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<p>Implementation of a simultaneous QR factorization of multiple matrices. Experimental.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include <utility></code><br/>
<code>#include <iostream></code><br/>
<code>#include <fstream></code><br/>
<code>#include <string></code><br/>
<code>#include <algorithm></code><br/>
<code>#include <vector></code><br/>
<code>#include <math.h></code><br/>
<code>#include <cmath></code><br/>
<code>#include <sstream></code><br/>
<code>#include "<a class="el" href="backend_8hpp_source.html">viennacl/ocl/backend.hpp</a>"</code><br/>
<code>#include "boost/numeric/ublas/vector.hpp"</code><br/>
<code>#include "boost/numeric/ublas/matrix.hpp"</code><br/>
<code>#include "boost/numeric/ublas/matrix_proxy.hpp"</code><br/>
<code>#include "boost/numeric/ublas/storage.hpp"</code><br/>
<code>#include "boost/numeric/ublas/io.hpp"</code><br/>
<code>#include "boost/numeric/ublas/matrix_expression.hpp"</code><br/>
<code>#include "boost/numeric/ublas/detail/matrix_assign.hpp"</code><br/>
<code>#include "<a class="el" href="vector_8hpp_source.html">viennacl/vector.hpp</a>"</code><br/>
<code>#include "<a class="el" href="matrix_8hpp_source.html">viennacl/matrix.hpp</a>"</code><br/>
<code>#include "<a class="el" href="block__matrix_8hpp_source.html">viennacl/linalg/detail/spai/block_matrix.hpp</a>"</code><br/>
<code>#include "<a class="el" href="block__vector_8hpp_source.html">viennacl/linalg/detail/spai/block_vector.hpp</a>"</code><br/>
<code>#include "<a class="el" href="opencl_2kernels_2spai_8hpp_source.html">viennacl/linalg/opencl/kernels/spai.hpp</a>"</code><br/>
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<p><a href="detail_2spai_2qr_8hpp_source.html">Go to the source code of this file.</a></p>
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Functions</h2></td></tr>
<tr class="memitem:aa237a50ec1e8dd5e279a0fb02ff0bf8f"><td class="memTemplParams" colspan="2">template<typename T , typename InputIteratorT > </td></tr>
<tr class="memitem:aa237a50ec1e8dd5e279a0fb02ff0bf8f"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aa237a50ec1e8dd5e279a0fb02ff0bf8f">viennacl::linalg::detail::spai::Print</a> (std::ostream &ostr, InputIteratorT it_begin, InputIteratorT it_end)</td></tr>
<tr class="separator:aa237a50ec1e8dd5e279a0fb02ff0bf8f"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a65295176395fdf1c526d3880f3d76b53"><td class="memTemplParams" colspan="2">template<typename VectorT , typename MatrixT > </td></tr>
<tr class="memitem:a65295176395fdf1c526d3880f3d76b53"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a65295176395fdf1c526d3880f3d76b53">viennacl::linalg::detail::spai::write_to_block</a> (VectorT &con_A_I_J, unsigned int start_ind, std::vector< unsigned int > const &I, std::vector< unsigned int > const &J, MatrixT &m)</td></tr>
<tr class="separator:a65295176395fdf1c526d3880f3d76b53"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7434114c0e1f546e32b4bc2a81a35ad1"><td class="memTemplParams" colspan="2">template<typename VectorT > </td></tr>
<tr class="memitem:a7434114c0e1f546e32b4bc2a81a35ad1"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a7434114c0e1f546e32b4bc2a81a35ad1">viennacl::linalg::detail::spai::print_continious_matrix</a> (VectorT &con_A_I_J, std::vector< cl_uint > &blocks_ind, std::vector< std::vector< unsigned int > > const &g_I, std::vector< std::vector< unsigned int > > const &g_J)</td></tr>
<tr class="separator:a7434114c0e1f546e32b4bc2a81a35ad1"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abbff207e6f84bc89822c0eab0aea0fe7"><td class="memTemplParams" colspan="2">template<typename VectorT > </td></tr>
<tr class="memitem:abbff207e6f84bc89822c0eab0aea0fe7"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#abbff207e6f84bc89822c0eab0aea0fe7">viennacl::linalg::detail::spai::print_continious_vector</a> (VectorT &con_v, std::vector< cl_uint > &block_ind, std::vector< std::vector< unsigned int > > const &g_J)</td></tr>
