diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index 35802a29..fdf8ac7d 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -6,8 +6,12 @@ In this chapter are illustrated data structures used for definition of routines interfaces. This include data structure for sparse matrix, communication descriptor and preconditioner. These data structures are used for calling PSBLAS routines in Fortran~90 language and will be used to next -chapters containing these callings. Their definitions are included in -the modules \verb|psb_spmat_type|, \verb|psb_descriptor_type| and \verb|psb_prec_type|. +chapters containing these callings. + +All the data types and subroutine interfaces are defined in the module +\verb|psb_sparse_mod|; this will have to be included by every user +subroutine that makes use of the library. + \subsection{Descriptor data structure} diff --git a/docs/pdf/intro.tex b/docs/pdf/intro.tex index 88d92aef..4d489589 100644 --- a/docs/pdf/intro.tex +++ b/docs/pdf/intro.tex @@ -22,7 +22,7 @@ subroutines. In this way, the library can take care of runtime memory requirements that are quite difficult or even impossible to predict at implementation or compilation time. The following presentation of the PSBLAS library follows the general structure of the proposal for -serial Sparse BLAS~\cite{sblas97}, which in its turn is based on the +serial Sparse BLAS~\cite{sblas97,sblas02}, which in its turn is based on the proposal for BLAS on dense matrices~\cite{BLAS1,BLAS2,BLAS3}. The applicability of sparse iterative solvers to many different areas @@ -63,7 +63,7 @@ the serial sparse BLAS, so that any extension made to the data structures of the serial kernels is available to the parallel version. The overall design and parallelization strategy have been influenced by the structure of the ScaLAPACK parallel -library~\cite{scalapack}. The layered structure of the PSBLAS library +library. The layered structure of the PSBLAS library is shown in figure~\ref{fig:psblas} ; lower layers of the library indicate an encapsulation relationship with upper layers. The ongoing discussion focuses on the Fortran~95 layer immediately below the @@ -76,7 +76,11 @@ that guarantees a portable and efficient communication layer. The Message Passing Interface code is encapsulated within the BLACS layer. However, in some cases, MPI routines are directly used either to improve efficiency or to implement communication patterns for which -the BLACS package doesn't provide any method. +the BLACS package doesn't provide any method. +We assume that the user program has initialized a BLACS process grid +with one column and as many rows as there are processes; the PSBLAS +initialization routines will take the communication context for this +grid and store internally for further use. \begin{figure}[h] \begin{center} \includegraphics[scale=0.45]{figures/psblas} @@ -87,7 +91,6 @@ the BLACS package doesn't provide any method. The PSBLAS library consists of two classes of subroutines that is, the {\em computational routines} and the {\em auxiliary routines}. The computational routine set includes: - \begin{itemize} \item Sparse matrix by dense matrix product; \item Sparse triangular systems solution for block diagonal matrices; @@ -177,6 +180,97 @@ fetched from (neighbouring) processes. The descriptor of the index space is built exactly for the purpose of properly sequencing the communication steps required to achieve this objective. +A simple application structure will walk through the index space +allocation, matrix/vector creation and linear system solution as +follows: +\begin{enumerate} +\item Initialize parallel environment with \verb|blacs_gridinit| +\item Initialize index space with \verb|psb_cdall| +\item Allocate sparse matrix and dense vectors with \verb|psb_spall| + and \verb|psb_geall| +\item Loop over all local rows, generate matrix and vector entries, + and insert them with \verb|psb_spins| and \verb|psb_geins| +\item Assemble the various entities: +\begin{enumerate} +\item \verb|psb_cdasb| +\item \verb|psb_spasb| +\item \verb|psb_geasb| +\end{enumerate} +\item Choose the preconditioner to be used with \verb|psb_precset| and + build it with \verb|psb_precbld| +\item Call the iterative method of choice, e.g. \verb|psb_bicgstab| +\end{enumerate} +This is the structure of the sample program +\verb|test/pargen/ppde90.f90|. + +For a simulation in which the same discretization mesh is used over +multiple time steps, the following structure may be more appropriate: +\begin{enumerate} +\item Initialize parallel environment with \verb|blacs_gridinit| +\item Initialize index space with \verb|psb_cdall| +\item Loop over the topology of the discretization mesh and build the + descriptor with \verb|psb_cdins| +\item Assemble the descriptor with \verb|psb_cdasb| +\item Allocate the sparse matrices and dense vectors with + \verb|psb_spall| and \verb|psb_geall| +\item Loop over the time steps: +\begin{enumerate} +\item If after first time step, + reinitialize the sparse matrix with \verb|psb_sprn|; also zero out + the dense vectors; +\item Loop over the mesh, generate the coefficients and insert/update + them with \verb|psb_spins| and \verb|psb_geins| +\item Assemble with \verb|psb_spasb| and \verb|psb_geasb| +\item Choose and build preconditioner with \verb|psb_precset| and + \verb|psb_precbld| +\item Call the iterative method of choice, e.g. \verb|psb_bicgstab| + \end{enumerate} +\end{enumerate} +The insertion routines will be called as many times as needed; it is +clear that they only need be called on the data that is actually +allocated to the current process, i.e. each process generates its own +data. + +In principle there is no specific order in the calls to +\verb|psb_spins|, nor is there a requirement to build a matrix row in +its entirety before calling the routine; this allows the application +programmer to walk through the discretization mesh element by element, +generating the main part of a given matrix row but also contributions +to the rows corresponding to neighbouring elements. + +From a functional point of view it is even possible to execute one +call for each nonzero coefficient; however this would have a +substantial computational overhead. It is therefore advisable to pack +a certain amount of data into each call to the insertion routine, say +touching on a few tens of rows; the best performng value would depend +on both the architecture of the computer being used and on the problem +structure. +At the opposite extreme, it would be possible to generate the entire +part of a coefficient matrix residing on a process and pass it in a +single call to \verb|psb_spins|; this, however, would entail a +doubling of memory occupation, and thus would be almost always far +from optimal. + +\subsection{Programming model} + +The PSBLAS librarary is based on the Single Program Multiple Data +(SPMD) programming model: each process participating in the +computation performs the same actions on a chunk of data. Parallelism +is thus data-driven. + +Because of this structure, practically all subroutines \emph{must} be +called simultaneously by all processes participating in the +computation, i.e each subroutine call acts implicitly as a +synchronization point. The exceptions to this rule are: +\begin{itemize} +\item The insertion routines \verb|psb_cdins|, \verb|psb_spins| and + \verb|psb_geins|; +\item The error handling routines. +\end{itemize} +In particular, as per the discussion in the previous section, the +insertion routines may be called a different number of times on each +process, depending on the data distribution chosen by the user. + %%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex index 0d169720..91ec73d2 100644 --- a/docs/pdf/methods.tex +++ b/docs/pdf/methods.tex @@ -2,8 +2,7 @@ \label{sec:methods} In this chapter we provide routines for preconditioners and iterative -methods. Their -interfaces are defined in the module \verb|psb_methd_mod| +methods. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% diff --git a/docs/pdf/precs.tex b/docs/pdf/precs.tex index 85b5db86..39f3e6c6 100644 --- a/docs/pdf/precs.tex +++ b/docs/pdf/precs.tex @@ -18,38 +18,118 @@ many parameters that is possible to adjust to fit the user's needs: -\subroutine{psb\_precset}{Sets the precodntioner type} +\subroutine{psb\_precset}{Sets the preconditioner type} -\syntax{call psb\_precset}{prec, ptype, iv, rs, rv, ierr} +\syntax{call psb\_precset}{prec, ptype, iv, rs, ierr} \begin{description} \item[\bf On Entry] \item[prec] -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ -Specified as: e pronditioner data structure \precdata. +Specified as: a pronditioner data structure \precdata. \item[ptype] the type of preconditioner. Scope: {\bf global} \\ Type: {\bf required}\\ -Specified as: a string. +Specified as: a character string, see usage notes. \item[iv] integer parameters for the precondtioner. Scope: {\bf global} \\ Type: {\bf required}\\ -Specified as: an integer array. +Specified as: an integer array, see usage notes. \item[rs] -Scope: {\bf } \\ -Type: {\bf }\\ -Specified as: . -\item[rv] -Scope: {\bf } \\ -Type: {\bf }\\ -Specified as: . +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Specified as: a long precision real number. + \item[ierr] -Scope: {\bf } \\ -Type: {\bf }\\ -Specified as: . +Scope: {\bf global} \\ +Type: {\bf required}\\ \end{description} - +\section*{Usage Notes} +The PSBLAS 2.0 contains a number of preconditioners, ranging from a +simple diagonal scaling to 2-level domain decomposition. These +preconditioners may use the SuperLU or the UMFPACK software, if +installed; see~\cite{SUPERLU,UMFPACK}. +Legal inputs to this subroutine are interpreted depending on the +$ptype$ string as follows\footnote{The string is case-insensitive}: +\begin{description} +\item[NONE] No preconditioning, i.e. the preconditioner is just a copy + operator. +\item[DIAG] Diagonal scaling; each entry of the input vector is + multiplied by the reciprocal of the sum of the absolute values of + the coefficients in the corresponding row of matrix $A$; +\item[ILU] Precondition by the incomplete LU factorization of the + block-diagonal of matrix $A$, where block boundaries are determined + by the data allocation boundaries for each process; requires no + communication. Only $ILU(0)$ is currently implemented. +\item[AS] Additive Schwarz preconditioner (see~\cite{PARA04}); in this + case the user may specify additional flags through the integer + vector \verb|ir| as follows: +\begin{description} +\item[$iv(1)$] Number of overlap levels, an integer $novr>0$, default + $novr=1$. +\item[$iv(2)$] Restriction operator, legal values: \verb|psb_halo_|, + \verb|psb_none_|; default: \verb|psb_halo_| +\item[$iv(3)$] Prolongation operator, legal values: \verb|psb_none_|, + \verb|psb_sum_|, \verb|psb_avg_|, default: \verb|psb_none_| +\item[$iv(4)$] Factorization type, legal values: \verb|f_ilu_n_|, + \verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|. +\end{description} +Note that the default corresponds to a Restricted Additive Schwarz +preconditioner with $ILU(0)$ and 1 level of overlap. +\end{description} +If a multilevel preconditioner is desired, the user should call +\verb|psb_precset| once choosing AS, and a second time specifying +$ptype=ML$ with the following optional parameters in $iv$ (see +also~\cite{APNUM,DD2}): +\begin{description} +\item[$iv(1)$] Type of multilevel correction, legal values: \verb|no_ml_|, + \verb|add_ml_prec_|, \verb|mult_ml_prec_|, + default: \verb|mult_ml_prec_|; +\item[$iv(2)$] Aggregation algorithm, legal values: \verb|loc_aggr_|; +\item[$iv(3)$] Smoother type, legal values: \verb|no_smth_|, + \verb|smth_omg_|, default: \verb|smth_omg_|; +\item[$iv(4)$] Coarse matrix allocation, legal values: + \verb|mat_distr_|, \verb|mat_repl_|, default: \verb|mat_distr_| +\item[$iv(5)$] Smoother position, legal values: \verb|pre_smooth_|, + \verb|post_smooth_|, \verb|smooth_both_|, default: + \verb|post_smooth_| +\item[$iv(6)$] Factorization type (for coarse matrix), legal values: \verb|f_ilu_n_|, + \verb|f_slu_|, \verb|f_umf_|, default: \verb|f_ilu_n_|; +\item[$iv(7)$] Number of Jacobi sweeps for coarse system correction, + default 1. +\item[$rs$] Set the smoother parameter $\omega$ a user defined value; + default: esitimate with the infinity norm of matrix $A$. +\end{description} +The 2-level preconditioners are based on the idea of building a +coarse-space approximation $A_C$ of the matrix $A$; given a set $W_C$ +of coarse vertices, with size $n_C$, and a suitable restriction +operator $R_C \in \Re^{n_C \times n}$, $A_C$ is defined as +\[ +A_C=R_C A R_C^T . +\] +The prolongator $R_C^T$ is built with the smoothed aggregation technique, +in which we start from a tentative prolongator that simply maps +fine-level entries onto their aggregates $P_C$; if the user chooses +\verb|no_smth_| this is the prolongator used, otherwise it is +multiplied by a smoother \[ S = I - \omega D^{-1} A \], where $D$ is +the diagonal of $A$ and $\omega$ may be imposed by the user or +estimated internally. +The coarse space correction may be added to the fine level solution +\verb|add_ml_prec_| +\[ +M_{2L-A}^{-1} = M_{C}^{-1} + M_{1L}^{-1}. +\] +or it can be composed in a multiplicative framework as a pre-smoothed +correction +\[ +M_{2L-H1}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}, +\] +post-smoothed correction +\[ +M_{2L-H2}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. +\] +or two-sided. @@ -60,11 +140,11 @@ Specified as: . \begin{description} \item[\bf On Entry] \item[a] the system sparse matrix. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a sparse matrix data structure \spdata. \item[desc\_a] the problem communication descriptor. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a communication descriptor data structure \descdata. \item[upd] @@ -75,14 +155,14 @@ Specified as: a character. \begin{description} \item[\bf On Return] -\item[prec] the precodntioner.\\ -Scope: {\bf global} \\ +\item[prec] the preconditioner.\\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a precondtioner data structure \precdata\\ \item[info] the return error code.\\ -Scope: {\bf local} \\ +Scope: {\bf global} \\ Type: {\bf required}\\ -Specified as: an integer.\\ +Specified as: an integer, upon successful completion $info=0$ \\ \end{description} @@ -95,15 +175,15 @@ Specified as: an integer.\\ \begin{description} \item[\bf On Entry] \item[prec] the preconditioner. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a preconditioner data structure \precdata. \item[x] the source vector. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf require}\\ Specified as: a double precision array. \item[desc\_a] the problem communication descriptor. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a communication data structure \descdata. \item[trans] @@ -119,13 +199,27 @@ Specified as: a double precision array. \begin{description} \item[\bf On Return] \item[y] the destination vector. -Scope: {\bf global} \\ +Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a double precision array. \item[info] the return error code.\\ Scope: {\bf local} \\ Type: {\bf required}\\ -Specified as: an integer.\\ +Specified as: an integer, upon successful completion $info=0$ .\\ +\end{description} + + + +\subroutine{psb\_prec\_descr}{Prints a description of current preconditioner} + +\syntax{call psb\_prec\_descr}{prec} + +\begin{description} +\item[\bf On Entry] +\item[prec] the preconditioner. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a preconditioner data structure \precdata. \end{description} diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index a8d7ea08..ff783479 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -65,6 +65,11 @@ Type: {\bf required}\\ Specified as: an integer variable.\\ \end{description} +\section*{Notes} +\begin{enumerate} +\item On exit from this routine the descriptor is in the build state +\end{enumerate} + % %% psb_cdins %% @@ -108,6 +113,11 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +\section*{Notes} +\begin{enumerate} +\item This routine may only be called if the descriptor is in the + build state +\end{enumerate} @@ -134,6 +144,11 @@ Type: {\bf required}\\ Specified as: an integer variable. %\item[arg] \end{description} +\section*{Notes} +\begin{enumerate} +\item On exit from this routine the descriptor is in the assembled + state. +\end{enumerate} @@ -285,6 +300,12 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +\section*{Notes} +\begin{enumerate} +\item On exit from this routine the sparse matrix is in the build + state. +\item The descriptor may be in either the build or assembled state. +\end{enumerate} @@ -342,6 +363,22 @@ Scope: {\bf local} \\ Type: {\bf required}\\ \end{description} +\section*{Notes} +\begin{enumerate} +\item On entry to this routine the descriptor may be in either the + build or assembled state. +\item On entry to this routine the sparse matrix may be in either the + build or update state. +\item If the descriptor is in the build state, then the sparse matrix + ought also be in the buld state; the action of the routine is to + (implicitly) call \verb|psb_cdins| to add entries to the sparsity + pattern; +\item If the descriptor is in the assembled state, then any entries in + the sparse matrix that would generate additional communication + requirements will be ignored; +\item If the matrix is in the update state, any entries in positions + that were not present in the original matrix will be ignored. +\end{enumerate} % %% psb_spasb %% @@ -383,6 +420,22 @@ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +\section*{Notes} +\begin{enumerate} +\item On entry to this routine the descriptor must be in the + assembled state, i.e. \verb|psb_cdasb| must already have been called. +\item The sparse matrix may be in either the build or update state; +\item Duplicate entries are detected and handled in both build and + update state, with the exception of the error action that is only + taken in the build state, i.e. on the first assembly; +\item If the update choice is \verb|psb_upd_perm_|, then subsequent + calls to \verb|psb_spins| to update the matrix must be arranged in + such a way as to produce exactly the same sequence of coefficient + values as encountered at the first assembly; +\item On exit from this routine the matrix is in the assembled state, + and thus is suitable for the computational routines. +\end{enumerate} + %% % @@ -474,7 +527,11 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: an integer variable. \end{description} - +\section*{Notes} +\begin{enumerate} +\item On exit from this routine the sparse matrix is in the update + state. +\end{enumerate} % %% psb_spupdate %% % @@ -591,7 +648,7 @@ Specified as: a structured data of type \descdata. Scope: {\bf global}.\\ Type: {\bf optional}.