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
|
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML3.2 EN">
<HTML>
<HEAD> <link rel="canonical" href="https://slepc.upv.es/documentation/current//Users/jroman/tmp/slepc-3.23.1/docs/manualpages/DS/DSNEP.html" />
<META NAME="GENERATOR" CONTENT="DOCTEXT">
<link rel="stylesheet" href="/slepc.css" type="text/css">
<TITLE>DSNEP</TITLE>
</HEAD>
<BODY BGCOLOR="FFFFFF">
<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
<div id="bugreport" align=right><a href="mailto:slepc-maint@upv.es?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: slepc-3.23.1 v3.23.1 /Users/jroman/tmp/slepc-3.23.1/docs/manualpages/DS/DSNEP.html "><small>Report Typos and Errors</small></a></div>
<H1>DSNEP</H1>
Dense Nonlinear Eigenvalue Problem.
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
The problem is expressed as T(lambda)*x = 0, where T(lambda) is a
parameter-dependent matrix written as T(lambda) = sum_i E_i*f_i(lambda).
The eigenvalues lambda are the arguments returned by <A HREF="../DS/DSSolve.html#DSSolve">DSSolve</A>()..
<P>
The coefficient matrices E_i are the extra matrices of the <A HREF="../DS/DS.html#DS">DS</A>, and
the scalar functions f_i are passed via <A HREF="../DS/DSNEPSetFN.html#DSNEPSetFN">DSNEPSetFN</A>(). Optionally, a
callback function to fill the E_i matrices can be set with
<A HREF="../DS/DSNEPSetComputeMatrixFunction.html#DSNEPSetComputeMatrixFunction">DSNEPSetComputeMatrixFunction</A>().
<P>
<H3><FONT COLOR="#883300">Used DS matrices</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>DS_MAT_Ex </B></TD><TD> - coefficient matrices of the split form of T(lambda)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_X</A> </B></TD><TD> - eigenvectors
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_A</A> </B></TD><TD> - (workspace) T(lambda) evaluated at a given lambda (SLP only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_B</A> </B></TD><TD> - (workspace) T'(lambda) evaluated at a given lambda (SLP only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Q</A> </B></TD><TD> - (workspace) left Hankel matrix (contour only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Z</A> </B></TD><TD> - (workspace) right Hankel matrix (contour only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_U</A> </B></TD><TD> - (workspace) left singular vectors (contour only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_V</A> </B></TD><TD> - (workspace) right singular vectors (contour only)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_W</A> </B></TD><TD> - (workspace) auxiliary matrix of size nxn
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Implemented methods</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>0 </B></TD><TD> - Successive Linear Problems (SLP), computes just one eigenpair
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>1 </B></TD><TD> - Contour integral, computes all eigenvalues inside a region
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../DS/DSCreate.html#DSCreate">DSCreate</A>(), <A HREF="../DS/DSSetType.html#DSSetType">DSSetType</A>(), <A HREF="../DS/DSType.html#DSType">DSType</A>, <A HREF="../DS/DSNEPSetFN.html#DSNEPSetFN">DSNEPSetFN</A>(), <A HREF="../DS/DSNEPSetComputeMatrixFunction.html#DSNEPSetComputeMatrixFunction">DSNEPSetComputeMatrixFunction</A>()
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>beginner<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/sys/classes/ds/impls/nep/dsnep.c.html#DSNEP">src/sys/classes/ds/impls/nep/dsnep.c</A>
<BR><BR><A HREF="./index.html">Index of all DS routines</A>
<BR><A HREF="../../../docs/manual.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
</BODY></HTML>
|
