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y(Isaacson,) i(E.) g(and) f(H.B.) h -(Keller,) p Fk 29 w(") p Fs(Analysis) e(of) h(Numerical) f(Metho) s -(ds,) p Fk(") p Fs 30 w(Wiley) -8 b(,) 31 b(1966.) 330 -3372 y(P) m(arlett,) g(B.,) p Fk 32 w(") p Fs(Symmetric) e(Eigen) m(v) --5 b(alue) 29 b(Problem,) p Fk(") p Fs 30 w(Pren) m(tice) h(Hall,) g -(1980.) 330 3509 y(Wilkinson,) e(J.H.,) p Fk 31 w(") p -Fs(Algebraic) i(Eigen) m(v) -5 b(alue) 29 b(Problem,) p -Fk(") p Fs 29 w(Oxford,) h(1988.) p Fr 150 3774 a(1.5) 68 -b(P) l(ortabilit) l(y) p Fs 275 3970 a(This) 21 b(pac) m(k) -5 -b(age) 25 b(is) e(self-con) m(tained) g(with) f(the) h(exception) h(of) -f(the) g(pro) s(cessor) g(sp) s(eci\014c) f(libraries) f(for) i(the) 150 -4080 y(BLAS) 31 b(and) g(LAP) -8 b(A) m(CK.) 31 b(It) h(is) e(curren) m -(tly) g(in) m(tended) g(for) h(cross) h(dev) m(elopmen) m(t) f(and) g -(cross) g(compilation) 150 4189 y(using) 25 b(Unix) h(as) h(the) g -(host) g(en) m(vironmen) m(t) f(and) g(GNU) i(utilites.) 37 -b(There) 26 b(is) g(also) h(a) g(Windo) m(ws) f(NT) g(v) m(ersion) 150 -4299 y(a) m(v) -5 b(ailable.) 275 4437 y(The) 22 b(comm) m(unication) g -(calls) g(are) h(made) g(through) f(a) h(set) g(of) g(co) s(de) g -(wrapp) s(ers) e(o) m(v) m(er) j(the) f(basic) f(message) 150 -4546 y(passing) i(pro) m(vided) g(b) m(y) h(some) h(of) g(the) f -(distributed) d(memory) k(parallel) d(computers) i(and) g(TCGMSG.) g(F) --8 b(or) 150 4656 y(the) 32 b(distributed) e(memory) i(computers) g(w) m -(e) g(do) g(supp) s(ort) f(nativ) m(e) h(message) i(passing) d(pro) m -(vided) g(b) m(y) h(the) p 150 4758 1200 4 v Fl 199 4826 -a(3) p Fj 275 4857 a(Inderjit) 25 b(Dhillon,) h(George) h(F) -6 -b(ann,) 26 b(Beresford) h(P) n(arlett,) g(siam8th) p -Fl 199 4930 a(4) p Fj 275 4962 a(F) -6 b(ann,) 28 b(G.) h(and) f(\045) g -(Little\014eld,) h(R.,) p Fi 29 w(") p Fj(P) n(arallel) i(In) n(v) n -(erse) c(Iteration) h(with) h(Reorthogonalization) p -Fi(") p Fj(,) j(\045) c(Pro) r(ceeding) h(of) 275 5053 -y(the) c(6th) g(SIAM) g(Conference) i(on) f(P) n(arallel) i(Pro) r -(cessing) f(for) g(\045) e(Scien) n(ti\014c) h(Computing,) f(SIAM,) g -(1993) p Fl 199 5126 a(5) p Fj 275 5157 a(F) -6 b(ann,) 36 -b(G.,) h(R.) e(Little\014eld,) i(and) d(\045) g(D.) h(Elw) n(o) r(o) r -(d,) p Fi 38 w(") p Fj(P) n(erformance) h(of) f(a) g(F) -6 -b(ully) 34 b(P) n(arallel) i(Dense) e(Real) h(Symmetric) 275 -5249 y(Eigensolv) n(er) d(\045) g(in) f(Quan) n(tum) e(Chemistry) i -(Applications) p Fi(") p Fj(,) j(in) e(High) f(P) n(erformance) h -(Computing) f(Symp) r(osium) e(\045) 275 5340 y(1995,) e(Pro) r -(ceedings) g(of) g(the) e(1995) i(Sim) n(ulation) e(Multiconference,) j -(The) e(Computer) f(\045) g(Sim) n(ulation) g(So) r(ciet) n(y) p -90 rotate dyy eop -%%Page: 5 6 -5 5 bop Fs 150 -116 a(Chapter) 30 b(1:) 41 b(P) m(eIGS:) 31 -b(an) f(o) m(v) m(erview) 2311 b(5) 150 299 y(In) m(tel) 27 -b(iPSC) p 569 299 28 4 v 31 w(860,) j(and) d(T) -8 b(ouc) m(hstone) 28 -b(DEL) -8 b(T) g(A.) 29 b(W) -8 b(e) 28 b(also) g(supp) s(ort) d(an) j -(in) m(terface) g(to) g(TCGMSG) f(and) g(to) 150 408 -y(MPI.) 275 543 y(The) e(installation) e(pro) s(cedure) i(creates) i(a) -f(BLAS) f(library) e(and) i(a) i(LAP) -8 b(A) m(CK) 25 -b(library) -8 b(.) 38 b(The) 25 b(user) g(can) 150 653 -y(replace) 32 b(these) g(libraries) d(with) h(a) i(more) g(e\016cien) m -(t) g(optimized) e(library) g(or) h(p) s(erhaps) f(new) m(er) i(v) m -(ersions) f(of) 150 762 y(the) 36 b(BLAS) h(and) e(LAP) -8 -b(A) m(CK) 37 b(libraries.) 55 b(The) 36 b(user) g(should) e(b) s(e) h -(a) m(w) m(are) j(that) f(there) f(ma) m(y) h(b) s(e) f(c) m(hanges) 150 -872 y(in) c(the) h(calling) e(syn) m(tax) j(of) f(the) g(latest) g(LAP) --8 b(A) m(CK) 34 b(that) f(ma) m(y) h(b) s(e) e(incompatible) f(with) h -(the) h(LAP) -8 b(A) m(CK) 150 981 y(included) 34 b(here.) 59 -b(The) 36 b(LAP) -8 b(A) m(CK) 37 b(co) s(des) f(that) h(are) g -(included) d(here) j(are) f(dated) h(\() g(Sept.) 59 -b(30,) 39 b(1994) f(\).) 150 1091 y(The) 32 b(sub) s(directory) p -Fo 30 w(/src/f77) p Fs 34 w(con) m(tains) h(a) g(n) m(um) m(b) s(er) e -(of) p Fk 33 w(") p Fs(\014xed) p Fk(") p Fs 31 w(co) s(des) i -(originating) d(from) i(LAP) -8 b(A) m(CK.) 150 1200 -y(These) p Fk 39 w(") p Fs(\014xed) p Fk(") p Fs 38 w(co) s(des) 39 -b(ha) m(v) m(e) i(the) e(same) h(LAP) -8 b(A) m(CK) 39 -b(name) g(with) f(a) i(n) m(um) m(b) s(er) e(after) h(their) g(\014le) f -(name) 150 1310 y(\(as) 29 b(is) f(the) h(case) g(with) e(their) h -(subroutine) e(name\)) j(to) h(distinguish) 25 b(them) j(from) g(the) h -(original) e(LAP) -8 b(A) m(CK) 150 1420 y(co) s(des.) p -Fo 49 w(The) 33 b(INST) -8 b(ALL) 32 b(\014le) h(in) g(the) g(top) h -(lev) m(el) g(of) g(the) f(P) m(eIGS) h(directory) g(sup) s(ersede) e -(the) h(follo) m(wing) 150 1529 y(installation) f(pro) s(cedure) p -Fs(.) p Fr 150 1787 a(1.6) 68 b(Supp) t(ort) p Fs 275 -1979 a(W) -8 b(e) 28 b(curren) m(tly) f(supp) s(ort) f(the) i(P) m -(eIGS) g(library) e(routines) g(that) i(are) h(do) s(cumen) m(ted) e -(in) g(the) g(next) h(c) m(hap-) 150 2089 y(ter.) 47 -b(All) 31 b(of) h(the) h(comm) m(unication) f(subroutines) e(are) i -(supp) s(orted) f(in) g(the) h(con) m(text) i(of) f(pro) m(viding) d -(com-) 150 2198 y(m) m(unication) 37 b(calls) h(used) g(b) m(y) g(the) h -(linear) e(algebra) h(subroutines.) 63 b(W) -8 b(e) 40 -b(supp) s(ort) c(the) j(pac) m(k) -5 b(age) 41 b(in) c(the) 150 -2308 y(sense) h(that) g(rep) s(orts) f(of) h(bugs,) h(errors) e(or) h -(p) s(o) s(or) f(p) s(erformance) g(will) e(get) k(our) e(immediate) g -(atten) m(tion.) 150 2418 y(W) -8 b(e) 32 b(will) 27 -b(try) k(to) g(solv) m(e) f(y) m(our) h(problems) d(and) i(will) e(pro) -m(vide) h(bug) h(\014xes.) p Fr 150 2675 a(1.7) 68 b(Thanks) p -Fs 275 2868 a(Our) 38 b(thanks) h(to) i(all) d(who) h(help) s(ed) f(to) -i(impro) m(v) m(e) g(this) f(w) m(ork.) 68 b(In) 39 b(particular,) i(w) -m(e) f(thank) f(Rob) s(ert) 150 2977 y(Harrison) 26 b(and) g(Eduardo) g -(Apra) g(for) h(assisting) f(us) g(in) g(understanding) e(c) m -(hemistry) i(problems) g(and) g(their) 150 3087 y(asso) s(ciated) 41 -b(sp) s(ectra.) 69 b(W) -8 b(e) 42 b(thank) e(Professor) f(Elizab) s -(eth) g(Jessup) g(of) h(Univ) m(ersit) m(y) f(of) i(Colorado) f(and) 150 -3196 y(Prof.) 68 b(Ken) 39 b(Bub) s(e) g(of) g(Univ) m(ersit) m(y) g -(of) h(W) -8 b(ashington) 39 b(for) h(advice) f(and) g(strategies) h -(for) g(P) m(eIGS2.) 69 b(W) -8 b(e) 150 3306 y(thank) 28 -b(Prof.) 39 b(Inderjit) 27 b(Dhillon) e(of) k(Univ) m(ersit) m(y) e(of) -h(T) -8 b(exas,) 30 b(Austin) d(and) g(Professor) h(Beresford) g(P) m -(arlett) 150 3416 y(of) 33 b(Univ) m(ersit) m(y) f(of) h(California,) e -(Berk) m(eley) i(for) g(sharing) e(with) h(us) g(their) f(ideas) i(and) -f(preliminary) d(co) s(des) 150 3525 y(for) 38 b(the) h(Berk) m(eley) g -(algorithm) e(in) g(Prof.) 64 b(P) m(arlett's) 39 b(preprin) m(ts) d -(and) i(Inderjit's) f(thesis.) 63 b(Their) 37 b(w) m(ork) 150 -3635 y(sho) m(w) m(ed) k(us) g(ho) m(w) g(to) h(reduce) f -(orthonormalization) f(costs) i(for) f(large) g(clusters) f(of) i -(eigen) m(v) -5 b(alues.) 72 b(All) 150 3744 y(mistak) m(es) 31 -b(are) f(our) g(o) m(wn.) 275 3879 y(W) -8 b(e) 41 b(thank) e(the) h(F) --8 b(ree) 41 b(Soft) m(w) m(are) g(F) -8 b(oundation) 40 -b(for) g(dev) m(eloping) f(soft) m(w) m(are) i(to) s(ols) f(that) g -(made) g(our) 150 3988 y(w) m(ork) 30 b(easier.) 275 -4123 y(W) -8 b(e) 40 b(thank) f(the) g(Molecular) g(Science) g -(Computing) f(F) -8 b(acilit) m(y) 39 b(at) h(the) f(En) m(vironmen) m -(tal) f(Molecular) 150 4232 y(Sciences) 20 b(Lab) s(oratory) h(for) f -(pro) m(viding) e(access) k(to) f(the) g(NWMPP1) h(and) e(NWECS1.) 37 -b(W) -8 b(e) 22 b(thank) e(NERSC) 150 4342 y(for) 28 -b(pro) m(ving) f(access) j(to) e(the) h(CRA) -8 b(Y-T3E.) 29 -b(MSCF) f(is) f(funded) f(b) m(y) i(OBER) g(and) f(NERSC) h(is) f -(funded) f(b) m(y) 150 4452 y(MICS.) 275 4586 y(The) 38 -b(researc) m(h) i(supp) s(ort) d(of) i(the) g(ev) m(olution) g(of) g(v) -m(ersion) f(2) i(to) f(v) m(ersion) g(3) g(of) g(P) m(eIGS) g(w) m(as) h -(funded) 150 4696 y(b) m(y) 33 b(DOE's) g(MICS) f(Grand) g(Challenge) g -(in) f(Computational) h(Chemistry) -8 b(.) 47 b(The) 32 -b(implemen) m(tation) g(and) 150 4805 y(main) m(tanence) f(supp) s(ort) -d(w) m(as) j(pro) m(vided) e(b) m(y) h(EMSL.) g(\(PNNL's) h(con) m -(tract) i(go) s(es) e(here\).) p 90 rotate dyy eop -%%Page: 6 7 -6 6 bop Fs 150 -116 a(6) 3301 b(P) m(eIGS) p 90 rotate -dyy eop -%%Page: 7 8 -7 7 bop Fs 150 -116 a(Chapter) 30 b(2:) 41 b(Installation) 2636 -b(7) p Fp 150 299 a(2) 80 b(Installation) p Fs 275 554 -a(This) 34 b(is) h(a) h(short) f(synopsis) f(of) i(ho) m(w) g(to) h -(install) d(P) m(eIGS) i(on) g(a) g(target) h(system.) p -Fo 58 w(The) e(user) h(should) 150 663 y(consult) d(the) h(INST) -8 -b(ALL) 32 b(\014le) h(in) g(the) g(top) g(lev) m(el) i(P) m(eIGS) f -(directory) g(for) g(up) d(to) j(date) g(information) f(re-) 150 -773 y(garding) 26 b(the) h(installation) h(pro) s(cedure.) p -Fs 38 w(W) -8 b(e) 28 b(curren) m(tly) d(only) g(supp) s(ort) g -(installation) f(on) i(Unix) f(systems) 150 882 y(with) 36 -b(the) i(resources) g(listed) e(b) s(elo) m(w) h(for) g(installing) e -(P) m(eIGS.) j(The) f(library) e(co) s(des) j(and) f(the) h(test) g -(pro-) 150 992 y(grams) 31 b(are) g(created) h(using) p -Fo 30 w(Mak) m(e\014le) p Fs(s.) 43 b(All) 30 b(mac) m(hine) g(sp) s -(eci\014c) g(data) h(is) f(con) m(tained) i(in) d(the) p -Fo 31 w(DEFS) p Fs 30 w(\014le) 150 1102 y(in) c(the) i(main) f(P) m -(eIGS) h(directory) -8 b(.) 40 b(Eac) m(h) 27 b(sub) s(directory) e -(has) h(a) p Fo 27 w(Mak) m(e\014le) p Fs 29 w(whic) m(h) p -Fk 25 w(") p Fs(includes) p Fk(") p Fs 24 w(the) p Fo -27 w(DEFS) p Fs 150 1211 a(\014le.) 38 b(Because) 28 -b(the) p Fo 26 w(Mak) m(e\014le) p Fs(s) f(use) p Fo -26 w(ifeq) p Fs 26 w(conditionals,) f(the) g(GNU) h(mak) m(e) g(v) m -(ersion) e(3.68) j(or) e(higher) e(from) 150 1321 y(the) 40 -b(F) -8 b(ree) 41 b(Soft) m(w) m(are) g(F) -8 b(oundation) 40 -b(is) f(required) f(as) i(the) p Fo 40 w(mak) m(e) p -Fs 41 w(utilit) m(y) -8 b(.) 68 b(If) 39 b(this) g(is) g(not) h(a) m(v) --5 b(ailable) 39 b(to) 150 1430 y(the) 30 b(installer) d(then) i(the) h -(installer) d(needs) i(to) i(edit) p Fo 29 w(DEFS) p -Fs 28 w(and) e(the) h(v) -5 b(arious) p Fo 28 w(Mak) m(e\014les) p -Fs 31 w(and) 29 b(commen) m(t) 150 1540 y(out) h(the) p -Fo 30 w(ifeq) p Fs 30 w(and) p Fo 29 w(endif) p Fs 29 -w(statemen) m(ts) h(and) e(lea) m(v) m(e) i(the) f(appropriate) f -(lines) f(for) h(the) h(in) m(tended) e(system.) p Fl -3712 1507 a(1) p Fs 150 1650 a(The) p Fo 31 w(DEFS) p -Fs 31 w(\014le) j(curren) m(tly) g(has) h(a) h(list) d(of) i(w) m -(orkstations) h(and) e(parallel) f(computers) i(and) f(their) g(corre-) -150 1759 y(sp) s(onding) 24 b(compilation) h(switc) m(hes.) 39 -b(Most) 27 b(of) g(the) f(curren) m(tly) g(a) m(v) -5 -b(ailable) 25 b(distributed) f(memory) i(parallel) 150 -1869 y(computers) h(are) h(on) f(this) f(list:) 38 b(Cra) m(y) 28 -b(T3D,) g(IBM) g(SP-1/2,) h(In) m(tel) e(DEL) -8 b(T) g(A,) 28 -b(In) m(tel) f(P) m(aragon,) j(SGI) d(P) m(o) m(w-) 150 -1978 y(erChallange,) j(Kendall) e(Square) j(Researc) m(h) g(KSR-2.) p -Fo 41 w(Homogeneous) p Fs 33 w(net) m(w) m(orks) g(of) g(w) m -(orkstations) g(are) 150 2088 y(also) f(supp) s(ort) f(via) h(TCGMSG) g -(or) g(MPI.) 275 2229 y(Th) m(us,) f(the) i(follo) m(wing) d(soft) m(w) -m(are) k(resources) f(are) f(needed) h(to) g(mak) m(e) g(the) g -(library:) 330 2371 y(1.) 41 b(ANSI-C) 30 b(compatible) g(C) g -(compiler) 330 2509 y(2.) 41 b(F) -8 b(ortran) 31 b(77) g(compiler) 330 -2647 y(3.) 41 b(GNU) 31 b(mak) m(e) g(utilit) m(y) -8 -b(,) 30 b(v) m(ersion) g(3.68) i(and) d(higher.) 275 -2816 y(W) -8 b(e) 29 b(assume) e(that) i(all) e(F) -8 -b(ortran) 28 b(callable) f(subroutines) e(ha) m(v) m(e) 30 -b(a) e(trailing) e(underscore) h(at) h(the) h(end) e(of) 150 -2926 y(their) c(name) h(in) f(the) h(name-space.) 39 -b(Th) m(us,) 25 b(w) m(e) f(assume) g(that) g(C) g(subroutines) d(call) -j(F) -8 b(ortran) 24 b(subroutines) 150 3036 y(using) 39 -b(subroutine) f(names) j(with) e(a) i(trailing) e(underscore) g(added) h -(to) h(the) g(end) f(of) h(their) e(name,) 44 b(e.g.) p -Fo 150 3145 a(f77name) p 486 3145 28 5 v Fs 33 w(.) 39 -b(W) -8 b(e) 24 b(also) f(assume) g(that) h(a) g(F) -8 -b(ortran) 24 b(subroutine) d(calls) i(a) g(C) g(subroutine) f(using) f -(a) j(subroutine) 150 3255 y(name) 35 b(with) f(a) i(trailing) d -(underscore) i(added) g(to) h(the) f(end) g(of) g(their) g(name,) i -(e.g.) p Fo 56 w(call) g(cname) p 3426 3255 V Fs 33 w(.) 55 -b(Users) 150 3364 y(of) 34 b(IBM) g(AIX) g(RS6000) h(v) m(ersion) e(3) h -(systems) g(m) m(ust) f(add) g(the) p Fo 34 w(-qextname) p -Fs 35 w(or) p Fo 33 w(-qEXTNAME) p Fs 34 w(options) 150 -3474 y(to) i(the) p Fo 34 w(xlf) p Fs 34 w(compiler) e(or) h(to) h(the) -p Fo 34 w(f77) p Fs 34 w(compiler.) 51 b(Users) 34 b(of) g(HP9000) i -(HP-UX) f(v) m(ersion) e(9.0) i(or) f(higher) 150 3583 -y(m) m(ust) 28 b(add) p Fk 28 w(+) p Fo(ppu) p Fs 26 -w(as) h(an) f(option) g(to) h(the) f(HP) p Fo 29 w(f77) p -Fs 29 w(compiler.) 38 b(Users) 28 b(of) h(other) g(dialects) e(of) i -(Unix) e(should) 150 3693 y(consult) 37 b(their) g(language) h(man) m -(uals) f(or) h(system) g(gurus) f(for) h(the) g(appropriate) e -(options.) 63 b(A) 38 b(separate) 150 3803 y(mak) m(e\014le) 32 -b(has) g(b) s(een) g(added) g(for) g(the) g(users) g(of) g(the) h(IBM) f -(RS6000) i(without) d(an) h(installed) e(GNU.) j(The) 150 -3912 y(user) d(is) f(advised) g(to) i(read) g(the) f(INST) -8 -b(ALL) 30 b(\014le) f(and) h(the) h(DEFS) f(\014les) g(in) f(the) h(P) m -(eIGS) h(directory) -8 b(.) 275 4054 y(In) 39 b(man) m(y) i(of) f(the) h -(calls) e(to) i(C) f(subroutines) e(from) i(F) -8 b(ortran) 41 -b(w) m(e) g(assume) f(that) h(the) g(C) p Fo 40 w(double) p -Fs 40 w(is) 150 4163 y(the) c(same) g(size) f(as) h(the) g(F) -8 -b(ortran) p Fo 37 w(double) 36 b(precision) p Fs(.) 60 -b(This) 35 b(is) g(not) i(a) g(serious) f(obstacle) h(since) f(man) m -(y) 150 4273 y(F) -8 b(ortran) 27 b(compilers) e(and) h(C) g(compilers) -e(ha) m(v) m(e) p Fo 28 w(8) p Fs 27 w(b) m(yte) j(switc) m(hes) f(for) -p Fo 26 w(real*8) p Fs 28 w(computataions.) 39 b(Also,) 27 -b(w) m(e) 150 4382 y(assume) 33 b(that) h(the) f(address) f(to) i -(double) d(precision) h(n) m(um) m(b) s(ers) f(is) h(less) h(than) g -(or) g(equal) f(to) i(the) f(size) g(of) h(a) 150 4492 -y(double) 25 b(precision) f(n) m(um) m(b) s(er.) 38 b(In) 25 -b(man) m(y) h(of) g(the) h(F) -8 b(ortran) 26 b(to) h(C) f(in) m -(terface) g(co) s(des) h(w) m(e) f(recast) h(some) g(of) f(the) 150 -4602 y(double) 33 b(precision) f(scratc) m(h) j(spaces) g(as) f(p) s -(oin) m(ters) f(to) i(double) e(precision) f(n) m(um) m(b) s(ers.) 51 -b(The) 33 b(user) h(should) 150 4711 y(also) e(c) m(hec) m(k) i -(whether) d(the) i(in) m(tended) p Fk 31 w(") p Fs(C) p -Fk(") p Fs 31 w(and) f(F) -8 b(ortran) 32 b(compilers) f(are) i -(compatible) e(in) g(in) m(teger) i(and) 150 4821 y(in) m(teger) h(p) s -(oin) m(ters) e(sizes.) 50 b(F) -8 b(or) 34 b(example,) h(on) e(mac) m -(hines) g(with) f(8) i(b) m(ytes) g(for) f(b) s(oth) p -Fo 33 w(in) m(t) p Fs 34 w(and) p Fo 33 w(long) h(in) m(t) p -Fs 34 w(it) 150 4930 y(is) k(imp) s(ortan) m(t) f(that) j(the) f(F) -8 -b(ortran) 39 b(in) m(teger) g(also) f(b) s(e) g(8) h(b) m(ytes.) 66 -b(This) 37 b(is) h(a) h(common) g(problem) e(when) 150 -5040 y(installing) 27 b(P) m(eIGS.) p 150 5149 1200 4 -v Fl 199 5217 a(1) p Fj 275 5249 a(GNU) f(mak) n(e) g(is) i(a) n(v) l -(ailable) g(via) g(anon) n(ymous) e(ftp) h(from) p Fh -27 w(prep.ai.mit.edu:18.71.0.38) p Fj 28 w(in) g(the) g(directory) p -Fh 28 w(/pub/gn) n(u) p Fj 25 w(as) p Fh 275 5340 a(mak) n(e###.tar.gz) -p Fj(.) p 90 rotate dyy eop -%%Page: 8 9 -8 8 bop Fs 150 -116 a(8) 3301 b(P) m(eIGS) 275 299 y(In) 28 -b(h/blas) p 646 299 28 4 v 32 w(lapac) m(k.h) h(w) m(e) g(ha) m(v) m(e) -h(tried) e(to) i(deal) e(with) g(some) h(of) h(the) f(computers,) g -(for) g(example,) g(Cra) m(y) 150 408 y(T3D) 46 b(and) e(the) h(KSR2) g -(where) f(the) i(single) d(precision) h(computation) h(is) f(p) s -(erformed) f(in) h(64) i(bits) e(of) 150 518 y(precision.) 275 -653 y(P) m(eIGS) 33 b(uses) g(mac) m(hine) g(sp) s(eci\014c) f -(arithmetic) g(constan) m(ts) i(\() g(obtained) e(from) h(LAP) -8 -b(A) m(CK's) p Fo 34 w(dlamac) m(h) p Fs 150 762 a(and) p -Fo 30 w(slamc) m(h) p Fs 31 w(\)) 30 b(in) f(a) i(n) m(um) m(b) s(er) e -(of) i(places.) 40 b(These) 30 b(constan) m(ts) i(are) f(de\014ned) e -(in) g(h/blas) p 3108 762 V 31 w(lapac) m(k.h.) 275 897 -y(Y) -8 b(ou) 42 b(will) d(probably) h(obtain) h(this) f(library) f(as) -j(a) g(compressed) g(tar) g(\014le) f(named) p Fo 41 -w(p) s(eigsXY.tar.Z) p Fs(,) 150 1006 y(where) 30 b(X.Y) h(is) e(the) i -(v) m(ersion) f(n) m(um) m(b) s(er.) 275 1141 y(T) -8 -b(o) 30 b(build) e(P) m(eIGS) i(on) h(a) f(Unix) g(system) g(using) p -Fo 29 w(csh) p Fs(:) p Fq 199 1275 a(\000) p Fs 60 w(t) m(yp) s(e) p -Fo 31 w(mak) m(e) h(-v) p Fs 30 w(to) g(mak) m(e) h(sure) d(that) i(y) m -(ou) g(are) g(using) e(the) h(GNU) h(mak) m(e) h(utilit) m(y) -8 -b(.) p Fq 199 1410 a(\000) p Fs 60 w(uncompress) 44 b(the) h(\014le) p -Fo 44 w(p) s(eigsXY.tar.Z) p Fs 44 w(b) m(y) g(t) m(yping) p -Fo 44 w(uncompress) f(p) s(eigsXY.tar.Z) p Fs 45 w(whic) m(h) g(will) -330 1519 y(create) 32 b(a) f(tar) f(\014le) g(called) p -Fo 29 w(p) s(eigsXY.tar) p Fs(.) p Fq 199 1654 a(\000) p -Fs 60 w(un) m(tar) i(the) g(\014le) f(p) s(eigsXY.tar) h(b) m(y) g(t) m -(yping) p Fo 31 w(tar) g(xvf) g(p) s(eigsXY.tar) p Fs(.) 45 -b(This) 30 b(will) g(create) j(a) f(directory) 330 1763 -y(called) p Fo 30 w(p) s(eigsX.Y) p Fs 30 w(with) d(a) h(n) m(um) m(b) s -(er) f(of) i(sub) s(directories) d(and) i(a) g(\014le) g(called) p -Fo 29 w(DEFS) p Fs(.) p Fq 199 1898 a(\000) p Fs 60 w(scan) 42 -b(through) f(the) g(\014le) p Fo 41 w(DEFS) p Fs 41 w(using) f(y) m -(our) h(fa) m(v) m(orite) i(editor) e(to) h(see) h(if) d(y) m(our) i -(target) h(parallel) 330 2007 y(computer) 31 b(is) f(supp) s(orted.) 41 -b(Mak) m(e) 32 b(the) g(appropriate) e(c) m(hanges,) i(if) e(necessary) --8 b(,) 32 b(for) f(the) g(compilers,) 330 2117 y(directory) g(paths,) g -(compiler) f(options) h(and) g(library) e(options.) 43 -b(If) 31 b(y) m(ou) h(w) m(an) m(t) g(to) g(use) f(MPI,) h(rather) 330 -2227 y(than) h(the) h(default) f(of) g(TCGMSG) h(or) f(In) m(tel) h -(NX,) g(then) f(follo) m(w) g(the) h(directions) e(in) p -Fo 32 w(DEFS) p Fs 32 w(ab) s(out) 330 2336 y(MPI) e(use.) p -Fq 199 2471 a(\000) p Fs 60 w(sa) m(v) m(e) i(the) f(corrected) g -(\014le) p Fo 29 w(DEFS) p Fs(.) p Fq 199 2605 a(\000) p -Fs 60 w(set) 37 b(the) g(en) m(vironmen) m(t) g(v) -5 -b(ariable) p Fo 35 w(T) d(AR) m(GET) p Fs(.) 