\\ Specified as: integer, possible values: \verb|psb_dupl_ovwrt_|, -\verb|psb_dupl_add_|, \verb|psb_dupl_err_|. +\verb|psb_dupl_add_|. \end{description} \begin{description} @@ -607,6 +664,14 @@ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +\section*{Notes} +\begin{enumerate} +\item Dense vectors/matrices do not have an associated state; +\item Duplicate entries are either overwritten or added, there is no + provision for raising an error condition. +\end{enumerate} + + % %% psb_asb %% % diff --git a/docs/pdf/userguide.tex b/docs/pdf/userguide.tex index b46ec2a3..f51a05c1 100644 --- a/docs/pdf/userguide.tex +++ b/docs/pdf/userguide.tex @@ -91,6 +91,139 @@ \include{methods} \include{precs} \include{error} + + +\clearpage + +\begin{thebibliography}{99} +% +\bibitem{BLAS1} +Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., + Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage, +{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979. +\bibitem{BLAS2} + Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., +An Extended Set of {F}ortran {B}asic {L}inear {A}lgebra {S}ubprograms, +{ACM Trans. Math. Softw.} vol.~{14}, 1--17, 1988. +\bibitem{BLAS3} + Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., +A Set of level 3 Basic Linear Algebra Subprograms, +{ACM Trans. Math. Softw.} vol.~{16}, 1--17, 1990. +\bibitem{DOUGLAS} +R.E.~Bank and C.C.~Douglas, +{\em SMMP: Sparse Matrix Multiplication Package}, +Advances in Computational Mathematics, 1993, 1, 127-137. +(See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html}) +% +\bibitem{PARA04FOREST} +G.~Bella, S.~Filippone, A.~De Maio and M.~Testa, +{\em A Simulation Model for Forest Fires}, +in J.~Dongarra, K.~Madsen, J.~Wasniewski, editors, +Proceedings of PARA~04 Workshop on State of the Art +in Scientific Computing, pp.~546--553, Lecture Notes in Computer Science, +Springer, 2005. +% +\bibitem{PARA04} +A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone, +{\em Extending PSBLAS to Build Parallel Schwarz Preconditioners}, +in , J.~Dongarra, K.~Madsen, J.~Wasniewski, editors, +Proceedings of PARA~04 Workshop on State of the Art +in Scientific Computing, pp.~593--602, Lecture Notes in Computer Science, +Springer, 2005. +% +\bibitem{CAI_SAAD} +X.~C.~Cai and Y.~Saad, +{\em Overlapping Domain Decomposition Algorithms for General Sparse Matrices}, +Numerical Linear Algebra with Applications, 3(3), pp.~221--237, 1996. +% +\bibitem{CAI_SARKIS} +X.C.~Cai and M.~Sarkis, +{\em A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems}, +SIAM Journal on Scientific Computing, 21(2), pp.~792--797, 1999. +% +\bibitem{CAI_WIDLUND} +X.C.~Cai and O.~B.~Widlund, +{\em Domain Decomposition Algorithms for Indefinite Elliptic Problems}, +SIAM Journal on Scientific and Statistical Computing, 13(1), pp.~243--258, 1992. +% +\bibitem{DD1} +T.~Chan and T.~Mathew, +{\em Domain Decomposition Algorithms}, +in A.~Iserles, editor, Acta Numerica 1994, pp.~61--143, 1994. +Cambridge University Press. +% +\bibitem{APNUM06} +P.~D'Ambra, D.~di Serafino and S.~Filippone, +On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners, +Applied Numerical Mathematics, to appear, 2006. +% +\bibitem{UMFPACK} +T.A.~Davis, +{\em Algorithm 832: UMFPACK - an Unsymmetric-pattern Multifrontal +Method with a Column Pre-ordering Strategy}, +ACM Transactions on Mathematical Software, 30, pp.~196--199, 2004. +(See also {\tt http://www.cise.ufl.edu/~davis/}) +% +\bibitem{SUPERLU} +J.W.~Demmel, S.C.~Eisenstat, J.R.~Gilbert, X.S.~Li and J.W.H.~Liu, +A supernodal approach to sparse partial pivoting, +SIAM Journal on Matrix Analysis and Applications, 20(3), pp.~720--755, 1999. +% +\bibitem{BLACS} +J.~J.~Dongarra and R.~C.~Whaley, +{\em A User's Guide to the BLACS v.~1.1}, +Lapack Working Note 94, Tech.\ Rep.\ UT-CS-95-281, University of +Tennessee, March 1995 (updated May 1997). +% +\bibitem{sblas97} +I.~Duff, M.~Marrone, G.~Radicati and C.~Vittoli, +{\em Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: +a User Level Interface}, +ACM Transactions on Mathematical Software, 23(3), pp.~379--401, 1997. +% +\bibitem{sblas02} +I.~Duff, M.~Heroux and R.~Pozo, +{\em An Overview of the Sparse Basic Linear +Algebra Subprograms: the New Standard from the BLAS Technical Forum}, +ACM Transactions on Mathematical Software, 28(2), pp.~239--267, 2002. +\bibitem{PSBLAS} +S.~Filippone and M.~Colajanni, +{\em PSBLAS: A Library for Parallel Linear Algebra +Computation on Sparse Matrices}, +\newblock +ACM Transactions on Mathematical Software, 26(4), pp.~527--550, 2000. +% +\bibitem{KIVA3PSBLAS} +S.~Filippone, P.~D'Ambra, M.~Colajanni, +{\em Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics +Applications Code on Linux Clusters}, +in G.~Joubert, A.~Murli, F.~Peters, M.~Vanneschi, editors, +Parallel Computing - Advances \& Current Issues, +pp.~441--448, Imperial College Press, 2002. +% +\bibitem{machiels} +{Machiels, L. and Deville, M.} +{\em Fortran 90: An entry to object-oriented programming for the solution + of partial differential equations.} +{ACM Trans. Math. Softw.} vol.~{23}, 32--49. +\bibitem{metcalf} +{Metcalf, M., Reid, J. and Cohen, M.} +{\em Fortran 95/2003 explained.} +{Oxford University Press}, 2004. +% +\bibitem{DD2} +B.~Smith, P.~Bjorstad and W.~Gropp, +{\em Domain Decomposition: Parallel Multilevel Methods for Elliptic +Partial Differential Equations}, +Cambridge University Press, 1996. +% +\bibitem{MPI1} +M.~Snir, S.~Otto, S.~Huss-Lederman, D.~Walker and J.~Dongarra, +{\em MPI: The Complete Reference. Volume 1 - The MPI Core}, second edition, +MIT Press, 1998. +% +\end{thebibliography} + \end{document} %%% Local Variables: %%% mode: latex diff --git a/docs/userguide.pdf b/docs/userguide.pdf index 90ff7eb4..3aa891db 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -24,357 +24,369 @@ endobj (2.1 Application structure) endobj 21 0 obj -<< /S /GoTo /D (section.3) >> +<< /S /GoTo /D (subsection.2.2) >> endobj 24 0 obj -(3 Data Structures) +(2.2 Programming model) endobj 25 0 obj -<< /S /GoTo /D (subsection.3.1) >> +<< /S /GoTo /D (section.3) >> endobj 28 0 obj -(3.1 Descriptor data structure) +(3 Data Structures) endobj 29 0 obj -<< /S /GoTo /D (subsubsection.3.1.1) >> +<< /S /GoTo /D (subsection.3.1) >> endobj 32 0 obj -(3.1.1 Named Constants) +(3.1 Descriptor data structure) endobj 33 0 obj -<< /S /GoTo /D (subsection.3.2) >> +<< /S /GoTo /D (subsubsection.3.1.1) >> endobj 36 0 obj -(3.2 Sparse Matrix data structure) +(3.1.1 Named Constants) endobj 37 0 obj -<< /S /GoTo /D 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1 0 0 1 443.606 553.637 cm 0 g 0 G -1 0 0 1 -343.711 -22.342 cm +1 0 0 1 -305.853 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -99.895 -531.295 cm +1 0 0 1 -137.753 -541.427 cm BT -/F29 9.963 Tf 99.895 531.295 Td[(4)-925(Al)-1(gebr)1(ai)-1(c)-383(routines)]TJ +/F8 9.963 Tf 137.753 541.427 Td[(3.3.1)-1144(Name)-1(d)-332(C)-1(on)1(s)-1(tan)29(ts)]TJ ET -1 0 0 1 206.995 531.295 cm +1 0 0 1 247.232 541.427 cm 0 g 0 G -1 0 0 1 -206.995 -531.295 cm +1 0 0 1 -247.232 -541.427 cm BT -/F29 9.963 Tf 432.149 531.295 Td[(12)]TJ +/F8 9.963 Tf 257.358 541.427 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET -1 0 0 1 114.839 519.085 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -519.085 cm -BT -/F8 9.963 Tf 114.839 519.085 Td[(psb)]TJ -ET -1 0 0 1 130.436 519.085 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -130.436 -519.085 cm +1 0 0 1 433.644 541.427 cm +0 g 0 G +1 0 0 1 -433.644 -541.427 cm BT -/F8 9.963 Tf 133.425 519.085 Td[(geaxpb)29(y)]TJ +/F8 9.963 Tf 433.644 541.427 Td[(11)]TJ ET -1 0 0 1 169.125 519.085 cm +1 0 0 1 443.606 541.427 cm 0 g 0 G -1 0 0 1 -169.125 -519.085 cm +1 0 0 1 -343.711 -22.342 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.895 -519.085 cm BT -/F8 9.963 Tf 172.123 519.085 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F29 9.963 Tf 99.895 519.085 Td[(4)-925(Al)-1(gebr)1(ai)-1(c)-383(routines)]TJ ET -1 0 0 1 433.644 519.085 cm +1 0 0 1 206.995 519.085 cm 0 g 0 G -1 0 0 1 -433.644 -519.085 cm +1 0 0 1 -206.995 -519.085 cm BT -/F8 9.963 Tf 433.644 519.085 Td[(13)]TJ +/F29 9.963 Tf 432.149 519.085 Td[(13)]TJ ET -1 0 0 1 443.606 519.085 cm -0 g 0 G -1 0 0 1 -328.767 -12.209 cm +1 0 0 1 114.839 506.876 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -506.876 cm BT @@ -685,19 +684,19 @@ S Q 1 0 0 1 -130.436 -506.876 cm BT -/F8 9.963 Tf 133.425 506.876 Td[(gedot)]TJ +/F8 9.963 Tf 133.425 506.876 Td[(geaxpb)29(y)]TJ ET -1 0 0 1 157.225 506.876 cm +1 0 0 1 169.125 506.876 cm 0 g 0 G -1 0 0 1 -157.225 -506.876 cm +1 0 0 1 -169.125 -506.876 cm BT -/F8 9.963 Tf 164.375 506.876 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 172.123 506.876 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET 1 0 0 1 433.644 506.876 cm 0 g 0 G 1 0 0 1 -433.644 -506.876 cm BT -/F8 9.963 Tf 433.644 506.876 Td[(15)]TJ +/F8 9.963 Tf 433.644 506.876 Td[(14)]TJ ET 1 0 0 1 443.606 506.876 cm 0 g 0 G @@ -730,7 +729,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -494.666 cm BT -/F8 9.963 Tf 433.644 494.666 Td[(17)]TJ +/F8 9.963 Tf 433.644 494.666 Td[(16)]TJ ET 1 0 0 1 443.606 494.666 cm 0 g 0 G @@ -751,19 +750,19 @@ S Q 1 0 0 1 -130.436 -482.457 cm BT -/F8 9.963 Tf 133.425 482.457 Td[(geam)-1(ax)]TJ +/F8 9.963 Tf 133.425 482.457 Td[(gedot)]TJ ET -1 0 0 1 166.357 482.457 cm +1 0 0 1 157.225 482.457 cm 0 g 0 G -1 0 0 1 -166.357 -482.457 cm +1 0 0 1 -157.225 -482.457 cm BT -/F8 9.963 Tf 172.123 482.457 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 164.375 482.457 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 482.457 cm 0 g 0 G 1 0 0 1 -433.644 -482.457 cm BT -/F8 9.963 Tf 433.644 482.457 Td[(19)]TJ +/F8 9.963 Tf 433.644 482.457 Td[(18)]TJ ET 1 0 0 1 443.606 482.457 cm 0 g 0 G @@ -817,11 +816,11 @@ S Q 1 0 0 1 -130.436 -458.038 cm BT -/F8 9.963 Tf 133.425 458.038 Td[(geas)-1(u)1(m)]TJ +/F8 9.963 Tf 133.425 458.038 Td[(geam)-1(ax)]TJ ET -1 0 0 1 165.582 458.038 cm +1 0 0 1 166.357 458.038 cm 0 g 0 G -1 0 0 1 -165.582 -458.038 cm +1 0 0 1 -166.357 -458.038 cm BT /F8 9.963 Tf 172.123 458.038 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -850,11 +849,11 @@ S Q 1 0 0 1 -130.436 -445.828 cm BT -/F8 9.963 Tf 133.425 445.828 Td[(genrm2)]TJ +/F8 9.963 Tf 133.425 445.828 Td[(geas)-1(u)1(m)]TJ ET -1 0 0 1 165.555 445.828 cm +1 0 0 1 165.582 445.828 cm 0 g 0 G -1 0 0 1 -165.555 -445.828 cm +1 0 0 1 -165.582 -445.828 cm BT /F8 9.963 Tf 172.123 445.828 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -883,11 +882,11 @@ S Q 1 0 0 1 -130.436 -433.619 cm BT -/F8 9.963 Tf 133.425 433.619 Td[(spnr)1(mi)]TJ +/F8 9.963 Tf 133.425 433.619 Td[(genrm2)]TJ ET -1 0 0 1 163.396 433.619 cm +1 0 0 1 165.555 433.619 cm 0 g 0 G -1 0 0 1 -163.396 -433.619 cm +1 0 0 1 -165.555 -433.619 cm BT /F8 9.963 Tf 172.123 433.619 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -916,13 +915,13 @@ S Q 1 0 0 1 -130.436 -421.409 cm BT -/F8 9.963 Tf 133.425 421.409 Td[(spmm)]TJ +/F8 9.963 Tf 133.425 421.409 Td[(spnr)1(mi)]TJ ET -1 0 0 1 159.494 421.409 cm +1 0 0 1 163.396 421.409 cm 0 g 0 G -1 0 0 1 -159.494 -421.409 cm +1 0 0 1 -163.396 -421.409 cm BT -/F8 9.963 Tf 164.375 421.409 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 172.123 421.409 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET 1 0 0 1 433.644 421.409 cm 0 g 0 G @@ -949,11 +948,11 @@ S Q 1 0 0 1 -130.436 -409.2 cm BT -/F8 9.963 Tf 133.425 409.2 Td[(spsm)]TJ +/F8 9.963 Tf 133.425 409.2 Td[(spmm)]TJ ET -1 0 0 1 155.122 409.2 cm +1 0 0 1 159.494 409.2 cm 0 g 0 G -1 0 0 1 -155.122 -409.2 cm +1 0 0 1 -159.494 -409.2 cm BT /F8 9.963 Tf 164.375 409.2 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -961,29 +960,17 @@ ET 0 g 0 G 1 0 0 1 -433.644 -409.2 cm BT -/F8 9.963 Tf 433.644 409.2 Td[(26)]TJ +/F8 9.963 Tf 433.644 409.2 Td[(25)]TJ ET 1 0 0 1 443.606 409.2 cm 0 g 0 G -1 0 0 1 -343.711 -22.342 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.895 -386.858 cm -BT -/F29 9.963 Tf 99.895 386.858 Td[(5)-925(Co)1(m)-1(m)32(unicat)-1(ion)-383(routines)]TJ -ET -1 0 0 1 238.328 386.858 cm -0 g 0 G -1 0 0 1 -238.328 -386.858 cm -BT -/F29 9.963 Tf 432.149 386.858 Td[(29)]TJ -ET -1 0 0 1 114.839 374.648 cm +1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -374.648 cm +1 0 0 1 -114.839 -396.99 cm BT -/F8 9.963 Tf 114.839 374.648 Td[(psb)]TJ +/F8 9.963 Tf 114.839 396.99 Td[(psb)]TJ ET -1 0 0 1 130.436 374.648 cm +1 0 0 1 130.436 396.99 cm q []0 d 0 J @@ -992,25 +979,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -374.648 cm +1 0 0 1 -130.436 -396.99 cm BT -/F8 9.963 Tf 133.425 374.648 Td[(hal)1(o)]TJ +/F8 9.963 Tf 133.425 396.99 Td[(spsm)]TJ ET -1 0 0 1 151.69 374.648 cm +1 0 0 1 155.122 396.99 cm 0 g 0 G -1 0 0 1 -151.69 -374.648 cm +1 0 0 1 -155.122 -396.99 cm BT -/F8 9.963 Tf 156.626 374.648 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 164.375 396.99 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET -1 0 0 1 433.644 374.648 cm +1 0 0 1 433.644 396.99 cm 0 g 0 G -1 0 0 1 -433.644 -374.648 cm +1 0 0 1 -433.644 -396.99 cm BT -/F8 9.963 Tf 433.644 374.648 Td[(30)]TJ +/F8 9.963 Tf 433.644 396.99 Td[(27)]TJ ET -1 0 0 1 443.606 374.648 cm +1 0 0 1 443.606 396.99 cm 0 g 0 G -1 0 0 1 -328.767 -12.209 cm +1 0 0 1 -343.711 -22.342 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.895 -374.648 cm +BT +/F29 9.963 Tf 99.895 374.648 Td[(5)-925(Co)1(m)-1(m)32(unicat)-1(ion)-383(routines)]TJ +ET +1 0 0 1 238.328 374.648 cm +0 g 0 G +1 0 0 1 -238.328 -374.648 cm +BT +/F29 9.963 Tf 432.149 374.648 Td[(30)]TJ +ET +1 0 0 1 114.839 362.439 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -362.439 cm BT @@ -1027,11 +1026,11 @@ S Q 1 0 0 1 -130.436 -362.439 cm BT -/F8 9.963 Tf 133.425 362.439 Td[(o)28(vrl)]TJ +/F8 9.963 Tf 133.425 362.439 Td[(hal)1(o)]TJ ET -1 0 0 1 150.057 362.439 cm +1 0 0 1 151.69 362.439 cm 0 g 0 G -1 0 0 1 -150.057 -362.439 cm +1 0 0 1 -151.69 -362.439 cm BT /F8 9.963 Tf 156.626 362.439 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET @@ -1039,7 +1038,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -362.439 cm BT -/F8 9.963 Tf 433.644 362.439 Td[(32)]TJ +/F8 9.963 Tf 433.644 362.439 Td[(31)]TJ ET 1 0 0 1 443.606 362.439 cm 0 g 0 G @@ -1060,19 +1059,19 @@ S Q 1 0 0 1 -130.436 -350.229 cm BT -/F8 9.963 Tf 133.425 350.229 Td[(gath)1(e)-1(r)]TJ +/F8 9.963 Tf 133.425 350.229 Td[(o)28(vrl)]TJ ET -1 0 0 1 161.127 350.229 cm +1 0 0 1 150.057 350.229 cm 0 g 0 G -1 0 0 1 -161.127 -350.229 cm +1 0 0 1 -150.057 -350.229 cm BT -/F8 9.963 Tf 164.375 350.229 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 350.229 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 350.229 cm 0 g 0 G 1 0 0 1 -433.644 -350.229 cm BT -/F8 9.963 Tf 433.644 350.229 Td[(34)]TJ +/F8 9.963 Tf 433.644 350.229 Td[(33)]TJ ET 1 0 0 1 443.606 350.229 cm 0 g 0 G @@ -1093,41 +1092,29 @@ S Q 1 0 0 1 -130.436 -338.02 cm BT -/F8 9.963 Tf 133.425 338.02 Td[(sc)-1(atter)]TJ +/F8 9.963 Tf 133.425 338.02 Td[(gath)1(e)-1(r)]TJ ET -1 0 0 1 162.843 338.02 cm +1 0 0 1 161.127 338.02 cm 0 g 0 G -1 0 0 1 -162.843 -338.02 cm +1 0 0 1 -161.127 -338.02 cm BT -/F8 9.963 Tf 172.123 338.02 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 164.375 338.02 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 338.02 cm 0 g 0 G 1 0 0 1 -433.644 -338.02 cm BT -/F8 9.963 Tf 433.644 338.02 Td[(36)]TJ +/F8 9.963 Tf 433.644 338.02 Td[(35)]TJ ET 1 0 0 1 443.606 338.02 cm 0 g 0 G -1 0 0 1 -343.711 -22.342 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.895 -315.678 cm -BT -/F29 9.963 Tf 99.895 315.678 Td[(6)-925(Data)-383(m)-1(anagemen)32(t)-383(and)-383(i)-1(niti)-1(ali)-1(zation)-384(r)1(outi)-1(nes)]TJ -ET -1 0 0 1 339.407 315.678 cm -0 g 0 G -1 0 0 1 -339.407 -315.678 cm -BT -/F29 9.963 Tf 432.149 315.678 Td[(38)]TJ -ET -1 0 0 1 114.839 303.468 cm +1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -303.468 cm +1 0 0 1 -114.839 -325.81 cm BT -/F8 9.963 Tf 114.839 303.468 Td[(psb)]TJ +/F8 9.963 Tf 114.839 325.81 Td[(psb)]TJ ET -1 0 0 1 130.436 303.468 cm +1 0 0 1 130.436 325.81 cm q []0 d 0 J @@ -1136,25 +1123,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -303.468 cm +1 0 0 1 -130.436 -325.81 cm BT -/F8 9.963 Tf 133.425 303.468 Td[(cdall)]TJ +/F8 9.963 Tf 133.425 325.81 Td[(sc)-1(atter)]TJ ET -1 0 0 1 153.904 303.468 cm +1 0 0 1 162.843 325.81 cm 0 g 0 G -1 0 0 1 -153.904 -303.468 cm +1 0 0 1 -162.843 -325.81 cm BT -/F8 9.963 Tf 156.626 303.468 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 172.123 325.81 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET -1 0 0 1 433.644 303.468 cm +1 0 0 1 433.644 325.81 cm 0 g 0 G -1 0 0 1 -433.644 -303.468 cm +1 0 0 1 -433.644 -325.81 cm BT -/F8 9.963 Tf 433.644 303.468 Td[(39)]TJ +/F8 9.963 Tf 433.644 325.81 Td[(37)]TJ ET -1 0 0 1 443.606 303.468 cm +1 0 0 1 443.606 325.81 cm 0 g 0 G -1 0 0 1 -328.767 -12.209 cm +1 0 0 1 -343.711 -22.342 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.895 -303.468 cm +BT +/F29 9.963 Tf 99.895 303.468 Td[(6)-925(Data)-383(m)-1(anagemen)32(t)-383(and)-383(i)-1(niti)-1(ali)-1(zation)-384(r)1(outi)-1(nes)]TJ +ET +1 0 0 1 339.407 303.468 cm +0 g 0 G +1 0 0 1 -339.407 -303.468 cm +BT +/F29 9.963 Tf 432.149 303.468 Td[(39)]TJ +ET +1 0 0 1 114.839 291.259 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -291.259 cm BT @@ -1171,19 +1170,19 @@ S Q 1 0 0 1 -130.436 -291.259 cm BT -/F8 9.963 Tf 133.425 291.259 Td[(cdin)1(s)]TJ +/F8 9.963 Tf 133.425 291.259 Td[(cdall)]TJ ET -1 0 0 1 155.62 291.259 cm +1 0 0 1 153.904 291.259 cm 0 g 0 G -1 0 0 1 -155.62 -291.259 cm +1 0 0 1 -153.904 -291.259 cm BT -/F8 9.963 Tf 164.375 291.259 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 291.259 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 291.259 cm 0 g 0 G 1 0 0 1 -433.644 -291.259 cm BT -/F8 9.963 Tf 433.644 291.259 Td[(41)]TJ +/F8 9.963 Tf 433.644 291.259 Td[(40)]TJ ET 1 0 0 1 443.606 291.259 cm 0 g 0 G @@ -1204,11 +1203,11 @@ S Q 1 0 0 1 -130.436 -279.049 cm BT -/F8 9.963 Tf 133.425 279.049 Td[(cdasb)]TJ +/F8 9.963 Tf 133.425 279.049 Td[(cdin)1(s)]TJ ET -1 0 0 1 157.834 279.049 cm +1 0 0 1 155.62 279.049 cm 0 g 0 G -1 0 0 1 -157.834 -279.049 cm +1 0 0 1 -155.62 -279.049 cm BT /F8 9.963 Tf 164.375 279.049 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1237,11 +1236,11 @@ S Q 1 0 0 1 -130.436 -266.84 cm BT -/F8 9.963 Tf 133.425 266.84 Td[(cdcp)28(y)]TJ +/F8 9.963 Tf 133.425 266.84 Td[(cdasb)]TJ ET -1 0 0 1 158.332 266.84 cm +1 0 0 1 157.834 266.84 cm 0 g 0 G -1 0 0 1 -158.332 -266.84 cm +1 0 0 1 -157.834 -266.84 cm BT /F8 9.963 Tf 164.375 266.84 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1270,11 +1269,11 @@ S Q 1 0 0 1 -130.436 -254.63 cm BT -/F8 9.963 Tf 133.425 254.63 Td[(cdfr)1(e)-1(e)]TJ +/F8 9.963 Tf 133.425 254.63 Td[(cdcp)28(y)]TJ ET -1 0 0 1 159.19 254.63 cm +1 0 0 1 158.332 254.63 cm 0 g 0 G -1 0 0 1 -159.19 -254.63 cm +1 0 0 1 -158.332 -254.63 cm BT /F8 9.963 Tf 164.375 254.63 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1303,13 +1302,13 @@ S Q 1 0 0 1 -130.436 -242.421 cm BT -/F8 9.963 Tf 133.425 242.421 Td[(spall)]TJ +/F8 9.963 Tf 133.425 242.421 Td[(cdfr)1(e)-1(e)]TJ ET -1 0 0 1 153.406 242.421 cm +1 0 0 1 159.19 242.421 cm 0 g 0 G -1 0 0 1 -153.406 -242.421 cm +1 0 0 1 -159.19 -242.421 cm BT -/F8 9.963 Tf 156.626 242.421 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 164.375 242.421 