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<H1><A NAME="SECTION031110000000000000000">
Notes</A>
</H1>

<P>
<DL COMPACT>
<DT>1.
<DD>The appendix consists mainly of indexes 
giving the nearest LAPACK equivalents of LINPACK and EISPACK routines.
These indexes should not be followed blindly or rigidly, 
especially when two or more
LINPACK or EISPACK routines are being used together: in many such cases
one of the LAPACK driver routines may be a suitable replacement.
<P>
<DT>2.
<DD>When two or more LAPACK routines are given in a single entry, these
routines must be combined to achieve the equivalent function.

<P>
<DT>3.
<DD>For LINPACK, an index is given for equivalents of the real LINPACK
routines; these equivalences apply also to the corresponding complex routines.
A separate table is included for equivalences of complex Hermitian routines.
For EISPACK, an index is given for all real and complex routines,
since there is no direct 1-to-1 correspondence between real and complex
routines in EISPACK.

<P>
<DT>4.
<DD>A few of the less commonly used routines in LINPACK and EISPACK have no
equivalents in Release 1.0 of LAPACK; equivalents for some of these (but not 
all) are planned for a future release.

<P>
<DT>5.
<DD>For some EISPACK routines, there are LAPACK routines providing similar
functionality, but using a significantly different method, or LAPACK routines
which provide only part of the functionality; such routines are marked by
a <IMG
 WIDTH="12" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img1009.png"
 ALT="$\dag $">.
For example, the EISPACK routine ELMHES uses non-orthogonal
transformations, whereas the nearest equivalent LAPACK routine, SGEHRD, uses
orthogonal transformations.

<P>
<DT>6.
<DD>In some cases the LAPACK equivalents require matrices to be stored
in a different storage scheme. For example:

<P>

<UL><LI>EISPACK routines BANDR<A NAME="22126"></A>, BANDV<A NAME="22127"></A>,
BQR<A NAME="22128"></A> and the driver routine RSB<A NAME="22129"></A>
require the lower triangle of
a symmetric band matrix to be stored in
a different storage scheme to that used in LAPACK, which is illustrated in
subsection&nbsp;<A HREF="node124.html#subsecband">5.3.3</A>. The corresponding storage scheme used by the 
EISPACK routines is:

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER">symmetric band matrix <B><I>A</I></B></TD>
<TD ALIGN="CENTER">EISPACK band storage</TD>
</TR>
<TR><TD ALIGN="CENTER">
<!-- MATH
 $\left( \begin{array}{ccccc}
a_{11} & a_{21} & a_{31} &              &              \\
a_{21} & a_{22}       & a_{32} & a_{42} &              \\
a_{31} & a_{32}       & a_{33}       & a_{43} & a_{53} \\
       & a_{42}       & a_{43}       & a_{44}       & a_{54} \\
       &              & a_{53}       & a_{54}       & a_{55}
\end{array} \right)$
 -->
<IMG
 WIDTH="229" HEIGHT="125" ALIGN="MIDDLE" BORDER="0"
 SRC="img1010.png"
 ALT="$
\left( \begin{array}{ccccc}
a_{11} &amp; a_{21} &amp; a_{31} &amp; &amp; \\
a_{21} &amp; a_{22} &amp;...
...a_{43} &amp; a_{44} &amp; a_{54} \\
&amp; &amp; a_{53} &amp; a_{54} &amp; a_{55}
\end{array} \right)
$"></TD>
<TD ALIGN="CENTER">
<!-- MATH
 $\begin{array}{ccccc}
 \ast  &  \ast  & a_{11} \\
 \ast  & a_{21} & a_{22} \\
a_{31} & a_{32} & a_{33} \\
a_{42} & a_{43} & a_{44} \\
a_{53} & a_{54} & a_{55} 
\end{array}$
 -->
<IMG
 WIDTH="123" HEIGHT="125" ALIGN="MIDDLE" BORDER="0"
 SRC="img1011.png"
 ALT="$
\begin{array}{ccccc}
\ast &amp; \ast &amp; a_{11} \\
\ast &amp; a_{21} &amp; a_{22} \\
a_{...
...&amp; a_{33} \\
a_{42} &amp; a_{43} &amp; a_{44} \\
a_{53} &amp; a_{54} &amp; a_{55}
\end{array}$"></TD>
</TR>
</TABLE>
</DIV>

