diff --git a/docs/html/index.html b/docs/html/index.html index 22e14a3e..aca21355 100644 --- a/docs/html/index.html +++ b/docs/html/index.html @@ -23,7 +23,7 @@ class="pplb7t-">Alfredo Buttari
Fabio Durastante
Software version: 3.9.0
Jun 1st, 2025 +class="newline" />June 9th, 2025 diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index 22e14a3e..aca21355 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -23,7 +23,7 @@ class="pplb7t-">Alfredo Buttari
Fabio Durastante
Software version: 3.9.0
Jun 1st, 2025 +class="newline" />June 9th, 2025 diff --git a/docs/html/userhtml30x.png b/docs/html/userhtml30x.png index c4cd68bb..8846254f 100644 Binary files a/docs/html/userhtml30x.png and b/docs/html/userhtml30x.png differ diff --git a/docs/html/userhtml34x.png b/docs/html/userhtml34x.png index c4cd68bb..8846254f 100644 Binary files a/docs/html/userhtml34x.png and b/docs/html/userhtml34x.png differ diff --git a/docs/html/userhtml6.html b/docs/html/userhtml6.html index 5e712393..655a0046 100644 --- a/docs/html/userhtml6.html +++ b/docs/html/userhtml6.html @@ -11,7 +11,7 @@
-

1In our prototype implementation we provide sample scatter/gather routines.

diff --git a/docs/html/userhtml7.html b/docs/html/userhtml7.html index e870a7bc..aed722b3 100644 --- a/docs/html/userhtml7.html +++ b/docs/html/userhtml7.html @@ -11,7 +11,7 @@
-

2This is the normal situation when the pattern of the sparse matrix is symmetric, which is equivalent to diff --git a/docs/html/userhtml8.html b/docs/html/userhtml8.html index c8c2f8ba..61ffca5a 100644 --- a/docs/html/userhtml8.html +++ b/docs/html/userhtml8.html @@ -11,7 +11,7 @@

-

3The subroutine style

The project is lead by Salvatore Filippone; a number of people have been contributing to this package over the years; contributors in roughly reverse chronological order: +
Luca Pep Sciarria
Theophane Loloum -
Fabio Durastante
Dimitri Walther
Andea Di Iorio
Stefano Petrilli @@ -50,7 +50,6 @@ chronological order:
Zaak Beekman
Ambra Abdullahi Hassan
Pasqua D’Ambra -
Alfredo Buttari
Daniela di Serafino
Michele Martone
Michele Colajanni @@ -59,11 +58,11 @@ chronological order:
Dario Pascucci

+

+ Salvatore Filippone
-

- Salvatore Filippone
Alfredo Buttari
Fabio Durastante

@@ -72,12 +71,12 @@ Fabio Durastante
-

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-

diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index 6bc82e3c..d6d5eaee 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -10,7 +10,7 @@ -

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1 Introduction

-

The PSBLAS library, developed with the aim to facilitate the parallelization of +

The PSBLAS library, developed with the aim to facilitate the parallelization of computationally intensive scientific applications, is designed to address parallel implementation of iterative solvers for sparse linear systems through the distributed memory paradigm. It includes routines for multiplying sparse @@ -27,11 +27,11 @@ diagonal entries, preprocessing sparse matrices, and contains additional routines for dense matrix operations. The current implementation of PSBLAS addresses a distributed memory execution model operating with message passing. -

The PSBLAS library version 3 is implemented in the Fortran 2008 [

The PSBLAS library version 3 is implemented in the Fortran 2008 [17] programming language, with reuse and/or adaptation of existing Fortran 77 and Fortran 95 software, plus a handful of C routines. -

The use of Fortran 2008 offers a number of advantages over Fortran 95, mostly +

The use of Fortran 2008 offers a number of advantages over Fortran 95, mostly in the handling of requirements for evolution and adaptation of the library to new computing architectures and integration of new algorithms. For a detailed discussion of our design see [19]; sufficient support for Fort from many compilers, including recent versions of the GNU Fortran compiler from the Free Software Foundation, and the FLANG compiler from the LLVM project. -

Previous approaches have been based on mixing Fortran 95, with its support for +

Previous approaches have been based on mixing Fortran 95, with its support for object-based design, with other languages; these have been advocated by a number of authors, e.g. [16]. Moreover, the Fortran 95 facilities for dynamic memory @@ -50,7 +50,7 @@ management and interface overloading greatly enhance the usability of the PSBLAS 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 presentation of the PSBLAS library follows the general structure of the +

The presentation of the PSBLAS library follows the general structure of the proposal for serial Sparse BLAS [8, 9], which in its turn is based on the proposal for @@ -58,7 +58,7 @@ BLAS on dense matrices [15, 5, 6]. -

The applicability of sparse iterative solvers to many different areas causes +

The applicability of sparse iterative solvers to many different areas causes some terminology problems because the same concept may be denoted through different names depending on the application area. The PSBLAS features presented in this document will be discussed referring to a finite @@ -67,7 +67,7 @@ the scope of the library is wider than that: for example, it can be applied to finite element discretizations of PDEs, and even to different classes of problems such as nonlinear optimization, for example in optimal control problems. -

The design of a solver for sparse linear systems is driven by many conflicting +

The design of a solver for sparse linear systems is driven by many conflicting objectives, such as limiting occupation of storage resources, exploiting regularities in the input data, exploiting hardware characteristics of the parallel platform. To @@ -88,12 +88,12 @@ applications. -

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diff --git a/docs/html/userhtmlse2.html b/docs/html/userhtmlse2.html index 4d1a8b9a..7dc3cb8f 100644 --- a/docs/html/userhtmlse2.html +++ b/docs/html/userhtmlse2.html @@ -10,7 +10,7 @@ -

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2 General overview

-

The PSBLAS library is designed to handle the implementation of iterative solvers for +

The PSBLAS library is designed to handle the implementation of iterative solvers for sparse linear systems on distributed memory parallel computers. The system coefficient matrix A must be square; it may be real or complex, nonsymmetric, and @@ -40,7 +40,7 @@ directly with MPI; however, in some cases, MPI routines are used directly to improve efficiency. For further details on our communication layer see Sec. 7. -

@@ -52,8 +52,8 @@ href="userhtmlse7.html#x13-1060007">7.
-

-

+

PIC


PSBLAS library components hierarchy.

-

The type of linear system matrices that we address typically arise in +

+

The type of linear system matrices that we address typically arise in the numerical solution of PDEs; in such a context, it is necessary to pay special attention to the structure of the problem from which the application originates. The nonzero pattern of a matrix arising from the discretization of a @@ -71,7 +71,7 @@ PDE is influenced by various factors, such as the shape of the domain, the discretization strategy, and the equation/unknown ordering. The matrix itself can be interpreted as the adjacency matrix of the graph associated with the discretization mesh. -

The distribution of the coefficient matrix for the linear system is based on the +

The distribution of the coefficient matrix for the linear system is based on the “owner computes” rule: the variable associated to each mesh point is assigned to a process that will own the corresponding row in the coefficient matrix and will carry out all related computations. This allocation strategy is equivalent to a @@ -88,7 +88,7 @@ the literature, e.g. METIS [14]. Dense vectors conform to sparse matrices, that is, the entries of a vector follow the same distribution of the matrix rows. -

We assume that the sparse matrix is built in parallel, where each process generates +

We assume that the sparse matrix is built in parallel, where each process generates its own portion. We never require that the entire matrix be available on a single node. However, it is possible to hold the entire matrix in one process and distribute it explicitly2.1 Basic Nomenclature -

Our computational model implies that the data allocation on the parallel distributed +

Our computational model implies that the data allocation on the parallel distributed memory machine is guided by the structure of the physical model, and specifically by the discretization mesh of the PDE. -

Each point of the discretization mesh will have (at least) one associated +

Each point of the discretization mesh will have (at least) one associated equation/variable, and therefore one index. We say that point i depends on point sub-domains assigned to the parallel processes, we classify the points of a given sub-domain as following.

-

+

Internal.

-

An internal point of a given domain

An internal point of a given domain depends only on points of the same domain. If all points of a domain are assigned to one process, then a computational step (e.g., a matrix-vector product) of the equations @@ -131,19 +131,19 @@ class="pplri7t-">depends only on points of the same associated with the internal points requires no data items from other domains and no communications.

-

+

Boundary.

-

A point of a given domain is a boundary point if it

A point of a given domain is a boundary point if it depends on points belonging to other domains.

-

+

Halo.

-

A halo point for a given domain is a point belonging to another domain +

A halo point for a given domain is a point belonging to another domain such that there is a boundary point which depends on it. Whenever performing a computational step, such as a matrix-vector product, the values associated @@ -151,22 +151,22 @@ class="pplri7t-">depends on it. Whenever performing a given domain is usually a halo point for some other domain2 ; - therefore the cardinality of the boundary points set denotes the amount + therefore the cardinality of the boundary points set determines the amount of data sent to other domains.

-

+

Overlap.

-

An overlap point is a boundary point assigned to multiple domains. Any +

An overlap point is a boundary point assigned to multiple domains. Any operation that involves an overlap point has to be replicated for each assignment.

-

Overlap points do not usually exist in the basic data distributions; however they are a +

Overlap points do not usually exist in the basic data distributions; however they are a feature of Domain Decomposition Schwarz preconditioners which are the subject of related research work [4, 3]. -

We denote the sets of internal, boundary and halo points for a given subdomain +

We denote the sets of internal, boundary and halo points for a given subdomain by I, |Hi|. -

@@ -215,8 +215,8 @@ class="zplmr7y-">|.
-

-

+

PIC


Point classfication.

-

This classification of mesh points guides the naming scheme that we adopted in +

+

This classification of mesh points guides the naming scheme that we adopted in the library internals and in the data structures. We explicitly note that “Halo” points are also often called “ghost” points in the literature.

2.2 Library contents

-

The PSBLAS library consists of various classes of subroutines: +

The PSBLAS library consists of various classes of subroutines:

-

+

Computational routines

-

comprising: +

comprising:

  • -

    Sparse matrix by dense matrix product; +

    Sparse matrix by dense matrix product;

  • -

    Sparse triangular systems solution for block diagonal matrices; +

    Sparse triangular systems solution for block diagonal matrices;

  • -

    Vector and matrix norms; +

    Vector and matrix norms;

  • -

    Dense matrix sums; +

    Dense matrix sums;

  • -

    Dot products.

+

Dot products.

-

+

Communication routines

-

handling halo and overlap communications; +

handling halo and overlap communications;

-

+

Data management and auxiliary routines

-

including: +

including:

  • -

    Parallel environment management +

    Parallel environment management

  • -

    Communication descriptors allocation; +

    Communication descriptors allocation;

  • -

    Dense and sparse matrix allocation; +

    Dense and sparse matrix allocation;

  • -

    Dense and sparse matrix build and update; +

    Dense and sparse matrix build and update;

  • -

    Sparse matrix and data distribution preprocessing.

+

Sparse matrix and data distribution preprocessing.

-

+

Preconditioner routines

-

+

-

+

Iterative methods

-

a subset of classical and Krylov subspace iterative methods

-

The following naming scheme has been adopted for all the symbols internally defined +

a subset of classical and Krylov subspace iterative methods +

The following naming scheme has been adopted for all the symbols internally defined in the PSBLAS software package:

  • -

    all symbols (i.e. subroutine names, data types...) are prefixed by

    all symbols (i.e. subroutine names, data types...) are prefixed by psb_

  • -

    all data type names are suffixed by

    all data type names are suffixed by _type

  • -

    all constants are suffixed by

    all constants are suffixed by _

  • -

    all top-level subroutine names follow the rule

    all top-level subroutine names follow the rule psb_xxname where xx can be either:

    • -

      ge: the routine is related to dense data,

    • -

      sp: the routine is related to sparse data,

    • -

      cd: the routine is related to communication descriptor (see 3).

    -

    For example the

    For example the psb_geins, psb_spins and psb_cdins perform the same @@ -339,33 +339,33 @@ class="cmtt-10">psb_cdins perform the same href="userhtmlse6.html#x12-780006">6) on dense matrices, sparse matrices and communication descriptors respectively. Interface overloading allows the usage of the same subroutine names for both real and complex data.

-

In the description of the subroutines, arguments or argument entries are classified +

In the description of the subroutines, arguments or argument entries are classified as:

-

+

global

-

For input arguments, the value must be the same on all processes +

For input arguments, the value must be the same on all processes participating in the subroutine call; for output arguments the value is guaranteed to be the same.

-

+

local

-

Each process has its own value(s) independently.

-

To finish our general description, we define a version string with the constant +

Each process has its own value(s) independently. +

To finish our general description, we define a version string with the constant

psb_version_string_
-

whose current value is

whose current value is 3.9.0 -

+

2.3 Application structure

-

The main underlying principle of the PSBLAS library is that the library objects are +

The main underlying principle of the PSBLAS library is that the library objects are created and exist with reference to a discretized space to which there corresponds an index space and a matrix sparsity pattern. As an example, consider a cell-centered finite-volume discretization of the Navier-Stokes equations on a @@ -375,13 +375,13 @@ class="zplmr7m-">n is isomorphic to the set of cell centers, whereas the pattern of the associated linear system matrix is isomorphic to the adjacency graph imposed on the discretization mesh by the discretization stencil. -

Thus the first order of business is to establish an index space, and this is done +

Thus the first order of business is to establish an index space, and this is done with a call to psb_cdall in which we specify the size of the index space n and the allocation of the elements of the index space to the various processes making up the MPI (virtual) parallel machine. -

The index space is partitioned among processes, and this creates a mapping from +

The index space is partitioned among processes, and this creates a mapping from the “global” numbering 1…n to a numbering “local” to each process; each process

For a given index space 1

For a given index space 1…n there are many possible associated topologies, i.e. many different discretization stencils; thus the description of the index space is not @@ -430,44 +430,44 @@ class="zplmr7m-">A, and thus they have to be 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, +

A simple application structure will walk through the index space allocation, matrix/vector creation and linear system solution as follows:

  1. -

    Initialize parallel environment with

    Initialize parallel environment with psb_init;

  2. -

    Initialize index space with

    Initialize index space with psb_cdall;

  3. -

    Allocate sparse matrix and dense vectors with

    Allocate sparse matrix and dense vectors with psb_spall and psb_geall;

  4. -

    Loop over all local rows, generate matrix and vector entries, and insert +

    Loop over all local rows, generate matrix and vector entries, and insert them with psb_spins and psb_geins

  5. -

    Assemble the various entities: +

    Assemble the various entities:

    1. -

      psb_cdasb,

    2. -

      psb_spasb, @@ -475,12 +475,12 @@ class="cmtt-10">psb_spasb,

    3. -

      psb_geasb;

  6. -

    Choose the preconditioner to be used with

    Choose the preconditioner to be used with prec%init and prec%set, and build it with 3

  7. -

    Call one of the iterative drivers with the method of choice, e.g.

    Call one of the iterative drivers with the method of choice, e.g. psb_krylov with bicgstab.

-

This is the structure of the sample programs in the directory

This is the structure of the sample programs in the directory test/pargen/. -

For a simulation in which the same discretization mesh is used over multiple +

For a simulation in which the same discretization mesh is used over multiple time steps, the following structure may be more appropriate:

  1. -

    Initialize parallel environment with

    Initialize parallel environment with psb_init

  2. -

    Initialize index space with

    Initialize index space with psb_cdall

  3. -

    Loop over the topology of the discretization mesh and build the +

    Loop over the topology of the discretization mesh and build the descriptor with psb_cdins;

  4. -

    Assemble the descriptor with

    Assemble the descriptor with psb_cdasb;

  5. -

    Allocate the sparse matrices and dense vectors with;

    Allocate the sparse matrices and dense vectors with; psb_spall and psb_geall; @@ -532,34 +532,34 @@ class="cmtt-10">psb_geall;

  6. -

    Loop over the time steps: +

    Loop over the time steps:

    1. -

      If after first time step, reinitialize the sparse matrix with

      If after first time step, reinitialize the sparse matrix with psb_sprn; also zero out the dense vectors;

    2. -

      Loop over the mesh, generate the coefficients and insert/update +

      Loop over the mesh, generate the coefficients and insert/update them with psb_spins and psb_geins;

    3. -

      Assemble with

      Assemble with psb_spasb and psb_geasb;

    4. -

      +

    5. -

      Choose the preconditioner to be used with

      Choose the preconditioner to be used with prec%init and prec%set, and build it with prec%build;

    6. -

      Call one of the iterative drivers with the method of choice, e.g. +

      Call one of the iterative drivers with the method of choice, e.g. psb_krylov with bicgstab.

-

The insertion routines will be called as many times as needed; they only need to be +

The insertion routines will be called as many times as needed; they only need to 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

In principle there is no specific order in the calls to 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 +

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 @@ -595,23 +595,23 @@ process and pass it in a single call to psb_spins; this, however, would entail a doubling of memory occupation, and thus would be almost always far from optimal. -

+

2.3.1 User-defined index mappings
-

PSBLAS supports user-defined global to local index mappings, subject to the +

PSBLAS supports user-defined global to local index mappings, subject to the constraints outlined in sec. 2.3:

  1. -

    The set of indices owned locally must be mapped to the set 1

    The set of indices owned locally must be mapped to the set 1…nrowi;

  2. -

    The set of halo points must be mapped to the set

    The set of halo points must be mapped to the set nrowi + 1…ncol i;

-

but otherwise the mapping is arbitrary. The user application is responsible to ensure +

but otherwise the mapping is arbitrary. The user application is responsible to ensure consistency of this mapping; some errors may be caught by the library, but this is not guaranteed. The application structure to support this usage is as follows:

  1. -

    Initialize index +

    Initialize index space with psb_cdall(ictx,desc,info,vl=vl,lidx=lidx) passing the vectors lidx(:) containing the corresponding local

  2. -

    Add the halo points

    Add the halo points ja(:) and their associated local indices lidx(:) with a(some) call(s) to psb_cdins(nz,ja,desc,info,lidx=lidx);

  3. -

    Assemble the descriptor with

    Assemble the descriptor with psb_cdasb;

  4. psb_cdasb; -

    Build the sparse matrices and vectors, optionally making use in +

    Build the sparse matrices and vectors, optionally making use in psb_spins and psb_geins of the local argument specifying that the class="cmtt-10">ia, ja and irw, respectively, are already local indices.

-

+

2.4 Programming model

-

The PSBLAS librarary is based on the Single Program Multiple Data (SPMD) +

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, many subroutines coordinate their action across the +

Because of this structure, many subroutines coordinate their action across the various processes, thus providing an implicit synchronization point, and therefore must be called simultaneously by all processes participating in the computation. This is certainly true for the data allocation and assembly routines, for all the computational routines and for some of the tools routines. -

However there are many cases where no synchronization, and indeed no +

However there are many cases where no synchronization, and indeed no communication among processes, is implied; for instance, all the routines in sec. 3 are only acting on the local data structures, and thus may be called independently. @@ -681,21 +681,21 @@ The most important case is that of the coefficient insertion routines: since the of coefficients in the sparse and dense matrices varies among the processors, and since the user is free to choose an arbitrary order in builiding the matrix entries, these routines cannot imply a synchronization. -

Throughout this user’s guide each subroutine will be clearly indicated +

Throughout this user’s guide each subroutine will be clearly indicated as:

-

+

Synchronous:

-

must be called simultaneously by all the processes in the relevant +

must be called simultaneously by all the processes in the relevant communication context;

-

+

Asynchronous:

-

may be called in a totally independent manner.

+

may be called in a totally independent manner. diff --git a/docs/html/userhtmlse5.html b/docs/html/userhtmlse5.html index a13f6730..fa33cd5e 100644 --- a/docs/html/userhtmlse5.html +++ b/docs/html/userhtmlse5.html @@ -21,7 +21,7 @@ href="userhtml.html#userhtmlse8.html" >up]