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 242.421 cm 0 g 0 G @@ -1336,13 +1335,13 @@ S Q 1 0 0 1 -130.436 -230.211 cm BT -/F8 9.963 Tf 133.425 230.211 Td[(spin)1(s)]TJ +/F8 9.963 Tf 133.425 230.211 Td[(spall)]TJ ET -1 0 0 1 155.122 230.211 cm +1 0 0 1 153.406 230.211 cm 0 g 0 G -1 0 0 1 -155.122 -230.211 cm +1 0 0 1 -153.406 -230.211 cm BT -/F8 9.963 Tf 164.375 230.211 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 230.211 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 230.211 cm 0 g 0 G @@ -1369,11 +1368,11 @@ S Q 1 0 0 1 -130.436 -218.002 cm BT -/F8 9.963 Tf 133.425 218.002 Td[(spasb)]TJ +/F8 9.963 Tf 133.425 218.002 Td[(spin)1(s)]TJ ET -1 0 0 1 157.336 218.002 cm +1 0 0 1 155.122 218.002 cm 0 g 0 G -1 0 0 1 -157.336 -218.002 cm +1 0 0 1 -155.122 -218.002 cm BT /F8 9.963 Tf 164.375 218.002 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1381,7 +1380,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -218.002 cm BT -/F8 9.963 Tf 433.644 218.002 Td[(48)]TJ +/F8 9.963 Tf 433.644 218.002 Td[(47)]TJ ET 1 0 0 1 443.606 218.002 cm 0 g 0 G @@ -1402,11 +1401,11 @@ S Q 1 0 0 1 -130.436 -205.792 cm BT -/F8 9.963 Tf 133.425 205.792 Td[(spfr)1(e)-1(e)]TJ +/F8 9.963 Tf 133.425 205.792 Td[(spasb)]TJ ET -1 0 0 1 158.692 205.792 cm +1 0 0 1 157.336 205.792 cm 0 g 0 G -1 0 0 1 -158.692 -205.792 cm +1 0 0 1 -157.336 -205.792 cm BT /F8 9.963 Tf 164.375 205.792 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1435,19 +1434,19 @@ S Q 1 0 0 1 -130.436 -193.583 cm BT -/F8 9.963 Tf 133.425 193.583 Td[(sprn)]TJ +/F8 9.963 Tf 133.425 193.583 Td[(spfr)1(e)-1(e)]TJ ET -1 0 0 1 152.327 193.583 cm +1 0 0 1 158.692 193.583 cm 0 g 0 G -1 0 0 1 -152.327 -193.583 cm +1 0 0 1 -158.692 -193.583 cm BT -/F8 9.963 Tf 156.626 193.583 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 164.375 193.583 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 193.583 cm 0 g 0 G 1 0 0 1 -433.644 -193.583 cm BT -/F8 9.963 Tf 433.644 193.583 Td[(50)]TJ +/F8 9.963 Tf 433.644 193.583 Td[(51)]TJ ET 1 0 0 1 443.606 193.583 cm 0 g 0 G @@ -1468,11 +1467,11 @@ S Q 1 0 0 1 -130.436 -181.373 cm BT -/F8 9.963 Tf 133.425 181.373 Td[(geall)]TJ +/F8 9.963 Tf 133.425 181.373 Td[(sprn)]TJ ET -1 0 0 1 153.351 181.373 cm +1 0 0 1 152.327 181.373 cm 0 g 0 G -1 0 0 1 -153.351 -181.373 cm +1 0 0 1 -152.327 -181.373 cm BT /F8 9.963 Tf 156.626 181.373 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET @@ -1480,7 +1479,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -181.373 cm BT -/F8 9.963 Tf 433.644 181.373 Td[(51)]TJ +/F8 9.963 Tf 433.644 181.373 Td[(52)]TJ ET 1 0 0 1 443.606 181.373 cm 0 g 0 G @@ -1501,19 +1500,19 @@ S Q 1 0 0 1 -130.436 -169.163 cm BT -/F8 9.963 Tf 133.425 169.163 Td[(geins)]TJ +/F8 9.963 Tf 133.425 169.163 Td[(geall)]TJ ET -1 0 0 1 155.066 169.163 cm +1 0 0 1 153.351 169.163 cm 0 g 0 G -1 0 0 1 -155.066 -169.163 cm +1 0 0 1 -153.351 -169.163 cm BT -/F8 9.963 Tf 164.375 169.163 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 169.163 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 169.163 cm 0 g 0 G 1 0 0 1 -433.644 -169.163 cm BT -/F8 9.963 Tf 433.644 169.163 Td[(52)]TJ +/F8 9.963 Tf 433.644 169.163 Td[(53)]TJ ET 1 0 0 1 443.606 169.163 cm 0 g 0 G @@ -1534,11 +1533,11 @@ S Q 1 0 0 1 -130.436 -156.954 cm BT -/F8 9.963 Tf 133.425 156.954 Td[(geas)-1(b)]TJ +/F8 9.963 Tf 133.425 156.954 Td[(geins)]TJ ET -1 0 0 1 157.28 156.954 cm +1 0 0 1 155.066 156.954 cm 0 g 0 G -1 0 0 1 -157.28 -156.954 cm +1 0 0 1 -155.066 -156.954 cm BT /F8 9.963 Tf 164.375 156.954 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1546,7 +1545,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -156.954 cm BT -/F8 9.963 Tf 433.644 156.954 Td[(53)]TJ +/F8 9.963 Tf 433.644 156.954 Td[(54)]TJ ET 1 0 0 1 443.606 156.954 cm 0 g 0 G @@ -1567,11 +1566,11 @@ S Q 1 0 0 1 -130.436 -144.744 cm BT -/F8 9.963 Tf 133.425 144.744 Td[(gefree)]TJ +/F8 9.963 Tf 133.425 144.744 Td[(geas)-1(b)]TJ ET -1 0 0 1 158.636 144.744 cm +1 0 0 1 157.28 144.744 cm 0 g 0 G -1 0 0 1 -158.636 -144.744 cm +1 0 0 1 -157.28 -144.744 cm BT /F8 9.963 Tf 164.375 144.744 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672.256 cm +0 g 0 G +1 0 0 1 -256.303 -672.256 cm +BT +/F29 9.963 Tf 482.959 672.256 Td[(61)]TJ +ET +1 0 0 1 165.649 660.301 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -165.649 -660.301 cm BT @@ -2133,19 +2132,19 @@ S Q 1 0 0 1 -181.246 -660.301 cm BT -/F8 9.963 Tf 184.235 660.301 Td[(cgs)]TJ +/F8 9.963 Tf 184.235 660.301 Td[(cg)]TJ ET -1 0 0 1 200.894 660.301 cm +1 0 0 1 196.965 660.301 cm 0 g 0 G -1 0 0 1 -200.894 -660.301 cm +1 0 0 1 -196.965 -660.301 cm BT -/F8 9.963 Tf 207.436 660.301 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 199.687 660.301 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ ET 1 0 0 1 484.453 660.301 cm 0 g 0 G 1 0 0 1 -484.453 -660.301 cm BT -/F8 9.963 Tf 484.453 660.301 Td[(61)]TJ +/F8 9.963 Tf 484.453 660.301 Td[(62)]TJ ET 1 0 0 1 494.416 660.301 cm 0 g 0 G @@ -2166,19 +2165,19 @@ S Q 1 0 0 1 -181.246 -648.346 cm BT -/F8 9.963 Tf 184.235 648.346 Td[(bi)1(c)-1(g)]TJ +/F8 9.963 Tf 184.235 648.346 Td[(cgs)]TJ ET -1 0 0 1 205.267 648.346 cm +1 0 0 1 200.894 648.346 cm 0 g 0 G -1 0 0 1 -205.267 -648.346 cm +1 0 0 1 -200.894 -648.346 cm BT -/F8 9.963 Tf 215.184 648.346 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 207.436 648.346 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 484.453 648.346 cm 0 g 0 G 1 0 0 1 -484.453 -648.346 cm BT -/F8 9.963 Tf 484.453 648.346 Td[(63)]TJ +/F8 9.963 Tf 484.453 648.346 Td[(64)]TJ ET 1 0 0 1 494.416 648.346 cm 0 g 0 G @@ -2199,19 +2198,19 @@ S Q 1 0 0 1 -181.246 -636.39 cm BT -/F8 9.963 Tf 184.235 636.39 Td[(bi)1(c)-1(gstab)]TJ +/F8 9.963 Tf 184.235 636.39 Td[(bi)1(c)-1(g)]TJ ET -1 0 0 1 223.587 636.39 cm +1 0 0 1 205.267 636.39 cm 0 g 0 G -1 0 0 1 -223.587 -636.39 cm +1 0 0 1 -205.267 -636.39 cm BT -/F8 9.963 Tf 230.682 636.39 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 215.184 636.39 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 484.453 636.39 cm 0 g 0 G 1 0 0 1 -484.453 -636.39 cm BT -/F8 9.963 Tf 484.453 636.39 Td[(65)]TJ +/F8 9.963 Tf 484.453 636.39 Td[(66)]TJ ET 1 0 0 1 494.416 636.39 cm 0 g 0 G @@ -2232,11 +2231,11 @@ S Q 1 0 0 1 -181.246 -624.435 cm BT -/F8 9.963 Tf 184.235 624.435 Td[(bi)1(c)-1(gstabl)]TJ +/F8 9.963 Tf 184.235 624.435 Td[(bi)1(c)-1(gstab)]TJ ET -1 0 0 1 226.355 624.435 cm +1 0 0 1 223.587 624.435 cm 0 g 0 G -1 0 0 1 -226.355 -624.435 cm +1 0 0 1 -223.587 -624.435 cm BT /F8 9.963 Tf 230.682 624.435 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ ET @@ -2244,7 +2243,7 @@ ET 0 g 0 G 1 0 0 1 -484.453 -624.435 cm BT -/F8 9.963 Tf 484.453 624.435 Td[(67)]TJ +/F8 9.963 Tf 484.453 624.435 Td[(68)]TJ ET 1 0 0 1 494.416 624.435 cm 0 g 0 G @@ -2265,41 +2264,29 @@ S Q 1 0 0 1 -181.246 -612.48 cm BT -/F8 9.963 Tf 184.235 612.48 Td[(gmres)]TJ +/F8 9.963 Tf 184.235 612.48 Td[(bi)1(c)-1(gstabl)]TJ ET -1 0 0 1 213.099 612.48 cm +1 0 0 1 226.355 612.48 cm 0 g 0 G -1 0 0 1 -213.099 -612.48 cm +1 0 0 1 -226.355 -612.48 cm BT -/F8 9.963 Tf 222.933 612.48 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 230.682 612.48 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ ET 1 0 0 1 484.453 612.48 cm 0 g 0 G 1 0 0 1 -484.453 -612.48 cm BT -/F8 9.963 Tf 484.453 612.48 Td[(69)]TJ +/F8 9.963 Tf 484.453 612.48 Td[(70)]TJ ET 1 0 0 1 494.416 612.48 cm 0 g 0 G -1 0 0 1 -343.711 -21.918 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -150.705 -590.562 cm -BT -/F29 9.963 Tf 150.705 590.562 Td[(8)-925(Precond)1(i)-1(ti)-1(on)1(er)-383(routines)]TJ -ET -1 0 0 1 284.288 590.562 cm -0 g 0 G -1 0 0 1 -284.288 -590.562 cm -BT -/F29 9.963 Tf 482.959 590.562 Td[(71)]TJ -ET -1 0 0 1 165.649 578.607 cm +1 0 0 1 -328.767 -11.955 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.649 -578.607 cm +1 0 0 1 -165.649 -600.525 cm BT -/F8 9.963 Tf 165.649 578.607 Td[(psb)]TJ +/F8 9.963 Tf 165.649 600.525 Td[(psb)]TJ ET -1 0 0 1 181.246 578.607 cm +1 0 0 1 181.246 600.525 cm q []0 d 0 J @@ -2308,25 +2295,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -181.246 -578.607 cm +1 0 0 1 -181.246 -600.525 cm BT -/F8 9.963 Tf 184.235 578.607 Td[(pr)1(e)-1(cse)-1(t)]TJ +/F8 9.963 Tf 184.235 600.525 Td[(gmres)]TJ ET -1 0 0 1 214.759 578.607 cm +1 0 0 1 213.099 600.525 cm 0 g 0 G -1 0 0 1 -214.759 -578.607 cm +1 0 0 1 -213.099 -600.525 cm BT -/F8 9.963 Tf 222.933 578.607 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 222.933 600.525 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET -1 0 0 1 484.453 578.607 cm +1 0 0 1 484.453 600.525 cm 0 g 0 G -1 0 0 1 -484.453 -578.607 cm +1 0 0 1 -484.453 -600.525 cm BT -/F8 9.963 Tf 484.453 578.607 Td[(72)]TJ +/F8 9.963 Tf 484.453 600.525 Td[(72)]TJ ET -1 0 0 1 494.416 578.607 cm +1 0 0 1 494.416 600.525 cm 0 g 0 G -1 0 0 1 -328.767 -11.955 cm +1 0 0 1 -343.711 -21.918 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -150.705 -578.607 cm +BT +/F29 9.963 Tf 150.705 578.607 Td[(8)-925(Precond)1(i)-1(ti)-1(on)1(er)-383(routines)]TJ +ET +1 0 0 1 284.288 578.607 cm +0 g 0 G +1 0 0 1 -284.288 -578.607 cm +BT +/F29 9.963 Tf 482.959 578.607 Td[(74)]TJ +ET +1 0 0 1 165.649 566.652 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -165.649 -566.652 cm BT @@ -2343,11 +2342,11 @@ S Q 1 0 0 1 -181.246 -566.652 cm BT -/F8 9.963 Tf 184.235 566.652 Td[(pr)1(e)-1(cbl)1(d)]TJ +/F8 9.963 Tf 184.235 566.652 Td[(pr)1(e)-1(cse)-1(t)]TJ ET -1 0 0 1 216.364 566.652 cm +1 0 0 1 214.759 566.652 cm 0 g 0 G -1 0 0 1 -216.364 -566.652 cm +1 0 0 1 -214.759 -566.652 cm BT /F8 9.963 Tf 222.933 566.652 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -2355,7 +2354,7 @@ ET 0 g 0 G 1 0 0 1 -484.453 -566.652 cm BT -/F8 9.963 Tf 484.453 566.652 Td[(73)]TJ +/F8 9.963 Tf 484.453 566.652 Td[(75)]TJ ET 1 0 0 1 494.416 566.652 cm 0 g 0 G @@ -2376,41 +2375,29 @@ S Q 1 0 0 1 -181.246 -554.697 cm BT -/F8 9.963 Tf 184.235 554.697 Td[(pr)1(e)-1(capl)1(y)]TJ +/F8 9.963 Tf 184.235 554.697 Td[(pr)1(e)-1(cbl)1(d)]TJ ET -1 0 0 1 221.069 554.697 cm +1 0 0 1 216.364 554.697 cm 0 g 0 G -1 0 0 1 -221.069 -554.697 cm +1 0 0 1 -216.364 -554.697 cm BT -/F8 9.963 Tf 230.682 554.697 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 222.933 554.697 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET 1 0 0 1 484.453 554.697 cm 0 g 0 G 1 0 0 1 -484.453 -554.697 cm BT -/F8 9.963 Tf 484.453 554.697 Td[(74)]TJ +/F8 9.963 Tf 484.453 554.697 Td[(78)]TJ ET 1 0 0 1 494.416 554.697 cm 0 g 0 G -1 0 0 1 -343.711 -21.918 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -150.705 -532.779 cm -BT -/F29 9.963 Tf 150.705 532.779 Td[(9)-925(E)1(rror)-383(h)1(andl)-1(ing)]TJ -ET -1 0 0 1 240.002 532.779 cm -0 g 0 G -1 0 0 1 -240.002 -532.779 cm -BT -/F29 9.963 Tf 482.959 532.779 Td[(75)]TJ -ET -1 0 0 1 165.649 520.824 cm +1 0 0 1 -328.767 -11.955 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.649 -520.824 cm +1 0 0 1 -165.649 -542.742 cm BT -/F8 9.963 Tf 165.649 520.824 Td[(psb)]TJ +/F8 9.963 Tf 165.649 542.742 Td[(psb)]TJ ET -1 0 0 1 181.246 520.824 cm +1 0 0 1 181.246 542.742 cm q []0 d 0 J @@ -2419,31 +2406,44 @@ q 2.989 0.199 l S Q -1 0 0 1 -181.246 -520.824 cm +1 0 0 1 -181.246 -542.742 cm BT -/F8 9.963 Tf 184.235 520.824 Td[(errp)1(ush)]TJ +/F8 9.963 Tf 184.235 542.742 Td[(pr)1(e)-1(capl)1(y)]TJ ET -1 0 0 1 217.001 520.824 cm +1 0 0 1 221.069 542.742 cm 0 g 0 G -1 0 0 1 -217.001 -520.824 cm +1 0 0 1 -221.069 -542.742 cm BT -/F8 9.963 Tf 222.933 520.824 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 230.682 542.742 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ ET -1 0 0 1 484.453 520.824 cm +1 0 0 1 484.453 542.742 cm 0 g 0 G -1 0 0 1 -484.453 -520.824 cm +1 0 0 1 -484.453 -542.742 cm BT -/F8 9.963 Tf 484.453 520.824 Td[(77)]TJ +/F8 9.963 Tf 484.453 542.742 Td[(79)]TJ ET -1 0 0 1 494.416 520.824 cm +1 0 0 1 494.416 542.742 cm 0 g 0 G -1 0 0 1 -328.767 -11.955 cm +1 0 0 1 -328.767 -11.956 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.649 -508.869 cm +1 0 0 1 -165.649 -530.786 cm +BT +/F8 9.963 Tf 165.649 530.786 Td[(psb)]TJ +ET +1 0 0 1 181.246 530.786 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +2.989 0.199 l +S +Q +1 0 0 1 -181.246 -530.786 cm BT -/F8 9.963 Tf 165.649 508.869 Td[(psb)]TJ +/F8 9.963 Tf 184.235 530.786 Td[(pr)1(e)-1(c)]TJ ET -1 0 0 1 181.246 508.869 cm +1 0 0 1 203.125 530.786 cm q []0 d 0 J @@ -2452,25 +2452,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -181.246 -508.869 cm +1 0 0 1 -203.125 -530.786 cm BT -/F8 9.963 Tf 184.235 508.869 Td[(error)]TJ +/F8 9.963 Tf 206.114 530.786 Td[(desc)-1(r)]TJ ET -1 0 0 1 205.35 508.869 cm +1 0 0 1 228.336 530.786 cm 0 g 0 G -1 0 0 1 -205.35 -508.869 cm +1 0 0 1 -228.336 -530.786 cm BT -/F8 9.963 Tf 215.184 508.869 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Td[(care)-298(of)-296(run)29(time)-298(me)-1(mory)-297(r)1(e)-1(q)1(uir)1(e)-1(me)-1(n)29(ts)-298(th)1(at)-297(are)-298(q)1(uite)-297(di\016cult)-297(or)-297(ev)28(en)-297(imp)-27(os)-1(sibl)1(e)]TJ 0 -11.955 Td[(to)-382(predi)1(c)-1(t)-382(at)-383(i)1(m)-1(p)1(lem)-1(en)28(tati)1(on)-383(or)-382(compilat)1(ion)-382(time)-1(.)-592(Th)1(e)-383(foll)1(o)27(wi)1(ng)-383(p)1(res)-1(en)28(tati)1(on)]TJ 0 -11.956 Td[(of)-393(th)1(e)-394(P)1(SBLAS)-393(lib)1(rar)1(y)-393(follo)28(ws)-394(th)1(e)-394(general)-393(stru)1(c)-1(tu)1(re)-394(o)1(f)-393(the)-393(prop)-27(osal)-393(for)-393(se)-1(r)1(ial)]TJ 0 -11.955 Td[(Sp)1(arse)-319(BLAS)-317([)]TJ/F29 9.963 Tf 63.706 0 Td[(?)]TJ/F8 9.963 Tf 5.41 0 Td[(],)-321(wh)1(ic)27(h)-317(in)-318(i)1(ts)-319(tu)1(rn)-317(is)-319(b)1(as)-1(ed)-318(on)-317(the)-318(p)1(rop)-27(os)-1(al)-318(f)1(or)-318(BLAS)-318(on)-317(dense)]TJ -69.116 -11.955 Td[(matrices)-334([)]TJ/F29 9.963 Tf 42.701 0 Td[(?)]TJ/F8 9.963 Tf 5.411 0 Td[(,)]TJ/F29 9.963 Tf 6.088 0 Td[(?)]TJ/F8 9.963 Tf 5.41 0 Td[(,)]TJ/F29 9.963 Tf 6.088 0 Td[(?)]TJ/F8 9.963 Tf 5.411 0 Td[(].)]TJ -56.165 -12.545 Td[(The)-403(app)1(licabil)1(it)28(y)-403(of)-403(spar)1(s)-1(e)-403(iterati)1(v)28(e)-404(solv)28(ers)-404(t)1(o)-403(m)-1(an)28(y)-402(di\013eren)28(t)-403(areas)-404(causes)]TJ -14.944 -11.955 Td[(som)-1(e)-317(t)1(e)-1(rmin)1(ology)-316(pr)1(obl)1(e)-1(ms)-317(b)-27(e)-1(cause)-317(th)1(e)-317(s)-1(ame)-317(concept)-316(m)-1(a)28(y)-316(b)-27(e)-317(deno)1(te)-1(d)-316(th)1(rou)1(gh)]TJ 0 -11.956 Td[(di)1(\013)-1(eren)28(t)-342(n)1(am)-1(es)-342(dep)-28(end)1(in)1(g)-342(on)-342(t)1(he)-342(app)1(lication)-341(area.)-470(T)-1(h)1(e)-342(PS)1(B)-1(LAS)-341(featur)1(e)-1(s)-342(p)1(re)-1(-)]TJ 0 -11.955 Td[(se)-1(n)28(ted)-361(in)-361(th)1(is)-362(se)-1(ction)-361(will)-361(b)-27(e)-362(discuss)-1(ed)-361(m)-1(ai)1(nly)-361(in)-361(terms)-362(of)-361(\014n)1(ite)-362(d)1(i\013e)-1(r)1(e)-1(n)1(c)-1(e)-362(d)1(is)-1(-)]TJ 0 -11.955 Td[(cre)-1(t)1(iz)-1(at)1(ions)-278(of)-278(P)29(artial)-277(Di\013e)-1(r)1(e)-1(n)28(ti)1(al)-278(Eq)1(uati)1(ons)-278(\050PDE)1(s)-1(\051.)-425(Ho)28(w)27(ev)28(e)-1(r)1(,)-289(the)-278(sc)-1(op)-27(e)-279(o)1(f)-278(th)1(e)]TJ 0 -11.955 Td[(lib)1(rar)1(y)-345(is)-345(wid)1(e)-1(r)-344(th)1(an)-344(that:)-466(for)-344(e)-1(x)1(am)-1(p)1(le,)-348(i)1(t)-345(can)-344(b)-28(e)-345(ap)1(pli)1(e)-1(d)-344(to)-344(\014n)1(ite)-345(e)-1(l)1(e)-1(me)-1(n)29(t)-345(d)1(is)-1(-)]TJ 0 -11.955 Td[(cre)-1(t)1(iz)-1(at)1(ions)-278(of)-278(P)1(DEs,)-289(an)1(d)-278(ev)28(e)-1(n)-277(to)-278(di\013eren)28(t)-278(clas)-1(ses)-279(of)-277(prob)1(lem)-1(s)-278(suc)27(h)-277(as)-279(n)1(onl)1(inear)]TJ 0 -11.955 Td[(opt)1(im)-1(i)1(z)-1(ati)1(on,)-333(f)1(or)-333(e)-1(xamp)1(le)-334(in)-333(op)1(timal)-333(c)-1(on)29(trol)-333(p)1(robl)1(e)-1(ms)-1(.)]TJ 14.944 -12.546 Td[(The)-489(des)-1(i)1(gn)-489(of)-489(a)-489(solv)28(er)-489(for)-488(s)-1(p)1(arse)-490(li)1(near)-489(s)-1(y)1(s)-1(tems)-490(is)-489(dr)1(iv)28(en)-489(b)28(y)-489(man)28(y)-489(con-)]TJ -14.944 -11.955 Td[(\015i)1(c)-1(ti)1(ng)-384(ob)-55(jec)-1(tiv)28(es,)-397(s)-1(u)1(c)27(h)-384(as)-385(li)1(m)-1(it)1(ing)-384(o)-28(cc)-1(u)1(pation)-384(of)-384(storag)1(e)-385(res)-1(ou)1(rc)-1(es,)-397(e)-1(xp)1(loiti)1(ng)]TJ 0 -11.955 Td[(regul)1(ariti)1(e)-1(s)-433(in)-432(the)-433(in)1(pu)1(t)-433(d)1(ata,)-458(exp)1(loitin)1(g)-433(h)1(ardw)28(are)-433(c)28(haracteristics)-433(of)-433(th)1(e)-433(par-)]TJ 0 -11.955 Td[(allel)-370(p)1(latf)1(orm.)-554(T)83(o)-370(ac)27(h)1(iev)28(e)-371(an)-369(opt)1(imal)-370(c)-1(omm)28(un)1(ic)-1(ati)1(on)-370(to)-369(c)-1(ompu)1(tation)-369(rati)1(o)-370(on)]TJ 0 -11.956 Td[(di)1(s)-1(tr)1(ibu)1(ted)-339(m)-1(emory)-339(mac)27(hi)1(nes)-340(it)-339(is)-340(ess)-1(en)28(tial)-339(to)-339(k)28(ee)-1(p)-339(th)1(e)]TJ/F19 9.963 Tf 244.68 0 Td[(data)-364(l)1(o)51(c)51(ality)]TJ/F8 9.963 Tf 55.629 0 Td[(as)-340(h)1(igh)-339(as)]TJ -300.309 -11.955 Td[(p)-27(os)-1(sib)1(le)-1(;)-306(this)-294(can)-294(b)-27(e)-294(don)1(e)-295(th)1(rou)1(gh)-294(an)-293(app)1(rop)1(riate)-294(dat)1(a)-294(allo)-28(cation)-293(strategy)83(.)-431(Th)1(e)]TJ 0 -11.955 Td[(c)27(h)1(oice)-400(of)-398(the)-399(pr)1(e)-1(cond)1(ition)1(e)-1(r)-398(is)-399(anoth)1(e)-1(r)-398(v)28(e)-1(r)1(y)-399(imp)-28(or)1(tan)28(t)-399(f)1(ac)-1(t)1(or)-399(tha)1(t)-399(a\013)-1(ec)-1(t)1(s)-400(e\016)-1(-)]TJ 0 -11.955 Td[(cie)-1(n)1(c)-1(y)-311(of)-311(the)-312(impl)1(e)-1(men)28(te)-1(d)-311(ap)1(pli)1(c)-1(ati)1(on.)-437(Op)1(timal)-312(d)1(ata)-312(d)1(is)-1(t)1(rib)1(ution)-311(r)1(e)-1(qu)1(ireme)-1(n)28(t)1(s)]TJ 0 -11.955 Td[(for)-248(a)-250(gi)1(v)28(e)-1(n)-249(p)1(rec)-1(on)1(di)1(tioner)-249(ma)28(y)-249(c)-1(on)1(\015ict)-249(with)-249(d)1(is)-1(t)1(rib)1(ution)-248(requir)1(e)-1(men)28(ts)-250(of)-248(the)-249(re)-1(st)]TJ 0 -11.955 Td[(of)-367(the)-368(solv)28(e)-1(r)1(.)-548(F)1(ind)1(ing)-367(the)-368(op)1(timal)-368(tr)1(ade-)-1(o\013)-368(ma)28(y)-368(b)-27(e)-368(v)28(e)-1(r)1(y)-368(d)1(i\016)-1(cul)1(t)-368(b)-27(e)-1(cause)-368(it)-368(i)1(s)]TJ 0 -11.956 Td[(app)1(lication)-270(d)1(e)-1(p)-27(e)-1(n)1(den)28(t.)-423(P)28(oss)-1(i)1(ble)-271(solut)1(ion)-270(to)-271(th)1(e)-1(se)-271(pr)1(oblems)-271(and)-270(other)-270(imp)-28(or)1(tan)28(t)]TJ 0 -11.955 Td[(in)1(pu)1(ts)-352(to)-351(th)1(e)-352(d)1(e)-1(v)28(elopmen)28(t)-351(of)-351(th)1(e)-352(P)1(SBLAS)-351(soft)28(w)28(are)-351(pac)27(k)56(age)-351(has)-351(c)-1(ome)-352(f)1(rom)-351(an)]TJ 0 -11.955 Td[(es)-1(tab)1(lished)-365(e)-1(xp)-27(erience)-366(in)-365(app)1(lyin)1(g)-366(th)1(e)-367(P)1(SBLAS)-365(s)-1(ol)1(v)28(e)-1(r)1(s)-367(t)1(o)-366(c)-1(omp)1(utati)1(onal)-365(\015ui)1(d)]TJ 0 -11.955 Td[(dy)1(namics)-334(app)1(lication)1(s)-1(.)]TJ/F18 14.346 Tf 0 -36.077 Td[(2)-1125(Gener)-1(al)-374(o)31(v)32(er)-1(vi)1(ew)]TJ/F8 9.963 Tf 0 -22.919 Td[(The)-519(PS)1(BLAS)-519(l)1(ibr)1(ary)-519(i)1(s)-520(d)1(e)-1(sign)1(e)-1(d)-518(to)-519(han)1(dl)1(e)-520(th)1(e)-519(im)-1(p)1(lem)-1(en)28(tat)1(ion)-519(of)-518(iterati)1(v)28(e)]TJ 0 -11.956 Td[(solv)28(e)-1(r)1(s)-502(f)1(or)-501(s)-1(p)1(arse)-502(lin)1(ear)-501(s)-1(ystem)-1(s)-501(on)-501(d)1(is)-1(tr)1(ibu)1(ted)-501(me)-1(mory)-501(p)1(arall)1(e)-1(l)-501(com)-1(p)1(uters.)]TJ +/F18 14.346 Tf 99.895 706.129 Td[(1)-1125(In)32(tro)-31(ducti)1(on)]TJ/F8 9.963 Tf 0 -22.919 Td[(The)-316(PS)1(BLAS)-316(l)1(ibr)1(ary)83(,)-319(d)1(e)-1(v)28(elop)-27(ed)-316(with)-315(th)1(e)-317(ai)1(m)-317(to)-315(facilit)1(ate)-317(t)1(he)-316(par)1(allelization)-315(of)]TJ 0 -11.956 Td[(com)-1(p)1(utati)1(onall)1(y)-324(in)28(tensiv)28(e)-324(s)-1(cien)28(ti\014)1(c)-325(ap)1(pli)1(c)-1(ati)1(ons,)-326(is)-324(des)-1(i)1(gned)-324(to)-324(ad)1(dress)-325(p)1(arallel)]TJ 0 -11.955 Td[(impl)1(e)-1(me)-1(n)29(tation)-427(of)-426(iterativ)28(e)-427(s)-1(ol)1(v)28(e)-1(rs)-427(for)-427(spar)1(s)-1(e)-427(lin)1(e)-1(ar)-427(system)-1(s)-427(thr)1(ough)-427(th)1(e)-428(d)1(is)-1(-)]TJ 0 -11.955 Td[(tri)1(bu)1(te)-1(d)-284(mem)-1(or)1(y)-284(para)1(digm.)