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<H1><A NAME="SECTION03810000000000000000">
Notes</A>
</H1>

<P>
<DL COMPACT>
<DT>1.
<DD>This index<A NAME="21182"></A><A NAME="21183"></A> lists related pairs of real and complex routines together,
for example, SBDSQR and CBDSQR. 
<P>
<DT>2.
<DD>Driver routines are listed in bold type, for example <B>SGBSV</B> and
<B>CGBSV</B>.

<P>
<DT>3.
<DD>Routines are listed in alphanumeric order
of the real (single precision) routine name (which always begins with S-).
(See subsection&nbsp;<A HREF="node24.html#subsecnaming">2.2.3</A> for details of the LAPACK naming scheme.)

<P>
<DT>4.
<DD>Double precision routines are not listed here;
they have names beginning with D- instead of
S-, or Z- instead of C-.

<P>
<DT>5.
<DD>This index gives only a brief description of the purpose of each
routine. For a precise description, consult the specifications
in Part&nbsp;<A HREF="node149.html#partroutines">2</A>, where the routines appear in the same
order as here.

<P>
<DT>6.
<DD>The text of the descriptions applies to both real and complex routines,
except where alternative words or phrases are indicated, for example
``symmetric/Hermitian'', ``orthogonal/unitary''
or ``quasi-triangular/triangular''. For the real routines <B><I>A</I><SUP><I>H</I></SUP></B> is equivalent
to <B><I>A</I><SUP><I>T</I></SUP></B>.
(The same convention is used in Part&nbsp;<A HREF="node149.html#partroutines">2</A>.)

<P>
<DT>7.
<DD>In a few cases, three routines are listed together, one for
real symmetric, one for complex symmetric, and one for complex Hermitian
matrices (for example SSPCON, CSPCON and CHPCON). 

<P>
<DT>8.
<DD>A few routines for real matrices have no complex equivalent (for example
SSTEBZ).

<P>
</DL>

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SBDSDC<A NAME="21200"></A></TD>
<TD ALIGN="LEFT">&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the singular value decomposition (SVD) of a real bidiagonal matrix,
using a divide and conquer method.</TD>
</TR>
<TR><TD ALIGN="LEFT">SBDSQR<A NAME="21201"></A></TD>
<TD ALIGN="LEFT">CBDSQR<A NAME="21202"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the singular value decomposition (SVD) of a real bidiagonal matrix,
using the bidiagonal <B><I>QR</I></B> algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT">SDISNA</TD>
<TD ALIGN="LEFT">&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the reciprocal condition numbers for the eigenvectors of a
real symmetric or complex Hermitian matrix or for the left or right
singular vectors of a general matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBBRD<A NAME="21203"></A></TD>
<TD ALIGN="LEFT">CGBBRD<A NAME="21204"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a general band matrix to real upper bidiagonal form
by an orthogonal/unitary transformation.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBCON<A NAME="21205"></A></TD>
<TD ALIGN="LEFT">CGBCON<A NAME="21206"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number
of a general band matrix, 
in either the 1-norm or the infinity-norm,
using the <B><I>LU</I></B> factorization computed by SGBTRF<A NAME="21207"></A>/CGBTRF<A NAME="21208"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBEQU<A NAME="21209"></A></TD>
<TD ALIGN="LEFT">CGBEQU<A NAME="21210"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes row and column scalings to equilibrate a general band matrix 
and reduce its condition number.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBRFS<A NAME="21211"></A></TD>
<TD ALIGN="LEFT">CGBRFS<A NAME="21212"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to a general banded system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGBSV<A NAME="21213"></A></B></TD>
<TD ALIGN="LEFT"><B> CGBSV<A NAME="21214"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general banded system of linear equations
<B><I>AX</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGBSVX<A NAME="21215"></A></B></TD>
<TD ALIGN="LEFT"><B> CGBSVX<A NAME="21216"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general banded system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBTRF<A NAME="21217"></A></TD>
<TD ALIGN="LEFT">CGBTRF<A NAME="21218"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>LU</I></B> factorization of a general band matrix,
using partial pivoting with row interchanges.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGBTRS<A NAME="21219"></A></TD>
<TD ALIGN="LEFT">CGBTRS<A NAME="21220"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general banded system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
using the <B><I>LU</I></B> factorization computed by SGBTRF<A NAME="21221"></A>/CGBTRF<A NAME="21222"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEBAK<A NAME="21223"></A></TD>
<TD ALIGN="LEFT">CGEBAK<A NAME="21224"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Transforms eigenvectors of a balanced matrix to those of the original matrix 
supplied to SGEBAL<A NAME="21225"></A>/CGEBAL<A NAME="21226"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEBAL<A NAME="21227"></A></TD>
<TD ALIGN="LEFT">CGEBAL<A NAME="21228"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Balances a general matrix
in order to improve the accuracy of computed eigenvalues.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEBRD<A NAME="21229"></A></TD>
<TD ALIGN="LEFT">CGEBRD<A NAME="21230"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a general rectangular matrix to  real bidiagonal form 
by an orthogonal/unitary transformation.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGECON<A NAME="21231"></A></TD>
<TD ALIGN="LEFT">CGECON<A NAME="21232"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number
of a general matrix, 
in either the 1-norm or the infinity-norm,
using the <B><I>LU</I></B> factorization computed by SGETRF<A NAME="21233"></A>/CGETRF<A NAME="21234"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEEQU<A NAME="21235"></A></TD>
<TD ALIGN="LEFT">CGEEQU<A NAME="21236"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes row and column scalings to equilibrate a general rectangular matrix 
and reduce its condition number.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGEES<A NAME="21237"></A></B></TD>
<TD ALIGN="LEFT"><B> CGEES<A NAME="21238"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the eigenvalues and Schur factorization of a general matrix, 
and orders the factorization so that selected eigenvalues are at the top left 
of the Schur form.</TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGEESX<A NAME="21251"></A></B></TD>
<TD ALIGN="LEFT"><B> CGEESX<A NAME="21252"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the eigenvalues and Schur factorization of a general matrix, 
orders the factorization so that selected eigenvalues are at the top left 
of the Schur form, 
and computes reciprocal condition numbers for the average of the selected
eigenvalues, 
and for the associated right invariant<A NAME="21253"></A>