The routines in this chapter implement various global communication operators on vectors associated with a discretization mesh. For auxiliary communication routines not tied to a discretization space see 6. +href="userhtmlse7.html#x13-1060007">7. diff --git a/docs/psblas-3.9.pdf b/docs/psblas-3.9.pdf index 3173d3c9..6f6505c6 100644 --- a/docs/psblas-3.9.pdf +++ b/docs/psblas-3.9.pdf @@ -665,7 +665,7 @@ endstream endobj 682 0 obj << -/Length 766 +/Length 767 >> stream 0 g 0 G @@ -701,7 +701,7 @@ Q 0 g 0 G 1 0 0 1 -168.637 -349.474 cm BT -/F75 9.9626 Tf 365.51 270.624 Td [(by)-250(Salvatore)-250(Filippone)]TJ 34.042 -11.956 Td [(Alfredo)-250(Buttari)]TJ -8.847 -11.955 Td [(Fabio)-250(Durastante)]TJ/F84 9.9626 Tf 23.333 -11.955 Td [(Jun)-250(1st,)-250(2025)]TJ +/F75 9.9626 Tf 365.51 270.624 Td [(by)-250(Salvatore)-250(Filippone)]TJ 34.042 -11.956 Td [(Alfredo)-250(Buttari)]TJ -8.847 -11.955 Td [(Fabio)-250(Durastante)]TJ/F84 9.9626 Tf 16.987 -11.955 Td [(June)-250(9th,)-250(2025)]TJ 0 g 0 G 0 g 0 G ET @@ -4524,18 +4524,18 @@ endstream endobj 893 0 obj << -/Length 4128 +/Length 4149 >> stream 0 g 0 G 0 g 0 G BT -/F75 14.3462 Tf 99.895 705.784 Td [(Preface)]TJ/F84 9.9626 Tf 0.98 0 0 1 99.587 683.082 Tm [(This)-249(manual)-250(describes)-249(the)-250(main)-250(featur)19(es)-250(of)-249(PSBLAS,)-250(a)-249(library)-250(for)-249(parallel)-250(sparse)]TJ 1 0 0 1 99.895 671.127 Tm [(computations)-250(that)-250(has)-250(been)-250(developed)-250(over)-250(a)-250(number)-250(of)-250(years.)]TJ 1.01 0 0 1 114.839 659.172 Tm [(Our)-248(work)-248(has)-248(been)-247(mainly)-248(devoted)-248(to)-248(pr)18(oviding)-248(a)-248(foundational)-248(toolkit)-247(on)]TJ 1.02 0 0 1 99.477 647.217 Tm [(which)-264(many)-265(algorithms)-264(can)-264(be)-265(implemented;)-274(the)-264(toolkit)-264(has)-265(pr)18(oven)-264(its)-265(ef)18(fec-)]TJ 1.02 0 0 1 99.895 635.261 Tm [(tiveness)-269(and)-268(\003exibility)-269(in)-268(many)-269(ways.)-374(The)-268(PSBLAS)-269(component)-268(deals)-269(mostly)]TJ 1.02 0 0 1 99.477 623.306 Tm [(with)-285(the)-286(computational)-285(kernels)-286(and)-285(envir)17(onment)-285(handling;)-306(it)-285(supports)-286(com-)]TJ 1.017 0 0 1 99.596 611.351 Tm [(putations)-245(on)-246(normal)-245(CPUs,)-246(including)-245(the)-245(usage)-246(of)-245(OpenMP)-246(for)-245(parallellizing)]TJ 1 0 0 1 99.895 599.396 Tm [(acr)18(oss)-250(multiple)-250(cor)18(es.)]TJ 1.02 0 0 1 114.839 587.441 Tm [(This)-283(foundational)-284(package)-283(pr)17(ovides)-283(linear)-283(solvers)-284(and)-283(some)-284(very)-283(simple)]TJ 1.019 0 0 1 99.596 575.486 Tm [(pr)18(econditioners;)-247(the)-246(companion)-246(package)-246(AMG4PSBLAS)-247(exp)1(lor)17(es)-246(how)-246(to)-246(use)]TJ 0.981 0 0 1 99.895 563.53 Tm [(the)-256(base)-256(toolkit)-256(to)-256(build)-256(much)-256(mor)18(e)-256(sophisticated)-256(pr)19(econditioners)-256(which)-256(can)-256(be)]TJ 1 0 0 1 99.596 551.575 Tm [(plugged)-250(seamlessly)-250(into)-250(the)-250(base)-250(solvers.)]TJ 0.98 0 0 1 114.839 539.62 Tm [(The)-253(softwar)19(e)-253(ar)18(chite)1(ctur)18(e)-253(allows)-252(us)-253(to)-253(of)19(f)-1(er)-252(support)-253(for)-252(many)-253(alternatives)-253(in)]TJ 1.005 0 0 1 99.895 527.665 Tm [(the)-249(implementation,)-250(including)-249(usage)-249(of)-250(heter)18(ogeneous)-249(platforms,)-249(and)-250(compu-)]TJ 1.02 0 0 1 99.895 515.71 Tm [(tations)-245(performed)-245(on)-245(GPUs)-246(thr)18(ouh)-245(CUDA.)-245(Ther)17(e)-245(is)-245(support)-245(for)-245(GPU)-245(compu-)]TJ 1.007 0 0 1 99.895 503.755 Tm [(tations)-247(thr)17(ough)-247(OpenACC,)-247(but)-248(it)-247(is)-248(at)-247(this)-248(time)-247(a)-248(highly)-247(experimental)-247(version;)]TJ 1.02 0 0 1 99.477 491.799 Tm [(we)-281(plan)-281(to)-281(also)-281(look)-281(at)-281(using)-281(accelerato)1(rs)-281(thr)17(ough)-281(OpenMP)-281(as)-281(support)-280(fr)17(om)]TJ 1 0 0 1 99.895 479.844 Tm [(compilers)-250(impr)18(oves.)]TJ 1.02 0 0 1 114.839 467.889 Tm [(The)-272(pr)17(oject)-272(is)-272(lead)-272(by)-272(Salvator)17(e)-272(Filippone;)-285(a)-273(numb)1(er)-273(of)-272(people)-272(have)-272(been)]TJ 1.02 0 0 1 99.895 455.934 Tm [(contributing)-317(to)-317(this)-318(package)-317(over)-317(the)-317(years;)-353(contributors)-318(in)-317(r)18(oughly)-317(r)17(everse)]TJ 1 0 0 1 99.895 443.979 Tm [(chr)18(onological)-250(or)18(der:)]TJ 14.944 -11.955 Td [(Theophane)-250(Loloum)]TJ 0 -11.956 Td [(Fabio)-250(Durastante)]TJ 0 -11.955 Td [(Dimitri)-250(W)92(alther)]TJ 0 -11.955 Td [(Andea)-250(Di)-250(Iorio)]TJ 0 -11.955 Td [(Stefano)-250(Petrilli)]TJ 0 -11.955 Td [(Sor)18(en)-250(Rasmussen)]TJ 0 -11.955 Td [(Zaak)-250(Beekman)]TJ 0 -11.956 Td [(Ambra)-250(Abdullahi)-250(Hassan)]TJ 0 -11.955 Td [(Pasqua)-250(D'Ambra)]TJ 0 -11.955 Td [(Alfr)18(edo)-250(Buttari)]TJ 0 -11.955 Td [(Daniela)-250(di)-250(Sera\002no)]TJ 0 -11.955 Td [(Michele)-250(Martone)]TJ 0 -11.956 Td [(Michele)-250(Colajanni)]TJ 0 -11.955 Td [(Fabio)-250(Cerioni)]TJ 0 -11.955 Td [(Stefano)-250(Maiolatesi)]TJ 0 -11.955 Td [(Dario)-250(Pascucci)]TJ +/F75 14.3462 Tf 99.895 705.784 Td [(Preface)]TJ/F84 9.9626 Tf 0.98 0 0 1 99.587 683.082 Tm [(This)-249(manual)-250(describes)-249(the)-250(main)-250(featur)19(es)-250(of)-249(PSBLAS,)-250(a)-249(library)-250(for)-249(parallel)-250(sparse)]TJ 1 0 0 1 99.895 671.127 Tm [(computations)-250(that)-250(has)-250(been)-250(developed)-250(over)-250(a)-250(number)-250(of)-250(years.)]TJ 1.01 0 0 1 114.839 659.172 Tm [(Our)-248(work)-248(has)-248(been)-247(mainly)-248(devoted)-248(to)-248(pr)18(oviding)-248(a)-248(foundational)-248(toolkit)-247(on)]TJ 1.02 0 0 1 99.477 647.217 Tm [(which)-264(many)-265(algorithms)-264(can)-264(be)-265(implemented;)-274(the)-264(toolkit)-264(has)-265(pr)18(oven)-264(its)-265(ef)18(fec-)]TJ 1.02 0 0 1 99.895 635.261 Tm [(tiveness)-269(and)-268(\003exibility)-269(in)-268(many)-269(ways.)-374(The)-268(PSBLAS)-269(component)-268(deals)-269(mostly)]TJ 1.02 0 0 1 99.477 623.306 Tm [(with)-285(the)-286(computational)-285(kernels)-286(and)-285(envir)17(onment)-285(handling;)-306(it)-285(supports)-286(com-)]TJ 1.017 0 0 1 99.596 611.351 Tm [(putations)-245(on)-246(normal)-245(CPUs,)-246(including)-245(the)-245(usage)-246(of)-245(OpenMP)-246(for)-245(parallellizing)]TJ 1 0 0 1 99.895 599.396 Tm [(acr)18(oss)-250(multiple)-250(cor)18(es.)]TJ 1.02 0 0 1 114.839 587.441 Tm [(This)-283(foundational)-284(package)-283(pr)17(ovides)-283(linear)-283(solvers)-284(and)-283(some)-284(very)-283(simple)]TJ 1.019 0 0 1 99.596 575.486 Tm [(pr)18(econditioners;)-247(the)-246(companion)-246(package)-246(AMG4PSBLAS)-247(exp)1(lor)17(es)-246(how)-246(to)-246(use)]TJ 0.981 0 0 1 99.895 563.53 Tm [(the)-256(base)-256(toolkit)-256(to)-256(build)-256(much)-256(mor)18(e)-256(sophisticated)-256(pr)19(econditioners)-256(which)-256(can)-256(be)]TJ 1 0 0 1 99.596 551.575 Tm [(plugged)-250(seamlessly)-250(into)-250(the)-250(base)-250(solvers.)]TJ 0.98 0 0 1 114.839 539.62 Tm [(The)-253(softwar)19(e)-253(ar)18(chite)1(ctur)18(e)-253(allows)-252(us)-253(to)-253(of)19(f)-1(er)-252(support)-253(for)-252(many)-253(alternatives)-253(in)]TJ 1.005 0 0 1 99.895 527.665 Tm [(the)-249(implementation,)-250(including)-249(usage)-249(of)-250(heter)18(ogeneous)-249(platforms,)-249(and)-250(compu-)]TJ 1.02 0 0 1 99.895 515.71 Tm [(tations)-245(performed)-245(on)-245(GPUs)-246(thr)18(ouh)-245(CUDA.)-245(Ther)17(e)-245(is)-245(support)-245(for)-245(GPU)-245(compu-)]TJ 1.007 0 0 1 99.895 503.755 Tm [(tations)-247(thr)17(ough)-247(OpenACC,)-247(but)-248(it)-247(is)-248(at)-247(this)-248(time)-247(a)-248(highly)-247(experimental)-247(version;)]TJ 1.02 0 0 1 99.477 491.799 Tm [(we)-281(plan)-281(to)-281(also)-281(look)-281(at)-281(using)-281(accelerato)1(rs)-281(thr)17(ough)-281(OpenMP)-281(as)-281(support)-280(fr)17(om)]TJ 1 0 0 1 99.895 479.844 Tm [(compilers)-250(impr)18(oves.)]TJ 1.02 0 0 1 114.839 467.889 Tm [(The)-272(pr)17(oject)-272(is)-272(lead)-272(by)-272(Salvator)17(e)-272(Filippone;)-285(a)-273(numb)1(er)-273(of)-272(people)-272(have)-272(been)]TJ 1.02 0 0 1 99.895 455.934 Tm [(contributing)-317(to)-317(this)-318(package)-317(over)-317(the)-317(years;)-353(contributors)-318(in)-317(r)18(oughly)-317(r)17(everse)]TJ 1 0 0 1 99.895 443.979 Tm [(chr)18(onological)-250(or)18(der:)]TJ 14.944 -11.955 Td [(Luca)-250(Pep)]TJ 41.494 0.025 Td [(\036)]TJ -0.727 -0.025 Td [(e)-250(Sciarria)]TJ -40.767 -11.956 Td [(Theophane)-250(Loloum)]TJ 0 -11.955 Td [(Dimitri)-250(W)92(alther)]TJ 0 -11.955 Td [(Andea)-250(Di)-250(Iorio)]TJ 0 -11.955 Td [(Stefano)-250(Petrilli)]TJ 0 -11.955 Td [(Sor)18(en)-250(Rasmussen)]TJ 0 -11.955 Td [(Zaak)-250(Beekman)]TJ 0 -11.956 Td [(Ambra)-250(Abdullahi)-250(Hassan)]TJ 0 -11.955 Td [(Pasqua)-250(D'Ambra)]TJ 0 -11.955 Td [(Daniela)-250(di)-250(Sera\002no)]TJ 0 -11.955 Td [(Michele)-250(Martone)]TJ 0 -11.955 Td [(Michele)-250(Colajanni)]TJ 0 -11.955 Td [(Fabio)-250(Cerioni)]TJ 0 -11.956 Td [(Stefano)-250(Maiolatesi)]TJ 0 -11.955 Td [(Dario)-250(Pascucci)]TJ 0 g 0 G 0 g 0 G 243.12 -21.918 Td [(Salvator)18(e)-250(Filippone)]TJ 18.729 -11.955 Td [(Alfr)18(edo)-250(Buttari)]TJ -8.847 -11.955 Td [(Fabio)-250(Durastante)]TJ 0 g 0 G - -98.581 -116.43 Td [(1)]TJ + -98.581 -128.385 Td [(1)]TJ 0 g 0 G ET @@ -4714,7 +4714,7 @@ BT 0 0 1 rg 0 0 1 RG /F84 7.5716 Tf 1 0 0 1 260.936 541.68 Tm [(1)]TJ 0 g 0 G -/F84 9.9626 Tf 0.98 0 0 1 265.22 538.064 Tm [(,)-210(even)-198(though)-199(the)-198(r)18(esulting)-198(memory)-199(bottleneck)-198(would)]TJ 1 0 0 1 150.705 526.109 Tm [(make)-250(this)-250(option)-250(unattractive)-250(in)-250(most)-250(cases.)]TJ/F75 11.9552 Tf 0 -33.074 Td [(2.1)-1000(Basic)-250(Nomenclature)]TJ/F84 9.9626 Tf 1.02 0 0 1 150.705 472.73 Tm [(Our)-254(computational)-254(model)-255(implies)-254(that)-254(the)-254(data)-255(alloc)1(ation)-255(on)-254(the)-254(parallel)-254(dis-)]TJ 0.981 0 0 1 150.705 460.774 Tm [(tributed)-253(memory)-254(machine)-254(is)-253(guided)-254(by)-253(the)-254(str)8(uctur)19(e)-254(of)-253(the)-254(physical)-253(model,)-254(and)]TJ 1 0 0 1 150.705 448.819 Tm [(speci\002cally)-250(by)-250(the)-250(discr)18(etization)-250(mesh)-250(of)-250(the)-250(PDE.)]TJ 1.02 0 0 1 165.649 436.172 Tm [(Each)-341(point)-341(of)-341(the)-341(discr)18(etization)-341(mesh)-341(will)-341(have)-341(\050at)-341(least\051)-341(one)-341(associated)]TJ 1.02 0 0 1 150.705 424.216 Tm [(equation/variable,)-353(and)-332(ther)18(efor)17(e)-331(one)-332(index.)-564(W)91(e)-332(say)-332(that)-332(point)]TJ/F78 9.9626 Tf 1 0 0 1 440.497 424.216 Tm [(i)]TJ 1.02 0 0 1 446.831 424.216 Tm [(depends)]TJ/F84 9.9626 Tf 1.02 0 0 1 482.953 424.216 Tm [(on)]TJ 1.02 0 0 1 150.406 412.261 Tm [(point)]TJ/F78 9.9626 Tf 1 0 0 1 177.509 412.261 Tm [(j)]TJ/F84 9.9626 Tf 1.02 0 0 1 183.194 412.261 Tm [(if)-275(the)-274(equation)-275(for)-274(a)-275(variable)-275(associate)1(d)-275(with)]TJ/F78 9.9626 Tf 1 0 0 1 386.696 412.261 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 392.451 412.261 Tm [(contains)-275(a)-274(term)-275(in)]TJ/F78 9.9626 Tf 1 0 0 1 476.753 412.261 Tm [(j)]TJ/F84 9.9626 Tf 1.02 0 0 1 479.647 412.261 Tm [(,)-282(or)]TJ 1.02 0 0 1 150.705 400.306 Tm [(equivalently)-262(if)]TJ/F78 9.9626 Tf 1 0 0 1 218.767 400.306 Tm [(a)]TJ/F78 7.5716 Tf 4.589 -1.96 Td [(i)-67(j)]TJ/F189 10.3811 Tf 8.519 1.96 Td [(6)]TJ/F191 10.3811 Tf 0.249 0 Td [(=)]TJ/F84 9.9626 Tf 1.02 0 0 1 243.403 400.306 Tm [(0.)-354(After)-262(the)-262(partition)-262(of)-262(the)-262(discr)18(etization)-262(mesh)-262(into)]TJ/F78 9.9626 Tf 1.02 0 0 1 478.378 400.306 Tm [(sub-)]TJ 1.02 0 0 1 150.705 388.351 Tm [(domains)]TJ/F84 9.9626 Tf 1.02 0 0 1 188.452 388.351 Tm [(assigned)-326(to)-325(the)-326(parallel)-325(pr)17(ocesses,)-345(we)-326(classify)-326(the)-325(points)-326(of)-325(a)-326(given)]TJ 1 0 0 1 150.705 376.396 Tm [(sub-domain)-250(as)-250(following.)]TJ +/F84 9.9626 Tf 0.98 0 0 1 265.22 538.064 Tm [(,)-210(even)-198(though)-199(the)-198(r)18(esulting)-198(memory)-199(bottleneck)-198(would)]TJ 1 0 0 1 150.705 526.109 Tm [(make)-250(this)-250(option)-250(unattractive)-250(in)-250(most)-250(cases.)]TJ/F75 11.9552 Tf 0 -33.074 Td [(2.1)-1000(Basic)-250(Nomenclature)]TJ/F84 9.9626 Tf 1.02 0 0 1 150.705 472.73 Tm [(Our)-254(computational)-254(model)-255(implies)-254(that)-254(the)-254(data)-255(alloc)1(ation)-255(on)-254(the)-254(parallel)-254(dis-)]TJ 0.981 0 0 1 150.705 460.774 Tm [(tributed)-253(memory)-254(machine)-254(is)-253(guided)-254(by)-253(the)-254(str)8(uctur)19(e)-254(of)-253(the)-254(physical)-253(model,)-254(and)]TJ 1 0 0 1 150.705 448.819 Tm [(speci\002cally)-250(by)-250(the)-250(discr)18(etization)-250(mesh)-250(of)-250(the)-250(PDE.)]TJ 1.02 0 0 1 165.649 436.172 Tm [(Each)-341(point)-341(of)-341(the)-341(discr)18(etization)-341(mesh)-341(will)-341(have)-341(\050at)-341(least\051)-341(one)-341(associated)]TJ 1.02 0 0 1 150.705 424.216 Tm [(equation/variable,)-353(and)-332(ther)18(efor)17(e)-331(one)-332(index.)-564(W)91(e)-332(say)-332(that)-332(point)]TJ/F78 9.9626 Tf 1 0 0 1 440.497 424.216 Tm [(i)]TJ 1.02 0 0 1 446.831 424.216 Tm [(depends)]TJ/F84 9.9626 Tf 1.02 0 0 1 482.953 424.216 Tm [(on)]TJ 1.02 0 0 1 150.406 412.261 Tm [(point)]TJ/F78 9.9626 Tf 1 0 0 1 177.509 412.261 Tm [(j)]TJ/F84 9.9626 Tf 1.02 0 0 1 183.194 412.261 Tm [(if)-275(the)-274(equation)-275(for)-274(a)-275(variable)-275(associate)1(d)-275(with)]TJ/F78 9.9626 Tf 1 0 0 1 386.696 412.261 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 392.451 412.261 Tm [(contains)-275(a)-274(term)-275(in)]TJ/F78 9.9626 Tf 1 0 0 1 476.753 412.261 Tm [(j)]TJ/F84 9.9626 Tf 1.02 0 0 1 479.647 412.261 Tm [(,)-282(or)]TJ 1.02 0 0 1 150.705 400.306 Tm [(equivalently)-262(if)]TJ/F78 9.9626 Tf 1 0 0 1 218.767 400.306 Tm [(a)]TJ/F78 7.5716 Tf 4.589 -1.96 Td [(i)-67(j)]TJ/F190 10.3811 Tf 8.519 1.96 Td [(6)]TJ/F192 10.3811 Tf 0.249 0 Td [(=)]TJ/F84 9.9626 Tf 1.02 0 0 1 243.403 400.306 Tm [(0.)-354(After)-262(the)-262(partition)-262(of)-262(the)-262(discr)18(etization)-262(mesh)-262(into)]TJ/F78 9.9626 Tf 1.02 0 0 1 478.378 400.306 Tm [(sub-)]TJ 1.02 0 0 1 150.705 388.351 Tm [(domains)]TJ/F84 9.9626 Tf 1.02 0 0 1 188.452 388.351 Tm [(assigned)-326(to)-325(the)-326(parallel)-325(pr)17(ocesses,)-345(we)-326(classify)-326(the)-325(points)-326(of)-325(a)-326(given)]TJ 1 0 0 1 150.705 376.396 Tm [(sub-domain)-250(as)-250(following.)]TJ 0 g 0 G /F75 9.9626 Tf 0 -22.003 Td [(Internal.)]TJ 0 g 0 G @@ -4726,11 +4726,11 @@ BT 0 g 0 G /F75 9.9626 Tf -24.906 -22.695 Td [(Halo.)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 179.925 249.227 Tm [(A)-357(halo)-357(point)-356(for)-357(a)-357(given)-357(domain)-357(is)-357(a)-357(point)-356(belonging)-357(to)-357(another)-357(do-)]TJ 1.009 0 0 1 175.611 237.271 Tm [(main)-248(such)-247(that)-247(ther)17(e)-247(is)-248(a)-247(boundary)-248(point)-247(which)]TJ/F78 9.9626 Tf 1.009 0 0 1 388.252 237.271 Tm [(depends)]TJ/F84 9.9626 Tf 1.009 0 0 1 423.138 237.271 Tm [(on)-247(it.)-308(Whenever)]TJ 1.02 0 0 1 175.313 225.316 Tm [(performing)-297(a)-297(computational)-297(step,)-311(such)-297(as)-297(a)-297(matrix-vector)-297(pr)17(oduct,)-310(the)]TJ 1.012 0 0 1 175.333 213.361 Tm [(values)-247(associated)-247(with)-247(halo)-248(points)-247(ar)18(e)-247(r)18(equested)-248(fr)18(om)-247(other)-247(domains.)-307(A)]TJ 1.005 0 0 1 175.611 201.406 Tm [(boundary)-248(point)-248(of)-248(a)-247(given)-248(domain)-248(is)-248(usually)-248(a)-248(halo)-247(point)-248(for)-248(some)-248(other)]TJ 0.994 0 0 1 175.611 189.451 Tm [(domain)]TJ +/F84 9.9626 Tf 1.02 0 0 1 179.925 249.227 Tm [(A)-357(halo)-357(point)-356(for)-357(a)-357(given)-357(domain)-357(is)-357(a)-357(point)-356(belonging)-357(to)-357(another)-357(do-)]TJ 1.009 0 0 1 175.611 237.271 Tm [(main)-248(such)-247(that)-247(ther)17(e)-247(is)-248(a)-247(boundary)-248(point)-247(which)]TJ/F78 9.9626 Tf 1.009 0 0 1 388.252 237.271 Tm [(depends)]TJ/F84 9.9626 Tf 1.009 0 0 1 423.138 237.271 Tm [(on)-247(it.)-308(Whenever)]TJ 1.02 0 0 1 175.313 225.316 Tm [(performing)-297(a)-297(computational)-297(step,)-311(such)-297(as)-297(a)-297(matrix-vector)-297(pr)17(oduct,)-310(the)]TJ 1.012 0 0 1 175.333 213.361 Tm [(values)-247(associated)-247(with)-247(halo)-248(points)-247(ar)18(e)-247(r)18(equested)-248(fr)18(om)-247(other)-247(domains.)-307(A)]TJ 1.005 0 0 1 175.611 201.406 Tm [(boundary)-248(point)-248(of)-248(a)-247(given)-248(domain)-248(is)-248(usually)-248(a)-248(halo)-247(point)-248(for)-248(some)-248(other)]TJ 0.999 0 0 1 175.611 189.451 Tm [(domain)]TJ 0 0 1 rg 0 0 1 RG -/F84 7.5716 Tf 1 0 0 1 209.41 193.067 Tm [(2)]TJ +/F84 7.5716 Tf 1 0 0 1 209.58 193.067 Tm [(2)]TJ 0 g 0 G -/F84 9.9626 Tf 0.994 0 0 1 213.694 189.451 Tm [(;)-252(ther)18(efor)18(e)-252(the)-252(car)18(d)1(inality)-252(of)-252(the)-252(boundary)-252(points)-252(set)-252(denotes)-252(the)]TJ 1 0 0 1 175.611 177.496 Tm [(amount)-250(of)-250(data)-250(sent)-250(to)-250(other)-250(domains.)]TJ +/F84 9.9626 Tf 0.999 0 0 1 213.864 189.451 Tm [(;)-250(ther)18(efor)18(e)-249(the)-249(car)18(dinality)-250(of)-249(the)-250(boundary)-249(points)-249(set)-250(determines)]TJ 1 0 0 1 175.611 177.496 Tm [(the)-250(amount)-250(of)-250(data)-250(sent)-250(to)-250(other)-250(domains.)]TJ 0 g 0 G ET q @@ -4766,7 +4766,7 @@ BT 1 0 0 rg 1 0 0 RG [-250(3)]TJ 0 g 0 G - [(].)]TJ 0.995 0 0 1 114.839 627.41 Tm [(W)92(e)-251(denote)-251(the)-251(sets)-251(of)-251(internal,)-251(boundary)-251(and)-251(halo)-251(points)-251(for)-251(a)-251(given)-251(subdo-)]TJ 1.001 0 0 1 99.895 615.455 Tm [(main)-250(by)]TJ/F189 10.3811 Tf 1 0 0 1 138.553 615.455 Tm [(I)]TJ/F84 9.9626 Tf 1.001 0 0 1 145.084 615.455 Tm [(,)]TJ/F189 10.3811 Tf 1 0 0 1 150.19 615.455 Tm [(B)]TJ/F84 9.9626 Tf 1.001 0 0 1 159.926 615.455 Tm [(and)]TJ/F189 10.3811 Tf 1 0 0 1 179.422 615.455 Tm [(H)]TJ/F84 9.9626 Tf 1.001 0 0 1 188.394 615.455 Tm [(.)-310(Each)-249(subdomain)-249(is)-250(assigned)-249(to)-250(one)-249(pr)18(ocess;)-250(each)-249(pr)18(ocess)]TJ 1.02 0 0 1 99.895 603.5 Tm [(usually)-286(owns)-285(one)-286(subdomain,)-295(although)-286(the)-285(user)-286(may)-286(choose)-285(to)-286(assign)-285(mor)17(e)]TJ 1.02 0 0 1 99.895 591.545 Tm [(than)-257(one)-257(subdomain)-257(to)-257(a)-257(pr)18(ocess.)-340(If)-257(each)-257(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 322.219 591.545 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 327.794 591.545 Tm [(owns)-257(one)-257(subdomain,)-260(the)]TJ 0.983 0 0 1 99.895 579.589 Tm [(number)-255(of)-255(r)19(ows)-255(in)-255(the)-255(local)-255(sparse)-255(matrix)-255(is)]TJ/F189 10.3811 Tf 1 0 0 1 292.255 579.589 Tm [(j)-24(I)]TJ/F78 7.5716 Tf 8.944 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F191 10.3811 Tf 5.067 0 Td [(+)]TJ/F189 10.3811 Tf 10.258 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.109 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F84 9.9626 Tf 0.983 0 0 1 335.387 579.589 Tm [(,)-255(and)-255(the)-255(number)-255(of)-254(local)]TJ 0.982 0 0 1 99.895 567.634 Tm [(columns)-254(\050i.e.)-316(those)-254(for)-255(which)-254(ther)18(e)-254(exists)-254(at)-255(least)-254(one)-254(non-zer)18(o)-255(ent)1(ry)-255(in)-254(the)-255(local)]TJ 1 0 0 1 99.895 555.679 Tm [(r)18(ows\051)-250(is)]TJ/F189 10.3811 Tf 37.275 0 Td [(j)-24(I)]TJ/F78 7.5716 Tf 8.944 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F191 10.3811 Tf 5.065 0 Td [(+)]TJ/F189 10.3811 Tf 10.256 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.109 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F191 10.3811 Tf 5.065 0 Td [(+)]TJ/F189 10.3811 Tf 10.256 0 Td [(j)-24(H)]TJ/F78 7.5716 Tf 12.052 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F84 9.9626 Tf 3.004 0 Td [(.)]TJ + [(].)]TJ 0.995 0 0 1 114.839 627.41 Tm [(W)92(e)-251(denote)-251(the)-251(sets)-251(of)-251(internal,)-251(boundary)-251(and)-251(halo)-251(points)-251(for)-251(a)-251(given)-251(subdo-)]TJ 1.001 0 0 1 99.895 615.455 Tm [(main)-250(by)]TJ/F190 10.3811 Tf 1 0 0 1 138.553 615.455 Tm [(I)]TJ/F84 9.9626 Tf 1.001 0 0 1 145.084 615.455 Tm [(,)]TJ/F190 10.3811 Tf 1 0 0 1 150.19 615.455 Tm [(B)]TJ/F84 9.9626 Tf 1.001 0 0 1 159.926 615.455 Tm [(and)]TJ/F190 10.3811 Tf 1 0 0 1 179.422 615.455 Tm [(H)]TJ/F84 9.9626 Tf 1.001 0 0 1 188.394 615.455 Tm [(.)