From 73014a7a05b59039c6ab9c39e0a4c1202a459c29 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Wed, 20 Feb 2008 11:07:19 +0000 Subject: [PATCH] psblas: docs/pdf/commrout.tex docs/pdf/datastruct.tex docs/pdf/intro.tex docs/pdf/penv.tex docs/pdf/precs.tex docs/pdf/toolsrout.tex docs/userguide.pdf Merged doc changes from 2.2-maint. --- docs/pdf/commrout.tex | 2 +- docs/pdf/datastruct.tex | 25 +- docs/pdf/intro.tex | 6 +- docs/pdf/penv.tex | 3 +- docs/pdf/precs.tex | 70 - docs/pdf/toolsrout.tex | 2 +- docs/userguide.pdf | 9472 ++++++++++++++++++++------------------- 7 files changed, 4883 insertions(+), 4697 deletions(-) diff --git a/docs/pdf/commrout.tex b/docs/pdf/commrout.tex index 799f92d6..dff67886 100644 --- a/docs/pdf/commrout.tex +++ b/docs/pdf/commrout.tex @@ -66,7 +66,7 @@ POINTER attribute. \item[data] index list selector.\\ Scope: {\bf global} \\ Type: {\bf optional} \\ -Specified as: an integer. Values:\verb|psb_comm_halo_|, +Specified as: an integer. Values:\verb|psb_comm_halo_|,\verb|psb_comm_mov_|, \verb|psb_comm_ext_|, default: \verb|psb_comm_halo_|. Chooses the index list on which to base the data exchange. diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index f78e609c..de0de9b4 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -79,15 +79,17 @@ current process, organized in groups like the previous vector: The list may contain an arbitrary number of groups; its end is marked by a -1.\\ Specified as: an allocatable integer array of rank one. +\item [{\bf ovr\_mst\_idx}] A list to retrieve the value of each + overlap element from the respective master process.\\ +Specified as: an allocatable integer array of rank one. \item [{\bf ovrlap\_elem}] For all overlap points belonging to th ecurrent process: \begin{enumerate} -\item Overlap point index; -\item Number of processes sharing that overlap points; +\item Overlap point index; +\item Number of processes sharing that overlap points; +\item Index of a ``master'' process: \end{enumerate} -The list may contain an arbitrary number of groups; its end is marked -by a -1.\\ -Specified as: an allocatable integer array of rank one. +Specified as: an allocatable integer array of rank two. \item[{\bf loc\_to\_glob}] each element $i$ of this array contains global identifier of the local variable $i$.\\ Specified as: an allocatable integer array of rank one. @@ -103,7 +105,9 @@ as follows: type psb_desc_type integer, allocatable :: matrix_data(:), halo_index(:) integer, allocatable :: ext_index(:) - integer, allocatable :: overlap_elem(:), overlap_index(:) + integer, allocatable :: ovrlap_elem(:,:) + integer, allocatable :: ovrlap_index(:) + integer, allocatable :: ovr_mst_idx(:) integer, allocatable :: loc_to_glob(:), glob_to_loc(:) integer, allocatable :: hashv(:), glb_lc(:,:) end type psb_desc_type @@ -145,6 +149,15 @@ sec.~\ref{sec:dataquery}. \item[psb\_halo\_] Fetch halo elements from neighbouring processes; \item[psb\_sum\_] Sum overlapped elements \item[psb\_avg\_] Average overlapped elements +\item[psb\_comm\_halo\_] Exchange data based on the \verb|halo_index| + list; +\item[psb\_comm\_ext\_] Exchange data based on the \verb|ext_index| + list; +\item[psb\_comm\_ovr\_] Exchange data based on the \verb|ovrlap_index| + list; +\item[psb\_comm\_mov\_] Exchange data based on the \verb|ovr_mst_idx| + list; + %% \item[psb\_square\_root\_] Update with the square root of the average %% of overlapped elements; %% \item[psb\_dec\_type\_] Entry holding decomposition type (in \verb|desc_a%matrix_data|) diff --git a/docs/pdf/intro.tex b/docs/pdf/intro.tex index 80654b1a..c76464af 100644 --- a/docs/pdf/intro.tex +++ b/docs/pdf/intro.tex @@ -188,9 +188,9 @@ multiple domains. Any operation that involves an overlap point has to be replicated for each assignment. \end{description} Overlap points do not usually exist in the basic data -distribution, but they are a feature of Domain Decomposition -Schwarz preconditioners which we are the subject of related research -work~\cite{2007c,2007d}. +distributions; however they are a feature of Domain Decomposition +Schwarz preconditioners which are the subject of related research +work~\cite{2007c,2007d}. We denote the sets of internal, boundary and halo points for a given subdomain by $\cal I$, $\cal B$ and $\cal H$. diff --git a/docs/pdf/penv.tex b/docs/pdf/penv.tex index 243f1555..c661ef6b 100644 --- a/docs/pdf/penv.tex +++ b/docs/pdf/penv.tex @@ -253,7 +253,8 @@ Scope: {\bf global}.\\ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. \ +scalar, or a rank 1 or 2 array, or a character or logical variable, +which may be a scalar or rank 1 array. \ Type, rank and size must agree on all processes. \item[root] Root process holding data to be broadcast.\\ Scope: {\bf global}.