void operator()(InputMatrixType &A,
int target_rank,
UMatrixType &U,
SingularValuesMatrixType &SV,
VMatrixType &V,
rand_svd_params_t params,
skylark::base::context_t& context) {
// TODO: input matrix should provide Height() and Width()
int input_height = A.Height();
int input_width = A.Width();
int sketch_size = target_rank + params.oversampling;
/**
* Sanity checks, raise an exception if:
* i) the target rank is too large for the given input matrix or
* ii) the number of columns of the sketched matrix either:
* - exceeds its width or
* - is less than the target rank
*/
if ((target_rank > std::min(input_height, input_width)) ||
(sketch_size > input_width) ||
(sketch_size < target_rank)) {
std::ostringstream msg;
msg << "Incompatible matrix dimensions and target rank\n";
SKYLARK_THROW_EXCEPTION(
skylark::base::skylark_exception()
<< skylark::base::error_msg(msg.str()));
}
/** Apply sketch transformation on the input matrix */
UMatrixType Q(input_height, sketch_size);
typedef typename SketchTransform<InputMatrixType, UMatrixType>::data_type sketch_data_type;
sketch_data_type sketch_data(input_width, sketch_size, context);
//typedef typename SketchTransform<InputMatrixType, UMatrixType> sketch_transform_type;
SketchTransform<InputMatrixType, UMatrixType> sketch_transform(sketch_data);
sketch_transform.apply(A, Q, skylark::sketch::rowwise_tag());
#if 0
if (params.transform == sketch::c::transform_type_t::JLT)
{
typedef typename skylark::sketch::JLT_t<InputMatrixType, UMatrixType>::data_type sketch_data_type;
sketch_data_type sketch_data(input_width, sketch_size, context);
typedef typename skylark::sketch::JLT_t<InputMatrixType, UMatrixType> sketch_transform_type;
sketch_transform_type sketch_transform(sketch_data);
sketch_transform.apply(A, Q, skylark::sketch::rowwise_tag());
}
else if (params.transform == sketch::c::transform_type_t::FJLT)
{
typedef typename skylark::sketch::FJLT_t<InputMatrixType, UMatrixType>::data_type sketch_data_type;
sketch_data_type sketch_data(input_width, sketch_size, context);
typedef typename skylark::sketch::FJLT_t<InputMatrixType, UMatrixType> sketch_transform_type;
sketch_transform_type sketch_transform(sketch_data);
sketch_transform.apply(A, Q, skylark::sketch::rowwise_tag());
}
else if (params.transform == sketch::c::transform_type_t::CWT)
{
/*typedef typename skylark::sketch::CWT_t<InputMatrixType, UMatrixType>::data_type sketch_data_type;
sketch_data_type sketch_data(input_width, sketch_size, context);
typedef typename skylark::sketch::CWT_t<InputMatrixType, UMatrixType> sketch_transform_type;
sketch_transform_type sketch_transform(sketch_data);
sketch_transform.apply(A, Q, skylark::sketch::rowwise_tag());*/
}
else
{
std::ostringstream msg;
msg << "Unknown sketch transform type\n";
SKYLARK_THROW_EXCEPTION(
skylark::base::skylark_exception()
<< skylark::base::error_msg(msg.str()));
}
#endif
/** The three steps of the sketched svd approach follow:
* - apply sketching
* - approximate range of A (find Q)
* - SVD
*/
UMatrixType Y;
/** Q = QR(Q) */
skylark::base::qr::Explicit(Q);
/** q steps of subspace iteration */
for(int step = 0; step < params.num_iterations; step++) {
/** Q = QR(A^T * Q) */
skylark::base::Gemm(elem::ADJOINT, elem::NORMAL,
double(1), A, Q, Y);
skylark::base::qr::Explicit(Y);
skylark::base::Gemm(elem::NORMAL, elem::NORMAL,
double(1), A,Y, Q);
if (!params.skip_qr)
skylark::base::qr::Explicit(Q);
}
/** SVD of projected A and then project-back left singular vectors */
UMatrixType B;
skylark::base::Gemm(elem::ADJOINT, elem::NORMAL,
double(1), Q, A, B);
skylark::base::SVD(B, SV, V);
skylark::base::Gemm(elem::NORMAL, elem::NORMAL,
double(1), Q, B, U);
}
int main(int argc, char* argv[]) {
/** Initialize MPI */
boost::mpi::environment env(argc, argv);
boost::mpi::communicator world;
/** Initialize Elemental */
El::Initialize (argc, argv);
MPI_Comm mpi_world(world);
El::Grid grid(mpi_world);
/** Example parameters */
int height = 20;
int width = 10;
int sketch_size = 5;
/** Define input matrix A */
#ifdef LOCAL
input_matrix_t A;
El::Uniform(A, height, width);
#else
dist_CIRC_CIRC_dense_matrix_t A_CIRC_CIRC(grid);
input_matrix_t A(grid);
El::Uniform(A_CIRC_CIRC, height, width);
A = A_CIRC_CIRC;
#endif
/** Initialize context */
skylark::base::context_t context(0);
#ifdef ROWWISE
/** Sketch transform (rowwise)*/
int size = width;
/** Distributed matrix computation */
output_matrix_t sketched_A(height, sketch_size);
sketch_transform_t sketch_transform(size, sketch_size, context);
sketch_transform.apply(A, sketched_A, skylark::sketch::rowwise_tag());
#else
/** Sketch transform (columnwise)*/
int size = height;
/** Distributed matrix computation */
output_matrix_t sketched_A(sketch_size, width);
sketch_transform_t sketch_transform(size, sketch_size, context);
sketch_transform.apply(A, sketched_A, skylark::sketch::columnwise_tag());
#endif
#ifdef ROOT_OUTPUT
if (world.rank() == 0) {
#endif
El::Print(sketched_A, "sketched_A");
#ifdef ROOT_OUTPUT
}
#endif
El::Finalize();
return 0;
}