-428(It)-284(inclu)1(des)-285(rou)1(tin)1(e)-1(s)-285(f)1(or)-284(m)27(u)1(ltip)1(lyi)1(ng)-284(s)-1(p)1(arse)-285(matrices)]TJ 0 -11.955 Td[(b)28(y)-342(dense)-344(matr)1(ic)-1(es,)-345(s)-1(olv)1(ing)-342(blo)-27(c)27(k)-343(d)1(iagon)1(al)-343(sys)-1(tems)-343(w)-1(i)1(th)-343(tr)1(ian)1(gular)-342(diag)1(onal)-343(en-)]TJ 0 -11.955 Td[(tri)1(e)-1(s,)-350(p)1(repro)-27(c)-1(es)-1(sin)1(g)-347(spar)1(s)-1(e)-347(matri)1(c)-1(es)-1(,)-349(and)-346(con)28(tai)1(ns)-347(ad)1(diti)1(onal)-346(rou)1(tines)-347(f)1(or)-346(dense)]TJ 0 -11.955 Td[(matrix)-439(op)-27(e)-1(r)1(ation)1(s)-1(.)-762(The)-440(cur)1(ren)28(t)-439(implem)-1(en)28(tat)1(ion)-439(of)-439(PS)1(BLAS)-439(add)1(res)-1(se)-1(s)-439(a)-440(d)1(is)-1(-)]TJ 0 -11.956 Td[(tri)1(bu)1(te)-1(d)-415(m)-1(emory)-416(exec)-1(u)1(tion)-416(mo)-28(d)1(e)-1(l)-416(op)-27(eratin)1(g)-416(with)-416(mes)-1(sage)-417(p)1(as)-1(sin)1(g.)-693(Ho)28(w)27(ev)28(er,)]TJ 0 -11.955 Td[(th)1(e)-373(o)28(v)28(erall)-371(des)-1(i)1(gn)-372(d)1(o)-28(es)-373(n)1(ot)-372(p)1(rec)-1(lu)1(de)-372(d)1(i\013e)-1(r)1(e)-1(n)28(t)-371(impleme)-1(n)28(t)1(ation)-371(parad)1(igms)-1(,)-381(suc)28(h)]TJ 0 -11.955 Td[(as)-334(th)1(os)-1(e)-333(base)-1(d)-333(on)-332(a)-334(shar)1(e)-1(d)-333(mem)-1(or)1(y)-333(m)-1(o)-27(del.)]TJ 14.944 -12.545 Td[(The)-382(PS)1(BLAS)-382(l)1(ibr)1(ary)-382(i)1(s)-383(i)1(n)28(ternal)1(ly)-382(i)1(m)-1(p)1(lem)-1(en)28(ted)-382(i)1(n)-382(a)-382(mix)1(tur)1(e)-383(of)-381(F)84(ortran)-381(77)]TJ -14.944 -11.956 Td[(and)-361(F)84(ortr)1(an)-362(95)-361([)]TJ +ET +1 0 0 1 172.337 551.113 cm +0 1 0 rg 0 1 0 RG +1 0 0 1 -172.337 -551.113 cm +BT +/F8 9.963 Tf 172.337 551.113 Td[(20)]TJ +ET +1 0 0 1 182.3 551.113 cm +0 g 0 G +1 0 0 1 -182.3 -551.113 cm +BT +/F8 9.963 Tf 182.3 551.113 Td[(])-362(p)1(rogr)1(am)-1(min)1(g)-362(lan)1(guages)-1(.)-529(A)-362(similar)-361(app)1(roac)28(h)-362(h)1(as)-362(b)-28(ee)-1(n)-361(ad)1(-)]TJ -82.405 -11.956 Td[(v)28(o)-28(cate)-1(d)-391(b)28(y)-391(a)-392(n)28(u)1(m)27(b)-27(er)-392(of)-391(aut)1(hors,)-406(e)-1(.)1(g.)-392([)]TJ +ET +1 0 0 1 270.547 539.157 cm +0 1 0 rg 0 1 0 RG +1 0 0 1 -270.547 -539.157 cm +BT +/F8 9.963 Tf 270.547 539.157 Td[(19)]TJ +ET +1 0 0 1 280.51 539.157 cm +0 g 0 G +1 0 0 1 -280.51 -539.157 cm +BT +/F8 9.963 Tf 280.51 539.157 Td[(].)-619(Mor)1(e)-1(o)28(v)28(e)-1(r)1(,)-406(the)-392(F)84(ortr)1(an)-392(95)-391(faciliti)1(e)-1(s)]TJ -180.615 -11.955 Td[(for)-257(d)1(ynamic)-258(me)-1(mory)-257(managem)-1(en)28(t)-257(and)-257(in)28(terf)1(ac)-1(e)-258(o)28(v)28(erload)1(ing)-257(greatly)-257(e)-1(n)1(han)1(c)-1(e)-258(th)1(e)]TJ 0 -11.955 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Td[(in)-370(whic)28(h)-371(w)28(e)-372(sp)-27(e)-1(cif)1(y)-371(the)-371(siz)-1(e)-371(of)-370(the)-371(in)1(dex)-371(space)]TJ/F11 9.963 Tf -137.878 -11.955 Td[(n)]TJ/F8 9.963 Tf 9.143 0 Td[(and)-316(the)-318(al)1(lo)-28(cation)-317(of)-317(th)1(e)-318(e)-1(l)1(e)-1(me)-1(n)29(ts)-318(of)-317(the)-317(ind)1(e)-1(x)-317(space)-318(to)-317(the)-318(v)56(ar)1(ious)-318(p)1(ro)-28(ces)-1(se)-1(s)]TJ -9.143 -11.955 Td[(makin)1(g)-334(u)1(p)-333(the)-333(MP)1(I)-334(\050v)1(irtu)1(al\051)-333(par)1(allel)-334(mac)28(hin)1(e)-1(.)]TJ 14.944 -12.149 Td[(The)-309(i)1(nd)1(e)-1(x)-308(space)-309(is)-309(p)1(artit)1(ioned)-308(among)-308(pr)1(o)-28(c)-1(ess)-1(es)-1(,)-313(an)1(d)-308(thi)1(s)-309(c)-1(r)1(e)-1(ates)-309(a)-308(m)-1(ap)1(pi)1(ng)]TJ -14.944 -11.955 Td[(fr)1(om)-250(t)1(he)-249(\134global)1(")-249(n)28(um)28(b)-28(eri)1(ng)-249(1)]TJ/F11 9.963 Tf 132.852 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.963 Tf 21.745 0 Td[(to)-249(a)-249(n)28(u)1(m)27(b)-27(erin)1(g)-249(\134lo)-28(cal")-249(to)-249(eac)27(h)-249(p)1(ro)-28(ces)-1(s;)-277(e)-1(ac)28(h)]TJ -154.597 -11.955 Td[(pr)1(o)-28(ce)-1(ss)]TJ/F11 9.963 Tf 33.772 0 Td[(i)]TJ/F8 9.963 Tf 5.793 0 Td[(will)-237(o)28(wn)-236(a)-237(c)-1(ertain)-236(s)-1(u)1(bse)-1(t)-236(1)]TJ/F11 9.963 Tf 113.509 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.963 Tf 19.263 -1.494 Td[(ro)28(w)]TJ/F9 4.981 Tf 15.802 -0.997 Td[(i)]TJ/F8 9.963 Tf 3.654 2.491 Td[(,)-256(eac)27(h)-237(elem)-1(en)28(t)-237(of)-236(whic)28(h)-237(corresp)-28(on)1(ds)]TJ -191.793 -11.955 Td[(to)-389(a)-390(ce)-1(rt)1(ain)-389(e)-1(leme)-1(n)29(t)-390(of)-389(1)]TJ/F11 9.963 Tf 111.314 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.963 Tf 19.263 0 Td[(.)-613(The)-390(u)1(s)-1(er)-389(do)-28(es)-390(not)-389(s)-1(et)-390(exp)1(licitly)-389(th)1(is)-390(m)-1(a)1(ppi)1(ng;)]TJ -130.577 -11.955 Td[(when)-392(th)1(e)-393(app)1(lication)-392(n)1(e)-1(eds)-392(to)-392(ind)1(icate)-393(to)-392(whic)28(h)-392(e)-1(l)1(e)-1(me)-1(n)29(t)-392(of)-392(the)-392(ind)1(e)-1(x)-392(space)-393(a)]TJ 0 -11.956 Td[(ce)-1(rt)1(ain)-273(i)1(te)-1(m)-273(is)-273(related,)-285(suc)28(h)-273(as)-273(th)1(e)-274(r)1(o)27(w)-273(an)1(d)-273(colu)1(m)-1(n)-272(ind)1(e)-1(x)-272(of)-273(a)-273(matr)1(ix)-273(co)-28(e\016)-1(cien)28(t,)]TJ +/F8 9.963 Tf 127.95 334.862 Td[(Ea)1(c)27(h)-333(pr)1(o)-28(ce)-1(ss)-334(has)-333(its)-334(o)28(wn)-333(v)56(alu)1(e)-1(\050s\051)-333(ind)1(e)-1(p)-27(end)1(e)-1(n)28(tl)1(y)83(.)]TJ/F18 11.955 Tf -28.055 -28.401 Td[(2.)1(1)-1125(A)1(ppli)1(cati)1(on)-375(s)1(tructure)]TJ/F8 9.963 Tf 0 -18.57 Td[(The)-274(m)-1(ain)-273(un)1(derlyi)1(ng)-274(pr)1(incip)1(le)-275(of)-274(th)1(e)-275(P)1(SBLAS)-274(lib)1(rar)1(y)-274(is)-275(th)1(at)-275(t)1(he)-275(l)1(ibr)1(ary)-274(ob)-55(jec)-1(t)1(s)]TJ 0 -11.955 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Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 446.188 cm +1 0 0 1 209.819 430.886 cm q []0 d 0 J @@ -3364,11 +3983,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -446.188 cm +1 0 0 1 -209.819 -430.886 cm BT -/F29 9.963 Tf 162.446 446.188 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 430.886 Td[(data[psb)]TJ ET -1 0 0 1 205.525 446.188 cm +1 0 0 1 256.334 430.886 cm q []0 d 0 J @@ -3377,11 +3996,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -446.188 cm +1 0 0 1 -256.334 -430.886 cm BT -/F29 9.963 Tf 208.962 446.188 Td[(dec)]TJ +/F29 9.963 Tf 259.771 430.886 Td[(dec)]TJ ET -1 0 0 1 226.357 446.188 cm +1 0 0 1 277.167 430.886 cm q []0 d 0 J @@ -3390,11 +4009,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -226.357 -446.188 cm +1 0 0 1 -277.167 -430.886 cm BT -/F29 9.963 Tf 229.794 446.188 Td[(t)32(yp)-32(e)]TJ +/F29 9.963 Tf 280.604 430.886 Td[(t)32(yp)-32(e)]TJ ET -1 0 0 1 252.6 446.188 cm +1 0 0 1 303.409 430.886 cm q []0 d 0 J @@ -3403,23 +4022,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -252.6 -446.188 cm +1 0 0 1 -303.409 -430.886 cm BT -/F29 9.963 Tf 256.037 446.188 Td[(])]TJ +/F29 9.963 Tf 306.847 430.886 Td[(])]TJ ET -1 0 0 1 259.22 446.188 cm +1 0 0 1 310.029 430.886 cm 0 g 0 G -1 0 0 1 -259.22 -446.188 cm +1 0 0 1 -310.029 -430.886 cm BT -/F8 9.963 Tf 264.201 446.188 Td[(Iden)28(ti)1(\014es)-223(th)1(e)-223(dec)-1(omp)-27(os)-1(i)1(tion)-222(t)28(yp)-27(e)-223(\050)1(global)1(\051;)]TJ -117.481 -11.955 Td[(th)1(e)-356(ac)-1(t)1(ual)-355(v)56(alu)1(e)-1(s)-356(ar)1(e)-356(in)28(t)1(e)-1(r)1(nally)-355(d)1(e)-1(\014)1(ned,)-360(s)-1(o)-355(th)1(e)-1(y)-355(shou)1(ld)-355(n)1(e)-1(v)28(er)-355(b)-28(e)-355(ac)-1(-)]TJ 0 -11.955 Td[(ce)-1(ss)-1(ed)-333(di)1(rec)-1(tl)1(y)83(.)]TJ +/F8 9.963 Tf 315.01 430.886 Td[(Iden)28(ti\014)1(es)-223(the)-222(dec)-1(omp)-27(os)-1(i)1(tion)-222(t)28(yp)-27(e)-223(\050)1(global)1(\051;)]TJ -117.481 -11.955 Td[(th)1(e)-356(ac)-1(t)1(ual)-355(v)56(alues)-356(ar)1(e)-356(in)28(t)1(e)-1(rn)1(ally)-355(d)1(e)-1(\014)1(ned,)-360(s)-1(o)-355(th)1(e)-1(y)-355(shou)1(ld)-355(n)1(e)-1(v)28(er)-355(b)-28(e)-355(ac)-1(-)]TJ 0 -11.956 Td[(ce)-1(ss)-1(ed)-333(di)1(rec)-1(tl)1(y)83(.)]TJ ET -1 0 0 1 119.821 405.336 cm +1 0 0 1 170.63 391.058 cm 0 g 0 G -1 0 0 1 -119.821 -405.336 cm +1 0 0 1 -170.63 -391.058 cm BT -/F29 9.963 Tf 124.802 405.336 Td[(matri)-1(x)]TJ +/F29 9.963 Tf 175.611 391.058 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 405.336 cm +1 0 0 1 209.819 391.058 cm q []0 d 0 J @@ -3428,11 +4047,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -405.336 cm +1 0 0 1 -209.819 -391.058 cm BT -/F29 9.963 Tf 162.446 405.336 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 391.058 Td[(data[psb)]TJ ET -1 0 0 1 205.525 405.336 cm +1 0 0 1 256.334 391.058 cm q []0 d 0 J @@ -3441,11 +4060,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -405.336 cm +1 0 0 1 -256.334 -391.058 cm BT -/F29 9.963 Tf 208.962 405.336 Td[(ctxt)]TJ +/F29 9.963 Tf 259.771 391.058 Td[(ctxt)]TJ ET -1 0 0 1 229.699 405.336 cm +1 0 0 1 280.508 391.058 cm q []0 d 0 J @@ -3454,23 +4073,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -229.699 -405.336 cm +1 0 0 1 -280.508 -391.058 cm BT -/F29 9.963 Tf 233.136 405.336 Td[(])]TJ +/F29 9.963 Tf 283.945 391.058 Td[(])]TJ ET -1 0 0 1 236.318 405.336 cm +1 0 0 1 287.128 391.058 cm 0 g 0 G -1 0 0 1 -236.318 -405.336 cm +1 0 0 1 -287.128 -391.058 cm BT -/F8 9.963 Tf 241.3 405.336 Td[(Comm)27(un)1(ication)-222(con)28(text)-222(as)-223(r)1(e)-1(tu)1(rn)1(e)-1(d)-221(b)28(y)-222(the)-222(B)-1(LA)28(CS)]TJ -94.58 -11.956 Td[(\050glob)1(al\051.)]TJ +/F8 9.963 Tf 292.109 391.058 Td[(Com)-1(m)28(un)1(ication)-222(con)28(text)-222(as)-223(r)1(e)-1(tu)1(rn)1(e)-1(d)-222(b)29(y)-222(the)-222(B)-1(LA)28(CS)]TJ -94.58 -11.955 Td[(\050glob)1(al\051.)]TJ ET -1 0 0 1 119.821 376.438 cm +1 0 0 1 170.63 363.185 cm 0 g 0 G -1 0 0 1 -119.821 -376.438 cm +1 0 0 1 -170.63 -363.185 cm BT -/F29 9.963 Tf 124.802 376.438 Td[(matri)-1(x)]TJ +/F29 9.963 Tf 175.611 363.185 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 376.438 cm +1 0 0 1 209.819 363.185 cm q []0 d 0 J @@ -3479,11 +4098,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -376.438 cm +1 0 0 1 -209.819 -363.185 cm BT -/F29 9.963 Tf 162.446 376.438 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 363.185 Td[(data[psb)]TJ ET -1 0 0 1 205.525 376.438 cm +1 0 0 1 256.334 363.185 cm q []0 d 0 J @@ -3492,11 +4111,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -376.438 cm +1 0 0 1 -256.334 -363.185 cm BT -/F29 9.963 Tf 208.962 376.438 Td[(m)]TJ +/F29 9.963 Tf 259.771 363.185 Td[(m)]TJ ET -1 0 0 1 219.197 376.438 cm +1 0 0 1 270.006 363.185 cm q []0 d 0 J @@ -3505,23 +4124,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -219.197 -376.438 cm +1 0 0 1 -270.006 -363.185 cm BT -/F29 9.963 Tf 222.634 376.438 Td[(])]TJ +/F29 9.963 Tf 273.443 363.185 Td[(])]TJ ET -1 0 0 1 225.816 376.438 cm +1 0 0 1 276.626 363.185 cm 0 g 0 G -1 0 0 1 -225.816 -376.438 cm +1 0 0 1 -276.626 -363.185 cm BT -/F8 9.963 Tf 230.798 376.438 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(e)-1(q)1(uatio)1(ns)-334(\050gl)1(obal\051.)]TJ +/F8 9.963 Tf 281.607 363.185 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(e)-1(q)1(uation)1(s)-334(\050gl)1(obal\051.)]TJ ET -1 0 0 1 119.821 359.496 cm +1 0 0 1 170.63 347.268 cm 0 g 0 G -1 0 0 1 -119.821 -359.496 cm +1 0 0 1 -170.63 -347.268 cm BT -/F29 9.963 Tf 124.802 359.496 Td[(matri)-1(x)]TJ +/F29 9.963 Tf 175.611 347.268 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 359.496 cm +1 0 0 1 209.819 347.268 cm q []0 d 0 J @@ -3530,11 +4149,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -359.496 cm +1 0 0 1 -209.819 -347.268 cm BT -/F29 9.963 Tf 162.446 359.496 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 347.268 Td[(data[psb)]TJ ET -1 0 0 1 205.525 359.496 cm +1 0 0 1 256.334 347.268 cm q []0 d 0 J @@ -3543,11 +4162,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -359.496 cm +1 0 0 1 -256.334 -347.268 cm BT -/F29 9.963 Tf 208.962 359.496 Td[(n)]TJ +/F29 9.963 Tf 259.771 347.268 Td[(n)]TJ ET -1 0 0 1 216.014 359.496 cm +1 0 0 1 266.824 347.268 cm q []0 d 0 J @@ -3556,23 +4175,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -216.014 -359.496 cm +1 0 0 1 -266.824 -347.268 cm BT -/F29 9.963 Tf 219.451 359.496 Td[(])]TJ +/F29 9.963 Tf 270.261 347.268 Td[(])]TJ ET -1 0 0 1 222.634 359.496 cm +1 0 0 1 273.443 347.268 cm 0 g 0 G -1 0 0 1 -222.634 -359.496 cm +1 0 0 1 -273.443 -347.268 cm BT -/F8 9.963 Tf 227.615 359.496 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(v)56(ariab)1(le)-1(s)-333(\050glob)1(al\051.)]TJ +/F8 9.963 Tf 278.424 347.268 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(v)56(ariab)1(le)-1(s)-333(\050glob)1(al\051.)]TJ ET -1 0 0 1 119.821 342.554 cm +1 0 0 1 170.63 331.351 cm 0 g 0 G -1 0 0 1 -119.821 -342.554 cm +1 0 0 1 -170.63 -331.351 cm BT -/F29 9.963 Tf 124.802 342.554 Td[(matri)-1(x)]TJ +/F29 9.963 Tf 175.611 331.351 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 342.554 cm +1 0 0 1 209.819 331.351 cm q []0 d 0 J @@ -3581,11 +4200,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -342.554 cm +1 0 0 1 -209.819 -331.351 cm BT -/F29 9.963 Tf 162.446 342.554 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 331.351 Td[(data[psb)]TJ ET -1 0 0 1 205.525 342.554 cm +1 0 0 1 256.334 331.351 cm q []0 d 0 J @@ -3594,11 +4213,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -342.554 cm +1 0 0 1 -256.334 -331.351 cm BT -/F29 9.963 Tf 208.962 342.554 Td[(n)]TJ +/F29 9.963 Tf 259.771 331.351 Td[(n)]TJ ET -1 0 0 1 216.014 342.554 cm +1 0 0 1 266.824 331.351 cm q []0 d 0 J @@ -3607,11 +4226,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -216.014 -342.554 cm +1 0 0 1 -266.824 -331.351 cm BT -/F29 9.963 Tf 219.451 342.554 Td[(ro)32(w)]TJ +/F29 9.963 Tf 270.261 331.351 Td[(ro)32(w)]TJ ET -1 0 0 1 238.542 342.554 cm +1 0 0 1 289.351 331.351 cm q []0 d 0 J @@ -3620,23 +4239,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -238.542 -342.554 cm +1 0 0 1 -289.351 -331.351 cm BT -/F29 9.963 Tf 241.979 342.554 Td[(])]TJ +/F29 9.963 Tf 292.788 331.351 Td[(])]TJ ET -1 0 0 1 245.161 342.554 cm +1 0 0 1 295.971 331.351 cm 0 g 0 G -1 0 0 1 -245.161 -342.554 cm +1 0 0 1 -295.971 -331.351 cm BT -/F8 9.963 Tf 250.143 342.554 Td[(Nu)1(m)27(b)-27(e)-1(r)-374(of)-375(gr)1(id)-375(v)56(ar)1(iables)-375(o)28(w)-1(n)1(e)-1(d)-374(b)28(y)-375(t)1(he)-375(c)-1(u)1(r-)]TJ -103.423 -11.955 Td[(ren)28(t)-429(pr)1(o)-28(c)-1(ess)-430(\050lo)-28(cal\051;)-477(equiv)56(al)1(e)-1(n)28(t)-429(to)-429(the)-430(n)29(um)28(b)-28(er)-429(of)-429(lo)-28(cal)-429(ro)28(ws)-430(in)-429(the)]TJ 0 -11.955 Td[(sparse)-334(co)-28(e\016)-1(cien)28(t)-333(m)-1(at)1(rix.)]TJ +/F8 9.963 Tf 300.952 331.351 Td[(Num)28(b)-27(e)-1(r)-374(of)-375(gr)1(id)-375(v)56(ari)1(ables)-375(o)27(wn)1(e)-1(d)-374(b)28(y)-375(t)1(he)-375(c)-1(u)1(r-)]TJ -103.423 -11.955 Td[(ren)28(t)-429(pr)1(o)-28(c)-1(ess)-430(\050lo)-28(cal\051;)-477(equiv)56(alen)28(t)-429(to)-429(the)-430(n)29(um)28(b)-28(er)-429(of)-429(lo)-28(cal)-429(ro)28(w)-1(s)-429(in)-429(the)]TJ 0 -11.956 Td[(sparse)-334(co)-28(e\016)-1(cien)28(t)-333(m)-1(at)1(rix.)]TJ ET -1 0 0 1 119.821 301.702 cm +1 0 0 1 170.63 291.523 cm 0 g 0 G -1 0 0 1 -119.821 -301.702 cm +1 0 0 1 -170.63 -291.523 cm BT -/F29 9.963 Tf 124.802 301.702 Td[(matri)-1(x)]TJ +/F29 9.963 Tf 175.611 291.523 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 159.009 301.702 cm +1 0 0 1 209.819 291.523 cm q []0 d 0 J @@ -3645,11 +4264,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -159.009 -301.702 cm +1 0 0 1 -209.819 -291.523 cm BT -/F29 9.963 Tf 162.446 301.702 Td[(data[)-1(p)1(sb)]TJ +/F29 9.963 Tf 213.256 291.523 Td[(data[psb)]TJ ET -1 0 0 1 205.525 301.702 cm +1 0 0 1 256.334 291.523 cm q []0 d 0 J @@ -3658,11 +4277,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -205.525 -301.702 cm +1 0 0 1 -256.334 -291.523 cm BT -/F29 9.963 Tf 208.962 301.702 Td[(n)]TJ +/F29 9.963 Tf 259.771 291.523 Td[(n)]TJ ET -1 0 0 1 216.014 301.702 cm +1 0 0 1 266.824 291.523 cm q []0 d 0 J @@ -3671,11 +4290,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -216.014 -301.702 cm +1 0 0 1 -266.824 -291.523 cm BT -/F29 9.963 Tf 219.451 301.702 Td[(col)]TJ +/F29 9.963 Tf 270.261 291.523 Td[(col)]TJ ET -1 0 0 1 234.142 301.702 cm +1 0 0 1 284.951 291.523 cm q []0 d 0 J @@ -3684,23 +4303,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -234.142 -301.702 cm +1 0 0 1 -284.951 -291.523 cm BT -/F29 9.963 Tf 237.579 301.702 Td[(])]TJ +/F29 9.963 Tf 288.388 291.523 Td[(])]TJ ET -1 0 0 1 240.761 301.702 cm +1 0 0 1 291.571 291.523 cm 0 g 0 G -1 0 0 1 -240.761 -301.702 cm +1 0 0 1 -291.571 -291.523 cm BT -/F8 9.963 Tf 245.742 301.702 Td[(T)83(otal)-230(n)29(um)28(b)-28(er)-230(of)-230(gr)1(id)-230(v)56(ari)1(ables)-231(r)1(e)-1(ad)-229(b)28(y)-230(th)1(e)-231(cur-)]TJ -99.022 -11.955 Td[(ren)28(t)-288(pro)-27(c)-1(es)-1(s)-289(\050lo)-27(c)-1(al\051)1(;)-304(equi)1(v)55(al)1(e)-1(n)29(t)-289(to)-289(th)1(e)-289(n)28(um)28(b)-28(er)-288(of)-289(lo)-27(c)-1(al)-288(c)-1(ol)1(umns)-289(in)-288(the)]TJ 0 -11.956 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Td[(Hold)1(s)-267(in)29(te)-1(ger)-266(in)1(for)1(m)-1(ati)1(on)-266(on)-266(d)1(is)-1(t)1(rib)1(uted)-266(sparse)-267(matr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.955 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(d)1(ata)-334(f)1(ormat)-333(use)-1(d)1(.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(p)-28(oi)1(n)28(ter)-333(to)-334(an)-332(in)28(tege)-1(r)-333(ar)1(ra)28(y)-333(of)-333(ran)1(k)-333(one.)]TJ +/F8 9.963 Tf 119.357 706.129 Td[(Hold)1(s)-267(in)29(te)-1(ger)-266(in)1(for)1(m)-1(ati)1(on)-266(on)-266(d)1(is)-1(t)1(rib)1(uted)-266(sparse)-267(matr)1(ix.)-422(Actual)-265(inf)1(ormation)]TJ 5.445 -11.955 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(d)1(ata)-333(format)-333(use)-1(d)1(.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(p)-28(oi)1(n)28(ter)-333(to)-334(an)-332(in)28(tege)-1(r)-333(ar)1(ra)28(y)-333(of)-333(ran)1(k)-333(one.)]TJ ET -1 0 0 1 145.724 662.678 cm +1 0 0 1 94.914 662.678 cm 0 g 0 G -1 0 0 1 -145.724 -662.678 cm +1 0 0 1 -94.914 -662.678 cm BT -/F29 9.963 Tf 150.705 662.678 Td[(inf)-1(oa)]TJ +/F29 9.963 Tf 99.895 662.678 Td[(inf)-1(oa)]TJ ET -1 0 0 1 175.051 662.678 cm +1 0 0 1 124.241 662.678 cm 0 g 0 G -1 0 0 1 -175.051 -662.678 cm +1 0 0 1 -124.241 -662.678 cm BT -/F8 9.963 Tf 180.032 662.678 Td[(On)-434(en)28(try)-434(can)-435(h)1(old)-434(aux)1(iliar)1(y)-435(i)1(nfor)1(mation)-434(on)-434(distri)1(but)1(e)-1(d)-434(sparse)-435(matrix)1(.)]TJ -4.421 -11.955 Td[(Actual)-333(in)1(for)1(m)-1(ati)1(on)-333(will)-333(dep)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-333(use)-1(d)1(.