<P>

<LI>EISPACK routines TRED1<A NAME="22173"></A>, TRED2<A NAME="22174"></A>,
TRED3<A NAME="22175"></A>, HTRID3<A NAME="22176"></A>,
HTRIDI<A NAME="22177"></A>, TQL1<A NAME="22178"></A>,
TQL2<A NAME="22179"></A>, IMTQL1<A NAME="22180"></A>,
IMTQL2<A NAME="22181"></A>, RATQR<A NAME="22182"></A>,
TQLRAT<A NAME="22183"></A> and the driver routine RST<A NAME="22184"></A>
store the off-diagonal elements of a symmetric tridiagonal
matrix in elements <B>2:<I>n</I></B> of the array E, whereas LAPACK routines use
elements <B>1:<I>n</I>-1</B>.

<P>

</UL>

<P>
<DT>7.
<DD>The EISPACK and LINPACK routines for the singular value decomposition 
return the matrix of right singular vectors, <B><I>V</I></B>, whereas the corresponding 
LAPACK routines return the transposed matrix <B><I>V</I><SUP><I>T</I></SUP></B>.

<P>
<DT>8.
<DD>In general, the argument lists of the
LAPACK routines are different from those of 
the corresponding EISPACK and LINPACK
routines, and the workspace requirements are often different.