-310(Each)-249(subdomain)-249(is)-250(assigned)-249(to)-250(one)-249(pr)18(ocess;)-250(each)-249(pr)18(ocess)]TJ 1.02 0 0 1 99.895 603.5 Tm [(usually)-286(owns)-285(one)-286(subdomain,)-295(although)-286(the)-285(user)-286(may)-286(choose)-285(to)-286(assign)-285(mor)17(e)]TJ 1.02 0 0 1 99.895 591.545 Tm [(than)-257(one)-257(subdomain)-257(to)-257(a)-257(pr)18(ocess.)-340(If)-257(each)-257(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 322.219 591.545 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 327.794 591.545 Tm [(owns)-257(one)-257(subdomain,)-260(the)]TJ 0.983 0 0 1 99.895 579.589 Tm [(number)-255(of)-255(r)19(ows)-255(in)-255(the)-255(local)-255(sparse)-255(matrix)-255(is)]TJ/F190 10.3811 Tf 1 0 0 1 292.255 579.589 Tm [(j)-24(I)]TJ/F78 7.5716 Tf 8.944 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F192 10.3811 Tf 5.067 0 Td [(+)]TJ/F190 10.3811 Tf 10.258 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.109 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F84 9.9626 Tf 0.983 0 0 1 335.387 579.589 Tm [(,)-255(and)-255(the)-255(number)-255(of)-254(local)]TJ 0.982 0 0 1 99.895 567.634 Tm [(columns)-254(\050i.e.)-316(those)-254(for)-255(which)-254(ther)18(e)-254(exists)-254(at)-255(least)-254(one)-254(non-zer)18(o)-255(ent)1(ry)-255(in)-254(the)-255(local)]TJ 1 0 0 1 99.895 555.679 Tm [(r)18(ows\051)-250(is)]TJ/F190 10.3811 Tf 37.275 0 Td [(j)-24(I)]TJ/F78 7.5716 Tf 8.944 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F192 10.3811 Tf 5.065 0 Td [(+)]TJ/F190 10.3811 Tf 10.256 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.109 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F192 10.3811 Tf 5.065 0 Td [(+)]TJ/F190 10.3811 Tf 10.256 0 Td [(j)-24(H)]TJ/F78 7.5716 Tf 12.052 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F84 9.9626 Tf 3.004 0 Td [(.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G @@ -4945,7 +4945,7 @@ stream 0 g 0 G 0 g 0 G BT -/F75 11.9552 Tf 99.895 706.129 Td [(2.3)-1000(Application)-250(structure)]TJ/F84 9.9626 Tf 0.999 0 0 1 99.587 686.748 Tm [(The)-249(main)-249(underlying)-250(principle)-249(of)-249(the)-249(PSBLAS)-250(library)-249(is)-249(that)-249(the)-249(library)-250(objects)]TJ 0.999 0 0 1 99.895 674.792 Tm [(ar)18(e)-251(cr)18(eated)-251(and)-251(exist)-251(with)-251(r)18(efer)18(ence)-251(to)-251(a)-251(discr)18(etized)-251(space)-251(to)-251(which)-251(ther)18(e)-251(corr)18(e-)]TJ 0.98 0 0 1 99.895 662.837 Tm [(sponds)-255(an)-254(index)-255(space)-255(and)-254(a)-255(matrix)-255(sparsity)-254(pattern.)-316(As)-255(an)-255(example,)-255(consider)-254(a)]TJ 1.015 0 0 1 99.895 650.882 Tm [(cell-center)18(ed)-246(\002nite-volume)-246(discr)18(etization)-246(of)-246(the)-246(Navier)18(-Stokes)-246(equations)-245(on)-246(a)]TJ 0.98 0 0 1 99.895 638.927 Tm [(simulation)-233(domain;)-240(the)-233(index)-233(space)-232(1)]TJ 1 0 0 1 261.657 638.927 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 0.98 0 0 1 282.794 638.927 Tm [(is)-233(isomorphic)-233(to)-232(the)-233(set)-233(of)-233(cell)-233(centers,)]TJ 1.02 0 0 1 99.477 626.972 Tm [(wher)18(eas)-332(the)-332(pattern)-332(of)-332(the)-332(associated)-332(linear)-332(system)-332(matrix)-332(is)-332(isomorphic)-332(to)]TJ 1.014 0 0 1 99.895 615.017 Tm [(the)-246(adjacency)-247(gr)1(aph)-247(imposed)-246(on)-246(the)-246(discr)17(etization)-246(mesh)-246(by)-246(the)-247(discr)18(etization)]TJ 1 0 0 1 99.895 603.061 Tm [(stencil.)]TJ 1.02 0 0 1 114.839 590.891 Tm [(Thus)-298(the)-297(\002rst)-298(or)18(der)-298(of)-297(business)-298(is)-298(to)-297(establish)-298(an)-298(i)1(ndex)-298(space,)-311(and)-297(this)-298(is)]TJ 0.989 0 0 1 99.895 578.936 Tm [(done)-253(with)-253(a)-253(call)-253(to)]TJ/F145 9.9626 Tf 1 0 0 1 182.801 578.936 Tm [(psb_cdall)]TJ/F84 9.9626 Tf 0.989 0 0 1 232.368 578.936 Tm [(in)-253(which)-253(we)-253(specify)-253(the)-253(size)-253(of)-253(the)-253(index)-253(space)]TJ/F78 9.9626 Tf 1 0 0 1 437.943 578.936 Tm [(n)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.895 566.98 Tm [(and)-250(the)-249(allocation)-249(of)-250(the)-249(elements)-250(of)-249(the)-250(index)-249(space)-250(to)-249(the)-250(various)-249(pr)17(ocesses)]TJ 1 0 0 1 99.895 555.025 Tm [(making)-250(up)-250(the)-250(MPI)-250(\050virtual\051)-250(parallel)-250(machine.)]TJ 0.987 0 0 1 114.839 542.855 Tm [(The)-254(index)-255(space)-254(is)-254(partitioned)-254(among)-255(pr)19(ocesses,)-255(and)-254(this)-254(cr)18(eates)-255(a)-254(mapping)]TJ 1.02 0 0 1 99.895 530.899 Tm [(fr)18(om)-313(the)-312(\223global\224)-313(numbering)-312(1)]TJ 1 0 0 1 243.306 530.899 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 1.02 0 0 1 265.345 530.899 Tm [(to)-312(a)-313(numbering)-312(\223local\224)-313(to)-312(each)-312(pr)17(ocess;)]TJ 1.02 0 0 1 99.895 518.944 Tm [(each)-357(pr)17(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 161.071 518.944 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 167.665 518.944 Tm [(will)-357(own)-357(a)-358(certain)-357(subset)-357(1)]TJ 1 0 0 1 294.248 518.944 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 5.664 -1.494 Td [(r)18(ow)]TJ/F78 5.9776 Tf 17.537 -1.649 Td [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 333.423 518.944 Tm [(,)-385(each)-357(element)-358(of)-357(which)]TJ 1.004 0 0 1 99.895 506.989 Tm [(corr)18(esponds)-250(to)-249(a)-250(certain)-249(element)-250(of)-249(1)]TJ 1 0 0 1 263.855 506.989 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 1.004 0 0 1 282.719 506.989 Tm [(.)-310(The)-250(user)-250(does)-249(not)-250(set)-249(explicitly)-250(this)]TJ 0.987 0 0 1 99.895 495.034 Tm [(mapping;)-253(when)-254(the)-253(application)-253(needs)-254(to)-253(indicate)-253(to)-254(which)-253(element)-253(of)-254(the)-253(index)]TJ 1.02 0 0 1 99.895 483.079 Tm [(space)-263(a)-262(certain)-263(item)-263(is)-262(r)17(elated,)-267(such)-262(as)-263(the)-263(r)18(ow)-263(and)-263(colu)1(mn)-263(index)-263(of)-263(a)-262(matrix)]TJ 1.011 0 0 1 99.895 471.124 Tm [(coef)18(\002cient,)-246(it)-247(does)-246(so)-246(in)-246(the)-246(\223global\224)-247(numbering,)-246(and)-246(the)-246(library)-247(will)-246(translate)]TJ 1 0 0 1 99.895 459.168 Tm [(into)-250(the)-250(appr)18(opriate)-250(\223local\224)-250(numbering.)]TJ 0.98 0 0 1 114.839 446.998 Tm [(For)-242(a)-242(given)-241(index)-242(space)-242(1)]TJ 1 0 0 1 225.057 446.998 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 0.98 0 0 1 246.282 446.998 Tm [(ther)18(e)-241(ar)18(e)-242(many)-242(possible)-242(associat)1(ed)-242(topologies,)]TJ 0.98 0 0 1 99.895 435.043 Tm [(i.e.)-308(many)-230(dif)18(fer)18(ent)-230(discr)19(etization)-230(stencils;)-239(thus)-230(the)-230(description)-230(of)-230(the)-230(index)-230(space)]TJ 1.011 0 0 1 99.895 423.087 Tm [(is)-247(not)-247(completed)-248(until)-247(the)-247(user)-247(has)-247(de\002ned)-248(a)-247(sparsity)-247(pattern,)-247(either)-247(explicitly)]TJ 0.98 0 0 1 99.895 411.132 Tm [(thr)18(ough)]TJ/F145 9.9626 Tf 1 0 0 1 137.076 411.132 Tm [(psb_cdins)]TJ/F84 9.9626 Tf 0.98 0 0 1 186.458 411.132 Tm [(or)-237(imp)1(licitly)-237(thr)18(ough)]TJ/F145 9.9626 Tf 1 0 0 1 279.084 411.132 Tm [(psb_spins)]TJ/F84 9.9626 Tf 0.98 0 0 1 326.157 411.132 Tm [(.)-310(The)-237(descriptor)-236(is)-237(\002nalized)]TJ 1.02 0 0 1 99.477 399.177 Tm [(with)-294(a)-294(call)-293(to)]TJ/F145 9.9626 Tf 1 0 0 1 161.528 399.177 Tm [(psb_cdasb)]TJ/F84 9.9626 Tf 1.02 0 0 1 211.587 399.177 Tm [(and)-294(a)-294(sparse)-293(matrix)-294(with)-294(a)-294(call)-294(to)]TJ/F145 9.9626 Tf 1 0 0 1 366.134 399.177 Tm [(psb_spasb)]TJ/F84 9.9626 Tf 1.02 0 0 1 413.207 399.177 Tm [(.)-450(After)]TJ/F145 9.9626 Tf 1 0 0 1 99.895 387.222 Tm [(psb_cdasb)]TJ/F84 9.9626 Tf 1.001 0 0 1 149.464 387.222 Tm [(each)-250(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 207.364 387.222 Tm [(i)]TJ/F84 9.9626 Tf 1.001 0 0 1 212.823 387.222 Tm [(will)-250(have)-250(de\002ned)-251(a)-250(set)-250(of)-250(\223halo\224)-250(\050or)-251(\223ghost\224\051)-250(indices)]TJ/F78 9.9626 Tf 1 0 0 1 100.02 375.267 Tm [(n)]TJ/F84 9.9626 Tf 5.664 -1.495 Td [(r)18(ow)]TJ/F78 5.9776 Tf 17.537 -1.648 Td [(i)]TJ/F191 10.3811 Tf 4.654 3.143 Td [(+)]TJ/F84 9.9626 Tf 0.98 0 0 1 137.825 375.267 Tm [(1)]TJ 1 0 0 1 144.492 375.267 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 5.664 -3.831 Td [(col)]TJ/F78 5.9776 Tf 12.795 -1.648 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 178.925 375.267 Tm [(,)-239(denoting)-235(elements)-235(of)-235(the)-235(index)-235(space)-235(that)-235(ar)18(e)]TJ/F78 9.9626 Tf 0.98 0 0 1 379.735 375.267 Tm [(not)]TJ/F84 9.9626 Tf 0.98 0 0 1 395.044 375.267 Tm [(assigned)-235(to)]TJ 1.01 0 0 1 99.596 361.477 Tm [(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 135.289 361.477 Tm [(i)]TJ/F84 9.9626 Tf 1.01 0 0 1 138.252 361.477 Tm [(;)-247(however)-246(the)-247(variables)-246(associated)-247(with)-246(them)-247(ar)18(e)-247(needed)-246(to)-247(complete)]TJ 1.02 0 0 1 99.895 349.522 Tm [(computations)-284(associated)-284(with)-285(the)-284(sparse)-284(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 318.756 349.522 Tm [(A)]TJ/F84 9.9626 Tf 1.02 0 0 1 326.074 349.522 Tm [(,)-294(and)-284(thus)-284(they)-285(have)-284(to)-284(be)]TJ 1.02 0 0 1 99.895 337.567 Tm [(fetched)-303(fr)18(om)-304(\050neighbouring\051)-303(pr)18(ocesses.)-478(The)-303(descriptor)-303(of)-303(the)-303(index)-304(space)-303(is)]TJ 1.007 0 0 1 99.895 325.612 Tm [(built)-249(exactly)-248(for)-249(the)-249(purpose)-249(of)-248(pr)17(op)1(erly)-249(sequencing)-249(the)-249(communication)-248(steps)]TJ 1 0 0 1 99.895 313.656 Tm [(r)18(equir)18(ed)-250(to)-250(achieve)-250(this)-250(objective.)]TJ 0.987 0 0 1 114.839 301.486 Tm [(A)-253(simple)-253(application)-254(str)8(u)1(ctur)18(e)-253(will)-254(walk)-253(thr)18(ough)-253(the)-253(index)-253(space)-253(allocation,)]TJ 1 0 0 1 99.895 289.531 Tm [(matrix/vector)-250(cr)18(eation)-250(and)-250(linear)-250(system)-250(solution)-250(as)-250(follows:)]TJ +/F75 11.9552 Tf 99.895 706.129 Td [(2.3)-1000(Application)-250(structure)]TJ/F84 9.9626 Tf 0.999 0 0 1 99.587 686.748 Tm [(The)-249(main)-249(underlying)-250(principle)-249(of)-249(the)-249(PSBLAS)-250(library)-249(is)-249(that)-249(the)-249(library)-250(objects)]TJ 0.999 0 0 1 99.895 674.792 Tm [(ar)18(e)-251(cr)18(eated)-251(and)-251(exist)-251(with)-251(r)18(efer)18(ence)-251(to)-251(a)-251(discr)18(etized)-251(space)-251(to)-251(which)-251(ther)18(e)-251(corr)18(e-)]TJ 0.98 0 0 1 99.895 662.837 Tm [(sponds)-255(an)-254(index)-255(space)-255(and)-254(a)-255(matrix)-255(sparsity)-254(pattern.)-316(As)-255(an)-255(example,)-255(consider)-254(a)]TJ 1.015 0 0 1 99.895 650.882 Tm [(cell-center)18(ed)-246(\002nite-volume)-246(discr)18(etization)-246(of)-246(the)-246(Navier)18(-Stokes)-246(equations)-245(on)-246(a)]TJ 0.98 0 0 1 99.895 638.927 Tm [(simulation)-233(domain;)-240(the)-233(index)-233(space)-232(1)]TJ 1 0 0 1 261.657 638.927 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 0.98 0 0 1 282.794 638.927 Tm [(is)-233(isomorphic)-233(to)-232(the)-233(set)-233(of)-233(cell)-233(centers,)]TJ 1.02 0 0 1 99.477 626.972 Tm [(wher)18(eas)-332(the)-332(pattern)-332(of)-332(the)-332(associated)-332(linear)-332(system)-332(matrix)-332(is)-332(isomorphic)-332(to)]TJ 1.014 0 0 1 99.895 615.017 Tm [(the)-246(adjacency)-247(gr)1(aph)-247(imposed)-246(on)-246(the)-246(discr)17(etization)-246(mesh)-246(by)-246(the)-247(discr)18(etization)]TJ 1 0 0 1 99.895 603.061 Tm [(stencil.)]TJ 1.02 0 0 1 114.839 590.891 Tm [(Thus)-298(the)-297(\002rst)-298(or)18(der)-298(of)-297(business)-298(is)-298(to)-297(establish)-298(an)-298(i)1(ndex)-298(space,)-311(and)-297(this)-298(is)]TJ 0.989 0 0 1 99.895 578.936 Tm [(done)-253(with)-253(a)-253(call)-253(to)]TJ/F145 9.9626 Tf 1 0 0 1 182.801 578.936 Tm [(psb_cdall)]TJ/F84 9.9626 Tf 0.989 0 0 1 232.368 578.936 Tm [(in)-253(which)-253(we)-253(specify)-253(the)-253(size)-253(of)-253(the)-253(index)-253(space)]TJ/F78 9.9626 Tf 1 0 0 1 437.943 578.936 Tm [(n)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.895 566.98 Tm [(and)-250(the)-249(allocation)-249(of)-250(the)-249(elements)-250(of)-249(the)-250(index)-249(space)-250(to)-249(the)-250(various)-249(pr)17(ocesses)]TJ 1 0 0 1 99.895 555.025 Tm [(making)-250(up)-250(the)-250(MPI)-250(\050virtual\051)-250(parallel)-250(machine.)]TJ 0.987 0 0 1 114.839 542.855 Tm [(The)-254(index)-255(space)-254(is)-254(partitioned)-254(among)-255(pr)19(ocesses,)-255(and)-254(this)-254(cr)18(eates)-255(a)-254(mapping)]TJ 1.02 0 0 1 99.895 530.899 Tm [(fr)18(om)-313(the)-312(\223global\224)-313(numbering)-312(1)]TJ 1 0 0 1 243.306 530.899 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)]TJ/F84 9.9626 Tf 1.02 0 0 1 265.345 530.899 Tm [(to)-312(a)-313(numbering)-312(\223local\224)-313(to)-312(each)-312(pr)17(ocess;)]TJ 1.02 0 0 1 99.895 518.944 Tm [(each)-357(pr)17(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 161.071 518.944 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 167.665 518.944 Tm [(will)-357(own)-357(a)-358(certain)-357(subset)-357(1)]TJ 1 0 0 1 294.248 518.944 Tm 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[(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F192 10.3811 Tf 2.875 1.96 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(j)]TJ/F192 10.3811 Tf 3.128 0 Td [(\051)]TJ/F145 9.9626 Tf -225.617 -22.974 Td [(psb_geamax\050x,)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G [-525(desc_a,)]TJ @@ -11207,7 +11207,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 151.016 706.129 Td [(geamaxs)-250(\227)-250(Generalized)-250(In\002nity)-250(Norm)]TJ/F84 9.9626 Tf 1.003 0 0 1 99.587 687.165 Tm [(This)-250(subr)18(outine)-250(computes)-250(a)-251(seri)1(es)-251(of)-250(in\002nity)-250(norms)-250(on)-250(the)-250(columns)-250(of)-251(a)-250(dense)]TJ 1 0 0 1 99.895 675.21 Tm [(matrix)]TJ/F78 9.9626 Tf 31.786 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 88.54 -11.955 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 12.293 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 7.041 0 Td [(\040)]TJ/F84 9.9626 Tf 13.273 0 Td [(max)]TJ/F78 7.5716 Tf 7.76 -7.336 Td [(k)]TJ/F189 10.3811 Tf 12.944 7.336 Td [(j)]TJ/F78 9.9626 Tf 3.298 0 Td [(x)]TJ/F191 10.3811 Tf 5.329 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(k)]TJ/F84 9.9626 Tf 4.598 0 Td [(,)]TJ/F78 9.9626 Tf 4.206 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(j)]TJ +/F75 11.9552 Tf 151.016 706.129 Td [(geamaxs)-250(\227)-250(Generalized)-250(In\002nity)-250(Norm)]TJ/F84 9.9626 Tf 1.003 0 0 1 99.587 687.165 Tm [(This)-250(subr)18(outine)-250(computes)-250(a)-251(seri)1(es)-251(of)-250(in\002nity)-250(norms)-250(on)-250(the)-250(columns)-250(of)-251(a)-250(dense)]TJ 1 0 0 1 99.895 675.21 Tm [(matrix)]TJ/F78 9.9626 Tf 31.786 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 88.54 -11.955 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 12.293 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.041 0 Td [(\040)]TJ/F84 9.9626 Tf 13.273 0 Td [(max)]TJ/F78 7.5716 Tf 7.76 -7.336 Td [(k)]TJ/F190 10.3811 Tf 12.944 7.336 Td [(j)]TJ/F78 9.9626 Tf 3.298 0 Td [(x)]TJ/F192 10.3811 Tf 5.329 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(k)]TJ/F84 9.9626 Tf 4.598 0 Td [(,)]TJ/F78 9.9626 Tf 4.206 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(j)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G 0.00 0.44 0.13 rg 0.00 0.44 0.13 RG @@ -11380,7 +11380,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 201.825 706.129 Td [(norm1)-250(\227)-250(1-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf -51.429 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(1-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 125.989 -21.269 Td [(a)-25(s)-25(u)-25(m)]TJ/F189 10.3811 Tf 25.353 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.006 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F84 9.9626 Tf -195.526 -21.269 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 71.974 -21.269 Td [(a)-25(s)-25(u)-25(m)]TJ/F189 10.3811 Tf 25.353 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 18.737 0 Td [(r)-17(e)]TJ/F191 10.3811 Tf 8.169 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F191 10.3811 Tf 6.346 1.858 Td [(+)]TJ/F189 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.369 0 Td [(i)-32(m)]TJ/F191 10.3811 Tf 11.089 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F145 9.9626 Tf -216.928 -19.411 Td [(psb_geasum\050x,)]TJ +/F75 11.9552 Tf 201.825 706.129 Td [(norm1)-250(\227)-250(1-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf -51.429 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(1-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 125.989 -21.269 Td [(a)-25(s)-25(u)-25(m)]TJ/F190 10.3811 Tf 25.353 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.006 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F84 9.9626 Tf -195.526 -21.269 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 71.974 -21.269 Td [(a)-25(s)-25(u)-25(m)]TJ/F190 10.3811 Tf 25.353 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 18.737 0 Td [(r)-17(e)]TJ/F192 10.3811 Tf 8.169 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F192 10.3811 Tf 6.346 1.858 Td [(+)]TJ/F190 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.369 0 Td [(i)-32(m)]TJ/F192 10.3811 Tf 11.089 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F145 9.9626 Tf -216.928 -19.411 Td [(psb_geasum\050x,)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G [-525(desc_a,)]TJ @@ -11658,7 +11658,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 201.825 706.129 Td [(geasums)-250(\227)-250(Generalized)-250(1-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf 0.988 0 0 1 150.396 685.937 Tm [(This)-253(subr)18(outine)-253(computes)-253(a)-253(series)-253(of)-253(1-norms)-253(on)-253(the)-254(co)1(lumns)-254(of)-253(a)-253(dense)-253(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 150.999 673.982 Tm [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 120.031 -13.856 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 7.042 0 Td [(\040)]TJ/F84 9.9626 Tf 13.273 0 Td [(max)]TJ/F78 7.5716 Tf 7.759 -7.335 Td [(k)]TJ/F189 10.3811 Tf 12.944 7.335 Td [(j)]TJ/F78 9.9626 Tf 3.298 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(k)]TJ/F84 9.9626 Tf 4.598 0 Td [(,)]TJ/F78 9.9626 Tf 4.206 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(j)]TJ/F84 9.9626 Tf -215.511 -24.535 Td [(This)-250(function)-250(computes)-250(the)-250(1-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 125.227 -23.185 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 7.042 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.006 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F84 9.9626 Tf -196.039 -23.185 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 71.212 -23.185 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 7.041 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 18.738 0 Td [(r)-17(e)]TJ/F191 10.3811 Tf 8.169 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F191 10.3811 Tf 6.346 1.858 Td [(+)]TJ/F189 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.369 0 Td [(i)-32(m)]TJ/F191 10.3811 Tf 11.089 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ +/F75 11.9552 Tf 201.825 706.129 Td [(geasums)-250(\227)-250(Generalized)-250(1-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf 0.988 0 0 1 150.396 685.937 Tm [(This)-253(subr)18(outine)-253(computes)-253(a)-253(series)-253(of)-253(1-norms)-253(on)-253(the)-254(co)1(lumns)-254(of)-253(a)-253(dense)-253(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 150.999 673.982 Tm [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 120.031 -13.856 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.042 0 Td [(\040)]TJ/F84 9.9626 Tf 13.273 0 Td [(max)]TJ/F78 7.5716 Tf 7.759 -7.335 Td [(k)]TJ/F190 10.3811 Tf 12.944 7.335 Td [(j)]TJ/F78 9.9626 Tf 3.298 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(k)]TJ/F84 9.9626 Tf 4.598 0 Td [(,)]TJ/F78 9.9626 Tf 4.206 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(j)]TJ/F84 9.9626 Tf -215.511 -24.535 Td [(This)-250(function)-250(computes)-250(the)-250(1-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 125.227 -23.185 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.042 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.006 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F84 9.9626 Tf -196.039 -23.185 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(1-norm)-250(as:)]TJ/F78 9.9626 Tf 71.212 -23.185 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.041 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 18.738 0 Td [(r)-17(e)]TJ/F192 10.3811 Tf 8.169 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ/F192 10.3811 Tf 6.346 1.858 Td [(+)]TJ/F190 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.369 0 Td [(i)-32(m)]TJ/F192 10.3811 Tf 11.089 0 Td [(\050)]TJ/F78 9.9626 Tf 4.443 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\051)]TJ/F190 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.858 Td [(1)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G 0.00 0.44 0.13 rg 0.00 0.44 0.13 RG @@ -11846,14 +11846,14 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 201.825 706.129 Td [(norm2)-250(\227)-250(2-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf -51.429 -20.076 Td [(This)-250(function)-250(computes)-250(the)-250(2-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(2-norm)-250(as:)]TJ/F78 9.9626 Tf 122.551 -25.46 Td [(n)-15(r)-35(m)]TJ/F84 9.9626 Tf 17.788 0 Td [(2)]TJ/F189 10.3811 Tf 7.873 0 Td [(\040)]TJ 13.398 9.727 Td [(p)]TJ +/F75 11.9552 Tf 201.825 706.129 Td [(norm2)-250(\227)-250(2-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf -51.429 -20.076 Td [(This)-250(function)-250(computes)-250(the)-250(2-norm)-250(of)-250(a)-250(vector)]TJ/F78 9.9626 Tf 206.349 0 Td [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(.)]TJ -211.245 -11.955 Td [(If)]TJ/F78 9.9626 Tf 9.459 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(r)18(eal)-250(vector)-250(it)-250(computes)-250(2-norm)-250(as:)]TJ/F78 9.9626 Tf 122.551 -25.46 Td [(n)-15(r)-35(m)]TJ/F84 9.9626 Tf 17.788 0 Td [(2)]TJ/F190 10.3811 Tf 7.873 0 Td [(\040)]TJ 13.398 9.727 Td [(p)]TJ ET q 1 0 0 1 338.242 658.569 cm []0 d 0 J 0.408 w 0 0 m 16.592 0 l S Q BT -/F78 9.9626 Tf 338.536 648.638 Td [(x)]TJ/F78 7.5716 Tf 5.398 2.88 Td [(T)]TJ/F78 9.9626 Tf 5.695 -2.88 Td [(x)]TJ/F84 9.9626 Tf -198.924 -23.065 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(2-norm)-250(as:)]TJ/F78 9.9626 Tf 103.113 -25.46 Td [(n)-15(r)-35(m)]TJ/F84 9.9626 Tf 17.788 0 Td [(2)]TJ/F189 10.3811 Tf 7.873 0 Td [(\040)]TJ 13.398 9.727 Td [(p)]TJ +/F78 9.9626 Tf 338.536 648.638 Td [(x)]TJ/F78 7.5716 Tf 5.398 2.88 Td [(T)]TJ/F78 9.9626 Tf 5.695 -2.88 Td [(x)]TJ/F84 9.9626 Tf -198.924 -23.065 Td [(else)-250(if)]TJ/F78 9.9626 Tf 28.159 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(is)-250(a)-250(complex)-250(vector)-250(then)-250(it)-250(computes)-250(2-norm)-250(as:)]TJ/F78 9.9626 Tf 103.113 -25.46 Td [(n)-15(r)-35(m)]TJ/F84 9.9626 Tf 17.788 0 Td [(2)]TJ/F190 10.3811 Tf 7.873 0 Td [(\040)]TJ 13.398 9.727 Td [(p)]TJ ET q 1 0 0 1 337.504 610.044 cm @@ -12120,7 +12120,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 201.825 706.129 Td [(genrm2s)-250(\227)-250(Generalized)-250(2-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf 0.988 0 0 1 150.396 687.165 Tm [(This)-253(subr)18(outine)-253(computes)-253(a)-253(series)-253(of)-253(2-norms)-253(on)-253(the)-254(co)1(lumns)-254(of)-253(a)-253(dense)-253(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 150.999 675.21 Tm [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 126.859 -11.955 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 7.041 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.007 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\050)]TJ/F84 9.9626 Tf 4.274 0 Td [(:)-12(,)]TJ/F78 9.9626 Tf 6.821 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ +/F75 11.9552 Tf 201.825 706.129 Td [(genrm2s)-250(\227)-250(Generalized)-250(2-Norm)-250(of)-250(V)111(ector)]TJ/F84 9.9626 Tf 0.988 0 0 1 150.396 687.165 Tm [(This)-253(subr)18(outine)-253(computes)-253(a)-253(series)-253(of)-253(2-norms)-253(on)-253(the)-254(co)1(lumns)-254(of)-253(a)-253(dense)-253(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 150.999 675.21 Tm [(x)]TJ/F84 9.9626 Tf 5.205 0 Td [(:)]TJ/F78 9.9626 Tf 126.859 -11.955 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 12.294 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.041 0 Td [(\040)-291(k)]TJ/F78 9.9626 Tf 19.007 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\050)]TJ/F84 9.9626 Tf 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-16.09 Td [(y)]TJ/F189 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F189 7.8896 Tf 6.546 4.114 Td [(\000)]TJ/F78 7.5716 Tf 6.42 0 Td [(T)]TJ/F78 9.9626 Tf 5.725 -4.114 Td [(D)-52(x)]TJ/F191 10.3811 Tf 15.536 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.648 0 Td [(y)]TJ -91.804 -16.091 Td [(y)]TJ/F189 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F189 7.8896 Tf 6.546 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.609 0 Td [(H)]TJ/F78 9.9626 Tf 6.982 -4.115 Td [(x)]TJ/F191 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -84.982 -16.09 Td [(y)]TJ/F189 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.709 0 Td [(D)-48(T)]TJ/F189 7.8896 Tf 14.774 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.61 0 Td [(H)]TJ/F78 9.9626 Tf 6.982 -4.115 Td [(x)]TJ/F191 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -93.281 -16.09 Td [(y)]TJ/F189 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F189 7.8896 Tf 6.545 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.61 0 Td [(H)]TJ/F78 9.9626 Tf 7.012 -4.115 Td [(D)-52(x)]TJ/F191 10.3811 Tf 15.536 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ/F84 9.9626 Tf -201.062 -38.202 Td [(wher)18(e:)]TJ +/F75 11.9552 Tf 156.993 706.129 Td [(spsm)-250(\227)-250(T)111(riangular)-250(System)-250(Solve)]TJ/F84 9.9626 Tf -57.406 -19.83 Td [(This)-250(subr)18(outine)-250(computes)-250(the)-250(T)90(riangular)-250(System)-250(Solve:)]TJ/F78 9.9626 Tf 123.033 -35.213 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.546 4.115 Td [(\000)]TJ/F84 7.5716 Tf 6.227 0 Td [(1)]TJ/F78 9.9626 Tf 4.578 -4.115 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -82.196 -16.139 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.709 0 Td [(D)-48(T)]TJ/F190 7.8896 Tf 14.774 4.114 Td [(\000)]TJ/F84 7.5716 Tf 6.228 0 Td [(1)]TJ/F78 9.9626 Tf 4.578 -4.114 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -90.495 -16.139 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.546 4.114 Td [(\000)]TJ/F84 7.5716 Tf 6.227 0 Td [(1)]TJ/F78 9.9626 Tf 4.608 -4.114 Td [(D)-52(x)]TJ/F192 10.3811 Tf 15.536 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -90.495 -16.09 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.546 4.114 Td [(\000)]TJ/F78 7.5716 Tf 6.42 0 Td [(T)]TJ/F78 9.9626 Tf 5.695 -4.114 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -83.506 -16.09 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.709 0 Td [(D)-48(T)]TJ/F190 7.8896 Tf 14.774 4.114 Td [(\000)]TJ/F78 7.5716 Tf 6.421 0 Td [(T)]TJ/F78 9.9626 Tf 5.695 -4.114 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.648 0 Td [(y)]TJ -91.804 -16.09 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.546 4.114 Td [(\000)]TJ/F78 7.5716 Tf 6.42 0 Td [(T)]TJ/F78 9.9626 Tf 5.725 -4.114 Td [(D)-52(x)]TJ/F192 10.3811 Tf 15.536 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.648 0 Td [(y)]TJ -91.804 -16.091 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.546 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.609 0 Td [(H)]TJ/F78 9.9626 Tf 6.982 -4.115 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -84.982 -16.09 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.709 0 Td [(D)-48(T)]TJ/F190 7.8896 Tf 14.774 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.61 0 Td [(H)]TJ/F78 9.9626 Tf 6.982 -4.115 Td [(x)]TJ/F192 10.3811 Tf 7.267 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ -93.281 -16.09 Td [(y)]TJ/F190 10.3811 Tf 15.193 0 Td [(\040)]TJ/F147 9.9626 Tf 20.592 0 Td [(a)]TJ/F78 9.9626 Tf 5.639 0 Td [(T)]TJ/F190 7.8896 Tf 6.545 4.115 Td [(\000)]TJ/F78 7.5716 Tf 6.61 0 Td [(H)]TJ/F78 9.9626 Tf 7.012 -4.115 Td [(D)-52(x)]TJ/F192 10.3811 Tf 15.536 0 Td [(+)]TJ/F147 9.9626 Tf 10.505 0 Td [(b)]TJ/F78 9.9626 Tf 5.649 0 Td [(y)]TJ/F84 9.9626 Tf -201.062 -38.202 Td [(wher)18(e:)]TJ 0 g 0 G /F78 9.9626 Tf -14.65 -21.265 Td [(x)]TJ 0 g 0 G @@ -13870,7 +13870,7 @@ BT 0 g 0 G /F75 9.9626 Tf -50.869 -16.302 Td [(trans)-250(=)-250('C')]TJ 0 g 0 G -/F84 9.9626 Tf 51.417 0 Td [(the)-250(operation)-250(is)-250(with)-250(conjugate)-250(transposed)-250(matrix.)]TJ -51.417 -20.65 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.956 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(t)-15(r)-50(a)-25(n)-25(s)]TJ/F191 10.3811 Tf 25.193 0 Td [(=)]TJ/F78 9.9626 Tf 11.435 0 Td [(N)]TJ/F84 9.9626 Tf -75.268 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(character)-250(variable.)]TJ +/F84 9.9626 Tf 51.417 0 Td [(the)-250(operation)-250(is)-250(with)-250(conjugate)-250(transposed)-250(matrix.)]TJ -51.417 -20.65 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.956 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(t)-15(r)-50(a)-25(n)-25(s)]TJ/F192 10.3811 Tf 25.193 0 Td [(=)]TJ/F78 9.9626 Tf 11.435 0 Td [(N)]TJ/F84 9.9626 Tf -75.268 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(character)-250(variable.)]TJ 0 g 0 G /F75 9.9626 Tf -24.906 -20.65 Td [(unitd)]TJ 0 g 0 G @@ -13902,7 +13902,7 @@ stream 0 g 0 G 0 g 0 G BT -/F84 9.9626 Tf 124.802 706.129 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(u)-25(n)-18(i)-32(t)-25(d)]TJ/F191 10.3811 Tf 26.159 0 Td [(=)]TJ/F78 9.9626 Tf 10.927 0 Td [(U)]TJ/F84 9.9626 Tf -75.726 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(character)-250(variable.)]TJ +/F84 9.9626 Tf 124.802 706.129 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(u)-25(n)-18(i)-32(t)-25(d)]TJ/F192 10.3811 Tf 26.159 0 Td [(=)]TJ/F78 9.9626 Tf 10.927 0 Td [(U)]TJ/F84 9.9626 Tf -75.726 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(character)-250(variable.)]TJ 0 g 0 G /F75 9.9626 Tf -24.907 -19.925 Td [(choice)]TJ 0 g 0 G @@ -13922,7 +13922,7 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -19.925 Td [(diag)]TJ 0 g 0 G -/F84 9.9626 Tf 24.907 0 Td [(the)-250(diagonal)-250(scaling)-250(matrix.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(d)-18(i)-47(a)-47(g)]TJ/F191 10.3811 Tf 18.52 0 Td [(\050)]TJ/F84 9.9626 Tf 4.149 0 Td [(1)]TJ/F191 10.3811 Tf 5.106 0 Td [(\051)-289(=)]TJ/F84 9.9626 Tf 18.003 0 Td [(1)]TJ/F191 10.3811 Tf 5.106 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)-25(o)-35(s)-25(c)-40(a)-25(l)-48(i)-32(n)-47(g)]TJ/F191 10.3811 Tf 41.384 0 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 124.802 423.19 Tm [(Speci\002ed)-253(as:)-316(a)-253(rank)-254(one)-253(array)-254(containing)-253(numbers)-253(of)-254(the)-253(type)-254(indicated)-253(in)]TJ 1 0 0 1 124.493 411.235 Tm [(T)92(able)]TJ +/F84 9.9626 Tf 24.907 0 Td [(the)-250(diagonal)-250(scaling)-250(matrix.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.64 0 Td [(d)-18(i)-47(a)-47(g)]TJ/F192 10.3811 Tf 18.52 0 Td [(\050)]TJ/F84 9.9626 Tf 4.149 0 Td [(1)]TJ/F192 10.3811 Tf 5.106 0 Td [(\051)-289(=)]TJ/F84 9.9626 Tf 18.003 0 Td [(1)]TJ/F192 10.3811 Tf 5.106 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)-25(o)-35(s)-25(c)-40(a)-25(l)-48(i)-32(n)-47(g)]TJ/F192 10.3811 Tf 41.384 0 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 124.802 423.19 Tm [(Speci\002ed)-253(as:)-316(a)-253(rank)-254(one)-253(array)-254(containing)-253(numbers)-253(of)-254(the)-253(type)-254(indicated)-253(in)]TJ 1 0 0 1 124.493 411.235 Tm [(T)92(able)]TJ 0 0 1 rg 0 0 1 RG [-250(13)]TJ 0 g 0 G @@ -13968,7 +13968,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 207.803 706.129 Td [(gemlt)-250(\227)-250(Entrywise)-250(Product)]TJ/F84 9.9626 Tf -57.407 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(entrywise)-250(pr)18(oduct)-250(between)-250(two)-250(vectors)]TJ/F78 9.9626 Tf 299.677 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(and)]TJ/F78 9.9626 Tf 19.482 0 Td [(y)]TJ -187.61 -21.112 Td [(d)-25(o)-35(t)]TJ/F189 10.3811 Tf 16.337 0 Td [(\040)]TJ/F78 9.9626 Tf 13.566 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F78 9.9626 Tf 4.274 0 Td [(y)]TJ/F191 10.3811 Tf 5.23 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.089 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ/F145 9.9626 Tf -187.464 -21.111 Td [(psb_gemlt\050x,)]TJ +/F75 11.9552 Tf 207.803 706.129 Td [(gemlt)-250(\227)-250(Entrywise)-250(Product)]TJ/F84 9.9626 Tf -57.407 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(entrywise)-250(pr)18(oduct)-250(between)-250(two)-250(vectors)]TJ/F78 9.9626 Tf 299.677 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(and)]TJ/F78 9.9626 Tf 19.482 0 Td [(y)]TJ -187.61 -21.112 Td [(d)-25(o)-35(t)]TJ/F190 10.3811 Tf 16.337 0 Td [(\040)]TJ/F78 9.9626 Tf 13.566 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F78 9.9626 Tf 4.274 0 Td [(y)]TJ/F192 10.3811 Tf 5.23 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.089 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ/F145 9.9626 Tf -187.464 -21.111 Td [(psb_gemlt\050x,)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G [-525(y,)]TJ @@ -14213,7 +14213,7 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 207.803 706.129 Td [(gediv)-250(\227)-250(Entrywise)-250(Division)]TJ/F84 9.9626 Tf -57.407 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(entrywise)-250(division)-250(between)-250(two)-250(vectors)]TJ/F78 9.9626 Tf 300.604 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(and)]TJ/F78 9.9626 Tf 19.481 0 Td [(y)]TJ/F84 9.9626 Tf -188.038 -21.112 Td [(/)]TJ/F189 10.3811 Tf 9.054 0 Td [(\040)]TJ/F78 9.9626 Tf 13.567 0 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 4.274 0 Td [(/)]TJ/F78 9.9626 Tf 6.287 0 Td [(y)]TJ/F191 10.3811 Tf 5.23 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.089 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ/F145 9.9626 Tf -186.966 -21.111 Td [(psb_gediv\050x,)]TJ +/F75 11.9552 Tf 207.803 706.129 Td [(gediv)-250(\227)-250(Entrywise)-250(Division)]TJ/F84 9.9626 Tf -57.407 -18.964 Td [(This)-250(function)-250(computes)-250(the)-250(entrywise)-250(division)-250(between)-250(two)-250(vectors)]TJ/F78 9.9626 Tf 300.604 0 Td [(x)]TJ/F84 9.9626 Tf 7.696 0 Td [(and)]TJ/F78 9.9626 Tf 19.481 0 Td [(y)]TJ/F84 9.9626 Tf -188.038 -21.112 Td [(/)]TJ/F190 10.3811 Tf 9.054 0 Td [(\040)]TJ/F78 9.9626 Tf 13.567 0 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 4.274 0 Td [(/)]TJ/F78 9.9626 Tf 6.287 0 Td [(y)]TJ/F192 10.3811 Tf 5.23 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.089 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ/F145 9.9626 Tf -186.966 -21.111 Td [(psb_gediv\050x,)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G [-525(y,)]TJ @@ -14386,7 +14386,7 @@ BT 0 g 0 G /F75 9.9626 Tf -222.214 -19.602 Td [(\003ag)]TJ 0 g 0 G -/F84 9.9626 Tf 0.994 0 0 1 172.294 243.218 Tm [(check)-252(if)-252(any)-252(of)-251(the)]TJ/F78 9.9626 Tf 1 0 0 1 254.535 243.218 Tm [(y)]TJ/F191 10.3811 Tf 5.231 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)-290(=)]TJ/F84 9.9626 Tf 0.994 0 0 1 285.074 243.218 Tm [(0,)-252(and)-252(in)-252(case)-252(r)19(eturns)-252(err)18(or)-252(halting)-252(the)-252(computa-)]TJ 1 0 0 1 175.611 231.262 Tm [(tion.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 40.677 0 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -108.662 -11.955 Td [(Speci\002ed)-250(as:)-310(the)-250(logical)-250(value)]TJ/F145 9.9626 Tf 132.133 0 Td [(flag)]TJ +/F84 9.9626 Tf 0.994 0 0 1 172.294 243.218 Tm [(check)-252(if)-252(any)-252(of)-251(the)]TJ/F78 9.9626 Tf 1 0 0 1 254.535 243.218 Tm [(y)]TJ/F192 10.3811 Tf 5.231 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)-290(=)]TJ/F84 9.9626 Tf 0.994 0 0 1 285.074 243.218 Tm [(0,)-252(and)-252(in)-252(case)-252(r)19(eturns)-252(err)18(or)-252(halting)-252(the)-252(computa-)]TJ 1 0 0 1 175.611 231.262 Tm [(tion.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 40.677 0 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -108.662 -11.955 Td [(Speci\002ed)-250(as:)-310(the)-250(logical)-250(value)]TJ/F145 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-11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(variable)]TJ/F189 10.3811 Tf 142.419 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F189 10.3811 Tf 7.873 0 Td [(\024)]TJ/F78 9.9626 Tf 10.987 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F189 10.3811 Tf 19.923 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)]TJ/F189 10.3811 Tf 43.889 0 Td [(\000)]TJ/F84 9.9626 Tf 8.195 0 Td [(1.)]TJ +/F84 9.9626 Tf 1.004 0 0 1 122.839 201.011 Tm [(The)-248(pr)18(ocess)-248(that)-248(holds)-248(the)-248(global)-248(copy)111(.)-308(If)]TJ/F78 9.9626 Tf 1 0 0 1 305.722 201.011 Tm [(r)-17(o)-35(o)-35(t)]TJ/F192 10.3811 Tf 19.923 0 Td [(=)]TJ/F190 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 1.004 0 0 1 344.925 201.011 Tm [(1)-248(all)-248(the)-248(pr)18(ocesses)-248(will)]TJ 1 0 0 1 124.802 189.056 Tm [(have)-250(a)-250(copy)-250(of)-250(the)-250(global)-250(vector)74(.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(variable)]TJ/F190 10.3811 Tf 142.419 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F190 10.3811 Tf 7.873 0 Td [(\024)]TJ/F78 9.9626 Tf 10.987 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F190 10.3811 Tf 19.923 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)]TJ/F190 10.3811 Tf 43.889 0 Td [(\000)]TJ/F84 9.9626 Tf 8.195 0 Td [(1.)]TJ 0 g 0 G /F75 9.9626 Tf -301.108 -20.909 Td [(On)-250(Return)]TJ 0 g 0 G @@ -16626,14 +16626,14 @@ q []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F78 9.9626 Tf 235.523 646.918 Td [(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F189 10.3811 Tf 5.642 1.96 Td [(\040)]TJ/F78 9.9626 Tf 13.397 0 Td [(s)-25(c)-40(a)-25(t)-25(t)-25(e)-15(r)]TJ/F191 10.3811 Tf 28.633 0 Td [(\050)]TJ/F78 9.9626 Tf 4.493 0 Td [(g)-25(l)-55(o)-35(b)]TJ +/F78 9.9626 Tf 235.523 646.918 Td [(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F190 10.3811 Tf 5.642 1.96 Td [(\040)]TJ/F78 9.9626 Tf 13.397 0 Td [(s)-25(c)-40(a)-25(t)-25(t)-25(e)-15(r)]TJ/F192 10.3811 Tf 28.633 0 Td [(\050)]TJ/F78 9.9626 Tf 4.493 0 Td [(g)-25(l)-55(o)-35(b)]TJ ET q 1 0 0 1 311.49 647.117 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F78 9.9626 Tf 314.773 646.918 Td [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\051)]TJ/F84 9.9626 Tf -220.626 -23.362 Td [(wher)18(e:)]TJ +/F78 9.9626 Tf 314.773 646.918 Td [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\051)]TJ/F84 9.9626 Tf -220.626 -23.362 Td [(wher)18(e:)]TJ 0 g 0 G /F78 9.9626 Tf 0.762 -22.091 Td [(g)-25(l)-55(o)-35(b)]TJ ET @@ -16798,7 +16798,7 @@ BT 0 g 0 G /F75 9.9626 Tf -258.11 -22.813 Td [(root)]TJ 0 g 0 G -/F84 9.9626 Tf 0.987 0 0 1 122.839 192.057 Tm [(The)-253(pr)18(ocess)-254(that)-253(holds)-254(the)-253(global)-254(copy)113(.)-315(If)]TJ/F78 9.9626 Tf 1 0 0 1 303.049 192.057 Tm [(r)-17(o)-35(o)-35(t)]TJ/F191 10.3811 Tf 19.927 0 Td [(=)]TJ/F189 10.3811 Tf 11.09 0 Td [(\000)]TJ/F84 9.9626 Tf 0.987 0 0 1 342.26 192.057 Tm [(1)-253(all)-254(the)-253(pr)18(ocesses)-254(have)]TJ 1 0 0 1 124.802 180.101 Tm [(a)-250(copy)-250(of)-250(the)-250(global)-250(vector)74(.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ 1.015 0 0 1 124.802 132.281 Tm [(Speci\002ed)-246(as:)-305(an)-246(integer)-246(variable)]TJ/F189 10.3811 Tf 1 0 0 1 269.144 132.281 Tm [(\000)]TJ/F84 9.9626 Tf 1.015 0 0 1 277.338 132.281 Tm [(1)]TJ/F189 10.3811 Tf 1 0 0 1 285.286 132.281 Tm [(\024)]TJ/F78 9.9626 Tf 10.987 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F189 10.3811 Tf 19.922 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.501 0 Td [(\000)]TJ/F84 9.9626 Tf 1.015 0 0 1 350.91 132.281 Tm [(1,)-246(default)]TJ/F145 9.9626 Tf 1 0 0 1 395.251 132.281 Tm [(psb_root_)]TJ/F84 9.9626 Tf 1.015 0 0 1 442.324 132.281 Tm [(,)]TJ 1 0 0 1 124.802 120.326 Tm [(i.e.)