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<p>Set of elimination based routines for dense linear algebra.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="fflas_8h.html">fflas-ffpack/fflas/fflas.h</a>"</code><br/>
<code>#include <list></code><br/>
<code>#include <vector></code><br/>
<code>#include <iostream></code><br/>
<code>#include "ffpack_ludivine.inl"</code><br/>
<code>#include "ffpack_minpoly.inl"</code><br/>
<code>#include "ffpack_charpoly_kglu.inl"</code><br/>
<code>#include "ffpack_charpoly_kgfast.inl"</code><br/>
<code>#include "ffpack_charpoly_kgfastgeneralized.inl"</code><br/>
<code>#include "ffpack_charpoly_danilevski.inl"</code><br/>
<code>#include "ffpack_charpoly.inl"</code><br/>
<code>#include "ffpack_krylovelim.inl"</code><br/>
<code>#include "ffpack_frobenius.inl"</code><br/>
<code>#include "ffpack_echelonforms.inl"</code><br/>
</div><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2><a name="namespaces"></a>
Namespaces</h2></td></tr>
<tr class="memitem:namespace_f_f_p_a_c_k"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html">FFPACK</a></td></tr>
<tr class="memdesc:namespace_f_f_p_a_c_k"><td class="mdescLeft"> </td><td class="mdescRight"><b>F</b>inite <b>F</b>ield <b>PACK</b> Set of elimination based routines for dense linear algebra. <br/></td></tr>
</table><table class="memberdecls">
<tr class="heading"><td colspan="2"><h2><a name="func-members"></a>
Functions</h2></td></tr>
<tr class="memitem:a351d9c1f0ced0913fe66360606a56f6c"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a351d9c1f0ced0913fe66360606a56f6c"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a351d9c1f0ced0913fe66360606a56f6c">applyP</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const <a class="el" href="namespace_f_f_l_a_s.html#afb7f98f2ba205ba04f6f90a5dfc8d838">FFLAS::FFLAS_TRANSPOSE</a> Trans, const size_t M, const int ibeg, const int iend, typename Field::Element *A, const size_t lda, const size_t *P)</td></tr>
<tr class="memdesc:a351d9c1f0ced0913fe66360606a56f6c"><td class="mdescLeft"> </td><td class="mdescRight">Apply a permutation submatrix of P (between ibeg and iend) to a matrix to (iend-ibeg) vectors of size M stored in A (as column for NoTrans and rows for Trans). <a href="#a351d9c1f0ced0913fe66360606a56f6c"></a><br/></td></tr>
<tr class="memitem:ae1bff74aa04c4e2f7ec69378b7a0f7da"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:ae1bff74aa04c4e2f7ec69378b7a0f7da"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#ae1bff74aa04c4e2f7ec69378b7a0f7da">Rank</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)</td></tr>
<tr class="memdesc:ae1bff74aa04c4e2f7ec69378b7a0f7da"><td class="mdescLeft"> </td><td class="mdescRight">Computes the rank of the given matrix using a LQUP factorization. <a href="#ae1bff74aa04c4e2f7ec69378b7a0f7da"></a><br/></td></tr>
<tr class="memitem:a8b2ee9cd225752641b69514532f11ee1"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a8b2ee9cd225752641b69514532f11ee1"><td class="memTemplItemLeft" align="right" valign="top">bool </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a8b2ee9cd225752641b69514532f11ee1">IsSingular</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)</td></tr>
<tr class="memdesc:a8b2ee9cd225752641b69514532f11ee1"><td class="mdescLeft"> </td><td class="mdescRight">Returns true if the given matrix is singular. <a href="#a8b2ee9cd225752641b69514532f11ee1"></a><br/></td></tr>
<tr class="memitem:aca11fe0e110480303d6e0d9f405429ef"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:aca11fe0e110480303d6e0d9f405429ef"><td class="memTemplItemLeft" align="right" valign="top">Field::Element </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#aca11fe0e110480303d6e0d9f405429ef">Det</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda)</td></tr>
<tr class="memdesc:aca11fe0e110480303d6e0d9f405429ef"><td class="mdescLeft"> </td><td class="mdescRight">Returns the determinant of the given matrix. <a href="#aca11fe0e110480303d6e0d9f405429ef"></a><br/></td></tr>
<tr class="memitem:abb4406620c331c82f4009c8d4652d55a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:abb4406620c331c82f4009c8d4652d55a"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#abb4406620c331c82f4009c8d4652d55a">solveLB2</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb)</td></tr>