38 b(F) -8 -b(or) 38 b(example,) g(for) e(the) h(iPSC) p 3042 2605 -V 31 w(860,) j(the) d(installer) 330 2715 y(w) m(ould) 29 -b(t) m(yp) s(e) p Fo 61 w(seten) m(v) i(T) -8 b(AR) m(GET) 32 -b(iPSC) p 1737 2715 28 5 v 32 w(860) p Fs(.) p Fq 199 -2849 a(\000) p Fs 60 w(Chec) m(k) 40 b(the) h(\014le) p -Fo 39 w(PEIGSDIR/h/blas) p 1692 2849 V 32 w(lapac) m(k.h) p -Fs 41 w(to) g(see) f(if) f(the) h(mac) m(hine) g(parameters) g(are) h -(de-) 330 2959 y(\014ned) 34 b(for) h(the) g(target) h(computer.) 55 -b(If) 35 b(not,) h(then) f(the) g(user) g(m) m(ust) f(de\014ne) h(his) e -(o) m(wn) i(parameters.) 330 3068 y(T) -8 b(o) 39 b(do) f(this) f(go) i -(to) g(the) p Fo 39 w(example) p Fs 38 w(directory) f(and) g(t) m(yp) s -(e) p Fk 38 w(") p Fs(mak) m(e) h(teslamac) m(h) p Fk(") p -Fs 39 w(to) g(generate) h(the) 330 3178 y(executable) 27 -b(co) s(de) g(teslamc) m(h.) 40 b(Run) 26 b(teslamc) m(h) h(on) f(one) h -(no) s(de) f(of) h(the) g(in) m(tended) e(parallel) g(mac) m(hine.) 330 -3288 y(The) 42 b(co) s(de) h(rep) s(orts) f(the) h(mac) m(hine) f -(arithmetic) g(parameters) h(that) g(need) f(to) i(b) s(e) e(inserted) f -(in) m(to) p Fo 330 3397 a(PEIGSDIR/h/blas) p 1087 3397 -V 33 w(lapac) m(k.h) p Fs(.) 48 b(On) 32 b(mac) m(hines) g(that) i(use) -e(8) h(b) m(ytes) h(for) e(single) g(precision) f(calcu-) 330 -3507 y(lations,) i(e.g.) 49 b(Cra) m(y) 33 b(T3D,) h(the) f(user) f(m) m -(ust) h(also) g(insert) p Fo 32 w(CODEOBJ=) e(SINGLE) p -Fs 32 w(in) h(the) p Fo 33 w(DEFS) p Fs 330 3616 a(\014le) k(so) h -(that) p Fo 37 w(mak) m(e) p Fs 38 w(can) g(build) c(the) k(single) f -(precision) f(fortran) h(co) s(des) h(in) p Fo 35 w(PEIGSDIR/src/f77) p -Fs(.) 330 3726 y(On) 30 b(other) g(mac) m(hines) g(the) h(user) e(m) m -(ust) i(set) p Fo 30 w(CODEOBJ=) e(DBLE) p Fs(.) p Fq -199 3861 a(\000) p Fs 60 w(t) m(yp) s(e) f(the) f(command) p -Fo 28 w(mak) m(e) p Fs(.) 40 b(The) 27 b(libraries) p -Fo 25 w(libblas.a) p Fs(,) p Fo 28 w(liblapac) m(k.a) p -Fs 29 w(and) p Fo 27 w(libp) s(eigs.a) p Fs 28 w(will) e(no) m(w) j(b) s -(e) 330 3970 y(built.) 275 4130 y(Compiler) 39 b(optimization) j(can) g -(cause) h(errors) e(and) h(unexp) s(ected) f(results) g(in) g(certain) h -(situations.) 150 4239 y(W) -8 b(e) 42 b(handle) e(this) g(in) g(the) p -Fo 41 w(Mak) m(e\014le) p Fs(s) i(b) m(y) f(ha) m(ving) g(the) g -(\014les) f(that) i(w) m(e) f(kno) m(w) g(do) g(not) h(optimize) e(w) m -(ell) 150 4349 y(compile) d(without) g(optimization.) 63 -b(The) 37 b(user) h(is) f(advised) g(that) h(m) m(uc) m(h) g(of) h(our) -e(C) h(utilit) m(y) e(co) s(des) i(fail) 150 4458 y(to) j(function) e -(with) g(the) h(GNU) p Fo 41 w(gcc) p Fs 41 w(compiler) f(with) g(the) p -Fo 40 w(-O2) p Fs 41 w(optimization.) 70 b(Some) 40 b(of) g(the) h -(utilit) m(y) 150 4568 y(co) s(des) 29 b(also) h(failed) d(to) j -(function) e(correctly) i(with) e(the) h(P) m(ortland) g(Group's) p -Fo 29 w(icc) p Fs 30 w(compiler) f(with) g(the) p Fo -29 w(-O3) p Fs 150 4677 a(optimization) g(option.) 40 -b(W) -8 b(e) 30 b(are) g(curren) m(tly) e(trying) h(to) h(remedy) e -(this) h(situation.) p Fo 39 w(The) g(user) g(is) g(advised) 150 -4787 y(that) d(the) g(latest) h(installation) g(instruction) f(is) g -(lo) s(cated) g(in) g(the) f(INST) -8 b(ALL) 25 b(\014le) h(at) g(the) g -(top) f(of) h(the) g(p) s(eigs) 150 4897 y(directory) -8 -b(.) p 90 rotate dyy eop -%%Page: 9 10 -9 9 bop Fs 150 -116 a(Chapter) 30 b(3:) 41 b(Con) m(ten) m(t:) h(Co) s -(de) 30 b(F) -8 b(unctionalities) 28 b(and) i(Data) i(Structure) 1081 -b(9) p Fp 150 141 a(3) 80 b(Con) l(ten) l(t:) e(Co) t(de) 53 -b(F) -13 b(unctionalities) 54 b(and) g(Data) 311 299 -y(Structure) p Fs 275 534 a(This) 29 b(section) i(lists) f(the) h -(subroutines) e(in) g(P) m(eIGS) j(and) e(their) g(functionalities.) 41 -b(P) m(eIGS) 31 b(is) f(designed) 150 644 y(using) e(the) h(b) s(ottom) -h(up) f(approac) m(h.) 40 b(Eac) m(h) 30 b(subroutine) e(is) g(built) f -(up) i(on) g(more) g(basic) g(routines.) 39 b(A) m(t) 31 -b(the) 150 754 y(top) 23 b(lev) m(el) f(are) h(driv) m(ers) f(to) h -(solv) m(e) g(the) g(symmetric) f(eigensystem) h(problems.) 36 -b(The) 23 b(second) f(lev) m(el) h(con) m(tains) 150 -863 y(factorization) 36 b(and) f(linear) f(algebra) i(subroutines) d -(that) j(are) g(required) e(b) m(y) h(the) h(eigensystem) g(solv) m -(ers.) 150 973 y(The) 31 b(last) g(lev) m(el) g(con) m(tains) g(in) m -(ternal) f(P) m(eIGS) h(routines) g(and) f(utilites) f(for) i(managing) -g(comm) m(unications,) 150 1082 y(list) d(pro) s(cessing,) h(and) g -(error) g(c) m(hec) m(king.) 41 b(In) 29 b(terms) g(of) h(data) g -(structure,) g(the) f(C) h(routines) e(are) i(the) g(most) 150 -1192 y(\015exible) 22 b(since) i(all) f(the) h(pro) s(cedure) f -(argumen) m(ts) h(are) h(p) s(oin) m(ters) e(or) h(one) g(dimensional) d -(arra) m(ys) k(of) f(p) s(oin) m(ters.) 150 1302 y(Th) m(us,) j(in) f -(man) m(y) h(applications,) g(minimal) d(data) k(mo) m(v) m(emen) m(ts) -h(are) f(required) d(to) j(use) f(these) h(subroutines) 150 -1411 y(since) j(no) h(cop) m(ying) g(or) g(data) h(mo) m(v) m(emen) m -(ts) g(are) g(needed.) 45 b(One) 31 b(only) g(needs) h(to) g(set) h -(the) f(address) f(to) i(the) 150 1521 y(correct) f(data) f(p) s -(ositions.) 275 1656 y(This) h(c) m(hapter) j(is) f(organized) g(in) g -(terms) g(of) h(subroutine) d(and) i(data) h(structure.) 53 -b(Section) 34 b(3.1) i(sum-) 150 1765 y(marizes) 25 b(the) h(routines) f -(that) h(are) g(supp) s(orted) e(in) g(this) g(v) m(ersion) h(of) h(P) m -(eIGS.) g(Section) g(3.2.) 40 b(describ) s(es) 24 b(ho) m(w) 150 -1875 y(the) i(input) d(data) j(are) g(exp) s(ected) g(in) e(F) -8 -b(ortran) 26 b(and) f(in) f(C.) i(W) -8 b(e) 26 b(assume) f(that) i -(the) e(reader) h(is) e(familiar) f(with) 150 1985 y(column) 29 -b(distribution) e(of) j(data) p Fl 1243 1952 a(1) p Fs -1281 1985 a(.) p Fr 150 2243 a(3.1) 68 b(Summary) p Fs -275 2436 a(Let) 35 b(us) g(summarize) f(the) i(subroutines) d(and) i -(their) f(functions.) 55 b(The) 35 b(follo) m(wing) e(is) i(a) h(short) -f(list) f(of) 150 2546 y(the) c(supp) s(orted) f(routines) g(in) f(P) m -(eIGS.) j(These) f(subroutines) e(are) i(protected) h(from) f(p) s -(ossible) e(comm) m(uni-) 150 2655 y(cation) g(deadlo) s(c) m(k) g(b) m -(y) g(enforcing) g(the) g(follo) m(wing) f(rules.) 38 -b(In) 27 b(the) i(generalized) e(eigenproblem) g(the) h(set) h(of) 150 -2765 y(pro) s(cessors) f(storing) f(the) i(matrix) p -Fo 27 w(A) p Fs(,) g(the) f(matrix) p Fo 28 w(B) p Fs -27 w(and) g(the) h(eigen) m(v) m(ectors) p Fo 30 w(Z) p -Fs 28 w(m) m(ust) f(b) s(e) f(the) i(same) f(set) 150 -2875 y(of) h(pro) s(cessors.) 40 b(In) 29 b(the) g(standard) f -(eigenproblem) g(the) h(set) h(of) g(pro) s(cessors) e(storing) h(the) g -(matrix) p Fo 29 w(A) p Fs 29 w(and) 150 2984 y(the) 36 -b(eigen) m(v) m(ectors) p Fo 39 w(Z) p Fs 35 w(m) m(ust) g(b) s(e) g -(the) g(same) h(set) g(of) f(pro) s(cessors.) 58 b(This) 35 -b(is) g(not) h(the) h(same) f(as) h(the) f(data) 150 -3094 y(distribution) 30 b(b) s(eing) i(the) h(same.) 50 -b(It) 34 b(means) f(that) h(the) p Fo 33 w(set) p Fs -34 w(of) g(pro) s(cessors) f(holding) e(one) i(matrix) g(m) m(ust) 150 -3203 y(b) s(e) d(the) g(same) h(as) g(the) f(set) h(of) g(pro) s -(cessors) f(holding) e(an) m(y) j(other) f(matrix.) 275 -3338 y(If) c(y) m(ou) h(are) h(solving) e(the) h(real) f(symmetric) h -(eigensystem) g(problem) p Fo 25 w(Ax) p Fs 25 w(=) p -Fn 25 w(\025) p Fo(x) p Fs 27 w(the) g(pro) s(cessors) g(hold-) 150 -3448 y(ing) 35 b(the) i(columns) e(of) h(matrix) p Fo -36 w(A) p Fs(,) g(and) f(the) i(pro) s(cessors) f(holding) e(the) i -(eigen) m(v) m(ectors) p Fo 38 w(X) p Fs 36 w(are) h(required) 150 -3557 y(to) f(b) s(e) f(the) h(same) g(set) g(or) g(the) f(pro) s -(cessors) g(holding) f(eigen) m(v) m(ectors) j(of) p -Fo 36 w(X) p Fs 35 w(m) m(ust) f(b) s(e) f(a) h(subset) f(of) g(those) -150 3667 y(holding) h(columns) i(of) p Fo 38 w(A) p Fs(.) h(This) e -(mild) f(restriction) h(is) h(curren) m(tly) g(necessary) h(to) g(a) m -(v) m(oid) g(p) s(ossible) d(race) 150 3777 y(conditions.) 47 -b(Using) 33 b(suc) m(h) f(input) f(restriction) h(and) h(no) g -(bu\013ering) e(assumptions) h(P) m(eIGS) h(can) g(b) s(e) g(used) 150 -3886 y(on) 39 b(strong) g(message) i(t) m(yping) d(message) j(passing) d -(soft) m(w) m(are) i(\(e.g.) 69 b(TCGMSG\)) 39 b({) h(with) e(no) h -(message) 150 3996 y(queues) c(or) g(bu\013ers.) 55 b(The) 35 -b(user) g(can,) i(of) f(course,) h(use) e(other) g(routines) g(in) f(P) -m(eIGS) i(but) e(at) i(their) f(o) m(wn) 150 4105 y(risk.) j(Some) 28 -b(of) g(the) f(unsupp) s(orted) e(and) i(in) m(ternal) f(P) m(eIGS) i -(routines,) f(with) f(certain) i(data) g(distributions) 150 -4215 y(and) k(insu\016cien) m(t) f(message) j(bu\013er) e(space,) i(ma) -m(y) f(encoun) m(ter) g(comm) m(unication) f(deadlo) s(c) m(k.) 48 -b(In) 32 b(this) g(re-) 150 4325 y(lease,) j(w) m(e) e(assume) h(that) g -(all) e(the) h(matrices) p Fo 34 w(A) p Fs 33 w(and) p -Fo 32 w(B) p Fs 33 w(for) g(the) h(general) f(eigensystem) h(problems) e -(and) 150 4434 y(the) 25 b(standard) f(symmetric) h(eigensystem) g -(problems) e(with) h(matrix) g(of) h(eigen) m(v) m(ectors) p -Fo 27 w(Z) p Fs 25 w(share) f(the) i(same) 150 4544 y(set) 31 -b(of) f(pro) s(cessors) g(for) g(their) g(data) h(distributions.) p -Fl 1923 4511 a(2) p Fs 275 4679 a(Lev) m(el) f(1) h(driv) m(ers:) p -Fq 199 4814 a(\000) p Fs 60 w(PDSPGV) g(:) f(General) g(real) g -(symmetric) g(eigensystem) h(solv) m(er) p Fq 199 4948 -a(\000) p Fs 60 w(PDSPEV:) f(Standard) f(real) i(symmetric) e -(eigensystem) i(solv) m(er) p 150 5045 1200 4 v Fl 199 -5113 a(1) p Fj 275 5144 a(Golub,) e(Gene) f(H.) g(and) f(Charles) j(F.) -e(V) -6 b(an) 27 b(Loan,) p Fi 30 w(") p Fj(Matrix) h(Computations,) p -Fi(") p Fj 29 w(2nd) f(ed,) i(Johns) g(Hopkins) e(Univ) n(ersit) n(y) -275 5236 y(Press,) g(1989.) p Fl 199 5308 a(2) p Fj 275 -5340 a(P) n(eIGS) e(no) h(longer) g(supp) r(ort) g(the) f(computation) g -(of) h(selected) h(eigen) n(v) l(alue) f(and) f(eigen) n(v) n(ector) h -(pairs.) p 90 rotate dyy eop -%%Page: 10 11 -10 10 bop Fs 150 -116 a(10) 3256 b(P) m(eIGS) p Fq 199 -299 a(\000) p Fs 60 w(PDSPTRI:) 30 b(Symmetric) f(tri-diagonal) g -(eigensystem) i(solv) m(er) 275 477 y(Lev) m(el) f(2) h(driv) m(ers:) p -Fq 199 624 a(\000) p Fs 60 w(CHOLESKI:) e(submatrix) f(Choleski) h -(factorization) p Fl 2159 591 a(3) p Fs 2197 624 a(.) p -Fq 199 765 a(\000) p Fs 60 w(INVERSEL:) h(the) g(in) m(v) m(erse) h(of) -f(a) h(lo) m(w) m(er) f(triangular) f(matrix) h(in) f(column) g -(distributed) f(format.) p Fq 199 906 a(\000) p Fs 60 -w(MXM*:) 48 b(a) 34 b(v) -5 b(ariet) m(y) 33 b(of) h(matrix) e(m) m -(ultiplication) f(routines) h(for) h(matrices) g(with) f(di\013eren) m -(t) h(shap) s(es) 330 1015 y(and) d(column/ro) m(w) g(distributions.) p -Fq 199 1156 a(\000) p Fs 60 w(TRED2:) 74 b(column) 46 -b(distributed) e(Householder) i(reduction) g(of) i(a) f(symmetric) f -(matrix) h(to) g(tri-) 330 1266 y(diagonal) 30 b(form) g(\() g(only) g -(the) g(C) g(v) m(ersion\).) p Fq 199 1407 a(\000) p -Fs 60 w(PSTEBZ:) i(a) i(parallel) d(v) m(ersion) i(of) g(LAP) -8 -b(A) m(CK's) 34 b(DSTEBZ) f(routine) f(for) h(computing) f(the) i -(eigen-) 330 1516 y(v) -5 b(alues) 30 b(of) g(real) g(tridiagonal) f -(matrices) i(using) d(bisection.) p Fq 199 1657 a(\000) p -Fs 60 w(PSTEIN*:) 44 b(a) 33 b(parallel) e(subspace) g(iteration) h -(metho) s(d) g(for) h(\014nding) d(eigen) m(v) m(ectors) k(of) f -(symmetric) 330 1767 y(tridiagonal) 40 b(matrices) h(using) f(the) h -(our) g(parallel) f(v) -5 b(arian) m(t) 41 b(of) g(the) h(Dhillon-P) m -(arlett) e(algorithm.) 330 1876 y(Computations) 29 b(in) m(v) m(olving) -g(clusters) h(are) h(dynamically) d(sc) m(heduled) h(based) h(on) g(sp) -s(ectrum.) p Fq 199 2017 a(\000) p Fs 60 w(TRESID:) 25 -b(a) h(parallel) e(routine) h(for) h(computing) f(the) g(residual) f -(of) i(the) g(tridiagonal) e(eigenproblem.) p Fq 199 -2158 a(\000) p Fs 60 w(RESID:) 30 b(a) h(parallel) d(routine) i(for) g -(computing) f(the) i(residual) d(of) j(the) f(standard) g -(eigenproblem.) p Fq 199 2299 a(\000) p Fs 60 w(RESIDUAL:) c(a) g -(parallel) d(routine) i(for) h(computing) e(the) i(residual) e(of) h -(the) h(generalized) g(eigenprob-) 330 2408 y(lem.) p -Fq 199 2549 a(\000) p Fs 60 w(OR) -8 b(THO:) 30 b(a) h(parallel) d -(routine) i(for) g(testing) g(the) h(orthogonalit) m(y) g(of) f(eigen) m -(v) m(ectors) p Fq 199 2690 a(\000) p Fs 60 w(BOR) -8 -b(THO:) 42 b(a) g(parallel) e(routine) h(for) g(testing) h(the) g -(B-orthogonalit) m(y) h(of) f(eigen) m(v) m(ectors) i(for) e(the) 330 -2799 y(generalized) 30 b(eigenproblem) p Fr 150 3088 -a(3.2) 68 b(Data) 46 b(La) l(y) l(out) p Fs 275 3293 -a(F) -8 b(rom) 25 b(the) h(user's) f(p) s(oin) m(t) f(of) i(view) e(P) m -(eIGS') i(data) g(structure) f(is) g(essen) m(tially) f(column\(ro) m -(w\)) h(wrapping) 150 3403 y(according) 30 b(to) h(a) f(list.) 39 -b(By) 31 b(this) e(w) m(e) h(mean) g(that) h(a) f(matrix) f(is) g -(partitioned) g(in) m(to) h(columns) f(\(ro) m(ws\)) h(with) 150 -3513 y(an) 41 b(in) m(teger) h(arra) m(y) p Fo 43 w(map) p -Fs 40 w(describing) e(whic) m(h) g(pro) s(cessor) h(holds) f(column) h -(\() h(ro) m(w) f(\)) p Fo 42 w(i) p Fs(.) 75 b(F) -8 -b(or) 42 b(example,) p Fo 150 3622 a(map\(i\)) 27 b(=) e(p) p -Fs 26 w(means) h(that) h(pro) s(cessor) p Fo 26 w(p) p -Fs 25 w(stores) g(column) e(\() h(ro) m(w) g(\)) p Fo -27 w(i) p Fs(.) 39 b(When) 26 b(using) f(MPI) h(this) f(de\014nition) -150 3732 y(is) k(c) m(hanged) i(sligh) m(tly) -8 b(.) 40 -b(See) 31 b(the) f(subsection) f(on) i(using) e(MPI) h(for) g(more) h -(details) e(on) h(this) g(case.) 275 3879 y(The) e(data) i(la) m(y) m -(out) h(is) d(used) h(in) f(a) i(compatible) e(w) m(a) m(y) j(in) d -(the) h(P) m(eIGS) h(subroutines.) 38 b(The) 29 b(data) h(struc-) 150 -3988 y(ture) 25 b(for) g(eac) m(h) h(routine) e(can) h(also) g(b) s(e) g -(used) f(as) h(input) e(to) j(another) g(P) m(eIGS) f(subroutine) e -(without) h(remap-) 150 4098 y(ping.) 39 b(Of) 30 b(course,) h(for) f -(optimal) f(p) s(erformance) h(the) h(user) e(is) h(advised) f(to) i -(minimize) d(comm) m(unication.) 275 4245 y(The) 38 b(follo) m(w) h -(subsections) f(describ) s(es) f(ho) m(w) i(to) h(input) d(data) j -(from) f(a) h(giv) m(en) f(pro) s(cessor's) g(p) s(oin) m(t) f(of) 150 -4355 y(view.) i(W) -8 b(e) 32 b(hop) s(e) d(that) i(the) g(examples) f -(are) g(informativ) m(e.) p Fg 150 4604 a(3.2.1) 63 b(F) -10 -b(ortran) 41 b(Data) f(Structure) p Fs 275 4809 a(Let) 32 -b(us) e(sho) m(w) i(ho) m(w) f(the) h(follo) m(wing) e(4) i(b) m(y) f -(4) h(matrix) f(can) h(b) s(e) p Fo 31 w(ro) m(w) g(mapp) s(ed) p -Fs 29 w(on) g(2) g(pro) s(cessors) f(\(pro-) 150 4919 -y(cessor) 36 b(0) h(and) e(pro) s(cessor) g(1\)) i(in) d(F) -8 -b(ortran) 37 b(using) d(our) h(structure.) 57 b(Let) p -Fo 36 w(mapA) p Fs 35 w(b) s(e) 35 b(the) h(in) m(teger) g(arra) m(y) -150 5029 y(describing) 28 b(pro) s(cessor) i(n) m(um) m(b) s(ers) f -(for) h(the) h(distribution) 26 b(of) 31 b(the) f(matrix.) p -150 5149 1200 4 v Fl 199 5217 a(3) p Fj 275 5249 a(Geist,) 38 -b(G.A.) d(and) g(M.T.) h(Heath,) p Fi 37 w(") p Fj(Matrix) g(F) -6 -b(actorization) 37 b(on) d(a) i(Hyp) r(ercub) r(e) d(Multipro) r -(cessor) p Fi(") p Fj(,) 40 b(in) 35 b(Hyp) r(ercub) r(e) 275 -5340 y(Multipro) r(cessors) 28 b(1986,) f(SIAM,) e(Philadelphia,) i -(1986,) h(pp.) 34 b(161-180) p 90 rotate dyy eop -%%Page: 11 12 -11 11 bop Fs 150 -116 a(Chapter) 30 b(3:) 41 b(Con) m(ten) m(t:) h(Co) s -(de) 30 b(F) -8 b(unctionalities) 28 b(and) i(Data) i(Structure) 1035 -b(11) p Fk 1917 299 a(1) 143 b(2) g(3) g(4) 1917 403 -y(5) g(6) g(7) g(8) 1917 506 y(9) 95 b(10) g(11) g(12) 1917 -610 y(13) 47 b(14) 95 b(15) g(16) p Fs 275 747 a(If) 39 -b(w) m(e) i(put) f(ro) m(w) g(1) h(and) f(ro) m(w) g(4) h(on) f(pro) s -(cessor) g(0) h(and) e(ro) m(w) i(2) f(and) g(ro) m(w) g(3) h(on) f -(pro) s(cessor) g(1,) k(the) 150 857 y(con) m(ten) m(ts) 32 -b(of) f(the) f(arra) m(y) p Fo 31 w(mapA) p Fs 30 w(on) g(b) s(oth) f -(pro) s(cessors) h(is) p Fo 275 993 a(mapA) p Fs 59 w(:) h(0) 61 -b(1) g(1) g(0) 275 1130 y(The) 29 b(con) m(ten) m(t) k(of) d(the) h -(one) f(dimensional) e(storage) k(arra) m(y) f(for) p -Fo 30 w(matrixA) p Fs 30 w(on) g(pro) s(cessor) f(0) g(is) p -Fo 275 1267 a(pro) s(c) g(0:) 41 b(matrixA) p Fs(:) 31 -b(1) 61 b(2) g(3) g(4) g(13) g(14) h(15) f(16) 275 1404 -y(The) 29 b(con) m(ten) m(t) k(of) d(the) h(one) f(dimensional) e -(storage) k(arra) m(y) f(for) p Fo 30 w(matrixA) p Fs -30 w(on) g(pro) s(cessor) f(1) g(is) p Fo 275 1541 a(pro) s(c) g(1:) 41 -b(matrixA) p Fs(:) 31 b(5) 61 b(6) g(7) g(8) g(9) g(10) g(11) h(12) 275 -1677 y(This) 28 b(is) i(the) g(arra) m(y) h(storage) h(that) f(is) e -(exp) s(ected) i(as) g(input) d(b) m(y) i(the) h(F) -8 -b(ortran) 31 b(driv) m(ers.) 275 1814 y(F) -8 b(or) 38 -b(symmetric) e(matrices) h(,) j(w) m(e) d(use) g(the) h(pac) m(k) m(ed) -g(storage) h(format.) 62 b(Here) 38 b(is) e(an) h(example) g(of) h(a) -150 1924 y(symmetric) 30 b(matrix) p Fo 29 w(A) p Fs -30 w(column) g(decomp) s(osed) g(and) f(stored) i(using) e(its) h(lo) m -(w) m(er) g(triangular) f(part.) p Fk 1917 2055 a(1) 1917 -2159 y(5) 143 b(6) 1917 2262 y(9) 95 b(10) g(11) 1917 -2366 y(13) 47 b(14) 95 b(15) g(16) p Fs 275 2503 a(If) 40 -b(w) m(e) h(put) f(columns) g(1) h(and) f(4) i(on) e(pro) s(cessor) h -(0) g(and) f(columns) g(2) h(and) f(3) h(on) g(pro) s(cessor) g(1,) j -(the) 150 2612 y(con) m(ten) m(ts) 32 b(of) f(the) f(arra) m(y) p -Fo 31 w(mapA) p Fs 30 w(on) g(b) s(oth) f(pro) s(cessors) h(are) p -Fo 275 2749 a(mapA) p Fs 59 w(:) h(0) 61 b(1) g(1) g(0) 275 -2886 y(The) 29 b(con) m(ten) m(t) k(of) d(the) h(one) f(dimensional) e -(storage) k(arra) m(y) f(for) p Fo 30 w(matrixA) p Fs -30 w(on) g(pro) s(cessor) f(0) g(is) p Fo 275 3023 a(pro) s(c) g(0:) 41 -b(matrixA) p Fs(:) 31 b(1) 61 b(5) g(9) g(13) g(16) 275 -3160 y(The) 29 b(con) m(ten) m(t) k(of) d(the) h(one) f(dimensional) e -(storage) k(arra) m(y) f(for) p Fo 30 w(matrixA) p Fs -30 w(on) g(pro) s(cessor) f(1) g(is) p Fo 275 3296 a(pro) s(c) g(1:) 41 -b(matrixA) p Fs(:) 31 b(6) 61 b(10) g(14) h(11) f(15) 275 -3433 y(This) 21 b(is) h(the) h(arra) m(y) h(storage) g(format) g(and) e -(the) h(mapping) f(format) h(that) h(is) e(exp) s(ected) h(as) h(input) -d(for) i(the) 150 3543 y(symmetric) g(matrices) p Fo -24 w(A) p Fs 24 w(and) p Fo 24 w(B) p Fs 23 w(in) g(the) h(the) h -(symmetric) e(eigensystem) h(solv) m(ers) p Fo 24 w(PDSPEV) p -Fs(,) p Fo 23 w(PDSPGV) p Fs(,) p Fo 150 3652 a(PDSPEVX) p -Fs 29 w(and) p Fo 29 w(PDSPGVX) p Fs(.) p Fg 150 3881 -a(3.2.2) 63 b(C) 40 b(Data) g(Structure) p Fs 275 4076 -a(The) 33 b(reader) h(can) g(disregard) e(this) h(section) h(if) f(F) -8 -b(ortran) 34 b(is) f(the) h(language) g(of) g(c) m(hoice.) 