subspace.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGEEV<A NAME="21254"></A> </B></TD>
<TD ALIGN="LEFT"><B> CGEEV<A NAME="21255"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the eigenvalues and left and right eigenvectors of a general matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGEEVX<A NAME="21256"></A></B></TD>
<TD ALIGN="LEFT"><B> CGEEVX<A NAME="21257"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the eigenvalues and left and right eigenvectors of a general matrix, 
with preliminary balancing of the matrix, 
and computes reciprocal condition numbers for the eigenvalues and right 
eigenvectors.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEHRD<A NAME="21258"></A></TD>
<TD ALIGN="LEFT">CGEHRD<A NAME="21259"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a general matrix to upper Hessenberg form 
by an orthogonal/unitary similarity transformation.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGELQF<A NAME="21260"></A></TD>
<TD ALIGN="LEFT">CGELQF<A NAME="21261"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>LQ</I></B> factorization of a general rectangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGELS<A NAME="21262"></A> </B></TD>
<TD ALIGN="LEFT"><B> CGELS<A NAME="21263"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the least squares solution to an overdetermined system of linear
equations, <B><I>A X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>, 
or the minimum norm solution of an underdetermined system,
where <B><I>A</I></B> is a general rectangular matrix of full rank, 
using a <B><I>QR</I></B> or <B><I>LQ</I></B> factorization of <B><I>A</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGELSD<A NAME="21264"></A></B></TD>
<TD ALIGN="LEFT"><B> CGELSD<A NAME="21265"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the minimum norm least squares solution
to an over- or underdetermined system of linear equations <B><I>A X</I>=<I>B</I></B>, 
using the singular value decomposition of <B><I>A</I></B> and a divide and 
conquer method.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGELSS<A NAME="21266"></A></B></TD>
<TD ALIGN="LEFT"><B> CGELSS<A NAME="21267"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the minimum norm least squares solution
to an over- or underdetermined system of linear equations <B><I>A X</I>=<I>B</I></B>, 
using the singular value decomposition of <B><I>A</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGELSY<A NAME="21268"></A></B></TD>
<TD ALIGN="LEFT"><B> CGELSY<A NAME="21269"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the minimum norm least squares solution
to an over- or underdetermined system of linear equations <B><I>A X</I>=<I>B</I></B>,
using a complete orthogonal factorization of <B><I>A</I></B> via xGEQP3.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEQLF<A NAME="21270"></A></TD>
<TD ALIGN="LEFT">CGEQLF<A NAME="21271"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a <B><I>QL</I></B> factorization of a general rectangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEQP3<A NAME="21272"></A></TD>
<TD ALIGN="LEFT">CGEQP3<A NAME="21273"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a <B><I>QR</I></B> factorization with column pivoting of a general rectangular 
matrix using Level 3 BLAS.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGEQRF<A NAME="21274"></A></TD>
<TD ALIGN="LEFT">CGEQRF<A NAME="21275"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a <B><I>QR</I></B> factorization of a general rectangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGERFS<A NAME="21276"></A></TD>
<TD ALIGN="LEFT">CGERFS<A NAME="21277"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to a general system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGERQF<A NAME="21278"></A></TD>
<TD ALIGN="LEFT">CGERQF<A NAME="21279"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>RQ</I></B> factorization of a general rectangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGESDD<A NAME="21280"></A></B></TD>
<TD ALIGN="LEFT"><B> CGESDD<A NAME="21281"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the singular value decomposition (SVD) of a general rectangular 
matrix using a divide and conquer method.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGESV<A NAME="21282"></A></B></TD>
<TD ALIGN="LEFT"><B> CGESV<A NAME="21283"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general system of linear equations <B><I>AX</I>=<I>B</I></B>.</TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGESVD<A NAME="21296"></A></B></TD>
<TD ALIGN="LEFT"><B> CGESVD<A NAME="21297"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the singular value decomposition (SVD) of a general rectangular 
matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGESVX<A NAME="21298"></A></B></TD>
<TD ALIGN="LEFT"><B> CGESVX<A NAME="21299"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGETRF<A NAME="21300"></A></TD>
<TD ALIGN="LEFT">CGETRF<A NAME="21301"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>LU</I></B> factorization of a general matrix,
using partial pivoting with row interchanges.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGETRI<A NAME="21302"></A></TD>
<TD ALIGN="LEFT">CGETRI<A NAME="21303"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of a general matrix, 
using the <B><I>LU</I></B> factorization computed by SGETRF<A NAME="21304"></A>/CGETRF<A NAME="21305"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGETRS<A NAME="21306"></A></TD>
<TD ALIGN="LEFT">CGETRS<A NAME="21307"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
using the <B><I>LU</I></B> factorization computed by SGETRF<A NAME="21308"></A>/CGETRF<A NAME="21309"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGBAK<A NAME="21310"></A></TD>
<TD ALIGN="LEFT">CGGBAK<A NAME="21311"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Forms the right or left eigenvectors of a real generalized
eigenvalue problem <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
by backward transformation on
the computed eigenvectors of the balanced pair of matrices output by
SGGBAL<A NAME="21312"></A>/CGGBAL<A NAME="21313"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGBAL<A NAME="21314"></A></TD>
<TD ALIGN="LEFT">CGGBAL<A NAME="21315"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Balances a pair of general matrices
to improve the accuracy of computed eigenvalues and/or
eigenvectors.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGES<A NAME="21316"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGES<A NAME="21317"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized eigenvalues, Schur form, and the left
and/or right Schur vectors for a pair of nonsymmetric matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGESX<A NAME="21318"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGESX<A NAME="21319"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized eigenvalues, Schur form, and, optionally, the left