<tr class="memdesc:abb4406620c331c82f4009c8d4652d55a"><td class="mdescLeft"> </td><td class="mdescRight">Solve L X = B in place. <a href="#abb4406620c331c82f4009c8d4652d55a"></a><br/></td></tr>
<tr class="memitem:a4a08c7a813c6c536bb5763669fb3ca8f"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a4a08c7a813c6c536bb5763669fb3ca8f"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a4a08c7a813c6c536bb5763669fb3ca8f">fgetrs</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, const size_t R, typename Field::Element *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *B, const size_t ldb, int *info)</td></tr>
<tr class="memdesc:a4a08c7a813c6c536bb5763669fb3ca8f"><td class="mdescLeft"> </td><td class="mdescRight">Solve the system <img class="formulaInl" alt="$A X = B$" src="form_36.png"/> or <img class="formulaInl" alt="$X A = B$" src="form_37.png"/>. <a href="#a4a08c7a813c6c536bb5763669fb3ca8f"></a><br/></td></tr>
<tr class="memitem:a37872384b0e0aaf827972e7555996019"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a37872384b0e0aaf827972e7555996019"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a37872384b0e0aaf827972e7555996019">fgetrs</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, const size_t NRHS, const size_t R, typename Field::Element *A, const size_t lda, const size_t *P, const size_t *Q, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info)</td></tr>
<tr class="memdesc:a37872384b0e0aaf827972e7555996019"><td class="mdescLeft"> </td><td class="mdescRight">Solve the system A X = B or X A = B. <a href="#a37872384b0e0aaf827972e7555996019"></a><br/></td></tr>
<tr class="memitem:a85ddf4dbb74dac566b1a8bf95062fb92"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a85ddf4dbb74dac566b1a8bf95062fb92"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a85ddf4dbb74dac566b1a8bf95062fb92">fgesv</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *B, const size_t ldb, int *info)</td></tr>
<tr class="memdesc:a85ddf4dbb74dac566b1a8bf95062fb92"><td class="mdescLeft"> </td><td class="mdescRight">Square system solver. <a href="#a85ddf4dbb74dac566b1a8bf95062fb92"></a><br/></td></tr>
<tr class="memitem:ad7b89ea22b699828aaa6c178af0b2b06"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:ad7b89ea22b699828aaa6c178af0b2b06"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#ad7b89ea22b699828aaa6c178af0b2b06">fgesv</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, const size_t NRHS, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, const typename Field::Element *B, const size_t ldb, int *info)</td></tr>
<tr class="memdesc:ad7b89ea22b699828aaa6c178af0b2b06"><td class="mdescLeft"> </td><td class="mdescRight">Rectangular system solver. <a href="#ad7b89ea22b699828aaa6c178af0b2b06"></a><br/></td></tr>
<tr class="memitem:a2ea44d6c4a5b97c18137094f31707373"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a2ea44d6c4a5b97c18137094f31707373"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a2ea44d6c4a5b97c18137094f31707373">Solve</a> (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *x, const int incx, const typename Field::Element *b, const int incb)</td></tr>
<tr class="memdesc:a2ea44d6c4a5b97c18137094f31707373"><td class="mdescLeft"> </td><td class="mdescRight">Solve the system Ax=b. <a href="#a2ea44d6c4a5b97c18137094f31707373"></a><br/></td></tr>
<tr class="memitem:a73513addc2f3a53b200838f1604f8702"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a73513addc2f3a53b200838f1604f8702"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a73513addc2f3a53b200838f1604f8702">NullSpaceBasis</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&NS, size_t &ldn, size_t &NSdim)</td></tr>
<tr class="memdesc:a73513addc2f3a53b200838f1604f8702"><td class="mdescLeft"> </td><td class="mdescRight">Computes a basis of the Left/Right nullspace of the matrix A. <a href="#a73513addc2f3a53b200838f1604f8702"></a><br/></td></tr>
<tr class="memitem:a372e1f2520d379dd2e7a3af4a99c5590"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a372e1f2520d379dd2e7a3af4a99c5590"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a372e1f2520d379dd2e7a3af4a99c5590">RowRankProfile</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile)</td></tr>