52 -b(Since) 33 b(the) h(C) 150 4186 y(user) c(can) g(call) g(F) -8 -b(ortran) 31 b(or) g(C) f(subroutines) e(the) i(information) f(in) g -(the) i(last) f(section) h(ma) m(y) g(b) s(e) f(useful) e(to) 150 -4295 y(the) j(C) f(programmer.) 275 4432 y(All) 36 b(of) i(the) g -(input) e(parameters) i(for) g(C) f(subroutines) f(in) g(P) m(eIGS) j -(are) f(p) s(oin) m(ters.) 62 b(F) -8 b(or) 39 b(the) f(matrix) p -Fo 150 4542 a(A) p Fs 38 w(ab) s(o) m(v) m(e,) k(the) d(input) d(for) i -(the) h(C) f(subroutine) e(requires) h(that) i(the) g(matrix) f(b) s(e) -g(presen) m(ted) g(as) h(a) g(one) 150 4651 y(dimenesional) 28 -b(arra) m(y) j(of) f(p) s(oin) m(ters) p Fo 29 w(ptr) p -Fs(.) 40 b(Eac) m(h) 31 b(p) s(oin) m(ter) p Fo 30 w(ptr[i]) p -Fs 31 w(p) s(oin) m(ts) e(to) i(the) f(storage) i(address) d(of) i(the) -150 4761 y(\014rst) f(elemen) m(t) g(of) h(the) g(i-th) e(column) g(o) m -(wned) i(b) m(y) f(the) h(pro) s(cessor.) 40 b(An) 30 -b(example) g(is) f(giv) m(en) i(b) s(elo) m(w.) 275 4898 -y(Again) f(consider) f(the) i(follo) m(wing) d(matrix.) p -Fk 1917 5029 a(1) 143 b(2) g(3) g(4) 1917 5132 y(5) g(6) g(7) g(8) 1917 -5236 y(9) 95 b(10) g(11) g(12) 1917 5340 y(13) 47 b(14) 95 -b(15) g(16) p 90 rotate dyy eop -%%Page: 12 13 -12 12 bop Fs 150 -116 a(12) 3256 b(P) m(eIGS) 275 299 -y(If) 26 b(w) m(e) i(distribute) d(columns) g(1) j(and) e(4) i(on) f -(pro) s(cessor) g(0) g(and) g(columns) f(2) h(and) g(3) g(on) h(pro) s -(cessor) e(1,) j(the) 150 408 y(con) m(ten) m(ts) j(of) f(the) f(arra) m -(y) p Fo 31 w(mapA) p Fs 30 w(on) g(b) s(oth) f(pro) s(cessors) h(are) p -Fo 1656 645 a(mapA) p Fs 25 w(:) 25 b(0) 31 b(1) g(1) f(0) 275 -798 y(Let) 45 b(us) g(use) g(the) h(notation) p Fo 45 -w(mem-address\(i\)) p Fs 46 w(to) g(denote) g(the) f(memory) h(lo) s -(cation) f(of) g(the) h(\014rst) 150 908 y(elemen) m(t) d(in) e(column) -g(i.) p Fo 76 w(W) -8 b(e) 43 b(assume) f(that) h(the) g(data) g(for) f -(column) g(i) h(are) g(stored) g(in) f(consecutiv) m(e) 150 -1017 y(memory) 31 b(lo) s(cations.) p Fs 275 1144 a(The) e(con) m(ten) m -(t) k(of) d(the) h(one) f(dimensional) e(arra) m(y) j(of) f(p) s(oin) m -(ters) p Fo 30 w(ptr) p Fs 30 w(on) g(pro) s(cessor) g(0) h(is) p -Fo 1065 1282 a(pro) s(c0) p Fs 25 w(:) p Fo 26 w(ptr) p -Fs 25 w(:) p Fo 25 w(mem) p Fq 20 w(\000) p Fo 20 w(addr) p -Fs(\() p Fo(1) p Fs(\)) p Fo 61 w(mem) p Fq 20 w(\000) p -Fo 20 w(addr) p Fs(\() p Fo(4) p Fs(\)) 150 1421 y(and,) f(the) h(con) m -(ten) m(t) h(of) e(the) h(one) g(dimensional) c(arra) m(y) k(of) g(p) s -(oin) m(ters) p Fo 29 w(ptr) p Fs 30 w(on) f(pro) s(cessor) g(1) h(is) e -(is) p Fo 1065 1559 a(pro) s(c1) p Fs 25 w(:) p Fo 26 -w(ptr) p Fs 25 w(:) p Fo 25 w(mem) p Fq 20 w(\000) p -Fo 20 w(addr) p Fs(\() p Fo(2) p Fs(\)) p Fo 61 w(mem) p -Fq 20 w(\000) p Fo 20 w(addr) p Fs(\() p Fo(3) p Fs(\)) 275 -1714 y(Notice) j(that) p Fo 32 w(ptr[0]) p Fs 32 w(stores) g(the) f -(starting) g(address) g(of) g(column) f(1) i(and) p Fo -31 w(ptr[1]) p Fs 32 w(stores) g(the) f(starting) 150 -1824 y(address) f(of) h(column) f(4.) 43 b(This) 29 b(is) h(b) s -(ecause) h(column) f(4) h(is) f(the) h(second) g(column) f(of) p -Fo 31 w(A) p Fs 30 w(that) i(pro) s(cessor) f(0) 150 -1934 y(o) m(wns.) 275 2060 y(If) 26 b(w) m(e) h(regard) p -Fo 27 w(ptr[0]) p Fs 28 w(and) p Fo 26 w(ptr[1]) p Fs -28 w(as) g(a) g(C) g(arra) m(y) g(then) g(the) g(con) m(ten) m(ts) h -(of) f(these) g(arra) m(ys) h(on) e(pro) s(cessor) 150 -2170 y(0) 31 b(will) c(b) s(e) p Fo 1493 2406 a(pro) s(c0) p -Fs 26 w(:) p Fo 25 w(ptr) p Fs([) p Fo(0) p Fs(]) f(:) g(1) k(5) h(9) g -(13) p Fo 1470 2542 a(pro) s(c0) p Fs 26 w(:) p Fo 25 -w(ptr) p Fs([) p Fo(1) p Fs(]) 26 b(:) g(4) 31 b(8) f(12) i(16) 275 -2695 y(F) -8 b(or) 33 b(symmetric) f(matrices) g(,) i(w) m(e) f(use) f -(the) h(pac) m(k) m(ed) h(storage) g(format.) 47 b(Here) 34 -b(is) d(an) i(example) f(of) h(the) 150 2805 y(input) 24 -b(data) j(for) f(a) g(column) f(distributed) e(symmetric) i(matrix) h -(stored) g(using) f(only) g(its) g(lo) m(w) m(er) i(triangular) 150 -2915 y(part.) p Fk 1917 3035 a(1) 1917 3139 y(5) 143 -b(6) 1917 3243 y(9) 95 b(10) g(11) 1917 3347 y(13) 47 -b(14) 95 b(15) g(16) p Fs 275 3473 a(If) 40 b(w) m(e) h(put) f(columns) -g(1) h(and) f(4) i(on) e(pro) s(cessor) h(0) g(and) f(columns) g(2) h -(and) f(3) h(on) g(pro) s(cessor) g(1,) j(the) 150 3583 -y(con) m(ten) m(ts) 32 b(of) f(the) f(arra) m(y) p Fo -31 w(mapA) p Fs 30 w(on) g(b) s(oth) f(pro) s(cessors) h(are) p -Fo 1656 3819 a(mapA) p Fs 25 w(:) 25 b(0) 31 b(1) g(1) f(0) 275 -3972 y(The) h(con) m(ten) m(t) i(of) f(the) g(one) g(dimensional) d(p) s -(oin) m(ter) h(arra) m(y) p Fo 33 w(ptr) p Fs 31 w(arra) m(y) i(for) p -Fo 32 w(matrixA) p Fs 32 w(on) f(pro) s(cessor) h(0) 150 -4082 y(is) p Fo 1042 4318 a(pro) s(c0) p Fs 25 w(:) p -Fo 26 w(ptr) p Fs 25 w(:) p Fo 25 w(mem) p Fq 21 w(\000) p -Fo 20 w(addr) p Fs(\() p Fo(1) p Fs(\)) p Fo 60 w(mem) p -Fq 21 w(\000) p Fo 19 w(addr) p Fs(\() p Fo(16) p Fs(\)) 275 -4471 y(The) d(con) m(ten) m(t) k(of) d(the) h(one-dimensional) d(p) s -(oin) m(ter) h(arra) m(y) p Fo 31 w(ptr) p Fs 30 w(on) i(pro) s(cessor) -f(1) g(is) p Fo 1042 4708 a(pro) s(c1) p Fs 25 w(:) p -Fo 26 w(ptr) p Fs 25 w(:) p Fo 25 w(mem) p Fq 21 w(\000) p -Fo 20 w(addr) p Fs(\() p Fo(6) p Fs(\)) p Fo 60 w(mem) p -Fq 21 w(\000) p Fo 19 w(addr) p Fs(\() p Fo(11) p Fs(\)) 275 -4861 y(This) c(is) g(the) i(con) m(ten) m(t) i(of) e(the) g -(one-dimensional) e(arra) m(y) i(of) g(p) s(oin) m(ters) f(that) h(is) f -(exp) s(ected) h(as) g(input) e(b) m(y) 150 4971 y(the) i(C) g -(subroutines.) 38 b(In) 28 b(particular,) f(the) i(matrix) p -Fo 27 w(A) p Fs 28 w(and) p Fo 28 w(B) p Fs 28 w(in) e(the) h(general) g -(symmetric) g(and) g(regular) 150 5080 y(symmetric) i(eigensolv) m(ers) -g(\() p Fo 31 w(PDSPEV) p Fs 29 w(and) p Fo 29 w(PDSPGV) p -Fs 30 w(\)) h(are) g(exp) s(ected) f(in) g(this) f(format) h(as) h -(input.) p Fl 3675 5047 a(4) p 150 5149 1200 4 v 199 -5217 a(4) p Fh 275 5249 a(Note:) p Fj 36 w(In) 26 b(the) g(header) h -(\014les) g(of) h(our) f(co) r(de) g(w) n(e) h(use) e(the) h(term) p -Fi 26 w(") p Fj(double) g(p) r(oin) n(ter.) p Fi(") p -Fj 27 w(This) h(term) e(is) h(confusing) h(and) e(the) 275 -5340 y(user) f(should) h(substitute) f(this) h(with) g(a) p -Fi 26 w(") p Fj 26 w(1-D) f(arra) n(y) h(of) g(p) r(oin) n(ters) g(to) g -(double) g(precision) g(n) n(um) n(b) r(ers.) p Fi(") p -90 rotate dyy eop -%%Page: 13 14 -13 13 bop Fs 150 -116 a(Chapter) 30 b(3:) 41 b(Con) m(ten) m(t:) h(Co) s -(de) 30 b(F) -8 b(unctionalities) 28 b(and) i(Data) i(Structure) 1035 -b(13) p Fg 150 299 a(3.2.3) 63 b(MPI) 41 b(Use) p Fs -275 491 a(The) 31 b(reader) i(can) g(disregard) e(this) g(section) i -(if) e(they) i(are) f(using) f(TCGMSG) i(or) f(In) m(tel) g(NX) h(for) f -(com-) 150 601 y(m) m(unication.) 275 736 y(The) d(P) m(eIGS) g -(implemen) m(tation) g(of) g(MPI) h(do) s(es) f(NOT) g(supp) s(ort) p -Fo 28 w(heterogeneous) p Fs 31 w(net) m(w) m(orks) h(of) g(com-) 150 -845 y(puters,) h(but) f(DOES) h(supp) s(ort) p Fo 29 -w(homogeneous) p Fs 32 w(net) m(w) m(orks) h(of) f(computers.) 42 -b(In) 31 b(particular,) f(MPI) h(nev) m(er) 150 955 y(kno) m(ws) 40 -b(the) h(real) f(data) h(t) m(yp) s(e) f(of) h(the) f(message,) 45 -b(a) 40 b(generic) h(MPI) p 2473 955 28 4 v 32 w(BYTE) g(t) m(yp) s(e) f -(is) g(used) f(b) m(y) h(P) m(eIGS,) 150 1064 y(hence) 33 -b(MPI) f(cannot) h(correctly) g(deal) f(with) f(di\013eren) m(t) h -(binary) f(represen) m(tations) h(of) h(data) g(on) f(di\013eren) m(t) -150 1174 y(computers.) 275 1308 y(P) m(eIGS) 48 b(do) s(es) f(not) i -(use) e(MPI) h(comm) m(unicators) g(explicitly) -8 b(.) 92 -b(Instead,) 52 b(to) d(use) f(MPI) g(one) g(sim-) 150 -1418 y(ply) e(c) m(hanges) i(the) f(de\014nition) e(of) i(the) p -Fo 48 w(map) p Fs 46 w(arra) m(ys) h(sligh) m(tly) -8 -b(.) 90 b(In) 46 b(particular,) k(when) c(using) g(MPI) p -Fo 150 1528 a(map\(i\)) 33 b(=) f(p) p Fs 31 w(means) g(that) h(column) -e(\(ro) m(w\)) p Fo 34 w(i) p Fs 32 w(is) g(stored) i(on) f(the) g(pro) -s(cessor) g(whic) m(h) f(has) p Fo 32 w(rank) h(p) p -Fs 32 w(in) f(the) p Fo 150 1637 a(MPI) p 339 1637 28 -5 v 33 w(Comm) p 635 1637 V 33 w(W) -8 b(orld) p Fs 34 -w(comm) m(unicator.) 51 b(Ev) m(erything) 33 b(else) g(is) g(iden) m -(tical) f(to) j(the) e(non-MPI) h(case.) 51 b(The) 150 -1747 y(pro) s(cessors) 26 b(o) m(wning) h(a) g(matrix) f(ma) m(y) i(b) s -(e) e(part) h(of) g(a) g(comm) m(unicator) h(other) f(than) p -Fo 27 w(MPI) p 3155 1747 V 33 w(Comm) p 3451 1747 V 32 -w(W) -8 b(orld) p Fs(,) 150 1856 y(but) 47 b(the) g(ranks) g(stored) g -(in) f(the) p Fo 47 w(map) p Fs 47 w(arra) m(ys) i(MUST) f(b) s(e) f -(the) i(ranks) e(of) i(the) f(pro) s(cessors) g(in) f(the) p -Fo 150 1966 a(MPI) p 339 1966 V 33 w(Comm) p 635 1966 -V 33 w(W) -8 b(orld) p Fs 44 w(comm) m(unicator.) 82 -b(The) 44 b(P) m(eIGS) g(routines) f(then) h(do) g(all) f(comm) m -(unication) g(us-) 150 2076 y(ing) h(the) p Fo 44 w(MPI) p -675 2076 V 33 w(Comm) p 971 2076 V 33 w(W) -8 b(orld) p -Fs 45 w(comm) m(unicator,) 48 b(but) c(restricting) f(comm) m -(unication) h(to) h(only) e(those) 150 2185 y(pro) s(cessors) 30 -b(listed) f(in) g(one) h(of) h(the) p Fo 31 w(map) p -Fs 29 w(arra) m(ys) g(passed) f(to) h(the) g(P) m(eIGS) f(routines.) p -90 rotate dyy eop -%%Page: 14 15 -14 14 bop Fs 150 -116 a(14) 3256 b(P) m(eIGS) p 90 rotate -dyy eop -%%Page: 15 16 -15 15 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(15) p Fp 150 299 a(4) 80 b(Calling) 56 -b(Syn) l(tax) p Fr 150 682 a(4.1) 68 b(Lev) l(el) 46 -b(I) f(Subroutines) p Fs 275 881 a(The) c(P) m(eIGS) h(pac) m(k) -5 -b(age) 43 b(has) f(t) m(w) m(o) h(main) d(routines) h(for) g(the) h -(solution) e(of) i(dense,) i(real) e(symmetric) 150 991 -y(eigensolv) m(ers:) p Fo 41 w(PDSPGV) p Fs 31 w(and) p -Fo 30 w(PDSPEV) p Fs 30 w(for) 30 b(the) h(generalized) g(and) f -(standard) g(eigenproblems.) 40 b(All) 150 1100 y(of) 31 -b(these) g(routines) e(can) i(b) s(e) f(called) g(from) g(either) g -(fortran) g(or) h(C) f(and) g(do) h(extensiv) m(e) g(c) m(hec) m(king) g -(of) g(input) 150 1210 y(data.) 41 b(See) 31 b(section) g(6) f(for) g -(more) h(ab) s(out) f(error) g(handling.) 275 1350 y(The) f(reduction) g -(algorithm,) g(from) g(the) h(general) g(symmetric) g(eigensystem) g -(problem) e(to) i(the) h(stan-) 150 1460 y(dard) h(eigensystem) h(used) -g(in) e(this) h(section,) j(is) d(to) i(in) m(v) m(ert) f(the) g -(Choleski) e(factor) p Fo 34 w(L) p Fs 33 w(of) p Fo -33 w(B) p Fs 33 w(and) h(p) s(erform) 150 1569 y(panel) d(blo) s(c) m -(k) m(ed) i(matrix) e(conjugation) i(to) g(arriv) m(e) f(at) p -Fo 31 w(L) p Ff 2044 1536 a(\000) p Fe(1) p Fo 2137 1569 -a(AL) p Ff 2261 1536 a(\000) p Fe(t) p Fn 2346 1569 a(:) p -Fs 275 1710 a(Since) i(the) i(scratc) m(h) g(arra) m(ys) g(are) g(dep) s -(enden) m(t) f(on) g(the) h(distribution) c(of) j(matrix) g(en) m -(tries) h(across) g(the) 150 1819 y(pro) s(cessors) c(P) m(eIGS) h(pro) -m(vides) f(a) h(subroutine,) e(FMEMREQ) i(in) e(F) -8 -b(ortran) 32 b(and) e(memreq) p 3234 1819 28 4 v 63 w(in) g(C,) g(whic) -m(h) 150 1929 y(returns) 37 b(the) h(dimensions) e(of) i(the) h(in) m -(teger,) h(double) d(precision,) i(and) e(p) s(oin) m(ter) g(arra) m -(ys) i(that) g(are) f(nec-) 150 2039 y(essary) c(for) g(the) g -(computation.) 51 b(The) 33 b(solv) m(er) p Fo 34 w(PDSPEV) p -Fs(,) p Fo 33 w(PDSPEVX) p Fs(,) p Fo 32 w(PDSPTRI) p -Fs(,) p Fo 34 w(PDSPGV) p Fs(,) h(and) p Fo 150 2148 -a(PDSPGVX) p Fs 30 w(are) c(curren) m(tly) g(supp) s(orted.) p -Fl 1599 2115 a(1) p Fs 275 2289 a(The) 36 b(requested) g(eigensystem) h -(is) f(returned) g(to) h(the) g(user) f(in) g(the) h(follo) m(wing) e -(manner.) 59 b(Let's) 37 b(sa) m(y) 150 2398 y(that) 42 -b(the) f(dimension) d(of) j(the) g(matrix) f(is) p Fo -40 w(n) p Fs 41 w(and) g(that) i(the) f(user) f(allo) s(cates) h(an) g -(arra) m(y) p Fo 41 w(ev) -5 b(al) p Fs 42 w(for) 41 -b(the) 150 2508 y(eigen) m(v) -5 b(alues,) 36 b(an) f(arra) m(y) p -Fo 35 w(matrixZ) p Fs 35 w(for) g(the) g(eigen) m(v) m(ector) i(and) e -(an) f(arra) m(y) p Fo 36 w(mapZ) p Fs 34 w(for) g(the) i(distribution) -150 2617 y(of) h(the) h(eigen) m(v) m(ectors) h(across) f(the) g(pro) s -(cessors.) 60 b(P) m(eIGS) 38 b(returns) e(all) g(the) i(requested) f -(eigen) m(v) -5 b(alues) 37 b(to) 150 2727 y(all) j(the) h(pro) s -(cessors) g(in) f(the) h(list) p Fo 40 w(mapZ) p Fs(.) f(P) m(eIGS) h -(also) g(returns) f(the) i(list) p Fo 39 w(mapZ) p Fs(,) f(v) m(ery) g -(lik) m(ely) f(to) i(b) s(e) 150 2836 y(di\013eren) m(t) 27 -b(than) g(the) h(input) d(list,) i(whic) m(h) f(informs) f(the) j -(calling) e(routine) g(whic) m(h) g(pro) s(cessor) h(stores) h(whic) m -(h) 150 2946 y(eigen) m(v) m(ector.) 55 b(Supp) s(ose) 33 -b(that) i(the) g(i-th) e(eigen) m(v) m(ector) k(of) e(A) f(is) g(the) g -(j-th) h(eigen) m(v) m(ector) h(of) f(A) f(stored) h(on) 150 -3056 y(the) j(curren) m(t) f(pro) s(cessor.) 61 b(Then,) 38 -b(the) g(eigenpair) e(for) h(the) g(i-th) g(eigen) m(v) -5 -b(alue) 37 b(is) g(giv) m(en) g(b) m(y) p Fo 37 w(\() h(ev) -5 -b(al\(i\),) 41 b(\() 150 3165 y(matrixZ\(j*n) p Fk(+) p -Fo(1\),) 31 b(matrixZ\(j*n) p Fk(+) p Fo(2\),) h(...,) f(matrixZ\(\(j) p -Fk(+) p Fo(1\)*n\)\)\)) p Fs(.) 275 3306 y(The) c(C) h(user) f(can) h -(replace) p Fo 29 w(matrixZ) p Fs 28 w(ab) s(o) m(v) m(e) h(as) f(a) h -(one-dimensional) d(arra) m(y) i(of) g(p) s(oin) m(ters) f(to) p -Fo 29 w(double) p Fs(,) 150 3415 y(sa) m(y) p Fo 31 w(v) m(ecZ) p -Fs(.) k(Then) f(the) g(i-th) g(eigenpair) f(\(in) g(C) h(indexing\)) e -(is) i(returned) f(as) p Fo 30 w(\(ev) -5 b(al[i],) 33 -b(v) m(ecZ[j]\)) p Fs 32 w(where) d(the) 150 3525 y(i-th) g(eigen) m(v) -m(ector) i(of) p Fo 31 w(A) p Fs 30 w(is) d(again) i(the) f(j-th) g -(eigen) m(v) m(ector) j(that) e(is) e(stored) i(on) f(this) f(pro) s -(cessor.) 275 3665 y(P) m(eIGS) e(pro) m(vides) f(a) i(utilit) m(y) e -(FIL) p 1409 3665 V 32 w(MAPVEC) i(\() f(F77) i(\)) e(and) g(\014l) p -2431 3665 V 31 w(map) m(v) m(ec) p 2756 3665 V 34 w(\() h(C) f(\)) g -(whic) m(h) f(returns) g(the) i(i) 150 3775 y(and) h(j) g(corresp) s -(ondence) g(b) s(et) m(w) m(een) h(the) f(global) g(matrix) g(index) f -(i) h(and) f(the) i(lo) s(cal) f(matrix) f(storage) j(index) 150 -3884 y(j.) 275 4025 y(Here's) i(an) h(example) e(of) i(ho) m(w) p -Fo 33 w(FMEMREQ) p Fs 34 w(and) p Fo 32 w(PDSPEV) p Fs -32 w(can) g(b) s(e) e(called) h(in) f(F) -8 b(ortran) 34 -b(to) g(solv) m(e) 150 4134 y(the) d(standard) e(symmetric) h -(eigensystem) g(problem) p Fo 29 w(Ax) p Fs 25 w(=) p -Fn 25 w(\025) p Fo(x) p Fs 30 w(.) 275 4275 y(Let) p -Fo 22 w(mapA) p Fs 22 w(and) p Fo 22 w(mapZ) p Fs 21 -w(b) s(e) 22 b(in) m(teger) g(arra) m(ys) h(of) g(dimension) p -Fo 19 w(n) p Fs 22 w(whic) m(h) e(con) m(tain) i(the) g(data) g -(distribution) 150 4384 y(information.) 39 b(Let) p Fo -30 w(isize) p Fs 30 w(b) s(e) 29 b(the) g(parameter) h(holding) e(the) h -(in) m(teger) h(scratc) m(h) g(arra) m(y) g(size.) 41 -b(Let) p Fo 29 w(rsize) p Fs 31 w(b) s(e) 150 4494 y(the) 24 -b(parameter) g(holding) e(the) i(double) f(precision) f(scratc) m(h) j -(arra) m(y) f(size.) 38 b(Let) p Fo 25 w(ptr) p 2883 -4494 28 5 v 32 w(size) p Fs 25 w(b) s(e) 23 b(the) h(parameter) 150 -4604 y(holding) 32 b(the) i(size) g(of) h(the) f(1) h(dimensional,) d -(double) h(precision) f(arra) m(y) j(whic) m(h) p Fo -33 w(PDSPEV) p Fs 33 w(will) c(con) m(v) m(ert) 150 4713 -y(to) f(a) f(scratc) m(h) h(arra) m(y) f(of) g(p) s(oin) m(ters) f(to) h -(double) e(precision) g(n) m(um) m(b) s(ers.) 39 b(F) -8 -b(or) 30 b(this) e(example,) p Fo 29 w(mapB) p Fs 27 -w(can) i(b) s(e) 150 4823 y(empt) m(y) 25 b(or) f(just) g(a) h(dumm) m -(y) e(v) -5 b(ariable.) 38 b(An) 24 b(in) m(teger) h(arra) m(y) p -Fo 25 w(iscratc) m(h\(1:3*n\)) p Fs 28 w(is) e(used) h(for) g(in) m -(teger) h(scratc) m(h) 150 4932 y(space.) 40 b(On) 26 -b(output,) p Fo 27 w(FMEMREQ) p Fs 27 w(returns) g(the) h(dimensions) d -(of) j(the) g(scratc) m(h) g(memory) g(necessary) g(for) 150 -5042 y(the) c(calculations) f(in) f(the) i(v) -5 b(ariables) p -Fo 22 w(isize) p Fs(,) p Fo 25 w(rsize) p Fs(,) p Fo -26 w(ptr) p 1985 5042 V 32 w(size) p Fs(.) 39 b(The) 23 -b(parameter) p Fo 23 w(it) m(yp) s(e) g(=) f(0) p Fs -24 w(indicates) f(that) p 150 5149 1200 4 v Fl 199 5217 -a(1) p Fj 275 5249 a(W) -6 b(e) 19 b(are) i(curren) n(tly) e(w) n -(orking) i(on) f(reducing) g(the) g(memory) e(requiremen) n(ts) h(for) i -(the) f(selected) g(eigensystem) g(problem\(see) 275 -5340 y(section) 26 b(7) g(Bug) g(1) g(\).) p 90 rotate -dyy eop -%%Page: 16 17 -16 16 bop Fs 150 -116 a(16) 3256 b(P) m(eIGS) p Fo 150 -299 a(PDSPGV) p Fs 33 w(or) p Fo 33 w(PDSPGVX) p Fs 32 -w(is) 33 b(to) h(b) s(e) e(called,) p Fo 33 w(it) m(yp) s(e) p -Fs 34 w(=) h(1) h(indicates) e(that) p Fo 34 w(PDSPEV) p -Fs 31 w(or) p Fo 34 w(PDSPEVX) p Fs 150 408 a(is) d(to) j(b) s(e) d -(called,) h(and) p Fo 30 w(it) m(yp) s(e) p Fs 31 w(=) g(2) h -(indicates) e(that) p Fo 31 w(PDSPTRI) p Fs 30 w(is) g(to) i(b) s(e) f -(called.) 275 547 y(The) 23 b(eigen) m(v) -5 b(alues) 24 -b(are) g(returned) f(in) f(an) i(arra) m(y) p Fo 25 w(ev) -5 -b(al) p Fs 24 w(on) 24 b(all) f(the) h(participating) e(pro) s(cessors) -h(\(those) i(in) p Fo 150 657 a(mapA) p Fs 30 w(or) p -Fo 31 w(mapZ) p Fs(\)) 30 b(with) g(the) h(eigen) m(v) m(ectors) i -(returned) d(using) f(a) j(one-dimensional) c(arra) m(y) k(in) d(the) j -(same) 150 767 y(manner) f(as) h(the) g(input) e(matrices) i(except) g -(that) h(it) e(is) g(not) h(in) e(a) j(symmetric) e(format.) 45 -b(It) 32 b(is) f(imp) s(ortan) m(t) 150 876 y(to) f(note) h(that) p -Fo 30 w(mapZ) p Fs 28 w(on) f(exit) f(from) h(the) f(v) -5 -b(arious) 29 b(P) m(eIGS) h(routines) e(will) f(generally) i(b) s(e) g -(di\013eren) m(t) g(than) 150 986 y(it) h(w) m(as) h(on) f(en) m(try) h -(\(i.e.,) g(the) f(output) g(arra) m(y) h(will) d(b) s(e) h(a) i(p) s -(erm) m(utation) f(of) g(the) h(input) d(arra) m(y\).) p -Fk 772 1119 a(integer) 46 b(isize,) g(rsize,) g(ptrsize,) f(itype,) h -(info) 772 1222 y(integer) g(iscratch\(n\)) 772 1326 -y(integer) g(iscrat\(*\)) 772 1430 y(integer) g(mapA\(*\),) f -(mapZ\(*\)) 772 1534 y(double) h(precision) f(matrixA\(*\),) g -(matrixZ\(*\),) g(eval\(*\)) 772 1638 y(double) h(precision) f -(dblptr\(*\)) 390 1741 y(c) 390 1845 y(c) i(see) g(note) g(on) g -(portability) 390 1949 y(c) 772 2053 y(itype) f(=) i(1) 772 -2156 y(call) e(memreq\() g(itype,) g(n,) i(mapA,) e(mapB,) g(mapZ,) h -(isize,) f(rsize,) 629 2260 y($) 333 b(ptr_size,) 46 -b(iscratch\)) 390 2364 y(c) 390 2468 y(c) h(make) g(sure) g(enough) f -(memory) g(was) h(allocated) e(for) i(the) g(scratch) f(space;) 390 -2572 y(c) h(at) h(least) e(as) h(much) g(as) g(requested) e(in) i -(isize,) g(rsize,) f(and) h(ptr_size) 390 2675 y(c) 772 -2779 y(call) f(pdspev\() g(n,) h(matrixA,) f(mapA,) g(matrixZ,) g -(mapZ,) g(eval,) h(iscrat,) 676 2883 y(1) 143 b(isize,) 46 -b(dblptr,) g(ptr_size,) f(scratch,) h(rsize,) g(info) h(\)) 390 -2987 y(c) 390 3090 y(c) 390 3194 y(c) p Fs 275 3333 a(Here's) e(an) g -(example) f(of) h(ho) m(w) p Fo 45 w(PDSPGV) p Fs 44 -w(can) h(b) s(e) e(called) g(in) f(C.) i(Assume) f(that) p -Fo 46 w(mapA[0:n-1]) p Fs(,) p Fo 150 3443 a(mapB[0:n-1]) p -Fs 31 w(and) p Fo 30 w(mapZ[0:n-1]) p Fs 31 w(ha) m(v) m(e) 32 -b(b) s(een) d(allo) s(cated) i(and) f(assigned) f(v) -5 -b(alues.) p Fk 772 3680 a(int) 47 b(itype,) f(indx,) g(info;) 772 -3783 y(int) h(n,) g(isize,) f(rsize,) g(ptr_size;) 772 -3887 y(int) h(*mapA,) f(*mapZ,) g(*mapB;) 772 3991 y(int) h(*iscratch;) -772 4198 y(double) f(**matrixA,) f(**matrixB,) g(**matrixZ;) 772 -4302 y(double) h(*iptr,) g(*scratch;) 772 4510 y(extern) g(void) h -(memreq_\(\),) e(pdspgv\(\);) 390 4717 y(...) 