

  return EXIT_SUCCESS;
}

Full Example Code

/* =========================================================================
   Copyright (c) 2010-2016, Institute for Microelectronics,
                            Institute for Analysis and Scientific Computing,
                            TU Wien.
   Portions of this software are copyright by UChicago Argonne, LLC.

                            -----------------
                  ViennaCL - The Vienna Computing Library
                            -----------------

   Project Head:    Karl Rupp                   rupp@iue.tuwien.ac.at

   (A list of authors and contributors can be found in the PDF manual)

   License:         MIT (X11), see file LICENSE in the base directory
============================================================================= */


// Activate ublas support in ViennaCL
#define VIENNACL_WITH_UBLAS

//
// Include necessary system headers
//
#include <iostream>

//
// ViennaCL includes
//
#include "viennacl/matrix.hpp"
#include "viennacl/linalg/prod.hpp"
#include "viennacl/linalg/qr.hpp"

//
// Boost includes
//
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/io.hpp>


template<typename MatrixType>
double check(MatrixType const & qr, MatrixType const & ref)
{
  bool do_break = false;
  double max_error = 0;
  for (std::size_t i=0; i<ref.size1(); ++i)
  {
    for (std::size_t j=0; j<ref.size2(); ++j)
    {
      if (qr(i,j) != 0.0 && ref(i,j) != 0.0)
      {
        double rel_err = fabs(qr(i,j) - ref(i,j)) / fabs(ref(i,j) );

        if (rel_err > max_error)
          max_error = rel_err;
      }


      /* Uncomment the following if you also want to check for NaNs.
      if (qr(i,j) != qr(i,j))
      {
        std::cout << "!!!" << std::endl;
        std::cout << "!!! NaN detected at i=" << i << " and j=" << j << std::endl;
        std::cout << "!!!" << std::endl;
        do_break = true;
        break;
      }*/
    }
    if (do_break)
      break;
  }
  return max_error;
}

int main (int, const char **)
{
  typedef double               ScalarType;     //feel free to change this to 'double' if supported by your hardware
  typedef boost::numeric::ublas::matrix<ScalarType>              MatrixType;
  typedef viennacl::matrix<ScalarType, viennacl::column_major>   VCLMatrixType;

  std::size_t rows = 113;   // number of rows in the matrix
  std::size_t cols = 54;    // number of columns

  MatrixType ublas_A(rows, cols);
  MatrixType Q(rows, rows);
  MatrixType R(rows, cols);

  // Some random data with a bit of extra weight on the diagonal
  for (std::size_t i=0; i<rows; ++i)
  {
    for (std::size_t j=0; j<cols; ++j)
    {
      ublas_A(i,j) = ScalarType(-1.0) + ScalarType((i+1)*(j+1))
                     + ScalarType( (rand() % 1000) - 500.0) / ScalarType(1000.0);

      if (i == j)
        ublas_A(i,j) += ScalarType(10.0);

      R(i,j) = 0.0;
    }

    for (std::size_t j=0; j<rows; ++j)
      Q(i,j) = ScalarType(0.0);
  }

  // keep initial input matrix for comparison
  MatrixType ublas_A_backup(ublas_A);


  VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());

  viennacl::copy(ublas_A, vcl_A);

  std::cout << "--- Boost.uBLAS ---" << std::endl;
  std::vector<ScalarType> ublas_betas = viennacl::linalg::inplace_qr(ublas_A);  //computes the QR factorization

  viennacl::linalg::recoverQ(ublas_A, ublas_betas, Q, R);
  MatrixType ublas_QR = prod(Q, R);
  double ublas_error = check(ublas_QR, ublas_A_backup);
  std::cout << "Maximum relative error (ublas): " << ublas_error << std::endl;

  std::cout << "--- Hybrid (default) ---" << std::endl;
  viennacl::copy(ublas_A_backup, vcl_A);
  std::vector<ScalarType> hybrid_betas = viennacl::linalg::inplace_qr(vcl_A);

  viennacl::copy(vcl_A, ublas_A);
  Q.clear(); R.clear();
  viennacl::linalg::recoverQ(ublas_A, hybrid_betas, Q, R);
  double hybrid_error = check(ublas_QR, ublas_A_backup);
  std::cout << "Maximum relative error (hybrid): " << hybrid_error << std::endl;


  std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;

  return EXIT_SUCCESS;
}