\begin{table}[h]
\begin{center}
\begin{tabular}{|p{3.2in}|p{0.72in}|p{0.65in}|l|}
\hline
{\bf Operation}
&
{\bf datatypes supported}
&
{\bf LAPACK interface}
&
{\bf Depends on...} \\ \hline
% --------------------------------------
Linear SPD system solve via Cholesky fact.
&
{\tt d}
&
{\tt ?posv()}
&
\potrf \\ \hline
% --------------------------------------
Linear SPD system solve via Cholesky fact. (expert)
&
{\tt d}
&
{\tt ?posvx()}
&
\potrf \\ \hline
% --------------------------------------
Linear system solve via LU factorization
&
{\tt d}
&
{\tt ?gesv()}
&
\getrf \\ \hline
% --------------------------------------
Linear system solve via LU factorization (expert)
&
{\tt d}
&
{\tt ?gesvx()}
&
\getrf \\ \hline
% --------------------------------------
Linear least squares solve (via simple SVD)
&
{\tt d}
&
{\tt ?gelss()}
&
\geqrf \gelqf \\ \hline
% --------------------------------------
Linear least squares solve (via divide-and-conquer SVD)
&
{\tt d}
&
{\tt ?gelsd()}
&
\geqrf \gelqf \\ \hline
% --------------------------------------
Linear equality-constrained least squares solve (via GRQ factorization)
&
{\tt d}
&
{\tt ?gglse()}
&
? \\ \hline
% --------------------------------------
Linear least squares solve (via complete orthogonal factorization)
&
{\tt d}
&
{\tt ?gelsy()}
&
? \\ \hline
% --------------------------------------
General Gauss-Markov linear model solve
&
{\tt d}
&
{\tt ?ggglm()}
&
? \\ \hline
% --------------------------------------
General SD eigenproblem
&
{\tt d}
&
{\tt ?sygv()}
&
\potrf \\ \hline
% --------------------------------------
General SD eigenproblem (expert)
&
{\tt d}
&
{\tt ?sygvx()}
&
\potrf \\ \hline
% --------------------------------------
General SD eigenproblem, divide-and-conquer
&
{\tt d}
&
{\tt ?sygvd()}
&
\potrf \\ \hline
% --------------------------------------
SVD, simple algorithm
&
{\tt d}
&
{\tt ?gesvd()}
&
\geqrf \gelqf \\ \hline
% --------------------------------------
SVD, divide-and-conquer algorithm
&
{\tt d}
&
{\tt ?gesdd()}
&
\geqrf \gelqf \\ \hline
% --------------------------------------
QR factorization with column pivoting
&
{\tt d}
&
{\tt ?geqp3()}
&
\geqrf \\ \hline
% --------------------------------------
QR factorization for two matrices
&
{\tt d}
&
{\tt ?ggqrf()}
&
\geqrf \\ \hline %\gerqf
% --------------------------------------
RQ factorization for two matrices
&
{\tt d}
&
{\tt ?ggrqf()}
&
\geqrf \\ \hline %\gerqf
% --------------------------------------
SPD inversion from pre-computed Cholesky factor
&
{\tt d}
&
{\tt ?potri()}
&
\trtri \lauum \\ \hline
% --------------------------------------
General matrix inversion from pre-computed LU factors
&
{\tt d}
&
{\tt ?getri()}
&
\trtri \\ \hline
% --------------------------------------
% --------------------------------------
\end{tabular}
\end{center}
\caption{
A list of LAPACK interfaces supported indirectly within \lapacktflamens.
In other words, these routines depend on functionality that has been
implemented natively within \libflamens.
}
\label{fig:lapack2flame-indirect}
\end{table}