772 4821 -y(/*) 867 4925 y(input) i(matrixA,) e(matrixB,) h(matrixZ) g(in) h(the) -g(manner) f(cited) 867 5029 y(in) h(the) g(C) h(input) e(section) 772 -5132 y(*/) 390 5236 y(...) p 90 rotate dyy eop -%%Page: 17 18 -17 17 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(17) p Fk 390 403 a(/*) 772 506 y(allocate) 45 -b(scratch) h(space) h(for) f(the) h(memory) f(routine) 390 -610 y(*/) 533 818 y(if) h(\(\(itemp) f(=) i(\(int) e(*\)) h(malloc\() f -(n) i(*) f(sizeof\(int\)\)\)) d(==) k(NULL) e(\)) i({) 772 -922 y(fprintf\(stderr,) 43 b(") 48 b(ERROR) e(in) h(memory) g -(allocation,) 1106 1025 y(not) g(enough) f(memory) g(for) h(integer) f -(scratch) g(space) g(for) h(memreq) f(\\n"\);) 724 1129 -y(exit\(-1\);) 772 1233 y(}) 390 1544 y(/*) 533 1648 -y(itype) h(=) g(0) g(specifies) f(memory) g(for) h(the) g(general) e -(symmetric) h(eigensystem) e(problem) 390 1752 y(*/) 533 -1959 y(itype) j(=) g(0;) 533 2063 y(memreq_) f(\(&itype,) g(&n,) g -(mapA,) h(mapB,) f(mapZ,) h(&isize,) e(&rsize,) h(&ptr_size,) f -(itemp\);) 533 2167 y(free\(itemp\);) 533 2374 y(if) i(\() h -(\(iscratch) d(=) j(\(int) e(*\)) h(malloc\() f(isize) h(*) g -(sizeof\(int\)\)\)) d(==) j(NULL) g(\){) 676 2478 y(fprintf\(stderr,) d -(") j(ERROR) g(in) g(memory) f(allocation,) 1058 2582 -y(not) h(enough) f(memory) g(for) h(integer) f(scratch) g(space) g -(\\n"\);) 676 2686 y(exit\(-1\);) 533 2790 y(}) 533 3101 -y(if) h(\() h(\(scratch) d(=) j(\(double) e(*\)) h(malloc\() f(rsize) g -(*) h(sizeof\(double\)\)\)) d(==) j(NULL) g(\){) 676 -3205 y(fprintf\(stderr,) d(") j(ERROR) g(in) g(memory) f(allocation,) -1058 3308 y(not) h(enough) f(memory) g(for) h(double) f(scratch) g -(space) g(\\n"\);) 676 3412 y(exit\(-1\);) 533 3516 y(}) 485 -3724 y(if) i(\() f(\(iptr) f(=) i(\(double) e(**\)) h(malloc\() e -(ptr_size) h(*) h(sizeof\(double) e(*\)\)\)) h(==) h(NULL) g(\){) 676 -3827 y(fprintf\(stderr,) d(") j(ERROR) g(in) g(memory) f(allocation,) -1058 3931 y(not) h(enough) f(memory) g(for) h(pointer) f(scratch) g -(space) g(\\n"\);) 581 4035 y(exit\(-1\);) 485 4139 y(}) 390 -4346 y(/*) 485 4450 y(ifact) h(=) g(1) h(specifies) d(that) i(matrix) f -(B) h(contains) f(B) h(and) g(should) f(be) h(Choleski) f(factored) 390 -4554 y(*/) 581 4658 y(ifact) g(=) i(1;) 581 4761 y(pdspgv) e(\(&ifact,) -g(&n,) g(matrixA,) g(mapA,) g(matrixB,) g(mapB,) g(matrixZ,) g(mapZ,) g -(eval,) 1249 4865 y(iscratch,) f(&isize,) h(iptr,) h(&ptr_size) e -(,scratch,) g(&rsize,) h(&info\);) 390 5073 y(...) p -90 rotate dyy eop -%%Page: 18 19 -18 18 bop Fs 150 -116 a(18) 3256 b(P) m(eIGS) p Fr 150 -299 a(4.2) 68 b(PDSPEV:) 45 b(Real) h(Symmetric) f(Eigensystem) i(Solv) -l(er) p Fo 275 505 a(PDSPEV) p Fs 34 w(solv) m(es) 35 -b(the) h(standard) e(real) h(symmetric) g(eigensystem) g(problem:) 49 -b(Giv) m(en) 35 b(a) h(real) f(sym-) 150 615 y(metric) 30 -b(matrix) p Fo 30 w(A) p Fs(,) g(\014nd) f(all) g(its) h(eigen-pairs) f -(\() p Fn(\025;) p Fo 15 w(x) p Fs(\)) j(suc) m(h) e(that) p -Fo 31 w(Ax) p Fs 25 w(=) p Fn 25 w(\025) p Fo(x) p Fs -30 w(.) 275 762 y(In) f(F) -8 b(ortran) 31 b(77) g(the) g(calling) e -(sequences) i(for) f(PDSPEV) g(and) f(PDSPEVX) i(are:) p -Fk 772 905 a(subroutine) 45 b(pdspev\() h(n,) h(vecA,) f(mapA,) h -(vecZ,) f(mapZ,) g(eval,) h(iscratch,) e(iscsize,) 629 -1008 y($) 1002 b(dblptr,) 45 b(ibuffsize,) g(scratch,) h(ssize,) g -(info\)) 724 1216 y(integer) 285 b(n,) 47 b(mapA,) f(mapZ,) g -(iscratch,) g(iscsize,) f(ibuffsize,) g(ssize,) h(info) 724 -1423 y(double) g(precision) 93 b(eval\(*\),) 46 b(scratch\(*\),) e -(vecA\(*\),) i(vecZ\(*\),) g(dblptr\(*\)) 390 1527 y(c) 390 -1631 y(c) h(The) g(input) g(arguments) e(are) i(the) g(same) f(as) i -(in) f(the) g(C) g(code) 390 1735 y(c) g(pdspev) g(except) f(that) g -(one) h(changes) f(the) h(arguments) e(of) i(type) 390 -1839 y(c) 334 b("1-D) 46 b(array) h(of) g(pointers) f(to) h -(DoublePrecision",) c(i.e.,) 390 1942 y(c) k(vecA,) g(vecZ) f(and) h -(dblptr,) f(to) h(type) 390 2046 y(c) g("1-D) g(array) f(of) i(double) e -(precision) f(numbers") h(and) g(store) h(the) g(data) f(in) 390 -2150 y(c) 334 b(these) 46 b(arrays) g(using) h(the) g(packed) f -(storage) f(format) i(described) e(previously.) 390 2254 -y(c) 334 b(Also,) 46 b(when) h(calling) f(from) g(fortran) g(use) h -(FMEMREQ,) f(rather) g(than) g(memreq_,) 390 2357 y(c) 334 -b(to) 47 b(get) g(the) g(required) e(size) i(of) g(workspace) e -(arrays.) 390 2461 y(c) 334 b(Finally,) 45 b(the) i(C) h(code) e -(describes) g(arrays) g(of) h(length) f(n) h(with) g(indices) 390 -2565 y(c) 334 b(of) 47 b(0) g(to) h(n-1,) e(for) h(fortran) f(usage) g -(the) h(indices) f(should) g(be) h(1) h(to) f(n.) 390 -2669 y(c) 772 2811 y(subroutine) e(pdspevx\() g(ivector,) h(irange,) g -(n,) h(vecA,) f(mapA,) 629 2915 y($) 143 b(lb,) 46 b(ub,) h(ilb,) g -(iub,) g(abstol,) 629 3019 y($) 143 b(meigval,) 45 b(vecZ,) h(mapZ,) h -(eval,) f(iscratch,) f(iscsize,) 629 3122 y($) 143 b(dblptr,) 45 -b(ibuffsize,) g(scratch,) h(ssize,) g(info\)) 724 3330 -y(integer) 285 b(ivector,) 45 b(irange,) h(n,) h(mapA,) f(ilb,) h(iub,) -g(meigval,) 629 3434 y($) 668 b(mapZ,) 46 b(iscratch,) f(iscsize,) h -(ibuffsize,) 629 3537 y($) 668 b(ssize,) 46 b(info) 724 -3745 y(double) g(precision) 427 b(lb,) 47 b(ub,) g(abstol,) f -(eval\(*\),) f(scratch\(*\)) 629 3849 y($) 1240 b(vecA\(*\),) 46 -b(vecZ\(*\),) f(dblptr\(*\)) 390 4056 y(c) 390 4160 y(c) i(The) g -(input) g(arguments) e(are) i(the) g(same) f(as) i(in) f(the) g(C) g -(code) 390 4264 y(c) g(pdspevx) f(except) g(that) h(one) g(changes) f -(the) h(arguments) e(of) i(type) 390 4368 y(c) 334 b("1-D) 46 -b(array) h(of) g(pointers) f(to) h(DoublePrecision",) c(i.e.,) 390 -4471 y(c) k(vecA,) g(vecZ) f(and) h(dblptr,) f(to) h(type) 390 -4575 y(c) g("1-D) g(array) f(of) i(double) e(precision) f(numbers") h -(and) g(store) h(the) g(data) f(in) 390 4679 y(c) 334 -b(these) 46 b(arrays) g(using) h(the) g(packed) f(storage) f(format) i -(described) e(previously.) 390 4783 y(c) 334 b(Also,) 46 -b(when) h(calling) f(from) g(fortran) g(use) h(FMEMREQ,) f(rather) g -(than) g(memreq_,) 390 4887 y(c) 334 b(to) 47 b(get) g(the) g(required) -e(size) i(of) g(workspace) e(arrays.) 390 4990 y(c) 334 -b(Finally,) 45 b(the) i(C) h(code) e(describes) g(arrays) g(of) h -(length) f(n) h(with) g(indices) 390 5094 y(c) 334 b(of) 47 -b(0) g(to) h(n-1,) e(for) h(fortran) f(usage) g(the) h(indices) f -(should) g(be) h(1) h(to) f(n.) 390 5198 y(c) 772 5340 -y(subroutine) e(pdspevx\() g(ivector,) h(irange,) g(n,) h(vecA,) f -(mapA,) p 90 rotate dyy eop -%%Page: 19 20 -19 19 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(19) p Fk 629 299 a($) 143 b(lb,) 46 -b(ub,) h(ilb,) g(iub,) g(abstol,) 629 403 y($) 143 b(meigval,) 45 -b(vecZ,) h(mapZ,) h(eval,) f(iscratch,) f(iscsize,) 629 -506 y($) 143 b(dblptr,) 45 b(ibuffsize,) g(scratch,) h(ssize,) g -(info\)) 724 714 y(integer) 285 b(ivector,) 45 b(irange,) h(n,) h -(mapA,) f(ilb,) h(iub,) g(meigval,) 629 818 y($) 668 -b(mapZ,) 46 b(iscratch,) f(iscsize,) h(ibuffsize,) 629 -922 y($) 668 b(ssize,) 46 b(info) 724 1129 y(double) g(precision) 427 -b(lb,) 47 b(ub,) g(abstol,) f(eval\(*\),) f(scratch\(*\)) 629 -1233 y($) 1240 b(vecA\(*\),) 46 b(vecZ\(*\),) f(dblptr\(*\)) 390 -1440 y(c) 390 1544 y(c) i(The) g(input) g(arguments) e(are) i(the) g -(same) f(as) i(in) f(the) g(C) g(code) 390 1648 y(c) g(pdspevx) f -(except) g(that) h(one) g(changes) f(the) h(arguments) e(of) i(type) 390 -1752 y(c) p 90 rotate dyy eop -%%Page: 20 21 -20 20 bop Fs 150 -116 a(20) 3256 b(P) m(eIGS) 275 299 -y(The) 29 b(calling) g(sequence) i(for) f(PDSPEV) g(in) f(C) h(is:) p -Fk 390 462 a(void) 47 b(pdspev\(n,) e(vecA,) h(mapA,) h(vecZ,) f(mapZ,) -g(eval,) h(iscratch,) e(iscsize,) 963 566 y(dblptr,) h(ibuffsize,) f -(scratch,) g(ssize,) h(info\)) 629 774 y(Integer) 570 -b(*n,) 47 b(*mapA,) f(*mapZ,) h(*iscratch,) e(*iscsize,) 1535 -878 y(*ibuffsize,) g(*ssize,) h(*info;) 629 981 y(DoublePrecision) 139 -b(**vecA,) 46 b(**vecZ,) f(*eval,) h(**dblptr,) g(*scratch;) 390 -1189 y(/*) 438 1396 y(*) 95 b(Our) 47 b(parallel) e(version) h(of) h -(LAPACK's) f(dspev.) 438 1708 y(*) 95 b(Purpose) 438 -1812 y(*) g(=======) 438 2019 y(*) g(pdspev) 46 b(computes) g(all) g -(of) i(the) f(eigenvalues) d(and) j(eigenvectors) e(of) i(a) 438 -2123 y(*) 95 b(real) 47 b(symmetric) e(eigenproblem,) f(of) j(the) g -(form) 438 2330 y(*) 95 b(A*x=\(lambda\)) 44 b(*) k(x.) 438 -2538 y(*) 95 b(Here) 47 b(A) g(is) g(assumed) f(to) h(be) g(symmetric.) -438 2642 y(*) 95 b(A) 47 b(uses) g(packed) f(storage.) 438 -2849 y(*) 95 b(Arguments) 438 2953 y(*) g(=========) 438 -3161 y(*) 47 b(The) g(current) f(code) h(assumes) e(mapA) i(and) g -(mapZ) g(each) f(contain) 438 3264 y(*) h(exactly) f(the) h(same) g -(set) f(of) i(processor) d(id's,) h(though) g(not) h(necessarily) 438 -3368 y(*) g(in) g(the) g(same) g(order.) 438 3576 y(*) g(All) g -(arguments) e(are) i(POINTERS) f(to) h(date) g(of) g(the) g(specified) e -(type) i(unless) 438 3680 y(*) g(otherwise) e(mentioned.) 93 -b(In) 47 b(particular,) e(INTEGER) h(=) h(\(Integer) f(*\)) h(and) 438 -3783 y(*) g(DOUBLE) f(PRECISION) g(=) h(\(DoublePrecision) c(*\)) 438 -4095 y(*) k(In) g(the) g(following) f(let:) 438 4198 -y(*) 190 b(n) 286 b(=) 48 b(dimension) d(of) i(matrix) f(A) 438 -4302 y(*) 190 b(me) 238 b(=) 48 b(this) f(processors) e(id) i(\(=) g -(mxmynd_\(\)\)) 438 4406 y(*) 190 b(nprocs) 46 b(=) i(number) e(of) h -(allocated) e(processors) g(\() j(=) f(mxnprc_\(\)\)) 438 -4510 y(*) 190 b(nvecsA) 46 b(=) i(number) e(of) h(entries) f(in) h -(mapA) g(equal) f(to) h(me) 438 4614 y(*) 620 b(\(=) 47 -b(count_list\() e(me,) i(mapA,) f(n) i(\)\)) 438 4717 -y(*) 190 b(nvecsZ) 46 b(=) i(number) e(of) h(entries) f(in) h(mapZ) g -(equal) f(to) h(me) 438 4821 y(*) 620 b(\(=) 47 b(count_list\() e(me,) i -(mapZ,) f(n) i(\)\)) 438 5029 y(*----------------------) o(----) o -(----) o(---) o(----) o(----) o(---) o(----) o(----) o(---) o(----) o -(----) o(--) 438 5236 y(*) 95 b(n) 334 b(\(input\)) 46 -b(INTEGER) 438 5340 y(*) 477 b(The) 47 b(number) f(of) h(rows) g(and) f -(columns) g(of) h(the) g(matrices) f(A) h(and) g(B.) p -90 rotate dyy eop -%%Page: 21 22 -21 21 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(21) p Fk 438 299 a(*) 477 b(N) 47 -b(>=) g(0.) 438 506 y(*) 95 b(vecA) 190 b(\(input/workspace\)) 43 -b(array) j(of) h(pointers) f(to) h(DoublePrecision) 438 -610 y(*) 1336 b(=) 47 b(\(DoublePrecision) d(**\)) j(dimension) e(\() i -(nvecsA) f(\)) 438 714 y(*) 477 b(On) 47 b(entry,) f(vecA[i],) g(i) h -(=) g(0) h(to) f(nvecsA-1,) e(points) h(to) i(an) 438 -818 y(*) 477 b(array) 46 b(containing) f(the) i(lower) f(triangular) f -(part) i(of) g(the) g(i-th) 438 922 y(*) 477 b(column) 46 -b(of) h(A) g(which) g(is) g(owned) f(by) i(this) e(processor.) 93 -b(The) 438 1025 y(*) 477 b(columns) 46 b(of) h(A) g(owned) g(by) g -(this) f(processer) g(are) h(determined) e(by) i(mapA) 438 -1129 y(*) 477 b(\(See) 46 b(below\).) 438 1337 y(*) 477 -b(On) 47 b(exit,) f(the) h(contents) f(of) h(matrixA) f(are) h -(destroyed.) 438 1544 y(*) 95 b(mapA) 190 b(\(input\)) 46 -b(INTEGER) f(array,) h(dimension) g(\(N\)) 438 1648 y(*) 477 -b(mapA\(i\)) 46 b(=) h(the) g(id) g(of) g(the) g(processor) e(which) i -(owns) f(column) h(i) 438 1752 y(*) 954 b(of) 47 b(the) g(A) h(matrix,) -d(i) j(=) f(0) h(to) f(n-1.) 438 1959 y(*) 95 b(vecZ) 190 -b(\(output\)) 45 b(array) i(of) g(pointers) e(to) j(DoublePrecision) 43 -b(\(DoublePreci-) 390 2063 y(sion) k(**\)) 438 2167 y(*) 906 -b(dimension) 46 b(\() h(nvecsZ) f(\)) 438 2271 y(*) 477 -b(On) 47 b(entry,) f(vecZ[i],) g(i) h(=) g(0) h(to) f(nvecsZ-1,) e -(should) h(point) h(to) g(an) 438 2374 y(*) 477 b(array) 46 -b(of) h(length) f(n.) 438 2582 y(*) 477 b(On) 47 b(exit:) 438 -2790 y(*) 572 b(vecZ[i],) 46 b(i) h(=) h(0) f(to) g(nvecsZ-1,) f -(points) g(to) h(the) g(i-th) f(eigenvector) 438 2893 -y(*) 572 b(\(as) 47 b(determined) e(by) i(the) g(exit) g(values) f(in) h -(mapZ\)) f(owned) h(by) g(this) 438 2997 y(*) 572 b(processor.) 438 -3205 y(*) g(The) 47 b(eigenvectors) e(are) h(normalized) f(such) i -(that:) f(Z'*Z) h(=) h(I.) 438 3412 y(*) 95 b(mapZ) 190 -b(\(input/output\)) 44 b(INTEGER) h(array,) i(dimension) e(\(N\)) 438 -3516 y(*) 477 b(On) 47 b(entry:) 438 3724 y(*) 477 b(mapZ\(i\)) 46 -b(=) h(the) g(id) g(of) g(a) h(processor) d(which) h(has) h(room) g -(for) g(the) 438 3827 y(*) 954 b(i-th) 47 b(eigenvector,) d(i) k(=) f -(0) g(to) h(n-1.) 438 3931 y(*) 477 b(On) 47 b(exit:) 438 -4035 y(*) 572 b(mapZ\(i\)) 46 b(=) h(the) g(id) h(of) f(the) g -(processor) e(which) h(actually) g(owns) g(the) h(i-) 390 -4139 y(th) 438 4242 y(*) 1049 b(eigenvector,) 45 b(i) i(=) h(0) f(to) g -(n-1.) 438 4450 y(*) 95 b(eval) 190 b(\(output\)) 45 -b(DOUBLE) h(PRECISION) g(array,) g(dimension) f(\(N\)) 438 -4554 y(*) 477 b(If) 47 b(INFO) g(=) g(0,) g(the) g(eigenvalues) 93 -b(of) 47 b(the) g(matrix) 438 4658 y(*) 477 b(in) 47 -b(no) g(particular) e(order.) 438 4865 y(*) 95 b(iscratch) 45 -b(\(workspace\)) g(INTEGER) h(array,) g(dimension) 438 -4969 y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g -(utility) g(routine) g(memreq_) 438 5176 y(*) 95 b(iscsize) e -(\(input\)) 46 b(INTEGER) 438 5280 y(*) 524 b(The) 47 -b(number) f(of) i(usable) e(elements) f(in) i(array) g("iscratch".) p -90 rotate dyy eop -%%Page: 22 23 -22 22 bop Fs 150 -116 a(22) 3256 b(P) m(eIGS) p Fk 438 -299 a(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g -(utility) g(routine) g(memreq_) 438 506 y(*) 95 b(dblptr) 141 -b(\(workspace\)) 45 b(DoublePrecision) f(pointer) i(to) 438 -610 y(*) 524 b(DoublePrecision) 44 b(\(DoublePrecision) f(**\),) 438 -714 y(*) 524 b(dblprt[0]) 46 b(must) g(point) h(to) g(the) g(start) f -(of) h(an) h(array) e(consising) f(of) 438 818 y(*) 524 -b(pointers) 46 b(to) h(DoublePrecision) d(\(DoublePrecision) f(*\).) 438 -922 y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g -(utility) g(routine) g(memreq_) 438 1129 y(*) 95 b(ibuffsize\(input\)) -43 b(INTEGER) 438 1233 y(*) 524 b(The) 47 b(number) f(of) i(usable) e -(elements) f(in) i(array) g("dblptr".) 438 1337 y(*) 524 -b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g(utility) g -(routine) g(memreq_) 438 1544 y(*) 95 b(scratch) e(\(workspace\)) 45 -b(DOUBLE) h(PRECISION) g(array,) g(dimension) 438 1648 -y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g(utility) g -(routine) g(memreq_) 438 1856 y(*) 95 b(ssize) 189 b(\(input\)) 46 -b(INTEGER) 438 1959 y(*) 524 b(The) 47 b(number) f(of) i(usable) e -(elements) f(in) i(array) g("scratch".) 438 2063 y(*) 524 -b(Must) 47 b(be) g(>=) g(that) g(returned) f(in) h(utility) f(routine) f -(memreq_) 438 2271 y(*) 95 b(INFO) 190 b(\(output\)) 45 -b(INTEGER) 438 2478 y(*) 477 b(=) 47 b(0:) 95 b(successful) 45 -b(exit.) 438 2686 y(*) 477 b(-50) 47 b(<=) g(INFO) f(<) i(0,) f(the) g -(-INFOth) f(argument) f(had) i(an) g(illegal) f(value.) 438 -2893 y(*) 477 b(INFO) 46 b(=) i(-51,) 285 b(Input) 46 -b(data) h(which) f(must) h(be) g(the) g(same) g(on) g(all) 438 -2997 y(*) 1288 b(processors) 45 b(is) i(NOT) g(the) g(same) g(on) g -(all) g(processors) 438 3101 y(*) 1288 b(in) 47 b(mapZ.) 438 -3308 y(*) 477 b(=) 47 b(1,) 620 b(Error) 46 b(computing) g(the) h -(eigenvalues) d(of) k(the) 438 3412 y(*) 1288 b(tridiagonal) 45 -b(eigenproblem.) 92 b(In) 47 b(this) g(case) 438 3516 -y(*) 1288 b('pstebz_') 45 b(returned) h(a) h(non-zero) f(info,) g -(whose) 438 3620 y(*) 1288 b(value) 46 b(was) h(printed) f(to) h -(stderr.) 438 3827 y(*) 477 b(=) 47 b(2,) 620 b(Error) 46 -b(computing) g(the) h(eigenvectors) d(of) j(the) 438 -3931 y(*) 1288 b(tridiagonal) 45 b(eigenproblem.) 92 -b(In) 47 b(this) g(case) 438 4035 y(*) 1288 b('pstein') 46 -b(returned) f(a) j(non-zero) d(info,) i(whose) 438 4139 -y(*) 1288 b(value) 46 b(was) h(printed) f(to) h(stderr.) 438 -4346 y(*) 477 b(Any) 47 b(processor) e(with) i(a) g(negative) f(INFO) g -(stops) h(program) e(execution.) 438 4554 y(*) 477 b(If) 47 -b(-50) g(<=) g(INFO) g(<) g(0,) g(then) g(bad) g(data) f(was) h(passed) -f(to) i(this) e(routine) 438 4658 y(*) 1431 b(and) 47 -b(no) g(attempt) f(is) h(made) g(to) g(make) g(sure) f(that) 438 -4761 y(*) 1431 b(INFO) 47 b(is) g(the) g(same) g(on) g(all) g -(processors.) 438 4969 y(*) 477 b(All) 47 b(other) f(INFO) 285 -b(INFO) 47 b(should) f(be) h(the) g(same) g(on) g(all) g(processors) e -(in) 438 5073 y(*) 1431 b(mapA,Z.) 94 b(If) 47 b(this) g(routine) e -(calls) i(a) g(routine) 438 5176 y(*) 1431 b(which) 47 -b(returns) e(a) j(negative) d(info,) i(then) f(info) 438 -5280 y(*) 1431 b(may) 47 b(not) g(be) g(the) g(same) g(on) g(all) g -(processors.) p 90 rotate dyy eop -%%Page: 23 24 -23 23 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(23) p Fk 438 299 a(*) 1431 b(This,) 47 -b(however,) e(should) h(never) h(happen.) 438 403 y -(*----------------------) o(----) o(----) o(---) o(----) o(----) o(---) -o(----) o(----) o(---) o(----) o(----) o(---) o(---) 438 -610 y(*/) p 90 rotate dyy eop -%%Page: 24 25 -24 24 bop Fs 150 -116 a(24) 3256 b(P) m(eIGS) 275 299 -y(The) 29 b(calling) g(sequence) i(for) f(PDSPEVX) g(in) f(C) h(is:) p -Fk 390 462 a(void) 47 b(pdspevx) e(\() j(ivector,) d(irange,) h(n,) h -(vecA,) g(mapA,) f(lb,) h(ub,) g(ilb,) g(iub,) f(abstol,) 676 -566 y(meigval,) g(vecZ,) g(mapZ,) h(eval,) f(iscratch,) f(iscsize,) 676 -670 y(dblptr,) h(ibuffsize,) f(scratch,) h(ssize,) g(info\)) 629 -774 y(Integer) 475 b(*ivector,) 45 b(*irange,) h(*n,) h(*mapA,) f -(*ilb,) g(*iub,) h(*meigval;) 629 878 y(Integer) 475 -b(*mapZ,) 46 b(*iscratch,) f(*iscsize,) g(*ibuffsize,) g(*ssize,) h -(*info;) 629 981 y(DoublePrecision) 91 b(*lb,) 47 b(*ub,) f(*abstol,) g -(*eval,) g(*scratch;) 629 1085 y(DoublePrecision) 91 -b(**vecA,) 46 b(**vecZ,) g(**dblptr;) 390 1293 y(/*) 438 -1500 y(*) 95 b(Our) 47 b(parallel) e(version) h(of) h(LAPACK's) f -(dspevx.) 