\\ diff --git a/docs/pdf/precs.tex b/docs/pdf/precs.tex index 575ded05..5c02434a 100644 --- a/docs/pdf/precs.tex +++ b/docs/pdf/precs.tex @@ -75,77 +75,7 @@ $ptype$ string as follows\footnote{The string is case-insensitive}: by the data allocation boundaries for each process; requires no communication. Only the incomplete factorization $ILU(0)$ 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. -%% \item[2L] Second level of a multilevel preconditioner, see below -%% \end{description} -%% If a multilevel preconditioner is desired, the user should call -%% \verb|psb_precset| twice, the first time choosing an AS variant, and -%% a second time specifying -%% $ptype=2L$ with the following optional parameters in $iv$ (see -%% also~\cite{APNUM06,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 -%% (\verb|mult_ml_prec_|)as a pre-smoothed correction (\verb|pre_smooth_|) -%% \[ -%% M_{2L-H1}^{-1} = M_{C}^{-1} + \left( I - M_{C}^{-1}A \right) M_{1L}^{-1}, -%% \] -%% post-smoothed correction (\verb|post_smooth_|) -%% \[ -%% M_{2L-H2}^{-1} = M_{1L}^{-1} + \left( I - M_{1L}^{-1}A \right) M_{C}^{-1}. -%% \] -%% or two-sided for symmetric matrices (\verb|smooth_both_|). - \subroutine{psb\_precbld}{Builds a preconditioner} diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index 25180c4e..81cf607f 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -1322,7 +1322,7 @@ Returned as: an integer number. \end{description} -\subroutine{}{Sorting utilities} +\subroutine{Sorting utilities}{} 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Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(t)28(w)27(o.)]TJ ET -1 0 0 1 145.7235 555.952 cm +1 0 0 1 145.7235 525.2535 cm 0 g 0 G -1 0 0 1 -145.7235 -555.952 cm +1 0 0 1 -145.7235 -525.2535 cm BT -/F29 9.9626 Tf 150.7049 555.952 Td[(lo)-32(c)]TJ +/F29 9.9626 Tf 150.7049 525.2535 Td[(lo)-32(c)]TJ ET -1 0 0 1 165.7135 555.952 cm +1 0 0 1 165.7135 525.2535 cm q []0 d 0 J @@ -7010,11 +7066,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -165.7135 -555.952 cm +1 0 0 1 -165.7135 -525.2535 cm BT -/F29 9.9626 Tf 169.1506 555.952 Td[(to)]TJ +/F29 9.9626 Tf 169.1506 525.2535 Td[(to)]TJ ET -1 0 0 1 180.0219 555.952 cm +1 0 0 1 180.0219 525.2535 cm q []0 d 0 J @@ -7023,23 +7079,23 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -180.0219 -555.952 cm +1 0 0 1 -180.0219 -525.2535 cm BT -/F29 9.9626 Tf 183.4591 555.952 Td[(glob)]TJ +/F29 9.9626 Tf 183.4591 525.2535 Td[(glob)]TJ ET -1 0 0 1 204.4635 555.952 cm +1 0 0 1 204.4635 525.2535 cm 0 g 0 G -1 0 0 1 -204.4635 -555.952 cm +1 0 0 1 -204.4635 -525.2535 cm BT -/F8 9.9626 Tf 209.4448 555.952 Td[(eac)27(h)-362(e)-1(leme)-1(n)28(t)]TJ/F11 9.9626 Tf 59.8081 0 Td[(i)]TJ/F8 9.9626 Tf 7.0459 0 Td[(of)-362(this)-363(ar)1(ra)28(y)-363(con)28(tain)1(s)-363(global)-362(iden)28(ti)1(\014er)-363(of)-362(the)-363(lo)-27(c)-1(al)]TJ -100.6873 -11.9552 Td[(v)56(ariab)1(le)]TJ/F11 9.9626 Tf 37.3876 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(.)]TJ -40.8199 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ +/F8 9.9626 Tf 209.4448 525.2535 Td[(eac)27(h)-362(e)-1(leme)-1(n)28(t)]TJ/F11 9.9626 Tf 59.8081 0 Td[(i)]TJ/F8 9.9626 Tf 7.0459 0 Td[(of)-362(this)-363(ar)1(ra)28(y)-363(con)28(tain)1(s)-363(global)-362(iden)28(ti)1(\014er)-363(of)-362(the)-363(lo)-27(c)-1(al)]TJ -100.6873 -11.9552 Td[(v)56(ariab)1(le)]TJ/F11 9.9626 Tf 37.3876 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(.)]TJ -40.8199 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ ET -1 0 0 1 145.7235 510.6242 cm +1 0 0 1 145.7235 481.1599 cm 0 g 0 G -1 0 0 1 -145.7235 -510.6242 cm +1 0 0 1 -145.7235 -481.1599 cm BT -/F29 9.9626 Tf 150.7049 510.6242 Td[(glob)]TJ +/F29 9.9626 Tf 150.7049 481.1599 Td[(glob)]TJ ET -1 0 0 1 172.3967 510.6242 cm +1 0 0 1 172.3967 481.1599 cm q []0 d 0 J @@ -7048,11 +7104,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -172.3967 -510.6242 cm +1 0 0 1 -172.3967 -481.1599 cm BT -/F29 9.9626 Tf 175.8338 510.6242 Td[(to)]TJ +/F29 9.9626 Tf 175.8338 481.1599 Td[(to)]TJ ET -1 0 0 1 186.7052 510.6242 cm +1 0 0 1 186.7052 481.1599 cm q []0 d 0 J @@ -7061,11 +7117,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -186.7052 -510.6242 cm +1 0 0 1 -186.7052 -481.1599 cm BT -/F29 9.9626 Tf 190.1423 510.6242 Td[(lo)-32(c,)-384(gl)-1(b)]TJ +/F29 9.9626 Tf 190.1423 481.1599 Td[(lo)-32(c,)-384(gl)-1(b)]TJ ET -1 0 0 1 227.4283 510.6242 cm +1 0 0 1 227.4283 481.1599 cm q []0 d 0 J @@ -7074,22 +7130,22 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -227.4283 -510.6242 cm +1 0 0 1 -227.4283 -481.1599 cm BT -/F29 9.9626 Tf 230.8655 510.6242 Td[(lc)-1(,)-383(hash)32(v)]TJ +/F29 9.9626 Tf 230.8655 481.1599 Td[(lc)-1(,)-383(hash)32(v)]TJ ET -1 0 0 1 274.6884 510.6242 cm +1 0 0 1 274.6884 481.1599 cm 0 g 0 G -1 0 0 1 -274.6884 -510.6242 cm +1 0 0 1 -274.6884 -481.1599 cm BT -/F8 9.9626 Tf 279.6697 510.6242 