<P>
</DL>

<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of LINPACK routines for real matrices</TD>
</TR>
<TR><TD ALIGN="LEFT">LINPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of LINPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">SCHDC<A NAME="22198"></A><A NAME="22199"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization with diagonal pivoting option</TD>
</TR>
<TR><TD ALIGN="LEFT">SCHDD<A NAME="22200"></A><A NAME="22201"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Rank-1 downdate of a Cholesky factorization or the triangular factor 
of a <B><I>QR</I></B> factorization</TD>
</TR>
<TR><TD ALIGN="LEFT">SCHEX<A NAME="22202"></A><A NAME="22203"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Modifies a Cholesky factorization under permutations of the original
matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SCHUD<A NAME="22204"></A><A NAME="22205"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Rank-1 update of a Cholesky factorization or the triangular factor
of a <B><I>QR</I></B> factorization</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBCO<A NAME="22206"></A><A NAME="22207"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SLANGB SGBTRF<A NAME="22208"></A><A NAME="22209"></A> SGBCON<A NAME="22210"></A><A NAME="22211"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331><B><I>LU</I></B> factorization and condition estimation of a general band 
matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBDI<A NAME="22212"></A><A NAME="22213"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant of a general band matrix, after factorization by SGBCO<A NAME="22214"></A> or SGBFA<A NAME="22215"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SGBFA<A NAME="22216"></A><A NAME="22217"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGBTRF<A NAME="22218"></A><A NAME="22219"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331><B><I>LU</I></B> factorization of a general band matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBSL<A NAME="22220"></A><A NAME="22221"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGBTRS<A NAME="22222"></A><A NAME="22223"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a general band system of linear equations, after factorization 
by SGBCO<A NAME="22224"></A> or SGBFA<A NAME="22225"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SGECO<A NAME="22226"></A><A NAME="22227"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SLANGE SGETRF<A NAME="22228"></A><A NAME="22229"></A> SGECON<A NAME="22230"></A><A NAME="22231"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331><B><I>LU</I></B> factorization and condition estimation of a general matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEDI<A NAME="22232"></A><A NAME="22233"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGETRI<A NAME="22234"></A><A NAME="22235"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant and inverse of a general matrix, after factorization by
SGECO<A NAME="22236"></A> or SGEFA<A NAME="22237"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SGEFA<A NAME="22238"></A><A NAME="22239"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGETRF<A NAME="22240"></A><A NAME="22241"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331><B><I>LU</I></B> factorization of a general matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SGESL<A NAME="22242"></A><A NAME="22243"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGETRS<A NAME="22244"></A><A NAME="22245"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a general system of linear equations, after factorization by
SGECO<A NAME="22246"></A> or SGEFA<A NAME="22247"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SGTSL<A NAME="22248"></A><A NAME="22249"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SGTSV<A NAME="22250"></A><A NAME="22251"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a general tridiagonal system of linear equations</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBCO<A NAME="22252"></A><A NAME="22253"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SLANSB SPBTRF<A NAME="22254"></A><A NAME="22255"></A> SPBCON<A NAME="22256"></A><A NAME="22257"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization and condition estimation
of a symmetric positive definite band matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBDI<A NAME="22258"></A><A NAME="22259"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant of a symmetric positive definite band matrix, after
factorization by SPBCO<A NAME="22260"></A> or SPBFA<A NAME="22261"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SPBFA<A NAME="22262"></A><A NAME="22263"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SPBTRF<A NAME="22264"></A><A NAME="22265"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization of a symmetric positive definite band matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBSL<A NAME="22266"></A><A NAME="22267"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SPBTRS<A NAME="22268"></A><A NAME="22269"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric positive definite band system of linear equations,
after factorization by SPBCO<A NAME="22270"></A> or SPBFA<A NAME="22271"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SPOCO<A NAME="22272"></A><A NAME="22273"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SLANSY SPOTRF<A NAME="22274"></A><A NAME="22275"></A> SPOCON<A NAME="22276"></A><A NAME="22277"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization and condition estimation
of a symmetric positive definite matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SPODI<A NAME="22278"></A><A NAME="22279"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SPOTRI<A NAME="22280"></A><A NAME="22281"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant and inverse of a symmetric positive definite matrix, after
factorization by SPOCO<A NAME="22282"></A> or SPOFA<A NAME="22283"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SPOFA<A NAME="22284"></A><A NAME="22285"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SPOTRF<A NAME="22286"></A><A NAME="22287"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization of a symmetric positive definite matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOSL<A NAME="22288"></A><A NAME="22289"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SPOTRS<A NAME="22290"></A><A NAME="22291"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric positive definite system of linear equations,
after factorization by SPOCO<A NAME="22292"></A> or SPOFA<A NAME="22293"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SPPCO<A NAME="22294"></A><A NAME="22295"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=50>SLANSY SPPTRF<A NAME="22296"></A><A NAME="22297"></A> SPPCON<A NAME="22298"></A><A NAME="22299"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization and condition estimation
of a symmetric positive definite matrix (packed storage)</TD>
</TR>
</TABLE>
</DIV>