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(in)29(te)-1(ger)-333(arr)1(a)27(y)-333(of)-333(l)1(e)-1(n)1(gth)]TJ/F32 9.963 Tf 158.711 0 Td[(psb_ifasize_)]TJ/F8 9.963 Tf 62.764 0 Td[(.)]TJ +/F8 9.963 Tf 129.223 662.678 Td[(On)-434(en)28(try)-434(can)-435(h)1(old)-434(aux)1(iliar)1(y)-435(i)1(nfo)1(rmation)-434(on)-434(distri)1(bu)1(te)-1(d)-434(sparse)-435(matrix)1(.)]TJ -4.421 -11.955 Td[(Actual)-333(in)1(for)1(m)-1(ati)1(on)-333(will)-333(dep)-27(e)-1(n)1(d)-333(on)-333(d)1(ata)-334(f)1(ormat)-333(use)-1(d)1(.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(in)29(te)-1(ger)-333(arr)1(a)27(y)-333(of)-333(l)1(e)-1(n)1(gth)]TJ/F32 9.963 Tf 158.711 0 Td[(psb_ifasize_)]TJ/F8 9.963 Tf 62.764 0 Td[(.)]TJ ET -1 0 0 1 145.724 619.227 cm +1 0 0 1 94.914 619.227 cm 0 g 0 G -1 0 0 1 -145.724 -619.227 cm +1 0 0 1 -94.914 -619.227 cm BT -/F29 9.963 Tf 150.705 619.227 Td[(\014da)]TJ +/F29 9.963 Tf 99.895 619.227 Td[(\014da)]TJ ET -1 0 0 1 169.004 619.227 cm +1 0 0 1 118.195 619.227 cm 0 g 0 G -1 0 0 1 -169.004 -619.227 cm +1 0 0 1 -118.195 -619.227 cm BT -/F8 9.963 Tf 173.985 619.227 Td[(De\014n)1(e)-1(s)-334(t)1(he)-334(f)1(ormat)-333(of)-333(the)-333(distri)1(but)1(e)-1(d)-333(spar)1(s)-1(e)-334(matr)1(ix.)]TJ 1.626 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(ing)-333(of)-333(l)1(e)-1(n)1(gth)-333(5)]TJ +/F8 9.963 Tf 123.176 619.227 Td[(De\014n)1(e)-1(s)-334(t)1(he)-334(f)1(ormat)-333(of)-333(the)-333(distri)1(but)1(e)-1(d)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix.)]TJ 1.626 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(in)1(g)-334(of)-333(l)1(e)-1(n)1(gth)-333(5)]TJ ET -1 0 0 1 145.724 587.732 cm +1 0 0 1 94.914 587.732 cm 0 g 0 G -1 0 0 1 -145.724 -587.732 cm +1 0 0 1 -94.914 -587.732 cm BT -/F29 9.963 Tf 150.705 587.732 Td[(descr)1(a)]TJ +/F29 9.963 Tf 99.895 587.732 Td[(descr)1(a)]TJ ET -1 0 0 1 182.22 587.732 cm +1 0 0 1 131.41 587.732 cm 0 g 0 G -1 0 0 1 -182.22 -587.732 cm +1 0 0 1 -131.41 -587.732 cm BT -/F8 9.963 Tf 187.201 587.732 Td[(Des)-1(crib)-27(e)-334(th)1(e)-334(c)28(haracteristic)-334(of)-332(the)-334(d)1(istrib)1(uted)-333(sparse)-334(matri)1(x.)]TJ -11.59 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(arr)1(a)28(y)-334(of)-332(c)27(har)1(ac)-1(ter)-333(of)-333(leng)1(th)-333(9.)]TJ +/F8 9.963 Tf 136.392 587.732 Td[(Des)-1(crib)-27(e)-334(t)1(he)-334(c)28(haracteristic)-334(of)-332(the)-334(d)1(istrib)1(uted)-333(spar)1(s)-1(e)-334(matr)1(ix.)]TJ -11.59 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(arr)1(a)28(y)-334(o)1(f)-333(c)27(har)1(ac)-1(t)1(e)-1(r)-333(of)-333(l)1(e)-1(n)1(gth)-333(9.)]TJ ET -1 0 0 1 145.724 556.236 cm +1 0 0 1 94.914 556.236 cm 0 g 0 G -1 0 0 1 -145.724 -556.236 cm +1 0 0 1 -94.914 -556.236 cm BT -/F29 9.963 Tf 150.705 556.236 Td[(pl)]TJ +/F29 9.963 Tf 99.895 556.236 Td[(pl)]TJ ET -1 0 0 1 160.252 556.236 cm +1 0 0 1 109.443 556.236 cm 0 g 0 G -1 0 0 1 -160.252 -556.236 cm +1 0 0 1 -109.443 -556.236 cm BT -/F8 9.963 Tf 165.234 556.236 Td[(Sp)-27(ec)-1(i)1(\014es)-353(the)-353(lo)-27(c)-1(al)-352(ro)28(w)-353(p)-27(erm)27(u)1(tation)-352(of)-352(d)1(is)-1(t)1(rib)1(uted)-352(s)-1(p)1(arse)-353(m)-1(at)1(rix.)-502(If)-352(p)1(l\0501\051)-352(is)]TJ 10.377 -11.955 Td[(equal)-333(to)-333(0,)-333(then)-333(th)1(e)-1(r)1(e)-334(isn't)-333(r)1(o)27(w)-333(p)-27(e)-1(rm)28(ut)1(ation.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-452(as:)-681(p)-27(oin)28(ter)-451(to)-452(i)1(n)28(tege)-1(r)-451(arr)1(a)27(y)-451(of)-451(di)1(m)-1(ension)-451(equal)-451(to)-452(n)29(um)28(b)-28(er)-451(of)]TJ 0 -11.955 Td[(lo)-28(cal)-333(ro)28(w)-333(\050m)-1(atr)1(ix)]TJ +/F8 9.963 Tf 114.424 556.236 Td[(Sp)-27(ec)-1(i)1(\014es)-353(the)-353(lo)-27(c)-1(al)-352(ro)28(w)-353(p)-27(erm)27(u)1(tation)-352(of)-352(d)1(is)-1(t)1(rib)1(uted)-352(s)-1(p)1(arse)-353(m)-1(atr)1(ix.)-502(If)-352(p)1(l\0501\051)-352(is)]TJ 10.378 -11.955 Td[(equal)-333(to)-333(0,)-333(th)1(e)-1(n)-333(th)1(e)-1(r)1(e)-334(isn't)-333(r)1(o)27(w)-333(p)-27(e)-1(r)1(m)27(ut)1(ation.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-452(as:)-681(p)-27(oin)28(t)1(e)-1(r)-451(to)-452(i)1(n)28(tege)-1(r)-451(arr)1(a)27(y)-451(of)-451(di)1(m)-1(ension)-451(equal)-451(to)-452(n)29(um)28(b)-28(er)-451(of)]TJ 0 -11.955 Td[(lo)-28(cal)-333(ro)28(w)-333(\050m)-1(at)1(rix)]TJ ET -1 0 0 1 251.815 520.371 cm +1 0 0 1 201.005 520.371 cm q []0 d 0 J @@ -4854,11 +5473,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -251.815 -520.371 cm +1 0 0 1 -201.005 -520.371 cm BT -/F8 9.963 Tf 254.804 520.371 Td[(d)1(ata[psb)]TJ +/F8 9.963 Tf 203.994 520.371 Td[(dat)1(a[psb)]TJ ET -1 0 0 1 292.54 520.371 cm +1 0 0 1 241.73 520.371 cm q []0 d 0 J @@ -4867,11 +5486,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -292.54 -520.371 cm +1 0 0 1 -241.73 -520.371 cm BT -/F8 9.963 Tf 295.529 520.371 Td[(n)]TJ +/F8 9.963 Tf 244.719 520.371 Td[(n)]TJ ET -1 0 0 1 301.661 520.371 cm +1 0 0 1 250.852 520.371 cm q []0 d 0 J @@ -4880,11 +5499,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -301.661 -520.371 cm +1 0 0 1 -250.852 -520.371 cm BT -/F8 9.963 Tf 304.65 520.371 Td[(ro)28(w)]TJ +/F8 9.963 Tf 253.841 520.371 Td[(ro)28(w)]TJ ET -1 0 0 1 321.05 520.371 cm +1 0 0 1 270.24 520.371 cm q []0 d 0 J @@ -4893,23 +5512,23 @@ q 2.989 0.199 l S Q -1 0 0 1 -321.05 -520.371 cm +1 0 0 1 -270.24 -520.371 cm BT -/F8 9.963 Tf 324.039 520.371 Td[(]\051)]TJ +/F8 9.963 Tf 273.229 520.371 Td[(]\051)]TJ ET -1 0 0 1 145.724 500.83 cm +1 0 0 1 94.914 500.83 cm 0 g 0 G -1 0 0 1 -145.724 -500.83 cm +1 0 0 1 -94.914 -500.83 cm BT -/F29 9.963 Tf 150.705 500.83 Td[(pr)]TJ +/F29 9.963 Tf 99.895 500.83 Td[(pr)]TJ ET -1 0 0 1 161.788 500.83 cm +1 0 0 1 110.979 500.83 cm 0 g 0 G -1 0 0 1 -161.788 -500.83 cm +1 0 0 1 -110.979 -500.83 cm BT -/F8 9.963 Tf 166.77 500.83 Td[(S)1(p)-28(ec)-1(i)1(\014es)-513(th)1(e)-513(l)1(o)-28(c)-1(al)-511(c)-1(ol)1(umn)-512(p)-27(e)-1(r)1(m)27(u)1(tation)-511(of)-512(d)1(is)-1(t)1(rib)1(uted)-512(spar)1(s)-1(e)-512(matrix.)-980(If)]TJ 8.841 -11.955 Td[(PR\0501\051)-333(i)1(s)-334(e)-1(q)1(ual)-333(to)-333(0,)-333(then)-333(th)1(e)-1(re)-333(isn't)-333(columnm)-333(p)-27(e)-1(rm)28(ut)1(ation.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-452(as:)-681(p)-27(oin)28(ter)-451(to)-452(i)1(n)28(tege)-1(r)-451(arr)1(a)27(y)-451(of)-451(di)1(m)-1(ension)-451(equal)-451(to)-452(n)29(um)28(b)-28(er)-451(of)]TJ 0 -11.955 Td[(lo)-28(cal)-333(ro)28(w)-333(\050m)-1(atr)1(ix)]TJ +/F8 9.963 Tf 115.96 500.83 Td[(Sp)-27(ec)-1(i)1(\014es)-513(th)1(e)-513(l)1(o)-28(c)-1(al)-511(c)-1(olu)1(mn)-512(p)-27(e)-1(r)1(m)27(u)1(tation)-511(of)-512(d)1(is)-1(t)1(rib)1(uted)-512(spar)1(s)-1(e)-512(m)-1(at)1(rix.)-980(If)]TJ 8.842 -11.955 Td[(PR\050)1(1\051)-334(i)1(s)-334(e)-1(q)1(ual)-333(to)-333(0,)-333(then)-333(th)1(e)-1(r)1(e)-334(isn't)-333(column)1(m)-334(p)-27(e)-1(rm)28(ut)1(ation.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-452(as:)-681(p)-27(oin)28(t)1(e)-1(r)-451(to)-452(i)1(n)28(tege)-1(r)-451(arr)1(a)27(y)-451(of)-451(di)1(m)-1(ension)-451(equal)-451(to)-452(n)29(um)28(b)-28(er)-451(of)]TJ 0 -11.955 Td[(lo)-28(cal)-333(ro)28(w)-333(\050m)-1(at)1(rix)]TJ ET -1 0 0 1 251.815 464.965 cm +1 0 0 1 201.005 464.965 cm q []0 d 0 J @@ -4918,11 +5537,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -251.815 -464.965 cm +1 0 0 1 -201.005 -464.965 cm BT -/F8 9.963 Tf 254.804 464.965 Td[(d)1(ata[psb)]TJ +/F8 9.963 Tf 203.994 464.965 Td[(dat)1(a[psb)]TJ ET -1 0 0 1 292.54 464.965 cm +1 0 0 1 241.73 464.965 cm q []0 d 0 J @@ -4931,11 +5550,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -292.54 -464.965 cm +1 0 0 1 -241.73 -464.965 cm BT -/F8 9.963 Tf 295.529 464.965 Td[(n)]TJ +/F8 9.963 Tf 244.719 464.965 Td[(n)]TJ ET -1 0 0 1 301.661 464.965 cm +1 0 0 1 250.852 464.965 cm q []0 d 0 J @@ -4944,11 +5563,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -301.661 -464.965 cm +1 0 0 1 -250.852 -464.965 cm BT -/F8 9.963 Tf 304.65 464.965 Td[(col)]TJ +/F8 9.963 Tf 253.841 464.965 Td[(col)]TJ ET -1 0 0 1 317.424 464.965 cm +1 0 0 1 266.615 464.965 cm q []0 d 0 J @@ -4957,52 +5576,52 @@ q 2.989 0.199 l S Q -1 0 0 1 -317.424 -464.965 cm +1 0 0 1 -266.615 -464.965 cm BT -/F8 9.963 Tf 320.413 464.965 Td[(]\051)]TJ +/F8 9.963 Tf 269.604 464.965 Td[(]\051)]TJ ET -1 0 0 1 145.724 445.424 cm +1 0 0 1 94.914 445.424 cm 0 g 0 G -1 0 0 1 -145.724 -445.424 cm +1 0 0 1 -94.914 -445.424 cm BT -/F29 9.963 Tf 150.705 445.424 Td[(m)]TJ +/F29 9.963 Tf 99.895 445.424 Td[(m)]TJ ET -1 0 0 1 160.252 445.424 cm +1 0 0 1 109.443 445.424 cm 0 g 0 G -1 0 0 1 -160.252 -445.424 cm +1 0 0 1 -109.443 -445.424 cm BT -/F8 9.963 Tf 165.234 445.424 Td[(Nu)1(m)27(b)-27(e)-1(r)-243(of)-243(ro)28(ws)-1(;)-273(if)-243(ro)28(w)-244(in)1(di)1(c)-1(es)-244(are)-244(s)-1(tor)1(e)-1(d)-243(expl)1(ic)-1(i)1(tly)84(,)-262(as)-244(in)-243(Co)-28(or)1(din)1(ate)-244(Stor)1(age)-1(,)]TJ 10.377 -11.955 Td[(shoul)1(d)-225(b)-27(e)-225(greater)-225(th)1(an)-225(or)-224(equal)-224(to)-225(th)1(e)-225(m)-1(ax)1(im)27(u)1(m)-225(ro)28(w)-225(in)1(dex)-225(actuall)1(y)-225(p)1(res)-1(en)28(t)]TJ 0 -11.955 Td[(in)-333(th)1(e)-334(spar)1(s)-1(e)-334(matr)1(ix.)-444(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(in)28(teger)-333(v)55(ar)1(iab)1(le)-1(.)]TJ +/F8 9.963 Tf 114.424 445.424 Td[(Num)28(b)-27(e)-1(r)-243(of)-243(ro)28(ws)-1(;)-273(if)-243(ro)28(w)-244(in)1(dices)-245(ar)1(e)-244(s)-1(tor)1(e)-1(d)-243(expl)1(ic)-1(i)1(tly)84(,)-262(as)-244(in)-243(Co)-28(ord)1(in)1(ate)-244(Stor)1(age)-1(,)]TJ 10.378 -11.955 Td[(shou)1(ld)-225(b)-27(e)-225(greater)-225(th)1(an)-225(o)1(r)-225(equal)-224(to)-225(th)1(e)-225(m)-1(ax)1(im)27(u)1(m)-225(ro)28(w)-225(in)1(dex)-225(actual)1(ly)-225(p)1(res)-1(en)28(t)]TJ 0 -11.955 Td[(in)-333(th)1(e)-334(spar)1(s)-1(e)-334(matr)1(ix.)-444(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(in)28(t)1(e)-1(ger)-333(v)56(ariab)1(le)-1(.)]TJ ET -1 0 0 1 145.724 401.974 cm +1 0 0 1 94.914 401.974 cm 0 g 0 G -1 0 0 1 -145.724 -401.974 cm +1 0 0 1 -94.914 -401.974 cm BT -/F29 9.963 Tf 150.705 401.974 Td[(k)]TJ +/F29 9.963 Tf 99.895 401.974 Td[(k)]TJ ET -1 0 0 1 156.752 401.974 cm +1 0 0 1 105.942 401.974 cm 0 g 0 G -1 0 0 1 -156.752 -401.974 cm +1 0 0 1 -105.942 -401.974 cm BT -/F8 9.963 Tf 161.733 401.974 Td[(Num)28(b)-27(e)-1(r)-337(of)-338(column)1(s)-1(;)-340(if)-337(column)-338(i)1(nd)1(ic)-1(es)-338(are)-338(s)-1(tor)1(e)-1(d)-337(e)-1(x)1(pli)1(c)-1(itl)1(y)83(,)-339(as)-338(in)-337(Co)-28(ord)1(inat)1(e)]TJ 13.878 -11.955 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-533.198 cm +1 0 0 1 -181.132 -533.198 cm BT -/F8 9.963 Tf 135.304 533.198 Td[(St)1(ate)-307(en)28(tered)-306(aft)1(e)-1(r)-306(th)1(e)-307(\014)1(rst)-306(allo)-28(cation)1(,)-311(and)-306(b)-27(efore)-306(the)-306(\014r)1(s)-1(t)-306(ass)-1(em)28(bly;)-314(in)]TJ -10.502 -11.955 Td[(th)1(is)-334(state)-334(it)-333(is)-333(p)-28(oss)-1(i)1(ble)-333(to)-334(ad)1(d)-333(n)1(onze)-1(r)1(o)-334(en)28(tri)1(e)-1(s.)]TJ +/F8 9.963 Tf 186.114 533.198 Td[(S)1(tate)-307(en)28(tered)-306(aft)1(e)-1(r)-306(t)1(he)-307(\014)1(rst)-306(allo)-27(c)-1(ation)1(,)-311(and)-306(b)-27(efor)1(e)-307(th)1(e)-307(\014r)1(s)-1(t)-306(asse)-1(m)28(bly)1(;)-315(in)]TJ -10.503 -11.955 Td[(th)1(is)-334(state)-334(it)-333(is)-333(p)-28(oss)-1(i)1(ble)-333(to)-334(ad)1(d)-333(n)1(onze)-1(ro)-333(en)28(tri)1(e)-1(s.)]TJ ET -1 0 0 1 94.914 500.987 cm +1 0 0 1 145.724 500.987 cm 0 g 0 G -1 0 0 1 -94.914 -500.987 cm +1 0 0 1 -145.724 -500.987 cm BT -/F29 9.963 Tf 99.895 500.987 Td[(Assem)32(bled:)]TJ +/F29 9.963 Tf 150.705 500.987 Td[(Assem)32(bled:)]TJ ET -1 0 0 1 156.422 500.987 cm +1 0 0 1 207.231 500.987 cm 0 g 0 G -1 0 0 1 -156.422 -500.987 cm +1 0 0 1 -207.231 -500.987 cm BT -/F8 9.963 Tf 161.403 500.987 Td[(St)1(ate)-374(en)28(te)-1(r)1(e)-1(d)-372(after)-373(the)-373(as)-1(se)-1(m)28(bly)1(;)-393(c)-1(ompu)1(tation)1(s)-374(usin)1(g)-374(t)1(he)-374(spar)1(s)-1(e)]TJ -36.601 -11.956 Td[(matrix)1(,)-333(s)-1(u)1(c)27(h)-333(as)-334(matr)1(ix-v)28(e)-1(ctor)-333(pr)1(o)-28(du)1(cts)-1(,)-333(are)-333(only)-333(p)-27(oss)-1(ib)1(le)-334(i)1(n)-333(thi)1(s)-334(s)-1(t)1(ate)-1(;)]TJ +/F8 9.963 Tf 212.213 500.987 Td[(St)1(ate)-374(en)28(tere)-1(d)-372(after)-373(the)-373(as)-1(se)-1(m)28(bly)1(;)-393(c)-1(ompu)1(tation)1(s)-374(u)1(s)-1(in)1(g)-374(t)1(he)-374(spar)1(s)-1(e)]TJ -36.602 -11.956 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Td[(in)-395(wh)1(ic)27(h)-394(the)-395(s)-1(ame)-396(spar)1(s)-1(it)28(y)-395(p)1(attern)-395(i)1(s)-396(used)-395(m)27(u)1(ltip)1(le)-396(t)1(im)-1(es)-396(wit)1(h)-395(di)1(\013)-1(eren)28(t)]TJ 0 -11.955 Td[(co)-28(e)-1(\016cie)-1(n)29(ts)-1(.)-426(In)-280(th)1(is)-281(state)-280(it)-280(is)-280(only)-280(p)-27(oss)-1(ib)1(le)-280(to)-280(e)-1(n)28(ter)-280(co)-28(e\016)-1(cien)28(ts)-281(f)1(or)-280(alr)1(e)-1(ad)1(y)]TJ 0 -11.956 Td[(existing)-333(n)1(onze)-1(ro)-333(en)28(tri)1(e)-1(s.)]TJ/F29 9.963 Tf -24.906 -26.335 Td[(3.2.)-1(1)-1150(Named)-383(Cons)1(tan)32(t)-1(s)]TJ ET -1 0 0 1 94.914 388.031 cm +1 0 0 1 145.724 388.031 cm 0 g 0 G -1 0 0 1 -94.914 -388.031 cm +1 0 0 1 -145.724 -388.031 cm BT -/F29 9.963 Tf 99.895 388.031 Td[(ps)1(b)]TJ +/F29 9.963 Tf 150.705 388.031 Td[(ps)1(b)]TJ ET -1 0 0 1 117.832 388.031 cm +1 0 0 1 168.641 388.031 cm q []0 d 0 J @@ -5225,11 +5844,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -117.832 -388.031 cm +1 0 0 1 -168.641 -388.031 cm BT -/F29 9.963 Tf 121.269 388.031 Td[(dupl)]TJ +/F29 9.963 Tf 172.078 388.031 Td[(dupl)]TJ ET -1 0 0 1 144.234 388.031 cm +1 0 0 1 195.043 388.031 cm q []0 d 0 J @@ -5238,11 +5857,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -144.234 -388.031 cm +1 0 0 1 -195.043 -388.031 cm BT -/F29 9.963 Tf 147.671 388.031 Td[(o)32(vw)1(rt)]TJ +/F29 9.963 Tf 198.48 388.031 Td[(o)32(vwr)1(t)]TJ ET -1 0 0 1 177.264 388.031 cm +1 0 0 1 228.073 388.031 cm q []0 d 0 J @@ -5253,17 +5872,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -180.701 -388.031 cm +1 0 0 1 -231.51 -388.031 cm BT -/F8 9.963 Tf 185.682 388.031 Td[(Du)1(pli)1(c)-1(ate)-315(c)-1(o)-27(e)-1(\016cie)-1(n)29(ts)-316(shou)1(ld)-314(b)-28(e)-315(o)28(v)28(e)-1(r)1(w)-1(r)1(itten)-315(\050i)1(.e)-1(.)-438(i)1(gnore)-315(d)1(u-)]TJ -60.88 -11.955 Td[(pl)1(ic)-1(a)1(tions\051)]TJ +/F8 9.963 Tf 236.492 388.031 Td[(Du)1(pli)1(c)-1(ate)-315(c)-1(o)-27(e)-1(\016cie)-1(n)29(ts)-316(shou)1(ld)-314(b)-28(e)-315(o)28(v)28(e)-1(r)1(w)-1(r)1(itten)-315(\050)1(i.e.)-439(i)1(gnor)1(e)-316(d)1(u-)]TJ -60.881 -11.955 Td[(pl)1(ic)-1(at)1(ions\051)]TJ ET -1 0 0 1 94.914 355.819 cm +1 0 0 1 145.724 355.819 cm 0 g 0 G -1 0 0 1 -94.914 -355.819 cm +1 0 0 1 -145.724 -355.819 cm BT -/F29 9.963 Tf 99.895 355.819 Td[(ps)1(b)]TJ +/F29 9.963 Tf 150.705 355.819 Td[(ps)1(b)]TJ ET -1 0 0 1 117.832 355.819 cm +1 0 0 1 168.641 355.819 cm q []0 d 0 J @@ -5272,11 +5891,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -117.832 -355.819 cm +1 0 0 1 -168.641 -355.819 cm BT -/F29 9.963 Tf 121.269 355.819 Td[(dupl)]TJ +/F29 9.963 Tf 172.078 355.819 Td[(dupl)]TJ ET -1 0 0 1 144.234 355.819 cm +1 0 0 1 195.043 355.819 cm q []0 d 0 J @@ -5285,11 +5904,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -144.234 -355.819 cm +1 0 0 1 -195.043 -355.819 cm BT -/F29 9.963 Tf 147.671 355.819 Td[(add)]TJ +/F29 9.963 Tf 198.48 355.819 Td[(add)]TJ ET -1 0 0 1 166.658 355.819 cm +1 0 0 1 217.467 355.819 cm q []0 d 0 J @@ -5300,17 +5919,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -170.095 -355.819 cm +1 0 0 1 -220.904 -355.819 cm BT -/F8 9.963 Tf 175.076 355.819 Td[(Du)1(pli)1(c)-1(ate)-334(co)-28(e\016c)-1(ien)28(ts)-333(s)-1(h)1(ould)-333(b)-27(e)-334(ad)1(ded;)]TJ +/F8 9.963 Tf 225.886 355.819 Td[(Du)1(pli)1(c)-1(ate)-333(c)-1(o)-28(e\016c)-1(ien)28(ts)-333(s)-1(h)1(ould)-333(b)-27(e)-334(ad)1(ded;)]TJ ET -1 0 0 1 94.914 335.563 cm +1 0 0 1 145.724 335.563 cm 0 g 0 G -1 0 0 1 -94.914 -335.563 cm +1 0 0 1 -145.724 -335.563 cm BT -/F29 9.963 Tf 99.895 335.563 Td[(ps)1(b)]TJ +/F29 9.963 Tf 150.705 335.563 Td[(ps)1(b)]TJ ET -1 0 0 1 117.832 335.563 cm +1 0 0 1 168.641 335.563 cm q []0 d 0 J @@ -5319,11 +5938,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -117.832 -335.563 cm +1 0 0 1 -168.641 -335.563 cm BT -/F29 9.963 Tf 121.269 335.563 Td[(dupl)]TJ +/F29 9.963 Tf 172.078 335.563 Td[(dupl)]TJ ET -1 0 0 1 144.234 335.563 cm +1 0 0 1 195.043 335.563 cm q []0 d 0 J @@ -5332,11 +5951,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -144.234 -335.563 cm +1 0 0 1 -195.043 -335.563 cm BT -/F29 9.963 Tf 147.671 335.563 Td[(err)]TJ +/F29 9.963 Tf 198.48 335.563 Td[(err)]TJ ET -1 0 0 1 163.046 335.563 cm +1 0 0 1 213.856 335.563 cm q []0 d 0 J @@ -5347,17 +5966,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -166.483 -335.563 cm +1 0 0 1 -217.293 -335.563 cm BT -/F8 9.963 Tf 171.465 335.563 Td[(Du)1(pli)1(c)-1(ate)-333(c)-1(o)-28(e\016c)-1(ien)28(ts)-333(s)-1(h)1(ould)-333(t)1(rigger)-333(an)-333(error)-333(cond)1(itin)1(o)]TJ +/F8 9.963 Tf 222.274 335.563 Td[(Du)1(pli)1(c)-1(ate)-334(co)-28(e\016c)-1(ien)28(ts)-333(s)-1(h)1(ould)-333(t)1(rigger)-333(an)-333(e)-1(r)1(ror)-333(cond)1(itin)1(o)]TJ ET -1 0 0 1 94.914 315.306 cm +1 0 0 1 145.724 315.306 cm 0 g 0 G -1 0 0 1 -94.914 -315.306 cm +1 0 0 1 -145.724 -315.306 cm BT -/F29 9.963 Tf 99.895 315.306 Td[(ps)1(b)]TJ +/F29 9.963 Tf 150.705 315.306 Td[(ps)1(b)]TJ ET -1 0 0 1 117.832 315.306 cm +1 0 0 1 168.641 315.306 cm q []0 d 0 J @@ -5366,11 +5985,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -117.832 -315.306 cm +1 0 0 1 -168.641 -315.306 cm BT -/F29 9.963 Tf 121.269 315.306 Td[(up)-32(d)]TJ +/F29 9.963 Tf 172.078 315.306 Td[(up)-32(d)]TJ ET -1 0 0 1 141.37 315.306 cm +1 0 0 1 192.179 315.306 cm q []0 d 0 J @@ -5379,11 +5998,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -141.37 -315.306 cm +1 0 0 1 -192.179 -315.306 cm BT -/F29 9.963 Tf 144.807 315.306 Td[(d\015t)]TJ +/F29 9.963 Tf 195.616 315.306 Td[(d\015t)]TJ ET -1 0 0 1 162.68 315.306 cm +1 0 0 1 213.489 315.306 cm q []0 d 0 J @@ -5394,17 +6013,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -166.117 -315.306 cm +1 0 0 1 -216.926 -315.306 cm BT -/F8 9.963 Tf 171.098 315.306 Td[(Defau)1(lt)-333(up)-27(date)-333(s)-1(tr)1(ate)-1(gy)-333(f)1(or)-333(matrix)-333(co)-28(e\016)-1(cien)28(ts;)]TJ +/F8 9.963 Tf 221.907 315.306 Td[(Defau)1(lt)-333(up)-27(date)-333(s)-1(tr)1(ate)-1(gy)-333(f)1(or)-333(m)-1(a)1(trix)-333(co)-28(e\016)-1(cien)28(ts;)]TJ ET -1 0 0 1 94.914 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151.255 0 Td[(iprcparm)]TJ/F8 9.963 Tf 46.134 0 Td[(and)]TJ/F32 9.963 Tf 20.343 0 Td[(dprcparm)]TJ/F8 9.963 Tf 46.134 0 Td[(de\014)1(ne)-431(tha)-430(t)28(yp)-28(e)-431(of)]TJ -263.866 -11.956 Td[(pr)1(e)-1(cond)1(ition)1(e)-1(r)-349(alon)1(g)-350(with)-349(al)1(l)-350(th)1(e)-350(paramete)-1(r)1(s)-350(related)-350(t)1(o)-350(it;)-357(th)28(u)1(s)-1(,)]TJ/F32 9.963 Tf 282.334 0 Td[(iprcparm)]TJ/F8 9.963 Tf 45.326 0 Td[(and)]TJ/F32 9.963 Tf -327.66 -11.955 Td[(dprcparm)]TJ/F8 9.963 Tf 45.164 0 Td[(de\014n)1(e)-334(h)1(o)27(w)-333(th)1(e)-334(other)-333(rec)-1(or)1(ds)-333(ha)28(v)28(e)-334(to)-333(b)-27(e)-334(in)28(terp)1(rete)-1(d)1(.)]TJ ET -1 0 0 1 150.705 584.003 cm +1 0 0 1 99.895 584.003 cm 0 g 0 G 1 0 0 1 2.301 -128.419 cm 0 g 0 G @@ -5618,14 +6237,14 @@ q 0.199 231.631 l S Q -1 0 0 1 3.387 218.182 cm +1 0 0 1 3.388 218.182 cm 0 g 0 G 0 g 0 G -1 0 0 1 -161.374 -560.192 cm +1 0 0 1 -110.565 -560.192 cm BT -/F36 8.966 Tf 175.77 560.192 Td[(type)-525(psb_base_prec)]TJ 