438 1812 y(*) 95 b(Purpose) 438 1915 y(*) g(=======) 438 -2123 y(*) g(pdspevx) 46 b(computes) f(some) i(or) g(all) g(of) g(the) g -(eigenvalues) e(and,) h(optionally,) 438 2227 y(*) 95 -b(eigenvectors) 44 b(of) k(a) f(real) g(symmetric) e(eigenproblem,) f -(of) j(the) g(form) 438 2434 y(*) 95 b(A*x=\(lambda\)) 44 -b(*) k(x.) 438 2642 y(*) 95 b(Here) 47 b(A) g(is) g(assumed) f(to) h -(be) g(symmetric.) 438 2746 y(*) 95 b(A) 47 b(uses) g(packed) f -(storage.) 438 2953 y(*) 95 b(Arguments) 438 3057 y(*) g(=========) 438 -3264 y(*) 47 b(The) g(current) f(code) h(assumes) e(mapA) i(and) g -(mapZ) g(each) f(contain) 438 3368 y(*) h(exactly) f(the) h(same) g -(set) f(of) i(processor) d(id's,) h(though) g(not) h(necessarily) 438 -3472 y(*) g(in) g(the) g(same) g(order.) 438 3680 y(*) g(All) g -(arguments) e(are) i(POINTERS) f(to) h(date) g(of) g(the) g(specified) e -(type) i(unless) 438 3783 y(*) g(otherwise) e(mentioned.) 93 -b(In) 47 b(particular,) e(INTEGER) h(=) h(\(Integer) f(*\)) h(and) 438 -3887 y(*) g(DOUBLE) f(PRECISION) g(=) h(\(DoublePrecision) c(*\)) 438 -4198 y(*) k(In) g(the) g(following) f(let:) 438 4302 -y(*) 190 b(n) 286 b(=) 48 b(dimension) d(of) i(matrix) f(A) 438 -4406 y(*) 190 b(me) 238 b(=) 48 b(this) f(processors) e(id) i(\(=) g -(mxmynd_\(\)\)) 438 4510 y(*) 190 b(nprocs) 46 b(=) i(number) e(of) h -(allocated) e(processors) g(\() j(=) f(mxnprc_\(\)\)) 438 -4614 y(*) 190 b(nvecsA) 46 b(=) i(number) e(of) h(entries) f(in) h -(mapA) g(equal) f(to) h(me) 438 4717 y(*) 620 b(\(=) 47 -b(count_list\() e(me,) i(mapA,) f(n) i(\)\)) 438 4821 -y(*) 190 b(nvecsZ) 46 b(=) i(number) e(of) h(entries) f(in) h(mapZ) g -(equal) f(to) h(me) 438 4925 y(*) 620 b(\(=) 47 b(count_list\() e(me,) i -(mapZ,) f(n) i(\)\)) 438 5132 y(*----------------------) o(----) o -(----) o(---) o(----) o(----) o(---) o(----) o(----) o(---) o(----) o -(----) o(--) 438 5236 y(*) 95 b(ivector) 46 b(\(input\)) g(INTEGER) 438 -5340 y(*) 477 b(=) 47 b(0:) 191 b(Compute) 45 b(eigenvalues) g(only;) p -90 rotate dyy eop -%%Page: 25 26 -25 25 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(25) p Fk 438 299 a(*) 477 b(=) 47 -b(1:) 191 b(Compute) 45 b(eigenvalues) g(and) i(eigenvectors.) 438 -506 y(*) 95 b(irange) f(\(input\)) 46 b(INTEGER) 438 -610 y(*) 477 b(=) 47 b(1:) 143 b(all) 47 b(eigenvalues) d(will) j(be) g -(found;) 438 714 y(*) 477 b(=) 47 b(2:) 143 b(all) 47 -b(eigenvalues) d(in) k(the) f(half-open) e(interval) g(\(lb,) i(ub]) 438 -818 y(*) 811 b(will) 46 b(be) i(found;) 438 922 y(*) 477 -b(=) 47 b(3:) 143 b(the) 47 b(ilb-th) f(through) g(iub-th) g -(eigenvalues) e(will) j(be) g(found.) 438 1233 y(*) 95 -b(n) 334 b(\(input\)) 46 b(INTEGER) 438 1337 y(*) 477 -b(The) 47 b(number) f(of) h(rows) g(and) f(columns) g(of) h(the) g -(matrices) f(A) h(and) g(B.) 438 1440 y(*) 477 b(N) 47 -b(>=) g(0.) 438 1648 y(*) 95 b(vecA) 190 b(\(input/workspace\)) 43 -b(array) j(of) h(pointers) f(to) h(DoublePrecision) d(\(Dou-) 390 -1752 y(blePrecision) g(**\)) 438 1856 y(*) 1336 b(dimension) 45 -b(\() j(nvecsA) e(\)) 438 1959 y(*) 477 b(On) 47 b(entry,) f(vecA[i],) g -(i) h(=) g(0) h(to) f(nvecsA-1,) e(points) h(to) i(an) 438 -2063 y(*) 477 b(array) 46 b(containing) f(the) i(lower) f(triangular) f -(part) i(of) g(the) g(i-th) 438 2167 y(*) 477 b(column) 46 -b(of) h(A) g(which) g(is) g(owned) f(by) i(this) e(processor.) 93 -b(The) 438 2271 y(*) 477 b(columns) 46 b(of) h(A) g(owned) g(by) g -(this) f(processer) g(are) h(determined) e(by) i(mapA) 438 -2374 y(*) 477 b(\(See) 46 b(below\).) 438 2582 y(*) 477 -b(On) 47 b(exit,) f(the) h(contents) f(of) h(matrixA) f(are) h -(destroyed.) 438 2790 y(*) 95 b(mapA) 190 b(\(input\)) 46 -b(INTEGER) f(array,) h(dimension) g(\(N\)) 438 2893 y(*) 477 -b(mapA\(i\)) 46 b(=) h(the) g(id) g(of) g(the) g(processor) e(which) i -(owns) f(column) h(i) 438 2997 y(*) 954 b(of) 47 b(the) g(A) h(matrix,) -d(i) j(=) f(0) h(to) f(n-1.) 438 3205 y(*) 95 b(lb) 286 -b(\(input\)) 46 b(DOUBLE) g(PRECISION) 438 3308 y(*) 477 -b(If) 47 b(IRANGE=2,) 93 b(the) 47 b(lower) f(bound) h(of) g(the) g -(interval) e(to) i(be) h(searched) 438 3412 y(*) 477 -b(for) 47 b(eigenvalues.) 92 b(Not) 47 b(referenced) e(if) i(IRANGE) f -(=) h(1) h(or) f(3,) g(but) 438 3516 y(*) 477 b(must) 46 -b(not) h(be) g(a) h(pointer) e(to) h(NULL.) 438 3724 -y(*) 95 b(ub) 286 b(\(input\)) 46 b(DOUBLE) g(PRECISION) 438 -3827 y(*) 477 b(If) 47 b(IRANGE=2,) 93 b(the) 47 b(upper) f(bound) h -(of) g(the) g(interval) e(to) i(be) h(searched) 438 3931 -y(*) 477 b(for) 47 b(eigenvalues.) 92 b(Not) 47 b(referenced) e(if) i -(IRANGE) f(=) h(1) h(or) f(3,) g(but) 438 4035 y(*) 477 -b(must) 46 b(not) h(be) g(a) h(pointer) e(to) h(NULL.) 438 -4242 y(*) 95 b(ilb) 238 b(\(input\)) 46 b(INTEGER) 438 -4346 y(*) 477 b(If) 47 b(IRANGE=3,) 93 b(the) 47 b(index) f(\(from) h -(smallest) e(to) i(largest\)) f(of) h(the) 438 4450 y(*) 477 -b(smallest) 45 b(eigenvalue) g(to) i(be) h(returned.) 93 -b(ilb) 47 b(>=) g(1.) 438 4554 y(*) 477 b(Not) 47 b(referenced) e(if) i -(IRANGE) f(=) h(1) h(or) f(2,) g(but) 438 4658 y(*) 477 -b(must) 46 b(not) h(be) g(a) h(pointer) e(to) h(NULL.) 438 -4865 y(*) 95 b(iub) 238 b(\(input\)) 46 b(INTEGER) 438 -4969 y(*) 477 b(If) 47 b(RANGE=3,) e(the) i(index) g(\(from) f -(smallest) g(to) h(largest\)) e(of) j(the) 438 5073 y(*) 477 -b(largest) 46 b(eigenvalue) f(to) i(be) g(returned.) 93 -b(min\(ilb,N\)) 45 b(<=) i(iub) g(<=) g(N.) 438 5176 -y(*) 477 b(Not) 47 b(referenced) e(if) i(IRANGE) f(=) h(1) h(or) f(2,) g -(but) 438 5280 y(*) 477 b(must) 46 b(not) h(be) g(a) h(pointer) e(to) h -(NULL.) p 90 rotate dyy eop -%%Page: 26 27 -26 26 bop Fs 150 -116 a(26) 3256 b(P) m(eIGS) p Fk 438 -403 a(*) 95 b(abstol) f(\(input\)) 46 b(DOUBLE) g(PRECISION) 438 -506 y(*) 477 b(The) 47 b(absolute) e(error) i(tolerance) e(for) i(the) g -(eigenvalues.) 438 610 y(*) 477 b(An) 47 b(approximate) e(eigenvalue) g -(is) i(accepted) e(as) j(converged) 438 714 y(*) 477 -b(when) 46 b(it) i(is) f(determined) e(to) i(lie) g(in) g(an) g -(interval) f([a,b]) 438 818 y(*) 477 b(of) 47 b(width) f(less) h(than) g -(or) g(equal) f(to) 438 1025 y(*) 859 b(ABSTOL) 46 b(+) h(EPS) g(*) 143 -b(max\() 47 b(|a|,|b|) e(\)) j(,) 438 1233 y(*) 477 b(where) 46 -b(EPS) h(is) g(the) g(machine) f(precision.) 93 b(If) 47 -b(ABSTOL) f(is) h(less) g(than) 438 1337 y(*) 477 b(or) 47 -b(equal) f(to) h(zero,) g(then) 94 b(EPS*|T|) g(will) 46 -b(be) i(used) e(in) h(its) g(place,) 438 1440 y(*) 477 -b(where) 46 b(|T|) h(is) g(the) g(1-norm) f(of) h(the) g(tridiagonal) e -(matrix) h(obtained) 438 1544 y(*) 477 b(by) 47 b(reducing) e(matrix) i -(A) g(to) g(tridiagonal) e(form.) 438 1752 y(*) 477 b(See) 47 -b("Computing) e(Small) h(Singular) g(Values) g(of) h(Bidiagonal) e -(Matrices) 438 1856 y(*) 477 b(with) 46 b(Guaranteed) f(High) i -(Relative) f(Accuracy,") f(by) i(Demmel) f(and) 438 1959 -y(*) 477 b(Kahan,) 46 b(LAPACK) g(Working) g(Note) g(#3.) 438 -2167 y(*) 95 b(meigval) 46 b(\(output\)) f(INTEGER) 438 -2271 y(*) 477 b(The) 47 b(total) f(number) g(of) h(eigenvalues) e -(found.) 94 b(0) 47 b(<=) g(meigval) f(<=) h(N.) 438 -2374 y(*) 477 b(If) 47 b(IRANGE) f(=) h(1,) 143 b(M) 48 -b(=) f(N,) g(and) g(if) g(RANGE) g(=) g(3,) 143 b(M) 47 -b(=) h(IUB-ILB+1.) 438 2582 y(*) 95 b(vecZ) 190 b(\(output\)) 45 -b(array) i(of) g(pointers) e(to) j(DoublePrecision) 43 -b(\(DoublePreci-) 390 2686 y(sion) k(**\)) 438 2790 y(*) 906 -b(dimension) 46 b(\() h(nvecsZ) f(\)) 438 2893 y(*) 477 -b(On) 47 b(entry,) f(vecZ[i],) g(i) h(=) g(0) h(to) f(nvecsZ-1,) e -(should) h(point) h(to) g(an) 438 2997 y(*) 477 b(array) 46 -b(of) h(length) f(n.) 438 3205 y(*) 477 b(On) 47 b(exit:) 438 -3412 y(*) 572 b(vecZ[i],) 46 b(i) h(=) h(0) f(to) g(nvecsZ-1,) f -(points) g(to) h(the) g(i-th) f(eigenvector) 438 3516 -y(*) 572 b(\(as) 47 b(determined) e(by) i(the) g(exit) g(values) f(in) h -(mapZ\)) f(owned) h(by) g(this) 438 3620 y(*) 572 b(processor.) 438 -3827 y(*) g(The) 47 b(eigenvectors) e(are) h(normalized) f(such) i -(that:) f(Z'*Z) h(=) h(I.) 438 4035 y(*) 95 b(mapZ) 190 -b(\(input/output\)) 44 b(INTEGER) h(array,) i(dimension) e(\(N\)) 438 -4139 y(*) 477 b(On) 47 b(entry:) 438 4346 y(*) 477 b(mapZ\(i\)) 46 -b(=) h(the) g(id) g(of) g(a) h(processor) d(which) h(has) h(room) g -(for) g(the) 438 4450 y(*) 954 b(i-th) 47 b(eigenvector,) d(i) k(=) f -(0) g(to) h(n-1) f(\(current) e(code) 438 4554 y(*) 954 -b(requires) 46 b(this) g(even) h(when) f(computing) g(only) g(some) h -(eigenvalues.) 438 4658 y(*) 477 b(On) 47 b(exit:) 438 -4761 y(*) 572 b(mapZ\(i\)) 46 b(=) h(the) g(id) h(of) f(the) g -(processor) e(which) h(actually) g(owns) g(the) h(i-) 390 -4865 y(th) 438 4969 y(*) 1049 b(eigenvector,) 45 b(i) i(=) h(0) f(to) g -(n-1.) 438 5176 y(*) 95 b(eval) 190 b(\(output\)) 45 -b(DOUBLE) h(PRECISION) g(array,) g(dimension) f(\(N\)) 438 -5280 y(*) 477 b(If) 47 b(INFO) g(=) g(0,) g(the) g(eigenvalues) 93 -b(of) 47 b(the) g(matrix) p 90 rotate dyy eop -%%Page: 27 28 -27 27 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(27) p Fk 438 299 a(*) 477 b(in) 47 -b(no) g(particular) e(order.) 438 506 y(*) 95 b(iscratch) 45 -b(\(workspace\)) g(INTEGER) h(array,) g(dimension) 438 -610 y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g -(utility) g(routine) g(memreq_) 438 818 y(*) 95 b(iscsize) e(\(input\)) -46 b(INTEGER) 438 922 y(*) 524 b(The) 47 b(number) f(of) i(usable) e -(elements) f(in) i(array) g("iscratch".) 438 1025 y(*) 524 -b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g(utility) g -(routine) g(memreq_) 438 1233 y(*) 95 b(dblptr) 141 b(\(workspace\)) 45 -b(DoublePrecision) f(pointer) i(to) 438 1337 y(*) 1097 -b(DoublePrecision) 44 b(\(DoublePrecision) f(**\),) 438 -1440 y(*) 524 b(dblprt[0]) 46 b(must) g(point) h(to) g(the) g(start) f -(of) h(an) h(array) e(consising) f(of) 438 1544 y(*) 524 -b(pointers) 46 b(to) h(DoublePrecision) d(\(DoublePrecision) f(*\).) 438 -1648 y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g -(utility) g(routine) g(memreq_) 438 1856 y(*) 95 b(ibuffsize\(input\)) -43 b(INTEGER) 438 1959 y(*) 524 b(The) 47 b(number) f(of) i(usable) e -(elements) f(in) i(array) g("dblptr".) 438 2063 y(*) 524 -b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g(utility) g -(routine) g(memreq_) 438 2271 y(*) 95 b(scratch) e(\(workspace\)) 45 -b(DOUBLE) h(PRECISION) g(array,) g(dimension) 438 2374 -y(*) 524 b(Must) 47 b(be) g(>=) g(that) g(returned) f(from) g(utility) g -(routine) g(memreq_) 438 2582 y(*) 95 b(ssize) 189 b(\(input\)) 46 -b(INTEGER) 438 2686 y(*) 524 b(The) 47 b(number) f(of) i(usable) e -(elements) f(in) i(array) g("scratch".) 438 2790 y(*) 524 -b(Must) 47 b(be) g(>=) g(that) g(returned) f(in) h(utility) f(routine) f -(memreq_) 438 2997 y(*) 95 b(INFO) 190 b(\(output\)) 45 -b(INTEGER) 438 3205 y(*) 477 b(=) 47 b(0:) 95 b(successful) 45 -b(exit.) 438 3412 y(*) 477 b(-50) 47 b(<=) g(INFO) f(<) i(0,) f(the) g -(-INFOth) f(argument) f(had) i(an) g(illegal) f(value.) 438 -3620 y(*) 477 b(INFO) 46 b(=) i(-51,) 285 b(Input) 46 -b(data) h(which) f(must) h(be) g(the) g(same) g(on) g(all) 438 -3724 y(*) 1288 b(processors) 45 b(is) i(NOT) g(the) g(same) g(on) g -(all) g(processors) 438 3827 y(*) 1288 b(in) 47 b(mapZ.) 438 -4035 y(*) 477 b(=) 47 b(1,) 620 b(Error) 46 b(computing) g(the) h -(eigenvalues) d(of) k(the) 438 4139 y(*) 1288 b(tridiagonal) 45 -b(eigenproblem.) 92 b(In) 47 b(this) g(case) 438 4242 -y(*) 1288 b('pstebz_') 45 b(returned) h(a) h(non-zero) f(info,) g -(whose) 438 4346 y(*) 1288 b(value) 46 b(was) h(printed) f(to) h -(stderr.) 438 4554 y(*) 477 b(=) 47 b(2,) 620 b(Error) 46 -b(computing) g(the) h(eigenvectors) d(of) j(the) 438 -4658 y(*) 1288 b(tridiagonal) 45 b(eigenproblem.) 92 -b(In) 47 b(this) g(case) 438 4761 y(*) 1288 b('pstein') 46 -b(returned) f(a) j(non-zero) d(info,) i(whose) 438 4865 -y(*) 1288 b(value) 46 b(was) h(printed) f(to) h(stderr.) 438 -5073 y(*) 477 b(Any) 47 b(processor) e(with) i(a) g(negative) f(INFO) g -(stops) h(program) e(execution.) 438 5280 y(*) 477 b(If) 47 -b(-50) g(<=) g(INFO) g(<) g(0,) g(then) g(bad) g(data) f(was) h(passed) -f(to) i(this) e(routine) p 90 rotate dyy eop -%%Page: 28 29 -28 28 bop Fs 150 -116 a(28) 3256 b(P) m(eIGS) p Fk 438 -299 a(*) 1431 b(and) 47 b(no) g(attempt) f(is) h(made) g(to) g(make) g -(sure) f(that) 438 403 y(*) 1431 b(INFO) 47 b(is) g(the) g(same) g(on) g -(all) g(processors.) 438 610 y(*) 477 b(All) 47 b(other) f(INFO) 285 -b(INFO) 47 b(should) f(be) h(the) g(same) g(on) g(all) g(processors) e -(in) 438 714 y(*) 1431 b(mapA,Z.) 94 b(If) 47 b(this) g(routine) e -(calls) i(a) g(routine) 438 818 y(*) 1431 b(which) 47 -b(returns) e(a) j(negative) d(info,) i(then) f(info) 438 -922 y(*) 1431 b(may) 47 b(not) g(be) g(the) g(same) g(on) g(all) g -(processors.) 438 1025 y(*) 1431 b(This,) 47 b(however,) e(should) h -(never) h(happen.) 438 1129 y(*----------------------) o(----) o(----) o -(---) o(----) o(----) o(---) o(----) o(----) o(---) o(----) o(----) o -(---) o(---) 438 1337 y(*/) p 90 rotate dyy eop -%%Page: 29 30 -29 29 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(29) p Fr 150 166 a(4.3) 68 b(PDSPGV) 44 -b(and) g(PDSPGVX:) g(Generalized) i(Symmetric) 389 299 -y(Eigensystem) h(Solv) l(er) p Fs 275 489 a(This) 26 -b(is) g(the) i(real) g(general) f(symmetric) h(eigensystem) f(problem:) -38 b(Giv) m(en) 28 b(a) g(real) g(symmetric) f(matrix) p -Fo 150 598 a(A) p Fs 33 w(and) 33 b(a) h(p) s(ositiv) m(e) f -(de\014nite) f(real) i(symmetric) f(matrix) p Fo 33 w(B) p -Fs(,) g(\014nd) f(all) h(its) g(eigen-pairs) f(\() p -Fn(\025;) p Fo 15 w(x) p Fs(\)) j(suc) m(h) e(that) p -Fo 150 708 a(Ax) p Fs 25 w(=) p Fn 25 w(\025) p Fo(Bx) p -Fs 30 w(.) 275 840 y(F) -8 b(or) 33 b(one) h(pro) s(cessor) e(w) m(e) i -(use) f(the) g(standard) f(algorithm) p Fm 32 w(\(c.f.) 50 -b(Wilkinson,) 32 b(J.) h(H.,) h(The) e(Algebraic) 150 -949 y(Eigen) m(v) -5 b(alue) 32 b(Problem,) f(page) i(337-339\)) p -Fs(.) 50 b(F) -8 b(or) 33 b(m) m(ulti-pro) s(cessors) e(w) m(e) h(p) s -(erform) f(the) i(reduction) e(to) i(the) 150 1059 y(standard) 23 -b(eigensystem) i(problem) e(b) m(y) h(computing) f(the) i(in) m(v) m -(erse) f(of) g(the) h(lo) m(w) m(er) f(triangular) f(matrix) g(from) 150 -1169 y(the) 34 b(Choleski) e(factorization,) k(and) d(then) g(p) s -(erform) g(matrix) g(conjugation) h(to) g(obtain) p Fo -33 w(L) p Fd 3226 1136 a(T) p Fo 3278 1169 a(AL) p Ff -3402 1136 a(\000) p Fd(T) p Fn 3506 1169 a(:) p Fo 34 -w(Cur-) 150 1278 y(ren) m(tly) -8 b(,) 27 b(the) d(m) m(ulti-pro) s -(cessor) h(reduction) f(algorithm) h(is) f(used) f(ev) m(en) i(when) e -(using) g(only) h(one) g(pro) s(cessor) p Fs(.) 275 1410 -y(In) 33 b(some) i(applications,) e(the) i(matrix) p -Fo 33 w(B) p Fs 34 w(ma) m(y) g(already) f(ha) m(v) m(e) h(b) s(een) f -(factored) h(and) e(the) i(in) m(v) m(erse) f(of) 150 -1520 y(the) f(c) m(holeski) g(factor) h(is) f(stored) g(in) p -Fo 32 w(B) p Fs(.) g(A) g(parameter) p Fo 34 w(ifact) h(=) f(0) p -Fs 34 w(is) f(used) h(as) g(an) g(input) f(to) p Fo 34 -w(p) s(dspgv) p Fs 31 w(to) 150 1629 y(skip) d(the) j(c) m(holeski) e -(factorization) i(\() f(for) f(serial) g(\)) h(and) g(its) f(in) m(v) m -(erse) h(computations) f(\() i(for) e(parallel) f(\).) 43 -b(A) 150 1739 y(v) -5 b(alue) p Fo 30 w(ifact) 31 b(=) f(1) p -Fs 31 w(is) f(used) h(to) h(sp) s(ecify) e(that) p Fo -31 w(B) p Fs 30 w(is) g(not) i(the) g(Choleski) d(factor) k(of) p -Fo 30 w(B) p Fs 30 w(or) f(its) e(in) m(v) m(erse.) 275 -1871 y(In) g(F) -8 b(ortran) 31 b(77) g(the) g(calling) e(sequences) i -(for) f(PDSPGV) g(and) g(PDSPGVX) h(are:) p Fk 581 1997 -a(subroutine) 45 b(pdspgv) h(\(ifact,) g(n,) h(matrixA,) f(mapA,) 1488 -2101 y(matrixB,) f(mapB,) i(matZ,) f(mapZ,) g(eval,) 1488 -2204 y(iscratch,) f(iscsize,) h(dblptr,) f(ibuffsz,) 1488 -2308 y(scratch,) g(rsize,) h(info\)) 581 2516 y(integer) 93 -b(ifact,) 47 b(n,) g(mapA\(*\),) e(mapB\(*\),) h(mapZ\(*\),) f -(iscratch\(*\),) g(iscsize,) 1201 2619 y(ibuffsz,) h(rsize,) g(info;) -581 2827 y(double) g(precision) 93 b(matrixA\(*\),) 45 -b(matrixB\(*\),) f(matZ\(*\),) i(eval\(*\),) g(scratch\(*\);) 581 -2931 y(double) g(precision) 93 b(dblptr\(*\)) 390 3138 -y(c) 47 b(The) g(input) g(arguments) e(are) i(the) g(same) f(as) i(in) f -(the) g(C) g(code) 390 3242 y(c) g(pdspgv) g(except) f(that) g(one) h -(changes) f(the) h(arguments) e(of) i(type) 390 3346 -y(c) 334 b("1-D) 46 b(array) h(of) g(pointers) f(to) h -(DoublePrecision",) c(i.e.,) 390 3450 y(c) k(vecA,) g(vecB,) f(vecZ) h -(and) g(dblptr,) f(to) h(type) 390 3553 y(c) g("1-D) g(array) f(of) i -(double) e(precision) f(numbers") h(and) g(store) h(the) g(data) f(in) -390 3657 y(c) 334 b(these) 46 b(arrays) g(using) h(the) g(packed) f -(storage) f(format) i(described) e(previously.) 390 3761 -y(c) 334 b(Also,) 46 b(when) h(calling) f(from) g(fortran) g(use) h -(FMEMREQ,) f(rather) g(than) g(memreq_,) 390 3865 y(c) 334 -b(to) 47 b(get) g(the) g(required) e(size) i(of) g(workspace) e -(arrays.) 390 3969 y(c) 334 b(Finally,) 45 b(the) i(C) h(code) e -(describes) g(arrays) g(of) h(length) f(n) h(with) g(indices) 390 -4072 y(c) 334 b(of) 47 b(0) g(to) h(n-1,) e(for) h(fortran) f(usage) g -(the) h(indices) f(should) g(be) h(1) h(to) f(n.) 390 -4176 y(c) 581 4302 y(subroutine) e(pdspgvx) h(\(ifact,) g(ivector,) f -(irange,) h(n,) h(matrixA,) f(mapA,) 1488 4406 y(matrixB,) f(mapB,) i -(matZ,) f(mapZ,) g(eval,) 1488 4510 y(iscratch,) f(iscsize,) h(dblptr,) -f(ibuffsz,) 1488 4614 y(scratch,) g(rsize,) h(info\)) 581 -4821 y(integer) 93 b(ifact,) 47 b(n,) g(mapA\(*\),) e(mapB\(*\),) h -(mapZ\(*\),) f(iscratch\(*\),) g(iscsize,) 1201 4925 -y(ibuffsz,) h(rsize,) g(info;) 581 5132 y(double) g(precision) 93 -b(matrixA\(*\),) 45 b(matrixB\(*\),) f(matZ\(*\),) i(eval\(*\),) g -(scratch\(*\);) 581 5236 y(double) g(precision) 93 b(dblptr\(*\)) p -90 rotate dyy eop -%%Page: 30 31 -30 30 bop Fs 150 -116 a(30) 3256 b(P) m(eIGS) p Fk 390 -299 a(c) 47 b(The) g(input) g(arguments) e(are) i(the) g(same) f(as) i -(in) f(the) g(C) g(code) 390 403 y(c) g(pdspgvx) f(except) g(that) h -(one) g(changes) f(the) h(arguments) e(of) i(type) 390 -506 y(c) 334 b("1-D) 46 b(array) h(of) g(pointers) f(to) h -(DoublePrecision",) c(i.e.,) 390 610 y(c) k(vecA,) g(vecB,) f(vecZ) h -(and) g(dblptr,) f(to) h(type) 390 714 y(c) g("1-D) g(array) f(of) i -(double) e(precision) f(numbers") h(and) g(store) h(the) g(data) f(in) -390 818 y(c) 334 b(these) 46 b(arrays) g(using) h(the) g(packed) f -(storage) f(format) i(described) e(previously.) 390 922 -y(c) 334 b(Also,) 46 b(when) h(calling) f(from) g(fortran) g(use) h -(FMEMREQ,) f(rather) g(than) g(memreq_,) 390 1025 y(c) 334 -b(to) 47 b(get) g(the) g(required) e(size) i(of) g(workspace) e -(arrays.) 