and/or right matrices of Schur vectors.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGEV<A NAME="21320"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGEV<A NAME="21321"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized eigenvalues and the left and/or right
generalized eigenvectors for a pair of nonsymmetric matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGEVX<A NAME="21322"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGEVX<A NAME="21323"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized eigenvalues and, optionally, the left and/or right
generalized eigenvectors.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGGLM<A NAME="21324"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGGLM<A NAME="21325"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general Gauss-Markov linear model (GLM)<A NAME="21326"></A> problem using a generalized QR
factorization.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGHRD<A NAME="21327"></A></TD>
<TD ALIGN="LEFT">CGGHRD<A NAME="21328"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a pair of matrices to generalized upper Hessenberg form
using orthogonal/unitary transformations.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGLSE<A NAME="21329"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGLSE<A NAME="21330"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves the linear equality-constrained least squares (LSE)<A NAME="21331"></A> problem using a
generalized RQ factorization.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGQRF<A NAME="21332"></A></TD>
<TD ALIGN="LEFT">CGGQRF<A NAME="21333"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a generalized QR factorization of a pair of matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGRQF<A NAME="21334"></A></TD>
<TD ALIGN="LEFT">CGGRQF<A NAME="21335"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a generalized RQ factorization of a pair of matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGGSVD<A NAME="21336"></A></B></TD>
<TD ALIGN="LEFT"><B> CGGSVD<A NAME="21337"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized singular value decomposition (GSVD) of a pair
of general rectangular matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGGSVP<A NAME="21338"></A></TD>
<TD ALIGN="LEFT">CGGSVP<A NAME="21339"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes orthogonal/unitary matrices U, V, and Q as the preprocessing
step for computing the generalized singular value decomposition (GSVD).</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SGTCON<A NAME="21352"></A></TD>
<TD ALIGN="LEFT">CGTCON<A NAME="21353"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of a general tridiagonal 
matrix, 
in either the 1-norm or the infinity-norm,
using the <B><I>LU</I></B> factorization computed by SGTTRF<A NAME="21354"></A>/CGTTRF<A NAME="21355"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGTRFS<A NAME="21356"></A></TD>
<TD ALIGN="LEFT">CGTRFS<A NAME="21357"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to a general tridiagonal system of linear 
equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGTSV<A NAME="21358"></A></B></TD>
<TD ALIGN="LEFT"><B> CGTSV<A NAME="21359"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general tridiagonal system of linear equations <B><I>AX</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SGTSVX<A NAME="21360"></A></B></TD>
<TD ALIGN="LEFT"><B> CGTSVX<A NAME="21361"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general tridiagonal system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGTTRF<A NAME="21362"></A></TD>
<TD ALIGN="LEFT">CGTTRF<A NAME="21363"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>LU</I></B> factorization of a general tridiagonal matrix,
using partial pivoting with row interchanges.</TD>
</TR>
<TR><TD ALIGN="LEFT">SGTTRS<A NAME="21364"></A></TD>
<TD ALIGN="LEFT">CGTTRS<A NAME="21365"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a general tridiagonal system of linear equations
<B><I>AX</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
using the <B><I>LU</I></B> factorization computed by SGTTRF<A NAME="21366"></A>/CGTTRF<A NAME="21367"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SHGEQZ<A NAME="21368"></A></TD>
<TD ALIGN="LEFT">CHGEQZ<A NAME="21369"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Implements a single-/double-shift version of the QZ
method for finding the generalized eigenvalues of a pair of general
matrices, which can simultaneously be reduced to generalized Schur form
using orthogonal/unitary transformations.</TD>
</TR>
<TR><TD ALIGN="LEFT">SHSEIN<A NAME="21370"></A></TD>
<TD ALIGN="LEFT">CHSEIN<A NAME="21371"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes specified right and/or left eigenvectors of an upper Hessenberg matrix 
by inverse iteration.</TD>
</TR>
<TR><TD ALIGN="LEFT">SHSEQR<A NAME="21372"></A></TD>
<TD ALIGN="LEFT">CHSEQR<A NAME="21373"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the eigenvalues and Schur factorization of an upper Hessenberg matrix, 
using the multishift <B><I>QR</I></B> algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT">SOPGTR<A NAME="21374"></A></TD>
<TD ALIGN="LEFT">CUPGTR<A NAME="21375"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates the orthogonal/unitary transformation matrix
from a reduction to tridiagonal form determined by SSPTRD<A NAME="21376"></A>/CHPTRD<A NAME="21377"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SOPMTR<A NAME="21378"></A></TD>
<TD ALIGN="LEFT">CUPMTR<A NAME="21379"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary transformation matrix
from a reduction to tridiagonal form determined by SSPTRD<A NAME="21380"></A>/CHPTRD<A NAME="21381"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGBR<A NAME="21382"></A></TD>
<TD ALIGN="LEFT">CUNGBR<A NAME="21383"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates the orthogonal/unitary transformation matrices
from a reduction to bidiagonal form determined by SGEBRD<A NAME="21384"></A>/CGEBRD<A NAME="21385"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGHR<A NAME="21386"></A></TD>
<TD ALIGN="LEFT">CUNGHR<A NAME="21387"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates the orthogonal/unitary transformation matrix
from a reduction to Hessenberg form determined by SGEHRD<A NAME="21388"></A>/CGEHRD<A NAME="21389"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGLQ<A NAME="21390"></A></TD>
<TD ALIGN="LEFT">CUNGLQ<A NAME="21391"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates all or part of the orthogonal/unitary matrix <B><I>Q</I></B> 
from an <B><I>LQ</I></B> factorization determined by SGELQF<A NAME="21392"></A>/CGELQF<A NAME="21393"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGQL<A NAME="21394"></A></TD>
<TD ALIGN="LEFT">CUNGQL<A NAME="21395"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates all or part of the orthogonal/unitary matrix <B><I>Q</I></B> 
from a <B><I>QL</I></B> factorization determined by SGEQLF<A NAME="21396"></A>/CGEQLF<A NAME="21397"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGQR<A NAME="21398"></A></TD>