<P>
<TABLE  WIDTH="100%">
<TR><TD>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of LINPACK routines for real matrices
(continued)</TD>
</TR>
<TR><TD ALIGN="LEFT">LINPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of LINPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPDI<A NAME="22316"></A><A NAME="22317"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SPPTRI<A NAME="22318"></A><A NAME="22319"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant and inverse of a symmetric positive definite matrix, after
factorization by SPPCO<A NAME="22320"></A><A NAME="22321"></A> or SPPFA<A NAME="22322"></A> (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPFA<A NAME="22323"></A><A NAME="22324"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SPPTRF<A NAME="22325"></A><A NAME="22326"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Cholesky factorization of a symmetric positive definite matrix 
(packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPSL<A NAME="22327"></A><A NAME="22328"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SPPTRS<A NAME="22329"></A><A NAME="22330"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric positive definite system of linear equations,
after factorization by SPPCO<A NAME="22331"></A> or SPPFA<A NAME="22332"></A> (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTSL<A NAME="22333"></A><A NAME="22334"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SPTSV<A NAME="22335"></A><A NAME="22336"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric positive definite tridiagonal system of linear equations</TD>
</TR>
<TR><TD ALIGN="LEFT">SQRDC<A NAME="22337"></A><A NAME="22338"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGEQPF<A NAME="22339"></A><A NAME="22340"></A> or SGEQRF<A NAME="22342"></A><A NAME="22343"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331><B><I>QR</I></B> factorization with optional column pivoting</TD>
</TR>
<TR><TD ALIGN="LEFT">SQRSL<A NAME="22344"></A><A NAME="22345"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SORMQR<A NAME="22346"></A><A NAME="22347"></A> STRSV<A NAME="tex2html3354"
HREF="#footmp22348"><SUP>1</SUP></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves linear least squares problems after factorization by SQRDC<A NAME="22349"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SSICO<A NAME="22350"></A><A NAME="22351"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SLANSY SSYTRF<A NAME="22352"></A><A NAME="22353"></A> SSYCON<A NAME="22354"></A><A NAME="22355"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Symmetric indefinite factorization and condition estimation
of a symmetric indefinite matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SSIDI<A NAME="22356"></A><A NAME="22357"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSYTRI<A NAME="22358"></A><A NAME="22359"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant, inertia and inverse of a symmetric indefinite matrix, after
factorization by SSICO<A NAME="22360"></A> or SSIFA<A NAME="22361"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SSIFA<A NAME="22362"></A><A NAME="22363"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSYTRF<A NAME="22364"></A><A NAME="22365"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Symmetric indefinite factorization of a symmetric indefinite matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">SSISL<A NAME="22366"></A><A NAME="22367"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSYTRS<A NAME="22368"></A><A NAME="22369"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric indefinite system of linear equations,
after factorization by SSICO<A NAME="22370"></A> or SSIFA<A NAME="22371"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">SSPCO<A NAME="22372"></A><A NAME="22373"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SLANSP SSPTRF<A NAME="22374"></A><A NAME="22375"></A> SSPCON<A NAME="22376"></A><A NAME="22377"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Symmetric indefinite factorization and condition estimation
of a symmetric indefinite matrix (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPDI<A NAME="22378"></A><A NAME="22379"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSPTRI<A NAME="22380"></A><A NAME="22381"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant, inertia and inverse of a symmetric indefinite matrix, after
factorization by SSPCO<A NAME="22382"></A> or SSPFA<A NAME="22383"></A> (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPFA<A NAME="22384"></A><A NAME="22385"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSPTRF<A NAME="22386"></A><A NAME="22387"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Symmetric indefinite factorization of a symmetric indefinite matrix 
(packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPSL<A NAME="22388"></A><A NAME="22389"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSPTRS<A NAME="22390"></A><A NAME="22391"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a symmetric indefinite system of linear equations,
after factorization by SSPCO<A NAME="22392"></A> or SSPFA<A NAME="22393"></A> (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">SSVDC<A NAME="22394"></A><A NAME="22395"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGESVD<A NAME="22396"></A><A NAME="22397"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All or part of the singular value decomposition of a general matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">STRCO<A NAME="22398"></A><A NAME="22399"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STRCON<A NAME="22400"></A><A NAME="22401"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Condition estimation of a triangular matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">STRDI<A NAME="22402"></A><A NAME="22403"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STRTRI<A NAME="22404"></A><A NAME="22405"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Determinant and inverse of a triangular matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">STRSL<A NAME="22406"></A><A NAME="22407"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STRTRS<A NAME="22408"></A><A NAME="22409"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves a triangular system of linear equations</TD>
</TR>
</TABLE>
</DIV></TD></TR>
</TABLE>