9.415 -21.918 Td[(type\050psb_spmat_type\051,)-525(pointer)-1050(::)-525(a)-1(v\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3150(::)-525(d)-1(\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.958 Td[(type\050psb_desc_type\051,)-525(pointer)-1575(::)-525(d)-1(esc_data)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7875(::)-525(i)-1(prcparm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3150(::)-525(d)-1(prcparm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7875(::)-525(p)-1(erm\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7875(::)-525(m)-1(lia\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7875(::)-525(i)-1(nvperm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7875(::)-525(n)-1(laggr\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(type\050psb_spmat_type\051,)-525(pointer)-1050(::)-525(a)-1(orig)-2100(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3150(::)-525(d)-1(orig\050:\051)-525(=>)-525(null\050\051)]TJ -14.122 -21.917 Td[(end)-525(type)-525(psb_base_prec)]TJ 4.707 -21.918 Td[(type)-525(psb_prec_type)]TJ 9.415 -10.959 Td[(type\050psb_base_prec\051,)-525(pointer)-1050(::)-525(ba)-1(seprecv\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer)-12075(::)-525(pr)-1(ec,)-525(base_prec)]TJ -14.122 -10.959 Td[(end)-525(type)-525(psb_prec_type)]TJ +/F36 8.966 Tf 124.961 560.192 Td[(type)-525(psb_base_prec)]TJ 9.414 -21.918 Td[(type\050psb_spmat_type\051,)-525(pointer)-1051(::)-525(av\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3151(::)-525(d\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.958 Td[(type\050psb_desc_type\051,)-525(pointer)-1576(::)-525(desc_data)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7876(::)-525(iprcparm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3151(::)-525(dprcparm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7876(::)-525(perm\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7876(::)-525(mlia\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7876(::)-525(invperm\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer,)-525(pointer)-7876(::)-525(nlaggr\050:\051)-1050(=>)-525(null\050\051)]TJ 0 -10.959 Td[(type\050psb_spmat_type\051,)-525(pointer)-1051(::)-525(aorig)-2100(=>)-525(null\050\051)]TJ 0 -10.959 Td[(real\050kind\0501.d0\051\051,)-525(pointer)-3151(::)-525(dorig\050:\051)-525(=>)-525(null\050\051)]TJ -14.122 -21.917 Td[(end)-525(type)-525(psb_base_prec)]TJ 4.708 -21.918 Td[(type)-525(psb_prec_type)]TJ 9.414 -10.959 Td[(type\050psb_base_prec\051,)-525(pointer)-1050(:)-1(:)-525(baseprecv\050:\051)-525(=>)-525(null\050\051)]TJ 0 -10.959 Td[(integer)-12075(:)-1(:)-525(prec,)-525(base_prec)]TJ -14.122 -10.959 Td[(end)-525(type)-525(psb_prec_type)]TJ ET -1 0 0 1 486.735 342.01 cm +1 0 0 1 435.926 342.01 cm q []0 d 0 J @@ -5634,7 +6253,7 @@ q 0.199 231.631 l S Q -1 0 0 1 -328.748 -0.398 cm +1 0 0 1 -328.749 -0.398 cm q []0 d 0 J @@ -5645,25 +6264,25 @@ S Q 1 0 0 1 4.687 -27.84 cm 0 g 0 G -1 0 0 1 -162.674 -313.772 cm +1 0 0 1 -111.864 -313.772 cm BT -/F8 9.963 Tf 162.674 313.772 Td[(Fi)1(gure)-333(4:)-445(Th)1(e)-334(PS)1(BLAS)-333(de\014n)1(e)-1(d)-333(d)1(ata)-333(t)28(yp)-27(e)-334(that)-333(con)28(tain)1(s)-334(a)-333(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ +/F8 9.963 Tf 111.864 313.772 Td[(Figu)1(re)-333(4:)-445(Th)1(e)-334(PS)1(B)-1(L)1(AS)-333(de\014n)1(e)-1(d)-333(d)1(ata)-333(t)28(yp)-28(e)-333(that)-333(con)28(tain)1(s)-334(a)-333(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ ET -1 0 0 1 482.447 313.772 cm +1 0 0 1 431.638 313.772 cm 0 g 0 G -1 0 0 1 -331.742 -1.937 cm +1 0 0 1 -331.743 -1.937 cm 0 g 0 G -1 0 0 1 -150.705 -311.835 cm +1 0 0 1 -99.895 -311.835 cm BT -/F29 9.963 Tf 150.705 274.881 Td[(3.3.)-1(1)-1150(Named)-383(Cons)1(tan)32(t)-1(s)]TJ +/F29 9.963 Tf 99.895 274.881 Td[(3.3.)-1(1)-1150(Named)-383(Cons)1(tan)32(t)-1(s)]TJ ET -1 0 0 1 145.724 256.157 cm +1 0 0 1 94.914 256.157 cm 0 g 0 G -1 0 0 1 -145.724 -256.157 cm +1 0 0 1 -94.914 -256.157 cm BT -/F29 9.963 Tf 150.705 256.157 Td[(f)]TJ +/F29 9.963 Tf 99.895 256.157 Td[(f)]TJ ET -1 0 0 1 154.893 256.157 cm +1 0 0 1 104.083 256.157 cm q []0 d 0 J @@ -5672,11 +6291,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -154.893 -256.157 cm +1 0 0 1 -104.083 -256.157 cm BT -/F29 9.963 Tf 158.33 256.157 Td[(il)-1(u)]TJ +/F29 9.963 Tf 107.521 256.157 Td[(il)-1(u)]TJ ET -1 0 0 1 171.747 256.157 cm +1 0 0 1 120.938 256.157 cm q []0 d 0 J @@ -5685,11 +6304,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -171.747 -256.157 cm +1 0 0 1 -120.938 -256.157 cm BT -/F29 9.963 Tf 175.185 256.157 Td[(n)]TJ +/F29 9.963 Tf 124.375 256.157 Td[(n)]TJ ET -1 0 0 1 182.237 256.157 cm +1 0 0 1 131.427 256.157 cm q []0 d 0 J @@ -5698,19 +6317,19 @@ q 3.437 0.199 l S Q -1 0 0 1 3.437 0 cm +1 0 0 1 3.438 0 cm 0 g 0 G -1 0 0 1 -185.674 -256.157 cm +1 0 0 1 -134.865 -256.157 cm BT -/F8 9.963 Tf 190.655 256.157 Td[(Incomplete)-232(LU)-230(factorization)-230(w)-1(i)1(th)]TJ/F11 9.963 Tf 144.701 0 Td[(n)]TJ/F8 9.963 Tf 8.282 0 Td[(lev)28(e)-1(l)1(s)-232(of)-231(\014)1(ll-in)1(;)-265(c)-1(u)1(rr)1(e)-1(n)28(tl)1(y)-231(onl)1(y)]TJ/F11 9.963 Tf 126.533 0 Td[(n)]TJ/F8 9.963 Tf 8.748 0 Td[(=)-277(0)]TJ -303.308 -11.956 Td[(is)-334(i)1(m)-1(p)1(lem)-1(en)28(ted;)]TJ +/F8 9.963 Tf 139.846 256.157 Td[(Incomplete)-231(LU)-231(factorization)-230(w)-1(i)1(th)]TJ/F11 9.963 Tf 144.701 0 Td[(n)]TJ/F8 9.963 Tf 8.282 0 Td[(lev)28(e)-1(l)1(s)-232(of)-231(\014)1(ll-in)1(;)-265(c)-1(u)1(rr)1(e)-1(n)28(tl)1(y)-231(onl)1(y)]TJ/F11 9.963 Tf 126.533 0 Td[(n)]TJ/F8 9.963 Tf 8.747 0 Td[(=)-278(0)]TJ -303.307 -11.956 Td[(is)-334(i)1(m)-1(p)1(lem)-1(en)28(ted;)]TJ ET -1 0 0 1 145.724 223.555 cm +1 0 0 1 94.914 223.555 cm 0 g 0 G -1 0 0 1 -145.724 -223.555 cm +1 0 0 1 -94.914 -223.555 cm BT -/F29 9.963 Tf 150.705 223.555 Td[(f)]TJ +/F29 9.963 Tf 99.895 223.555 Td[(f)]TJ ET -1 0 0 1 154.893 223.555 cm +1 0 0 1 104.084 223.555 cm q []0 d 0 J @@ -5719,11 +6338,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -154.893 -223.555 cm +1 0 0 1 -104.084 -223.555 cm BT -/F29 9.963 Tf 158.33 223.555 Td[(slu)]TJ +/F29 9.963 Tf 107.521 223.555 Td[(slu)]TJ ET -1 0 0 1 173.084 223.555 cm +1 0 0 1 122.275 223.555 cm q []0 d 0 J @@ -5734,17 +6353,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -176.521 -223.555 cm +1 0 0 1 -125.712 -223.555 cm BT -/F8 9.963 Tf 181.503 223.555 Td[(S)1(parse)-334(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-333(usin)1(g)-334(S)1(up)-27(erLU;)]TJ +/F8 9.963 Tf 130.693 223.555 Td[(Sp)1(arse)-334(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-333(usin)1(g)-334(S)1(up)-27(erLU;)]TJ ET -1 0 0 1 145.724 202.91 cm +1 0 0 1 94.914 202.91 cm 0 g 0 G -1 0 0 1 -145.724 -202.91 cm +1 0 0 1 -94.914 -202.91 cm BT -/F29 9.963 Tf 150.705 202.91 Td[(f)]TJ +/F29 9.963 Tf 99.895 202.91 Td[(f)]TJ ET -1 0 0 1 154.893 202.91 cm +1 0 0 1 104.084 202.91 cm q []0 d 0 J @@ -5753,11 +6372,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -154.893 -202.91 cm +1 0 0 1 -104.084 -202.91 cm BT -/F29 9.963 Tf 158.33 202.91 Td[(umf)]TJ +/F29 9.963 Tf 107.521 202.91 Td[(umf)]TJ ET -1 0 0 1 178.431 202.91 cm +1 0 0 1 127.621 202.91 cm q []0 d 0 J @@ -5768,17 +6387,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -181.868 -202.91 cm +1 0 0 1 -131.058 -202.91 cm BT -/F8 9.963 Tf 186.849 202.91 Td[(Sp)1(arse)-334(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-333(usin)1(g)-334(UM)1(FP)84(A)28(C)-1(K)1(;)]TJ +/F8 9.963 Tf 136.04 202.91 Td[(Sp)1(arse)-334(f)1(ac)-1(tor)1(iz)-1(at)1(ion)-333(usin)1(g)-334(UM)1(FP)84(A)28(C)-1(K)1(;)]TJ ET -1 0 0 1 145.724 182.264 cm +1 0 0 1 94.914 182.264 cm 0 g 0 G -1 0 0 1 -145.724 -182.264 cm +1 0 0 1 -94.914 -182.264 cm BT -/F29 9.963 Tf 150.705 182.264 Td[(add)]TJ +/F29 9.963 Tf 99.895 182.264 Td[(add)]TJ ET -1 0 0 1 169.692 182.264 cm +1 0 0 1 118.882 182.264 cm q []0 d 0 J @@ -5787,11 +6406,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -169.692 -182.264 cm +1 0 0 1 -118.882 -182.264 cm BT -/F29 9.963 Tf 173.129 182.264 Td[(ml)]TJ +/F29 9.963 Tf 122.319 182.264 Td[(ml)]TJ ET -1 0 0 1 186.546 182.264 cm +1 0 0 1 135.737 182.264 cm q []0 d 0 J @@ -5800,11 +6419,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -186.546 -182.264 cm +1 0 0 1 -135.737 -182.264 cm BT -/F29 9.963 Tf 189.983 182.264 Td[(pr)1(e)-1(c)]TJ +/F29 9.963 Tf 139.174 182.264 Td[(pr)1(ec)]TJ ET -1 0 0 1 212.097 182.264 cm +1 0 0 1 161.288 182.264 cm q []0 d 0 J @@ -5815,17 +6434,17 @@ S Q 1 0 0 1 3.437 0 cm 0 g 0 G -1 0 0 1 -215.534 -182.264 cm +1 0 0 1 -164.725 -182.264 cm BT -/F8 9.963 Tf 220.515 182.264 Td[(Add)1(itiv)28(e)-333(m)27(u)1(ltilev)28(el)-333(c)-1(or)1(re)-1(ction)1(;)]TJ +/F8 9.963 Tf 169.706 182.264 Td[(Add)1(iti)1(v)28(e)-334(m)27(u)1(ltil)1(e)-1(v)28(el)-333(c)-1(or)1(re)-1(ction)1(;)]TJ ET -1 0 0 1 145.724 161.618 cm +1 0 0 1 94.914 161.618 cm 0 g 0 G -1 0 0 1 -145.724 -161.618 cm +1 0 0 1 -94.914 -161.618 cm BT -/F29 9.963 Tf 150.705 161.618 Td[(m)32(ul)-1(t)]TJ +/F29 9.963 Tf 99.895 161.618 Td[(m)32(ul)-1(t)]TJ ET -1 0 0 1 174.624 161.618 cm +1 0 0 1 123.815 161.618 cm q []0 d 0 J @@ -5834,11 +6453,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -174.624 -161.618 cm +1 0 0 1 -123.815 -161.618 cm BT -/F29 9.963 Tf 178.062 161.618 Td[(ml)]TJ +/F29 9.963 Tf 127.252 161.618 Td[(ml)]TJ ET -1 0 0 1 191.479 161.618 cm +1 0 0 1 140.669 161.618 cm q []0 d 0 J @@ -5847,11 +6466,11 @@ q 3.437 0.199 l S Q -1 0 0 1 -191.479 -161.618 cm +1 0 0 1 -140.669 -161.618 cm BT -/F29 9.963 Tf 194.916 161.618 Td[(pr)1(e)-1(c)]TJ +/F29 9.963 Tf 144.107 161.618 Td[(pr)1(ec)]TJ ET -1 0 0 1 217.03 161.618 cm +1 0 0 1 166.22 161.618 cm q []0 d 0 J @@ -5860,19 +6479,19 @@ q 3.437 0.199 l S Q -1 0 0 1 3.437 0 cm +1 0 0 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Td[(j)]TJ/F11 9.963 Tf 2.767 0 Td[(im)]TJ/F8 9.963 Tf 12.18 0 Td[(\050)]TJ/F11 9.963 Tf 3.874 0 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F8 9.963 Tf 3.317 1.494 Td[(\051)]TJ/F14 9.963 Tf 3.874 0 Td[(j)]TJ/F8 9.963 Tf 2.768 0 Td[(\051)]TJ/F18 14.346 Tf -241.37 -32.945 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 109.685 -21.821 Td[(psb)]TJ +/F18 14.346 Tf 180.814 680.226 Td[(geam)1(ax|In\014ni)1(t)31(y)1(-Norm)-375(o)1(f)-375(V)94(ect)1(or)]TJ/F8 9.963 Tf -30.109 -29.791 Td[(Thi)1(s)-334(fu)1(nction)-333(com)-1(p)1(ut)1(e)-1(s)-334(th)1(e)-334(in)1(\014n)1(it)28(y-nor)1(m)-334(of)-333(a)-333(v)28(e)-1(ctor)]TJ/F11 9.963 Tf 233.181 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -238.875 -11.955 Td[(If)]TJ/F11 9.963 Tf 9.963 0 Td[(x)]TJ/F8 9.963 Tf 9.014 0 Td[(is)-334(a)-333(d)1(oub)1(le)-334(pr)1(e)-1(cision)-333(r)1(e)-1(al)-333(v)28(ec)-1(tor)-333(compu)1(te)-1(s)-334(i)1(n\014)1(nit)28(y)-333(n)1(orm)-334(as:)]TJ/F11 9.963 Tf 115.269 -21.918 Td[(ama)1(x)]TJ/F14 9.963 Tf 27.741 0 Td[(\040)]TJ/F8 9.963 Tf 12.73 0 Td[(max)]TJ/F10 6.974 Tf 7.861 -6.275 Td[(i)]TJ/F14 9.963 Tf 12.341 6.275 Td[(j)]TJ/F11 9.963 Tf 2.767 0 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F14 9.963 Tf 3.317 1.494 Td[(j)]TJ/F8 9.963 Tf -206.697 -25.149 Td[(els)-1(e)-333(if)]TJ/F11 9.963 Tf 28.006 0 Td[(x)]TJ/F8 9.963 Tf 9.015 0 Td[(is)-333(a)-334(d)1(oub)1(le)-334(p)1(re)-1(cision)-333(com)-1(p)1(lex)-333(v)28(e)-1(ctor)-333(th)1(e)-1(n)-333(compu)1(te)-1(s)-334(i)1(n\014)1(nit)28(y-n)1(orm)-334(as:)]TJ/F11 9.963 Tf 61.446 -21.918 Td[(ama)1(x)]TJ/F14 9.963 Tf 27.741 0 Td[(\040)]TJ/F8 9.963 Tf 12.73 0 Td[(max)]TJ/F10 6.974 Tf 7.861 -6.275 Td[(i)]TJ/F8 9.963 Tf 12.341 6.275 Td[(\050)]TJ/F14 9.963 Tf 3.874 0 Td[(j)]TJ/F11 9.963 Tf 2.768 0 Td[(r)-28(e)]TJ/F8 9.963 Tf 9.41 0 Td[(\050)]TJ/F11 9.963 Tf 3.874 0 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F8 9.963 Tf 3.317 1.494 Td[(\051)]TJ/F14 9.963 Tf 3.875 0 Td[(j)]TJ/F8 9.963 Tf 4.981 0 Td[(+)]TJ/F14 9.963 Tf 9.962 0 Td[(j)]TJ/F11 9.963 Tf 2.768 0 Td[(i)1(m)]TJ/F8 9.963 Tf 12.179 0 Td[(\050)]TJ/F11 9.963 Tf 3.875 0 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F8 9.963 Tf 3.317 1.494 Td[(\051)]TJ/F14 9.963 Tf 3.874 0 Td[(j)]TJ/F8 9.963 Tf 2.767 0 Td[(\051)]TJ/F18 14.346 Tf -241.369 -32.945 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 109.685 -21.821 Td[(psb)]TJ ET -1 0 0 1 225.177 514.729 cm +1 0 0 1 275.987 514.729 cm q []0 d 0 J @@ -7398,11 +8017,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -225.177 -514.729 cm +1 0 0 1 -275.987 -514.729 cm BT -/F8 9.963 Tf 228.166 514.729 Td[(geam)-1(ax)-333(\050)]TJ/F19 9.963 Tf 40.128 0 Td[(x,)-357(desc)]TJ +/F8 9.963 Tf 278.976 514.729 Td[(geam)-1(ax)-333(\050)]TJ/F19 9.963 Tf 40.127 0 Td[(x,)-357(desc)]TJ ET -1 0 0 1 298.477 514.729 cm +1 0 0 1 349.286 514.729 cm q []0 d 0 J @@ -7411,16 +8030,16 @@ q 3.055 0.199 l S Q -1 0 0 1 -298.477 -514.729 cm +1 0 0 1 -349.286 -514.729 cm BT -/F19 9.963 Tf 301.532 514.729 Td[(a,)-358(i)1(nfo)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ +/F19 9.963 Tf 352.342 514.729 Td[(a,)-357(info)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ ET -1 0 0 1 99.895 488.328 cm +1 0 0 1 150.705 488.328 cm 0 g 0 G -1 0 0 1 26.31 -21.021 cm +1 0 0 1 26.309 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.981 20.622 cm +1 0 0 1 4.982 20.622 cm q []0 d 0 J @@ -7429,11 +8048,11 @@ q 281.13 0.199 l S Q -1 0 0 1 -131.186 -487.929 cm +1 0 0 1 -181.996 -487.929 cm BT -/F11 9.963 Tf 137.164 479.561 Td[(ama)1(x)-7465(x)]TJ/F29 9.963 Tf 217.656 0 Td[(F)96(un)1(c)-1(tion)]TJ +/F11 9.963 Tf 187.973 479.561 Td[(ama)1(x)-7465(x)]TJ/F29 9.963 Tf 217.657 0 Td[(F)96(un)1(c)-1(tion)]TJ ET -1 0 0 1 131.186 475.576 cm +1 0 0 1 181.996 475.576 cm q []0 d 0 J @@ -7442,11 +8061,11 @@ q 281.13 0.199 l S Q -1 0 0 1 -131.186 -475.576 cm +1 0 0 1 -181.996 -475.576 cm BT -/F8 9.963 Tf 137.164 467.207 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(i)1(s)-1(ion)-333(Real)-3102(psb)]TJ +/F8 9.963 Tf 187.973 467.207 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(sb)]TJ ET -1 0 0 1 370.417 467.207 cm +1 0 0 1 421.227 467.207 cm q []0 d 0 J @@ -7455,11 +8074,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -370.417 -467.207 cm +1 0 0 1 -421.227 -467.207 cm BT -/F8 9.963 Tf 373.406 467.207 Td[(geam)-1(ax)]TJ -236.242 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(i)1(s)-1(ion)-333(Compl)1(e)-1(x)-1199(psb)]TJ +/F8 9.963 Tf 424.215 467.207 Td[(geam)-1(ax)]TJ -236.242 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(sb)]TJ ET -1 0 0 1 370.417 455.252 cm +1 0 0 1 421.227 455.252 cm q []0 d 0 J @@ -7468,11 +8087,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -370.417 -455.252 cm +1 0 0 1 -421.227 -455.252 cm BT -/F8 9.963 Tf 373.406 455.252 Td[(geam)-1(ax)]TJ +/F8 9.963 Tf 424.215 455.252 Td[(geam)-1(ax)]TJ ET -1 0 0 1 131.186 451.267 cm +1 0 0 1 181.996 451.267 cm q []0 d 0 J @@ -7483,53 +8102,53 @@ S Q 1 0 0 1 96.881 -27.84 cm 0 g 0 G -1 0 0 1 -228.067 -423.427 cm +1 0 0 1 -278.877 -423.427 cm BT -/F8 9.963 Tf 228.067 423.427 Td[(T)83(ab)1(le)-334(4:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 278.877 423.427 Td[(T)83(ab)1(le)-334(4:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 315.434 423.427 cm +1 0 0 1 366.244 423.427 cm 0 g 0 G 1 0 0 1 -215.539 -1.938 cm 0 g 0 G 1 0 0 1 -4.981 -31.382 cm 0 g 0 G -1 0 0 1 -94.914 -390.107 cm +1 0 0 1 -145.724 -390.107 cm BT -/F29 9.963 Tf 99.895 390.107 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.963 Tf 150.705 390.107 Td[(On)-383(En)33(t)-1(r)1(y)]TJ ET -1 0 0 1 147.481 390.107 cm +1 0 0 1 198.29 390.107 cm 0 g 0 G -1 0 0 1 -52.567 -19.925 cm +1 0 0 1 -52.566 -19.925 cm 0 g 0 G -1 0 0 1 -94.914 -370.182 cm +1 0 0 1 -145.724 -370.182 cm BT -/F29 9.963 Tf 99.895 370.182 Td[(x)]TJ +/F29 9.963 Tf 150.705 370.182 Td[(x)]TJ ET -1 0 0 1 105.942 370.182 cm +1 0 0 1 156.752 370.182 cm 0 g 0 G -1 0 0 1 -105.942 -370.182 cm +1 0 0 1 -156.752 -370.182 cm BT -/F8 9.963 Tf 110.923 370.182 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.933 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)84(able)]TJ +/F8 9.963 Tf 161.733 370.182 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.934 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 163.822 322.361 cm +1 0 0 1 214.632 322.361 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -163.822 -322.361 cm +1 0 0 1 -214.632 -322.361 cm BT -/F8 9.963 Tf 163.822 322.361 Td[(4)]TJ +/F8 9.963 Tf 214.632 322.361 Td[(4)]TJ ET -1 0 0 1 168.804 322.361 cm +1 0 0 1 219.613 322.361 cm 0 g 0 G -1 0 0 1 -168.804 -322.361 cm +1 0 0 1 -219.613 -322.361 cm BT -/F8 9.963 Tf 168.804 322.361 Td[(.)]TJ +/F8 9.963 Tf 219.613 322.361 Td[(.)]TJ ET -1 0 0 1 94.914 302.436 cm +1 0 0 1 145.724 302.436 cm 0 g 0 G -1 0 0 1 -94.914 -302.436 cm +1 0 0 1 -145.724 -302.436 cm BT -/F29 9.963 Tf 99.895 302.436 Td[(desc)]TJ +/F29 9.963 Tf 150.705 302.436 Td[(desc)]TJ ET -1 0 0 1 121.81 302.436 cm +1 0 0 1 172.619 302.436 cm q []0 d 0 J @@ -7538,23 +8157,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -121.81 -302.436 cm +1 0 0 1 -172.619 -302.436 cm BT -/F29 9.963 Tf 125.247 302.436 Td[(a)]TJ +/F29 9.963 Tf 176.057 302.436 Td[(a)]TJ ET -1 0 0 1 130.816 302.436 cm +1 0 0 1 181.626 302.436 cm 0 g 0 G -1 0 0 1 -130.816 -302.436 cm +1 0 0 1 -181.626 -302.436 cm BT -/F8 9.963 Tf 135.798 302.436 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 186.607 302.436 Td[(con)28(tain)1(s)-334(data)-333(stru)1(c)-1(tu)1(res)-334(for)-333(comm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 266.57 cm +1 0 0 1 346.526 266.57 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -266.57 cm +1 0 0 1 -346.526 -266.57 cm BT -/F32 9.963 Tf 295.717 266.57 Td[(psb)]TJ +/F32 9.963 Tf 346.526 266.57 Td[(psb)]TJ ET -1 0 0 1 312.036 266.57 cm +1 0 0 1 362.845 266.57 cm q []0 d 0 J @@ -7563,11 +8182,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -266.57 cm +1 0 0 1 -362.845 -266.57 cm BT -/F32 9.963 Tf 315.174 266.57 Td[(desc)]TJ +/F32 9.963 Tf 365.983 266.57 Td[(desc)]TJ ET -1 0 0 1 336.723 266.57 cm +1 0 0 1 387.532 266.57 cm q []0 d 0 J @@ -7576,112 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Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.956 Td[(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 163.822 602.517 cm +1 0 0 1 214.632 602.517 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -163.822 -602.517 cm +1 0 0 1 -214.632 -602.517 cm BT -/F8 9.963 Tf 163.822 602.517 Td[(9)]TJ +/F8 9.963 Tf 214.632 602.517 Td[(9)]TJ ET -1 0 0 1 168.804 602.517 cm +1 0 0 1 219.613 602.517 cm 0 g 0 G -1 0 0 1 -168.804 -602.517 cm +1 0 0 1 -219.613 -602.517 cm BT -/F8 9.963 Tf 168.804 602.517 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.017 0 Td[(y)]TJ/F8 9.963 Tf 8.563 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ +/F8 9.963 Tf 219.613 602.517 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.018 0 Td[(y)]TJ/F8 9.963 Tf 8.563 0 Td[(m)28(ust)-334(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.711 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ ET -1 0 0 1 94.914 582.592 cm +1 0 0 1 145.724 582.592 cm 0 g 0 G -1 0 0 1 -94.914 -582.592 cm +1 0 0 1 -145.724 -582.592 cm BT -/F29 9.963 Tf 99.895 582.592 Td[(desc)]TJ +/F29 9.963 Tf 150.705 582.592 Td[(desc)]TJ ET -1 0 0 1 121.81 582.592 cm +1 0 0 1 172.619 582.592 