File: MatSetNullSpace.html

package info (click to toggle)
petsc 3.7.5%2Bdfsg1-4
  • links: PTS, VCS
  • area: main
  • in suites: stretch
  • size: 163,864 kB
  • ctags: 618,438
  • sloc: ansic: 515,133; python: 29,793; makefile: 20,458; fortran: 18,998; cpp: 6,515; f90: 3,914; sh: 1,012; xml: 621; objc: 445; csh: 240; java: 13
file content (62 lines) | stat: -rw-r--r-- 4,825 bytes parent folder | download
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
<HTML>
<HEAD> <link rel="canonical" href="http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Mat/MatSetNullSpace.html" />
<META NAME="GENERATOR" CONTENT="DOCTEXT">
<TITLE>MatSetNullSpace</TITLE>
</HEAD>
<BODY BGCOLOR="FFFFFF">
   <div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
   <div id="bugreport" align=right><a href="mailto:petsc-maint@mcs.anl.gov?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: petsc-3.7.5 v3.7.5 docs/manualpages/Mat/MatSetNullSpace.html "><small>Report Typos and Errors</small></a></div>
<A NAME="MatSetNullSpace"><H1>MatSetNullSpace</H1></A>
attaches a null space to a matrix. 
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscmat.h" 
PetscErrorCode MatSetNullSpace(Mat mat,MatNullSpace nullsp)
</PRE>
Logically Collective on <A HREF="../Mat/Mat.html#Mat">Mat</A> and <A HREF="../Mat/MatNullSpace.html#MatNullSpace">MatNullSpace</A>
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>mat </B></TD><TD>- the matrix
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>nullsp </B></TD><TD>- the null space object
</TD></TR></TABLE>
<P>

<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
This null space is used by the linear solvers. Overwrites any previous null space that may have been attached
<P>
For inconsistent singular systems (linear systems where the right hand side is not in the range of the operator) you also likely should
call <A HREF="../Mat/MatSetTransposeNullSpace.html#MatSetTransposeNullSpace">MatSetTransposeNullSpace</A>(). This allows the linear system to be solved in a least squares sense.
<P>
You can remove the null space by calling this routine with an nullsp of NULL
<P>
<P>
The fundamental theorem of linear algebra (Gilbert Strang, Introduction to Applied Mathematics, page 72) states that
the domain of a matrix A (from R^n to R^m (m rows, n columns) R^n = the direct sum of the null space of A, n(A), + the range of A^T, R(A^T).
Similarly R^m = direct sum n(A^T) + R(A).  Hence the linear system A x = b has a solution only if b in R(A) (or correspondingly b is orthogonal to
n(A^T)) and if x is a solution then x + alpha n(A) is a solution for any alpha. The minimum norm solution is orthogonal to n(A). For problems without a solution
the solution that minimizes the norm of the residual (the least squares solution) can be obtained by solving A x = \hat{b} where \hat{b} is b orthogonalized to the n(A^T).
<P>
Krylov solvers can produce the minimal norm solution to the least squares problem by utilizing <A HREF="../Mat/MatNullSpaceRemove.html#MatNullSpaceRemove">MatNullSpaceRemove</A>().
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
 <A HREF="../Mat/MatCreate.html#MatCreate">MatCreate</A>(), <A HREF="../Mat/MatNullSpaceCreate.html#MatNullSpaceCreate">MatNullSpaceCreate</A>(), <A HREF="../Mat/MatSetNearNullSpace.html#MatSetNearNullSpace">MatSetNearNullSpace</A>(), <A HREF="../Mat/MatGetNullSpace.html#MatGetNullSpace">MatGetNullSpace</A>(), <A HREF="../Mat/MatSetTransposeNullSpace.html#MatSetTransposeNullSpace">MatSetTransposeNullSpace</A>(), <A HREF="../Mat/MatGetTransposeNullSpace.html#MatGetTransposeNullSpace">MatGetTransposeNullSpace</A>(), <A HREF="../Mat/MatNullSpaceRemove.html#MatNullSpaceRemove">MatNullSpaceRemove</A>()
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>advanced
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/mat/interface/matrix.c.html#MatSetNullSpace">src/mat/interface/matrix.c</A>
<BR><A HREF="./index.html">Index of all Mat routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex4.c.html">src/ksp/ksp/examples/tutorials/ex4.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex29.c.html">src/ksp/ksp/examples/tutorials/ex29.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex32.c.html">src/ksp/ksp/examples/tutorials/ex32.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex34.c.html">src/ksp/ksp/examples/tutorials/ex34.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex50.c.html">src/ksp/ksp/examples/tutorials/ex50.c.html</A><BR>
<A HREF="../../../src/snes/examples/tutorials/ex7.c.html">src/snes/examples/tutorials/ex7.c.html</A><BR>
<A HREF="../../../src/snes/examples/tutorials/ex12.c.html">src/snes/examples/tutorials/ex12.c.html</A><BR>
<A HREF="../../../src/snes/examples/tutorials/ex62.c.html">src/snes/examples/tutorials/ex62.c.html</A><BR>
</BODY></HTML>