Td[(Con)28(tain)-333(a)-333(mapp)1(ing)-333(fr)1(om)-334(glob)1(al)-333(to)-334(l)1(o)-28(c)-1(al)-333(in)1(di)1(c)-1(es)-1(.)]TJ -128.9648 -21.0444 Td[(The)-334(F)84(ortr)1(an)-333(95)-333(de\014ni)1(tion)-333(for)]TJ/F32 9.9626 Tf 129.4592 0 Td[(psb_desc_type)]TJ/F8 9.9626 Tf 71.3153 0 Td[(structu)1(re)-1(s)-333(is)-334(as)-334(f)1(ollo)28(ws)-1(:)]TJ +/F8 9.9626 Tf 279.6697 481.1599 Td[(Con)28(tain)-333(a)-333(mapp)1(ing)-333(fr)1(om)-334(glob)1(al)-333(to)-334(l)1(o)-28(c)-1(al)-333(in)1(di)1(c)-1(es)-1(.)]TJ -128.9648 -20.1187 Td[(The)-334(F)84(ortr)1(an)-333(95)-333(de\014ni)1(tion)-333(for)]TJ/F32 9.9626 Tf 129.4592 0 Td[(psb_desc_type)]TJ/F8 9.9626 Tf 71.3153 0 Td[(structu)1(re)-1(s)-333(is)-334(as)-334(f)1(ollo)28(ws)-1(:)]TJ ET -1 0 0 1 150.7049 474.6646 cm +1 0 0 1 150.7049 446.7431 cm 0 g 0 G -1 0 0 1 2.1762 -60.8385 cm +1 0 0 1 2.1762 -72.7937 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.9813 50.4774 cm +1 0 0 1 4.9813 62.4325 cm q []0 d 0 J @@ -7098,29 +7154,29 @@ q 329.396 0.1992 l S Q -1 0 0 1 0 -95.9735 cm +1 0 0 1 0 -119.8837 cm q []0 d 0 J 0.3985 w 0.1992 0 m -0.1992 95.9734 l +0.1992 119.8838 l S Q -1 0 0 1 3.3873 81.9151 cm +1 0 0 1 3.3873 105.8254 cm 0 g 0 G 0 g 0 G -1 0 0 1 -161.2497 -450.2451 cm +1 0 0 1 -161.2497 -422.3236 cm BT -/F32 9.9626 Tf 166.231 450.2451 Td[(type)-525(psb_desc_type)]TJ 15.6911 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(matrix_data\050:\051,)-525(halo_index\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(ext_index\050:\051)]TJ 0 -11.9551 Td[(integer,)-525(allocatable)-525(::)-525(overlap_elem\050:\051,)-525(overlap_index\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(loc_to_glob\050:\051,)-525(glob_to_loc\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(hashv\050:\051,)-525(glb_lc\050:,:\051)]TJ -15.6911 -11.9551 Td[(end)-525(type)-525(psb_desc_type)]TJ +/F32 9.9626 Tf 166.231 422.3236 Td[(type)-525(psb_desc_type)]TJ 15.6911 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(matrix_data\050:\051,)-525(halo_index\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(ext_index\050:\051)]TJ 0 -11.9551 Td[(integer,)-525(allocatable)-525(::)-525(ovrlap_elem\050:,:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(ovrlap_index\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(ovr_mst_idx\050:\051)]TJ 0 -11.9551 Td[(integer,)-525(allocatable)-525(::)-525(loc_to_glob\050:\051,)-525(glob_to_loc\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(hashv\050:\051,)-525(glb_lc\050:,:\051)]TJ -15.6911 -11.9552 Td[(end)-525(type)-525(psb_desc_type)]TJ ET -1 0 0 1 486.8599 368.33 cm +1 0 0 1 486.8599 316.4982 cm q []0 d 0 J 0.3985 w 0.1992 0 m -0.1992 95.9734 l +0.1992 119.8838 l S Q 1 0 0 1 -328.9975 -0.3985 cm @@ -7132,51 +7188,39 @@ q 329.396 0.1992 l S Q -1 0 0 1 -157.8624 -367.9315 cm -BT -/F8 9.9626 Tf 150.7049 340.0915 Td[(Figu)1(re)-464(3:)-705(T)-1(h)1(e)-465(P)1(SBLAS)-463(de\014ned)-463(data)-464(t)28(yp)-27(e)-464(that)-464(con)28(tai)1(ns)-464(the)-464(c)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9552 Td[(desc)-1(ri)1(ptor)1(.)]TJ -ET -1 0 0 1 150.7049 326.1991 cm -0 g 0 G -1 0 0 1 -150.7049 -326.1991 cm +1 0 0 1 -157.8624 -316.0997 cm BT -/F8 9.9626 Tf 165.6488 303.3836 Td[(A)-445(com)-1(m)28(un)1(ic)-1(at)1(ion)-445(d)1(e)-1(sc)-1(r)1(iptor)-444(as)-1(so)-28(ciate)-1(d)-444(with)-445(a)-445(spar)1(s)-1(e)-445(matrix)-445(h)1(as)-446(a)-445(state,)]TJ -14.9439 -11.9552 Td[(whic)28(h)-333(c)-1(an)-332(tak)28(e)-334(the)-333(foll)1(o)27(win)1(g)-334(v)56(alu)1(e)-1(s:)]TJ +/F8 9.9626 Tf 150.7049 288.2596 Td[(Figu)1(re)-464(3:)-705(T)-1(h)1(e)-465(P)1(SBLAS)-463(de\014ned)-463(data)-464(t)28(yp)-27(e)-464(that)-464(con)28(tai)1(ns)-464(the)-464(c)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9551 Td[(desc)-1(ri)1(ptor)1(.)]TJ ET -1 0 0 1 145.7235 270.384 cm +1 0 0 1 150.7049 274.3673 cm 0 g 0 G -1 0 0 1 -145.7235 -270.384 cm +1 0 0 1 -150.7049 -274.3673 cm BT -/F29 9.9626 Tf 150.7049 270.384 Td[(Buil)-1(d:)]TJ +/F8 9.9626 Tf 165.6488 252.4774 Td[(A)-445(com)-1(m)28(un)1(ic)-1(at)1(ion)-445(d)1(e)-1(sc)-1(r)1(iptor)-444(as)-1(so)-28(ciate)-1(d)-444(with)-445(a)-445(spar)1(s)-1(e)-445(matrix)-445(h)1(as)-446(a)-445(state,)]TJ -14.9439 -11.9552 Td[(whic)28(h)-333(c)-1(an)-332(tak)28(e)-334(the)-333(foll)1(o)27(win)1(g)-334(v)56(alu)1(e)-1(s:)]TJ ET -1 0 0 1 181.1323 270.384 cm +1 0 0 1 145.7235 220.4035 cm 0 g 0 G -1 0 0 1 -181.1323 -270.384 cm +1 0 0 1 -145.7235 -220.4035 cm BT -/F8 9.9626 Tf 186.1136 270.384 Td[(St)1(ate)-307(en)28(tere)-1(d)-305(after)-306(th)1(e)-307(\014r)1(s)-1(t)-306(al)1(lo)-28(cation,)-311(and)-305(b)-28(efor)1(e)-307(th)1(e)-307(\014)1(rs)-1(t)-306(ass)-1(em)27(b)1(ly;)-315(i)1(n)]TJ -10.5021 -11.9552 Td[(th)1(is)-224(s)-1(tate)-224(i)1(t)-224(is)-224(p)-27(oss)-1(ib)1(le)-224(to)-224(ad)1(d)-223(c)-1(omm)27(u)1(nication)-223(r)1(e)-1(qu)1(irem)-1(en)28(ts)-224(among)-223(di\013eren)28(t)]TJ 