<P>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of LINPACK routines for complex Hermitian matrices</TD>
</TR>
<TR><TD ALIGN="LEFT">LINPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of LINPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">CHICO<A NAME="22425"></A><A NAME="22426"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHECON<A NAME="22427"></A><A NAME="22428"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Factors a complex Hermitian matrix by elimination with symmetric pivoting and
estimates the condition number of the matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">CHIDI<A NAME="22429"></A><A NAME="22430"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHETRI<A NAME="22431"></A><A NAME="22432"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Computes the determinant, inertia and inverse of a complex Hermitian matrix
using the factors from CHIFA<A NAME="22433"></A><A NAME="22434"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">CHIFA<A NAME="22435"></A><A NAME="22436"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHETRF<A NAME="22437"></A><A NAME="22438"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Factors a complex Hermitian matrix by elimination with symmetric pivoting</TD>
</TR>
<TR><TD ALIGN="LEFT">CHISL<A NAME="22439"></A><A NAME="22440"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHETRS<A NAME="22441"></A><A NAME="22442"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves the complex Hermitian system Ax=b using the factors computed by CHIFA<A NAME="22443"></A><A NAME="22444"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">CHPCO<A NAME="22445"></A><A NAME="22446"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHPCON<A NAME="22447"></A><A NAME="22448"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Factors a complex Hermitian matrix stored in packed form by elimination with
symmetric pivoting and estimates the condition number of the matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">CHPDI<A NAME="22449"></A><A NAME="22450"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHPTRI<A NAME="22451"></A><A NAME="22452"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Computes the determinant, intertia and inverse of a complex Hermitian matrix
using the factors from CHPFA<A NAME="22453"></A><A NAME="22454"></A>,
where the matrix is stored in packed form</TD>
</TR>
<TR><TD ALIGN="LEFT">CHPFA<A NAME="22455"></A><A NAME="22456"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHPTRF<A NAME="22457"></A><A NAME="22458"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Factors a complex Hermitian matrix stored in packed form by elimination
with symmetric pivoting</TD>
</TR>
<TR><TD ALIGN="LEFT">CHPSL<A NAME="22459"></A><A NAME="22460"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHPTRS<A NAME="22461"></A><A NAME="22462"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Solves the complex Hermitian system Ax=b using the factors computed by
CHPFA<A NAME="22463"></A><A NAME="22464"></A></TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of EISPACK routines</TD>
</TR>
<TR><TD ALIGN="LEFT">EISPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of EISPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">BAKVEC<A NAME="22479"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors after transformation by FIGI<A NAME="22480"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">BALANC<A NAME="22481"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGEBAL<A NAME="22482"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Balance a real matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">BALBAK<A NAME="22483"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGEBAK<A NAME="22484"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a real matrix after balancing by BALANC</TD>
</TR>
<TR><TD ALIGN="LEFT">BANDR<A NAME="22485"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSBTRD<A NAME="22486"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real symmetric band matrix to tridiagonal form</TD>
</TR>
<TR><TD ALIGN="LEFT">BANDV<A NAME="22487"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSBEVX<A NAME="22488"></A> SGBSV<A NAME="22489"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Selected eigenvectors of a real band matrix by inverse iteration</TD>
</TR>
