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<p>Solves the system of linear equations A*X=B.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include "<a class="el" href="slu__ddefs_8h_source.html">slu_ddefs.h</a>"</code><br />
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Functions</h2></td></tr>
<tr class="memitem:a78e780216de6dd0e85a5003c9d064952"><td class="memItemLeft" align="right" valign="top">void </td><td class="memItemRight" valign="bottom"><a class="el" href="dgssv_8c.html#a78e780216de6dd0e85a5003c9d064952">dgssv</a> (<a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> *options, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="zsymv_8c.html#af5d6242ff783dd9efca51eeec1c234f7">A</a>, int *perm_c, int *perm_r, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *L, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *<a class="el" href="zlarnv_8c.html#aa856a8508457fb5628c7d60f266c5596">U</a>, <a class="el" href="structSuperMatrix.html">SuperMatrix</a> *B, <a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> *stat, <a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> *info)</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p >Copyright (c) 2003, The Regents of the University of California, through Lawrence Berkeley National Laboratory (subject to receipt of any required approvals from U.S. Dept. of Energy)</p>
<p >All rights reserved.</p>
<p >The source code is distributed under BSD license, see the file License.txt at the top-level directory.</p>
<pre>
-- SuperLU routine (version 7.0.0) --
Univ. of California Berkeley, Xerox Palo Alto Research Center,
and Lawrence Berkeley National Lab.
October 15, 2003
August 2024
</pre> </div><h2 class="groupheader">Function Documentation</h2>
<a id="a78e780216de6dd0e85a5003c9d064952" name="a78e780216de6dd0e85a5003c9d064952"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a78e780216de6dd0e85a5003c9d064952">◆ </a></span>dgssv()</h2>
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<td class="memname">void dgssv </td>
<td>(</td>
<td class="paramtype"><a class="el" href="structsuperlu__options__t.html">superlu_options_t</a> * </td>
<td class="paramname"><em>options</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>A</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm_c</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int * </td>
<td class="paramname"><em>perm_r</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>L</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>U</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperMatrix.html">SuperMatrix</a> * </td>
<td class="paramname"><em>B</em>, </td>
</tr>
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<td class="paramkey"></td>
<td></td>
<td class="paramtype"><a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a> * </td>
<td class="paramname"><em>stat</em>, </td>
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<td class="paramtype"><a class="el" href="superlu__config_8h.html#ab6fd6105e64ed14a0c9281326f05e623">int_t</a> * </td>
<td class="paramname"><em>info</em> </td>
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<pre>
Purpose
=======
DGSSV solves the system of linear equations A*X=B, using the
LU factorization from DGSTRF. It performs the following steps:
1. If A is stored column-wise (A->Stype = SLU_NC):
1.1. Permute the columns of A, forming A*Pc, where Pc
is a permutation matrix. For more details of this step,
see <a class="el" href="sp__preorder_8c.html" title="Permute and performs functions on columns of original matrix.">sp_preorder.c</a>.
1.2. Factor A as Pr*A*Pc=L*U with the permutation Pr determined
by Gaussian elimination with partial pivoting.
L is unit lower triangular with offdiagonal entries
bounded by 1 in magnitude, and U is upper triangular.
1.3. Solve the system of equations A*X=B using the factored
form of A.
2. If A is stored row-wise (A->Stype = SLU_NR), apply the
above algorithm to the transpose of A:
2.1. Permute columns of transpose(A) (rows of A),
forming transpose(A)*Pc, where Pc is a permutation matrix.
For more details of this step, see <a class="el" href="sp__preorder_8c.html" title="Permute and performs functions on columns of original matrix.">sp_preorder.c</a>.
2.2. Factor A as Pr*transpose(A)*Pc=L*U with the permutation Pr
determined by Gaussian elimination with partial pivoting.
L is unit lower triangular with offdiagonal entries
bounded by 1 in magnitude, and U is upper triangular.
2.3. Solve the system of equations A*X=B using the factored
form of A.
See <a class="el" href="supermatrix_8h.html" title="Matrix type definitions.">supermatrix.h</a> for the definition of '<a class="el" href="structSuperMatrix.html">SuperMatrix</a>' structure.
Arguments
=========
options (input) superlu_options_t*
The structure defines the input parameters to control
how the LU decomposition will be performed and how the
system will be solved.
A (input) SuperMatrix*
Matrix A in A*X=B, of dimension (A->nrow, A->ncol). The number
of linear equations is A->nrow. Currently, the type of A can be:
Stype = SLU_NC or SLU_NR; Dtype = SLU_D; Mtype = SLU_GE.
In the future, more general A may be handled.
perm_c (input/output) int*
If A->Stype = SLU_NC, column permutation vector of size A->ncol
which defines the permutation matrix Pc; perm_c[i] = j means
column i of A is in position j in A*Pc.
If A->Stype = SLU_NR, column permutation vector of size A->nrow
which describes permutation of columns of transpose(A)
(rows of A) as described above.
If options->ColPerm = MY_PERMC or options->Fact = SamePattern or
options->Fact = SamePattern_SameRowPerm, it is an input argument.
On exit, perm_c may be overwritten by the product of the input
perm_c and a permutation that postorders the elimination tree
of Pc'*A'*A*Pc; perm_c is not changed if the elimination tree
is already in postorder.
Otherwise, it is an output argument.
perm_r (input/output) int*
If A->Stype = SLU_NC, row permutation vector of size A->nrow,
which defines the permutation matrix Pr, and is determined
by partial pivoting. perm_r[i] = j means row i of A is in
position j in Pr*A.
If A->Stype = SLU_NR, permutation vector of size A->ncol, which
determines permutation of rows of transpose(A)
(columns of A) as described above.
If options->RowPerm = MY_PERMR or
options->Fact = SamePattern_SameRowPerm, perm_r is an
input argument.
otherwise it is an output argument.
L (output) SuperMatrix*
The factor L from the factorization
Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
Uses compressed row subscripts storage for supernodes, i.e.,
L has types: Stype = SLU_SC, Dtype = SLU_D, Mtype = SLU_TRLU.
U (output) SuperMatrix*
The factor U from the factorization
Pr*A*Pc=L*U (if A->Stype = SLU_NC) or
Pr*transpose(A)*Pc=L*U (if A->Stype = SLU_NR).
Uses column-wise storage scheme, i.e., U has types:
Stype = SLU_NC, Dtype = SLU_D, Mtype = SLU_TRU.
B (input/output) SuperMatrix*
B has types: Stype = SLU_DN, Dtype = SLU_D, Mtype = SLU_GE.
On entry, the right hand side matrix.
On exit, the solution matrix if info = 0;
stat (output) SuperLUStat_t*
Record the statistics on runtime and floating-point operation count.
See util.h for the definition of '<a class="el" href="structSuperLUStat__t.html">SuperLUStat_t</a>'.
info (output) int*
= 0: successful exit
> 0: if info = i, and i is
<= A->ncol: <a class="el" href="zlarnv_8c.html#aa856a8508457fb5628c7d60f266c5596">U(i,i)</a> is exactly zero. The factorization has
been completed, but the factor U is exactly singular,
so the solution could not be computed.
> A->ncol: number of bytes allocated when memory allocation
failure occurred, plus A->ncol.
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