0 -11.9551 Td[(pr)1(o)-28(ce)-1(ss)-1(es)-1(.)]TJ +/F29 9.9626 Tf 150.7049 220.4035 Td[(Buil)-1(d:)]TJ ET -1 0 0 1 145.7235 225.0562 cm +1 0 0 1 181.1323 220.4035 cm 0 g 0 G -1 0 0 1 -145.7235 -225.0562 cm +1 0 0 1 -181.1323 -220.4035 cm BT -/F29 9.9626 Tf 150.7049 225.0562 Td[(Assem)32(ble)-1(d)1(:)]TJ +/F8 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9.9626 Tf 127.3769 494.4185 Td[(Con)28(tain)1(s)-334(v)56(alues)-334(of)-333(th)1(e)-334(lo)-27(c)-1(al)-333(di)1(s)-1(tr)1(ibu)1(te)-1(d)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix.)]TJ -2.5749 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-430(as:)-639(an)-431(all)1(o)-28(c)-1(atab)1(le)-431(arr)1(a)27(y)-430(of)-431(r)1(ank)-430(one)-431(of)-430(t)27(y)1(p)-28(e)-431(corres)-1(p)-27(ond)1(in)1(g)-431(to)]TJ 0 -11.9552 Td[(matrix)-333(en)28(tri)1(e)-1(s)-334(t)28(y)1(p)-28(e.)]TJ +/F29 9.9626 Tf 155.3089 521.239 Td[(halo)]TJ ET -1 0 0 1 94.9141 450.6457 cm -0 g 0 G -1 0 0 1 -94.9141 -450.6457 cm -BT -/F29 9.9626 Tf 99.8954 450.6457 Td[(ia1)]TJ -ET -1 0 0 1 114.3757 450.6457 cm -0 g 0 G -1 0 0 1 -114.3757 -450.6457 cm -BT -/F8 9.9626 Tf 119.357 450.6457 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9552 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ -ET -1 0 0 1 94.9141 406.8728 cm -0 g 0 G -1 0 0 1 -94.9141 -406.8728 cm -BT -/F29 9.9626 Tf 99.8954 406.8728 Td[(ia2)]TJ -ET -1 0 0 1 114.3757 406.8728 cm -0 g 0 G -1 0 0 1 -114.3757 -406.8728 cm -BT -/F8 9.9626 Tf 119.357 406.8728 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9551 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ -ET -1 0 0 1 94.9141 363.1 cm -0 g 0 G -1 0 0 1 -94.9141 -363.1 cm -BT -/F29 9.9626 Tf 99.8954 363.1 Td[(inf)-1(oa)]TJ -ET -1 0 0 1 124.2414 363.1 cm -0 g 0 G -1 0 0 1 -124.2414 -363.1 cm -BT -/F8 9.9626 Tf 129.2228 363.1 Td[(On)-434(en)28(try)-434(c)-1(an)-434(h)1(old)-434(auxi)1(liary)-434(in)1(formation)-434(on)-434(di)1(s)-1(tr)1(ibu)1(te)-1(d)-434(sparse)-435(matrix.)]TJ -4.4208 -11.9551 Td[(Actual)-333(in)1(formation)-332(w)-1(il)1(l)-333(dep)-28(end)-333(on)-333(d)1(ata)-333(format)-333(use)-1(d)1(.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(arra)28(y)-333(of)-333(length)]TJ/F32 9.9626 Tf 172.5477 0 Td[(psb_ifasize_)]TJ/F8 9.9626 Tf 62.7641 0 Td[(.)]TJ -ET -1 0 0 1 94.9141 319.3272 cm +1 0 0 1 176.8416 521.239 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S +Q +1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -94.9141 -319.3272 cm +1 0 0 1 -180.2787 -521.239 cm BT -/F29 9.9626 Tf 99.8954 319.3272 Td[(\014da)]TJ +/F8 9.9626 Tf 185.2601 521.239 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(halo_index)]TJ/F8 9.9626 Tf 55.6242 0 Td[(list;)]TJ ET -1 0 0 1 118.1947 319.3272 cm +1 0 0 1 94.9141 500.5609 cm 0 g 0 G -1 0 0 1 -118.1947 -319.3272 cm +1 0 0 1 -94.9141 -500.5609 cm BT -/F8 9.9626 Tf 123.176 319.3272 Td[(De\014n)1(e)-1(s)-334(th)1(e)-334(f)1(ormat)-334(of)-333(t)1(he)-334(d)1(is)-1(tr)1(ibu)1(ted)-333(s)-1(p)1(arse)-334(m)-1(at)1(rix.)]TJ 1.626 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(ing)-333(of)-333(length)-333(5)]TJ +/F29 9.9626 Tf 99.8954 500.5609 Td[(ps)1(b)]TJ ET -1 0 0 1 94.9141 287.5096 cm -0 g 0 G -1 0 0 1 -94.9141 -287.5096 cm +1 0 0 1 117.8319 500.5609 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S +Q +1 0 0 1 -117.8319 -500.5609 cm BT -/F29 9.9626 Tf 99.8954 287.5096 Td[(descr)1(a)]TJ +/F29 9.9626 Tf 121.269 500.5609 Td[(comm)]TJ ET -1 0 0 1 131.4104 287.5096 cm -0 g 0 G -1 0 0 1 -131.4104 -287.5096 cm +1 0 0 1 151.8718 500.5609 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S +Q +1 0 0 1 -151.8718 -500.5609 cm BT -/F8 9.9626 Tf 136.3917 287.5096 Td[(Des)-1(crib)-27(e)-334(th)1(e)-334(c)27(h)1(aracte)-1(r)1(is)-1(t)1(ic)-334(of)-333(th)1(e)-334(distri)1(bu)1(te)-1(d)-333(spar)1(s)-1(e)-334(matr)1(ix.)]TJ -11.5897 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(arr)1(a)27(y)-333(of)-333(c)28(haracter)-333(of)-333(le)-1(n)1(gth)-333(9.)]TJ +/F29 9.9626 Tf 155.3089 500.5609 Td[(ext)]TJ ET -1 0 0 1 94.9141 255.6919 cm +1 0 0 1 171.7497 500.5609 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S +Q +1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -94.9141 -255.6919 cm +1 0 0 1 -175.1868 -500.5609 cm BT -/F29 9.9626 Tf 99.8954 255.6919 Td[(pl)]TJ +/F8 9.9626 Tf 180.1681 500.5609 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ext_index)]TJ/F8 9.9626 Tf 50.3939 0 Td[(list;)]TJ ET -1 0 0 1 109.4429 255.6919 cm +1 0 0 1 94.9141 479.8828 cm 0 g 0 G -1 0 0 1 -109.4429 -255.6919 cm +1 0 0 1 -94.9141 -479.8828 cm BT -/F8 9.9626 Tf 114.4242 255.6919 Td[(Sp)-27(ec)-1(i\014)1(e)-1(s)-353(t)1(he)-353(lo)-28(cal)-352(ro)28(w)-353(p)-27(e)-1(rm)28(utat)1(ion)-352(of)-352(distrib)1(uted)-352(s)-1(p)1(arse)-353(m)-1(at)1(rix.)