<TD ALIGN="LEFT">CUNGQR<A NAME="21399"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates all or part of the orthogonal/unitary matrix <B><I>Q</I></B> 
from a <B><I>QR</I></B> factorization determined by SGEQRF<A NAME="21400"></A>/CGEQRF<A NAME="21401"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGRQ<A NAME="21402"></A></TD>
<TD ALIGN="LEFT">CUNGRQ<A NAME="21403"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates all or part of the orthogonal/unitary matrix <B><I>Q</I></B> 
from an <B><I>RQ</I></B> factorization determined by SGERQF<A NAME="21404"></A>/CGERQF<A NAME="21405"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORGTR<A NAME="21406"></A></TD>
<TD ALIGN="LEFT">CUNGTR<A NAME="21407"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Generates the orthogonal/unitary transformation matrix 
from a reduction to tridiagonal form determined by SSYTRD<A NAME="21408"></A>/CHETRD<A NAME="21409"></A>.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMBR<A NAME="21422"></A></TD>
<TD ALIGN="LEFT">CUNMBR<A NAME="21423"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by one of the orthogonal/unitary transformation 
matrices 
from a reduction to bidiagonal form determined by SGEBRD<A NAME="21424"></A>/CGEBRD<A NAME="21425"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMHR<A NAME="21426"></A></TD>
<TD ALIGN="LEFT">CUNMHR<A NAME="21427"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary transformation matrix
from a reduction to Hessenberg form determined by SGEHRD<A NAME="21428"></A>/CGEHRD<A NAME="21429"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMLQ<A NAME="21430"></A></TD>
<TD ALIGN="LEFT">CUNMLQ<A NAME="21431"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary matrix 
from an <B><I>LQ</I></B> factorization determined by SGELQF<A NAME="21432"></A>/CGELQF<A NAME="21433"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMQL<A NAME="21434"></A></TD>
<TD ALIGN="LEFT">CUNMQL<A NAME="21435"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary matrix 
from a <B><I>QL</I></B> factorization determined by SGEQLF<A NAME="21436"></A>/CGEQLF<A NAME="21437"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMQR<A NAME="21438"></A></TD>
<TD ALIGN="LEFT">CUNMQR<A NAME="21439"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary matrix 
from a <B><I>QR</I></B> factorization determined by SGEQRF<A NAME="21440"></A>/CGEQRF<A NAME="21441"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMRQ<A NAME="21442"></A></TD>
<TD ALIGN="LEFT">CUNMRQ<A NAME="21443"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary matrix 
from an <B><I>RQ</I></B> factorization determined by SGERQF<A NAME="21444"></A>/CGERQF<A NAME="21445"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMRZ<A NAME="21446"></A></TD>
<TD ALIGN="LEFT">CUNMRZ<A NAME="21447"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary matrix
from an <B><I>RZ</I></B> factorization determined by STZRZF<A NAME="21448"></A>/CTZRZF<A NAME="21449"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SORMTR<A NAME="21450"></A></TD>
<TD ALIGN="LEFT">CUNMTR<A NAME="21451"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Multiplies a general matrix by the orthogonal/unitary transformation matrix
from a reduction to tridiagonal form determined by SSYTRD<A NAME="21452"></A>/CHETRD<A NAME="21453"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBCON<A NAME="21454"></A></TD>
<TD ALIGN="LEFT">CPBCON<A NAME="21455"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of 
a symmetric/Hermitian positive definite band matrix,
using the Cholesky factorization computed by SPBTRF<A NAME="21456"></A>/CPBTRF<A NAME="21457"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBEQU<A NAME="21458"></A></TD>
<TD ALIGN="LEFT">CPBEQU<A NAME="21459"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes row and column scalings to equilibrate 
a symmetric/Hermitian positive definite band matrix 
and reduce its condition number.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBRFS<A NAME="21460"></A></TD>
<TD ALIGN="LEFT">CPBRFS<A NAME="21461"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a symmetric/Hermitian positive definite banded system of linear equations
<B><I>A X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBSTF<A NAME="21462"></A></TD>
<TD ALIGN="LEFT">CPBSTF<A NAME="21463"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes a split Cholesky factorization of a real/complex
symmetric/Hermitian positive definite band matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPBSV<A NAME="21464"></A></B></TD>
<TD ALIGN="LEFT"><B> CPBSV<A NAME="21465"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite banded system of linear 
equations <B><I>A X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPBSVX<A NAME="21466"></A></B></TD>
<TD ALIGN="LEFT"><B> CPBSVX<A NAME="21467"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite banded system of linear 
equations
<B><I>A X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBTRF<A NAME="21468"></A></TD>
<TD ALIGN="LEFT">CPBTRF<A NAME="21469"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the Cholesky factorization of 
a symmetric/Hermitian positive definite band matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPBTRS<A NAME="21470"></A></TD>
<TD ALIGN="LEFT">CPBTRS<A NAME="21471"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite banded system of linear 
equations <B><I>A X</I>=<I>B</I></B>, 
using the Cholesky factorization computed by SPBTRF<A NAME="21472"></A>/CPBTRF<A NAME="21473"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOCON<A NAME="21474"></A></TD>
<TD ALIGN="LEFT">CPOCON<A NAME="21475"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of 
a symmetric/Hermitian positive definite matrix,
using the Cholesky factorization computed by SPOTRF<A NAME="21476"></A>/CPOTRF<A NAME="21477"></A>.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOEQU<A NAME="21491"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPOEQU<A NAME="21492"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes row and column scalings to equilibrate 
a symmetric/Hermitian positive definite matrix 
and reduce its condition number.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPORFS<A NAME="21493"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPORFS<A NAME="21494"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a symmetric/Hermitian positive definite system of linear equations <B><I>A X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPOSV<A NAME="21495"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPOSV<A NAME="21496"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPOSVX<A NAME="21497"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPOSVX<A NAME="21498"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOTRF<A NAME="21499"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPOTRF<A NAME="21500"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the Cholesky factorization of 