<tr class="memdesc:a372e1f2520d379dd2e7a3af4a99c5590"><td class="mdescLeft"> </td><td class="mdescRight">Computes the row rank profile of A. <a href="#a372e1f2520d379dd2e7a3af4a99c5590"></a><br/></td></tr>
<tr class="memitem:a60ef015ff1808d4c0f82d39c8d938df8"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a60ef015ff1808d4c0f82d39c8d938df8"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a60ef015ff1808d4c0f82d39c8d938df8">ColumnRankProfile</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rkprofile)</td></tr>
<tr class="memdesc:a60ef015ff1808d4c0f82d39c8d938df8"><td class="mdescLeft"> </td><td class="mdescRight">Computes the column rank profile of A. <a href="#a60ef015ff1808d4c0f82d39c8d938df8"></a><br/></td></tr>
<tr class="memitem:a612288fb51aca8a605caff22127392cb"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a612288fb51aca8a605caff22127392cb"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a612288fb51aca8a605caff22127392cb">RowRankProfileSubmatrixIndices</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)</td></tr>
<tr class="memdesc:a612288fb51aca8a605caff22127392cb"><td class="mdescLeft"> </td><td class="mdescRight">RowRankProfileSubmatrixIndices. <a href="#a612288fb51aca8a605caff22127392cb"></a><br/></td></tr>
<tr class="memitem:ae07cfdd71d97c2c60f5061be93d2697a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:ae07cfdd71d97c2c60f5061be93d2697a"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#ae07cfdd71d97c2c60f5061be93d2697a">ColRankProfileSubmatrixIndices</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *&rowindices, size_t *&colindices, size_t &R)</td></tr>
<tr class="memdesc:ae07cfdd71d97c2c60f5061be93d2697a"><td class="mdescLeft"> </td><td class="mdescRight">Computes the indices of the submatrix r*r X of A whose columns correspond to the column rank profile of A. <a href="#ae07cfdd71d97c2c60f5061be93d2697a"></a><br/></td></tr>
<tr class="memitem:aae8665073e58a37543e0eee958fde2d3"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:aae8665073e58a37543e0eee958fde2d3"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#aae8665073e58a37543e0eee958fde2d3">RowRankProfileSubmatrix</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R)</td></tr>
<tr class="memdesc:aae8665073e58a37543e0eee958fde2d3"><td class="mdescLeft"> </td><td class="mdescRight">Compute the r*r submatrix X of A, by picking the row rank profile rows of A. <a href="#aae8665073e58a37543e0eee958fde2d3"></a><br/></td></tr>
<tr class="memitem:a8386f234e440215744bbbf3a90d8dde4"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a8386f234e440215744bbbf3a90d8dde4"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a8386f234e440215744bbbf3a90d8dde4">ColRankProfileSubmatrix</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, typename Field::Element *&X, size_t &R)</td></tr>
<tr class="memdesc:a8386f234e440215744bbbf3a90d8dde4"><td class="mdescLeft"> </td><td class="mdescRight">Compute the <img class="formulaInl" alt="$ r\times r$" src="form_38.png"/> submatrix X of A, by picking the row rank profile rows of A. <a href="#a8386f234e440215744bbbf3a90d8dde4"></a><br/></td></tr>
<tr class="memitem:a2c37575f0b9a909953b200477a4843b8"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a2c37575f0b9a909953b200477a4843b8"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a2c37575f0b9a909953b200477a4843b8">LQUPtoInverseOfFullRankMinor</a> (const Field &F, const size_t rank, typename Field::Element *A_factors, const size_t lda, const size_t *QtPointer, typename Field::Element *X, const size_t ldx)</td></tr>
<tr class="memdesc:a2c37575f0b9a909953b200477a4843b8"><td class="mdescLeft"> </td><td class="mdescRight">LQUPtoInverseOfFullRankMinor. <a href="#a2c37575f0b9a909953b200477a4843b8"></a><br/></td></tr>
<tr class="memitem:afb1a104de48f4c8f6a65288f0cc1c2e0"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:afb1a104de48f4c8f6a65288f0cc1c2e0"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#afb1a104de48f4c8f6a65288f0cc1c2e0">TURBO</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const size_t cutoff)</td></tr>