-502(If)-352(p)1(l\0501\051)-353(i)1(s)]TJ 10.3778 -11.9552 Td[(equal)-333(to)-333(0,)-333(then)-333(th)1(e)-1(re)-333(is)-1(n)1('t)-333(ro)28(w)-334(p)-27(erm)27(u)1(tation)1(.)]TJ 0 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-301(as)-1(:)-428(an)-302(allo)-27(c)-1(atab)1(le)-303(i)1(n)28(tege)-1(r)-302(ar)1(ra)28(y)-302(of)-302(d)1(ime)-1(nsion)-301(e)-1(qu)1(al)-302(to)-302(n)28(u)1(m)27(b)-27(e)-1(r)-302(of)]TJ 0 -11.9552 Td[(lo)-28(cal)-333(ro)28(w)-334(\050)1(m)-1(atr)1(ix)]TJ +/F29 9.9626 Tf 99.8954 479.8828 Td[(ps)1(b)]TJ ET -1 0 0 1 201.0053 219.8264 cm +1 0 0 1 117.8319 479.8828 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -201.0053 -219.8264 cm +1 0 0 1 -117.8319 -479.8828 cm BT -/F8 9.9626 Tf 203.9941 219.8264 Td[(dat)1(a[psb)]TJ +/F29 9.9626 Tf 121.269 479.8828 Td[(comm)]TJ ET -1 0 0 1 241.7305 219.8264 cm +1 0 0 1 151.8718 479.8828 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -241.7305 -219.8264 cm +1 0 0 1 -151.8718 -479.8828 cm BT -/F8 9.9626 Tf 244.7193 219.8264 Td[(n)]TJ +/F29 9.9626 Tf 155.3089 479.8828 Td[(o)32(vr)]TJ ET -1 0 0 1 250.8518 219.8264 cm +1 0 0 1 172.1717 479.8828 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -250.8518 -219.8264 cm +1 0 0 1 3.4371 0 cm +0 g 0 G +1 0 0 1 -175.6088 -479.8828 cm +BT +/F8 9.9626 Tf 180.5901 479.8828 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ovrlap_index)]TJ/F8 9.9626 Tf 66.085 0 Td[(list;)]TJ +ET +1 0 0 1 94.9141 459.2048 cm +0 g 0 G +1 0 0 1 -94.9141 -459.2048 cm BT -/F8 9.9626 Tf 253.8407 219.8264 Td[(ro)28(w)]TJ +/F29 9.9626 Tf 99.8954 459.2048 Td[(ps)1(b)]TJ ET -1 0 0 1 270.2403 219.8264 cm +1 0 0 1 117.8319 459.2048 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -270.2403 -219.8264 cm -BT -/F8 9.9626 Tf 273.2291 219.8264 Td[(]\051)]TJ -ET -1 0 0 1 94.9141 199.9639 cm -0 g 0 G -1 0 0 1 -94.9141 -199.9639 cm +1 0 0 1 -117.8319 -459.2048 cm BT -/F29 9.9626 Tf 99.8954 199.9639 Td[(pr)]TJ +/F29 9.9626 Tf 121.269 459.2048 Td[(comm)]TJ ET -1 0 0 1 110.9788 199.9639 cm -0 g 0 G -1 0 0 1 -110.9788 -199.9639 cm -BT -/F8 9.9626 Tf 115.9601 199.9639 Td[(Sp)-27(ec)-1(i\014)1(e)-1(s)-512(th)1(e)-513(lo)-27(c)-1(al)-512(colu)1(m)-1(n)-511(p)-28(erm)28(utati)1(on)-512(of)-512(d)1(istrib)1(uted)-512(spar)1(s)-1(e)-512(m)-1(atr)1(ix.)-980(If)]TJ 8.8419 -11.9551 Td[(PR\0501\051)-333(is)-333(e)-1(qu)1(al)-333(to)-333(0,)-334(t)1(hen)-333(there)-334(isn')1(t)-334(colu)1(m)-1(n)1(m)-334(p)-27(e)-1(r)1(m)27(u)1(tation.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-301(as)-1(:)-428(an)-302(allo)-27(c)-1(atab)1(le)-303(i)1(n)28(tege)-1(r)-302(ar)1(ra)28(y)-302(of)-302(d)1(ime)-1(n)1(s)-1(ion)-301(e)-1(qu)1(al)-302(to)-302(n)28(u)1(m)27(b)-27(e)-1(r)-302(of)]TJ 0 -11.9552 Td[(lo)-28(cal)-333(ro)28(w)-334(\050)1(m)-1(atr)1(ix)]TJ -ET -1 0 0 1 201.0053 164.0984 cm +1 0 0 1 151.8718 459.2048 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -201.0053 -164.0984 cm +1 0 0 1 -151.8718 -459.2048 cm BT -/F8 9.9626 Tf 203.9941 164.0984 Td[(dat)1(a[psb)]TJ +/F29 9.9626 Tf 155.3089 459.2048 Td[(mo)32(v)]TJ ET -1 0 0 1 241.7305 164.0984 cm +1 0 0 1 177.0008 459.2048 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -241.7305 -164.0984 cm +1 0 0 1 3.4371 0 cm +0 g 0 G +1 0 0 1 -180.4379 -459.2048 cm BT -/F8 9.9626 Tf 244.7193 164.0984 Td[(n)]TJ +/F8 9.9626 Tf 185.4192 459.2048 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ovr_mst_idx)]TJ/F8 9.9626 Tf 60.8546 0 Td[(list;)]TJ/F18 11.9552 Tf -272.7658 -28.887 Td[(3.)-1(2)-1125(Spar)-1(se)-375(Matr)-1(ix)-375(dat)-1(a)-374(st)-1(ruct)-1(ure)]TJ/F8 9.9626 Tf 0 -18.7396 Td[(The)]TJ/F32 9.9626 Tf 19.7465 0 Td[(psb)]TJ ET -1 0 0 1 250.8518 164.0984 cm +1 0 0 1 135.9605 411.5782 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -250.8518 -164.0984 cm +1 0 0 1 -135.9605 -411.5782 cm BT -/F8 9.9626 Tf 253.8407 164.0984 Td[(col)]TJ +/F32 9.9626 Tf 139.0987 411.5782 Td[(spmat)]TJ ET -1 0 0 1 266.615 164.0984 cm +1 0 0 1 165.878 411.5782 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -266.615 -164.0984 cm +1 0 0 1 -165.878 -411.5782 cm +BT +/F32 9.9626 Tf 169.0162 411.5782 Td[(type)]TJ/F8 9.9626 Tf 23.51 0 Td[(dat)1(a)-260(s)-1(tr)1(uctur)1(e)-261(con)28(tain)1(s)-260(all)-260(in)1(for)1(m)-1(ati)1(on)-260(ab)-27(out)-259(lo)-28(cal)-260(p)-27(ortion)]TJ -92.6308 -11.9552 Td[(of)-374(th)1(e)-375(spar)1(s)-1(e)-375(matr)1(ix)-374(and)-374(i)1(ts)-375(storage)-374(m)-1(o)-28(d)1(e)-1(.)