a symmetric/Hermitian positive definite matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOTRI<A NAME="21501"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPOTRI<A NAME="21502"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of 
a symmetric/Hermitian positive definite matrix,
using the Cholesky factorization computed by SPOTRF<A NAME="21503"></A>/CPOTRF<A NAME="21504"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPOTRS<A NAME="21505"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPOTRS<A NAME="21506"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>,
using the Cholesky factorization computed by SPOTRF<A NAME="21507"></A>/CPOTRF<A NAME="21508"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPCON<A NAME="21509"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPCON<A NAME="21510"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of 
a symmetric/Hermitian positive definite matrix in packed storage,
using the Cholesky factorization computed by SPPTRF<A NAME="21511"></A>/CPPTRF<A NAME="21512"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPEQU<A NAME="21513"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPEQU<A NAME="21514"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes row and column scalings to equilibrate 
a symmetric/Hermitian positive definite matrix in packed storage
and reduce its condition number.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPRFS<A NAME="21515"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPRFS<A NAME="21516"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a symmetric/Hermitian positive definite system of linear equations <B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPPSV<A NAME="21517"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPPSV<A NAME="21518"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPPSVX<A NAME="21519"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPPSVX<A NAME="21520"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPTRF<A NAME="21521"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPTRF<A NAME="21522"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the Cholesky factorization of 
a symmetric/Hermitian positive definite matrix in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPTRI<A NAME="21523"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPTRI<A NAME="21524"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of 
a symmetric/Hermitian positive definite matrix in packed storage,
using the Cholesky factorization computed by SPPTRF<A NAME="21525"></A>/CPPTRF<A NAME="21526"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPPTRS<A NAME="21527"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPPTRS<A NAME="21528"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite system of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
using the Cholesky factorization computed by SPPTRF<A NAME="21529"></A>/CPPTRF<A NAME="21530"></A>.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTCON<A NAME="21544"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPTCON<A NAME="21545"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the reciprocal of the condition number of 
a symmetric/Hermitian positive definite tridiagonal matrix,
using the <B><I>LDL</I><SUP><I>H</I></SUP></B> factorization computed by SPTTRF<A NAME="21546"></A>/CPTTRF<A NAME="21547"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTEQR<A NAME="21548"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPTEQR<A NAME="21549"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and eigenvectors of 
a real symmetric positive definite tridiagonal matrix,
by computing the SVD of its bidiagonal Cholesky factor.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTRFS<A NAME="21550"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPTRFS<A NAME="21551"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a symmetric/Hermitian positive definite tridiagonal system of linear equations
<B><I>A X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPTSV<A NAME="21552"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPTSV<A NAME="21553"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite tridiagonal system of linear 
equations
<B><I>A X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SPTSVX<A NAME="21554"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CPTSVX<A NAME="21555"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite tridiagonal system of linear 
equations
<B><I>A X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTTRF<A NAME="21556"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPTTRF<A NAME="21557"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the <B><I>LDL</I><SUP><I>H</I></SUP></B> factorization of 
a symmetric/Hermitian positive definite tridiagonal matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SPTTRS<A NAME="21558"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CPTTRS<A NAME="21559"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a symmetric/Hermitian positive definite tridiagonal system of linear 
equations, 
using the <B><I>LDL</I><SUP><I>H</I></SUP></B> factorization computed by SPTTRF<A NAME="21560"></A>/CPTTRF<A NAME="21561"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBEV<A NAME="21562"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBEV<A NAME="21563"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian band matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBEVD<A NAME="21564"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBEVD<A NAME="21565"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian band matrix.  If eigenvectors are desired, it uses
a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBEVX<A NAME="21566"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBEVX<A NAME="21567"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and eigenvectors of 
a symmetric/Hermitian band matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSBGST<A NAME="21568"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHBGST<A NAME="21569"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a real/complex symmetric-/Hermitian-definite banded
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 standard form,
where <B><I>B</I></B> has been factorized by SPBSTF/CPBSTF (Crawford's algorithm).</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBGV<A NAME="21570"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBGV<A NAME="21571"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all of the eigenvalues, and optionally, the eigenvectors 
of a real/complex generalized symmetric-/Hermitian-definite banded 
eigenproblem 
<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBGVD<A NAME="21572"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBGVD<A NAME="21573"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues, and optionally, the eigenvectors 
of a real/complex generalized symmetric-/Hermitian-definite banded 
eigenproblem 
<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">.
