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<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
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<H1>DSHEP</H1>
Dense Hermitian Eigenvalue Problem.
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
The problem is expressed as A*X = X*Lambda, where A is real symmetric
(or complex Hermitian). Lambda is a diagonal matrix whose diagonal
elements are the arguments of <A HREF="../DS/DSSolve.html#DSSolve">DSSolve</A>(). After solve, A is overwritten
with Lambda.
<P>
In the intermediate state A is reduced to tridiagonal form. In compact
storage format, the symmetric tridiagonal matrix is stored in T.
<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><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_A</A> </B></TD><TD> - problem matrix (used only if compact=false)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_T</A> </B></TD><TD> - symmetric tridiagonal matrix
</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> - orthogonal/unitary transformation that reduces to tridiagonal form
(intermediate step) or matrix of orthogonal eigenvectors, which is equal to X
</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> - Implicit QR (_steqr)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>1 </B></TD><TD> - Multiple Relatively Robust Representations (_stevr)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>2 </B></TD><TD> - Divide and Conquer (_stedc)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>3 </B></TD><TD> - Block Divide and Conquer (real scalars only)
</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>
<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/hep/dshep.c.html#DSHEP">src/sys/classes/ds/impls/hep/dshep.c</A>
<BR><BR><A HREF="./index.html">Index of all DS routines</A>
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