-566(Most)-375(of)-373(thes)-1(e)-374(\014elds)-374(are)-375(set)-374(b)28(y)-374(the)]TJ 0 -11.9551 Td[(to)-28(ol)1(s)-350(r)1(outi)1(nes)-350(wh)1(e)-1(n)-348(in)1(s)-1(ertin)1(g)-349(a)-348(new)-349(s)-1(p)1(arse)-350(matri)1(x;)-356(the)-349(u)1(s)-1(er)-349(n)1(e)-1(eds)-349(on)1(ly)-348(c)27(ho)-27(os)-1(e,)]TJ 0 -11.9552 Td[(if)-333(h)1(e)-1(/she)-333(s)-1(o)-333(whishes)-1(,)-333(a)-333(s)-1(p)-27(ec)-1(i\014)1(c)-334(matrix)-333(storage)-334(mo)-28(d)1(e)-1(.)]TJ +ET +1 0 0 1 94.9141 343.2677 cm +0 g 0 G +1 0 0 1 -94.9141 -343.2677 cm +BT +/F29 9.9626 Tf 99.8954 343.2677 Td[(aspk)]TJ +ET +1 0 0 1 122.3956 343.2677 cm +0 g 0 G +1 0 0 1 -122.3956 -343.2677 cm +BT +/F8 9.9626 Tf 127.3769 343.2677 Td[(Con)28(tain)1(s)-334(v)56(alues)-334(of)-333(th)1(e)-334(lo)-27(c)-1(al)-333(di)1(s)-1(tr)1(ibu)1(te)-1(d)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix.)]TJ -2.5749 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-430(as:)-639(an)-431(all)1(o)-28(c)-1(atab)1(le)-431(arr)1(a)27(y)-430(of)-431(r)1(ank)-430(one)-431(of)-430(t)27(y)1(p)-28(e)-431(corres)-1(p)-27(ond)1(in)1(g)-431(to)]TJ 0 -11.9552 Td[(matrix)-333(en)28(tri)1(e)-1(s)-334(t)28(y)1(p)-28(e.)]TJ +ET +1 0 0 1 94.9141 298.6793 cm +0 g 0 G +1 0 0 1 -94.9141 -298.6793 cm +BT +/F29 9.9626 Tf 99.8954 298.6793 Td[(ia1)]TJ +ET +1 0 0 1 114.3757 298.6793 cm +0 g 0 G +1 0 0 1 -114.3757 -298.6793 cm BT -/F8 9.9626 Tf 269.6038 164.0984 Td[(]\051)]TJ +/F8 9.9626 Tf 119.357 298.6793 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9552 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ ET -1 0 0 1 94.9141 144.236 cm +1 0 0 1 94.9141 254.0908 cm 0 g 0 G -1 0 0 1 -94.9141 -144.236 cm +1 0 0 1 -94.9141 -254.0908 cm BT -/F29 9.9626 Tf 99.8954 144.236 Td[(m)]TJ +/F29 9.9626 Tf 99.8954 254.0908 Td[(ia2)]TJ ET -1 0 0 1 109.4429 144.236 cm +1 0 0 1 114.3757 254.0908 cm 0 g 0 G -1 0 0 1 -109.4429 -144.236 cm +1 0 0 1 -114.3757 -254.0908 cm BT -/F8 9.9626 Tf 114.4242 144.236 Td[(Num)28(b)-27(e)-1(r)-243(of)-244(r)1(o)28(w)-1(s;)-273(if)-243(ro)28(w)-244(ind)1(ice)-1(s)-244(are)-244(stored)-244(exp)1(licitly)84(,)-262(as)-244(in)-243(Co)-28(or)1(din)1(ate)-244(Storage,)]TJ 10.3778 -11.9552 Td[(shoul)1(d)-225(b)-27(e)-225(greate)-1(r)-224(than)-224(or)-224(e)-1(qu)1(al)-225(to)-224(the)-225(maxim)28(um)-225(ro)28(w)-225(in)1(dex)-225(actuall)1(y)-225(p)1(re)-1(sen)28(t)]TJ 0 -11.9552 Td[(in)-333(th)1(e)-334(sparse)-334(matri)1(x.)-444(Sp)-27(e)-1(ci\014ed)-333(as:)-445(i)1(n)28(te)-1(ger)-333(v)56(ariab)1(le.)]TJ +/F8 9.9626 Tf 119.357 254.0908 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9551 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ +ET +1 0 0 1 94.9141 209.5024 cm +0 g 0 G +1 0 0 1 -94.9141 -209.5024 cm +BT +/F29 9.9626 Tf 99.8954 209.5024 Td[(inf)-1(oa)]TJ +ET +1 0 0 1 124.2414 209.5024 cm +0 g 0 G +1 0 0 1 -124.2414 -209.5024 cm +BT +/F8 9.9626 Tf 129.2228 209.5024 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obj << /Type /Encoding /Differences [ 0 /.notdef 40/parenleft/parenright 42/.notdef 44/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine 58/.notdef 66/B 67/.notdef 71/G 72/.notdef 73/I 74/.notdef 76/L 77/.notdef 79/O/P 81/.notdef 84/T 85/.notdef 88/X 89/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 108/l/m/n/o/p/q/r/s/t/u/v/w/x/y 122/.notdef] >> endobj @@ -32962,7 +33203,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /ARRBOS+CMR6 def +/FontName /IFWRVZ+CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -32995,18 +33236,18 @@ endobj 617 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1558 0 R +/Encoding 1559 0 R /FirstChar 49 /LastChar 51 -/Widths 1559 0 R -/BaseFont /ARRBOS+CMR6 +/Widths 1560 0 R +/BaseFont /IFWRVZ+CMR6 /FontDescriptor 615 0 R >> endobj 615 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /ARRBOS+CMR6 +/FontName /IFWRVZ+CMR6 /ItalicAngle 0 /StemV 83 /XHeight 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stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /IOUPPN+CMR7 def +/FontName /WCZYOZ+CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33279,18 +33520,18 @@ endobj 607 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1564 0 R +/Encoding 1565 0 R /FirstChar 49 /LastChar 58 -/Widths 1565 0 R -/BaseFont /IOUPPN+CMR7 +/Widths 1566 0 R +/BaseFont /WCZYOZ+CMR7 /FontDescriptor 605 0 R >> endobj 605 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /IOUPPN+CMR7 +/FontName /WCZYOZ+CMR7 /ItalicAngle 0 /StemV 79 /XHeight 431 @@ -33299,10 +33540,10 @@ endobj /CharSet (/one/two/three/colon) /FontFile 606 0 R >> endobj -1565 0 obj +1566 0 obj [569 569 569 0 0 0 0 0 0 323 ] endobj -1564 0 obj << +1565 0 obj << /Type /Encoding /Differences [ 0 /.notdef 49/one/two/three 52/.notdef 58/colon 59/.notdef] >> endobj @@ -33326,7 +33567,7 @@ stream /ItalicAngle 0 def /isFixedPitch true def end readonly def -/FontName /ERAMWC+CMTT10 def +/FontName /VFKFBU+CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33458,18 +33699,18 @@ endobj 602 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1566 0 R +/Encoding 1567 0 R /FirstChar 40 /LastChar 126 -/Widths 1567 0 R -/BaseFont /ERAMWC+CMTT10 +/Widths 1568 0 R +/BaseFont /VFKFBU+CMTT10 /FontDescriptor 600 0 R >> endobj 600 0 obj << /Ascent 611 /CapHeight 611 /Descent -222 -/FontName /ERAMWC+CMTT10 +/FontName /VFKFBU+CMTT10 /ItalicAngle 0 /StemV 69 /XHeight 431 @@ -33478,10 +33719,10 @@ endobj /CharSet (/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/nine/colon/equal/A/B/C/E/F/I/K/L/M/N/O/P/S/T/W/Y/backslash/underscore/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/asciitilde) /FontFile 601 0 R >> endobj -1567 0 obj +1568 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 525 525 0 0 525 0 0 0 525 525 525 0 525 525 0 0 525 0 525 525 525 525 525 525 0 0 525 525 0 0 525 0 525 0 0 525 0 0 525 0 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 525 ] endobj -1566 0 obj << +1567 0 obj << /Type /Encoding /Differences [ 0 /.notdef 40/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six 55/.notdef 57/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C 68/.notdef 69/E/F 71/.notdef 73/I 74/.notdef 75/K/L/M/N/O/P 81/.notdef 83/S/T 85/.notdef 87/W 88/.notdef 89/Y 90/.notdef 92/backslash 93/.notdef 95/underscore 96/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef 126/asciitilde 127/.notdef] >> endobj @@ -33505,7 +33746,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /LFHQXB+CMMI10 def +/FontName /UBCUGU+CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33607,18 +33848,18 @@ endobj 586 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1568 0 R +/Encoding 1569 0 R /FirstChar 11 /LastChar 122 -/Widths 1569 0 R -/BaseFont /LFHQXB+CMMI10 +/Widths 1570 0 R +/BaseFont /UBCUGU+CMMI10 /FontDescriptor 584 0 R >> endobj 584 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /LFHQXB+CMMI10 +/FontName /UBCUGU+CMMI10 /ItalicAngle -14.04 /StemV 72 /XHeight 431 @@ -33627,10 +33868,10 @@ endobj /CharSet (/alpha/beta/period/comma/less/greater/A/D/I/L/N/O/P/Q/T/U/X/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/r/s/t/u/v/w/x/y/z) /FontFile 585 0 R >> endobj -1569 0 obj +1570 0 obj [640 566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 278 778 0 778 0 0 750 0 0 828 0 0 0 0 440 0 0 681 0 803 763 642 791 0 0 584 683 0 0 828 0 0 0 0 0 0 0 0 529 429 433 520 466 490 477 576 345 412 521 298 878 600 485 503 0 451 469 361 572 485 716 572 490 465 ] endobj -1568 0 obj << +1569 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/alpha/beta 13/.notdef 58/period/comma/less 61/.notdef 62/greater 63/.notdef 65/A 66/.notdef 68/D 69/.notdef 73/I 74/.notdef 76/L 77/.notdef 78/N/O/P/Q 82/.notdef 84/T/U 86/.notdef 88/X 89/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w/x/y/z 123/.notdef] >> endobj @@ -33654,7 +33895,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /WMJAXH+CMTI10 def +/FontName /OOOJNG+CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33805,18 +34046,18 @@ endobj 571 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1570 0 R +/Encoding 1571 0 R /FirstChar 11 /LastChar 122 -/Widths 1571 0 R -/BaseFont /WMJAXH+CMTI10 +/Widths 1572 0 R +/BaseFont /OOOJNG+CMTI10 /FontDescriptor 569 0 R >> endobj 569 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /WMJAXH+CMTI10 +/FontName /OOOJNG+CMTI10 /ItalicAngle -14.04 /StemV 68 /XHeight 431 @@ -33825,10 +34066,10 @@ endobj /CharSet (/ff/fi/fl/quoteright/comma/hyphen/period/slash/zero/one/two/three/five/nine/colon/equal/A/B/C/D/E/F/G/I/L/M/N/O/P/R/S/T/U/V/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) /FontFile 570 0 R >> endobj -1571 0 obj +1572 0 obj [613 562 588 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 307 0 0 0 0 307 358 307 511 511 511 511 511 0 511 0 0 0 511 307 0 0 767 0 0 0 743 704 716 755 678 653 774 0 386 0 0 627 897 743 767 678 0 729 562 716 743 743 0 0 0 0 0 0 0 0 0 0 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 409 332 537 460 664 464 486 409 ] endobj -1570 0 obj << +1571 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/ff/fi/fl 14/.notdef 39/quoteright 40/.notdef 44/comma/hyphen/period/slash/zero/one/two/three 52/.notdef 53/five 54/.notdef 57/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G 72/.notdef 73/I 74/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] >> endobj @@ -33852,7 +34093,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /UWMEYB+CMR10 def +/FontName /TKUGEF+CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -34005,18 +34246,18 @@ endobj 434 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1572 0 R +/Encoding 1573 0 R /FirstChar 11 /LastChar 123 -/Widths 1573 0 R -/BaseFont /UWMEYB+CMR10 +/Widths 1574 0 R +/BaseFont /TKUGEF+CMR10 /FontDescriptor 432 0 R >> endobj 432 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /UWMEYB+CMR10 +/FontName /TKUGEF+CMR10 /ItalicAngle 0 /StemV 69 /XHeight 431 @@ -34025,10 +34266,10 @@ endobj /CharSet (/ff/fi/fl/ffi/quotedblright/ampersand/quoteright/parenleft/parenright/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/equal/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/bracketleft/quotedblleft/bracketright/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash) /FontFile 