If eigenvectors are desired,
it uses a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSBGVX<A NAME="21574"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHBGVX<A NAME="21575"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues, and optionally, the eigenvectors 
of a real/complex generalized symmetric-/Hermitian-definite banded 
eigenproblem 
<!-- MATH
 $A x = \lambda B x$
 -->
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSBTRD<A NAME="21576"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHBTRD<A NAME="21577"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a symmetric/Hermitian band matrix 
to real symmetric tridiagonal form
by an orthogonal/unitary similarity transformation.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPCON<A NAME="21591"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSPCON<A NAME="21592"></A> CHPCON<A NAME="21593"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix in 
packed storage,
using the factorization computed by SSPTRF<A NAME="21594"></A>/CSPTRF<A NAME="21595"></A>/CHPTRF<A NAME="21596"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPEV<A NAME="21597"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPEV<A NAME="21598"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian matrix in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPEVD<A NAME="21599"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPEVD<A NAME="21600"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian matrix in packed storage.  If eigenvectors are
desired, it uses a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPEVX<A NAME="21601"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPEVX<A NAME="21602"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and eigenvectors of 
a symmetric/Hermitian matrix in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPGST<A NAME="21603"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHPGST<A NAME="21604"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a symmetric/Hermitian definite generalized eigenproblem 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">,
to standard form, 
where <B><I>A</I></B> and <B><I>B</I></B> are held in packed storage,
and <B><I>B</I></B> has been factorized by SPPTRF<A NAME="21605"></A>/CPPTRF<A NAME="21606"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPGV<A NAME="21607"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPGV<A NAME="21608"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">,
where <B><I>A</I></B> and <B><I>B</I></B> are in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPGVD<A NAME="21609"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPGVD<A NAME="21610"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues, and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">,
where <B><I>A</I></B> and <B><I>B</I></B> are in packed storage.  If eigenvectors are
desired, it uses a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPGVX<A NAME="21611"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHPGVX<A NAME="21612"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues, and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">,
where <B><I>A</I></B> and <B><I>B</I></B> are in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPRFS<A NAME="21613"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSPRFS<A NAME="21614"></A> CHPRFS<A NAME="21615"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a real symmetric/complex symmetric/complex Hermitian indefinite system of linear
equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPSV<A NAME="21616"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CSPSV<A NAME="21617"></A></B> <B> CHPSV<A NAME="21618"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSPSVX<A NAME="21619"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CSPSVX<A NAME="21620"></A></B> <B> CHPSVX<A NAME="21621"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPTRD<A NAME="21622"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHPTRD<A NAME="21623"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a symmetric/Hermitian matrix in packed storage
to real symmetric tridiagonal form 
by an orthogonal/unitary similarity transformation.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPTRF<A NAME="21637"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSPTRF<A NAME="21638"></A> CHPTRF<A NAME="21639"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the factorization of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix in 
packed storage,
using the diagonal pivoting<A NAME="21640"></A> method.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPTRI<A NAME="21641"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSPTRI<A NAME="21642"></A> CHPTRI<A NAME="21643"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix in 
packed storage,
using the factorization computed by SSPTRF<A NAME="21644"></A>/CSPTRF<A NAME="21645"></A>/CHPTRF<A NAME="21646"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSPTRS<A NAME="21647"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSPTRS<A NAME="21648"></A> CHPTRS<A NAME="21649"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage,
using the factorization computed by SSPTRF<A NAME="21650"></A>/CSPTRF<A NAME="21651"></A>/CHPTRF<A NAME="21652"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTEBZ<A NAME="21653"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues of a real symmetric tridiagonal matrix 
by bisection.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTEDC<A NAME="21654"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSTEDC<A NAME="21655"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of a
symmetric tridiagonal matrix using the divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTEGR<A NAME="21656"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSTEGR<A NAME="21657"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and, optionally, eigenvectors of 
a real symmetric tridiagonal matrix using the Relatively Robust
Representations.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTEIN<A NAME="21658"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSTEIN<A NAME="21659"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvectors of a real symmetric tridiagonal matrix 
by inverse iteration.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTEQR<A NAME="21660"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSTEQR<A NAME="21661"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and eigenvectors of 
a real symmetric tridiagonal matrix,
using the implicit <B><I>QL</I></B> or <B><I>QR</I></B> algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSTERF<A NAME="21662"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues of a real symmetric tridiagonal matrix,
using a root-free variant of the <B><I>QL</I></B> or <B><I>QR</I></B> algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSTEV<A NAME="21663"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a real symmetric tridiagonal matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSTEVD<A NAME="21664"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a real symmetric tridiagonal matrix.  If eigenvectors are desired, it
uses a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSTEVR<A NAME="21665"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and, optionally, eigenvectors of 
a real symmetric tridiagonal matrix using the Relatively Robust
Representations.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSTEVX<A NAME="21666"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>&nbsp;</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and eigenvectors of 
a real symmetric tridiagonal matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYCON<A NAME="21667"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSYCON<A NAME="21668"></A> CHECON<A NAME="21669"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix,
using the factorization computed by SSYTRF<A NAME="21670"></A>/CSYTRF<A NAME="21671"></A>/CHETRF<A NAME="21672"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYEV<A NAME="21673"></A> </B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEEV<A NAME="21674"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYEVD<A NAME="21675"></A> </B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEEVD<A NAME="21676"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian matrix.  If eigenvectors are desired, it
uses a divide and conquer algorithm.</TD>
</TR>
</TABLE>
</DIV>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYEVR<A NAME="21690"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEEVR<A NAME="21691"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and, optionally, eigenvectors of 
a real symmetric/Hermitian matrix using the Relatively Robust
Representations.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYEVX<A NAME="21692"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEEVX<A NAME="21693"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues and, optionally, eigenvectors of 
a symmetric/Hermitian matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYGST<A NAME="21694"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHEGST<A NAME="21695"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a symmetric/Hermitian definite generalized eigenproblem 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">,
to standard form, where <B><I>B</I></B> has been factorized by SPOTRF<A NAME="21696"></A>/CPOTRF<A NAME="21697"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYGV<A NAME="21698"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEGV<A NAME="21699"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues, and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYGVD<A NAME="21700"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEGVD<A NAME="21701"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes all eigenvalues, and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">.
