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<TITLE>EPSDenseSchur</TITLE>
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<H1>EPSDenseSchur</H1>
Computes the upper (quasi-)triangular form of a dense upper Hessenberg matrix.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepceps.h"
PetscErrorCode EPSDenseSchur(PetscInt n_,PetscInt k,PetscScalar *H,PetscInt ldh_,PetscScalar *Z,PetscScalar *wr,PetscScalar *wi)
</PRE>
Not Collective
<P>
<H3><FONT COLOR="#883300">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>n </B></TD><TD> - dimension of the matrix
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>k </B></TD><TD> - first active column
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ldh </B></TD><TD> - leading dimension of H
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Input/Output Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>H </B></TD><TD> - on entry, the upper Hessenber matrix; on exit, the upper
(quasi-)triangular matrix (T)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>Z </B></TD><TD> - on entry, initial transformation matrix; on exit, orthogonal
matrix of Schur vectors
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Output Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>wr </B></TD><TD> - pointer to the array to store the computed eigenvalues
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>wi </B></TD><TD> - imaginary part of the eigenvalues (only when using real numbers)
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
This function computes the (real) Schur decomposition of an upper
Hessenberg matrix H: H*Z = Z*T, where T is an upper (quasi-)triangular
matrix (returned in H), and Z is the orthogonal matrix of Schur vectors.
Eigenvalues are extracted from the diagonal blocks of T and returned in
wr,wi. Transformations are accumulated in Z so that on entry it can
contain the transformation matrix associated to the Hessenberg reduction.
<P>
Only active columns (from k to n) are computed.
<P>
Both H and Z are overwritten.
<P>
This routine uses LAPACK routines xHSEQR.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../EPS/EPSDenseHessenberg.html#EPSDenseHessenberg">EPSDenseHessenberg</A>(), <A HREF="../EPS/EPSSortDenseSchur.html#EPSSortDenseSchur">EPSSortDenseSchur</A>(), <A HREF="../EPS/EPSDenseTridiagonal.html#EPSDenseTridiagonal">EPSDenseTridiagonal</A>()
<BR><P><B><FONT COLOR="#883300">Location: </FONT></B><A HREF="../../../src/eps/interface/dense.c.html#EPSDenseSchur">src/eps/interface/dense.c</A>
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