<tr class="separator:abbff207e6f84bc89822c0eab0aea0fe7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9a76ae3dcfedb876ec9f2db3155b81a7"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a9a76ae3dcfedb876ec9f2db3155b81a7">viennacl::linalg::detail::spai::compute_blocks_size</a> (std::vector< std::vector< unsigned int > > const &g_I, std::vector< std::vector< unsigned int > > const &g_J, unsigned int &sz, std::vector< cl_uint > &blocks_ind, std::vector< cl_uint > &matrix_dims)</td></tr>
<tr class="memdesc:a9a76ae3dcfedb876ec9f2db3155b81a7"><td class="mdescLeft"> </td><td class="mdescRight">**************************************** BLOCK FUNCTIONS ************************************// <a href="#a9a76ae3dcfedb876ec9f2db3155b81a7">More...</a><br/></td></tr>
<tr class="separator:a9a76ae3dcfedb876ec9f2db3155b81a7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af7b43cbe43e0371cea55b325b410c1b4"><td class="memTemplParams" colspan="2">template<typename SizeT > </td></tr>
<tr class="memitem:af7b43cbe43e0371cea55b325b410c1b4"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af7b43cbe43e0371cea55b325b410c1b4">viennacl::linalg::detail::spai::get_size</a> (std::vector< std::vector< SizeT > > const &inds, SizeT &size)</td></tr>
<tr class="memdesc:af7b43cbe43e0371cea55b325b410c1b4"><td class="mdescLeft"> </td><td class="mdescRight">Computes size of particular container of index set. <a href="#af7b43cbe43e0371cea55b325b410c1b4">More...</a><br/></td></tr>
<tr class="separator:af7b43cbe43e0371cea55b325b410c1b4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa47df1186969f6872fe0dcaf83d4982b"><td class="memTemplParams" colspan="2">template<typename SizeT > </td></tr>
<tr class="memitem:aa47df1186969f6872fe0dcaf83d4982b"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aa47df1186969f6872fe0dcaf83d4982b">viennacl::linalg::detail::spai::init_start_inds</a> (std::vector< std::vector< SizeT > > const &inds, std::vector< cl_uint > &start_inds)</td></tr>
<tr class="memdesc:aa47df1186969f6872fe0dcaf83d4982b"><td class="mdescLeft"> </td><td class="mdescRight">Initializes start indices of particular index set. <a href="#aa47df1186969f6872fe0dcaf83d4982b">More...</a><br/></td></tr>
<tr class="separator:aa47df1186969f6872fe0dcaf83d4982b"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a7eeb3f2f51183bed7e6d0a1aeefc87bc"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename NumericT > </td></tr>
<tr class="memitem:a7eeb3f2f51183bed7e6d0a1aeefc87bc"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a7eeb3f2f51183bed7e6d0a1aeefc87bc">viennacl::linalg::detail::spai::dot_prod</a> (MatrixT const &A, unsigned int beg_ind, <a class="el" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> &res)</td></tr>
<tr class="memdesc:a7eeb3f2f51183bed7e6d0a1aeefc87bc"><td class="mdescLeft"> </td><td class="mdescRight">Dot prod of particular column of martix A with it's self starting at a certain index beg_ind. <a href="#a7eeb3f2f51183bed7e6d0a1aeefc87bc">More...</a><br/></td></tr>
<tr class="separator:a7eeb3f2f51183bed7e6d0a1aeefc87bc"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ae6d21631da144b8d5c5de25afcbe53e7"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT , typename NumericT > </td></tr>
<tr class="memitem:ae6d21631da144b8d5c5de25afcbe53e7"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ae6d21631da144b8d5c5de25afcbe53e7">viennacl::linalg::detail::spai::custom_inner_prod</a> (MatrixT const &A, VectorT const &v, unsigned int col_ind, unsigned int start_ind, <a class="el" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> &res)</td></tr>
<tr class="memdesc:ae6d21631da144b8d5c5de25afcbe53e7"><td class="mdescLeft"> </td><td class="mdescRight">Dot prod of particular matrix column with arbitrary vector: A(:, col_ind) <a href="#ae6d21631da144b8d5c5de25afcbe53e7">More...</a><br/></td></tr>
<tr class="separator:ae6d21631da144b8d5c5de25afcbe53e7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a9c9928b400d93d677b626c5ea9e51819"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT > </td></tr>