If eigenvectors
are desired, it uses a divide and conquer algorithm.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYGVX<A NAME="21702"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CHEGVX<A NAME="21703"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes selected eigenvalues, and optionally, the eigenvectors of 
a generalized symmetric/Hermitian definite generalized eigenproblem, 
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img176.png"
 ALT="$Ax = \lambda Bx$">,
<IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img951.png"
 ALT="$ABx=\lambda x$">,
or <IMG
 WIDTH="85" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="img952.png"
 ALT="$BAx=\lambda x$">.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYRFS<A NAME="21704"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSYRFS<A NAME="21705"></A> CHERFS<A NAME="21706"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Improves the computed solution to 
a real symmetric/complex symmetric/complex Hermitian indefinite system of linear
equations
<B><I>A X</I>=<I>B</I></B>,
and provides forward and backward error bounds for the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYSV<A NAME="21707"></A> </B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CSYSV<A NAME="21708"></A></B> <B> CHESV<A NAME="21709"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT"><B> SSYSVX<A NAME="21710"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54><B> CSYSVX<A NAME="21711"></A></B> <B> CHESVX<A NAME="21712"></A></B></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>,
and provides an estimate of the condition number 
and error bounds on the solution.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYTRD<A NAME="21713"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CHETRD<A NAME="21714"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reduces a symmetric/Hermitian matrix to 
real symmetric tridiagonal form 
by an orthogonal/unitary similarity transformation.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYTRF<A NAME="21715"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSYTRF<A NAME="21716"></A> CHETRF<A NAME="21717"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the factorization of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix,
using the diagonal pivoting<A NAME="21718"></A> method.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYTRI<A NAME="21719"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSYTRI<A NAME="21720"></A> CHETRI<A NAME="21721"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of 
a real symmetric/complex symmetric/complex Hermitian indefinite matrix,
using the factorization computed by SSYTRF<A NAME="21722"></A>/CSYTRF<A NAME="21723"></A>/CHETRF<A NAME="21724"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">SSYTRS<A NAME="21725"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CSYTRS<A NAME="21726"></A> CHETRS<A NAME="21727"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a real symmetric/complex symmetric/complex Hermitian indefinite system 
of linear equations
<B><I>A X</I>=<I>B</I></B>,
using the factorization computed by SSPTRF<A NAME="21728"></A>/CSPTRF<A NAME="21729"></A>/CHPTRF<A NAME="21730"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STBCON<A NAME="21731"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=54>CTBCON<A NAME="21732"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of a triangular band matrix,
in either the 1-norm or the infinity-norm.</TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">STBRFS<A NAME="21745"></A></TD>
<TD ALIGN="LEFT">CTBRFS<A NAME="21746"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Provides forward and backward error bounds for the solution of
a triangular banded system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STBTRS<A NAME="21747"></A></TD>
<TD ALIGN="LEFT">CTBTRS<A NAME="21748"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a triangular banded system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STGEVC<A NAME="21749"></A></TD>
<TD ALIGN="LEFT">CTGEVC<A NAME="21750"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes some or all of the right and/or left generalized eigenvectors of a
pair of upper triangular matrices.</TD>
</TR>
<TR><TD ALIGN="LEFT">STGEXC<A NAME="21751"></A></TD>
<TD ALIGN="LEFT">CTGEXC<A NAME="21752"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reorders the generalized real-Schur/Schur decomposition of a matrix pair <B>(<I>A</I>,<I>B</I>)</B>
using an orthogonal/unitary equivalence transformation so that the
diagonal block of <B>(<I>A</I>,<I>B</I>)</B> with row index <B><I>IFST</I></B> is moved to row <B><I>ILST</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STGSEN<A NAME="21753"></A></TD>
<TD ALIGN="LEFT">CTGSEN<A NAME="21754"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reorders the generalized real-Schur/Schur decomposition of a matrix pair
<B>(<I>A</I>,<I>B</I>)</B>, computes the generalized eigenvalues of the reordered matrix
pair, and, optionally, computes the estimates of reciprocal condition
numbers for eigenvalues and eigenspaces.</TD>
</TR>
<TR><TD ALIGN="LEFT">STGSJA<A NAME="21755"></A></TD>