<TR><TD ALIGN="LEFT">BISECT<A NAME="22490"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSTEBZ<A NAME="22491"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Eigenvalues in a specified interval of a real symmetric tridiagonal matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">BQR<A NAME="22492"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSBEVX<A NAME="22493"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Some eigenvalues of a real symmetric band matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">CBABK2<A NAME="22494"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CGEBAK<A NAME="22495"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a complex matrix after balancing by CBAL<A NAME="22496"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">CBAL<A NAME="22497"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CGEBAL<A NAME="22498"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Balance a complex matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">CG<A NAME="22499"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CGEEV<A NAME="22500"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a complex general matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">CH<A NAME="22501"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHEEV<A NAME="22502"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a complex Hermitian matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">CINVIT<A NAME="22503"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHSEIN<A NAME="22504"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Selected eigenvectors of a complex upper Hessenberg matrix by inverse 
iteration</TD>
</TR>
<TR><TD ALIGN="LEFT">COMBAK<A NAME="22505"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUNMHR<A NAME="22506"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a complex matrix after reduction by COMHES<A NAME="22507"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">COMHES<A NAME="22508"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CGEHRD<A NAME="22509"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a complex matrix to upper Hessenberg form by a
non-unitary transformation</TD>
</TR>
<TR><TD ALIGN="LEFT">COMLR<A NAME="22510"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHSEQR<A NAME="22511"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a complex upper Hessenberg matrix, by
the <B><I>LR</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">COMLR2<A NAME="22512"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUNGHR<A NAME="22513"></A> CHSEQR<A NAME="22514"></A> CTREVC<A NAME="22515"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues/vectors of a complex matrix 
by the <B><I>LR</I></B> algorithm, after reduction by COMHES<A NAME="22516"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">COMQR<A NAME="22517"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHSEQR<A NAME="22518"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a complex upper Hessenberg matrix by the
<B><I>QR</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">COMQR2<A NAME="22519"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUNGHR<A NAME="22520"></A> CHSEQR<A NAME="22521"></A> CTREVC<A NAME="22522"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues/vectors of a complex matrix by the <B><I>QR</I></B> algorithm,
after reduction by CORTH<A NAME="22523"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">CORTB<A NAME="22524"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUNMHR<A NAME="22525"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a complex matrix, after reduction by CORTH<A NAME="22526"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">CORTH<A NAME="22527"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CGEHRD<A NAME="22528"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a complex matrix to upper Hessenberg form by a unitary transformation</TD>
</TR>
<TR><TD ALIGN="LEFT">ELMBAK<A NAME="22529"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SORMHR<A NAME="22530"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a real matrix after reduction by ELMHES<A NAME="22531"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">ELMHES<A NAME="22532"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGEHRD<A NAME="22533"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real matrix to upper Hessenberg form by a
non-orthogonal transformation</TD>
</TR>
<TR><TD ALIGN="LEFT">ELTRAN<A NAME="22534"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SORGHR<A NAME="22535"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Generate transformation matrix used by ELMHES<A NAME="22536"></A></TD>
</TR>
</TABLE>
</DIV>