-310(pr)18(ocess)-250(0.)]TJ +/F84 9.9626 Tf 0.987 0 0 1 122.839 192.057 Tm [(The)-253(pr)18(ocess)-254(that)-253(holds)-254(the)-253(global)-254(copy)113(.)-315(If)]TJ/F78 9.9626 Tf 1 0 0 1 303.049 192.057 Tm [(r)-17(o)-35(o)-35(t)]TJ/F192 10.3811 Tf 19.927 0 Td [(=)]TJ/F190 10.3811 Tf 11.09 0 Td [(\000)]TJ/F84 9.9626 Tf 0.987 0 0 1 342.26 192.057 Tm [(1)-253(all)-254(the)-253(pr)18(ocesses)-254(have)]TJ 1 0 0 1 124.802 180.101 Tm [(a)-250(copy)-250(of)-250(the)-250(global)-250(vector)74(.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ 1.015 0 0 1 124.802 132.281 Tm [(Speci\002ed)-246(as:)-305(an)-246(integer)-246(variable)]TJ/F190 10.3811 Tf 1 0 0 1 269.144 132.281 Tm [(\000)]TJ/F84 9.9626 Tf 1.015 0 0 1 277.338 132.281 Tm [(1)]TJ/F190 10.3811 Tf 1 0 0 1 285.286 132.281 Tm [(\024)]TJ/F78 9.9626 Tf 10.987 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F190 10.3811 Tf 19.922 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.501 0 Td [(\000)]TJ/F84 9.9626 Tf 1.015 0 0 1 350.91 132.281 Tm [(1,)-246(default)]TJ/F145 9.9626 Tf 1 0 0 1 395.251 132.281 Tm [(psb_root_)]TJ/F84 9.9626 Tf 1.015 0 0 1 442.324 132.281 Tm [(,)]TJ 1 0 0 1 124.802 120.326 Tm [(i.e.)-310(pr)18(ocess)-250(0.)]TJ 0 g 0 G 141.968 -29.888 Td [(69)]TJ 0 g 0 G @@ -16972,7 +16972,7 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -19.066 Td [(vg)]TJ 0 g 0 G -/F84 9.9626 Tf 16.06 0 Td [(Data)-250(allocation:)-310(each)-250(index)]TJ/F78 9.9626 Tf 121.707 0 Td [(i)]TJ/F189 10.3811 Tf 5.856 0 Td [(2)-290(f)]TJ/F84 9.9626 Tf 15.245 0 Td [(1)-179(.)-192(.)-192(.)]TJ/F78 9.9626 Tf 19.967 0 Td [(m)-47(g)]TJ/F189 10.3811 Tf 13.449 0 Td [(g)]TJ/F84 9.9626 Tf 7.806 0 Td [(is)-250(allocated)-250(to)-250(pr)18(ocess)]TJ/F78 9.9626 Tf 98.455 0 Td [(v)-47(g)]TJ/F191 10.3811 Tf 10.679 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ -295.759 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 28.343 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -57.434 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 24 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -61.877 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ +/F84 9.9626 Tf 16.06 0 Td [(Data)-250(allocation:)-310(each)-250(index)]TJ/F78 9.9626 Tf 121.707 0 Td [(i)]TJ/F190 10.3811 Tf 5.856 0 Td [(2)-290(f)]TJ/F84 9.9626 Tf 15.245 0 Td [(1)-179(.)-192(.)-192(.)]TJ/F78 9.9626 Tf 19.967 0 Td [(m)-47(g)]TJ/F190 10.3811 Tf 13.449 0 Td [(g)]TJ/F84 9.9626 Tf 7.806 0 Td [(is)-250(allocated)-250(to)-250(pr)18(ocess)]TJ/F78 9.9626 Tf 98.455 0 Td [(v)-47(g)]TJ/F192 10.3811 Tf 10.679 0 Td [(\050)]TJ/F78 9.9626 Tf 4.205 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ -295.759 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 28.343 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -57.434 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 24 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -61.877 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ 0 g 0 G /F75 9.9626 Tf -24.907 -19.067 Td [(\003ag)]TJ 0 g 0 G @@ -16988,7 +16988,7 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -19.067 Td [(vl)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 113.733 180.101 Tm [(Data)-254(allocation:)-322(the)-255(set)-254(of)-254(global)-254(indices)]TJ/F78 9.9626 Tf 1 0 0 1 295.435 180.101 Tm [(v)-25(l)]TJ/F191 10.3811 Tf 8.548 0 Td [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 308.132 180.101 Tm [(1)]TJ 1 0 0 1 316.277 180.101 Tm [(:)]TJ/F78 9.9626 Tf 5.679 0 Td [(n)-25(l)]TJ/F191 10.3811 Tf 9.106 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 337.795 180.101 Tm [(belonging)-254(to)-254(the)-255(calling)]TJ 1 0 0 1 124.503 168.146 Tm [(pr)18(ocess.)]TJ 0.299 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 28.343 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -50.231 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 24 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -61.877 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ +/F84 9.9626 Tf 1.02 0 0 1 113.733 180.101 Tm [(Data)-254(allocation:)-322(the)-255(set)-254(of)-254(global)-254(indices)]TJ/F78 9.9626 Tf 1 0 0 1 295.435 180.101 Tm [(v)-25(l)]TJ/F192 10.3811 Tf 8.548 0 Td [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 308.132 180.101 Tm [(1)]TJ 1 0 0 1 316.277 180.101 Tm [(:)]TJ/F78 9.9626 Tf 5.679 0 Td [(n)-25(l)]TJ/F192 10.3811 Tf 9.106 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 337.795 180.101 Tm [(belonging)-254(to)-254(the)-255(calling)]TJ 1 0 0 1 124.503 168.146 Tm [(pr)18(ocess.)]TJ 0.299 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 28.343 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -50.231 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 24 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -61.877 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ 0 g 0 G 141.968 -29.888 Td [(71)]TJ 0 g 0 G @@ -17019,7 +17019,7 @@ BT 0 g 0 G /F75 9.9626 Tf -187.584 -20.135 Td [(lidx)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 173.39 478.351 Tm [(Data)-273(allocation:)-361(the)-274(set)-273(of)-274(local)-273(indices)]TJ/F78 9.9626 Tf 1 0 0 1 349.9 478.351 Tm [(l)-48(i)-32(d)-42(x)]TJ/F191 10.3811 Tf 17.066 0 Td [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 371.116 478.351 Tm [(1)]TJ 1 0 0 1 379.623 478.351 Tm [(:)]TJ/F78 9.9626 Tf 6.042 0 Td [(n)-25(l)]TJ/F191 10.3811 Tf 9.106 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 401.699 478.351 Tm [(to)-274(be)-273(assigned)-274(to)-273(the)]TJ 1 0 0 1 175.611 466.396 Tm [(global)-250(indices)]TJ/F78 9.9626 Tf 63.477 0 Td [(v)-25(l)]TJ/F84 9.9626 Tf 8.423 0 Td [(.)]TJ -71.9 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 28.344 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -50.231 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 23.999 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -61.878 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ +/F84 9.9626 Tf 1.02 0 0 1 173.39 478.351 Tm [(Data)-273(allocation:)-361(the)-274(set)-273(of)-274(local)-273(indices)]TJ/F78 9.9626 Tf 1 0 0 1 349.9 478.351 Tm [(l)-48(i)-32(d)-42(x)]TJ/F192 10.3811 Tf 17.066 0 Td [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 371.116 478.351 Tm [(1)]TJ 1 0 0 1 379.623 478.351 Tm [(:)]TJ/F78 9.9626 Tf 6.042 0 Td [(n)-25(l)]TJ/F192 10.3811 Tf 9.106 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 401.699 478.351 Tm [(to)-274(be)-273(assigned)-274(to)-273(the)]TJ 1 0 0 1 175.611 466.396 Tm [(global)-250(indices)]TJ/F78 9.9626 Tf 63.477 0 Td [(v)-25(l)]TJ/F84 9.9626 Tf 8.423 0 Td [(.)]TJ -71.9 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 28.344 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -50.231 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 23.999 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -61.878 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)]TJ 0 g 0 G /F75 9.9626 Tf -24.906 -22.128 Td [(On)-250(Return)]TJ 0 g 0 G @@ -17109,15 +17109,15 @@ BT 0 g 0 G /F75 9.9626 Tf -137.811 -13.774 Td [(pv)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 162.939 564.573 Tm [(A)-342(vector)-342(containing)-342(the)-342(indices)-343(of)-342(the)-342(pr)18(ocesses)-342(to)-343(which)-342(the)]TJ 1.02 0 0 1 165.35 552.618 Tm [(global)-309(index)-310(should)-309(be)-310(assigend;)-341(each)-310(entry)-309(must)-310(satisfy)-309(0)]TJ/F189 10.3811 Tf 1 0 0 1 435.412 552.618 Tm [(\024)]TJ/F78 9.9626 Tf -269.39 -11.956 Td [(p)-25(v)]TJ/F191 10.3811 Tf 10.461 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.089 0 Td [(\051)]TJ/F148 10.3811 Tf 8.296 0 Td [(<)]TJ/F78 9.9626 Tf 12.342 0 Td [(n)-80(p)]TJ/F84 9.9626 Tf 1.02 0 0 1 215.856 540.662 Tm [(;)-345(if)]TJ/F78 9.9626 Tf 1 0 0 1 231.538 540.662 Tm [(n)-25(v)]TJ/F148 10.3811 Tf 15.042 0 Td [(>)]TJ/F84 9.9626 Tf 1.02 0 0 1 258.797 540.662 Tm [(1)-312(we)-312(have)-311(an)-312(index)-312(assigned)-312(to)-312(multiple)]TJ 1 0 0 1 165.051 528.707 Tm [(pr)18(ocesses,)-250(i.e.)-310(we)-250(have)-250(an)-250(overlap)-250(among)-250(the)-250(subdomains.)]TJ +/F84 9.9626 Tf 1.02 0 0 1 162.939 564.573 Tm [(A)-342(vector)-342(containing)-342(the)-342(indices)-343(of)-342(the)-342(pr)18(ocesses)-342(to)-343(which)-342(the)]TJ 1.02 0 0 1 165.35 552.618 Tm [(global)-309(index)-310(should)-309(be)-310(assigend;)-341(each)-310(entry)-309(must)-310(satisfy)-309(0)]TJ/F190 10.3811 Tf 1 0 0 1 435.412 552.618 Tm [(\024)]TJ/F78 9.9626 Tf -269.39 -11.956 Td [(p)-25(v)]TJ/F192 10.3811 Tf 10.461 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.089 0 Td [(\051)]TJ/F148 10.3811 Tf 8.296 0 Td [(<)]TJ/F78 9.9626 Tf 12.342 0 Td [(n)-80(p)]TJ/F84 9.9626 Tf 1.02 0 0 1 215.856 540.662 Tm [(;)-345(if)]TJ/F78 9.9626 Tf 1 0 0 1 231.538 540.662 Tm [(n)-25(v)]TJ/F148 10.3811 Tf 15.042 0 Td [(>)]TJ/F84 9.9626 Tf 1.02 0 0 1 258.797 540.662 Tm [(1)-312(we)-312(have)-311(an)-312(index)-312(assigned)-312(to)-312(multiple)]TJ 1 0 0 1 165.051 528.707 Tm [(pr)18(ocesses,)-250(i.e.)-310(we)-250(have)-250(an)-250(overlap)-250(among)-250(the)-250(subdomains.)]TJ 0 g 0 G /F75 9.9626 Tf -40.249 -15.593 Td [(vg)]TJ 0 g 0 G -/F84 9.9626 Tf 0.98 0 0 1 140.862 513.114 Tm [(In)-244(this)-244(case)-244(the)-244(association)-244(between)-244(an)-244(index)-244(and)-244(a)-245(pr)19(ocess)-244(is)-244(speci\002ed)]TJ 0.986 0 0 1 146.441 501.158 Tm [(via)-254(an)-254(integer)-253(vector)]TJ/F145 9.9626 Tf 1 0 0 1 237.956 501.158 Tm [(vg\0501:mg\051)]TJ/F84 9.9626 Tf 0.986 0 0 1 279.798 501.158 Tm [(;)-254(each)-254(index)]TJ/F78 9.9626 Tf 1 0 0 1 333.837 501.158 Tm [(i)]TJ/F189 10.3811 Tf 5.861 0 Td [(2)-290(f)]TJ/F84 9.9626 Tf 0.986 0 0 1 354.949 501.158 Tm [(1)]TJ 1 0 0 1 361.645 501.158 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.201 0 Td [(m)-47(g)]TJ/F189 10.3811 Tf 13.449 0 Td [(g)]TJ/F84 9.9626 Tf 0.986 0 0 1 396.104 501.158 Tm [(is)-254(assigned)]TJ 1.02 0 0 1 146.72 489.203 Tm [(to)-260(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 194.476 489.203 Tm [(v)-47(g)]TJ/F191 10.3811 Tf 10.68 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 216.598 489.203 Tm [(.)-349(The)-260(vector)]TJ/F145 9.9626 Tf 1 0 0 1 272.971 489.203 Tm [(vg)]TJ/F84 9.9626 Tf 1.02 0 0 1 286.073 489.203 Tm [(must)-260(be)-260(identical)-260(on)-260(all)-260(calling)-260(pr)18(o-)]TJ 1.02 0 0 1 146.72 477.248 Tm [(cesses;)-427(its)-366(entries)-366(may)-367(have)-366(the)-366(ranges)]TJ/F191 10.3811 Tf 1 0 0 1 329.283 477.248 Tm [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 333.433 477.248 Tm [(0)]TJ 1 0 0 1 340.299 477.248 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.96 0 Td [(\000)]TJ/F84 9.9626 Tf 1.02 0 0 1 378.046 477.248 Tm [(1)]TJ/F191 10.3811 Tf 1 0 0 1 383.252 477.248 Tm [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 391.123 477.248 Tm [(or)]TJ/F191 10.3811 Tf 1 0 0 1 404.532 477.248 Tm [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 408.681 477.248 Tm [(1)]TJ 1 0 0 1 415.547 477.248 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)-80(p)]TJ/F191 10.3811 Tf 11.567 0 Td [(\051)]TJ/F84 9.9626 Tf 0.993 0 0 1 146.72 465.293 Tm [(accor)18(ding)-252(to)-253(the)-252(value)-252(of)]TJ/F145 9.9626 Tf 1 0 0 1 257.41 465.293 Tm [(flag)]TJ/F84 9.9626 Tf 0.993 0 0 1 278.331 465.293 Tm [(.)-314(The)-253(size)]TJ/F78 9.9626 Tf 1 0 0 1 322.35 465.293 Tm [(m)-47(g)]TJ/F84 9.9626 Tf 0.993 0 0 1 338.172 465.293 Tm [(may)-252(be)-253(speci\002ed)-252(via)-253(the)]TJ 0.999 0 0 1 146.72 453.338 Tm [(optional)-250(ar)18(gument)]TJ/F145 9.9626 Tf 1 0 0 1 231.215 453.338 Tm [(mg)]TJ/F84 9.9626 Tf 0.999 0 0 1 241.676 453.338 Tm [(;)-250(the)-251(default)-250(is)-251(to)-250(use)-250(the)-251(entir)18(e)-250(vector)]TJ/F145 9.9626 Tf 1 0 0 1 408.907 453.338 Tm [(vg)]TJ/F84 9.9626 Tf 0.999 0 0 1 419.367 453.338 Tm [(,)-251(t)1(hus)]TJ 1 0 0 1 146.72 441.383 Tm [(having)]TJ/F145 9.9626 Tf 33.135 0 Td [(mg=size\050vg\051)]TJ/F84 9.9626 Tf 57.534 0 Td [(.)]TJ +/F84 9.9626 Tf 0.98 0 0 1 140.862 513.114 Tm [(In)-244(this)-244(case)-244(the)-244(association)-244(between)-244(an)-244(index)-244(and)-244(a)-245(pr)19(ocess)-244(is)-244(speci\002ed)]TJ 0.986 0 0 1 146.441 501.158 Tm [(via)-254(an)-254(integer)-253(vector)]TJ/F145 9.9626 Tf 1 0 0 1 237.956 501.158 Tm [(vg\0501:mg\051)]TJ/F84 9.9626 Tf 0.986 0 0 1 279.798 501.158 Tm [(;)-254(each)-254(index)]TJ/F78 9.9626 Tf 1 0 0 1 333.837 501.158 Tm [(i)]TJ/F190 10.3811 Tf 5.861 0 Td [(2)-290(f)]TJ/F84 9.9626 Tf 0.986 0 0 1 354.949 501.158 Tm [(1)]TJ 1 0 0 1 361.645 501.158 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.201 0 Td [(m)-47(g)]TJ/F190 10.3811 Tf 13.449 0 Td [(g)]TJ/F84 9.9626 Tf 0.986 0 0 1 396.104 501.158 Tm [(is)-254(assigned)]TJ 1.02 0 0 1 146.72 489.203 Tm [(to)-260(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 194.476 489.203 Tm [(v)-47(g)]TJ/F192 10.3811 Tf 10.68 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 216.598 489.203 Tm [(.)-349(The)-260(vector)]TJ/F145 9.9626 Tf 1 0 0 1 272.971 489.203 Tm [(vg)]TJ/F84 9.9626 Tf 1.02 0 0 1 286.073 489.203 Tm [(must)-260(be)-260(identical)-260(on)-260(all)-260(calling)-260(pr)18(o-)]TJ 1.02 0 0 1 146.72 477.248 Tm [(cesses;)-427(its)-366(entries)-366(may)-367(have)-366(the)-366(ranges)]TJ/F192 10.3811 Tf 1 0 0 1 329.283 477.248 Tm [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 333.433 477.248 Tm [(0)]TJ 1 0 0 1 340.299 477.248 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.96 0 Td [(\000)]TJ/F84 9.9626 Tf 1.02 0 0 1 378.046 477.248 Tm [(1)]TJ/F192 10.3811 Tf 1 0 0 1 383.252 477.248 Tm [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 391.123 477.248 Tm [(or)]TJ/F192 10.3811 Tf 1 0 0 1 404.532 477.248 Tm [(\050)]TJ/F84 9.9626 Tf 1.02 0 0 1 408.681 477.248 Tm [(1)]TJ 1 0 0 1 415.547 477.248 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(n)-80(p)]TJ/F192 10.3811 Tf 11.567 0 Td [(\051)]TJ/F84 9.9626 Tf 0.993 0 0 1 146.72 465.293 Tm [(accor)18(ding)-252(to)-253(the)-252(value)-252(of)]TJ/F145 9.9626 Tf 1 0 0 1 257.41 465.293 Tm [(flag)]TJ/F84 9.9626 Tf 0.993 0 0 1 278.331 465.293 Tm [(.)-314(The)-253(size)]TJ/F78 9.9626 Tf 1 0 0 1 322.35 465.293 Tm [(m)-47(g)]TJ/F84 9.9626 Tf 0.993 0 0 1 338.172 465.293 Tm [(may)-252(be)-253(speci\002ed)-252(via)-253(the)]TJ 0.999 0 0 1 146.72 453.338 Tm [(optional)-250(ar)18(gument)]TJ/F145 9.9626 Tf 1 0 0 1 231.215 453.338 Tm [(mg)]TJ/F84 9.9626 Tf 0.999 0 0 1 241.676 453.338 Tm [(;)-250(the)-251(default)-250(is)-251(to)-250(use)-250(the)-251(entir)18(e)-250(vector)]TJ/F145 9.9626 Tf 1 0 0 1 408.907 453.338 Tm [(vg)]TJ/F84 9.9626 Tf 0.999 0 0 1 419.367 453.338 Tm [(,)-251(t)1(hus)]TJ 1 0 0 1 146.72 441.383 Tm [(having)]TJ/F145 9.9626 Tf 33.135 0 Td [(mg=size\050vg\051)]TJ/F84 9.9626 Tf 57.534 0 Td [(.)]TJ 0 g 0 G /F75 9.9626 Tf -112.587 -15.594 Td [(vl)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 138.64 425.789 Tm [(In)-336(this)-335(case)-336(we)-335(ar)17(e)-335(specifying)-336(the)-335(list)-336(of)-335(indices)]TJ/F145 9.9626 Tf 1 0 0 1 359.058 425.789 Tm [(vl\0501:nl\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 404.311 425.789 Tm [(assigned)]TJ 1.018 0 0 1 146.72 413.834 Tm [(to)-245(the)-246(curr)18(ent)-245(pr)17(ocess;)-245(thus,)-246(th)1(e)-246(global)-245(pr)17(oblem)-245(size)]TJ/F78 9.9626 Tf 1 0 0 1 379.625 413.834 Tm [(m)-47(g)]TJ/F84 9.9626 Tf 1.018 0 0 1 395.438 413.834 Tm [(is)-245(given)-246(by)]TJ 1.02 0 0 1 146.72 401.878 Tm [(the)-255(range)-255(of)-255(the)-255(aggr)18(egate)-255(of)-255(the)-255(individual)-255(vectors)]TJ/F145 9.9626 Tf 1 0 0 1 379.117 401.878 Tm [(vl)]TJ/F84 9.9626 Tf 1.02 0 0 1 392.168 401.878 Tm [(speci\002ed)-255(in)]TJ 1.02 0 0 1 146.72 389.923 Tm [(the)-346(calling)-347(pr)18(ocesses.)-608(The)-347(size)-346(may)-347(be)-346(speci\002ed)-347(via)-346(the)-347(optional)]TJ 1.02 0 0 1 146.72 377.968 Tm [(ar)18(gument)]TJ/F145 9.9626 Tf 1 0 0 1 193.05 377.968 Tm [(nl)]TJ/F84 9.9626 Tf 1.02 0 0 1 203.511 377.968 Tm [(;)-257(the)-253(default)-252(is)-253(to)-253(use)-253(the)-253(entir)18(e)-253(vector)]TJ/F145 9.9626 Tf 1 0 0 1 374.525 377.968 Tm [(vl)]TJ/F84 9.9626 Tf 1.02 0 0 1 384.986 377.968 Tm [(,)-255(thus)-253(having)]TJ/F145 9.9626 Tf 1 0 0 1 146.72 366.013 Tm [(nl=size\050vl\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 204.254 366.013 Tm [(.)-306(If)]TJ/F145 9.9626 Tf 1 0 0 1 218.412 366.013 Tm [(globalcheck=.true.)]TJ/F84 9.9626 Tf 0.98 0 0 1 314.747 366.013 Tm [(the)-224(subr)18(outine)-224(will)-224(check)-224(how)]TJ 0.98 0 0 1 146.72 354.058 Tm [(many)-208(times)-209(each)-208(entry)-209(in)-208(the)-209(global)-208(index)-209(space)]TJ/F191 10.3811 Tf 1 0 0 1 352.531 354.058 Tm [(\050)]TJ/F84 9.9626 Tf 0.98 0 0 1 356.68 354.058 Tm [(1)]TJ 1 0 0 1 363.347 354.058 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(m)-47(g)]TJ/F191 10.3811 Tf 13.45 0 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 396.182 354.058 Tm [(is)-208(speci\002ed)]TJ 0.999 0 0 1 146.72 342.103 Tm [(in)-249(the)-250(input)-249(lists)]TJ/F145 9.9626 Tf 1 0 0 1 220.533 342.103 Tm [(vl)]TJ/F84 9.9626 Tf 0.999 0 0 1 230.994 342.103 Tm [(,)-250(thus)-249(allowing)-249(for)-250(the)-249(pr)18(esence)-249(of)-250(overlap)-249(in)-249(the)]TJ 1.005 0 0 1 146.72 330.147 Tm [(input,)-248(and)-249(checking)-248(for)-249(\223orphan\224)-248(indices.)-308(If)]TJ/F145 9.9626 Tf 1 0 0 1 342.972 330.147 Tm [(globalcheck=.false.)]TJ/F84 9.9626 Tf 1.005 0 0 1 442.349 330.147 Tm [(,)]TJ 1.018 0 0 1 146.72 318.192 Tm [(the)-246(subr)18(outine)-246(will)-247(not)-246(check)-246(for)-246(overlap,)-246(and)-246(may)-246(be)-247(signi\002)1(cantly)]TJ 1.02 0 0 1 146.72 306.237 Tm [(faster)73(,)-256(but)-253(the)-253(user)-253(is)-254(implicitly)-253(guaranteeing)-253(that)-253(ther)17(e)-253(ar)18(e)-253(neither)]TJ 1 0 0 1 146.72 294.282 Tm [(orphan)-250(nor)-250(overlap)-250(indices.)]TJ +/F84 9.9626 Tf 1.02 0 0 1 138.64 425.789 Tm [(In)-336(this)-335(case)-336(we)-335(ar)17(e)-335(specifying)-336(the)-335(list)-336(of)-335(indices)]TJ/F145 9.9626 Tf 1 0 0 1 359.058 425.789 Tm [(vl\0501:nl\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 404.311 425.789 Tm [(assigned)]TJ 1.018 0 0 1 146.72 413.834 Tm [(to)-245(the)-246(curr)18(ent)-245(pr)17(ocess;)-245(thus,)-246(th)1(e)-246(global)-245(pr)17(oblem)-245(size)]TJ/F78 9.9626 Tf 1 0 0 1 379.625 413.834 Tm [(m)-47(g)]TJ/F84 9.9626 Tf 1.018 0 0 1 395.438 413.834 Tm [(is)-245(given)-246(by)]TJ 1.02 0 0 1 146.72 401.878 Tm [(the)-255(range)-255(of)-255(the)-255(aggr)18(egate)-255(of)-255(the)-255(individual)-255(vectors)]TJ/F145 9.9626 Tf 1 0 0 1 379.117 401.878 Tm [(vl)]TJ/F84 9.9626 Tf 1.02 0 0 1 392.168 401.878 Tm [(speci\002ed)-255(in)]TJ 1.02 0 0 1 146.72 389.923 Tm [(the)-346(calling)-347(pr)18(ocesses.)-608(The)-347(size)-346(may)-347(be)-346(speci\002ed)-347(via)-346(the)-347(optional)]TJ 1.02 0 0 1 146.72 377.968 Tm [(ar)18(gument)]TJ/F145 9.9626 Tf 1 0 0 1 193.05 377.968 Tm [(nl)]TJ/F84 9.9626 Tf 1.02 0 0 1 203.511 377.968 Tm [(;)-257(the)-253(default)-252(is)-253(to)-253(use)-253(the)-253(entir)18(e)-253(vector)]TJ/F145 9.9626 Tf 1 0 0 1 374.525 377.968 Tm [(vl)]TJ/F84 9.9626 Tf 1.02 0 0 1 384.986 377.968 Tm [(,)-255(thus)-253(having)]TJ/F145 9.9626 Tf 1 0 0 1 146.72 366.013 Tm [(nl=size\050vl\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 204.254 366.013 Tm [(.)-306(If)]TJ/F145 9.9626 Tf 1 0 0 1 218.412 366.013 Tm [(globalcheck=.true.)]TJ/F84 9.9626 Tf 0.98 0 0 1 314.747 366.013 Tm [(the)-224(subr)18(outine)-224(will)-224(check)-224(how)]TJ 0.98 0 0 1 146.72 354.058 Tm [(many)-208(times)-209(each)-208(entry)-209(in)-208(the)-209(global)-208(index)-209(space)]TJ/F192 10.3811 Tf 1 0 0 1 352.531 354.058 Tm [(\050)]TJ/F84 9.9626 Tf 0.98 0 0 1 356.68 354.058 Tm [(1)]TJ 1 0 0 1 363.347 354.058 Tm [(.)-192(.)-191(.)]TJ/F78 9.9626 Tf 13.2 0 Td [(m)-47(g)]TJ/F192 10.3811 Tf 13.45 0 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 396.182 354.058 Tm [(is)-208(speci\002ed)]TJ 0.999 0 0 1 146.72 342.103 Tm [(in)-249(the)-250(input)-249(lists)]TJ/F145 9.9626 Tf 1 0 0 1 220.533 342.103 Tm [(vl)]TJ/F84 9.9626 Tf 0.999 0 0 1 230.994 342.103 Tm [(,)-250(thus)-249(allowing)-249(for)-250(the)-249(pr)18(esence)-249(of)-250(overlap)-249(in)-249(the)]TJ 1.005 0 0 1 146.72 330.147 Tm [(input,)-248(and)-249(checking)-248(for)-249(\223orphan\224)-248(indices.)