<TD ALIGN="LEFT">CTGSJA<A NAME="21756"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the generalized singular value decomposition (GSVD) of a pair
of upper triangular (or trapezoidal) matrices, which may be obtained by
the preprocessing subroutine SGGSVP/CGGSVP<A NAME="21757"></A><A NAME="21758"></A>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STGSNA<A NAME="21759"></A></TD>
<TD ALIGN="LEFT">CTGSNA<A NAME="21760"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates reciprocal condition numbers for specified
eigenvalues and/or eigenvectors of a matrix pair <B>(<I>A</I>,<I>B</I>)</B> in
generalized real-Schur/Schur canonical form</TD>
</TR>
<TR><TD ALIGN="LEFT">STGSYL<A NAME="21761"></A></TD>
<TD ALIGN="LEFT">CTGSYL<A NAME="21762"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves the generalized Sylvester equation</TD>
</TR>
<TR><TD ALIGN="LEFT">STPCON<A NAME="21763"></A></TD>
<TD ALIGN="LEFT">CTPCON<A NAME="21764"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of a triangular matrix
in packed storage,
in either the 1-norm or the infinity-norm.</TD>
</TR>
<TR><TD ALIGN="LEFT">STPRFS<A NAME="21765"></A></TD>
<TD ALIGN="LEFT">CTPRFS<A NAME="21766"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Provides forward and backward error bounds for the solution of
a triangular system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">STPTRI<A NAME="21767"></A></TD>
<TD ALIGN="LEFT">CTPTRI<A NAME="21768"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of a triangular matrix in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">STPTRS<A NAME="21769"></A></TD>
<TD ALIGN="LEFT">CTPTRS<A NAME="21770"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a triangular system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>,
where <B><I>A</I></B> is held in packed storage.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRCON<A NAME="21771"></A></TD>
<TD ALIGN="LEFT">CTRCON<A NAME="21772"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal of the condition number of a triangular matrix,
in either the 1-norm or the infinity-norm.</TD>
</TR>
<TR><TD ALIGN="LEFT">STREVC<A NAME="21773"></A></TD>
<TD ALIGN="LEFT">CTREVC<A NAME="21774"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes some or all of the right and/or left eigenvectors of 
an upper quasi-triangular/triangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">STREXC<A NAME="21775"></A></TD>
<TD ALIGN="LEFT">CTREXC<A NAME="21776"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reorders the Schur factorization of a matrix
by an orthogonal/unitary similarity transformation.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRRFS<A NAME="21777"></A></TD>
<TD ALIGN="LEFT">CTRRFS<A NAME="21778"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Provides forward and backward error bounds for the solution of
a triangular system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>.</TD>
</TR>
</TABLE>
</DIV>

<P>
<DIV ALIGN="CENTER">
<TABLE CELLPADDING=3 BORDER="1">
<TR><TD ALIGN="CENTER" COLSPAN=2>Routine</TD>
<TD ALIGN="CENTER" COLSPAN=1>Description</TD>
</TR>
<TR><TD ALIGN="LEFT">real</TD>
<TD ALIGN="LEFT">complex</TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>&nbsp;</TD>
</TR>
<TR><TD ALIGN="LEFT">STRSEN<A NAME="21791"></A></TD>
<TD ALIGN="LEFT">CTRSEN<A NAME="21792"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Reorders the Schur factorization of a matrix 
in order to find an orthonormal basis of a right invariant subspace
corresponding to selected eigenvalues,
and returns reciprocal condition numbers (sensitivities)
of the average of the cluster of eigenvalues and of the invariant subspace.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRSNA<A NAME="21793"></A></TD>
<TD ALIGN="LEFT">CTRSNA<A NAME="21794"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Estimates the reciprocal condition numbers (sensitivities) of 
selected eigenvalues and eigenvectors
of an upper quasi-triangular/triangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRSYL<A NAME="21795"></A></TD>
<TD ALIGN="LEFT">CTRSYL<A NAME="21796"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves the Sylvester matrix equation <IMG
 WIDTH="122" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="img156.png"
 ALT="$AX \pm XB=C$">
where <B><I>A</I></B> and <B><I>B</I></B> are upper quasi-triangular/triangular, 
and may be transposed.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRTRI<A NAME="21797"></A></TD>
<TD ALIGN="LEFT">CTRTRI<A NAME="21798"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes the inverse of a triangular matrix.</TD>
</TR>
<TR><TD ALIGN="LEFT">STRTRS<A NAME="21799"></A></TD>
<TD ALIGN="LEFT">CTRTRS<A NAME="21800"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Solves a triangular system of linear equations
<B><I>A X</I>=<I>B</I></B>, <B><I>A</I><SUP><I>T</I></SUP> <I>X</I>=<I>B</I></B> or <B><I>A</I><SUP><I>H</I></SUP> <I>X</I>=<I>B</I></B>.</TD>
</TR>
<TR><TD ALIGN="LEFT">STZRZF<A NAME="21801"></A></TD>
<TD ALIGN="LEFT">CTZRZF<A NAME="21802"></A></TD>
<TD ALIGN="LEFT" VALIGN="TOP" WIDTH=324>Computes an <B><I>RZ</I></B> factorization of an upper trapezoidal matrix (blocked
algorithm).</TD>
</TR>
</TABLE>
</DIV>

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