390 1129 y(c) 334 b(Finally,) 45 b(the) i(C) h(code) e -(describes) g(arrays) g(of) h(length) f(n) h(with) g(indices) 390 -1233 y(c) 334 b(of) 47 b(0) g(to) h(n-1,) e(for) h(fortran) f(usage) g -(the) h(indices) f(should) g(be) h(1) h(to) f(n.) 390 -1337 y(c) p Fs 275 1473 a(In) 29 b(C) h(the) h(calling) e(sequence) h -(for) g(PDSPGV) h(is:) p Fk 390 1604 a(void) 47 b(pdspgv\() e(ifact,) i -(n,) g(vecA,) f(mapA,) g(vecB,) h(mapB,) f(vecZ,) h(mapZ,) 581 -1708 y(eval,) f(iscratch,) g(iscsize,) f(dblptr,) h(ibuffsize,) f -(scratch,) g(ssize,) i(info\)) 629 1812 y(Integer) 475 -b(*ifact,) 46 b(*n,) h(*mapA,) f(*mapB,) g(*mapZ,) g(*iscratch,) 1440 -1915 y(*iscsize,) f(*ibuffsize,) g(*ssize,) h(*info;) 629 -2019 y(DoublePrecision) 91 b(**vecA,) 46 b(**vecB,) g(**vecZ,) f -(*eval,) i(**dblptr,) e(*scratch;) 485 2227 y(/*) 533 -2434 y(*) 95 b(Our) 47 b(parallel) f(version) g(of) h(LAPACK's) e -(dspgv.) 533 2746 y(*) 95 b(Purpose) 533 2849 y(*) g(=======) 533 -3057 y(*) g(pdspgv) 46 b(computes) g(all) h(of) g(the) g(eigenvalues) e -(and) i(eigenvectors) d(of) j(a) 533 3161 y(*) 95 b(real) 47 -b(generalized) e(symmetric-definite) e(eigenproblem,) h(of) j(the) g -(form) 533 3368 y(*) 95 b(A*x=\(lambda\)*B*x.) 533 3576 -y(*) g(Here) 47 b(A) g(and) g(B) h(are) f(assumed) f(to) h(be) g -(symmetric) e(and) i(B) h(is) f(also) 533 3680 y(*) 95 -b(positive) 46 b(definite.) f(The) i(matrices) f(A) h(and) g(B) g(use) g -(packed) f(storage.) 533 3887 y(*) 95 b(Arguments) 533 -3991 y(*) g(=========) 533 4198 y(*) 48 b(NOTE:) e(The) h(current) f -(code) g(assumes) g(mapA,) h(mapB) f(and) h(mapZ) g(each) f(contain) 533 -4302 y(*) 334 b(exactly) 46 b(the) h(same) f(set) h(of) g(processor) f -(id's,) g(though) g(not) h(necessarily) 533 4406 y(*) 334 -b(in) 47 b(the) g(same) g(order.) 533 4614 y(*) h(All) f(arguments) e -(are) i(POINTERS) e(to) i(date) g(of) g(the) g(specified) e(type) i -(unless) 533 4717 y(*) h(otherwise) d(mentioned.) 93 -b(In) 47 b(particular,) e(INTEGER) g(=) j(\(Integer) d(*\)) j(and) 533 -4821 y(*) g(DOUBLE) e(PRECISION) f(=) i(\(DoublePrecision) d(*\)) 533 -5132 y(*) k(In) f(the) g(following) e(let:) 533 5236 -y(*) 191 b(n) 286 b(=) 47 b(dimension) f(of) h(matrices) e(A) j(and) f -(B) 533 5340 y(*) 191 b(me) 238 b(=) 47 b(this) g(processors) e(id) i -(\(=) g(mxmynd_\(\)\)) p 90 rotate dyy eop -%%Page: 31 32 -31 31 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(31) p Fk 533 299 a(*) 191 b(nprocs) 46 -b(=) h(number) f(of) i(allocated) d(processors) g(\() i(=) h -(mxnprc_\(\)\)) 533 403 y(*) 191 b(nvecsA) 46 b(=) h(number) f(of) i -(entries) d(in) j(mapA) e(equal) h(to) g(me) 533 506 -y(*) 620 b(\(=) 48 b(count_list\() c(me,) j(mapA,) g(n) g(\)\)) 533 -610 y(*) 620 b(number) 46 b(of) i(columns) d(of) j(A) f(this) g -(processor) e(has) 533 714 y(*) 191 b(nvecsB) 46 b(=) h(number) f(of) i -(entries) d(in) j(mapB) e(equal) h(to) g(me) 533 818 -y(*) 620 b(\(=) 48 b(count_list\() c(me,) j(mapB,) g(n) g(\)\)) 533 -922 y(*) 620 b(number) 46 b(of) i(vectors) d(this) i(processor) e(has) -533 1025 y(*) 191 b(nvecsZ) 46 b(=) h(number) f(of) i(entries) d(in) j -(mapZ) e(equal) h(to) g(me) 533 1129 y(*) 620 b(\(=) 48 -b(count_list\() c(me,) j(mapZ,) g(n) g(\)\)) 533 1337 -y(*------------------------) o(----) o(---) o(----) o(----) o(---) o -(----) o(----) o(---) o(----) o(----) o(---) o(-) 533 -1544 y(*) 95 b(ifact) 142 b(\(input\)) 46 b(INTEGER) 533 -1648 y(*) 477 b(Specifies) 45 b(whether) h(or) h(not) g(to) h(factor) e -(the) h(B) g(matrix.) 533 1752 y(*) 477 b(=) 48 b(0:) 95 -b(Don't) 46 b(factor) g(B,) h(vecB) g(is) g(already) f(the) h(L) g(in) g -(B) h(=) f(L*L'.) 533 1856 y(*) 764 b(\(for) 46 b(serial) g(\)) i(or) f -(L**\(-1\)) f(for) h(parallel) 533 1959 y(*) 764 b(which) 46 -b(was) h(computed) e(on) j(a) f(previous) f(call) g(to) h(pdspgv.) 533 -2167 y(*) 477 b(=) 48 b(1:) 95 b(Factor) 46 b(B) 533 -2374 y(*) 95 b(n) 334 b(\(input\)) 46 b(INTEGER) 533 -2478 y(*) 477 b(The) 47 b(number) f(of) h(rows) g(and) g(columns) f(of) -h(the) g(matrices) e(A) j(and) f(B.) 533 2582 y(*) 477 -b(N) 48 b(>=) f(0.) 533 2790 y(*) 95 b(vecA) 190 b(\(input/workspace\)) -43 b(array) k(of) g(pointers) e(to) j(DoublePrecision) 43 -b(\(Dou-) 390 2893 y(blePrecision) h(**\)) 533 2997 y(*) 1336 -b(dimension) 46 b(\() h(nvecsA) f(\)) 533 3101 y(*) 477 -b(On) 47 b(entry,) f(vecA[i],) g(i) h(=) h(0) f(to) h(nvecsA-1,) d -(points) h(to) h(an) 533 3205 y(*) 477 b(array) 47 b(containing) e(the) -h(lower) h(triangular) e(part) h(of) i(the) f(i-th) 533 -3308 y(*) 477 b(column) 46 b(of) h(A) h(which) e(is) h(owned) g(by) g -(this) g(processor.) 92 b(The) 533 3412 y(*) 477 b(columns) 46 -b(of) h(A) h(owned) e(by) h(this) g(processer) e(are) i(determined) e -(by) i(mapA) 533 3516 y(*) 477 b(\(See) 47 b(below\).) 533 -3724 y(*) 477 b(On) 47 b(exit,) g(the) g(contents) e(of) i(matrixA) f -(are) h(destroyed.) 533 3931 y(*) 95 b(mapA) 190 b(\(input\)) 46 -b(INTEGER) g(array,) g(dimension) f(\(N\)) 533 4035 y(*) 477 -b(mapA\(i\)) 46 b(=) h(the) g(id) h(of) f(the) g(processor) e(which) h -(owns) h(column) f(i) 533 4139 y(*) 954 b(of) 48 b(the) f(A) g(matrix,) -f(i) h(=) h(0) f(to) g(n-1.) 533 4346 y(*) 95 b(vecB) 190 -b(\(input/output\)) 44 b(array) i(of) i(pointers) d(to) i -(DoublePrecision) d(\(Dou-) 390 4450 y(blePrecision) g(**\)) 533 -4554 y(*) 1336 b(dimension) 46 b(\() h(nvecsB) f(\)) 533 -4658 y(*) 477 b(On) 47 b(entry,) f(vecB[i],) g(i) h(=) h(0) f(to) h -(nvecsB-1,) d(points) h(to) h(an) 533 4761 y(*) 477 b(array) 47 -b(containing) e(the) h(lower) h(triangular) e(part) h(of) i(the) f -(i-th) 533 4865 y(*) 477 b(column) 46 b(of) h(B) h(which) e(is) h -(owned) g(by) g(this) g(processor.) 92 b(The) 533 4969 -y(*) 477 b(columns) 46 b(of) h(B) h(owned) e(by) h(this) g(processer) e -(are) i(determined) e(by) i(mapB) 533 5073 y(*) 477 b(\(See) 47 -b(below\).) 533 5280 y(*) 477 b(On) 47 b(exit) p 90 rotate -dyy eop -%%Page: 32 33 -32 32 bop Fs 150 -116 a(32) 3256 b(P) m(eIGS) p Fk 533 -299 a(*) 573 b(Let) 47 b(L) g(be) g(the) g(triangular) e(factor) h(L) i -(from) e(the) h(Choleski) 533 403 y(*) 573 b(factorization) 44 -b(B) j(=) h(L*L',) e(then) 533 610 y(*) 573 b(if) 47 -b(\(nprocs) f(=) h(1\):) g(vecB) g(contains) 93 b(L,) 477 -b(same) 46 b(storage) g(as) h(B) 533 714 y(*) 573 b(else) 524 -b(:) 47 b(vecB) g(contains) e(\(L) i(inverse\),) f(same) g(storage) g -(as) h(B) 533 1025 y(*) 95 b(mapB) 190 b(\(input\)) 46 -b(INTEGER) g(array,) g(dimension) f(\(N\)) 533 1129 y(*) 477 -b(mapB\(i\)) 46 b(=) h(the) g(id) h(of) f(the) g(processor) e(which) h -(owns) h(column) f(i) 533 1233 y(*) 954 b(of) 48 b(the) f(B) g(matrix,) -f(i) h(=) h(0) f(to) g(n-1.) 533 1440 y(*) 95 b(vecZ) 190 -b(\(output\)) 46 b(array) g(of) h(pointers) f(to) h(DoublePrecision) d -(\(DoublePre-) 390 1544 y(cision) i(**\)) 533 1648 y(*) 907 -b(dimension) 45 b(\() i(nvecsZ) g(\)) 533 1752 y(*) 477 -b(On) 47 b(entry,) f(vecZ[i],) g(i) h(=) h(0) f(to) h(nvecsZ-1,) d -(should) h(point) g(to) h(an) 533 1856 y(*) 477 b(array) 47 -b(of) g(length) f(n.) 533 2063 y(*) 477 b(On) 47 b(exit:) 533 -2271 y(*) 573 b(vecZ[i],) 45 b(i) j(=) f(0) h(to) f(nvecsZ-1,) e -(points) h(to) h(the) g(i-th) g(eigenvector) 533 2374 -y(*) 573 b(\(as) 47 b(determined) e(by) i(the) g(exit) f(values) g(in) i -(mapZ\)) e(owned) g(by) h(this) 533 2478 y(*) 573 b(processor.) 533 -2686 y(*) g(The) 47 b(eigenvectors) d(are) j(normalized) e(such) i -(that:) f(Z'*B*Z) g(=) h(I.) 533 2893 y(*) 95 b(mapZ) 190 -b(\(input/output\)) 44 b(INTEGER) i(array,) g(dimension) f(\(N\)) 533 -2997 y(*) 477 b(On) 47 b(entry:) 533 3205 y(*) 477 b(mapZ\(i\)) 46 -b(=) h(the) g(id) h(of) f(a) g(processor) e(which) i(has) g(room) f -(for) h(the) 533 3308 y(*) 954 b(i-th) 47 b(eigenvector,) e(i) i(=) g -(0) h(to) f(n-1.) 533 3412 y(*) 477 b(On) 47 b(exit:) 533 -3516 y(*) 573 b(mapZ\(i\)) 45 b(=) j(the) f(id) g(of) g(the) g -(processor) e(which) i(actually) e(owns) i(the) g(i-) 390 -3620 y(th) 533 3724 y(*) 1050 b(eigenvector,) 44 b(i) k(=) f(0) h(to) f -(n-1.) 533 3931 y(*) 95 b(eval) 190 b(\(output\)) 46 -b(DOUBLE) g(PRECISION) f(array,) h(dimension) f(\(N\)) 533 -4035 y(*) 477 b(If) 47 b(INFO) g(=) g(0,) h(the) f(eigenvalues) 92 -b(of) 47 b(the) g(matrix) 533 4139 y(*) 477 b(in) 47 -b(no) h(particular) d(order.) 533 4346 y(*) 95 b(iscratch) 46 -b(\(workspace\)) f(INTEGER) g(array,) i(dimension) e(\(??\)) 533 -4554 y(*) 95 b(iscsize) f(\(input\)) 46 b(INTEGER) 533 -4658 y(*) 525 b(The) 47 b(number) f(of) h(usable) f(elements) g(in) h -(array) f("iscratch".) 533 4761 y(*) 525 b(Must) 47 b(be) g(>=) g(???.) -533 4969 y(*) 95 b(dblptr) 142 b(\(workspace\)) 45 b(DoublePrecision) e -(pointer) j(to) h(DoublePrecision) d(\(Dou-) 390 5073 -y(blePrecision) g(**\),) 533 5176 y(*) 525 b(dblprt[0]) 45 -b(must) i(point) f(to) h(the) g(start) g(of) g(an) g(array) f -(consising) g(of) 533 5280 y(*) 525 b(???) 47 b(pointers) e(to) j -(DoublePrecision.) p 90 rotate dyy eop -%%Page: 33 34 -33 33 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(33) p Fk 533 403 a(*) 95 b(ibuffsize\(input\)) 44 -b(INTEGER) 533 506 y(*) 525 b(The) 47 b(number) f(of) h(usable) f -(elements) g(in) h(array) f("dblptr".) 533 610 y(*) 525 -b(Must) 47 b(be) g(>=) g(???.) 533 818 y(*) 95 b(scratch) f -(\(workspace\)) 45 b(DOUBLE) h(PRECISION) f(array,) h(dimension) f -(\(??\)) 533 1025 y(*) 95 b(ssize) 190 b(\(input\)) 46 -b(INTEGER) 533 1129 y(*) 525 b(The) 47 b(number) f(of) h(usable) f -(elements) g(in) h(array) f("scratch".) 533 1233 y(*) 525 -b(Must) 47 b(be) g(>=) g(???.) 533 1440 y(*) 95 b(INFO) 190 -b(\(output\)) 46 b(INTEGER) 533 1648 y(*) 477 b(=) 48 -b(0:) 95 b(successful) 45 b(exit.) 533 1856 y(*) 477 -b(-50) 47 b(<=) g(INFO) g(<) g(0,) h(the) e(-INFOth) g(argument) g(had) -h(an) g(illegal) f(value.) 533 2063 y(*) 477 b(INFO) 47 -b(=) g(-51,) 286 b(Input) 46 b(data) h(which) f(must) h(be) g(the) g -(same) f(on) h(all) 533 2167 y(*) 1289 b(processors) 45 -b(is) i(NOT) g(the) g(same) f(on) h(all) g(processors) 533 -2271 y(*) 1289 b(in) 47 b(mapZ.) 533 2478 y(*) 477 b(=) 48 -b(1,) 620 b(Error) 46 b(choleski) f(factoring) h(B.) 95 -b(In) 47 b(this) f(case) 533 2582 y(*) 1289 b('choleski') 45 -b(returned) g(a) j(non-zero) d(info,) h(whose) 533 2686 -y(*) 1289 b(value) 46 b(was) h(printed) f(to) h(stderr.) 533 -2893 y(*) 477 b(=) 48 b(2,) 620 b(Error) 46 b(computing) f(inverse) h -(of) h(L,) g(the) g(choleski) 533 2997 y(*) 1289 b(factor) 46 -b(of) h(B.) 95 b(In) 47 b(this) g(case) 533 3101 y(*) 1289 -b('inverseL') 45 b(returned) g(a) j(non-zero) d(info,) h(whose) 533 -3205 y(*) 1289 b(value) 46 b(was) h(printed) f(to) h(stderr.) 533 -3412 y(*) 477 b(=) 48 b(3,) 620 b(Error) 46 b(solving) g(the) h -(standard) e(eigenproblem.) 533 3516 y(*) 1289 b(In) 47 -b(this) f(case) 533 3620 y(*) 1289 b('pdspevx') 45 b(returned) g(a) j -(non-zero) d(info,) i(whose) 533 3724 y(*) 1289 b(value) 46 -b(was) h(printed) f(to) h(stderr.) 533 3931 y(*) 477 -b(Any) 47 b(processor) e(with) i(a) g(negative) f(INFO) h(stops) f -(program) g(execution.) 533 4139 y(*) 477 b(If) 47 b(-50) g(<=) g(INFO) -g(<) h(0,) f(then) f(bad) h(data) g(was) g(passed) f(to) h(this) g -(routine) 533 4242 y(*) 1432 b(and) 47 b(no) g(attempt) f(is) h(made) f -(to) i(make) e(sure) h(that) 533 4346 y(*) 1432 b(INFO) 46 -b(is) i(the) e(same) h(on) g(all) g(processors.) 533 -4554 y(*) 477 b(All) 47 b(other) f(INFO) 286 b(INFO) 46 -b(should) g(be) i(the) f(same) f(on) h(all) g(proces-) 390 -4658 y(sors) g(in) 533 4761 y(*) 1432 b(mapA,B,Z.) 93 -b(If) 47 b(this) g(routine) e(calls) i(a) g(routine) 533 -4865 y(*) 1432 b(which) 46 b(returns) g(a) h(negative) f(info,) g(then) -h(info) 533 4969 y(*) 1432 b(may) 47 b(not) g(be) g(the) g(same) f(on) h -(all) g(processors.) 533 5073 y(*) 1432 b(This,) 46 b(however,) g -(should) g(never) g(happen.) 533 5176 y(*) 239 b -(-----------------------) o(---) o(----) o(----) o(---) o(----) o(----) -o(---) o(----) o(----) o(---) o(---) 390 5280 y(-------) p -90 rotate dyy eop -%%Page: 34 35 -34 34 bop Fs 150 -116 a(34) 3256 b(P) m(eIGS) p Fk 533 -299 a(*/) p Fr 150 549 a(4.4) 68 b(Lev) l(el) 46 b(I) t(I) f -(Subroutines) p Fs 275 739 a(This) 39 b(section) j(describ) s(es) e -(the) i(lev) m(el) g(2) g(subroutines.) 72 b(As) 42 b(of) g(this) f -(writing) e(w) m(e) k(presen) m(t) e(a) h(brief) 150 -849 y(summary) 23 b(of) h(what) g(eac) m(h) h(routine) e(do) s(es.) 39 -b(These) 24 b(routines) e(are) j(called) e(in) g(supp) s(ort) f(of) j -(the) f(eigensystem) 150 958 y(solv) m(ers) 30 b(but) g(they) g(can) h -(b) s(e) f(useful) e(for) j(other) f(calculations) g(to) s(o.) 275 -1090 y(Man) m(y) 38 b(of) h(the) f(lev) m(el) g(I) s(I) f(routines) g -(do) h(little) e(or) j(no) f(c) m(hec) m(king) g(of) h(input) d(data,) -41 b(hence) d(are) g(not) h(as) 150 1200 y(robust) 32 -b(against) g(input) e(errors) i(as) h(the) f(lev) m(el) g(I) g -(routines.) 46 b(Also,) 32 b(some) h(of) f(the) h(routines) e(describ) s -(ed) f(in) 150 1310 y(this) 38 b(section) p Fo 38 w(cannot) p -Fs 40 w(curren) m(tly) f(b) s(e) i(called) e(directly) h(from) g -(fortran) g(\(only) h(b) s(ecause) f(the) h(fortran-C) 150 -1419 y(in) m(terface) 31 b(routines) e(ha) m(v) m(e) j(not) e(y) m(et) i -(b) s(een) e(tested\).) 275 1551 y(The) 36 b(lev) m(el) g(I) s(I) g -(routines) g(whic) m(h) f(can) j(curren) m(tly) d(b) s(e) i(called) f -(from) g(fortran) g(are:) 54 b(b) s(ortho,) 38 b(mxm25,) 150 -1661 y(mxm5x,) 30 b(mxm88,) h(ortho,) g(pstebz,) g(resid,) e(residual,) -g(and) g(tresid.) 275 1793 y(The) 35 b(memory) g(requiremen) m(ts) g -(for) h(the) f(lev) m(el) h(I) s(I) f(routines) f(are) i(desrib) s(ed) e -(in) g(the) i(headers) f(for) h(the) 150 1902 y(v) -5 -b(arious) 30 b(routines.) 40 b(The) 30 b(listed) f(memory) i -(requiremen) m(ts) f(are) h(b) s(eliev) m(ed) e(to) i(b) s(e) f(as) h -(large) g(or) g(somewhat) 150 2012 y(larger) k(than) h(what) f(the) h -(v) -5 b(arious) 35 b(routines) f(actually) i(use.) 56 -b(Ho) m(w) m(ev) m(er,) 39 b(this) c(has) g(not) h(curren) m(tly) f(b) s -(een) 150 2122 y(tested.) 275 2254 y(Finally) -8 b(,) 32 -b(b) s(efore) h(calling) e(an) m(y) i(of) h(P) m(eIGS) f(routines,) g -(except) h(the) f(lev) m(el) g(I) g(routines,) g(one) p -Fo 33 w(m) m(ust) g(call) 150 2363 y(the) e(fortran) f(routine) h -(mxinit\(\)) g(\(mxinit) p 1600 2363 28 5 v 34 w(\(\)) g(from) f(C\)) p -Fs 30 w(to) h(initialize) d(the) i(comm) m(unication) g(pac) m(k) -5 -b(age.) p Fg 150 2564 a(4.4.1) 63 b(Choleski) 41 b(F) -10 -b(actorization) 40 b(of) h(P) m(ositiv) m(e) f(De\014nite) h(Symmetric) -464 2689 y(Matrix) p Fs 275 2879 a(This) e(subroutine) g(p) s(erforms) g -(a) j(submatrix) d(Choleski) g(factorization) j(of) f(a) h(symmetric) e -(p) s(ositiv) m(e) 150 2989 y(matrix) 24 b(with) e(a) j(column) e(wrap) -g(using) g(a) h(list) f(of) i(pro) s(cessors.) 38 b(This) 22 -b(co) s(de) j(originated) e(from) h(Mik) m(e) g(Heath) p -Fm 150 3098 a(\(Geist,) 29 b(G.) f(A.,) h(and) e(M.) h(T.) f(Heath,) i -(\\Matrix) f(F) -8 b(actorization) 30 b(on) d(a) h(Hyp) s(ercub) s(e) e -(Multipro) s(cessor,") h(in) 150 3208 y(Hyp) s(ercub) s(e) j(Multipro) s -(cessors) f(1986,) k(SIAM,) e(Philadelphia,) d(1986,) 33 -b(pp.) 42 b(161-180\)) p Fs(.) k(W) -8 b(e) 32 b(mo) s(di\014ed) d(it) -150 3317 y(for) h(our) g(purp) s(oses) f(and) g(are) i(fully) d(resp) s -(onsible) g(for) i(an) m(y) g(bugs.) 275 3450 y(The) f(C) h(syn) m(tax) -h(is:) p Fk 390 3576 a(void) 47 b(choleski\() e(n,) i(vecA,) f(mapA,) h -(iscratch,) e(scratch,) h(info) g(\)) 629 3783 y(Integer) 570 -b(*n,) 47 b(*mapA,) f(*iscratch,) f(*info;) 629 3991 -y(DoublePrecision) 425 b(*scratch;) 629 4198 y(DoublePrecision) 377 -b(**vecA;) 485 4406 y(/*) 533 4510 y(*) 95 b -(==========================) o(===) o(====) o(====) o(===) o(====) o -(====) o(===) o(====) o(====) o(===) o(====) 533 4821 -y(*) g(The) 47 b(original) f(code) g(is) i(due) f(to) g(Mike) f(Heath.) -94 b(George) 46 b(Fann) 533 4925 y(*) 95 b(bastardized) 45 -b(it) i(for) g(our) g(code.) 94 b(We) 47 b(thank) g(Mike) 533 -5029 y(*) 95 b(for) 47 b(his) g(generosity.) 93 b(Any) 47 -b(bugs) f(and) h(problems) f(are) h(introduced) 533 5132 -y(*) 95 b(by) 48 b(us.) p 90 rotate dyy eop -%%Page: 35 36 -35 35 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(35) p Fk 533 299 a(*) 95 b(Currently,) 45 -b(this) i(procedure) e(only) i(handles) f(the) h(case) f(where) h(the) -533 403 y(*) 95 b(lower) 47 b(triangular) e(part) h(of) i(A) f(is) g -(distributed) e(to) i(processors) e(by) i(columns.) 533 -714 y(*) 95 b(Purpose) 533 818 y(*) g(=======) 533 1025 -y(*) g(choleski) 46 b(computes) f(the) i(Cholesky) f(factorization) e -(of) j(a) h(real) e(symmetric) 533 1129 y(*) 95 b(positive) 46 -b(definite) f(matrix) i(A) g(in) g(packed) f(storage) g(format.) 533 -1337 y(*) 95 b(The) 47 b(factorization) d(has) j(the) g(form) 533 -1440 y(*) 239 b(A) 47 b(=) g(L) 96 b(*) 47 b(L') 533 -1544 y(*) 95 b(where) 47 b(L) g(is) g(lower) g(triangular.) 92 -b(On) 47 b(output) f(the) h(matrix) f(A) i(is) f(overwrit-) 390 -1648 y(ten) g(by) 533 1752 y(*) 143 b(the) 47 b(Choleski) f(factor) g -(L.) 533 2063 y(*) 95 b(Arguments) 533 2167 y(*) g(=========) 533 -2374 y(*) g(In) 48 b(the) e(following) g(let:) 533 2582 -y(*) 239 b(me) f(=) 47 b(The) g(id) g(of) g(this) g(processor) 533 -2790 y(*) 239 b(nvecsA) 46 b(=) h(The) g(number) f(of) h(columns) f(of) -h(A) h(owned) e(by) h(this) g(processor.) 533 2893 y(*) 668 -b(In) 47 b(particular,) e(nvecsA) h(=) i(count_list\(me,) 43 -b(mapA,) k(n\).) 533 3101 y(*) 239 b(nprocsA) 45 b(=) j(Number) e(of) h -(distinct) f(processor) f(id's) i(in) g("mapA".) 93 b(In) 533 -3205 y(*) 716 b(particular,) 45 b(nprocs) h(=) h(reduce_list\() e(n,) i -(mapA,) f(iscratch) g(\)) 533 3412 y(*) 95 b(n) 334 b(\(input\)) 46 -b(\(Integer) g(*\)) h(scaler) 533 3516 y(*) 477 b(The) 47 -b(order) f(of) i(the) f(matrix) f(A.) 95 b(n) 47 b(>=) g(0.) 533 -3724 y(*) 95 b(vecA) 190 b(\(input/output\)) 44 b(\(DoublePrecision) f -(**\)) k(array,) f(length) h(\(nvecsA\)) 533 3827 y(*) 477 -b(On) 47 b(entry,) f(the) h(portion) f(of) h(the) g(lower) g -(triangular) e(part) h(of) h(the) 533 3931 y(*) 477 b(symmetric) 45 -b(matrix) i(A) g(owned) f(by) i(this) e(processor.) 533 -4139 y(*) 477 b(vecA[i]) 46 b(points) g(to) h(an) g(array) g -(containing) e(the) i(lower) f(triangular) 533 4242 y(*) 477 -b(part) 47 b(of) g(the) g(i-th) g(column) f(of) h(A) g(which) g(is) g -(owned) f(by) h(this) 533 4346 y(*) 477 b(processor,) 45 -b(i) j(=) f(0) h(to) f(nvecsA.) 533 4554 y(*) 477 b(On) 47 -b(exit,) g(if) g(*info) f(=) i(0,) f(the) g(factor) f(L) h(from) g(the) -g(Cholesky) 533 4658 y(*) 477 b(factorization) 44 b(A) k(=) f -(L*L^\(T\).) 533 4865 y(*) 95 b(mapA) 190 b(\(input\)) 46 -b(\(Integer) g(*\)) h(array,) f(length) g(\(*n\)) 533 -4969 y(*) 477 b(mapA[i]) 46 b(=) h(the) g(id) h(of) f(the) g(processor) -e(which) h(owns) h(column) f(i) h(of) h(A,) 533 5073 -y(*) 477 b(i) 48 b(=) f(0) h(to) f(*n) g(-) g(1.) 