-308(If)]TJ/F145 9.9626 Tf 1 0 0 1 342.972 330.147 Tm [(globalcheck=.false.)]TJ/F84 9.9626 Tf 1.005 0 0 1 442.349 330.147 Tm [(,)]TJ 1.018 0 0 1 146.72 318.192 Tm [(the)-246(subr)18(outine)-246(will)-247(not)-246(check)-246(for)-246(overlap,)-246(and)-246(may)-246(be)-247(signi\002)1(cantly)]TJ 1.02 0 0 1 146.72 306.237 Tm [(faster)73(,)-256(but)-253(the)-253(user)-253(is)-254(implicitly)-253(guaranteeing)-253(that)-253(ther)17(e)-253(ar)18(e)-253(neither)]TJ 1 0 0 1 146.72 294.282 Tm [(orphan)-250(nor)-250(overlap)-250(indices.)]TJ 0 g 0 G /F75 9.9626 Tf -21.918 -15.594 Td [(lidx)]TJ 0 g 0 G @@ -17129,7 +17129,7 @@ BT 0 g 0 G /F75 9.9626 Tf -171.007 -15.593 Td [(nl)]TJ 0 g 0 G -/F84 9.9626 Tf 0.98 0 0 1 139.188 203.319 Tm [(If)-247(this)-248(ar)19(gument)-247(is)-248(speci\002ed)-247(alone)-247(\050i.e.)-314(without)]TJ/F145 9.9626 Tf 1 0 0 1 342.277 203.319 Tm [(vl)]TJ/F84 9.9626 Tf 0.98 0 0 1 352.737 203.319 Tm [(\051)-247(the)-248(r)19(esult)-247(is)-248(a)-247(gener)18(-)]TJ 0.98 0 0 1 146.72 191.364 Tm [(alized)-250(r)18(ow-block)-250(distribution)-250(in)-250(which)-250(each)-251(pr)19(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 372.364 191.364 Tm [(I)]TJ/F84 9.9626 Tf 0.98 0 0 1 378.657 191.364 Tm [(gets)-250(assigned)-250(a)]TJ 1 0 0 1 146.72 179.408 Tm [(consecutive)-250(chunk)-250(of)]TJ/F78 9.9626 Tf 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Tm [(j)-40(a)]TJ/F192 10.3811 Tf 7.841 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 0.985 0 0 1 225.677 120.326 Tm [(,)]TJ/F78 9.9626 Tf 1 0 0 1 229.915 120.326 Tm [(v)-40(a)-25(l)]TJ/F192 10.3811 Tf 13.37 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 0.985 0 0 1 254.727 120.326 Tm [(,)-253(for)]TJ/F78 9.9626 Tf 1 0 0 1 274.702 120.326 Tm [(i)]TJ/F192 10.3811 Tf 5.856 0 Td [(=)]TJ/F84 9.9626 Tf 0.985 0 0 1 291.52 120.326 Tm [(1,)]TJ 1 0 0 1 300.664 120.326 Tm [(.)-192(.)-191(.)]TJ 0.985 0 0 1 313.74 120.326 Tm [(,)]TJ/F78 9.9626 Tf 1 0 0 1 317.978 120.326 Tm [(n)-25(z)]TJ/F84 9.9626 Tf 0.985 0 0 1 328.315 120.326 Tm [(;)-253(these)-253(triples)-253(ar)18(e)-253(arbitrary;)]TJ 0 g 0 G 1 0 0 1 266.77 90.438 Tm [(85)]TJ 0 g 0 G @@ -18739,7 +18739,7 @@ stream BT /F84 9.9626 Tf 163.158 706.129 Td [(6.)]TJ 0 g 0 G - 1.02 0 0 1 175.611 706.129 Tm 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[(;)-254(thus,)-255(upon)-254(r)18(eturn)-254(fr)18(om)-254(the)-254(subr)18(outine,)-254(for)]TJ 1.02 0 0 1 124.802 518.831 Tm [(each)-260(index)]TJ/F78 9.9626 Tf 1 0 0 1 175.703 518.831 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 181.308 518.831 Tm [(we)-260(have)-260(in)]TJ/F78 9.9626 Tf 1 0 0 1 233.102 518.831 Tm [(i)-49(x)]TJ/F191 10.3811 Tf 8.588 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 255.772 518.831 Tm [(the)-260(position)-260(that)-260(the)-259(item)]TJ/F78 9.9626 Tf 1 0 0 1 371.842 518.831 Tm [(x)]TJ/F191 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F191 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 391.255 518.831 Tm [(occupied)-260(in)]TJ 1 0 0 1 124.802 506.876 Tm [(the)-250(original)-250(data)-250(sequence;)]TJ +/F84 9.9626 Tf 0.98 0 0 1 246.101 542.742 Tm [(then)-244(the)-244(entries)-244(in)]TJ/F78 9.9626 Tf 1 0 0 1 326.032 542.742 Tm [(i)-49(x)]TJ/F192 10.3811 Tf 8.587 0 Td [(\050)]TJ/F84 9.9626 Tf 0.98 0 0 1 338.769 542.742 Tm [(1)]TJ 1 0 0 1 346.542 542.742 Tm [(:)]TJ/F78 9.9626 Tf 5.507 0 Td [(n)]TJ/F192 10.3811 Tf 5.788 0 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 364.37 542.742 Tm [(wher)18(e)]TJ/F78 9.9626 Tf 1 0 0 1 393.733 542.742 Tm [(n)]TJ/F84 9.9626 Tf 0.98 0 0 1 401.779 542.742 Tm [(is)-244(the)-244(size)]TJ 0.984 0 0 1 124.802 530.786 Tm [(of)]TJ/F78 9.9626 Tf 1 0 0 1 136.206 530.786 Tm [(x)]TJ/F84 9.9626 Tf 0.984 0 0 1 143.904 530.786 Tm [(ar)18(e)-254(initialized)-254(to)]TJ/F78 9.9626 Tf 1 0 0 1 216.929 530.786 Tm [(i)-49(x)]TJ/F192 10.3811 Tf 8.588 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F190 10.3811 Tf 7.046 0 Td [(\040)]TJ/F78 9.9626 Tf 13.332 0 Td [(i)]TJ/F84 9.9626 Tf 0.984 0 0 1 256.15 530.786 Tm [(;)-254(thus,)-255(upon)-254(r)18(eturn)-254(fr)18(om)-254(the)-254(subr)18(outine,)-254(for)]TJ 1.02 0 0 1 124.802 518.831 Tm [(each)-260(index)]TJ/F78 9.9626 Tf 1 0 0 1 175.703 518.831 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 181.308 518.831 Tm [(we)-260(have)-260(in)]TJ/F78 9.9626 Tf 1 0 0 1 233.102 518.831 Tm [(i)-49(x)]TJ/F192 10.3811 Tf 8.588 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 255.772 518.831 Tm [(the)-260(position)-260(that)-260(the)-259(item)]TJ/F78 9.9626 Tf 1 0 0 1 371.842 518.831 Tm [(x)]TJ/F192 10.3811 Tf 5.33 0 Td [(\050)]TJ/F78 9.9626 Tf 4.204 0 Td [(i)]TJ/F192 10.3811 Tf 3.088 0 Td [(\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 391.255 518.831 Tm [(occupied)-260(in)]TJ 1 0 0 1 124.802 506.876 Tm [(the)-250(original)-250(data)-250(sequence;)]TJ 0 g 0 G -12.453 -19.925 Td [(5.)]TJ 0 g 0 G - 1.02 0 0 1 124.802 486.951 Tm [(If)]TJ/F78 9.9626 Tf 1 0 0 1 136.291 486.951 Tm [(f)-160(l)-70(a)-47(g)]TJ/F191 10.3811 Tf 22.147 0 Td [(=)]TJ/F78 9.9626 Tf 13.061 0 Td [(p)-25(s)-25(b)]TJ + 1.02 0 0 1 124.802 486.951 Tm [(If)]TJ/F78 9.9626 Tf 1 0 0 1 136.291 486.951 Tm [(f)-160(l)-70(a)-47(g)]TJ/F192 10.3811 Tf 22.147 0 Td [(=)]TJ/F78 9.9626 Tf 13.061 0 Td [(p)-25(s)-25(b)]TJ ET q 1 0 0 1 186.188 487.15 cm @@ -22068,19 +22068,19 @@ q []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F84 9.9626 Tf 1.02 0 0 1 252.283 486.951 Tm [(the)-321(r)18(outine)-321(will)-321(assume)-321(that)-321(the)-321(entries)-321(in)]TJ/F78 9.9626 Tf 1 0 0 1 124.857 474.996 Tm [(i)-49(x)]TJ/F191 10.3811 Tf 8.587 0 Td [(\050)]TJ/F84 9.9626 Tf 4.274 0 Td [(:)]TJ/F191 10.3811 Tf 2.74 0 Td [(\051)]TJ/F84 9.9626 Tf 6.64 0 Td [(have)-250(alr)18(eady)-250(been)-250(initialized)-250(by)-250(the)-250(user;)]TJ +/F84 9.9626 Tf 1.02 0 0 1 252.283 486.951 Tm [(the)-321(r)18(outine)-321(will)-321(assume)-321(that)-321(the)-321(entries)-321(in)]TJ/F78 9.9626 Tf 1 0 0 1 124.857 474.996 Tm [(i)-49(x)]TJ/F192 10.3811 Tf 8.587 0 Td [(\050)]TJ/F84 9.9626 Tf 4.274 0 Td [(:)]TJ/F192 10.3811 Tf 2.74 0 Td [(\051)]TJ/F84 9.9626 Tf 6.64 0 Td [(have)-250(alr)18(eady)-250(been)-250(initialized)-250(by)-250(the)-250(user;)]TJ 0 g 0 G -34.749 -19.926 Td [(6.)]TJ 0 g 0 G - 1.008 0 0 1 124.493 455.07 Tm [(The)-249(thr)18(ee)-249(sorting)-248(algorithms)-249(have)-249(a)-248(similar)]TJ/F78 9.9626 Tf 1 0 0 1 317.915 455.07 Tm [(O)]TJ/F191 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.273 0 Td [(n)]TJ/F84 9.9626 Tf 7.325 0 Td [(log)]TJ/F78 9.9626 Tf 15.662 0 Td [(n)]TJ/F191 10.3811 Tf 5.789 0 Td [(\051)]TJ/F84 9.9626 Tf 1.008 0 0 1 365.611 455.07 Tm [(expected)-249(r)8(unning)]TJ 1.008 0 0 1 124.802 443.115 Tm [(time;)-248(in)-248(the)-248(average)-248(case)-248(quicksort)-248(will)-247(be)-248(the)-248(fastest)-248(and)-248(mer)18(ge-sort)-248(the)]TJ 1 0 0 1 124.802 431.16 Tm [(slowest.)-310(However)-250(note)-250(that:)]TJ + 1.008 0 0 1 124.493 455.07 Tm [(The)-249(thr)18(ee)-249(sorting)-248(algorithms)-249(have)-249(a)-248(similar)]TJ/F78 9.9626 Tf 1 0 0 1 317.915 455.07 Tm [(O)]TJ/F192 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.273 0 Td [(n)]TJ/F84 9.9626 Tf 7.325 0 Td [(log)]TJ/F78 9.9626 Tf 15.662 0 Td [(n)]TJ/F192 10.3811 Tf 5.789 0 Td [(\051)]TJ/F84 9.9626 Tf 1.008 0 0 1 365.611 455.07 Tm [(expected)-249(r)8(unning)]TJ 1.008 0 0 1 124.802 443.115 Tm [(time;)-248(in)-248(the)-248(average)-248(case)-248(quicksort)-248(will)-247(be)-248(the)-248(fastest)-248(and)-248(mer)18(ge-sort)-248(the)]TJ 1 0 0 1 124.802 431.16 Tm [(slowest.)-310(However)-250(note)-250(that:)]TJ 0 g 0 G 5.32 -19.925 Td [(\050a\051)]TJ 0 g 0 G - 0.98 0 0 1 146.411 411.235 Tm [(The)-241(worst)-240(case)-241(r)8(unning)-241(time)-240(for)-241(quicksort)-241(is)]TJ/F78 9.9626 Tf 1 0 0 1 338.306 411.235 Tm [(O)]TJ/F191 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)]TJ/F84 7.5716 Tf 5.664 3.616 Td [(2)]TJ/F191 10.3811 Tf 4.408 -3.616 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 364.802 411.235 Tm [(;)-245(the)-241(algorithm)-241(im-)]TJ 1.007 0 0 1 146.421 399.28 Tm [(plemented)-246(her)18(e)-246(follows)-246(the)-246(well-known)-246(median-of-thr)18(ee)-246(heuristics,)]TJ 1 0 0 1 146.72 387.324 Tm [(but)-250(the)-250(worst)-250(case)-250(may)-250(still)-250(apply;)]TJ + 0.98 0 0 1 146.411 411.235 Tm [(The)-241(worst)-240(case)-241(r)8(unning)-241(time)-240(for)-241(quicksort)-241(is)]TJ/F78 9.9626 Tf 1 0 0 1 338.306 411.235 Tm [(O)]TJ/F192 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)]TJ/F84 7.5716 Tf 5.664 3.616 Td [(2)]TJ/F192 10.3811 Tf 4.408 -3.616 Td [(\051)]TJ/F84 9.9626 Tf 0.98 0 0 1 364.802 411.235 Tm [(;)-245(the)-241(algorithm)-241(im-)]TJ 1.007 0 0 1 146.421 399.28 Tm [(plemented)-246(her)18(e)-246(follows)-246(the)-246(well-known)-246(median-of-thr)18(ee)-246(heuristics,)]TJ 1 0 0 1 146.72 387.324 Tm [(but)-250(the)-250(worst)-250(case)-250(may)-250(still)-250(apply;)]TJ 0 g 0 G -17.126 -15.94 Td [(\050b\051)]TJ 0 g 0 G - 0.98 0 0 1 146.411 371.384 Tm [(The)-194(worst)-194(case)-194(r)9(unning)-194(time)-194(for)-194(mer)18(ge-sort)-193(and)-194(heap-sort)-194(is)]TJ/F78 9.9626 Tf 1 0 0 1 402.204 371.384 Tm [(O)]TJ/F191 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)]TJ/F84 9.9626 Tf 7.324 0 Td [(log)]TJ/F78 9.9626 Tf 15.663 0 Td [(n)]TJ/F191 10.3811 Tf 5.788 0 Td [(\051)]TJ/F84 9.9626 Tf -296.533 -11.955 Td [(as)-250(the)-250(average)-250(case;)]TJ + 0.98 0 0 1 146.411 371.384 Tm [(The)-194(worst)-194(case)-194(r)9(unning)-194(time)-194(for)-194(mer)18(ge-sort)-193(and)-194(heap-sort)-194(is)]TJ/F78 9.9626 Tf 1 0 0 1 402.204 371.384 Tm [(O)]TJ/F192 10.3811 Tf 8 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(n)]TJ/F84 9.9626 Tf 7.324 0 Td [(log)]TJ/F78 9.9626 Tf 15.663 0 Td [(n)]TJ/F192 10.3811 Tf 5.788 0 Td [(\051)]TJ/F84 9.9626 Tf -296.533 -11.955 Td [(as)-250(the)-250(average)-250(case;)]TJ 0 g 0 G -16.04 -15.94 Td [(\050c\051)]TJ 0 g 0 G @@ -22159,7 +22159,7 @@ BT 0 g 0 G /F75 9.9626 Tf -277.188 -18.32 Td [(ids)]TJ 0 g 0 G -/F84 9.9626 Tf 1.02 0 0 1 118.705 459.715 Tm [(Identities)-374(of)-374(the)-374(pr)18(ocesses)-374(to)-374(use)-374(for)-374(t)1(he)-374(new)-374(context;)-439(the)-373(ar)17(gument)-374(is)]TJ 1.02 0 0 1 124.802 447.76 Tm [(ignor)18(ed)-287(when)]TJ/F145 9.9626 Tf 1 0 0 1 190.771 447.76 Tm [(np)]TJ/F84 9.9626 Tf 1.02 0 0 1 204.14 447.76 Tm [(is)-286(not)-286(speci\002ed.)-428(This)-286(allows)-286(the)-286(pr)17(ocesses)-286(in)-286(the)-286(new)]TJ 1 0 0 1 124.802 435.805 Tm [(envir)18(onment)-250(to)-250(be)-250(in)-250(an)-250(or)18(der)-250(dif)18(fer)18(ent)-250(fr)18(om)-250(the)-250(original)-250(one.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)-560(Default:)-310(use)-250(the)-250(indices)]TJ/F191 10.3811 Tf 240.57 0 Td [(\050)]TJ/F84 9.9626 Tf 4.149 0 Td [(0)-179(.)-192(.)-192(.)]TJ/F78 9.9626 Tf 19.967 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.504 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1)]TJ/F191 10.3811 Tf 5.106 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ +/F84 9.9626 Tf 1.02 0 0 1 118.705 459.715 Tm [(Identities)-374(of)-374(the)-374(pr)18(ocesses)-374(to)-374(use)-374(for)-374(t)1(he)-374(new)-374(context;)-439(the)-373(ar)17(gument)-374(is)]TJ 1.02 0 0 1 124.802 447.76 Tm [(ignor)18(ed)-287(when)]TJ/F145 9.9626 Tf 1 0 0 1 190.771 447.76 Tm [(np)]TJ/F84 9.9626 Tf 1.02 0 0 1 204.14 447.76 Tm [(is)-286(not)-286(speci\002ed.)-428(This)-286(allows)-286(the)-286(pr)17(ocesses)-286(in)-286(the)-286(new)]TJ 1 0 0 1 124.802 435.805 Tm [(envir)18(onment)-250(to)-250(be)-250(in)-250(an)-250(or)18(der)-250(dif)18(fer)18(ent)-250(fr)18(om)-250(the)-250(original)-250(one.)]TJ 0 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(array)111(.)-560(Default:)-310(use)-250(the)-250(indices)]TJ/F192 10.3811 Tf 240.57 0 Td [(\050)]TJ/F84 9.9626 Tf 4.149 0 Td [(0)-179(.)-192(.)-192(.)]TJ/F78 9.9626 Tf 19.967 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.504 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1)]TJ/F192 10.3811 Tf 5.106 0 Td [(\051)]TJ/F84 9.9626 Tf 4.149 0 Td [(.)]TJ 0 g 0 G /F75 9.9626 Tf -322.483 -18.319 Td [(extcomm)]TJ 0 g 0 G @@ -22236,7 +22236,7 @@ BT 0 g 0 G 0 -19.925 Td [(iam)]TJ 0 g 0 G -/F84 9.9626 Tf 22.137 0 Td [(Identi\002er)-250(of)-250(curr)18(ent)-250(pr)18(ocess)-250(in)-250(the)-250(PSBLAS)-250(virtual)-250(parallel)-250(machine.)]TJ 2.769 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.319 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf 39.292 0 Td [(.)]TJ -66.072 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.745 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value.)]TJ/F189 10.3811 Tf 134.191 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F189 10.3811 Tf 7.873 0 Td [(\024)]TJ/F78 9.9626 Tf 11.016 0 Td [(i)-47(a)-25(m)]TJ/F189 10.3811 Tf 18.678 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.504 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1)]TJ +/F84 9.9626 Tf 22.137 0 Td [(Identi\002er)-250(of)-250(curr)18(ent)-250(pr)18(ocess)-250(in)-250(the)-250(PSBLAS)-250(virtual)-250(parallel)-250(machine.)]TJ 2.769 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.319 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf 39.292 0 Td [(.)]TJ -66.072 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.745 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value.)]TJ/F190 10.3811 Tf 134.191 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F190 10.3811 Tf 7.873 0 Td [(\024)]TJ/F78 9.9626 Tf 11.016 0 Td [(i)-47(a)-25(m)]TJ/F190 10.3811 Tf 18.678 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.504 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1)]TJ 0 g 0 G /F75 9.9626 Tf -239.579 -19.925 Td [(np)]TJ 0 g 0 G @@ -22244,11 +22244,11 @@ BT 0 g 0 G /F84 9.9626 Tf 12.453 -19.925 Td [(1.)]TJ 0 g 0 G - 1.02 0 0 1 175.611 332.495 Tm [(For)-337(pr)18(ocesses)-337(in)-337(the)-337(virtual)-337(parallel)-337(machine)-336(the)-337(identi\002er)-337(will)-337(satisfy)]TJ 1 0 0 1 175.611 320.54 Tm [(0)]TJ/F189 10.3811 Tf 7.874 0 Td [(\024)]TJ/F78 9.9626 Tf 11.016 0 Td [(i)-47(a)-25(m)]TJ/F189 10.3811 Tf 18.678 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1;)]TJ + 1.02 0 0 1 175.611 332.495 Tm [(For)-337(pr)18(ocesses)-337(in)-337(the)-337(virtual)-337(parallel)-337(machine)-336(the)-337(identi\002er)-337(will)-337(satisfy)]TJ 1 0 0 1 175.611 320.54 Tm [(0)]TJ/F190 10.3811 Tf 7.874 0 Td [(\024)]TJ/F78 9.9626 Tf 11.016 0 Td [(i)-47(a)-25(m)]TJ/F190 10.3811 Tf 18.678 0 Td [(\024)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1;)]TJ 0 g 0 G -84.741 -19.925 Td [(2.)]TJ 0 g 0 G - 1.02 0 0 1 175.611 300.615 Tm [(If)-304(the)-303(user)-304(has)-304(r)18(equested)-304(on)]TJ/F145 9.9626 Tf 1 0 0 1 305.201 300.615 Tm [(psb_init)]TJ/F84 9.9626 Tf 1.02 0 0 1 350.13 300.615 Tm [(a)-304(number)-303(of)-304(pr)18(ocesses)-304(less)-304(than)]TJ 1.02 0 0 1 175.611 288.659 Tm [(the)-253(total)-254(available)-253(in)-253(the)-254(parallel)-253(execution)-253(envir)17(onment,)-255(the)-253(r)17(emaining)]TJ 0.992 0 0 1 175.313 276.704 Tm [(pr)18(ocesses)-251(will)-251(have)-251(on)-252(r)19(eturn)]TJ/F78 9.9626 Tf 1 0 0 1 305.592 276.704 Tm [(i)-47(a)-25(m)]TJ/F191 10.3811 Tf 18.677 0 Td [(=)]TJ/F189 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 0.992 0 0 1 343.549 276.704 Tm [(1;)-252(the)-251(only)-251(call)-251(involving)]TJ/F145 9.9626 Tf 1 0 0 1 453.875 276.704 Tm [(ctxt)]TJ/F84 9.9626 Tf 0.992 0 0 1 477.279 276.704 Tm [(that)]TJ 1 0 0 1 175.611 264.749 Tm [(any)-250(such)-250(pr)18(ocess)-250(may)-250(execute)-250(is)-250(to)]TJ/F145 9.9626 Tf 155.296 0 Td [(psb_exit)]TJ/F84 9.9626 Tf 41.843 0 Td [(.)]TJ + 1.02 0 0 1 175.611 300.615 Tm [(If)-304(the)-303(user)-304(has)-304(r)18(equested)-304(on)]TJ/F145 9.9626 Tf 1 0 0 1 305.201 300.615 Tm [(psb_init)]TJ/F84 9.9626 Tf 1.02 0 0 1 350.13 300.615 Tm [(a)-304(number)-303(of)-304(pr)18(ocesses)-304(less)-304(than)]TJ 1.02 0 0 1 175.611 288.659 Tm [(the)-253(total)-254(available)-253(in)-253(the)-254(parallel)-253(execution)-253(envir)17(onment,)-255(the)-253(r)17(emaining)]TJ 0.992 0 0 1 175.313 276.704 Tm [(pr)18(ocesses)-251(will)-251(have)-251(on)-252(r)19(eturn)]TJ/F78 9.9626 Tf 1 0 0 1 305.592 276.704 Tm [(i)-47(a)-25(m)]TJ/F192 10.3811 Tf 18.677 0 Td [(=)]TJ/F190 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 0.992 0 0 1 343.549 276.704 Tm [(1;)-252(the)-251(only)-251(call)-251(involving)]TJ/F145 9.9626 Tf 1 0 0 1 453.875 276.704 Tm [(ctxt)]TJ/F84 9.9626 Tf 0.992 0 0 1 477.279 276.704 Tm [(that)]TJ 1 0 0 1 175.611 264.749 Tm [(any)-250(such)-250(pr)18(ocess)-250(may)-250(execute)-250(is)-250(to)]TJ/F145 9.9626 Tf 155.296 0 Td [(psb_exit)]TJ/F84 9.9626 Tf 41.843 0 Td [(.)]TJ 0 g 0 G -57.662 -174.311 Td [(114)]TJ 0 g 0 G @@ -22293,7 +22293,7 @@ BT 0 g 0 G /F84 9.9626 Tf 12.454 -19.925 Td [(1.)]TJ 0 g 0 G - 0.98 0 0 1 124.493 426.144 Tm [(This)-218(r)19(outine)-218(may)-217(be)-218(called)-217(even)-218(if)-218(a)-217(pr)18(evious)-217(call)-218(to)]TJ/F145 9.9626 Tf 1 0 0 1 345.207 426.144 Tm [(psb_info)]TJ/F84 9.9626 Tf 0.98 0 0 1 389.174 426.144 Tm [(has)-218(r)19(eturned)]TJ 1.02 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9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F190 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ 0 g 0 G /F75 9.9626 Tf -254.344 -32.364 Td [(mode)]TJ 0 g 0 G @@ -23656,7 +23656,7 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -20.409 Td [(root)]TJ 0 g 0 G -/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F189 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F189 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ +/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F190 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F190 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ 0 g 0 G /F75 9.9626 Tf -254.344 -32.364 Td [(mode)]TJ 0 g 0 G @@ -23839,7 +23839,7 @@ BT 0 g 0 G /F75 9.9626 Tf 1 0 0 1 99.895 443.056 Tm [(root)]TJ 0 g 0 G -/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F189 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F189 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ +/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F190 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F190 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ 0 g 0 G /F75 9.9626 Tf -254.344 -32.364 Td [(mode)]TJ 0 g 0 G @@ -24020,7 +24020,7 @@ BT 0 g 0 G /F75 9.9626 Tf 1 0 0 1 99.895 443.056 Tm [(root)]TJ 0 g 0 G -/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F189 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F189 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ +/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F190 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F190 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ 0 g 0 G /F75 9.9626 Tf -254.344 -32.364 Td [(mode)]TJ 0 g 0 G @@ -24203,7 +24203,7 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -20.409 Td [(root)]TJ 0 g 0 G -/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F189 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F189 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ +/F84 9.9626 Tf 0.986 0 0 1 123.148 443.056 Tm [(Pr)18(ocess)-253(to)-254(hold)-253(the)-253(\002nal)-254(value,)-253(or)]TJ/F190 10.3811 Tf 1 0 0 1 270.3 443.056 Tm [(\000)]TJ/F84 9.9626 Tf 0.986 0 0 1 278.495 443.056 Tm [(1)-253(to)-254(make)-253(it)-254(available)-253(on)-253(all)-254(pr)19(ocesses.)]TJ 1 0 0 1 124.802 431.101 Tm [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)]TJ/F190 10.3811 Tf 131.102 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1)]TJ/F148 10.3811 Tf 7.873 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 10.986 0 Td [(r)-17(o)-35(o)-35(t)]TJ/F148 10.3811 Tf 19.923 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.132 