<tr class="memitem:a92af9e6caef5d3d736e0a35b5e970035"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a92af9e6caef5d3d736e0a35b5e970035"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a92af9e6caef5d3d736e0a35b5e970035">LUdivine</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> Diag, const <a class="el" href="namespace_f_f_l_a_s.html#afb7f98f2ba205ba04f6f90a5dfc8d838">FFLAS::FFLAS_TRANSPOSE</a> trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP, const size_t cutoff=0)</td></tr>
<tr class="memdesc:a92af9e6caef5d3d736e0a35b5e970035"><td class="mdescLeft"> </td><td class="mdescRight">Compute the LQUP factorization of the given matrix. <a href="#a92af9e6caef5d3d736e0a35b5e970035"></a><br/></td></tr>
<tr class="memitem:a4b442db4c48fb0f561e906aed7893516"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a4b442db4c48fb0f561e906aed7893516"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a4b442db4c48fb0f561e906aed7893516">LUpdate</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> Diag, const <a class="el" href="namespace_f_f_l_a_s.html#afb7f98f2ba205ba04f6f90a5dfc8d838">FFLAS::FFLAS_TRANSPOSE</a> trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t R, const size_t K, typename Field::Element *B, const size_t ldb, size_t *P, size_t *Q, const FFPACK::FFPACK_LUDIVINE_TAG LuTag=FFPACK::FfpackLQUP, const size_t cutoff=0)</td></tr>
<tr class="memdesc:a4b442db4c48fb0f561e906aed7893516"><td class="mdescLeft"> </td><td class="mdescRight">LUpdate. <a href="#a4b442db4c48fb0f561e906aed7893516"></a><br/></td></tr>
<tr class="memitem:aa0dc4f7f42112bc8acda6b88d6ea09d1"><td class="memTemplParams" colspan="2"><a class="anchor" id="aa0dc4f7f42112bc8acda6b88d6ea09d1"></a>
template<class Field > </td></tr>
<tr class="memitem:aa0dc4f7f42112bc8acda6b88d6ea09d1"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#aa0dc4f7f42112bc8acda6b88d6ea09d1">LUdivine_small</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> Diag, const <a class="el" href="namespace_f_f_l_a_s.html#afb7f98f2ba205ba04f6f90a5dfc8d838">FFLAS::FFLAS_TRANSPOSE</a> trans, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP)</td></tr>
<tr class="memdesc:aa0dc4f7f42112bc8acda6b88d6ea09d1"><td class="mdescLeft"> </td><td class="mdescRight">LUdivine small case. <br/></td></tr>
<tr class="memitem:a29b195deaec1e10eed1ece6dc70ceed2"><td class="memTemplParams" colspan="2"><a class="anchor" id="a29b195deaec1e10eed1ece6dc70ceed2"></a>
template<class Field > </td></tr>
<tr class="memitem:a29b195deaec1e10eed1ece6dc70ceed2"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a29b195deaec1e10eed1ece6dc70ceed2">LUdivine_gauss</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> Diag, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Q, const FFPACK_LUDIVINE_TAG LuTag=FfpackLQUP)</td></tr>
<tr class="memdesc:a29b195deaec1e10eed1ece6dc70ceed2"><td class="mdescLeft"> </td><td class="mdescRight">LUdivine gauss. <br/></td></tr>
<tr class="memitem:abfc9470a2202c1149a8486d39d93bd67"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:abfc9470a2202c1149a8486d39d93bd67"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#abfc9470a2202c1149a8486d39d93bd67">ftrtri</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#aa1ddb4c9a57b5865e78475034486c2a2">FFLAS::FFLAS_UPLO</a> Uplo, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> Diag, const size_t N, typename Field::Element *A, const size_t lda)</td></tr>
<tr class="memdesc:abfc9470a2202c1149a8486d39d93bd67"><td class="mdescLeft"> </td><td class="mdescRight">Compute the inverse of a triangular matrix. <a href="#abfc9470a2202c1149a8486d39d93bd67"></a><br/></td></tr>
<tr class="memitem:a8a687ea989b281c7afad1dbf27b8660d"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a8a687ea989b281c7afad1dbf27b8660d"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a8a687ea989b281c7afad1dbf27b8660d">ftrtrm</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a953b1159fd5330713d8a05ec27fbb068">FFLAS::FFLAS_DIAG</a> diag, const size_t N, typename Field::Element *A, const size_t lda)</td></tr>
<tr class="memdesc:a8a687ea989b281c7afad1dbf27b8660d"><td class="mdescLeft"> </td><td class="mdescRight">Compute the product UL. <a href="#a8a687ea989b281c7afad1dbf27b8660d"></a><br/></td></tr>