533 -5280 y(*) 95 b(iscratch) f(\(integer) 45 b(workspace\)) g(\(Integer) h -(*\)) h(array,) f(length) g(\(2) h(n) h(+) f(1\)) p 90 rotate -dyy eop -%%Page: 36 37 -36 36 bop Fs 150 -116 a(36) 3256 b(P) m(eIGS) p Fk 533 -403 a(*) 95 b(scratch) 142 b(\(DoublePrecision) 43 b(workspace\)) i -(\(DoublePrecision) e(*\)) 48 b(array,) e(length) g(\(n+1\)) 533 -610 y(*) 573 b(scratch) 45 b(must) i(contain) f(at) h(least) f(bufsiz) h -(bytes) f(\(see) h(cmbbrf.h\)) 533 922 y(*) 95 b(info) 286 -b(\(output\)) 45 b(\(Integer) h(*\)) h(scaler) 533 1025 -y(*) 573 b(=) 47 b(0:) g(successful) e(exit) 533 1129 -y(*) 573 b(<) 47 b(0:) g(if) g(info) g(=) h(-k,) e(the) h(k-th) g -(argument) f(had) g(an) i(illegal) d(value) 533 1233 -y(*) 573 b(>) 47 b(0:) g(if) g(info) g(=) h(k,) f(1<=) g(k) g(<=) g(n,) -g(the) g(leading) f(minor) h(of) g(order) 533 1337 y(*) 811 -b(k) 48 b(is) f(not) g(positive) e(definite,) h(and) h(the) f -(factorization) 533 1440 y(*) 811 b(could) 47 b(not) g(be) g -(completed.) 533 1648 y(*) 95 b(==========================) o(===) o -(====) o(====) o(===) o(====) o(====) o(===) o(====) o(====) o(===) o -(====) 533 1752 y(*/) p Fg 150 1971 a(4.4.2) 63 b(In) m(v) m(erse) 40 -b(of) h(Lo) m(w) m(er) f(T) -10 b(riangular) 41 b(Matrix) p -Fs 275 2162 a(The) 36 b(subroutine) p Fo 35 w(in) m(v) m(erseL) p -Fs 38 w(computes) i(the) f(in) m(v) m(erse) g(of) g(a) h(lo) m(w) m(er) -f(triangular) f(matrix) g(in) g(column) 150 2272 y(wrapp) s(ed) k -(form\(according) h(to) h(a) g(list\).) 74 b(On) 40 b(output) h(the) h -(input) e(matrix) h(is) f(o) m(v) m(erwritten) i(with) f(its) 150 -2382 y(output.) 275 2515 y(The) 29 b(C) h(syn) m(tax) h(is:) p -Fk 390 2642 a(void) 47 b(inverseL) e(\() j(msize,) e(col,) g(map,) h -(iwork,) f(buffer,) g(info\)) 629 2746 y(Integer) f(*msize,) h(*map,) h -(*iwork,) e(*info;) 629 2849 y(DoublePrecision) e(**col,) j(*buffer;) -629 3057 y(/*) 724 3161 y(This) h(routine) f(computes) f(the) i -(inverse) f(of) h(a) g(lower) g(triangular) e(matrix.) 724 -3264 y(On) i(output,) f(the) h(lower) f(triangular) f(matrix) h(is) i -(overwritten) c(by) k(its) e(inverse.) 724 3368 y(The) h(matrix) f(is) h -(assume) f(to) i(be) f(column) f(wrapped) g(and) h(distributed) d -(according) 724 3472 y(to) j(the) g(array) g(map.) 94 -b(Thus,) 46 b(map[i]) g(=) i(processor) d(id) i(which) g(holds) f -(column) 724 3576 y(i) i(of) f(the) g(matrix.) 724 3783 -y(Arguments:) 724 3991 y(msize) f(=) i(\(input\)) e(integer,) f(size) i -(of) g(the) g(matrix) 724 4198 y(col) g(=) g(\(input/1-D) e(array) i -(of) g(pointers) f(to) h(DoublePrecision) c(numbers\)) 629 -4302 y(col[j]) j(->) h(the) g(address) f(of) h(the) g(j-th) f(vector) g -(that) h(this) g(processor) e(owns) 724 4510 y(map) i(=) g -(\(input/integer) d(array\)) i(integer) g(array,) g(length) g(n,) i -(such) e(that) h(for) 1058 4614 y(the) g(i-th) g(column,) 629 -4717 y(map[i]) f(=) h(real) g(processor) e(id) i(holding) f(this) h -(column) 724 4925 y(iscratch) f(=) h(\(scratch/integer\)) c(integer) j -(scratch) g(space) g(of) h(size) g(nprocs) 724 5132 y(buffer) f(=) i -(\(scratch\)) d(DoublePrecision) f(precision) h(array) 724 -5340 y(info) 94 b(=) 48 b(\(output/integer\)) p 90 rotate -dyy eop -%%Page: 37 38 -37 37 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(37) p Fk 1106 299 a(if) 47 b(info) g(==) g(0) g -(normal) 1106 403 y(if) g(info) g(==) g(i) g(>) h(0) f(then) g(the) g -(i-th) f(diagonal) g(element) 1010 506 y(\() i(in) f(Fortran) f -(notation) f(\)) j(is) f(smaller) f(than) 1392 610 y(dlamch\("s"\),) f -(the) i(safe) f(inverse) g(limit:) g(overflow) 1392 714 -y(may) h(have) g(occurred.) 629 818 y(*/) p Fg 150 1037 -a(4.4.3) 63 b(Matrix) 40 b(Multiplication) p Fs 275 1227 -a(There) 29 b(are) i(sev) m(eral) f(di\013eren) m(t) g(matrix) f(m) m -(ultiplication) f(routines) h(dep) s(ending) e(on) j(ho) m(w) h(the) f -(data) h(is) 150 1337 y(distributed) 22 b(and) i(the) h(shap) s(e) f -(of) h(the) h(matrix.) 38 b(The) 24 b(F) -8 b(ortran) 26 -b(77) g(calling) d(syn) m(tax) i(is) f(giv) m(en) h(in) f(v) m(ery) h -(little) 150 1447 y(detail.) 49 b(Most) 34 b(of) f(the) h(detail) e -(and) h(descriptions) e(of) i(the) h(routines) e(are) i(included) c -(with) i(the) i(C) e(calling) 150 1556 y(syn) m(tax.) 275 -1689 y(The) d(F) -8 b(ortran) 31 b(77) h(syn) m(tax) f(is:) p -Fk 629 1816 a(SUBROUTINE) 45 b(mxm25) h(\() h(n1,) g(n2,) g(rowQ,) g -(mapQ,) f(m,) h(colW,) g(mapW,) f(colZ,) g(iwork,) g(work\)) 629 -1920 y(INTEGER) 475 b(n1,) 47 b(n2,) g(mapQ\(*\),) e(m,) j(mapW\(*\),) d -(iwork\(*\)) 629 2023 y(Double) h(Precision) f(rowQ\(*\),) h -(colW\(*\),) f(colZ\(*\),) h(work\(*\)) 629 2150 y(SUBROUTINE) f -(mxm5x\() h(n,) h(rowU,) f(mapU,) h(m,) g(colF,) f(mapF,) h(iscratch,) e -(scratch\)) 629 2254 y(Integer) 475 b(n,) 47 b(mapU\(*\),) f -(mapF\(*\),) 93 b(m,) 47 b(iscratch\(*\)) 629 2358 y(Double) f -(Precision) f(colF\(*\),) h(rowU\(*\),) f(scratch\(*\)) 629 -2485 y(SUBROUTINE) g(mxm88) h(\() h(n,) h(colQ,) e(mapQ,) g(m,) i -(colW,) e(mapW,) g(iwork,) g(work) h(\)) 629 2589 y(Integer) 475 -b(n,) 47 b(mapQ\(*\),) f(m,) h(mapW\(*\),) e(iwork\(*\)) 629 -2692 y(Double) h(Precision) f(colQ\(*\),) h(colW\(*\),) f(work\(*\)) 390 -2900 y(C) 95 b(Note) 47 b(that) f(the) h(C) h(routine) e(mxm88) g(has) h -(one) g(more) f(argument,) g(iptr,) g(than) h(the) 390 -3004 y(C) 95 b(Fortran) 46 b(77) h(call) g(syntax) f(listed) g(here.) p -Fs 275 3136 a(The) 28 b(input) f(argumen) m(ts) j(for) e(the) i(ab) s -(o) m(v) m(e) g(routines) e(are) h(the) h(same) f(as) g(in) f(the) h(C) -g(co) s(des) g(listed) f(b) s(elo) m(w) 150 3246 y(except) h(that) f -(one) g(c) m(hanges) h(the) f(argumen) m(ts) g(of) g(t) m(yp) s(e) p -Fk 28 w(") p Fs(1-D) h(arra) m(y) g(of) f(p) s(oin) m(ters) e(to) j -(DoublePrecision) p Fk(") p Fs(,) 150 3356 y(i.e.,) k(ro) m(wQ,) f -(colW,) h(etc,) g(to) g(t) m(yp) s(e) p Fk 32 w(") p -Fs(1-D) g(arra) m(y) g(of) f(double) e(precision) h(n) m(um) m(b) s -(ers) p Fk(") p Fs 30 w(and) g(store) i(the) f(data) 150 -3465 y(in) 26 b(these) j(arra) m(ys) f(using) e(the) i(pac) m(k) m(ed) h -(storage) g(format) f(describ) s(ed) e(previously) -8 -b(.) 38 b(The) 27 b(C) h(co) s(de) g(describ) s(es) 150 -3575 y(arra) m(ys) j(of) f(length) g(n) g(with) f(indices) f(of) j(0) g -(to) g(n-1,) g(for) f(fortran) g(usage) h(the) f(indices) f(should) f -(b) s(e) i(1) h(to) g(n.) 275 3708 y(The) 23 b(double) g(precision) f -(w) m(ork) j(arra) m(ys) f(for) g(the) h(F) -8 b(ortran) 25 -b(77) g(co) s(des) f(m) m(ust) g(b) s(e) g(somewhat) g(larger) g(than) -150 3817 y(listed) 34 b(b) s(elo) m(w) h(in) f(the) i(C) f(calling) f -(syn) m(tax.) 57 b(In) 35 b(particular,) g(let) g(ME,) h(b) s(e) f(the) -h(id) e(of) i(a) g(pro) s(cessor,) h(and) 150 3927 y(let) 30 -b(n) m(v) m(ecsX) h(b) s(e) e(the) h(n) m(um) m(b) s(er) f(of) h(en) m -(tries) g(in) e(arra) m(y) j(mapX) e(equal) h(to) g(ME,) h(where) e(X) h -(=) g(Q,W,U,) h(or) e(F.) 150 4036 y(Then,) h(on) g(pro) s(cessor) g -(ME) g(the) h(extra) g(memory) f(requiremen) m(ts) g(for) g(the) g(F) -8 -b(ortran) 31 b(77) h(routines) d(are:) p Fq 199 4169 -a(\000) p Fs 60 w(MXM25:) 42 b(increase) 31 b(size) f(of) g(w) m(ork) h -(b) m(y) f(n) m(v) m(ecsQ) p Fk(+) p Fs(n) m(v) m(ecsW) p -Fk(+) p Fs(n) m(v) m(ecsZ) p Fq 199 4302 a(\000) p Fs -60 w(MXM5x:) 42 b(increase) 30 b(size) g(of) h(scratc) m(h) g(b) m(y) g -(n) m(v) m(ecsU) p Fk(+) p Fs(n) m(v) m(ecsF) p Fk(+) p -Fs(2) p Fq 199 4435 a(\000) p Fs 60 w(MXM88:) 42 b(increase) 31 -b(size) f(of) g(w) m(ork) h(b) m(y) f(n) m(v) m(ecsQ) p -Fk(+) p Fs(2*n) m(v) m(ecsW) p Fk(+) p Fs(3) 275 4590 -y(The) f(C) h(syn) m(tax) h(is:) p Fk 390 4717 a(void) 47 -b(mxm25) f(\() h(n1,) g(n2,) g(rowQ,) g(mapQ,) f(m,) h(colW,) g(mapW,) f -(colZ,) g(iwork,) g(work\)) 629 4821 y(Integer) f(*n1,) i(*n2,) g -(*mapQ,) f(*m,) h(*mapW,) f(*iwork;) 629 4925 y(DoublePrecision) d -(**rowQ,) j(**colW,) g(**colZ,) g(*work;) 390 5132 y -(/***********************) o(****) o(****) o(***) o(****) o(****) o -(***) o(****) o(****) o(***) o(****) o(**) 438 5236 y(*) 438 -5340 y(*) h(Subroutine) e(mxm25) p 90 rotate dyy eop -%%Page: 38 39 -38 38 bop Fs 150 -116 a(38) 3256 b(P) m(eIGS) p Fk 438 -299 a(*) 533 403 y(This) 47 b(subroutine) e(does) h(the) h(matrix) f -(multiplication) e(Z) k(<-) f(Q*W) 533 610 y(where) g(matrix) f(Q) h -(is) g(a) h(n1) f(x) g(n2) h(general) d(matrix) h(in) i(packed) e -(storage) g(format,) 820 714 y(distributed) e(by) j(rows,) 820 -922 y(matrix) f(W) h(is) g(a) h(general) e(n2) h(x) g(m) h(matrix) e -(in) h(packed) f(storage) g(format,) 820 1025 y(distributed) e(by) j -(columns.) 820 1233 y(and) f(matrix) h(Z) g(is) g(the) g(n1) g(x) h(m) f -(product) f(Q*W,) h(distributed) d(the) j(same) g(as) g(W.) 533 -1440 y(In) g(this) g(version) f(we) h(assume) f(that) h(Q) g(and) g(W) h -(share) e(the) h(same) f(processors) 533 1544 y(\() i(perhaps) d -(different) h(data) g(distributions) f(\)) 533 1752 y(It) i(is) h(ok) f -(to) g(have) g(colZ) f(=) i(colW.) 94 b(However,) 45 -b(in) i(this) 533 1856 y(case) g(each) f(colZ[i]=colW[i]) e(must) j -(point) f(to) h(a) h(vector) e(of) 533 1959 y(length) g(=) i(MAX\() e -(n1,) h(n2) g(\).) 533 2167 y(ARGUMENTS) 533 2271 y(---------) 533 -2374 y(In) g(the) g(following:) 629 2582 y(INTEGER) 475 -b(=) 47 b("pointer) f(to) h(Integer") 629 2686 y(DOUBLE) f(PRECISION) f -(=) i("pointer) f(to) h(DoublePrecision") 629 2893 y(me) 238 -b(=) 47 b(this) g(processor's) e(id) i(\(=) g(mxmynd_\(\)\)) 629 -2997 y(nprocs) f(=) h(number) f(of) h(allocated) f(processors) f(\() i -(=) h(mxnprc_\(\)\)) 629 3101 y(nvecsW) e(=) h(number) f(of) h(entries) -f(in) h(mapW) g(equal) f(to) i(me) 1249 3205 y(\(=) f(count_list\() e -(me,) i(mapW,) f(m) i(\)\)) 629 3308 y(nvecsQ) e(=) h(number) f(of) h -(entries) f(in) h(mapQ) g(equal) f(to) i(me) 1249 3412 -y(\(=) f(count_list\() e(me,) i(mapQ,) f(n1) h(\)\)) 629 -3516 y(nvecsQ_max) e(=) i(maximum) f(number) g(of) h(entries) f(in) h -(mapQ) g(equal) f(to) h(i,) 1249 3620 y(i) h(=) f(0) g(to) h(nprocs-1) -1249 3724 y(\(=) f(max) g(over) g(i) g(of) g(count_list\() e(i,) i -(mapQ,) g(n1) g(\)\)) 629 3827 y(sDP) 190 b(=) 47 b(sizeof\() f -(DoublePrecision) e(\)) 533 4035 y(n1) j(.....) g(\(input\)) f(INTEGER) -963 4139 y(The) h(number) f(of) h(rows) g(in) g(matrix) f(Q) 533 -4346 y(n2) h(.....) g(\(input\)) f(INTEGER) 963 4450 -y(The) h(number) f(of) h(columns) f(in) h(matrix) f(Q) 963 -4554 y(and) h(the) g(number) f(of) h(rows) f(in) i(matrix) e(W) 533 -4761 y(rowQ) h(...) g(\(input\)) f(array) g(of) h(pointers) f(to) h -(DoublePrecision,) 1345 4865 y(length) f(\(nvecsQ\)) 963 -4969 y(The) h(part) f(of) h(matrix) g(Q) g(owned) f(by) i(this) e -(processer) f(stored) 963 5073 y(in) i(packed) f(format,) g(i.e.,) g -(rowQ[i]) g(points) g(to) h(the) g(start) 963 5176 y(of) g(the) g(i-th) -f(row) h(of) h(Q) 963 5280 y(owned) e(by) h(this) g(processor,) e(i) i -(=) h(0) f(to) g(nvecsQ-1.) p 90 rotate dyy eop -%%Page: 39 40 -39 39 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(39) p Fk 533 403 a(mapQ) 47 b(...) g(\(input\)) f -(INTEGER) f(array,) h(length) h(\(n1\)) 963 506 y(The) g(i-th) f(row) h -(of) g(Q) h(is) f(owned) f(by) i(processor) 963 610 y(mapQ[i],) d(i) j -(=) f(0) h(to) f(n1-1.) 533 818 y(m) h(......) e(\(input\)) g(INTEGER) -963 922 y(The) h(number) f(of) h(columns) f(in) h(W.) 533 -1129 y(colW) g(...) g(\(input\)) f(array) g(of) h(pointers) f(to) h -(DoublePrecision,) 1679 1233 y(length) f(\(nvecsW\)) 963 -1440 y(The) h(part) f(of) h(matrix) g(W) g(owned) f(by) i(this) e -(processer) f(stored) 963 1544 y(in) i(packed) f(format) g(by) h -(columns,) f(i.e.,) g(colW[i]) g(points) 963 1648 y(to) h(the) g(first) -f(element) g(of) h(the) g(i-th) g(column) f(of) h(W) 963 -1752 y(owned) f(by) h(this) g(processor,) e(i) i(=) h(0) f(to) g -(nvecsW-1.) 533 1959 y(mapW) g(...) g(\(input\)) f(INTEGER) f(array,) h -(length) h(\(m\)) 963 2063 y(The) g(i-th) f(column) g(of) i(W) f(is) 963 -2167 y(owned) f(by) h(processor) f(mapW[i],) f(i) j(=) f(0) g(to) h -(m-1.) 533 2374 y(colZ) f(...) g(\(output\)) e(array) i(of) g(pointers) -e(to) j(DoublePrecision,) 1392 2478 y(length) e(\(nvecsW\)) 1010 -2686 y(The) h(result) f(matrix) h(Z) g(=) g(Q) h(*) f(W) h(stored) e -(identical) f(to) i(W.) 1010 2893 y(It) h(is) f(ok) g(to) g(have) g -(colZ) f(=) i(colW.) 94 b(However,) 46 b(in) h(this) 1010 -2997 y(case) g(each) g(colZ[i]=colW[i]) c(must) k(point) f(to) i(a) f -(vector) f(of) 1010 3101 y(length) h(=) g(MAX\() g(n1,) g(n2) g(\).) 533 -3308 y(iwork) g(..) g(\(workspace\)) d(INTEGER) i(array,) g(length) g -(\() i(3) f(*) h(n1) f(+) g(2) h(*) f(m) h(\)) 533 3516 -y(work) f(...) g(\(workspace\)) d(DOUBLE) j(PRECISION) e(array,) 1535 -3620 y(length) i(\() g(maximum) f(\() h(n1) g(+) h(m,) f(\(nvecsW) f(+) -h(2) h(*) f(nvecsQ_max\)) e(*) i(n2) h(\)) 390 3724 y(*/) 390 -3887 y(void) f(mxm5x\() f(n,) h(rowU,) f(mapU,) h(m,) g(colF,) f(mapF,) -h(iscratch,) e(scratch\)) 629 3991 y(Integer) g(*n,) i(*mapU,) f -(*mapF,) 94 b(*m,) 47 b(*iscratch;) 629 4095 y(DoublePrecision) c -(**colF,) j(**rowU,) g(*scratch;) 390 4302 y(/***********************) o -(****) o(****) o(***) o(****) o(****) o(***) o(****) o(****) o(***) o -(****) o(**) 438 4406 y(*) 438 4510 y(*) h(Subroutine) e(mxm5x) 438 -4614 y(*) 533 4717 y(This) i(subroutine) e(does) h(the) h(matrix) f -(multiplication) e(F) k(<-) f(U) g(*) h(F) 533 4925 y(where) f(U) g(is) -g(a) h(n) f(x) h(n) f(upper) f(trianguler) f(matrix) h(in) i(packed) e -(storage) g(format,) 533 5029 y(and) h(row) g(distributed,) 533 -5132 y(and) g(matrix) f(F) i(is) f(a) g(general) f(n) i(x) f(m) g -(matrix) g(distributed) d(by) j(columns.) 533 5340 y(ARGUMENTS) p -90 rotate dyy eop -%%Page: 40 41 -40 40 bop Fs 150 -116 a(40) 3256 b(P) m(eIGS) p Fk 533 -299 a(---------) 533 403 y(In) 47 b(the) g(following:) 629 -610 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h(Integer") 629 -714 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h(DoublePrecision") -629 922 y(me) 238 b(=) 47 b(this) g(processor's) e(id) i(\(=) g -(mxmynd_\(\)\)) 629 1025 y(nprocs) f(=) h(number) f(of) h(allocated) f -(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 1129 y(nvecsU) e(=) h -(number) f(of) h(entries) f(in) h(mapU) g(equal) f(to) i(me) 1058 -1233 y(\(=) f(count_list\() e(me,) i(mapU,) f(n) i(\)\)) 629 -1337 y(neleU_max) d(=) i(maximum) f(number) g(of) h(elements) f(of) h -(U) h(owned) e(by) h(any) 1201 1440 y(processor.) 1201 -1544 y(\(=) h(max) e(over) h(i) h(of) f(ci_size_\() e(i,) i(n,) g -(mapU\)) g(\)) 629 1648 y(nvecsF) f(=) h(number) f(of) h(entries) f(in) -h(mapF) g(equal) f(to) i(me) 1058 1752 y(\(=) f(count_list\() e(me,) i -(mapF,) f(m) i(\)\)) 629 1856 y(sDP) 190 b(=) 47 b(sizeof\() f -(DoublePrecision) e(\)) 533 2063 y(n) k(......) e(\(input\)) g(INTEGER) -963 2167 y(The) h(number) f(of) h(rows) g(and) f(columns) g(of) h(U,) h -(and) f(the) f(number) 963 2271 y(of) h(rows) g(of) g(F.) 533 -2478 y(rowU) g(...) g(\(input\)) f(array) g(of) h(pointers) f(to) h -(DoublePrecision,) 1345 2582 y(length) f(\(nvecsU\)) 963 -2686 y(The) h(part) f(of) h(matrix) g(U) g(owned) f(by) i(this) e -(processer) f(stored) 963 2790 y(in) i(packed) f(format,) g(i.e.,) g -(rowU[i]) g(points) g(to) h(the) g(diagonal) 963 2893 -y(element) f(of) h(the) g(i-th) f(row) h(of) g(U) 963 -2997 y(owned) f(by) h(this) g(processor,) e(i) i(=) h(0) f(to) g -(nvecsU-1.) 533 3205 y(mapU) g(...) g(\(input\)) f(INTEGER) f(array,) h -(length) h(\(n\)) 963 3308 y(The) g(i-th) f(row) h(of) g(U) h(is) 963 -3412 y(owned) e(by) h(processor) f(mapU[i],) f(i) j(=) f(0) g(to) h -(n-1.) 533 3620 y(m) g(......) e(\(input\)) g(INTEGER) 963 -3724 y(m) h(is) g(the) g(number) f(of) i(columns) d(in) j(F.) 533 -3931 y(colF) f(...) g(\(input/output\)) d(array) i(of) h(pointers) f -(to) h(DoublePrecision,) 1679 4035 y(length) f(\(nvecsF\)) 963 -4242 y(On) h(Entry:) 1058 4346 y(The) g(part) g(of) g(matrix) f(F) h -(owned) g(by) g(this) g(processer) e(stored) 1058 4450 -y(in) i(packed) f(format) h(by) g(columns,) e(i.e.,) i(colF[i]) e -(points) 1058 4554 y(to) i(the) g(first) g(element) e(of) j(the) f -(i-th) f(column) g(of) h(F) 1058 4658 y(owned) g(by) g(this) f -(processor,) f(i) j(=) f(0) h(to) f(nvecsF-1.) 963 4865 -y(On) g(Exit:) 1058 4969 y(The) g(result) f(matrix) g(U) i(*) f(F) h -(stored) e(in) h(the) g(same) f(manner) h(as) 1058 5073 -y(F) h(on) f(entry.) 533 5280 y(mapF) g(...) g(\(input\)) f(INTEGER) f -(array,) h(length) h(\(m\)) p 90 rotate dyy eop -%%Page: 41 42 -41 41 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(41) p Fk 963 299 a(The) 47 b(i-th) f(column) g(of) -i(F) f(is) 963 403 y(owned) f(by) h(processor) f(mapF[i],) f(i) j(=) f -(0) g(to) h(m-1.) 533 610 y(iscratch) e(..) h(\(workspace\)) e(INTEGER) -g(array,) i(length) f(\() h(3*n+2*m) f(+1) h(\)) 533 -818 y(scratch....) e(\(workspace\)) g(DOUBLE) h(PRECISION) f(array,) -1535 922 y(length) i(\() g(maximum) f(\() h(n+m,) g(mxlbuf_\(\)/sDP) d -(+) k(1,) 2442 1025 y(\(nvecsF) e(*) i(n) f(+) g(2) h(*) f(neleU_max) f -(\)) 390 1129 y(*/) 390 1293 y(void) h(mxm88) f(\() h(n,) h(colQ,) e -(mapQ,) g(m,) i(colW,) e(mapW,) g(iwork,) g(work,) h(iptr\)) 629 -1396 y(Integer) e(*n,) i(*mapQ,) f(*m,) h(*mapW,) f(*iwork;) 629 -1500 y(DoublePrecision) d(**colQ,) j(**colW,) g(*work,) g(**iptr;) 390 -1708 y(/***********************) o(****) o(****) o(***) o(****) o(****) -o(***) o(****) o(****) o(***) o(****) o(**) 438 1812 -y(*) 438 1915 y(*) h(Subroutine) e(mxm88) 438 2019 y(*) 533 -2123 y(This) i(subroutine) e(does) h(the) h(matrix) f(multiplication) e -(W) k(<-) f(Q) g(*) h(W) 533 2330 y(where) f(Q) g(is) g(a) h(n) f(x) h -(n) f(symmetric) e(matrix) h(in) i(packed) e(storage) f(format,) 533 -2434 y(and) i(row) g(\(or) g(equivalently) d(column\)) i(distributed,) -533 2538 y(and) h(matrix) f(W) i(is) f(a) g(general) f(n) i(x) f(m) g -(matrix) g(distributed) d(by) j(columns.) 533 2746 y(ARGUMENTS) 533 -2849 y(---------) 533 2953 y(In) g(the) g(following:) 629 -3161 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h(Integer") 629 -3264 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h(DoublePrecision") -629 3472 y(me) 238 b(=) 47 b(this) g(processor's) e(id) i(\(=) g -(mxmynd_\(\)\)) 629 3576 y(nprocs) f(=) h(number) f(of) h(allocated) f -(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 3680 y(nvecsW) e(=) h -(number) f(of) h(entries) f(in) h(mapW) g(equal) f(to) i(me) 1249 -3783 y(\(=) f(count_list\() e(me,) i(mapW,) f(m) i(\)\)) 629 -3887 y(nvecsQ) e(=) h(number) f(of) h(entries) f(in) h(mapQ) g(equal) f -(to) i(me) 1249 3991 y(\(=) f(count_list\() e(me,) i(mapQ,) f(n) i -(\)\)) 629 4095 y(sDP) 190 b(=) 47 b(sizeof\() f(DoublePrecision) e(\)) -533 4302 y(n) k(......) e(\(input\)) g(INTEGER) 963 4406 -y(n) h(is) g(the) g(dimension) f(of) h(the) g(symmetric) e(matrix) h(Q) -533 4614 y(colQ) h(...) g(\(input\)) f(array) g(of) h(pointers) f(to) h -(DoublePrecision,) 1345 4717 y(length) f(\(nvecsQ\)) 963 -4821 y(The) h(part) f(of) h(matrix) g(Q) g(owned) f(by) i(this) e -(processer) f(stored) 963 4925 y(in) i(packed) f(format,) g(i.e.,) g -(colQ[i]) g(points) g(to) h(the) g(diagonal) 963 5029 -y(element) f(of) h(the) g(i-th) f(column) g(\(or) h(equivalently) e -(row\)) h(of) i(Q) 963 5132 y(owned) e(by) h(this) g(processor,) e(i) i -(=) h(0) f(to) g(nvecsQ-1.) 