int main (int, const char **)
{
typedef float ScalarType; //feel free to change this to 'double' if supported by your hardware
typedef boost::numeric::ublas::matrix<ScalarType> MatrixType;
typedef boost::numeric::ublas::vector<ScalarType> VectorType;
typedef viennacl::matrix<ScalarType, viennacl::column_major> VCLMatrixType;
typedef viennacl::vector<ScalarType> VCLVectorType;
//
// Create vectors and matrices with data, cf. http://tutorial.math.lamar.edu/Classes/LinAlg/QRDecomposition.aspx
//
VectorType ublas_b(4);
ublas_b(0) = -4;
ublas_b(1) = 2;
ublas_b(2) = 5;
ublas_b(3) = -1;
MatrixType ublas_A(4, 3);
MatrixType Q = boost::numeric::ublas::zero_matrix<ScalarType>(4, 4);
MatrixType R = boost::numeric::ublas::zero_matrix<ScalarType>(4, 3);
ublas_A(0, 0) = 2; ublas_A(0, 1) = -1; ublas_A(0, 2) = 1;
ublas_A(1, 0) = 1; ublas_A(1, 1) = -5; ublas_A(1, 2) = 2;
ublas_A(2, 0) = -3; ublas_A(2, 1) = 1; ublas_A(2, 2) = -4;
ublas_A(3, 0) = 1; ublas_A(3, 1) = -1; ublas_A(3, 2) = 1;
//
// Setup the matrix in ViennaCL:
//
VCLVectorType vcl_b(ublas_b.size());
VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());
viennacl::copy(ublas_b, vcl_b);
viennacl::copy(ublas_A, vcl_A);
//////////// Part 1: Use Boost.uBLAS for all computations ////////////////
std::cout << "--- Boost.uBLAS ---" << std::endl;
std::vector<ScalarType> ublas_betas = viennacl::linalg::inplace_qr(ublas_A); //computes the QR factorization
// compute modified RHS of the minimization problem:
// b' := Q^T b
viennacl::linalg::inplace_qr_apply_trans_Q(ublas_A, ublas_betas, ublas_b);
// Final step: triangular solve: Rx = b'', where b'' are the first three entries in b'
// We only need the upper left square part of A, which defines the upper triangular matrix R
boost::numeric::ublas::range ublas_range(0, 3);
boost::numeric::ublas::matrix_range<MatrixType> ublas_R(ublas_A, ublas_range, ublas_range);
boost::numeric::ublas::vector_range<VectorType> ublas_b2(ublas_b, ublas_range);
boost::numeric::ublas::inplace_solve(ublas_R, ublas_b2, boost::numeric::ublas::upper_tag());
std::cout << "Result: " << ublas_b2 << std::endl;
//////////// Part 2: Use ViennaCL types for BLAS 3 computations, but use Boost.uBLAS for the panel factorization ////////////////
std::cout << "--- ViennaCL (hybrid implementation) ---" << std::endl;
std::vector<ScalarType> hybrid_betas = viennacl::linalg::inplace_qr(vcl_A);
// compute modified RHS of the minimization problem:
// b := Q^T b
viennacl::linalg::inplace_qr_apply_trans_Q(vcl_A, hybrid_betas, vcl_b);
// Final step: triangular solve: Rx = b'.
// We only need the upper part of A such that R is a square matrix
viennacl::range vcl_range(0, 3);
viennacl::matrix_range<VCLMatrixType> vcl_R(vcl_A, vcl_range, vcl_range);
viennacl::vector_range<VCLVectorType> vcl_b2(vcl_b, vcl_range);
viennacl::linalg::inplace_solve(vcl_R, vcl_b2, viennacl::linalg::upper_tag());
std::cout << "Result: " << vcl_b2 << std::endl;
//
// That's it.
//
std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
return EXIT_SUCCESS;
}
/**
* The minimization problem of finding x such that \f$ \Vert Ax - b \Vert \f$ is solved as follows:
* - Compute the QR-factorization of A = QR.
* - Compute \f$ b' = Q^{\mathrm{T}} b \f$ for the equivalent minimization problem \f$ \Vert Rx - Q^{\mathrm{T}} b \f$.
* - Solve the triangular system \f$ \tilde{R} x = b' \f$, where \f$ \tilde{R} \f$ is the upper square matrix of R.