0 Td [(1,)-250(default)-250(-1.)]TJ 0 g 0 G /F75 9.9626 Tf -254.344 -32.364 Td [(mode)]TJ 0 g 0 G @@ -24246,7 +24246,7 @@ BT 0 g 0 G -12.453 -19.925 Td [(2.)]TJ 0 g 0 G - 0.999 0 0 1 175.611 540.749 Tm [(Denoting)-251(by)]TJ/F78 9.9626 Tf 1 0 0 1 232.93 540.749 Tm [(d)-40(a)-25(t)]TJ/F78 7.5716 Tf 13.536 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.999 0 0 1 251.713 540.749 Tm [(the)-251(value)-251(of)-250(the)-251(variable)]TJ/F78 9.9626 Tf 1 0 0 1 360.51 540.749 Tm [(d)-40(a)-25(t)]TJ/F84 9.9626 Tf 0.999 0 0 1 376.501 540.749 Tm [(on)-251(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 425.568 540.749 Tm [(i)]TJ/F84 9.9626 Tf 0.999 0 0 1 428.532 540.749 Tm [(,)-251(the)-251(output)]TJ/F78 9.9626 Tf 1 0 0 1 482.247 540.749 Tm [(r)-17(e)-25(s)]TJ/F84 9.9626 Tf -306.636 -11.955 Td [(is)-250(equivalent)-250(to)-250(the)-250(computation)-250(of)]TJ/F78 9.9626 Tf 124.797 -25.467 Td [(r)-17(e)-25(s)]TJ/F191 10.3811 Tf 15.061 0 Td [(=)]TJ/F17 9.9626 Tf 11.086 10.922 Td [(r)]TJ + 0.999 0 0 1 175.611 540.749 Tm [(Denoting)-251(by)]TJ/F78 9.9626 Tf 1 0 0 1 232.93 540.749 Tm [(d)-40(a)-25(t)]TJ/F78 7.5716 Tf 13.536 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.999 0 0 1 251.713 540.749 Tm [(the)-251(value)-251(of)-250(the)-251(variable)]TJ/F78 9.9626 Tf 1 0 0 1 360.51 540.749 Tm [(d)-40(a)-25(t)]TJ/F84 9.9626 Tf 0.999 0 0 1 376.501 540.749 Tm [(on)-251(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 425.568 540.749 Tm [(i)]TJ/F84 9.9626 Tf 0.999 0 0 1 428.532 540.749 Tm [(,)-251(the)-251(output)]TJ/F78 9.9626 Tf 1 0 0 1 482.247 540.749 Tm [(r)-17(e)-25(s)]TJ/F84 9.9626 Tf -306.636 -11.955 Td [(is)-250(equivalent)-250(to)-250(the)-250(computation)-250(of)]TJ/F78 9.9626 Tf 124.797 -25.467 Td [(r)-17(e)-25(s)]TJ/F192 10.3811 Tf 15.061 0 Td [(=)]TJ/F17 9.9626 Tf 11.086 10.922 Td [(r)]TJ ET q 1 0 0 1 336.642 514.443 cm @@ -24399,11 +24399,11 @@ BT 0 g 0 G /F75 9.9626 Tf -24.907 -19.925 Td [(dst)]TJ 0 g 0 G -/F84 9.9626 Tf 18.81 0 Td [(Destination)-250(pr)18(ocess.)]TJ 6.097 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf 39.293 0 Td [(.)]TJ -66.072 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)-250(0)]TJ/F148 10.3811 Tf 138.85 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(d)-25(s)-25(t)]TJ/F148 10.3811 Tf 15.689 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F189 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1.)]TJ +/F84 9.9626 Tf 18.81 0 Td [(Destination)-250(pr)18(ocess.)]TJ 6.097 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf 39.293 0 Td [(.)]TJ -66.072 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)-250(0)]TJ/F148 10.3811 Tf 138.85 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(d)-25(s)-25(t)]TJ/F148 10.3811 Tf 15.689 0 Td [(<)]TJ/F192 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(n)-80(p)]TJ/F190 10.3811 Tf 13.503 0 Td [(\000)]TJ/F84 9.9626 Tf 10.131 0 Td [(1.)]TJ 0 g 0 G /F75 9.9626 Tf -241.89 -31.88 Td [(m)]TJ 0 g 0 G -/F84 9.9626 Tf 13.838 0 Td [(Number)-250(of)-250(r)18(ows.)]TJ 11.069 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf 28.782 0 Td [(.)]TJ -60.523 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(Optional)]TJ/F84 9.9626 Tf 40.946 0 Td [(.)]TJ -67.725 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(value)-250(0)]TJ/F148 10.3811 Tf 138.85 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(m)]TJ/F148 10.3811 Tf 10.767 0 Td [(<)]TJ/F191 10.3811 Tf 8.319 0 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(s)-18(i)-32(z)-25(e)]TJ/F191 10.3811 Tf 15.94 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(d)-40(a)-25(t)]TJ/F84 9.9626 Tf 13.494 0 Td [(,)-167(1)]TJ/F191 10.3811 Tf 9.257 0 Td [(\051)]TJ/F84 9.9626 Tf 4.15 0 Td [(.)]TJ 1.02 0 0 1 124.304 294.637 Tm [(When)]TJ/F78 9.9626 Tf 1 0 0 1 153.769 294.637 Tm [(d)-40(a)-25(t)]TJ/F84 9.9626 Tf 1.02 0 0 1 169.747 294.637 Tm [(is)-244(a)-245(rank)-244(2)-245(array)109(,)-244(speci\002es)-245(the)-244(number)-244(of)-245(r)18(ows)-244(to)-245(be)-244(sent)-245(inde-)]TJ 0.98 0 0 1 124.503 282.682 Tm [(pendently)-236(of)-236(the)-236(leading)-236(dimension)]TJ/F78 9.9626 Tf 1 0 0 1 280.369 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[(itrace)]TJ 0 g 0 G -/F84 9.9626 Tf 0.98 0 0 1 129.773 274.035 Tm [(If)]TJ/F148 10.3811 Tf 1 0 0 1 138.672 274.035 Tm [(>)]TJ/F84 9.9626 Tf 0.98 0 0 1 149.634 274.035 Tm [(0)-229(print)-228(out)-229(an)-229(informational)-228(message)-229(about)-229(conver)19(gence)-229(every)]TJ/F78 9.9626 Tf 1 0 0 1 419.702 274.035 Tm [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F84 9.9626 Tf -294.9 -11.955 Td [(iterations.)-310(If)]TJ/F191 10.3811 Tf 56.313 0 Td [(=)]TJ/F84 9.9626 Tf 10.962 0 Td [(0)-250(print)-250(a)-250(message)-250(in)-250(case)-250(of)-250(conver)18(gence)-250(failur)18(e.)]TJ -67.275 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.57 0 Td [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F191 10.3811 Tf 26.797 0 Td [(=)]TJ/F189 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1.)]TJ +/F84 9.9626 Tf 0.98 0 0 1 129.773 274.035 Tm [(If)]TJ/F148 10.3811 Tf 1 0 0 1 138.672 274.035 Tm [(>)]TJ/F84 9.9626 Tf 0.98 0 0 1 149.634 274.035 Tm [(0)-229(print)-228(out)-229(an)-229(informational)-228(message)-229(about)-229(conver)19(gence)-229(every)]TJ/F78 9.9626 Tf 1 0 0 1 419.702 274.035 Tm [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F84 9.9626 Tf -294.9 -11.955 Td [(iterations.)-310(If)]TJ/F192 10.3811 Tf 56.313 0 Td [(=)]TJ/F84 9.9626 Tf 10.962 0 Td [(0)-250(print)-250(a)-250(message)-250(in)-250(case)-250(of)-250(conver)18(gence)-250(failur)18(e.)]TJ -67.275 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.57 0 Td [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F192 10.3811 Tf 26.797 0 Td [(=)]TJ/F190 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1.)]TJ 0 g 0 G /F75 9.9626 Tf -109.554 -34.158 Td [(irst)]TJ 0 g 0 G @@ -29075,40 +29075,40 @@ q []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 156.993 706.129 Td [(richardson)-250(\227)-250(Richardson)-250(Iteration)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf -57.406 -19.209 Td [(This)-250(subr)18(outine)-250(is)-250(a)-250(driver)-250(implementig)-250(a)-250(Richar)18(dson)-250(iteration)]TJ/F78 9.9626 Tf 111.157 -22.171 Td [(x)]TJ/F78 7.5716 Tf 5.2 -2.085 Td [(k)]TJ/F191 7.8896 Tf 3.589 0 Td [(+)]TJ/F84 7.5716 Tf 6.228 0 Td [(1)]TJ/F191 10.3811 Tf 7.176 2.085 Td [(=)]TJ/F78 9.9626 Tf 11.534 0 Td [(M)]TJ/F189 7.8896 Tf 9.674 4.115 Td [(\000)]TJ/F84 9.9626 Tf 6.726 -4.115 Td [(1)]TJ/F191 10.3811 Tf 5.105 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(b)]TJ/F189 10.3811 Tf 6.799 0 Td [(\000)]TJ/F78 9.9626 Tf 10.754 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.812 -2.085 Td [(k)]TJ/F191 10.3811 Tf 4.117 2.085 Td [(\051)-209(+)]TJ/F78 9.9626 Tf 16.636 0 Td [(x)]TJ/F78 7.5716 Tf 5.201 -2.085 Td [(k)]TJ/F84 9.9626 Tf 3.992 2.085 Td [(,)]TJ -231.084 -22.17 Td [(with)-250(the)-250(pr)18(econditioner)-250(operator)]TJ/F78 9.9626 Tf 147.599 0 Td [(M)]TJ/F84 9.9626 Tf 12.07 0 Td [(de\002ned)-250(in)-250(the)-250(pr)18(evious)-250(section.)]TJ -144.307 -12.082 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ +/F75 11.9552 Tf 156.993 706.129 Td [(richardson)-250(\227)-250(Richardson)-250(Iteration)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf -57.406 -19.209 Td [(This)-250(subr)18(outine)-250(is)-250(a)-250(driver)-250(implementig)-250(a)-250(Richar)18(dson)-250(iteration)]TJ/F78 9.9626 Tf 111.157 -22.171 Td [(x)]TJ/F78 7.5716 Tf 5.2 -2.085 Td [(k)]TJ/F192 7.8896 Tf 3.589 0 Td [(+)]TJ/F84 7.5716 Tf 6.228 0 Td [(1)]TJ/F192 10.3811 Tf 7.176 2.085 Td [(=)]TJ/F78 9.9626 Tf 11.534 0 Td [(M)]TJ/F190 7.8896 Tf 9.674 4.115 Td [(\000)]TJ/F84 9.9626 Tf 6.726 -4.115 Td [(1)]TJ/F192 10.3811 Tf 5.105 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(b)]TJ/F190 10.3811 Tf 6.799 0 Td [(\000)]TJ/F78 9.9626 Tf 10.754 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.812 -2.085 Td [(k)]TJ/F192 10.3811 Tf 4.117 2.085 Td [(\051)-209(+)]TJ/F78 9.9626 Tf 16.636 0 Td [(x)]TJ/F78 7.5716 Tf 5.201 -2.085 Td [(k)]TJ/F84 9.9626 Tf 3.992 2.085 Td [(,)]TJ -231.084 -22.17 Td [(with)-250(the)-250(pr)18(econditioner)-250(operator)]TJ/F78 9.9626 Tf 147.599 0 Td [(M)]TJ/F84 9.9626 Tf 12.07 0 Td [(de\002ned)-250(in)-250(the)-250(pr)18(evious)-250(section.)]TJ -144.307 -12.082 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ 0 g 0 G /F75 9.9626 Tf -14.944 -20.304 Td [(1)]TJ 0 g 0 G -/F84 9.9626 Tf 0.99 0 0 1 109.858 610.193 Tm [(normwise)-252(backwar)18(d)-253(err)18(or)-252(in)-253(the)-252(in\002nity)-253(norm;)-252(the)-253(iteration)-252(is)-253(stopped)-252(when)]TJ/F78 9.9626 Tf 1 0 0 1 218.894 581.636 Tm [(e)-15(r)-25(r)]TJ/F191 10.3811 Tf 15.14 0 Td [(=)]TJ/F189 10.3811 Tf 40.62 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 0.99 0 0 1 109.858 610.193 Tm [(normwise)-252(backwar)18(d)-253(err)18(or)-252(in)-253(the)-252(in\002nity)-253(norm;)-252(the)-253(iteration)-252(is)-253(stopped)-252(when)]TJ/F78 9.9626 Tf 1 0 0 1 218.894 581.636 Tm [(e)-15(r)-25(r)]TJ/F192 10.3811 Tf 15.14 0 Td [(=)]TJ/F190 10.3811 Tf 40.62 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q 1 0 0 1 246.191 584.127 cm []0 d 0 J 0.398 w 0 0 m 74.372 0 l S Q BT -/F191 10.3811 Tf 246.316 574.802 Td [(\050)]TJ/F189 10.3811 Tf 4.274 0 Td [(k)]TJ/F78 9.9626 Tf 5.938 0 Td [(A)]TJ/F189 10.3811 Tf 7.442 0 Td [(k)-24(k)]TJ/F78 9.9626 Tf 11.048 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F191 10.3811 Tf 7.376 0 Td [(+)]TJ/F189 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.44 0 Td [(b)]TJ/F189 10.3811 Tf 4.861 0 Td [(k)]TJ/F191 10.3811 Tf 5.44 0 Td [(\051)]TJ/F148 10.3811 Tf 8.236 6.834 Td [(<)]TJ/F78 9.9626 Tf 11.087 0 Td [(e)-80(p)-25(s)]TJ +/F192 10.3811 Tf 246.316 574.802 Td [(\050)]TJ/F190 10.3811 Tf 4.274 0 Td [(k)]TJ/F78 9.9626 Tf 5.938 0 Td [(A)]TJ/F190 10.3811 Tf 7.442 0 Td [(k)-24(k)]TJ/F78 9.9626 Tf 11.048 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F192 10.3811 Tf 7.376 0 Td [(+)]TJ/F190 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.44 0 Td [(b)]TJ/F190 10.3811 Tf 4.861 0 Td [(k)]TJ/F192 10.3811 Tf 5.44 0 Td [(\051)]TJ/F148 10.3811 Tf 8.236 6.834 Td [(<)]TJ/F78 9.9626 Tf 11.087 0 Td [(e)-80(p)-25(s)]TJ 0 g 0 G /F75 9.9626 Tf -235.842 -32.142 Td [(2)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 136.209 -28.557 Td [(e)-15(r)-25(r)]TJ/F191 10.3811 Tf 15.141 0 Td [(=)]TJ/F189 10.3811 Tf 13.446 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 136.209 -28.557 Td [(e)-15(r)-25(r)]TJ/F192 10.3811 Tf 15.141 0 Td [(=)]TJ/F190 10.3811 Tf 13.446 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q 1 0 0 1 273.365 523.428 cm []0 d 0 J 0.398 w 0 0 m 20.025 0 l S Q BT -/F189 10.3811 Tf 273.49 514.103 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F189 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F148 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ +/F190 10.3811 Tf 273.49 514.103 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F190 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F148 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ 0 g 0 G /F75 9.9626 Tf -208.668 -32.082 Td [(3)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -28.556 Td [(e)-15(r)-25(r)]TJ/F191 10.3811 Tf 15.14 0 Td [(=)]TJ/F189 10.3811 Tf 15.17 6.744 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F189 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -28.556 Td [(e)-15(r)-25(r)]TJ/F192 10.3811 Tf 15.14 0 Td [(=)]TJ/F190 10.3811 Tf 15.17 6.744 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F190 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q 1 0 0 1 271.641 462.789 cm []0 d 0 J 0.398 w 0 0 m 23.472 0 l S Q BT -/F189 10.3811 Tf 271.766 453.464 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F189 10.3811 Tf 4.408 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F148 10.3811 Tf 8.371 8.579 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.587 428.217 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 99.895 416.261 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 144.027 416.261 Tm [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 153.866 416.261 Tm [(is)-199(the)-199(tentat)1(ive)-199(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 273.705 416.261 Tm [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F191 10.3811 Tf 5.643 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F189 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.758 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 328.46 416.261 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 99.895 404.306 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.305 -18.185 Td [(c)-175(a)-175(l)-174(l)-888(p)-113(s)-113(b)]TJ +/F190 10.3811 Tf 271.766 453.464 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F190 10.3811 Tf 4.408 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F148 10.3811 Tf 8.371 8.579 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.587 428.217 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 99.895 416.261 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 144.027 416.261 Tm [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 153.866 416.261 Tm [(is)-199(the)-199(tentat)1(ive)-199(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 273.705 416.261 Tm [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F192 10.3811 Tf 5.643 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F190 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.758 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 328.46 416.261 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 99.895 404.306 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.305 -18.185 Td [(c)-175(a)-175(l)-174(l)-888(p)-113(s)-113(b)]TJ ET q 1 0 0 1 150.598 386.32 cm @@ -29285,11 +29285,11 @@ BT 0 g 0 G /F75 9.9626 Tf -258.11 -19.428 Td [(itmax)]TJ 0 g 0 G -/F84 9.9626 Tf 30.127 0 Td [(The)-250(maximum)-250(number)-250(of)-250(iterations)-250(to)-250(perform.)]TJ -5.221 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.57 0 Td [(i)-32(t)-25(m)-40(a)-42(x)]TJ/F191 10.3811 Tf 27.744 0 Td [(=)]TJ/F84 9.9626 Tf 10.961 0 Td [(1000.)]TJ -77.275 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(variable)]TJ/F78 9.9626 Tf 142.35 0 Td [(i)-32(t)-25(m)-40(a)-42(x)]TJ/F189 10.3811 Tf 27.743 0 Td [(\025)]TJ/F84 9.9626 Tf 10.962 0 Td [(1.)]TJ +/F84 9.9626 Tf 30.127 0 Td [(The)-250(maximum)-250(number)-250(of)-250(iterations)-250(to)-250(perform.)]TJ -5.221 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.57 0 Td [(i)-32(t)-25(m)-40(a)-42(x)]TJ/F192 10.3811 Tf 27.744 0 Td [(=)]TJ/F84 9.9626 Tf 10.961 0 Td [(1000.)]TJ -77.275 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(integer)-250(variable)]TJ/F78 9.9626 Tf 142.35 0 Td [(i)-32(t)-25(m)-40(a)-42(x)]TJ/F190 10.3811 Tf 27.743 0 Td [(\025)]TJ/F84 9.9626 Tf 10.962 0 Td [(1.)]TJ 0 g 0 G /F75 9.9626 Tf -205.961 -19.428 Td [(itrace)]TJ 0 g 0 G -/F84 9.9626 Tf 0.98 0 0 1 180.583 425.182 Tm [(If)]TJ/F148 10.3811 Tf 1 0 0 1 189.481 425.182 Tm [(>)]TJ/F84 9.9626 Tf 0.98 0 0 1 200.443 425.182 Tm [(0)-229(print)-228(out)-229(an)-229(informational)-228(message)-229(about)-229(conver)19(gence)-229(every)]TJ/F78 9.9626 Tf 1 0 0 1 470.511 425.182 Tm [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F84 9.9626 Tf -294.9 -11.955 Td [(iterations.)-310(If)]TJ/F191 10.3811 Tf 56.313 0 Td [(=)]TJ/F84 9.9626 Tf 10.962 0 Td [(0)-250(print)-250(a)-250(message)-250(in)-250(case)-250(of)-250(conver)18(gence)-250(failur)18(e.)]TJ -67.275 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Default:)]TJ/F78 9.9626 Tf 38.57 0 Td [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F191 10.3811 Tf 26.797 0 Td [(=)]TJ/F189 10.3811 Tf 11.086 0 Td [(\000)]TJ/F84 9.9626 Tf 8.194 0 Td [(1.)]TJ +/F84 9.9626 Tf 0.98 0 0 1 180.583 425.182 Tm [(If)]TJ/F148 10.3811 Tf 1 0 0 1 189.481 425.182 Tm [(>)]TJ/F84 9.9626 Tf 0.98 0 0 1 200.443 425.182 Tm [(0)-229(print)-228(out)-229(an)-229(informational)-228(message)-229(about)-229(conver)19(gence)-229(every)]TJ/F78 9.9626 Tf 1 0 0 1 470.511 425.182 Tm [(i)-32(t)-15(r)-50(a)-25(c)-25(e)]TJ/F84 9.9626 Tf -294.9 -11.955 Td 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[(\050)]TJ/F75 9.9626 Tf 0.98 0 0 1 194.032 263.883 Tm [(HLL)]TJ/F84 9.9626 Tf 0.98 0 0 1 214.096 263.883 Tm [(\051)-236(format)-236(alleviates)-236(the)-236(main)-236(pr)19(oblem)-236(of)-236(the)-236(ELLP)94(ACK)]TJ 0.989 0 0 1 99.895 251.928 Tm [(format,)-252(that)-253(is,)-252(the)-252(amount)-253(of)-252(memory)-252(r)18(equir)18(ed)-252(by)-252(padding)-252(for)-253(sparse)-252(matrices)]TJ 1 0 0 1 99.895 239.973 Tm [(in)-250(which)-250(the)-250(maximum)-250(r)18(ow)-250(length)-250(is)-250(lar)18(ger)-250(than)-250(the)-250(average.)]TJ 1.02 0 0 1 114.839 227.97 Tm [(The)-421(number)-421(of)-422(elements)-421(allocated)-421(to)-421(padding)-421(is)]TJ/F191 10.3811 Tf 1 0 0 1 345.511 227.97 Tm [([)-24(\050)]TJ/F78 9.9626 Tf 7.403 0 Td [(m)]TJ/F189 10.3811 Tf 10.6 0 Td [(\003)]TJ/F78 9.9626 Tf 8.039 0 Td [(m)-40(a)-42(x)-70(N)-76(R)]TJ/F191 10.3811 Tf 34.072 0 Td [(\051)]TJ/F189 10.3811 Tf 6.874 0 Td [(\000)]TJ/F191 10.3811 Tf 10.919 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td 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1 0 0 1 287.784 204.06 Tm [(m)-40(a)-42(x)-70(N)-76(R)]TJ/F84 9.9626 Tf 0.995 0 0 1 324.229 204.06 Tm [(is)-252(the)-252(maximum)-252(number)-252(of)]TJ 0.998 0 0 1 99.895 192.104 Tm [(nonzer)18(o)-251(elements)-251(in)-251(every)-251(r)18(ow)-252(and)]TJ/F78 9.9626 Tf 1 0 0 1 257.847 192.104 Tm [(a)-25(v)-47(g)-60(N)-76(R)]TJ/F84 9.9626 Tf 0.998 0 0 1 291.322 192.104 Tm [(is)-251(the)-251(average)-251(number)-252(of)-251(nonzer)18(os.)]TJ 1.017 0 0 1 99.587 180.149 Tm [(Ther)18(efor)17(e)-245(a)-246(single)-245(densely)-246(populated)-245(r)17(ow)-245(can)-246(seriously)-246(af)18(fec)1(t)-246(the)-246(total)-245(size)-246(of)]TJ 1 0 0 1 99.895 168.194 Tm [(the)-250(allocation.)]TJ 1.02 0 0 1 114.839 156.191 Tm [(T)90(o)-335(limit)-336(this)-335(ef)18(fect,)-358(in)-336(t)1(he)-336(HLL)-335(format)-336(we)-335(br)18(eak)-336(the)-335(original)-336(matrix)-335(into)]TJ 0.985 0 0 1 99.895 144.236 Tm [(equally)-254(sized)-253(gr)18(oups)-253(of)-254(r)18(ows)-253(\050called)]TJ/F78 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0.989 0 0 1 99.895 251.928 Tm [(format,)-252(that)-253(is,)-252(the)-252(amount)-253(of)-252(memory)-252(r)18(equir)18(ed)-252(by)-252(padding)-252(for)-253(sparse)-252(matrices)]TJ 1 0 0 1 99.895 239.973 Tm [(in)-250(which)-250(the)-250(maximum)-250(r)18(ow)-250(length)-250(is)-250(lar)18(ger)-250(than)-250(the)-250(average.)]TJ 1.02 0 0 1 114.839 227.97 Tm [(The)-421(number)-421(of)-422(elements)-421(allocated)-421(to)-421(padding)-421(is)]TJ/F192 10.3811 Tf 1 0 0 1 345.511 227.97 Tm [([)-24(\050)]TJ/F78 9.9626 Tf 7.403 0 Td [(m)]TJ/F190 10.3811 Tf 10.6 0 Td [(\003)]TJ/F78 9.9626 Tf 8.039 0 Td [(m)-40(a)-42(x)-70(N)-76(R)]TJ/F192 10.3811 Tf 34.072 0 Td [(\051)]TJ/F190 10.3811 Tf 6.874 0 Td [(\000)]TJ/F192 10.3811 Tf 10.919 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(m)]TJ/F190 10.3811 Tf 10.6 0 Td [(\003)]TJ/F78 9.9626 Tf -338.123 -11.955 Td [(a)-25(v)-47(g)-60(N)-76(R)]TJ/F192 10.3811 Tf 31.104 0 Td [(\051)-537(=)]TJ/F78 9.9626 Tf 23.266 0 Td [(m)]TJ/F190 10.3811 Tf 10.451 0 Td 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[(nonzer)18(o)-251(elements)-251(in)-251(every)-251(r)18(ow)-252(and)]TJ/F78 9.9626 Tf 1 0 0 1 257.847 192.104 Tm [(a)-25(v)-47(g)-60(N)-76(R)]TJ/F84 9.9626 Tf 0.998 0 0 1 291.322 192.104 Tm [(is)-251(the)-251(average)-251(number)-252(of)-251(nonzer)18(os.)]TJ 1.017 0 0 1 99.587 180.149 Tm [(Ther)18(efor)17(e)-245(a)-246(single)-245(densely)-246(populated)-245(r)17(ow)-245(can)-246(seriously)-246(af)18(fec)1(t)-246(the)-246(total)-245(size)-246(of)]TJ 1 0 0 1 99.895 168.194 Tm [(the)-250(allocation.)]TJ 1.02 0 0 1 114.839 156.191 Tm [(T)90(o)-335(limit)-336(this)-335(ef)18(fect,)-358(in)-336(t)1(he)-336(HLL)-335(format)-336(we)-335(br)18(eak)-336(the)-335(original)-336(matrix)-335(into)]TJ 0.985 0 0 1 99.895 144.236 Tm [(equally)-254(sized)-253(gr)18(oups)-253(of)-254(r)18(ows)-253(\050called)]TJ/F78 9.9626 Tf 0.985 0 0 1 259.082 144.236 Tm [(hacks)]TJ/F84 9.9626 Tf 0.985 0 0 1 280.514 144.236 Tm 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[(hackOffsets)]TJ/F84 9.9626 Tf 0.993 0 0 1 374.299 658.242 Tm [(is)-252(pr)18(ovided)-251(to)-252(keep)-252(track)-252(of)]TJ 1.009 0 0 1 150.705 646.287 Tm [(the)-248(individual)-248(submatrices.)