<tr class="memitem:a72a66b046cfced673b499ea8ac3918b9"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a72a66b046cfced673b499ea8ac3918b9"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a72a66b046cfced673b499ea8ac3918b9">ColumnEchelonForm</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, bool transform=true)</td></tr>
<tr class="memdesc:a72a66b046cfced673b499ea8ac3918b9"><td class="mdescLeft"> </td><td class="mdescRight">Compute the Column Echelon form of the input matrix in-place. <a href="#a72a66b046cfced673b499ea8ac3918b9"></a><br/></td></tr>
<tr class="memitem:a4a2b8cde37af6d5751b94ef90109aece"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a4a2b8cde37af6d5751b94ef90109aece"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a4a2b8cde37af6d5751b94ef90109aece">RowEchelonForm</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=false)</td></tr>
<tr class="memdesc:a4a2b8cde37af6d5751b94ef90109aece"><td class="mdescLeft"> </td><td class="mdescRight">Compute the Row Echelon form of the input matrix in-place. <a href="#a4a2b8cde37af6d5751b94ef90109aece"></a><br/></td></tr>
<tr class="memitem:aa39e7d3a3573ce79573db2bc7a58e78a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:aa39e7d3a3573ce79573db2bc7a58e78a"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#aa39e7d3a3573ce79573db2bc7a58e78a">ReducedColumnEchelonForm</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)</td></tr>
<tr class="memdesc:aa39e7d3a3573ce79573db2bc7a58e78a"><td class="mdescLeft"> </td><td class="mdescRight">Compute the Reduced Column Echelon form of the input matrix in-place. <a href="#aa39e7d3a3573ce79573db2bc7a58e78a"></a><br/></td></tr>
<tr class="memitem:afddaaf2693e89260f3ef82983807fe98"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:afddaaf2693e89260f3ef82983807fe98"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#afddaaf2693e89260f3ef82983807fe98">ReducedRowEchelonForm</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)</td></tr>
<tr class="memdesc:afddaaf2693e89260f3ef82983807fe98"><td class="mdescLeft"> </td><td class="mdescRight">Compute the Reduced Row Echelon form of the input matrix in-place. <a href="#afddaaf2693e89260f3ef82983807fe98"></a><br/></td></tr>
<tr class="memitem:a112b0c68352d6a1f91b181d604e28f12"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a112b0c68352d6a1f91b181d604e28f12"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a112b0c68352d6a1f91b181d604e28f12">ReducedRowEchelonForm2</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, size_t *P, size_t *Qt, const bool transform=true)</td></tr>
<tr class="memdesc:a112b0c68352d6a1f91b181d604e28f12"><td class="mdescLeft"> </td><td class="mdescRight">Variant by the block recursive algorithm. <a href="#a112b0c68352d6a1f91b181d604e28f12"></a><br/></td></tr>
<tr class="memitem:ad750b259c6be65b804d3cb741791eb2a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:ad750b259c6be65b804d3cb741791eb2a"><td class="memTemplItemLeft" align="right" valign="top">size_t </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#ad750b259c6be65b804d3cb741791eb2a">REF</a> (const Field &F, const size_t M, const size_t N, typename Field::Element *A, const size_t lda, const size_t colbeg, const size_t rowbeg, const size_t colsize, size_t *Qt, size_t *P)</td></tr>
<tr class="memdesc:ad750b259c6be65b804d3cb741791eb2a"><td class="mdescLeft"> </td><td class="mdescRight">REF. <a href="#ad750b259c6be65b804d3cb741791eb2a"></a><br/></td></tr>
<tr class="memitem:a46774fee6e6031f356bd46eb5dc5660a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a46774fee6e6031f356bd46eb5dc5660a"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a46774fee6e6031f356bd46eb5dc5660a">Invert</a> (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, int &nullity)</td></tr>
<tr class="memdesc:a46774fee6e6031f356bd46eb5dc5660a"><td class="mdescLeft"> </td><td class="mdescRight">Invert the given matrix in place or computes its nullity if it is singular. <a href="#a46774fee6e6031f356bd46eb5dc5660a"></a><br/></td></tr>
<tr class="memitem:a80556bc89548c5f1fd59fdc848afebf6"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a80556bc89548c5f1fd59fdc848afebf6"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a80556bc89548c5f1fd59fdc848afebf6">Invert</a> (const Field &F, const size_t M, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity)</td></tr>