cm q []0 d 0 J @@ -9443,23 +10062,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -121.81 -582.592 cm +1 0 0 1 -172.619 -582.592 cm BT -/F29 9.963 Tf 125.247 582.592 Td[(a)]TJ +/F29 9.963 Tf 176.057 582.592 Td[(a)]TJ ET -1 0 0 1 130.816 582.592 cm +1 0 0 1 181.626 582.592 cm 0 g 0 G -1 0 0 1 -130.816 -582.592 cm +1 0 0 1 -181.626 -582.592 cm BT -/F8 9.963 Tf 135.798 582.592 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 186.607 582.592 Td[(con)28(tain)1(s)-334(data)-333(stru)1(c)-1(tu)1(res)-334(for)-333(comm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 546.727 cm +1 0 0 1 346.526 546.727 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -546.727 cm +1 0 0 1 -346.526 -546.727 cm BT -/F32 9.963 Tf 295.717 546.727 Td[(psb)]TJ +/F32 9.963 Tf 346.526 546.727 Td[(psb)]TJ ET -1 0 0 1 312.036 546.727 cm +1 0 0 1 362.845 546.727 cm q []0 d 0 J @@ -9468,11 +10087,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -546.727 cm +1 0 0 1 -362.845 -546.727 cm BT -/F32 9.963 Tf 315.174 546.727 Td[(desc)]TJ +/F32 9.963 Tf 365.983 546.727 Td[(desc)]TJ ET -1 0 0 1 336.723 546.727 cm +1 0 0 1 387.532 546.727 cm q []0 d 0 J @@ -9481,238 +10100,238 @@ q 3.138 0.199 l S Q -1 0 0 1 -336.723 -546.727 cm +1 0 0 1 -387.532 -546.727 cm BT -/F32 9.963 Tf 339.861 546.727 Td[(type)]TJ +/F32 9.963 Tf 390.67 546.727 Td[(type)]TJ ET -1 0 0 1 360.782 546.727 cm +1 0 0 1 411.592 546.727 cm 0 g 0 G -1 0 0 1 -360.782 -546.727 cm +1 0 0 1 -411.592 -546.727 cm BT -/F8 9.963 Tf 360.782 546.727 Td[(.)]TJ +/F8 9.963 Tf 411.592 546.727 Td[(.)]TJ ET -1 0 0 1 94.914 526.801 cm +1 0 0 1 145.724 526.801 cm 0 g 0 G -1 0 0 1 -94.914 -526.801 cm +1 0 0 1 -145.724 -526.801 cm BT -/F29 9.963 Tf 99.895 526.801 Td[(trans)]TJ +/F29 9.963 Tf 150.705 526.801 Td[(trans)]TJ ET -1 0 0 1 125.523 526.801 cm +1 0 0 1 176.332 526.801 cm 0 g 0 G -1 0 0 1 -125.523 -526.801 cm +1 0 0 1 -176.332 -526.801 cm BT -/F8 9.963 Tf 130.504 526.801 Td[(in)1(dicate)-334(wh)1(at)-334(k)1(ind)-333(o)1(f)-333(op)-28(erati)1(on)-333(to)-333(p)-28(erf)1(orm.)]TJ +/F8 9.963 Tf 181.314 526.801 Td[(in)1(dicate)-334(wh)1(at)-334(k)1(ind)-332(of)-333(op)-28(erati)1(on)-333(to)-333(p)-28(erf)1(orm.)]TJ ET -1 0 0 1 119.821 506.876 cm +1 0 0 1 170.63 506.876 cm 0 g 0 G -1 0 0 1 -119.821 -506.876 cm +1 0 0 1 -170.63 -506.876 cm BT -/F29 9.963 Tf 124.802 506.876 Td[(trans)-383(=)-383(N)]TJ +/F29 9.963 Tf 175.611 506.876 Td[(trans)-383(=)-383(N)]TJ ET -1 0 0 1 175.945 506.876 cm +1 0 0 1 226.754 506.876 cm 0 g 0 G -1 0 0 1 -175.945 -506.876 cm +1 0 0 1 -226.754 -506.876 cm BT -/F8 9.963 Tf 180.926 506.876 Td[(th)1(e)-334(op)-27(e)-1(rat)1(ion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equ)1(ation)]TJ +/F8 9.963 Tf 231.735 506.876 Td[(th)1(e)-334(op)-28(erat)1(ion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equ)1(ation)]TJ ET -1 0 0 1 347.385 506.876 cm +1 0 0 1 398.195 506.876 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -347.385 -506.876 cm +1 0 0 1 -398.195 -506.876 cm BT -/F8 9.963 Tf 347.385 506.876 Td[(1)]TJ +/F8 9.963 Tf 398.195 506.876 Td[(1)]TJ ET -1 0 0 1 352.367 506.876 cm +1 0 0 1 403.176 506.876 cm 0 g 0 G 1 0 0 1 -232.546 -15.94 cm 0 g 0 G -1 0 0 1 -119.821 -490.936 cm +1 0 0 1 -170.63 -490.936 cm BT -/F29 9.963 Tf 124.802 490.936 Td[(trans)-383(=)-383(T)]TJ +/F29 9.963 Tf 175.611 490.936 Td[(trans)-383(=)-383(T)]TJ ET -1 0 0 1 174.948 490.936 cm +1 0 0 1 225.758 490.936 cm 0 g 0 G -1 0 0 1 -174.948 -490.936 cm +1 0 0 1 -225.758 -490.936 cm BT -/F8 9.963 Tf 179.93 490.936 Td[(th)1(e)-334(op)-27(e)-1(rat)1(ion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)29(y)-334(equ)1(ation)]TJ +/F8 9.963 Tf 230.739 490.936 Td[(th)1(e)-334(op)-27(e)-1(rat)1(ion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equ)1(ation)]TJ ET -1 0 0 1 346.389 490.936 cm +1 0 0 1 397.199 490.936 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.389 -490.936 cm +1 0 0 1 -397.199 -490.936 cm BT -/F8 9.963 Tf 346.389 490.936 Td[(2)]TJ +/F8 9.963 Tf 397.199 490.936 Td[(2)]TJ ET -1 0 0 1 351.37 490.936 cm +1 0 0 1 402.18 490.936 cm 0 g 0 G -1 0 0 1 -231.549 -15.94 cm +1 0 0 1 -231.55 -15.94 cm 0 g 0 G -1 0 0 1 -119.821 -474.996 cm +1 0 0 1 -170.63 -474.996 cm BT -/F29 9.963 Tf 124.802 474.996 Td[(trans)-383(=)-383(C)]TJ +/F29 9.963 Tf 175.611 474.996 Td[(trans)-383(=)-383(C)]TJ ET -1 0 0 1 175.253 474.996 cm +1 0 0 1 226.062 474.996 cm 0 g 0 G -1 0 0 1 -175.253 -474.996 cm +1 0 0 1 -226.062 -474.996 cm BT -/F8 9.963 Tf 180.234 474.996 Td[(th)1(e)-334(op)-27(e)-1(rat)1(ion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equ)1(ation)]TJ +/F8 9.963 Tf 231.044 474.996 Td[(th)1(e)-334(op)-27(e)-1(ra)1(tion)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)29(y)-334(equ)1(ation)]TJ ET -1 0 0 1 346.694 474.996 cm +1 0 0 1 397.503 474.996 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.694 -474.996 cm +1 0 0 1 -397.503 -474.996 cm BT -/F8 9.963 Tf 346.694 474.996 Td[(3)]TJ +/F8 9.963 Tf 397.503 474.996 Td[(3)]TJ ET -1 0 0 1 351.675 474.996 cm +1 0 0 1 402.484 474.996 cm 0 g 0 G -1 0 0 1 -351.675 -474.996 cm +1 0 0 1 -402.484 -474.996 cm BT -/F8 9.963 Tf 124.802 455.07 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(optional)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Defau)1(lt:)]TJ/F11 9.963 Tf 39.436 0 Td[(tr)-28(ans)]TJ/F8 9.963 Tf 27.052 0 Td[(=)]TJ/F11 9.963 Tf 10.516 0 Td[(N)]TJ/F8 9.963 Tf -77.004 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(c)27(h)1(aracte)-1(r)-333(v)56(ari)1(able.)]TJ +/F8 9.963 Tf 175.611 455.07 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(optional)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Defau)1(lt:)]TJ/F11 9.963 Tf 39.436 0 Td[(tr)-28(ans)]TJ/F8 9.963 Tf 27.052 0 Td[(=)]TJ/F11 9.963 Tf 10.517 0 Td[(N)]TJ/F8 9.963 Tf -77.005 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(c)27(h)1(arac)-1(t)1(e)-1(r)-333(v)56(ari)1(able.)]TJ ET -1 0 0 1 94.914 399.28 cm +1 0 0 1 145.724 399.28 cm 0 g 0 G -1 0 0 1 -94.914 -399.28 cm +1 0 0 1 -145.724 -399.28 cm BT -/F29 9.963 Tf 99.895 399.28 Td[(w)32(or)1(k)]TJ +/F29 9.963 Tf 150.705 399.28 Td[(w)32(or)1(k)]TJ ET -1 0 0 1 124.345 399.28 cm +1 0 0 1 175.155 399.28 cm 0 g 0 G -1 0 0 1 -124.345 -399.28 cm +1 0 0 1 -175.155 -399.28 cm BT -/F8 9.963 Tf 129.327 399.28 Td[(w)28(ork)-333(arr)1(a)27(y)84(.)]TJ -4.525 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(optional)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-487(as)-1(:)-752(a)-488(r)1(ank)-487(one)-488(ar)1(ra)28(y)-487(of)-487(the)-488(same)-488(t)28(yp)-27(e)-488(of)]TJ/F11 9.963 Tf 239.183 0 Td[(x)]TJ/F8 9.963 Tf 10.55 0 Td[(and)]TJ/F11 9.963 Tf 20.908 0 Td[(y)]TJ/F8 9.963 Tf 10.098 0 Td[(with)-487(th)1(e)]TJ -280.739 -11.955 Td[(T)83(AR)28(GE)1(T)-334(attr)1(ibu)1(te.)]TJ +/F8 9.963 Tf 180.136 399.28 Td[(w)28(ork)-333(arr)1(a)27(y)84(.)]TJ -4.525 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(optional)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-487(as)-1(:)-752(a)-488(r)1(ank)-487(one)-488(ar)1(ra)28(y)-487(of)-487(the)-488(same)-488(t)28(yp)-27(e)-488(of)]TJ/F11 9.963 Tf 239.183 0 Td[(x)]TJ/F8 9.963 Tf 10.551 0 Td[(and)]TJ/F11 9.963 Tf 20.907 0 Td[(y)]TJ/F8 9.963 Tf 10.099 0 Td[(with)-487(th)1(e)]TJ -280.74 -11.955 Td[(T)83(AR)28(GE)1(T)-334(attr)1(ibu)1(te.)]TJ ET -1 0 0 1 94.914 331.534 cm +1 0 0 1 145.724 331.534 cm 0 g 0 G -1 0 0 1 -94.914 -331.534 cm +1 0 0 1 -145.724 -331.534 cm BT -/F29 9.963 Tf 99.895 331.534 Td[(On)-383(R)-1(etur)1(n)]TJ +/F29 9.963 Tf 150.705 331.534 Td[(On)-383(Re)-1(tur)1(n)]TJ ET -1 0 0 1 154.434 331.534 cm +1 0 0 1 205.243 331.534 cm 0 g 0 G -1 0 0 1 -59.52 -19.926 cm +1 0 0 1 -59.519 -19.926 cm 0 g 0 G -1 0 0 1 -94.914 -311.608 cm +1 0 0 1 -145.724 -311.608 cm BT -/F29 9.963 Tf 99.895 311.608 Td[(y)]TJ +/F29 9.963 Tf 150.705 311.608 Td[(y)]TJ ET -1 0 0 1 105.942 311.608 cm +1 0 0 1 156.752 311.608 cm 0 g 0 G -1 0 0 1 -105.942 -311.608 cm +1 0 0 1 -156.752 -311.608 cm BT -/F8 9.963 Tf 110.923 311.608 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(r)1(e)-1(sul)1(t)-334(sub)1(matrix)]TJ/F11 9.963 Tf 162.364 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ -153.727 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 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-11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(t)28(yp)-27(e)-334(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)-332(in)]TJ/F14 9.963 Tf 211.375 0 Td[(x)]TJ ET -1 0 0 1 343.925 615.004 cm +1 0 0 1 394.735 615.004 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -343.925 -615.004 cm +1 0 0 1 -394.735 -615.004 cm BT -/F8 9.963 Tf 343.925 615.004 Td[(3)]TJ +/F8 9.963 Tf 394.735 615.004 Td[(3)]TJ ET -1 0 0 1 348.906 615.004 cm +1 0 0 1 399.716 615.004 cm 0 g 0 G -1 0 0 1 -348.906 -615.004 cm +1 0 0 1 -399.716 -615.004 cm BT -/F8 9.963 Tf 348.906 615.004 Td[(.)]TJ +/F8 9.963 Tf 399.716 615.004 Td[(.)]TJ ET -1 0 0 1 94.914 595.61 cm +1 0 0 1 145.724 595.61 cm 0 g 0 G -1 0 0 1 -94.914 -595.61 cm +1 0 0 1 -145.724 -595.61 cm BT -/F29 9.963 Tf 99.895 595.61 Td[(x)]TJ +/F29 9.963 Tf 150.705 595.61 Td[(x)]TJ ET -1 0 0 1 105.942 595.61 cm +1 0 0 1 156.752 595.61 cm 0 g 0 G -1 0 0 1 -105.942 -595.61 cm +1 0 0 1 -156.752 -595.61 cm BT -/F8 9.963 Tf 110.923 595.61 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.933 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)84(able)]TJ +/F8 9.963 Tf 161.733 595.61 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.934 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 163.822 547.789 cm +1 0 0 1 214.632 547.789 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -163.822 -547.789 cm +1 0 0 1 -214.632 -547.789 cm BT -/F8 9.963 Tf 163.822 547.789 Td[(10)]TJ +/F8 9.963 Tf 214.632 547.789 Td[(10)]TJ ET -1 0 0 1 173.785 547.789 cm +1 0 0 1 224.595 547.789 cm 0 g 0 G -1 0 0 1 -173.785 -547.789 cm +1 0 0 1 -224.595 -547.789 cm BT -/F8 9.963 Tf 173.785 547.789 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.018 0 Td[(x)]TJ/F8 9.963 Tf 9.014 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ +/F8 9.963 Tf 224.595 547.789 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.017 0 Td[(x)]TJ/F8 9.963 Tf 9.015 0 Td[(m)27(u)1(st)-334(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ ET -1 0 0 1 94.914 528.395 cm +1 0 0 1 145.724 528.395 cm 0 g 0 G -1 0 0 1 -94.914 -528.395 cm +1 0 0 1 -145.724 -528.395 cm BT -/F29 9.963 Tf 99.895 528.395 Td[(b)-32(eta)]TJ +/F29 9.963 Tf 150.705 528.395 Td[(b)-32(eta)]TJ ET -1 0 0 1 121.855 528.395 cm +1 0 0 1 172.664 528.395 cm 0 g 0 G -1 0 0 1 -121.855 -528.395 cm +1 0 0 1 -172.664 -528.395 cm BT -/F8 9.963 Tf 126.836 528.395 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.963 Tf 45.468 0 Td[(\014)]TJ/F8 9.963 Tf 6.161 0 Td[(.)]TJ -53.663 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(n)28(um)28(b)-27(e)-1(r)-333(of)-333(th)1(e)-334(d)1(ata)-333(t)27(y)1(p)-28(e)-333(ind)1(icate)-1(d)-333(i)1(n)-333(T)83(abl)1(e)]TJ +/F8 9.963 Tf 177.645 528.395 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.963 Tf 45.469 0 Td[(\014)]TJ/F8 9.963 Tf 6.161 0 Td[(.)]TJ -53.664 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(n)28(um)28(b)-27(e)-1(r)-333(of)-333(th)1(e)-334(d)1(ata)-334(t)28(y)1(p)-28(e)-333(ind)1(ic)-1(at)1(e)-1(d)-333(i)1(n)-333(T)83(abl)1(e)]TJ ET -1 0 0 1 383.084 492.53 cm +1 0 0 1 433.893 492.53 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -383.084 -492.53 cm +1 0 0 1 -433.893 -492.53 cm BT -/F8 9.963 Tf 383.084 492.53 Td[(10)]TJ +/F8 9.963 Tf 433.893 492.53 Td[(10)]TJ ET -1 0 0 1 393.047 492.53 cm +1 0 0 1 443.856 492.53 cm 0 g 0 G -1 0 0 1 -393.047 -492.53 cm +1 0 0 1 -443.856 -492.53 cm BT -/F8 9.963 Tf 393.047 492.53 Td[(.)]TJ +/F8 9.963 Tf 443.856 492.53 Td[(.)]TJ ET -1 0 0 1 94.914 473.136 cm +1 0 0 1 145.724 473.136 cm 0 g 0 G -1 0 0 1 -94.914 -473.136 cm +1 0 0 1 -145.724 -473.136 cm BT -/F29 9.963 Tf 99.895 473.136 Td[(y)]TJ +/F29 9.963 Tf 150.705 473.136 Td[(y)]TJ ET -1 0 0 1 105.942 473.136 cm +1 0 0 1 156.752 473.136 cm 0 g 0 G -1 0 0 1 -105.942 -473.136 cm +1 0 0 1 -156.752 -473.136 cm BT -/F8 9.963 Tf 110.923 473.136 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ -167.481 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)84(able)]TJ +/F8 9.963 Tf 161.733 473.136 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ -167.482 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-290(as:)-422(a)-290(ran)1(k)-289(one)-290(or)-289(t)28(w)27(o)-289(arra)28(y)-289(c)-1(on)29(taini)1(ng)-289(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-27(e)-290(sp)-28(ec)-1(i)1(\014ed)]TJ 0 -11.955 Td[(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 163.822 425.315 cm +1 0 0 1 214.632 425.315 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -163.822 -425.315 cm +1 0 0 1 -214.632 -425.315 cm BT -/F8 9.963 Tf 163.822 425.315 Td[(10)]TJ +/F8 9.963 Tf 214.632 425.315 Td[(10)]TJ ET -1 0 0 1 173.785 425.315 cm +1 0 0 1 224.595 425.315 cm 0 g 0 G -1 0 0 1 -173.785 -425.315 cm +1 0 0 1 -224.595 -425.315 cm BT -/F8 9.963 Tf 173.785 425.315 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.018 0 Td[(y)]TJ/F8 9.963 Tf 8.562 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ +/F8 9.963 Tf 224.595 425.315 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.017 0 Td[(y)]TJ/F8 9.963 Tf 8.563 0 Td[(m)27(u)1(st)-334(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ ET -1 0 0 1 94.914 405.921 cm +1 0 0 1 145.724 405.921 cm 0 g 0 G -1 0 0 1 -94.914 -405.921 cm +1 0 0 1 -145.724 -405.921 cm BT -/F29 9.963 Tf 99.895 405.921 Td[(desc)]TJ +/F29 9.963 Tf 150.705 405.921 Td[(desc)]TJ ET -1 0 0 1 121.81 405.921 cm +1 0 0 1 172.619 405.921 cm q []0 d 0 J @@ -10097,23 +10716,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -121.81 -405.921 cm +1 0 0 1 -172.619 -405.921 cm BT -/F29 9.963 Tf 125.247 405.921 Td[(a)]TJ +/F29 9.963 Tf 176.057 405.921 Td[(a)]TJ ET -1 0 0 1 130.816 405.921 cm +1 0 0 1 181.626 405.921 cm 0 g 0 G -1 0 0 1 -130.816 -405.921 cm +1 0 0 1 -181.626 -405.921 cm BT -/F8 9.963 Tf 135.798 405.921 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 186.607 405.921 Td[(con)28(tain)1(s)-334(data)-333(stru)1(c)-1(tu)1(res)-334(for)-333(comm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 370.056 cm +1 0 0 1 346.526 370.056 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -370.056 cm +1 0 0 1 -346.526 -370.056 cm BT -/F32 9.963 Tf 295.717 370.056 Td[(psb)]TJ +/F32 9.963 Tf 346.526 370.056 Td[(psb)]TJ ET -1 0 0 1 312.036 370.056 cm +1 0 0 1 362.845 370.056 cm q []0 d 0 J @@ -10122,11 +10741,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -370.056 cm +1 0 0 1 -362.845 -370.056 cm BT -/F32 9.963 Tf 315.174 370.056 Td[(desc)]TJ +/F32 9.963 Tf 365.983 370.056 Td[(desc)]TJ ET -1 0 0 1 336.723 370.056 cm +1 0 0 1 387.532 370.056 cm q []0 d 0 J @@ -10135,405 +10754,405 @@ q 3.138 0.199 l S Q -1 0 0 1 -336.723 -370.056 cm +1 0 0 1 -387.532 -370.056 cm BT -/F32 9.963 Tf 339.861 370.056 Td[(type)]TJ +/F32 9.963 Tf 390.67 370.056 Td[(type)]TJ ET -1 0 0 1 360.782 370.056 cm +1 0 0 1 411.592 370.056 cm 0 g 0 G -1 0 0 1 -360.782 -370.056 cm +1 0 0 1 -411.592 -370.056 cm BT -/F8 9.963 Tf 360.782 370.056 Td[(.)]TJ +/F8 9.963 Tf 411.592 370.056 Td[(.)]TJ ET -1 0 0 1 94.914 350.662 cm +1 0 0 1 145.724 350.662 cm 0 g 0 G -1 0 0 1 -94.914 -350.662 cm +1 0 0 1 -145.724 -350.662 cm BT -/F29 9.963 Tf 99.895 350.662 Td[(trans)]TJ +/F29 9.963 Tf 150.705 350.662 Td[(trans)]TJ ET -1 0 0 1 125.523 350.662 cm +1 0 0 1 176.332 350.662 cm 0 g 0 G -1 0 0 1 -125.523 -350.662 cm +1 0 0 1 -176.332 -350.662 cm BT -/F8 9.963 Tf 130.504 350.662 Td[(sp)-28(ec)-1(i)1(fy)-333(with)]TJ/F19 9.963 Tf 55.68 0 Td[(unitd)]TJ/F8 9.963 Tf 25.726 0 Td[(th)1(e)-334(op)-27(e)-1(rat)1(ion)-333(to)-333(p)-28(erf)1(orm.)]TJ +/F8 9.963 Tf 181.314 350.662 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Td[(;j)-58(y)]TJ/F7 6.974 Tf 10.357 0 Td[(:)]TJ/F10 6.974 Tf 2.255 0 Td[(j)-58(y)]TJ/F7 6.974 Tf 7.991 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(n)]TJ/F13 6.974 Tf 4.924 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ +/F11 9.963 Tf 256.963 576.972 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.495 Td[(iy)]TJ/F7 6.974 Tf 7.11 0 Td[(:)]TJ/F10 6.974 Tf 2.255 0 Td[(iy)]TJ/F7 6.974 Tf 7.109 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(m)]TJ/F13 6.974 Tf 7.07 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ/F10 6.974 Tf 3.971 0 Td[(;j)-58(y)]TJ/F7 6.974 Tf 10.356 0 Td[(:)]TJ/F10 6.974 Tf 2.256 0 Td[(j)-57(y)]TJ/F7 6.974 Tf 7.99 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(n)]TJ/F13 6.974 Tf 4.925 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ ET -1 0 0 1 145.724 557.427 cm +1 0 0 1 94.914 557.427 cm 0 g 0 G -1 0 0 1 -145.724 -557.427 cm +1 0 0 1 -94.914 -557.427 cm BT -/F11 9.963 Tf 150.705 557.427 Td[(l)-20(oc)]TJ +/F11 9.963 Tf 99.895 557.427 Td[(l)-20(oc)]TJ ET -1 0 0 1 163.701 557.427 cm +1 0 0 1 112.892 557.427 cm q []0 d 0 J @@ -11704,34 +12323,34 @@ q 3.437 0.199 l S Q -1 0 0 1 -163.701 -557.427 cm +1 0 0 1 -112.892 -557.427 cm BT -/F11 9.963 Tf 167.139 557.427 Td[(x)]TJ/F10 6.974 Tf 5.693 -1.494 Td[(i)]TJ +/F11 9.963 Tf 116.329 557.427 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ ET -1 0 0 1 176.149 557.427 cm +1 0 0 1 125.34 557.427 cm 0 g 0 G -1 0 0 1 -176.149 -557.427 cm +1 0 0 1 -125.34 -557.427 cm BT -/F8 9.963 Tf 181.131 557.427 Td[(is)-333(the)-334(l)1(o)-28(c)-1(al)-333(p)-27(orti)1(on)-333(of)-333(glob)1(al)-333(dense)-334(matrix)-333(on)-333(p)1(ro)-27(c)-1(es)-1(s)]TJ/F11 9.963 Tf 234.703 0 Td[(i)]TJ/F8 9.963 Tf 3.433 0 Td[(.)]TJ +/F8 9.963 Tf 130.321 557.427 Td[(is)-334(t)1(he)-334(l)1(o)-28(c)-1(al)-333(p)-27(orti)1(on)-333(of)-333(glob)1(al)-333(dense)-334(matrix)-333(on)-333(p)1(ro)-28(ces)-1(s)]TJ/F11 9.963 Tf 234.704 0 Td[(i)]TJ/F8 9.963 Tf 3.432 0 Td[(.)]TJ ET -1 0 0 1 145.724 537.883 cm +1 0 0 1 94.914 537.883 cm 0 g 0 G -1 0 0 1 -145.724 -537.883 cm +1 0 0 1 -94.914 -537.883 cm BT -/F11 9.963 Tf 150.705 537.883 Td[(co)1(l)-20(l)-21(e)1(ct)]TJ +/F11 9.963 Tf 99.895 537.883 Td[(co)1(l)-21(l)-20(e)1(ct)]TJ ET -1 0 0 1 178.731 537.883 cm +1 0 0 1 127.921 537.883 cm 0 g 0 G -1 0 0 1 -178.731 -537.883 cm +1 0 0 1 -127.921 -537.883 cm BT -/F8 9.963 Tf 183.712 537.883 Td[(is)-334(t)1(he)-334(collect)-334(f)1(un)1(c)-1(ti)1(on.)]TJ +/F8 9.963 Tf 132.902 537.883 Td[(is)-334(t)1(he)-334(collec)-1(t)-333(f)1(un)1(c)-1(ti)1(on.)]TJ ET -1 0 0 1 150.705 519.1 cm +1 0 0 1 99.895 519.1 cm 0 g 0 G 1 0 0 1 74.163 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.981 20.623 cm +1 0 0 1 4.982 20.623 cm q []0 d 0 J @@ -11740,11 +12359,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -518.702 cm +1 0 0 1 -179.04 -518.702 cm BT -/F11 9.963 Tf 235.827 510.333 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.316 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ +/F11 9.963 Tf 185.017 510.333 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.317 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 229.849 506.348 cm +1 0 0 1 179.04 506.348 cm q []0 d 0 J @@ -11753,11 +12372,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -506.348 cm +1 0 0 1 -179.04 -506.348 cm BT -/F8 9.963 Tf 