433 0 R >> endobj -1573 0 obj +1574 0 obj [583 556 556 833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 778 278 389 389 0 778 278 333 278 500 500 500 500 500 500 500 500 500 500 500 278 278 0 778 0 0 0 750 708 722 764 681 653 785 750 361 514 778 625 917 750 778 681 0 736 556 722 750 750 1028 0 0 0 278 500 278 0 0 0 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 556 528 392 394 389 556 528 722 528 528 444 500 ] endobj -1572 0 obj << +1573 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/ff/fi/fl/ffi 15/.notdef 34/quotedblright 35/.notdef 38/ampersand/quoteright/parenleft/parenright 42/.notdef 43/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon 60/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P 81/.notdef 82/R/S/T/U/V/W 88/.notdef 91/bracketleft/quotedblleft/bracketright 94/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] >> endobj @@ -34052,7 +34293,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /AQCNIF+CMBX10 def +/FontName /BFCJMM+CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -34188,18 +34429,18 @@ endobj 431 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1574 0 R +/Encoding 1575 0 R /FirstChar 12 /LastChar 123 -/Widths 1575 0 R -/BaseFont /AQCNIF+CMBX10 +/Widths 1576 0 R +/BaseFont /BFCJMM+CMBX10 /FontDescriptor 429 0 R >> endobj 429 0 obj << /Ascent 694 /CapHeight 686 /Descent -194 -/FontName /AQCNIF+CMBX10 +/FontName /BFCJMM+CMBX10 /ItalicAngle 0 /StemV 114 /XHeight 444 @@ -34208,10 +34449,10 @@ endobj /CharSet (/fi/fl/quotedblright/quoteright/comma/period/zero/one/two/three/four/five/six/seven/eight/nine/colon/equal/A/B/C/D/E/F/G/H/I/J/L/M/N/O/P/R/S/T/U/V/quotedblleft/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash) /FontFile 430 0 R >> endobj -1575 0 obj +1576 0 obj [639 639 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 603 0 0 0 0 319 0 0 0 0 319 0 319 0 575 575 575 575 575 575 575 575 575 575 319 0 0 894 0 0 0 869 818 831 882 756 724 904 900 436 594 0 692 1092 900 864 786 0 862 639 800 885 869 0 0 0 0 0 603 0 0 0 0 559 639 511 639 527 351 575 639 319 351 607 319 958 639 575 639 607 474 454 447 639 607 831 607 607 511 575 ] endobj -1574 0 obj << +1575 0 obj << /Type /Encoding /Differences [ 0 /.notdef 12/fi/fl 14/.notdef 34/quotedblright 35/.notdef 39/quoteright 40/.notdef 44/comma 45/.notdef 46/period 47/.notdef 48/zero/one/two/three/four/five/six/seven/eight/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G/H/I/J 75/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 92/quotedblleft 93/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] >> endobj @@ -34235,7 +34476,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /GHFTGL+CMTI12 def +/FontName /BCYQSS+CMTI12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -34301,18 +34542,18 @@ endobj 428 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1576 0 R +/Encoding 1577 0 R /FirstChar 65 /LastChar 121 -/Widths 1577 0 R -/BaseFont /GHFTGL+CMTI12 +/Widths 1578 0 R +/BaseFont /BCYQSS+CMTI12 /FontDescriptor 426 0 R >> endobj 426 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /GHFTGL+CMTI12 +/FontName /BCYQSS+CMTI12 /ItalicAngle -14.04 /StemV 63 /XHeight 431 @@ -34321,10 +34562,10 @@ endobj /CharSet (/A/B/L/P/S/a/b/c/d/e/f/g/h/i/l/n/o/p/r/s/t/u/y) /FontFile 427 0 R >> endobj -1577 0 obj +1578 0 obj [727 688 0 0 0 0 0 0 0 0 0 613 0 0 0 663 0 0 550 0 0 0 0 0 0 0 0 0 0 0 0 0 500 450 450 500 450 300 450 500 300 0 0 250 0 550 500 500 0 413 400 325 525 0 0 0 475 ] endobj -1576 0 obj << +1577 0 obj << /Type /Encoding /Differences [ 0 /.notdef 65/A/B 67/.notdef 76/L 77/.notdef 80/P 81/.notdef 83/S 84/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 108/l 109/.notdef 110/n/o/p 113/.notdef 114/r/s/t/u 118/.notdef 121/y 122/.notdef] >> endobj @@ -34348,7 +34589,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /IIOZWT+CMBX12 def +/FontName /NOBWKE+CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -34469,18 +34710,18 @@ endobj 425 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1578 0 R +/Encoding 1579 0 R /FirstChar 12 /LastChar 124 -/Widths 1579 0 R -/BaseFont /IIOZWT+CMBX12 +/Widths 1580 0 R +/BaseFont /NOBWKE+CMBX12 /FontDescriptor 423 0 R >> endobj 423 0 obj << /Ascent 694 /CapHeight 686 /Descent -194 -/FontName /IIOZWT+CMBX12 +/FontName /NOBWKE+CMBX12 /ItalicAngle 0 /StemV 109 /XHeight 444 @@ -34489,181 +34730,181 @@ endobj /CharSet (/fi/quoteright/parenleft/parenright/hyphen/period/zero/one/two/three/four/five/six/seven/eight/nine/A/B/C/D/E/F/G/H/I/K/L/M/N/O/P/Q/R/S/T/U/V/W/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash/emdash) /FontFile 424 0 R >> endobj -1579 0 obj +1580 0 obj [625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 312 437 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