<P>
<TABLE  WIDTH="100%">
<TR><TD>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of EISPACK routines (continued)</TD>
</TR>
<TR><TD ALIGN="LEFT">EISPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of EISPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">FIGI<A NAME="22553"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Transform a nonsymmetric tridiagonal matrix of special form to a symmetric
matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">FIGI2<A NAME="22554"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>As FIGI, with generation of the transformation matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">HQR<A NAME="22555"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SHSEQR<A NAME="22556"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a complex upper Hessenberg matrix by the
<B><I>QR</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">HQR2<A NAME="22557"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SHSEQR<A NAME="22558"></A> STREVC<A NAME="22559"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues/vectors of a real upper Hessenberg matrix by the <B><I>QR</I></B> 
algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">HTRIB3<A NAME="22560"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUPMTR<A NAME="22561"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a complex Hermitian matrix after reduction
by HTRID3<A NAME="22562"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">HTRIBK<A NAME="22563"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CUNMTR<A NAME="22564"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a complex Hermitian matrix after reduction
by HTRIDI<A NAME="22565"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">HTRID3<A NAME="22566"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHPTRD<A NAME="22567"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a complex Hermitian matrix to tridiagonal form (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">HTRIDI<A NAME="22568"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>CHETRD<A NAME="22569"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a complex Hermitian matrix to tridiagonal form</TD>
</TR>
<TR><TD ALIGN="LEFT">IMTQL1<A NAME="22570"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSTEQR<A NAME="22571"></A> or SSTERF<A NAME="22572"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a symmetric tridiagonal matrix, by the 
implicit <B><I>QL</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">IMTQL2<A NAME="22573"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSTEQR<A NAME="22574"></A> or SSTEDC<A NAME="22576"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues/vectors of a symmetric tridiagonal matrix, by the implicit
<B><I>QL</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">IMTQLV<A NAME="22577"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSTEQR<A NAME="22578"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>As IMTQL1<A NAME="22579"></A>, preserving the input matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">INVIT<A NAME="22580"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SHSEIN<A NAME="22581"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Selected eigenvectors of a real upper Hessenberg matrix, by inverse 
iteration</TD>
</TR>
<TR><TD ALIGN="LEFT">MINFIT<A NAME="22582"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGELSS<A NAME="22583"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Minimum norm solution of a linear least squares problem, using the singular
value decomposition</TD>
</TR>
<TR><TD ALIGN="LEFT">ORTBAK<A NAME="22584"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SORMHR<A NAME="22585"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a real matrix after reduction to upper 
Hessenberg form by ORTHES<A NAME="22586"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">ORTHES<A NAME="22587"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGEHRD<A NAME="22588"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real matrix to upper Hessenberg form by an orthogonal 
transformation</TD>
</TR>
<TR><TD ALIGN="LEFT">ORTRAN<A NAME="22589"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SORGHR<A NAME="22590"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Generate orthogonal transformation matrix used by ORTHES</TD>
</TR>
<TR><TD ALIGN="LEFT">QZHES<A NAME="22591"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SGGHRD<A NAME="22592"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real generalized eigenproblem 
<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">
to
a form in which <B><I>A</I></B> is upper Hessenberg and <B><I>B</I></B> is upper triangular</TD>
</TR>
<TR><TD ALIGN="LEFT">QZIT<A NAME="22593"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SHGEQZ<A NAME="22594"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Generalized Schur factorization of a real generalized
eigenproblem,</TD>
</TR>
<TR><TD ALIGN="LEFT">QZVAL<A NAME="22595"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>after reduction by QZHES<A NAME="22596"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">QZVEC<A NAME="22597"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STGEVC<A NAME="22598"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvectors of a real generalized eigenproblem from generalized
Schur factorization</TD>
</TR>
<TR><TD ALIGN="LEFT">RATQR<A NAME="22599"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>SSTEBZ<A NAME="22600"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Extreme eigenvalues of a symmetric tridiagonal matrix using the rational QR 
algorithm with Newton corrections</TD>
</TR>
<TR><TD ALIGN="LEFT">REBAK<A NAME="22601"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STRSM<A NAME="tex2html3545"
HREF="#footmp22602"><SUP>1</SUP></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a symmetric definite generalized eigenproblem