<tr class="memdesc:a80556bc89548c5f1fd59fdc848afebf6"><td class="mdescLeft"> </td><td class="mdescRight">Invert the given matrix in place or computes its nullity if it is singular. <a href="#a80556bc89548c5f1fd59fdc848afebf6"></a><br/></td></tr>
<tr class="memitem:a59f1200ec102a5cc7657a9275a8706f8"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:a59f1200ec102a5cc7657a9275a8706f8"><td class="memTemplItemLeft" align="right" valign="top">Field::Element * </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a59f1200ec102a5cc7657a9275a8706f8">Invert2</a> (const Field &F, const size_t M, typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, int &nullity)</td></tr>
<tr class="memdesc:a59f1200ec102a5cc7657a9275a8706f8"><td class="mdescLeft"> </td><td class="mdescRight">Invert the given matrix or computes its nullity if it is singular. <a href="#a59f1200ec102a5cc7657a9275a8706f8"></a><br/></td></tr>
<tr class="memitem:a364e39068cae2bda9e80e360a8de23e6"><td class="memTemplParams" colspan="2"><a class="anchor" id="a364e39068cae2bda9e80e360a8de23e6"></a>
template<class Field , class Polynomial > </td></tr>
<tr class="memitem:a364e39068cae2bda9e80e360a8de23e6"><td class="memTemplItemLeft" align="right" valign="top">std::list< Polynomial > & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a364e39068cae2bda9e80e360a8de23e6">CharPoly</a> (const Field &F, std::list< Polynomial > &charp, const size_t N, typename Field::Element *A, const size_t lda, const FFPACK_CHARPOLY_TAG CharpTag=FfpackArithProg)</td></tr>
<tr class="memdesc:a364e39068cae2bda9e80e360a8de23e6"><td class="mdescLeft"> </td><td class="mdescRight">Compute the characteristic polynomial of A using Krylov Method, and LUP factorization of the Krylov matrix. <br/></td></tr>
<tr class="memitem:a780c41a978181bb6748e7408afafb8bd"><td class="memTemplParams" colspan="2">template<class Field , class Polynomial > </td></tr>
<tr class="memitem:a780c41a978181bb6748e7408afafb8bd"><td class="memTemplItemLeft" align="right" valign="top">Polynomial & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a780c41a978181bb6748e7408afafb8bd">MinPoly</a> (const Field &F, Polynomial &minP, const size_t N, const typename Field::Element *A, const size_t lda, typename Field::Element *X, const size_t ldx, size_t *P, const FFPACK::FFPACK_MINPOLY_TAG MinTag=FFPACK::FfpackDense, const size_t kg_mc=0, const size_t kg_mb=0, const size_t kg_j=0)</td></tr>
<tr class="memdesc:a780c41a978181bb6748e7408afafb8bd"><td class="mdescLeft"> </td><td class="mdescRight">Compute the minimal polynomial. <a href="#a780c41a978181bb6748e7408afafb8bd"></a><br/></td></tr>
<tr class="memitem:ae80a3042ee78c779583421aca1fb627a"><td class="memTemplParams" colspan="2">template<class Field > </td></tr>
<tr class="memitem:ae80a3042ee78c779583421aca1fb627a"><td class="memTemplItemLeft" align="right" valign="top">void </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#ae80a3042ee78c779583421aca1fb627a">solveLB</a> (const Field &F, const <a class="el" href="namespace_f_f_l_a_s.html#a3682647a50fad9d8d612055cd8e66d66">FFLAS::FFLAS_SIDE</a> Side, const size_t M, const size_t N, const size_t R, typename Field::Element *L, const size_t ldl, const size_t *Q, typename Field::Element *B, const size_t ldb)</td></tr>
<tr class="memdesc:ae80a3042ee78c779583421aca1fb627a"><td class="mdescLeft"> </td><td class="mdescRight">Solve L X = B or X L = B in place. <a href="#ae80a3042ee78c779583421aca1fb627a"></a><br/></td></tr>
<tr class="memitem:a365881372ad0e812ff22f4ccf9544aa4"><td class="memTemplParams" colspan="2">template<class Field , class Polynomial > </td></tr>
<tr class="memitem:a365881372ad0e812ff22f4ccf9544aa4"><td class="memTemplItemLeft" align="right" valign="top">std::list< Polynomial > & </td><td class="memTemplItemRight" valign="bottom"><a class="el" href="namespace_f_f_p_a_c_k.html#a365881372ad0e812ff22f4ccf9544aa4">CharpolyArithProg</a> (const Field &F, std::list< Polynomial > &frobeniusForm, const size_t N, typename Field::Element *A, const size_t lda, const size_t c)</td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><p>Set of elimination based routines for dense linear algebra. </p>
<p>Matrices are supposed over finite prime field of characteristic less than 2^26. </p>
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