<tr class="memitem:a9c9928b400d93d677b626c5ea9e51819"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a9c9928b400d93d677b626c5ea9e51819">viennacl::linalg::detail::spai::copy_vector</a> (MatrixT const &A, VectorT &v, unsigned int beg_ind)</td></tr>
<tr class="memdesc:a9c9928b400d93d677b626c5ea9e51819"><td class="mdescLeft"> </td><td class="mdescRight">Copying part of matrix column. <a href="#a9c9928b400d93d677b626c5ea9e51819">More...</a><br/></td></tr>
<tr class="separator:a9c9928b400d93d677b626c5ea9e51819"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a34b989396d25d3ec653ea0aa1e620f55"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT , typename NumericT > </td></tr>
<tr class="memitem:a34b989396d25d3ec653ea0aa1e620f55"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a34b989396d25d3ec653ea0aa1e620f55">viennacl::linalg::detail::spai::householder_vector</a> (MatrixT const &A, unsigned int j, VectorT &v, <a class="el" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> &b)</td></tr>
<tr class="memdesc:a34b989396d25d3ec653ea0aa1e620f55"><td class="mdescLeft"> </td><td class="mdescRight">Computation of Householder vector, householder reflection c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.210. <a href="#a34b989396d25d3ec653ea0aa1e620f55">More...</a><br/></td></tr>
<tr class="separator:a34b989396d25d3ec653ea0aa1e620f55"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a08cfda20cf63c245a5c22034875743da"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT , typename NumericT > </td></tr>
<tr class="memitem:a08cfda20cf63c245a5c22034875743da"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a08cfda20cf63c245a5c22034875743da">viennacl::linalg::detail::spai::apply_householder_reflection</a> (MatrixT &A, unsigned int iter_cnt, VectorT &v, <a class="el" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> b)</td></tr>
<tr class="memdesc:a08cfda20cf63c245a5c22034875743da"><td class="mdescLeft"> </td><td class="mdescRight">Inplace application of Householder vector to a matrix A. <a href="#a08cfda20cf63c245a5c22034875743da">More...</a><br/></td></tr>
<tr class="separator:a08cfda20cf63c245a5c22034875743da"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:abcaaf643f5b021ac04dd7690904e59f9"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT > </td></tr>
<tr class="memitem:abcaaf643f5b021ac04dd7690904e59f9"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#abcaaf643f5b021ac04dd7690904e59f9">viennacl::linalg::detail::spai::store_householder_vector</a> (MatrixT &A, unsigned int ind, VectorT &v)</td></tr>
<tr class="memdesc:abcaaf643f5b021ac04dd7690904e59f9"><td class="mdescLeft"> </td><td class="mdescRight">Storage of vector v in column(A, ind), starting from ind-1 index of a column. <a href="#abcaaf643f5b021ac04dd7690904e59f9">More...</a><br/></td></tr>
<tr class="separator:abcaaf643f5b021ac04dd7690904e59f9"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a6e707b637111b93ec04a6149aa72eac4"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT > </td></tr>
<tr class="memitem:a6e707b637111b93ec04a6149aa72eac4"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a6e707b637111b93ec04a6149aa72eac4">viennacl::linalg::detail::spai::single_qr</a> (MatrixT &R, VectorT &b_v)</td></tr>
<tr class="memdesc:a6e707b637111b93ec04a6149aa72eac4"><td class="mdescLeft"> </td><td class="mdescRight">Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224. <a href="#a6e707b637111b93ec04a6149aa72eac4">More...</a><br/></td></tr>
<tr class="separator:a6e707b637111b93ec04a6149aa72eac4"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:af12bfcc7a652ea6bc9150c302dae81a7"><td class="memTemplParams" colspan="2">template<typename SizeT > </td></tr>
<tr class="memitem:af12bfcc7a652ea6bc9150c302dae81a7"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#af12bfcc7a652ea6bc9150c302dae81a7">viennacl::linalg::detail::spai::get_max_block_size</a> (std::vector< std::vector< SizeT > > const &inds, SizeT &max_size)</td></tr>