<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">
or 
<!-- MATH
 $A B x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">
after reduction by REDUC<A NAME="22603"></A> or REDUC2<A NAME="22604"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">REBAKB<A NAME="22605"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=47>STRMM<A NAME="tex2html3546"
HREF="#footmp22606"><SUP>2</SUP></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a symmetric definite generalized eigenproblem

<!-- MATH
 $B A x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">
after reduction by REDUC2<A NAME="22607"></A></TD>
</TR>
</TABLE>
</DIV></TD></TR>
</TABLE>

<P>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of EISPACK routines (continued)</TD>
</TR>
<TR><TD ALIGN="LEFT">EISPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of EISPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">REDUC<A NAME="22623"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYGST<A NAME="22624"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce the symmetric definite generalized eigenproblem 
<!-- MATH
 $Ax = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">
to a standard symmetric eigenproblem</TD>
</TR>
<TR><TD ALIGN="LEFT">REDUC2<A NAME="22625"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYGST<A NAME="22626"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce the symmetric definite generalized eigenproblem 
<!-- MATH
 $A B x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">
or 
<!-- MATH
 $B A x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">
to a standard symmetric eigenproblem</TD>
</TR>
<TR><TD ALIGN="LEFT">RG<A NAME="22627"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SGEEV<A NAME="22628"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real general matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RGG<A NAME="22629"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SGEGV<A NAME="22630"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors or a real generalized 
eigenproblem (driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RS<A NAME="22631"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYEV<A NAME="22632"></A> or SSYEVD<A NAME="22633"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSB<A NAME="22634"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSBEV<A NAME="22635"></A> or SSBEVD<A NAME="22637"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric band matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSG<A NAME="22638"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYGV<A NAME="22639"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric definite
generalized eigenproblem 
<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSGAB<A NAME="22640"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYGV<A NAME="22641"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric definite
generalized eigenproblem 
<!-- MATH
 $A B x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSGBA<A NAME="22642"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYGV<A NAME="22643"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric definite
generalized eigenproblem 
<!-- MATH
 $B A x = \lambda x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSM<A NAME="22644"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYEVX<A NAME="22645"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Selected eigenvalues and optionally eigenvectors of a real symmetric matrix 
(driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RSP<A NAME="22646"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSPEV<A NAME="22647"></A> or SSPEVD<A NAME="22648"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric matrix
(packed storage) (driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RST<A NAME="22649"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEV<A NAME="22650"></A> or SSTEVD<A NAME="22651"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real symmetric tridiagonal
matrix (driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">RT<A NAME="22652"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues and optionally eigenvectors of a real tridiagonal matrix 
of special form (driver routine)</TD>
</TR>
<TR><TD ALIGN="LEFT">SVD<A NAME="22653"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SGESVD<A NAME="22654"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Singular value decomposition of a real matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">TINVIT<A NAME="22655"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEIN<A NAME="22656"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Selected eigenvectors of a symmetric tridiagonal matrix by inverse
iteration</TD>
</TR>
<TR><TD ALIGN="LEFT">TQL1<A NAME="22657"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEQR<A NAME="22658"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag">
<BR>
or SSTERF<A NAME="22660"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a symmetric tridiagonal matrix by the explicit 
<B><I>QL</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">TQL2<A NAME="22661"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEQR<A NAME="22662"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag">
<BR>
or SSTEDC<A NAME="22664"></A><IMG
 WIDTH="8" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="img1012.png"
 ALT="\dag"></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues/vectors of a symmetric tridiagonal matrix by the explicit
<B><I>QL</I></B> algorithm</TD>
</TR>
<TR><TD ALIGN="LEFT">TQLRAT<A NAME="22665"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTERF<A NAME="22666"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>All eigenvalues of a symmetric tridiagonal matrix by a rational variant of
the <B><I>QL</I></B> algorithm</TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">

<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=3>LAPACK equivalents of EISPACK routines (continued)</TD>
</TR>
<TR><TD ALIGN="LEFT">EISPACK</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>LAPACK</TD>
<TD ALIGN="CENTER" COLSPAN=1>Function of EISPACK routine</TD>
</TR>
<TR><TD ALIGN="LEFT">TRBAK1<A NAME="22681"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SORMTR<A NAME="22682"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a real symmetric matrix after reduction by
TRED1<A NAME="22683"></A></TD>
</TR>
<TR><TD ALIGN="LEFT">TRBAK3<A NAME="22684"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SOPMTR<A NAME="22685"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Backtransform eigenvectors of a real symmetric matrix after reduction by
TRED3<A NAME="22686"></A> (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">TRED1<A NAME="22687"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYTRD<A NAME="22688"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real symmetric matrix to tridiagonal form</TD>
</TR>
<TR><TD ALIGN="LEFT">TRED2<A NAME="22689"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSYTRD<A NAME="22690"></A> SORGTR<A NAME="22691"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>As TRED1<A NAME="22692"></A>, but also generating the orthogonal transformation matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">TRED3<A NAME="22693"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSPTRD<A NAME="22694"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Reduce a real symmetric matrix to tridiagonal form (packed storage)</TD>
</TR>
<TR><TD ALIGN="LEFT">TRIDIB<A NAME="22695"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEBZ<A NAME="22696"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Eigenvalues between specified indices of a symmetric tridiagonal matrix</TD>
</TR>
<TR><TD ALIGN="LEFT">TSTURM<A NAME="22697"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=43>SSTEBZ<A NAME="22698"></A> SSTEIN<A NAME="22699"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=331>Eigenvalues in a specified interval of a symmetric tridiagonal matrix,
and corresponding eigenvectors by inverse iteration</TD>
</TR>
</TABLE>
</DIV>

<P>
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<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
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