-308(All)-248(hacks)-249(have)-248(the)-248(same)-248(number)-248(of)-248(r)18(ows)]TJ/F78 9.9626 Tf 1.009 0 0 1 458.348 646.287 Tm [(hackSize)]TJ/F84 9.9626 Tf 1.009 0 0 1 493.148 646.287 Tm [(;)]TJ 0.985 0 0 1 150.705 634.332 Tm [(hence,)-255(the)]TJ/F78 9.9626 Tf 0.985 0 0 1 196.944 634.332 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 0.985 0 0 1 244.865 634.332 Tm [(vector)-254(is)-255(an)-254(array)-255(of)]TJ/F191 10.3811 Tf 1 0 0 1 333.788 634.332 Tm [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(m)]TJ/F84 9.9626 Tf 8 0 Td [(/)]TJ/F78 9.9626 Tf 6.336 0 Td [(h)-40(a)-25(c)-25(k)-30(S)-18(i)-32(z)-25(e)]TJ/F191 10.3811 Tf 36.682 0 Td [(\051)-210(+)]TJ/F84 9.9626 Tf 0.985 0 0 1 405.427 634.332 Tm [(1)-254(elements,)-255(each)-254(one)]TJ 0.985 0 0 1 150.406 622.377 Tm [(pointing)-253(to)-253(the)-253(\002rst)-253(index)-253(of)-253(a)-253(submatrix)-254(ins)1(ide)-254(the)-253(stacked)]TJ/F78 9.9626 Tf 0.985 0 0 1 408.705 622.377 Tm [(cM)]TJ/F84 9.9626 Tf 0.985 0 0 1 421.963 622.377 Tm [(/)]TJ/F78 9.9626 Tf 0.985 0 0 1 427.91 622.377 Tm [(rP)]TJ/F84 9.9626 Tf 0.985 0 0 1 440.206 622.377 Tm [(buf)18(fers,)-253(plus)]TJ 1.02 0 0 1 150.705 610.422 Tm [(an)-269(additional)-269(element)-268(pointing)-269(past)-269(the)-269(end)-269(of)-268(the)-269(last)-269(block,)-275(wher)18(e)-269(the)-269(next)]TJ 1.006 0 0 1 150.705 598.467 Tm [(one)-248(would)-249(begin.)-308(W)92(e)-249(thus)-248(have)-249(the)-248(pr)18(operty)-249(that)-248(the)-249(el)1(ements)-249(of)-248(the)]TJ/F78 9.9626 Tf 1 0 0 1 456.901 598.467 Tm [(k)]TJ/F84 9.9626 Tf 1.006 0 0 1 461.498 598.467 Tm [(-th)]TJ/F78 9.9626 Tf 1.006 0 0 1 476.426 598.467 Tm [(hack)]TJ/F84 9.9626 Tf 0.995 0 0 1 150.705 586.511 Tm [(ar)18(e)-252(stor)18(ed)-251(between)]TJ/F145 9.9626 Tf 1 0 0 1 236.017 586.511 Tm [(hackOffsets[k])]TJ/F84 9.9626 Tf 0.995 0 0 1 311.738 586.511 Tm [(and)]TJ/F145 9.9626 Tf 1 0 0 1 331.016 586.511 Tm [(hackOffsets[k+1])]TJ/F84 9.9626 Tf 0.995 0 0 1 414.702 586.511 Tm [(,)-252(similarly)-252(to)-252(what)]TJ 1 0 0 1 150.705 574.556 Tm [(happens)-250(in)-250(the)-250(CSR)-250(format.)]TJ +/F84 9.9626 Tf 1.002 0 0 1 150.705 706.129 Tm [(number)-250(of)-250(nonzer)18(os)-251(we)-250(obtain)-250(essentially)-250(the)-250(JAgged)-250(Diagonals)-251(format.)-311(If)-250(the)]TJ 1.02 0 0 1 150.705 694.174 Tm [(r)18(ows)-295(ar)18(e)-294(not)-294(in)-295(the)-294(original)-294(or)18(der)72(,)-306(then)-294(an)-295(additional)-294(vector)]TJ/F78 9.9626 Tf 1.02 0 0 1 423.988 694.174 Tm [(rIdx)]TJ/F84 9.9626 Tf 1.02 0 0 1 444.477 694.174 Tm [(is)-294(r)17(equir)18(ed,)]TJ 1 0 0 1 150.705 682.219 Tm [(storing)-250(the)-250(actual)-250(r)18(ow)-250(index)-250(for)-250(each)-250(r)18(ow)-250(in)-250(the)-250(data)-250(str)8(uctur)18(e.)]TJ 0.981 0 0 1 165.649 670.198 Tm [(The)-255(multiple)-255(ELLP)94(ACK-like)-255(buf)18(fers)-255(ar)18(e)-255(stac)1(ked)-255(together)-255(inside)-255(a)-255(single,)-255(one)]TJ 0.993 0 0 1 150.705 658.242 Tm [(dimensional)-252(array;)-252(an)-251(additional)-252(vector)]TJ/F78 9.9626 Tf 0.993 0 0 1 326.015 658.242 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 0.993 0 0 1 374.299 658.242 Tm [(is)-252(pr)18(ovided)-251(to)-252(keep)-252(track)-252(of)]TJ 1.009 0 0 1 150.705 646.287 Tm [(the)-248(individual)-248(submatrices.)-308(All)-248(hacks)-249(have)-248(the)-248(same)-248(number)-248(of)-248(r)18(ows)]TJ/F78 9.9626 Tf 1.009 0 0 1 458.348 646.287 Tm [(hackSize)]TJ/F84 9.9626 Tf 1.009 0 0 1 493.148 646.287 Tm [(;)]TJ 0.985 0 0 1 150.705 634.332 Tm [(hence,)-255(the)]TJ/F78 9.9626 Tf 0.985 0 0 1 196.944 634.332 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 0.985 0 0 1 244.865 634.332 Tm [(vector)-254(is)-255(an)-254(array)-255(of)]TJ/F192 10.3811 Tf 1 0 0 1 333.788 634.332 Tm [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(m)]TJ/F84 9.9626 Tf 8 0 Td [(/)]TJ/F78 9.9626 Tf 6.336 0 Td [(h)-40(a)-25(c)-25(k)-30(S)-18(i)-32(z)-25(e)]TJ/F192 10.3811 Tf 36.682 0 Td [(\051)-210(+)]TJ/F84 9.9626 Tf 0.985 0 0 1 405.427 634.332 Tm [(1)-254(elements,)-255(each)-254(one)]TJ 0.985 0 0 1 150.406 622.377 Tm [(pointing)-253(to)-253(the)-253(\002rst)-253(index)-253(of)-253(a)-253(submatrix)-254(ins)1(ide)-254(the)-253(stacked)]TJ/F78 9.9626 Tf 0.985 0 0 1 408.705 622.377 Tm [(cM)]TJ/F84 9.9626 Tf 0.985 0 0 1 421.963 622.377 Tm [(/)]TJ/F78 9.9626 Tf 0.985 0 0 1 427.91 622.377 Tm [(rP)]TJ/F84 9.9626 Tf 0.985 0 0 1 440.206 622.377 Tm [(buf)18(fers,)-253(plus)]TJ 1.02 0 0 1 150.705 610.422 Tm [(an)-269(additional)-269(element)-268(pointing)-269(past)-269(the)-269(end)-269(of)-268(the)-269(last)-269(block,)-275(wher)18(e)-269(the)-269(next)]TJ 1.006 0 0 1 150.705 598.467 Tm [(one)-248(would)-249(begin.)-308(W)92(e)-249(thus)-248(have)-249(the)-248(pr)18(operty)-249(that)-248(the)-249(el)1(ements)-249(of)-248(the)]TJ/F78 9.9626 Tf 1 0 0 1 456.901 598.467 Tm [(k)]TJ/F84 9.9626 Tf 1.006 0 0 1 461.498 598.467 Tm [(-th)]TJ/F78 9.9626 Tf 1.006 0 0 1 476.426 598.467 Tm [(hack)]TJ/F84 9.9626 Tf 0.995 0 0 1 150.705 586.511 Tm [(ar)18(e)-252(stor)18(ed)-251(between)]TJ/F145 9.9626 Tf 1 0 0 1 236.017 586.511 Tm [(hackOffsets[k])]TJ/F84 9.9626 Tf 0.995 0 0 1 311.738 586.511 Tm [(and)]TJ/F145 9.9626 Tf 1 0 0 1 331.016 586.511 Tm [(hackOffsets[k+1])]TJ/F84 9.9626 Tf 0.995 0 0 1 414.702 586.511 Tm [(,)-252(similarly)-252(to)-252(what)]TJ 1 0 0 1 150.705 574.556 Tm [(happens)-250(in)-250(the)-250(CSR)-250(format.)]TJ 0 g 0 G ET 1 0 0 1 197.579 452.455 cm @@ -31018,7 +31018,7 @@ BT [-525(idiag\050:\051,)]TJ 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G - 18.829 -10.959 Td [(hkoffs\050:\051)]TJ/F148 5.1905 Tf -15.277 0 Td [(,)]TJ/F189 5.1905 Tf 0.61 0 Td [(!)]TJ + 18.829 -10.959 Td [(hkoffs\050:\051)]TJ/F148 5.1905 Tf -15.277 0 Td [(,)]TJ/F190 5.1905 Tf 0.61 0 Td [(!)]TJ 0 g 0 G 0.73 0.73 0.73 rg 0.73 0.73 0.73 RG 0 g 0 G @@ -31058,7 +31058,7 @@ BT 0 0 1 rg 0 0 1 RG [-248(8)]TJ 0 g 0 G - [(\051)-248(has)-248(a)-247(2-dimensional)-248(array)]TJ/F145 9.9626 Tf 1 0 0 1 483.955 180.167 Tm [(AS)]TJ/F84 9.9626 Tf 0.98 0 0 1 150.705 168.212 Tm [(containing)-223(in)-222(each)-223(column)-223(the)-222(coef)18(\002cients)-223(along)-223(a)-222(diagonal)-223(of)-223(the)-222(matrix,)-229(and)-223(an)]TJ 0.98 0 0 1 150.705 156.257 Tm [(integer)-254(array)]TJ/F145 9.9626 Tf 1 0 0 1 208.91 156.257 Tm [(OFFSET)]TJ/F84 9.9626 Tf 0.98 0 0 1 242.771 156.257 Tm [(that)-254(determines)-254(wher)19(e)-254(each)-254(diagonal)-254(starts.)-316(The)-253(diagonals)]TJ 1 0 0 1 150.705 144.302 Tm [(in)]TJ/F145 9.9626 Tf 11.188 0 Td [(AS)]TJ/F84 9.9626 Tf 12.951 0 Td [(ar)18(e)-250(padded)-250(with)-250(zer)18(os)-250(as)-250(necessary)111(.)]TJ 1.01 0 0 1 165.649 132.281 Tm [(The)-248(code)-248(to)-249(compute)-248(the)-248(matrix-vector)-248(pr)17(oduct)]TJ/F78 9.9626 Tf 1 0 0 1 378.488 132.281 Tm [(y)]TJ/F191 10.3811 Tf 8.011 0 Td [(=)]TJ/F78 9.9626 Tf 11.598 0 Td [(A)-42(x)]TJ/F84 9.9626 Tf 1.01 0 0 1 413.412 132.281 Tm [(is)-248(shown)-249(in)-248(Alg.)]TJ + [(\051)-248(has)-248(a)-247(2-dimensional)-248(array)]TJ/F145 9.9626 Tf 1 0 0 1 483.955 180.167 Tm [(AS)]TJ/F84 9.9626 Tf 0.98 0 0 1 150.705 168.212 Tm [(containing)-223(in)-222(each)-223(column)-223(the)-222(coef)18(\002cients)-223(along)-223(a)-222(diagonal)-223(of)-223(the)-222(matrix,)-229(and)-223(an)]TJ 0.98 0 0 1 150.705 156.257 Tm [(integer)-254(array)]TJ/F145 9.9626 Tf 1 0 0 1 208.91 156.257 Tm [(OFFSET)]TJ/F84 9.9626 Tf 0.98 0 0 1 242.771 156.257 Tm [(that)-254(determines)-254(wher)19(e)-254(each)-254(diagonal)-254(starts.)-316(The)-253(diagonals)]TJ 1 0 0 1 150.705 144.302 Tm [(in)]TJ/F145 9.9626 Tf 11.188 0 Td [(AS)]TJ/F84 9.9626 Tf 12.951 0 Td [(ar)18(e)-250(padded)-250(with)-250(zer)18(os)-250(as)-250(necessary)111(.)]TJ 1.01 0 0 1 165.649 132.281 Tm [(The)-248(code)-248(to)-249(compute)-248(the)-248(matrix-vector)-248(pr)17(oduct)]TJ/F78 9.9626 Tf 1 0 0 1 378.488 132.281 Tm [(y)]TJ/F192 10.3811 Tf 8.011 0 Td [(=)]TJ/F78 9.9626 Tf 11.598 0 Td [(A)-42(x)]TJ/F84 9.9626 Tf 1.01 0 0 1 413.412 132.281 Tm [(is)-248(shown)-249(in)-248(Alg.)]TJ 0 0 1 rg 0 0 1 RG [-248(2)]TJ 0 g 0 G @@ -31630,7 +31630,7 @@ stream 0 g 0 G 0 g 0 G BT -/F84 9.9626 Tf 1.004 0 0 1 150.705 706.129 Tm [(the)-248(amount)-247(of)-248(needed)-248(padding;)-248(mor)18(eover)74(,)-248(while)-248(the)-248(DIA)-248(code)-247(is)-248(easily)-248(vector)18(-)]TJ 0.999 0 0 1 150.705 694.174 Tm [(ized,)-249(it)-249(does)-249(not)-249(necessarily)-250(make)-249(optimal)-249(use)-249(of)-249(the)-249(memory)-249(hierar)18(chy)111(.)-310(While)]TJ 0.99 0 0 1 150.406 682.219 Tm [(pr)18(ocessing)-252(each)-252(diagonal)-252(we)-252(ar)18(e)-252(updating)-252(entries)-252(in)-252(the)-252(output)-252(vector)]TJ/F145 9.9626 Tf 1 0 0 1 457.277 682.219 Tm [(y)]TJ/F84 9.9626 Tf 0.99 0 0 1 462.508 682.219 Tm [(,)-252(which)]TJ 0.98 0 0 1 150.705 670.263 Tm [(is)-248(then)-248(accessed)-247(multiple)-248(times;)-250(if)-248(the)-248(vector)]TJ/F145 9.9626 Tf 1 0 0 1 342.631 670.263 Tm [(y)]TJ/F84 9.9626 Tf 0.98 0 0 1 350.281 670.263 Tm [(is)-248(too)-248(lar)19(ge)-248(to)-248(r)19(emain)-248(in)-248(the)-248(cache)]TJ 1 0 0 1 150.705 658.308 Tm [(memory)111(,)-250(the)-250(associated)-250(cache)-250(miss)-250(penalty)-250(is)-250(paid)-250(multiple)-250(times.)]TJ 1.02 0 0 1 165.649 646.353 Tm [(The)]TJ/F78 9.9626 Tf 1.02 0 0 1 186.392 646.353 Tm [(hacked)-367(DIA)]TJ/F84 9.9626 Tf 1.02 0 0 1 239.757 646.353 Tm [(\050)]TJ/F75 9.9626 Tf 1.02 0 0 1 243.141 646.353 Tm [(HDIA)]TJ/F84 9.9626 Tf 1.02 0 0 1 271.929 646.353 Tm [(\051)-367(format)-368(was)-367(designed)-367(to)-367(contain)-368(the)-367(amount)-367(of)]TJ 1.02 0 0 1 150.406 634.398 Tm [(padding,)-346(by)-325(br)18(eaking)-326(the)-325(original)-326(matrix)-325(into)-326(equally)-325(sized)-325(gr)17(oups)-325(of)-326(r)18(ows)]TJ 1.013 0 0 1 150.376 622.443 Tm [(\050)]TJ/F78 9.9626 Tf 1.013 0 0 1 153.737 622.443 Tm [(hacks)]TJ/F84 9.9626 Tf 1.013 0 0 1 175.778 622.443 Tm [(\051,)-246(and)-245(then)-245(storing)-246(these)-245(gr)18(oups)-246(as)-245(independent)-246(matrices)-245(in)-245(DIA)-246(format.)]TJ 1.004 0 0 1 150.396 610.488 Tm [(This)-250(appr)18(oach)-250(is)-250(similar)-250(to)-250(that)-250(of)-250(HLL,)-250(and)-250(r)18(equir)18(es)-250(using)-250(an)-250(of)17(f)1(set)-250(vector)-250(for)]TJ 1.013 0 0 1 150.705 598.532 Tm [(each)-247(submatrix.)-306(Again,)-247(similarly)-246(to)-247(HLL,)-247(the)-247(various)-247(submatrices)-246(ar)17(e)-246(stacked)]TJ 0.991 0 0 1 150.705 586.577 Tm [(inside)-253(a)-252(linear)-253(array)-253(to)-252(impr)18(ove)-253(memory)-252(management.)-314(The)-253(fact)-252(that)-253(the)-253(matrix)]TJ 0.98 0 0 1 150.705 574.622 Tm [(is)-212(accessed)-212(in)-212(slices)-212(help)1(s)-212(in)-212(r)18(educing)-212(cache)-212(misses,)-220(especially)-212(r)18(egar)19(ding)-212(accesses)]TJ 1 0 0 1 150.705 562.667 Tm [(to)-250(the)-250(vector)]TJ/F145 9.9626 Tf 57.424 0 Td [(y)]TJ/F84 9.9626 Tf 5.23 0 Td [(.)]TJ 1.003 0 0 1 165.649 550.712 Tm [(An)-248(a)-1(ddi)1(tional)-249(vector)]TJ/F78 9.9626 Tf 1.003 0 0 1 259.673 550.712 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 1.003 0 0 1 308.411 550.712 Tm [(is)-249(pr)18(ovided)-248(to)-249(complete)-248(the)-249(matrix)-248(format;)]TJ 0.999 0 0 1 150.705 538.757 Tm [(given)-250(that)]TJ/F78 9.9626 Tf 0.999 0 0 1 197.561 538.757 Tm [(hackSize)]TJ/F84 9.9626 Tf 0.999 0 0 1 234.51 538.757 Tm [(is)-250(the)-251(number)-250(of)-251(r)18(ows)-250(of)-251(each)-250(hack,)-251(the)]TJ/F78 9.9626 Tf 0.999 0 0 1 408.824 538.757 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 0.999 0 0 1 457.388 538.757 Tm [(vector)-250(is)]TJ 1.013 0 0 1 150.705 526.801 Tm [(made)-246(by)-246(an)-246(array)-246(of)]TJ/F191 10.3811 Tf 1 0 0 1 242.857 526.801 Tm [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(m)]TJ/F84 9.9626 Tf 8 0 Td [(/)]TJ/F78 9.9626 Tf 6.336 0 Td [(h)-40(a)-25(c)-25(k)-30(S)-18(i)-32(z)-25(e)]TJ/F191 10.3811 Tf 36.682 0 Td [(\051)-209(+)]TJ/F84 9.9626 Tf 1.013 0 0 1 314.476 526.801 Tm [(1)-246(elements,)-246(pointing)-246(to)-246(the)-246(\002rst)-246(diagonal)]TJ 0.98 0 0 1 150.705 514.846 Tm [(of)18(fset)-215(of)-215(a)-214(submatrix)-215(inside)-215(the)-215(stacked)]TJ/F78 9.9626 Tf 0.98 0 0 1 318.648 514.846 Tm [(offsets)]TJ/F84 9.9626 Tf 0.98 0 0 1 345.153 514.846 Tm [(buf)18(fers,)-223(plus)-215(an)-214(additional)-215(element)]TJ 0.98 0 0 1 150.705 502.891 Tm [(equal)-226(to)-225(the)-226(number)-225(of)-226(nonzer)18(o)-225(diagonals)-226(in)-226(the)-225(whole)-226(matrix.)-306(W)94(e)-226(thus)-226(have)-225(the)]TJ 0.98 0 0 1 150.406 490.936 Tm [(pr)18(operty)-202(that)-202(the)-201(number)-202(of)-202(diagonals)-202(of)-202(the)]TJ/F78 9.9626 Tf 1 0 0 1 341.485 490.936 Tm [(k)]TJ/F84 9.9626 Tf 0.98 0 0 1 346.083 490.936 Tm [(-th)]TJ/F78 9.9626 Tf 0.98 0 0 1 360.171 490.936 Tm [(hack)]TJ/F84 9.9626 Tf 0.98 0 0 1 379.718 490.936 Tm [(is)-202(given)-202(by)]TJ/F78 9.9626 Tf 0.98 0 0 1 427.587 490.936 Tm [(hackOffsets[k+1])]TJ 1 0 0 1 149.709 478.981 Tm [(-)-250(hackOffsets[k])]TJ/F84 9.9626 Tf 62.983 0 Td [(.)]TJ +/F84 9.9626 Tf 1.004 0 0 1 150.705 706.129 Tm [(the)-248(amount)-247(of)-248(needed)-248(padding;)-248(mor)18(eover)74(,)-248(while)-248(the)-248(DIA)-248(code)-247(is)-248(easily)-248(vector)18(-)]TJ 0.999 0 0 1 150.705 694.174 Tm [(ized,)-249(it)-249(does)-249(not)-249(necessarily)-250(make)-249(optimal)-249(use)-249(of)-249(the)-249(memory)-249(hierar)18(chy)111(.)-310(While)]TJ 0.99 0 0 1 150.406 682.219 Tm [(pr)18(ocessing)-252(each)-252(diagonal)-252(we)-252(ar)18(e)-252(updating)-252(entries)-252(in)-252(the)-252(output)-252(vector)]TJ/F145 9.9626 Tf 1 0 0 1 457.277 682.219 Tm [(y)]TJ/F84 9.9626 Tf 0.99 0 0 1 462.508 682.219 Tm [(,)-252(which)]TJ 0.98 0 0 1 150.705 670.263 Tm [(is)-248(then)-248(accessed)-247(multiple)-248(times;)-250(if)-248(the)-248(vector)]TJ/F145 9.9626 Tf 1 0 0 1 342.631 670.263 Tm [(y)]TJ/F84 9.9626 Tf 0.98 0 0 1 350.281 670.263 Tm [(is)-248(too)-248(lar)19(ge)-248(to)-248(r)19(emain)-248(in)-248(the)-248(cache)]TJ 1 0 0 1 150.705 658.308 Tm [(memory)111(,)-250(the)-250(associated)-250(cache)-250(miss)-250(penalty)-250(is)-250(paid)-250(multiple)-250(times.)]TJ 1.02 0 0 1 165.649 646.353 Tm [(The)]TJ/F78 9.9626 Tf 1.02 0 0 1 186.392 646.353 Tm [(hacked)-367(DIA)]TJ/F84 9.9626 Tf 1.02 0 0 1 239.757 646.353 Tm [(\050)]TJ/F75 9.9626 Tf 1.02 0 0 1 243.141 646.353 Tm [(HDIA)]TJ/F84 9.9626 Tf 1.02 0 0 1 271.929 646.353 Tm [(\051)-367(format)-368(was)-367(designed)-367(to)-367(contain)-368(the)-367(amount)-367(of)]TJ 1.02 0 0 1 150.406 634.398 Tm [(padding,)-346(by)-325(br)18(eaking)-326(the)-325(original)-326(matrix)-325(into)-326(equally)-325(sized)-325(gr)17(oups)-325(of)-326(r)18(ows)]TJ 1.013 0 0 1 150.376 622.443 Tm [(\050)]TJ/F78 9.9626 Tf 1.013 0 0 1 153.737 622.443 Tm [(hacks)]TJ/F84 9.9626 Tf 1.013 0 0 1 175.778 622.443 Tm [(\051,)-246(and)-245(then)-245(storing)-246(these)-245(gr)18(oups)-246(as)-245(independent)-246(matrices)-245(in)-245(DIA)-246(format.)]TJ 1.004 0 0 1 150.396 610.488 Tm [(This)-250(appr)18(oach)-250(is)-250(similar)-250(to)-250(that)-250(of)-250(HLL,)-250(and)-250(r)18(equir)18(es)-250(using)-250(an)-250(of)17(f)1(set)-250(vector)-250(for)]TJ 1.013 0 0 1 150.705 598.532 Tm [(each)-247(submatrix.)-306(Again,)-247(similarly)-246(to)-247(HLL,)-247(the)-247(various)-247(submatrices)-246(ar)17(e)-246(stacked)]TJ 0.991 0 0 1 150.705 586.577 Tm [(inside)-253(a)-252(linear)-253(array)-253(to)-252(impr)18(ove)-253(memory)-252(management.)-314(The)-253(fact)-252(that)-253(the)-253(matrix)]TJ 0.98 0 0 1 150.705 574.622 Tm [(is)-212(accessed)-212(in)-212(slices)-212(help)1(s)-212(in)-212(r)18(educing)-212(cache)-212(misses,)-220(especially)-212(r)18(egar)19(ding)-212(accesses)]TJ 1 0 0 1 150.705 562.667 Tm [(to)-250(the)-250(vector)]TJ/F145 9.9626 Tf 57.424 0 Td [(y)]TJ/F84 9.9626 Tf 5.23 0 Td [(.)]TJ 1.003 0 0 1 165.649 550.712 Tm [(An)-248(a)-1(ddi)1(tional)-249(vector)]TJ/F78 9.9626 Tf 1.003 0 0 1 259.673 550.712 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 1.003 0 0 1 308.411 550.712 Tm [(is)-249(pr)18(ovided)-248(to)-249(complete)-248(the)-249(matrix)-248(format;)]TJ 0.999 0 0 1 150.705 538.757 Tm [(given)-250(that)]TJ/F78 9.9626 Tf 0.999 0 0 1 197.561 538.757 Tm [(hackSize)]TJ/F84 9.9626 Tf 0.999 0 0 1 234.51 538.757 Tm [(is)-250(the)-251(number)-250(of)-251(r)18(ows)-250(of)-251(each)-250(hack,)-251(the)]TJ/F78 9.9626 Tf 0.999 0 0 1 408.824 538.757 Tm [(hackOffsets)]TJ/F84 9.9626 Tf 0.999 0 0 1 457.388 538.757 Tm [(vector)-250(is)]TJ 1.013 0 0 1 150.705 526.801 Tm [(made)-246(by)-246(an)-246(array)-246(of)]TJ/F192 10.3811 Tf 1 0 0 1 242.857 526.801 Tm [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(m)]TJ/F84 9.9626 Tf 8 0 Td [(/)]TJ/F78 9.9626 Tf 6.336 0 Td [(h)-40(a)-25(c)-25(k)-30(S)-18(i)-32(z)-25(e)]TJ/F192 10.3811 Tf 36.682 0 Td [(\051)-209(+)]TJ/F84 9.9626 Tf 1.013 0 0 1 314.476 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F@ FA FB FC FD FE FF FG FH FI FJ FK FL FM FN FO FP FQ FR FS FT FU FV FW FX FY FZ F[ F\ F] F^ F_ F` Fa Fb Fc+s+u6 endstream endobj startxref -2848042 +2848054 %%EOF diff --git a/docs/src/commrout.tex b/docs/src/commrout.tex index f2e38965..d1d831a4 100644 --- a/docs/src/commrout.tex +++ b/docs/src/commrout.tex @@ -6,7 +6,7 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% The routines in this chapter implement various global communication operators on vectors associated with a discretization mesh. For auxiliary communication -routines not tied to a discretization space see~\ref{sec:toolsrout}. +routines not tied to a discretization space see~\ref{sec:parenv}. \clearpage\subsection{psb\_halo --- Halo Data Communication} diff --git a/docs/src/intro.tex b/docs/src/intro.tex index cf1e0f27..a7bef845 100644 --- a/docs/src/intro.tex +++ b/docs/src/intro.tex @@ -28,8 +28,8 @@ accelerators through OpenMP as support from compilers improves. The project is lead by Salvatore Filippone; a number of people have been contributing to this package over the years; contributors in roughly reverse chronological order: \begin{obeylines} + Luca Pepè Sciarria Theophane Loloum - Fabio Durastante Dimitri Walther Andea Di Iorio Stefano Petrilli @@ -37,7 +37,6 @@ years; contributors in roughly reverse chronological order: Zaak Beekman Ambra Abdullahi Hassan Pasqua D'Ambra - Alfredo Buttari Daniela di Serafino Michele Martone Michele Colajanni @@ -251,7 +250,7 @@ domain is usually a halo point for some other domain\footnote{This is two variables is reciprocal. If the matrix pattern is non-symmetric we may have one-way interactions, and these could cause a situation in which a boundary point is not a halo point for its neighbour.}; therefore -the cardinality of the boundary points set denotes the amount of data +the cardinality of the boundary points set determines the amount of data sent to other domains. \item[Overlap.] An overlap point is a boundary point assigned to multiple domains. Any operation that involves an overlap point diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index a78805e9..2b1e89f3 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -136,7 +136,7 @@ by Salvatore Filippone\\ Alfredo Buttari \\ Fabio Durastante}\\ -Jun 1st, 2025 +June 9th, 2025 \end{minipage}} } %\addtolength{\textwidth}{\centeroffset} diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index eced4fb2..2ac85f59 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -106,7 +106,7 @@ Fabio Durastante } \\ %\today Software version: 3.9.0\\ %\today -Jun 1st, 2025 +June 9th, 2025 \cleardoublepage \begingroup \renewcommand*{\thepage}{toc}