<tr class="memdesc:af12bfcc7a652ea6bc9150c302dae81a7"><td class="mdescLeft"> </td><td class="mdescRight">Getting max size of rows/columns from container of index set. <a href="#af12bfcc7a652ea6bc9150c302dae81a7">More...</a><br/></td></tr>
<tr class="separator:af12bfcc7a652ea6bc9150c302dae81a7"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a0f734abea08b6732fb5a6d3d50f36319"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT , typename NumericT > </td></tr>
<tr class="memitem:a0f734abea08b6732fb5a6d3d50f36319"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a0f734abea08b6732fb5a6d3d50f36319">viennacl::linalg::detail::spai::custom_dot_prod</a> (MatrixT const &A, VectorT const &v, unsigned int ind, <a class="el" href="tests_2src_2bisect_8cpp.html#a52b5d30a2d7b064678644a3bf49b7f6c">NumericT</a> &res)</td></tr>
<tr class="memdesc:a0f734abea08b6732fb5a6d3d50f36319"><td class="mdescLeft"> </td><td class="mdescRight">Dot_prod(column(A, ind), v) starting from index ind+1. <a href="#a0f734abea08b6732fb5a6d3d50f36319">More...</a><br/></td></tr>
<tr class="separator:a0f734abea08b6732fb5a6d3d50f36319"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:ab3b64ba7bb53a1526cc852daf0d4d53e"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT > </td></tr>
<tr class="memitem:ab3b64ba7bb53a1526cc852daf0d4d53e"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#ab3b64ba7bb53a1526cc852daf0d4d53e">viennacl::linalg::detail::spai::apply_q_trans_vec</a> (MatrixT const &R, VectorT const &b_v, VectorT &y)</td></tr>
<tr class="memdesc:ab3b64ba7bb53a1526cc852daf0d4d53e"><td class="mdescLeft"> </td><td class="mdescRight">Recovery Q from matrix R and vector of betas b_v. <a href="#ab3b64ba7bb53a1526cc852daf0d4d53e">More...</a><br/></td></tr>
<tr class="separator:ab3b64ba7bb53a1526cc852daf0d4d53e"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:a1bcb9bff13f114739f5f7d70d5b38223"><td class="memTemplParams" colspan="2">template<typename MatrixT , typename VectorT > </td></tr>
<tr class="memitem:a1bcb9bff13f114739f5f7d70d5b38223"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#a1bcb9bff13f114739f5f7d70d5b38223">viennacl::linalg::detail::spai::apply_q_trans_mat</a> (MatrixT const &R, VectorT const &b_v, MatrixT &A)</td></tr>
<tr class="memdesc:a1bcb9bff13f114739f5f7d70d5b38223"><td class="mdescLeft"> </td><td class="mdescRight">Multiplication of Q'*A, where Q is in implicit for lower part of R and vector of betas - b_v. <a href="#a1bcb9bff13f114739f5f7d70d5b38223">More...</a><br/></td></tr>
<tr class="separator:a1bcb9bff13f114739f5f7d70d5b38223"><td class="memSeparator" colspan="2"> </td></tr>
<tr class="memitem:aa50a771c3604ad3913905871d54176f4"><td class="memTemplParams" colspan="2">template<typename NumericT > </td></tr>
<tr class="memitem:aa50a771c3604ad3913905871d54176f4"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespaceviennacl_1_1linalg_1_1detail_1_1spai.html#aa50a771c3604ad3913905871d54176f4">viennacl::linalg::detail::spai::block_qr</a> (std::vector< std::vector< unsigned int > > &g_I, std::vector< std::vector< unsigned int > > &g_J, block_matrix &g_A_I_J_vcl, block_vector &g_bv_vcl, std::vector< cl_uint > &g_is_update, <a class="el" href="classviennacl_1_1context.html">viennacl::context</a> ctx)</td></tr>
<tr class="memdesc:aa50a771c3604ad3913905871d54176f4"><td class="mdescLeft"> </td><td class="mdescRight">Inplace QR factorization via Householder reflections c.f. Gene H. Golub, Charles F. Van Loan "Matrix Computations" 3rd edition p.224 performed on GPU. <a href="#aa50a771c3604ad3913905871d54176f4">More...</a><br/></td></tr>
<tr class="separator:aa50a771c3604ad3913905871d54176f4"><td class="memSeparator" colspan="2"> </td></tr>
</table>
<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p>Implementation of a simultaneous QR factorization of multiple matrices. Experimental. </p>
<p>SPAI code contributed by Nikolay Lukash </p>
<p>Definition in file <a class="el" href="detail_2spai_2qr_8hpp_source.html">qr.hpp</a>.</p>
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