*
**/
int main (int, const char **)
{
typedef float ScalarType; //feel free to change this to 'double' if supported by your hardware
typedef boost::numeric::ublas::matrix<ScalarType> MatrixType;
typedef boost::numeric::ublas::vector<ScalarType> VectorType;
typedef viennacl::matrix<ScalarType, viennacl::column_major> VCLMatrixType;
typedef viennacl::vector<ScalarType> VCLVectorType;
/**
* Create vectors and matrices with data:
**/
VectorType ublas_b(4);
ublas_b(0) = -4;
ublas_b(1) = 2;
ublas_b(2) = 5;
ublas_b(3) = -1;
MatrixType ublas_A(4, 3);
ublas_A(0, 0) = 2;
ublas_A(0, 1) = -1;
ublas_A(0, 2) = 1;
ublas_A(1, 0) = 1;
ublas_A(1, 1) = -5;
ublas_A(1, 2) = 2;
ublas_A(2, 0) = -3;
ublas_A(2, 1) = 1;
ublas_A(2, 2) = -4;
ublas_A(3, 0) = 1;
ublas_A(3, 1) = -1;
ublas_A(3, 2) = 1;
/**
* Setup the matrix and vector with ViennaCL objects and copy the data from the uBLAS objects:
**/
VCLVectorType vcl_b(ublas_b.size());
VCLMatrixType vcl_A(ublas_A.size1(), ublas_A.size2());
viennacl::copy(ublas_b, vcl_b);
viennacl::copy(ublas_A, vcl_A);
/**
* <h2>Option 1: Using Boost.uBLAS</h2>
*
* The implementation in ViennaCL accepts both uBLAS and ViennaCL types.
* We start with a single-threaded implementation using Boost.uBLAS.
**/
std::cout << "--- Boost.uBLAS ---" << std::endl;
/**
* The first (and computationally most expensive) step is to compute the QR factorization of A.
* Since we do not need A later, we directly overwrite A with the householder reflectors and the upper triangular matrix R.
* The returned vector holds the scalar coefficients (betas) for the Householder reflections \f$ I - \beta v v^{\mathrm{T}} \f$
**/
std::vector<ScalarType> ublas_betas = viennacl::linalg::inplace_qr(ublas_A);
/**
* Compute the modified RHS of the minimization problem from the QR factorization, but do not form \f$ Q^{\mathrm{T}} \f$ explicitly:
* b' := Q^T b
**/
viennacl::linalg::inplace_qr_apply_trans_Q(ublas_A, ublas_betas, ublas_b);
/**
* Final step: triangular solve: Rx = b'', where b'' are the first three entries in b'
* We only need the upper left square part of A, which defines the upper triangular matrix R
**/
boost::numeric::ublas::range ublas_range(0, 3);
boost::numeric::ublas::matrix_range<MatrixType> ublas_R(ublas_A, ublas_range, ublas_range);
boost::numeric::ublas::vector_range<VectorType> ublas_b2(ublas_b, ublas_range);
boost::numeric::ublas::inplace_solve(ublas_R, ublas_b2, boost::numeric::ublas::upper_tag());
std::cout << "Result: " << ublas_b2 << std::endl;
/**
* <h2>Option 2: Use ViennaCL types</h2>
*
* ViennaCL is used for the computationally intensive BLAS 3 computations.
* Boost.uBLAS is used for the panel factorization on the host (CPU).
*/
std::cout << "--- ViennaCL (hybrid implementation) ---" << std::endl;
std::vector<ScalarType> hybrid_betas = viennacl::linalg::inplace_qr(vcl_A);
/**
* compute modified RHS of the minimization problem: \f$ b' := Q^T b \f$
**/
viennacl::linalg::inplace_qr_apply_trans_Q(vcl_A, hybrid_betas, vcl_b);
/**
* Final step: triangular solve: Rx = b'.
* We only need the upper part of A such that R is a square matrix
**/
viennacl::range vcl_range(0, 3);
viennacl::matrix_range<VCLMatrixType> vcl_R(vcl_A, vcl_range, vcl_range);
viennacl::vector_range<VCLVectorType> vcl_b2(vcl_b, vcl_range);
viennacl::linalg::inplace_solve(vcl_R, vcl_b2, viennacl::linalg::upper_tag());
std::cout << "Result: " << vcl_b2 << std::endl;
/**
* That's it.
**/
std::cout << "!!!! TUTORIAL COMPLETED SUCCESSFULLY !!!!" << std::endl;
return EXIT_SUCCESS;
}