235.827 497.979 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ +/F8 9.963 Tf 185.017 497.979 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 497.979 cm +1 0 0 1 318.921 497.979 cm q []0 d 0 J @@ -11766,11 +12385,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -497.979 cm +1 0 0 1 -318.921 -497.979 cm BT -/F8 9.963 Tf 372.719 497.979 Td[(gath)1(e)-1(r)]TJ -136.892 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ +/F8 9.963 Tf 321.91 497.979 Td[(gath)1(e)-1(r)]TJ -136.893 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 486.024 cm +1 0 0 1 318.921 486.024 cm q []0 d 0 J @@ -11779,11 +12398,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -486.024 cm +1 0 0 1 -318.921 -486.024 cm BT -/F8 9.963 Tf 372.719 486.024 Td[(gath)1(e)-1(r)]TJ +/F8 9.963 Tf 321.91 486.024 Td[(gath)1(e)-1(r)]TJ ET -1 0 0 1 229.849 482.039 cm +1 0 0 1 179.04 482.039 cm q []0 d 0 J @@ -11794,19 +12413,19 @@ S Q 1 0 0 1 46.537 -27.84 cm 0 g 0 G -1 0 0 1 -276.386 -454.199 cm +1 0 0 1 -225.577 -454.199 cm BT -/F8 9.963 Tf 276.386 454.199 Td[(T)83(ab)1(le)-334(13:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 225.577 454.199 Td[(T)83(ab)1(le)-334(13:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 368.735 454.199 cm +1 0 0 1 317.925 454.199 cm 0 g 0 G 1 0 0 1 -218.03 -1.937 cm 0 g 0 G -1 0 0 1 -150.705 -452.262 cm +1 0 0 1 -99.895 -452.262 cm BT -/F18 14.346 Tf 150.705 407.906 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 5.266 -21.821 Td[(call)-333(psb)]TJ +/F18 14.346 Tf 99.895 407.906 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 5.267 -21.821 Td[(call)-333(psb)]TJ ET -1 0 0 1 189.833 386.085 cm +1 0 0 1 139.024 386.085 cm q []0 d 0 J @@ -11815,11 +12434,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -189.833 -386.085 cm +1 0 0 1 -139.024 -386.085 cm BT -/F8 9.963 Tf 192.822 386.085 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ +/F8 9.963 Tf 142.013 386.085 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 245.134 386.085 cm +1 0 0 1 194.324 386.085 cm q []0 d 0 J @@ -11828,11 +12447,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -245.134 -386.085 cm +1 0 0 1 -194.324 -386.085 cm BT -/F19 9.963 Tf 248.189 386.085 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 197.38 386.085 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 271.753 386.085 cm +1 0 0 1 220.943 386.085 cm q []0 d 0 J @@ -11841,11 +12460,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -271.753 -386.085 cm +1 0 0 1 -220.943 -386.085 cm BT -/F19 9.963 Tf 274.808 386.085 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 223.998 386.085 Td[(x,)-357(desc)]TJ ET -1 0 0 1 304.991 386.085 cm +1 0 0 1 254.182 386.085 cm q []0 d 0 J @@ -11854,11 +12473,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -304.991 -386.085 cm +1 0 0 1 -254.182 -386.085 cm BT -/F19 9.963 Tf 308.046 386.085 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(jglobx)1(,)-358(il)1(o)51(cx,)-357(jlo)52(cx,)-358(k)]TJ/F8 9.963 Tf 177.229 0 Td[(\051)]TJ/F18 14.346 Tf -334.57 -29.888 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 39.421 -21.821 Td[(call)-333(psb)]TJ +/F19 9.963 Tf 257.237 386.085 Td[(a,)-357(info,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(jgl)1(o)-1(bx)1(,)-358(i)1(lo)51(cx,)-357(jl)1(o)51(cx,)-358(k)]TJ/F8 9.963 Tf 177.228 0 Td[(\051)]TJ/F18 14.346 Tf -334.57 -29.888 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 39.422 -21.821 Td[(call)-333(psb)]TJ ET -1 0 0 1 223.988 334.376 cm +1 0 0 1 173.179 334.376 cm q []0 d 0 J @@ -11867,11 +12486,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -223.988 -334.376 cm +1 0 0 1 -173.179 -334.376 cm BT -/F8 9.963 Tf 226.977 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ +/F8 9.963 Tf 176.168 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 279.289 334.376 cm +1 0 0 1 228.479 334.376 cm q []0 d 0 J @@ -11880,11 +12499,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -279.289 -334.376 cm +1 0 0 1 -228.479 -334.376 cm BT -/F19 9.963 Tf 282.344 334.376 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 231.535 334.376 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 305.908 334.376 cm +1 0 0 1 255.098 334.376 cm q []0 d 0 J @@ -11893,11 +12512,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -305.908 -334.376 cm +1 0 0 1 -255.098 -334.376 cm BT -/F19 9.963 Tf 308.963 334.376 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 258.153 334.376 Td[(x,)-357(desc)]TJ ET -1 0 0 1 339.146 334.376 cm +1 0 0 1 288.337 334.376 cm q []0 d 0 J @@ -11906,25 +12525,25 @@ q 3.055 0.199 l S Q -1 0 0 1 -339.146 -334.376 cm +1 0 0 1 -288.337 -334.376 cm BT -/F19 9.963 Tf 342.201 334.376 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(ilo)51(c)1(x)]TJ/F8 9.963 Tf 108.919 0 Td[(\051)]TJ +/F19 9.963 Tf 291.392 334.376 Td[(a,)-357(info,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(il)1(o)51(cx)]TJ/F8 9.963 Tf 108.918 0 Td[(\051)]TJ ET -1 0 0 1 145.724 310.466 cm +1 0 0 1 94.914 310.466 cm 0 g 0 G -1 0 0 1 -145.724 -310.466 cm +1 0 0 1 -94.914 -310.466 cm BT -/F29 9.963 Tf 150.705 310.466 Td[(On)-383(En)33(t)-1(r)1(y)]TJ +/F29 9.963 Tf 99.895 310.466 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 198.29 310.466 cm +1 0 0 1 147.481 310.466 cm 0 g 0 G -1 0 0 1 -52.566 -19.545 cm +1 0 0 1 -52.567 -19.545 cm 0 g 0 G -1 0 0 1 -145.724 -290.921 cm +1 0 0 1 -94.914 -290.921 cm BT -/F29 9.963 Tf 150.705 290.921 Td[(lo)-32(c)]TJ +/F29 9.963 Tf 99.895 290.921 Td[(lo)-32(c)]TJ ET -1 0 0 1 165.713 290.921 cm +1 0 0 1 114.904 290.921 cm q []0 d 0 J @@ -11933,17 +12552,17 @@ q 3.437 0.199 l S Q -1 0 0 1 -165.713 -290.921 cm +1 0 0 1 -114.904 -290.921 cm BT -/F29 9.963 Tf 169.151 290.921 Td[(x)]TJ +/F29 9.963 Tf 118.341 290.921 Td[(x)]TJ ET -1 0 0 1 175.197 290.921 cm +1 0 0 1 124.388 290.921 cm 0 g 0 G -1 0 0 1 -175.197 -290.921 cm +1 0 0 1 -124.388 -290.921 cm BT -/F8 9.963 Tf 180.179 290.921 Td[(th)1(e)-334(lo)-28(cal)-333(p)-27(ortion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.117 0 Td[(g)-36(l)-20(ob)]TJ +/F8 9.963 Tf 129.369 290.921 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(g)-36(l)-20(ob)]TJ ET -1 0 0 1 374.277 290.921 cm +1 0 0 1 323.467 290.921 cm q []0 d 0 J @@ -11952,29 +12571,29 @@ q 2.989 0.199 l S Q -1 0 0 1 -374.277 -290.921 cm +1 0 0 1 -323.467 -290.921 cm BT -/F11 9.963 Tf 377.266 290.921 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -207.349 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-472(as)-1(:)-722(a)-473(r)1(ank)-472(one)-472(or)-472(t)27(w)28(o)-472(arra)28(y)-472(con)28(tain)1(ing)-472(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-473(of)-472(th)1(e)-473(t)28(yp)-28(e)]TJ 0 -11.955 Td[(in)1(dicated)-333(in)-333(T)83(ab)1(le)]TJ +/F11 9.963 Tf 326.456 290.921 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -207.348 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-472(as)-1(:)-722(a)-473(r)1(ank)-472(on)1(e)-473(or)-472(t)28(w)27(o)-472(arra)28(y)-472(con)28(tain)1(ing)-472(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-473(of)-472(th)1(e)-473(t)28(yp)-27(e)]TJ 0 -11.955 Td[(in)1(dicated)-333(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 257.803 243.101 cm +1 0 0 1 206.994 243.101 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -257.803 -243.101 cm +1 0 0 1 -206.994 -243.101 cm BT -/F8 9.963 Tf 257.803 243.101 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9.963 Tf 29.155 -22.092 Td[(call)-333(psb)]TJ +/F14 9.963 Tf 299.404 561.441 Td[(k)]TJ/F11 9.963 Tf 4.982 0 Td[(b)]TJ/F14 9.963 Tf 4.275 0 Td[(k)]TJ/F7 6.974 Tf 4.981 -1.494 Td[(2)]TJ/F11 9.963 Tf 8.433 8.328 Td[(<)-277(eps)]TJ/F8 9.963 Tf -171.37 -24.715 Td[(acc)-1(or)1(din)1(g)-334(t)1(o)-334(th)1(e)-334(v)56(alu)1(e)-334(pass)-1(ed)-333(th)1(rou)1(gh)-333(the)-333(is)-1(top)-332(argumen)28(t)-333(\050s)-1(ee)-334(lat)1(e)-1(r)1(\051.)]TJ/F18 14.346 Tf 0 -34.616 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 29.154 -22.092 Td[(call)-333(psb)]TJ ET -1 0 0 1 162.911 486.852 cm +1 0 0 1 213.721 486.852 cm q []0 d 0 J @@ -18490,11 +19471,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -162.911 -486.852 cm +1 0 0 1 -213.721 -486.852 cm BT -/F8 9.963 Tf 165.9 486.852 Td[(bi)1(c)-1(g)-333(\050)]TJ/F19 9.963 Tf 24.907 0 Td[(a,pr)52(e)51(c,b,x)1(,eps,desc)]TJ +/F8 9.963 Tf 216.71 486.852 Td[(bi)1(c)-1(g)-333(\050)]TJ/F19 9.963 Tf 24.906 0 Td[(a,pr)52(e)51(c,b,x)1(,eps,desc)]TJ ET -1 0 0 1 270.51 486.852 cm +1 0 0 1 321.319 486.852 cm q []0 d 0 J @@ -18503,37 +19484,37 @@ q 3.055 0.199 l S Q -1 0 0 1 -270.51 -486.852 cm +1 0 0 1 -321.319 -486.852 cm BT -/F19 9.963 Tf 273.565 486.852 Td[(a,i)1(n)-1(f)1(o,itmax,)1(iter,)1(err,)1(itr)51(ac)51(e,)1(istop)]TJ/F8 9.963 Tf 137.013 0 Td[(\051)]TJ +/F19 9.963 Tf 324.374 486.852 Td[(a,i)1(n)-1(f)1(o,itmax,)1(iter,)1(err,)1(itr)51(ac)51(e,)1(istop)]TJ/F8 9.963 Tf 137.013 0 Td[(\051)]TJ ET -1 0 0 1 94.914 462.627 cm +1 0 0 1 145.724 462.627 cm 0 g 0 G -1 0 0 1 -94.914 -462.627 cm +1 0 0 1 -145.724 -462.627 cm BT -/F29 9.963 Tf 99.895 462.627 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.963 Tf 150.705 462.627 Td[(On)-383(En)33(t)-1(r)1(y)]TJ ET -1 0 0 1 147.481 462.627 cm +1 0 0 1 198.29 462.627 cm 0 g 0 G -1 0 0 1 -52.567 -21.185 cm +1 0 0 1 -52.566 -21.185 cm 0 g 0 G -1 0 0 1 -94.914 -441.442 cm +1 0 0 1 -145.724 -441.442 cm BT -/F29 9.963 Tf 99.895 441.442 Td[(a)]TJ +/F29 9.963 Tf 150.705 441.442 Td[(a)]TJ ET -1 0 0 1 105.465 441.442 cm +1 0 0 1 156.274 441.442 cm 0 g 0 G -1 0 0 1 -105.465 -441.442 cm +1 0 0 1 -156.274 -441.442 cm BT -/F8 9.963 Tf 110.446 441.442 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(g)1(lobal)-333(spar)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 178.968 0 Td[(A)]TJ/F8 9.963 Tf 7.472 0 Td[(.)]TJ -172.084 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 161.256 441.442 Td[(th)1(e)-334(lo)-28(cal)-333(p)-27(ortion)-333(of)-332(global)-333(spar)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 178.968 0 Td[(A)]TJ/F8 9.963 Tf 7.472 0 Td[(.)]TJ -172.085 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 405.576 cm +1 0 0 1 346.526 405.576 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -405.576 cm +1 0 0 1 -346.526 -405.576 cm BT -/F32 9.963 Tf 295.717 405.576 Td[(psb)]TJ +/F32 9.963 Tf 346.526 405.576 Td[(psb)]TJ ET -1 0 0 1 312.036 405.576 cm +1 0 0 1 362.845 405.576 cm q []0 d 0 J @@ -18542,11 +19523,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -405.576 cm +1 0 0 1 -362.845 -405.576 cm BT -/F32 9.963 Tf 315.174 405.576 Td[(spmat)]TJ +/F32 9.963 Tf 365.983 405.576 Td[(spmat)]TJ ET -1 0 0 1 341.953 405.576 cm +1 0 0 1 392.763 405.576 cm q []0 d 0 J @@ -18555,35 +19536,35 @@ q 3.138 0.199 l S Q -1 0 0 1 -341.953 -405.576 cm +1 0 0 1 -392.763 -405.576 cm BT -/F32 9.963 Tf 345.091 405.576 Td[(type)]TJ +/F32 9.963 Tf 395.901 405.576 Td[(type)]TJ ET -1 0 0 1 366.013 405.576 cm +1 0 0 1 416.822 405.576 cm 0 g 0 G -1 0 0 1 -366.013 -405.576 cm +1 0 0 1 -416.822 -405.576 cm BT -/F8 9.963 Tf 366.013 405.576 Td[(.)]TJ +/F8 9.963 Tf 416.822 405.576 Td[(.)]TJ ET -1 0 0 1 94.914 384.392 cm +1 0 0 1 145.724 384.392 cm 0 g 0 G -1 0 0 1 -94.914 -384.392 cm +1 0 0 1 -145.724 -384.392 cm BT -/F29 9.963 Tf 99.895 384.392 Td[(pr)1(e)-1(c)]TJ +/F29 9.963 Tf 150.705 384.392 Td[(pr)1(e)-1(c)]TJ ET -1 0 0 1 121.322 384.392 cm +1 0 0 1 172.131 384.392 cm 0 g 0 G -1 0 0 1 -121.322 -384.392 cm +1 0 0 1 -172.131 -384.392 cm BT -/F8 9.963 Tf 126.303 384.392 Td[(The)-334(d)1(ata)-333(s)-1(tr)1(uctur)1(e)-334(con)28(tain)1(ing)-333(th)1(e)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -1.501 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.956 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 177.113 384.392 Td[(The)-333(data)-333(s)-1(t)1(ructur)1(e)-334(con)28(tain)1(ing)-333(th)1(e)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -1.502 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.956 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 348.526 cm +1 0 0 1 346.526 348.526 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -348.526 cm +1 0 0 1 -346.526 -348.526 cm BT -/F32 9.963 Tf 295.717 348.526 Td[(psb)]TJ +/F32 9.963 Tf 346.526 348.526 Td[(psb)]TJ ET -1 0 0 1 312.036 348.526 cm +1 0 0 1 362.845 348.526 cm q []0 d 0 J @@ -18592,11 +19573,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -348.526 cm +1 0 0 1 -362.845 -348.526 cm BT -/F32 9.963 Tf 315.174 348.526 Td[(prec)]TJ +/F32 9.963 Tf 365.983 348.526 Td[(prec)]TJ ET -1 0 0 1 336.723 348.526 cm +1 0 0 1 387.532 348.526 cm q []0 d 0 J @@ -18605,59 +19586,59 @@ q 3.138 0.199 l S Q -1 0 0 1 -336.723 -348.526 cm +1 0 0 1 -387.532 -348.526 cm BT -/F32 9.963 Tf 339.861 348.526 Td[(type)]TJ +/F32 9.963 Tf 390.67 348.526 Td[(type)]TJ ET -1 0 0 1 360.782 348.526 cm +1 0 0 1 411.592 348.526 cm 0 g 0 G -1 0 0 1 -360.782 -348.526 cm +1 0 0 1 -411.592 -348.526 cm BT -/F8 9.963 Tf 360.782 348.526 Td[(.)]TJ +/F8 9.963 Tf 411.592 348.526 Td[(.)]TJ ET -1 0 0 1 94.914 327.342 cm +1 0 0 1 145.724 327.342 cm 0 g 0 G -1 0 0 1 -94.914 -327.342 cm +1 0 0 1 -145.724 -327.342 cm BT -/F29 9.963 Tf 99.895 327.342 Td[(b)]TJ +/F29 9.963 Tf 150.705 327.342 Td[(b)]TJ ET -1 0 0 1 106.26 327.342 cm +1 0 0 1 157.07 327.342 cm 0 g 0 G -1 0 0 1 -106.26 -327.342 cm +1 0 0 1 -157.07 -327.342 cm BT -/F8 9.963 Tf 111.242 327.342 Td[(The)-333(R)-1(HS)-332(v)28(e)-1(ctor.)]TJ 13.56 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(ran)1(k)-333(one)-334(ar)1(ra)28(y)83(.)]TJ +/F8 9.963 Tf 162.051 327.342 Td[(The)-333(R)-1(HS)-332(v)28(e)-1(ctor.)]TJ 13.56 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(ran)1(k)-334(on)1(e)-334(ar)1(ra)28(y)83(.)]TJ ET -1 0 0 1 94.914 270.291 cm +1 0 0 1 145.724 270.291 cm 0 g 0 G -1 0 0 1 -94.914 -270.291 cm +1 0 0 1 -145.724 -270.291 cm BT -/F29 9.963 Tf 99.895 270.291 Td[(x)]TJ +/F29 9.963 Tf 150.705 270.291 Td[(x)]TJ ET -1 0 0 1 105.942 270.291 cm +1 0 0 1 156.752 270.291 cm 0 g 0 G -1 0 0 1 -105.942 -270.291 cm +1 0 0 1 -156.752 -270.291 cm BT -/F8 9.963 Tf 110.923 270.291 Td[(The)-334(i)1(nit)1(ial)-333(gues)-1(s.)]TJ 13.879 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(ran)1(k)-333(one)-334(ar)1(ra)28(y)83(.)]TJ +/F8 9.963 Tf 161.733 270.291 Td[(The)-333(init)1(ial)-333(gues)-1(s.)]TJ 13.878 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(ran)1(k)-334(on)1(e)-334(ar)1(ra)28(y)83(.)]TJ ET -1 0 0 1 94.914 213.241 cm +1 0 0 1 145.724 213.241 cm 0 g 0 G -1 0 0 1 -94.914 -213.241 cm +1 0 0 1 -145.724 -213.241 cm BT -/F29 9.963 Tf 99.895 213.241 Td[(eps)]TJ +/F29 9.963 Tf 150.705 213.241 Td[(eps)]TJ ET -1 0 0 1 116.031 213.241 cm +1 0 0 1 166.84 213.241 cm 0 g 0 G -1 0 0 1 -116.031 -213.241 cm +1 0 0 1 -166.84 -213.241 cm BT -/F8 9.963 Tf 121.012 213.241 Td[(The)-333(s)-1(top)1(pin)1(g)-333(tole)-1(r)1(ance)-1(.)]TJ 3.79 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(real)-333(n)28(um)28(b)-28(er.)]TJ +/F8 9.963 Tf 171.821 213.241 Td[(The)-334(stop)1(pin)1(g)-334(t)1(ole)-1(r)1(ance)-1(.)]TJ 3.79 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(real)-333(n)28(um)28(b)-28(er.)]TJ ET -1 0 0 1 94.914 156.191 cm +1 0 0 1 145.724 156.191 cm 0 g 0 G -1 0 0 1 -94.914 -156.191 cm +1 0 0 1 -145.724 -156.191 cm BT -/F29 9.963 Tf 99.895 156.191 Td[(desc)]TJ +/F29 9.963 Tf 150.705 156.191 Td[(desc)]TJ ET -1 0 0 1 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b/src/modules/psb_prec_type.f90 index e6fe68b0..c80d2bc3 100644 --- a/src/modules/psb_prec_type.f90 +++ b/src/modules/psb_prec_type.f90 @@ -158,7 +158,8 @@ module psb_prec_type end interface interface psb_prec_descr - module procedure psb_file_prec_descr, psb_zfile_prec_descr + module procedure psb_out_prec_descr, psb_file_prec_descr, & + & psb_zout_prec_descr, psb_zfile_prec_descr end interface interface psb_prec_short_descr @@ -167,6 +168,16 @@ module psb_prec_type contains + subroutine psb_out_prec_descr(p) + type(psb_dprec_type), intent(in) :: p + call psb_file_prec_descr(6,p) + end subroutine psb_out_prec_descr + + subroutine psb_zout_prec_descr(p) + type(psb_zprec_type), intent(in) :: p + call psb_zfile_prec_descr(6,p) + end subroutine psb_zout_prec_descr + subroutine psb_file_prec_descr(iout,p) integer, intent(in) :: iout type(psb_dprec_type), intent(in) :: p diff --git a/src/prec/psb_dprecset.f90 b/src/prec/psb_dprecset.f90 index 37a930b5..d552bbbd 100644 --- a/src/prec/psb_dprecset.f90 +++ b/src/prec/psb_dprecset.f90 @@ -179,10 +179,8 @@ subroutine psb_dprecset(p,ptype,iv,rs,rv,info) if (isz >= 3) p%baseprecv(2)%iprcparm(smth_kind_) = iv(3) if (isz >= 4) p%baseprecv(2)%iprcparm(coarse_mat_) = iv(4) if (isz >= 5) p%baseprecv(2)%iprcparm(smth_pos_) = iv(5) - if (isz >= 6) p%baseprecv(2)%iprcparm(glb_smth_) = iv(6) - if (isz >= 7) p%baseprecv(2)%iprcparm(f_type_) = iv(7) - if (isz >= 8) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(8) - + if (isz >= 6) p%baseprecv(2)%iprcparm(f_type_) = iv(6) + if (isz >= 7) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(7) end if if (present(rs)) then diff --git a/src/prec/psb_zprecset.f90 b/src/prec/psb_zprecset.f90 index 953d105d..9f8167e8 100644 --- a/src/prec/psb_zprecset.f90 +++ b/src/prec/psb_zprecset.f90 @@ -179,9 +179,8 @@ subroutine psb_zprecset(p,ptype,iv,rs,rv,info) if (isz >= 3) p%baseprecv(2)%iprcparm(smth_kind_) = iv(3) if (isz >= 4) p%baseprecv(2)%iprcparm(coarse_mat_) = iv(4) if (isz >= 5) p%baseprecv(2)%iprcparm(smth_pos_) = iv(5) - if (isz >= 6) p%baseprecv(2)%iprcparm(glb_smth_) = iv(6) - if (isz >= 7) p%baseprecv(2)%iprcparm(f_type_) = iv(7) - if (isz >= 8) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(8) + if (isz >= 6) p%baseprecv(2)%iprcparm(f_type_) = iv(6) + if (isz >= 7) p%baseprecv(2)%iprcparm(jac_sweeps_) = iv(7) end if diff --git a/test/Fileread/df_sample.f90 b/test/Fileread/df_sample.f90 index 7deb0828..19e9dd5c 100644 --- a/test/Fileread/df_sample.f90 +++ b/test/Fileread/df_sample.f90 @@ -251,11 +251,11 @@ program df_sample case(7) call psb_precset(pre,'asm',iv=(/ml,halo_,none_/)) call psb_precset(pre,'ml',& - & iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,1,f_ilu_n_,4/)) + & iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,f_ilu_n_,4/)) case(8) call psb_precset(pre,'asm',iv=(/ml,halo_,none_/)) call psb_precset(pre,'ml',& - & iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,1,f_umf_,4/)) + & iv=(/mult_ml_prec_,loc_aggr_,smth_omg_,mat_distr_,post_smooth_,f_umf_,4/)) case default call psb_precset(pre,'ilu') diff --git a/test/pargen/ppde90.f90 b/test/pargen/ppde90.f90 index 32edc7d0..aca7e581 100644 --- a/test/pargen/ppde90.f90 +++ b/test/pargen/ppde90.f90 @@ -173,19 +173,6 @@ program pde90 call psb_precset(pre,'asm',iv=(/novr,halo_,none_/)) case(rash_) call psb_precset(pre,'asm',iv=(/novr,nohalo_,none_/)) - case(ras2lv_) - ptype='asm' - call psb_precset(pre,ptype,iv=(/novr,halo_,none_/)) - ptype='ml' - call psb_precset(pre,ptype,& - &iv=(/add_ml_prec_,loc_aggr_,no_smth_,mat_repl_,& - & pre_smooth_/),rs=0.d0) - case(ras2lvm_) - ptype='asm' - call psb_precset(pre,ptype,iv=(/novr,halo_,none_/)) - ptype='ml' - call psb_precset(pre,ptype,& - & iv=(/mult_ml_prec_,glb_aggr_,pre_smooth_/),rs=0.d0) end select call blacs_barrier(icontxt,'ALL')