533 5340 y(mapQ) g(...) g(\(input\)) f -(INTEGER) f(array,) h(length) h(\(n\)) p 90 rotate dyy -eop -%%Page: 42 43 -42 42 bop Fs 150 -116 a(42) 3256 b(P) m(eIGS) p Fk 963 -299 a(The) 47 b(i-th) f(column) g(\(or) h(equivalently) e(row\)) h(of) i -(Q) f(is) 963 403 y(owned) f(by) h(processor) f(mapQ[i],) f(i) j(=) f -(0) g(to) h(n-1.) 533 610 y(m) g(......) e(\(input\)) g(INTEGER) 963 -714 y(m) h(is) g(the) g(number) f(of) i(columns) d(in) j(W.) 533 -922 y(colW) f(...) g(\(input/output\)) d(array) i(of) h(pointers) f(to) -h(DoublePrecision,) 1679 1025 y(length) f(\(nvecsW\)) 963 -1233 y(On) h(Entry:) 1058 1337 y(The) g(part) g(of) g(matrix) f(W) h -(owned) g(by) g(this) g(processer) e(stored) 1058 1440 -y(in) i(packed) f(format) h(by) g(columns,) e(i.e.,) i(colW[i]) e -(points) 1058 1544 y(to) i(the) g(first) g(element) e(of) j(the) f -(i-th) f(column) g(of) h(W) 1058 1648 y(owned) g(by) g(this) f -(processor,) f(i) j(=) f(0) h(to) f(nvecsW-1.) 963 1856 -y(On) g(Exit:) 1058 1959 y(The) g(result) f(matrix) g(Q) i(*) f(W) h -(stored) e(in) h(the) g(same) f(manner) h(as) 1058 2063 -y(W) h(on) f(entry.) 533 2271 y(mapW) g(...) g(\(input\)) f(INTEGER) f -(array,) h(length) h(\(m\)) 963 2374 y(The) g(i-th) f(column) g(of) i -(W) f(is) 963 2478 y(owned) f(by) h(processor) f(mapW[i],) f(i) j(=) f -(0) g(to) h(m-1.) 533 2790 y(iwork) f(..) g(\(workspace\)) d(INTEGER) i -(array,) g(length) g(\() i(2*\(n+m\)+nvecsW+nvecsQ) 42 -b(\)) 533 2997 y(work) 47 b(...) g(\(workspace\)) d(DOUBLE) j -(PRECISION) e(array,) 1535 3101 y(length) i(\() g(maximum) f(\() h -(\(nvecsW+1\)*n,) d(mxlbuf_\(\)/sDP) h(+) i(1) h(\)) 533 -3308 y(iptr) f(...) g(\(workspace) e(\)) i(array) g(of) g(pointers) e -(to) i(DoublePrecision,) 1583 3412 y(length) f(\(nvecsW\)) 390 -3620 y(*/) p Fg 150 3813 a(4.4.4) 63 b(TRED2:) e(Householder) 43 -b(reduction) e(of) g(a) f(symmetric) f(matrix) h(to) 464 -3938 y(tridiagonal) h(form) p Fs 275 4131 a(Let) p Fo -31 w(A) p Fs 30 w(b) s(e) 30 b(a) g(symmetric) g(matrix) g(stored) h -(in) e(pac) m(k) m(ed.) 42 b(Then) 30 b(subroutine) e(TRED2) j -(computes) g(the) 150 4240 y(Householder) e(transformation) h(matrix) g -(Q) g(and) g(the) g(tridiagonal) f(matrix) p Fo 30 w(T) p -Fs 30 w(suc) m(h) h(that) p Fo 31 w(A) p Fs 25 w(=) p -Fo 25 w(QTQ) p Fe 3658 4207 a(T) p Fs 275 4375 a(This) c(co) s(de) i -(originates) f(from) g(Shirish) e(Chinc) m(halk) -5 b(ar.) 37 -b(W) -8 b(e) 30 b(ha) m(v) m(e) f(mo) s(di\014ed) c(it) j(to) g(suit) f -(our) g(purp) s(ose.) 150 4485 y(W) -8 b(e) 32 b(are) e(resp) s -(onsible) e(for) i(in) m(tro) s(ducing) e(an) m(y) j(bugs) e(or) i -(errors.) p Fk 390 4614 a(int) 47 b(tred2) f(\(n,) h(vecA,) g(mapA,) f -(Q,) h(mapQ,) f(diag,) h(upperdiag,) e(iwork,) h(work) h(\)) 629 -4717 y(double) f(**vecA,) 714 b(/*) 47 b(matrix) f(to) h(be) g(reduced) -f(*/) 724 4821 y(**Q,) 763 b(/*) 47 b(Householder) e(matrix) h(*/) 724 -4925 y(*diag,) 619 b(/*) 47 b(diagonal) f(elements) f(of) i -(tri-diagonal) e(matrix) h(*/) 724 5029 y(*upperdiag,) 379 -b(/*) 47 b(upper) f(diagonal) g(elements) g(of) h(tri-diagonal) d(ma-) -390 5132 y(trix) j(*/) 724 5236 y(*work;) 523 b(/*) 48 -b(Householder) c(vector) i(\(temp) h(space) f(of) h(size) g(n) g(dou-) -390 5340 y(bles\)) f(*/) p 90 rotate dyy eop -%%Page: 43 44 -43 43 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(43) p Fk 629 403 a(int) 142 b(*n,) 858 -b(/*) 47 b(problem) f(size) h(*/) 724 506 y(*mapA,) 724 -610 y(*mapQ,) 724 714 y(*iwork;) 475 b(/*) 48 b(integer) d(scratch) h -(work) h(space) f(*/) 485 922 y(/*) 438 1129 y(TRED2) g(:) i(reduction) -d(of) i(a) g(real) g(symmetric) e(matrix) h(to) i(tri-diagonal) c(form) -820 1233 y(Uses) i(Householder) f(reductions.) 438 1440 -y(INPUT:) 581 1544 y(n) 238 b(->) 95 b(integer) 46 b(,) h(matrix) g -(size.) 581 1752 y(**A) 142 b(->) 95 b(\(1-D) 47 b(array) f(of) h -(pointers) f(to) h(doubles\)) f(input) g(matrix) g(to) h(be) g -(reduced.) 581 1959 y(mapA) 94 b(->) h(\(integer) 46 -b(array/) g(input\)) g(integer) g(array) g(of) h(length) f(n) 1488 -2063 y(distribution) e(the) 533 2271 y(**Q) 190 b(->) 95 -b(\(1-D) 47 b(array) f(of) h(pointers) f(to) h(doubles\)) f -(Householder) e(matrix) i(to) i(be) f(stored) 1535 2374 -y(in) h(packed) e(storage) g(format) g(as) h(discussed) e(in) i -(section) f(3.2.) 1535 2478 y(currently) g(assumes) g(that) g(mapA[i]) g -(=) h(mapQ[i]) f(for) h(all) g(i) 533 2686 y(mapQ) 381 -b(->) 95 b(\(integer) 45 b(array/) h(input\)) h(integer) e(array) i(of) -g(length) f(n) 1488 2790 y(distribution) e(the) j(same) g(as) g(mapA) -581 2997 y(OUTPUT:) 581 3205 y(diag[0:n-1]) 426 b(->) 95 -b(diagonal) 46 b(elements) f(of) j(the) f(tri-diagonal) d(matrix) 1535 -3308 y(obtained) i(from) h(A) 581 3412 y(upperdiag[1:n-1]) 186 -b(->) 95 b(upper) 47 b(diagonal) e(elements) h(of) h(the) g -(tri-diagonal) d(matrix) 1535 3516 y(obtained) i(from) h(A.) g -(upperdiag[0]) d(is) j(set) g(to) h(0.0) e(and) 1535 -3620 y(upperdiag[1]) f(to) i(upperdiag[n-1]) d(contains) i(the) g -(desired) 1535 3724 y(result) 581 3931 y(**Q) 190 b(->) 95 -b(Householder) 45 b(matrix) h(\() h(generated) e(by) j(Householder) c -(reflections\)) 1106 4035 y(distributed) h(by) i(rows\(or) f(columns\)) -f(in) i(a) h(wrap) e(fashion) g(\(compact\)) 1106 4139 -y(same) h(distribution) d(as) j(mapA) 581 4346 y(mapQ) 333 -b(\(integer) 45 b(array) i(of) g(length) f(n\)) h(current) f(returns) g -(a) h(copy) g(of) g(mapA,) 1106 4450 y(same) g(distribution) d(as) j -(matrixA) 533 4658 y(*/) p Fg 150 4913 a(4.4.5) 63 b(PSTEBZ) 41 -b(eigen) m(v) -7 b(alues) 41 b(of) g(real) g(symmetric) e(tridiagonal) i -(matrix) p Fs 275 5121 a(Giv) m(en) d(a) h(real) f(symmetric) g -(tridiagonal) e(matrix) p Fo 38 w(T) p Fs(.) j(The) f(subroutine) p -Fo 36 w(PSTEBZ) p Fs 37 w(computes) h(the) 150 5230 y(sp) s(eci\014ed) -31 b(eigen) m(v) -5 b(alues) 32 b(of) p Fo 33 w(T) p -Fs 33 w(b) m(y) g(bisection) g(using) f(Sturm) g(sequence.) 48 -b(The) 32 b(syn) m(tax) h(used) e(is) h(not) h(quit) 150 -5340 y(that) e(of) g(curren) m(t) f(LAP) -8 b(A) m(CK) 30 -b(dstebz) h(\() f(notice) h(that) g(the) f(e-arra) m(y) i(is) d -(di\013eren) m(t) h(\).) p 90 rotate dyy eop -%%Page: 44 45 -44 44 bop Fs 150 -116 a(44) 3256 b(P) m(eIGS) p Fk 676 -299 a(subroutine) 45 b(pstebz\() h(job,) h(n,) g(lb,) g(ub,) g(jjjlb,) f -(jjjub,) g(abstol,) g(d,) h(e,) 629 403 y($) 906 b(mapZ,) 47 -b(neigval,) e(nsplit,) h(eval,) g(iblock,) g(isplit,) 629 -506 y($) 906 b(work,) 47 b(iwork,) f(info\)) 676 714 -y(Integer) 571 b(job,) 47 b(n,) g(jjjlb,) f(jjjub,) g(mapZ\(*\),) g -(neigval,) f(nsplit,) 629 818 y($) 906 b(iblock\(*\),) 45 -b(isplit\(*\),) g(iwork\(*\),) g(info) 676 922 y(Double) h(Precision) -141 b(lb,) 47 b(ub,) g(abstol,) f(d\(*\),) g(e\(*\),) h(eval\(*\),) e -(work\(*\)) 390 1025 y(c) 390 1129 y(c) 238 b(Arguments) 46 -b(are) h(the) f(same) h(as) g(for) g(the) g(C) h(call) e(sequence,) f -(but) i(any) 390 1233 y(c) 238 b(reference) 46 b(to) h("pointer) e(to) j -(data) e(type") h(should) f(be) h(interpreted) e(as) 390 -1337 y(c) 238 b("array) 46 b(of) i(data) e(type".) 94 -b(Also,) 46 b(C) i(routine) e(indexing) f("from) i(0) g(to) g(k-1") g -(should) 390 1440 y(c) 238 b(be) 48 b(interpreted) c(as) j(indexing) f -("from) g(1) i(to) f(k") g(in) g(fortran.) 390 1544 y(c) 390 -1708 y(void) g(pstebz_\() e(job,) i(n,) g(lb,) g(ub,) g(jjjlb,) f -(jjjub,) g(abstol,) g(d,) h(e,) g(mapZ,) g(neigval,) 629 -1812 y(nsplit,) e(eval,) i(iblock,) f(isplit,) f(work,) i(iwork,) f -(info\)) 629 2019 y(Integer) 570 b(*job,) 47 b(*n,) g(*jjjlb,) f -(*jjjub,) f(*mapZ,) h(*neigval,) g(*nsplit,) 1345 2123 -y(*iblock,) f(*isplit,) h(*iwork,) f(*info;) 629 2227 -y(DoublePrecision) 425 b(*lb,) 47 b(*ub,) f(*abstol,) g(*d,) h(*e,) g -(*eval,) f(*work;) 390 2434 y(/*) 438 2538 y(*) 95 b(Parallel) 45 -b(version) h(of) h(LAPACK's) f(DSTEBZ.) 438 2746 y(*) 95 -b(This) 47 b(routine) e(is) j(directly) d(callable) h(from) g(both) h -(FORTRAN) f(and) h(C.) 438 2849 y(*) 95 b(The) 47 b(documentation) d -(below) i(always) g(uses) h(FORTRAN) f(array) g(indexing,) 438 -2953 y(*) 95 b(i.e.,) 46 b(1) i(to) f(N,) g(rather) f(then) h(C) g -(array) g(indexing,) e(i.e.,) 94 b(0) 47 b(to) h(N-1.) 438 -3057 y(*) 95 b(This) 47 b(should) f(be) h(kept) f(in) i(mind) e(when) h -(calling) f(this) g(routine) g(from) h(C.) 438 3161 y(*) 95 -b(Also) 47 b(when) f(calling) g(this) h(routine) e(from) i(C) 438 -3264 y(*) 190 b(INTEGER) 46 b(\(array\)) 523 b(means) 47 -b("pointer) e(to) i(Integer") f(and) 438 3368 y(*) 190 -b(DOUBLE) 46 b(PREICISION) f(\(array\)) h(means) h("pointer) e(to) i -(DoublePrecision") 438 3680 y(*) 95 b(Purpose) 438 3783 -y(*) g(=======) 438 3991 y(*) g(PSTEBZ) 46 b(computes) g(the) g -(eigenvalues) f(of) i(a) h(symmetric) d(tridiagonal) 438 -4095 y(*) 95 b(matrix) 46 b(T.) 95 b(The) 47 b(user) f(may) h(ask) g -(for) g(all) g(eigenvalues,) e(all) h(eigenvalues) 438 -4198 y(*) 95 b(in) 47 b(the) g(half-open) e(interval) h(\(LB,) g(UB],) h -(or) g(the) g(JJJLB-th) f(through) g(JJJUB-th) 438 4302 -y(*) 95 b(eigenvalues.) 438 4510 y(*) g(To) 47 b(avoid) f(overflow,) g -(the) h(matrix) f(must) g(be) i(scaled) e(so) h(that) f(its) 438 -4614 y(*) 95 b(largest) 46 b(element) g(is) h(no) g(greater) f(than) g -(overflow**\(1/2\)) e(*) 438 4717 y(*) 95 b(underflow**\(1/4\)) 43 -b(in) k(absolute) f(value,) g(and) h(for) g(greatest) 438 -4821 y(*) 95 b(accuracy,) 45 b(it) i(should) f(not) h(be) h(much) e -(smaller) g(than) h(that.) 438 5029 y(*) 95 b(See) 47 -b(W.) g(Kahan) f("Accurate) g(Eigenvalues) e(of) k(a) f(Symmetric) e -(Tridiagonal) 438 5132 y(*) 95 b(Matrix",) 45 b(Report) i(CS41,) f -(Computer) f(Science) h(Dept.,) g(Stanford) 438 5236 -y(*) 95 b(University,) 45 b(July) h(21,) h(1966.) p 90 rotate -dyy eop -%%Page: 45 46 -45 45 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(45) p Fk 438 299 a(*) 95 b(Arguments) 438 -403 y(*) g(=========) 438 714 y(*) g(JOB) 238 b(\(input\)) 46 -b(INTEGER) 438 818 y(*) 477 b(=) 47 b(1) 95 b(:) 48 b(\("All"\)) 141 -b(all) 47 b(eigenvalues) e(will) h(be) i(found.) 438 -922 y(*) 477 b(=) 47 b(2) 95 b(:) 48 b(\("Value"\)) d(all) i -(eigenvalues) e(in) i(the) g(half-open) e(interval) 438 -1025 y(*) 1288 b(\(LB,) 47 b(UB]) g(will) f(be) h(found.) 438 -1129 y(*) 477 b(=) 47 b(3) 95 b(:) 48 b(\("Index"\)) d(the) i(JJJLB-th) -f(through) f(JJJUB-th) h(eigenvalues) f(\(of) i(the) 438 -1233 y(*) 1288 b(entire) 46 b(matrix\)) g(will) h(be) g(found.) 438 -1440 y(*) 95 b(N) 334 b(\(input\)) 46 b(INTEGER) 438 -1544 y(*) 477 b(The) 47 b(order) f(of) h(the) g(tridiagonal) e(matrix) h -(T.) 95 b(N) 47 b(>=) g(0.) 438 1752 y(*) 95 b(LB) 286 -b(\(input\)) 46 b(DOUBLE) g(PRECISION) 438 1856 y(*) 95 -b(UB) 286 b(\(input\)) 46 b(DOUBLE) g(PRECISION) 438 -1959 y(*) 477 b(If) 47 b(JOB=2,) f(the) h(lower) f(and) h(upper) g -(bounds) f(of) h(the) g(interval) e(to) 438 2063 y(*) 477 -b(be) 47 b(searched) e(for) i(eigenvalues.) 93 b(Eigenvalues) 44 -b(less) j(than) g(or) g(equal) 438 2167 y(*) 477 b(to) 47 -b(LB,) g(or) g(greater) f(than) g(UB,) h(will) g(not) g(be) g -(returned.) 93 b(LB) 47 b(<) h(UB.) 438 2271 y(*) 477 -b(Not) 47 b(referenced) e(if) i(JOB) g(=) g(1) h(or) f(3.) 438 -2478 y(*) 95 b(JJJLB) 142 b(\(input\)) 46 b(INTEGER) 438 -2582 y(*) 95 b(JJJUB) 142 b(\(input\)) 46 b(INTEGER) 438 -2686 y(*) 477 b(If) 47 b(JOB=3,) f(the) h(indices) f(\(in) h(ascending) -e(order\)) h(of) h(the) 438 2790 y(*) 477 b(smallest) 45 -b(and) i(largest) f(eigenvalues) f(to) i(be) g(returned.) 438 -2893 y(*) 477 b(1) 47 b(<=) g(JJJLB) g(<=) g(JJJUB) f(<=) h(N,) h(if) f -(N) g(>) h(0.) 438 2997 y(*) 477 b(Not) 47 b(referenced) e(if) i(JOB) g -(=) g(1) h(or) f(2.) 438 3205 y(*) 95 b(ABSTOL) f(\(input\)) 46 -b(DOUBLE) g(PRECISION) 438 3308 y(*) 477 b(The) 47 b(absolute) e -(tolerance) g(for) i(the) g(eigenvalues.) 92 b(An) 48 -b(eigenvalue) 438 3412 y(*) 477 b(\(or) 47 b(cluster\)) e(is) i -(considered) e(to) j(be) f(located) f(if) h(it) g(has) g(been) 438 -3516 y(*) 477 b(determined) 45 b(to) i(lie) g(in) g(an) g(interval) f -(whose) g(width) g(is) i(ABSTOL) e(or) 438 3620 y(*) 477 -b(less.) 94 b(If) 47 b(ABSTOL) f(is) h(less) g(than) g(or) g(equal) f -(to) h(zero,) g(then) f(ULP*|T|) 438 3724 y(*) 477 b(will) 46 -b(be) i(used,) e(where) g(|T|) h(means) g(the) f(1-norm) h(of) g(T.) 438 -3931 y(*) 477 b(Eigenvalues) 44 b(will) j(be) g(computed) f(most) g -(accurately) f(when) i(ABSTOL) f(is) 438 4035 y(*) 477 -b(set) 47 b(to) g(twice) f(the) h(underflow) e(threshold) h -(2*DLAMCH\('S'\),) e(not) i(zero.) 438 4242 y(*) 95 b(D) 334 -b(\(input\)) 46 b(DOUBLE) g(PRECISION) f(array,) h(dimension) f(\(N\)) -438 4346 y(*) 477 b(The) 47 b(n) g(diagonal) f(elements) f(of) i(the) g -(tridiagonal) e(matrix) h(T.) 438 4554 y(*) 95 b(E) 334 -b(\(input\)) 46 b(DOUBLE) g(PRECISION) f(array,) h(dimension) f(\(N\)) -438 4658 y(*) 477 b(The) 47 b(first) f(element) g(of) h(E,) g(E\(1\),) g -(is) g(junk,) f(the) h(rest) g(of) g(E,) g(E\(2:N\),) 438 -4761 y(*) 477 b(contains) 45 b(the) i(\(n-1\)) g(off-diagonal) d -(elements) i(of) h(the) g(tridiagonal) 438 4865 y(*) 477 -b(matrix) 46 b(T.) 438 5073 y(*) 95 b(MAPZ) 190 b(\(input\)) 46 -b(INTEGER) f(array,) h(dimension) g(\(N\)) 438 5176 y(*) 477 -b(A) 47 b(list) g(of) g(the) g(ids) g(of) g(the) g(processors) e(which) -h(are) h(to) g(participate) 438 5280 y(*) 477 b(in) 47 -b(the) g(eigenvalue) e(computation.) p 90 rotate dyy -eop -%%Page: 46 47 -46 46 bop Fs 150 -116 a(46) 3256 b(P) m(eIGS) p Fk 438 -403 a(*) 95 b(NEIGVAL) 46 b(\(output\)) f(INTEGER) 438 -506 y(*) 477 b(The) 47 b(actual) f(number) g(of) h(eigenvalues) e -(found.) h(0) h(<=) g(NEIGVAL) f(<=) h(N.) 438 714 y(*) 95 -b(NSPLIT) f(\(output\)) 45 b(INTEGER) 438 818 y(*) 477 -b(The) 47 b(number) f(of) h(diagonal) e(blocks) i(in) g(the) g(matrix) f -(T.) 438 922 y(*) 477 b(1) 47 b(<=) g(NSPLIT) f(<=) i(N.) 438 -1129 y(*) 95 b(EVAL) 190 b(\(output\)) 45 b(DOUBLE) h(PRECISION) g -(array,) g(dimension) f(\(N\)) 438 1233 y(*) 477 b(On) 47 -b(exit,) f(the) h(first) g(NEIGVAL) e(elements) h(of) h(EVAL) g(will) f -(contain) g(the) 438 1337 y(*) 477 b(eigenvalues.) 92 -b(\(PSTEBZ) 46 b(may) h(use) g(the) f(remaining) g(N-NEIGVAL) f -(elements) h(as) 438 1440 y(*) 477 b(workspace.\)) 438 -1544 y(*) g(The) 47 b(eigenvalues) d(will) j(be) g(grouped) f(by) h -(split-off) e(block) i(\(see) f(IBLOCK,) 438 1648 y(*) 477 -b(ISPLIT\)) 46 b(and) g(ordered) g(from) h(smallest) e(to) j(largest) d -(within) i(the) f(block.) 438 1856 y(*) 95 b(IBLOCK) f(\(output\)) 45 -b(INTEGER) h(array,) g(dimension) f(\(N\)) 438 1959 y(*) 477 -b(At) 47 b(each) g(row/column) e(j) i(where) f(E\(j\)) h(is) g(zero) g -(or) g(small,) f(the) 438 2063 y(*) 477 b(matrix) 46 -b(T) h(is) g(considered) e(to) j(split) e(into) h(a) g(block) f -(diagonal) 438 2167 y(*) 477 b(matrix.) 93 b(On) 47 b(exit,) g(if) g -(INFO) g(=) g(0,) g(IBLOCK\(i\)) f(specifies) f(to) i(which) 438 -2271 y(*) 477 b(block) 46 b(\(from) g(1) i(to) f(the) g(number) f(of) h -(blocks\)) f(the) h(eigenvalue) e(EVAL\(i\)) 438 2374 -y(*) 477 b(belongs.) 93 b(\(DSTEBZ) 46 b(may) h(use) g(the) g -(remaining) e(N-NEIGVAL) g(elements) h(as) 438 2478 y(*) 477 -b(workspace.\)) 438 2686 y(*) 95 b(ISPLIT) f(\(output\)) 45 -b(INTEGER) h(array,) g(dimension) f(\(N\)) 438 2790 y(*) 477 -b(The) 47 b(splitting) e(points,) h(at) h(which) f(T) i(breaks) e(up) h -(into) g(submatrices.) 438 2893 y(*) 477 b(The) 47 b(first) f -(submatrix) f(consists) h(of) h(rows/columns) d(1) k(to) f -(ISPLIT\(1\),) 438 2997 y(*) 477 b(the) 47 b(second) f(of) h -(rows/columns) d(ISPLIT\(1\)+1) h(through) h(ISPLIT\(2\),) 438 -3101 y(*) 477 b(etc.,) 46 b(and) h(the) g(NSPLIT-th) e(consists) h(of) h -(rows/columns) 438 3205 y(*) 477 b(ISPLIT\(NSPLIT-1\)+1) 43 -b(through) i(ISPLIT\(NSPLIT\)=N.) 438 3308 y(*) 477 b(\(Only) 46 -b(the) h(first) f(NSPLIT) g(elements) g(will) h(actually) e(be) i -(used,) g(but) 438 3412 y(*) 477 b(since) 46 b(the) h(user) g(cannot) f -(know) g(a) i(priori) e(what) h(value) f(NSPLIT) g(will) 438 -3516 y(*) 477 b(have,) 46 b(N) i(words) e(must) h(be) g(reserved) e -(for) i(ISPLIT.\)) 438 3724 y(*) 95 b(WORK) 190 b(\(workspace\)) 44 -b(DOUBLE) j(PRECISION) e(array,) h(dimension) f(\() j(\)) 438 -3931 y(*) 95 b(IWORK) 142 b(\(workspace\)) 44 b(INTEGER) i(array,) g -(dimension) g(\() h(\)) 438 4139 y(*) 95 b(INFO) 190 -b(\(output\)) 45 b(INTEGER) 438 4346 y(*) 477 b(PSTEBZ) 46 -b(attempts) f(to) j(return) e(the) h(same) f(INFO) h(on) g(all) g -(processors) e(in) i(MAPZ.) 438 4450 y(*) 477 b(Currently,) 45 -b(however,) g(if) i(the) g(input) g(data) f(is) i(invalid,) d(-50) i(<) -g(INFO) g(<) h(0,) 438 4554 y(*) 477 b(then) 46 b(INFO) h(will) g(be) g -(different) e(on) i(different) f(processors.) 438 4761 -y(*) 477 b(=) 47 b(0:) 143 b(successful) 45 b(exit) 438 -4969 y(*) 477 b(<) 47 b(0) h(&) 438 5073 y(*) 477 b(>) 47 -b(-50:) g(if) g(INFO) g(=) g(-i,) g(the) g(i-th) g(argument) e(had) i -(an) g(illegal) f(value) 438 5280 y(*) 477 b(=) 47 b(-51:) g(Then) f -(the) h(input) g(data) f(was) h(not) g(the) g(same) g(on) g(all) g -(processors) e(in) i(MAPZ) p 90 rotate dyy eop -%%Page: 47 48 -47 47 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(47) p Fk 438 403 a(*) 477 b(>) 47 -b(0:) 143 b(some) 46 b(or) i(all) f(of) g(the) g(eigenvalues) d(failed) -i(to) i(converge) d(or) 438 506 y(*) 811 b(were) 46 b(not) h(computed,) -f(or) h(they) f(were) h(computed) f(incorrectly:) 438 -714 y(*) 811 b(=1:) 47 b(routine) f(DSTEBZ3) f(returned) h(a) h -(non-zero) f(info.) 94 b(Meaning) 438 818 y(*) 1002 b(that) 46 -b(on) i(one) e(or) i(more) e(processors) f(some) i(or) g(all) g(of) g -(the) 438 922 y(*) 1002 b(eigenvalues) 44 b(failed) j(to) g(converge) e -(or) i(were) g(not) g(computed) 438 1025 y(*) 1002 b(In) 47 -b(this) g(case) f(the) h(processor) e(with) i(a) g(non-zero) f(info) h -(from) 438 1129 y(*) 1002 b(DSETBZ3) 46 b(prints) g(and) h(error) f -(message) g(to) h(stderr.) 438 1337 y(*) 811 b(=2:) 47 -b(NSPLIT) f(and/or) g(ISPLIT) g(were) h(not) g(the) f(same) h(on) g -(all) g(processors) 438 1544 y(*) 811 b(=3:) 47 b(Relative) e -(processor) h(i) h(computed) f(an) h(eigenvalue) e(larger) h(than) 438 -1648 y(*) 1002 b(the) 47 b(smallest) e(eigenvalue) g(computed) h(by) h -(relative) e(pro-) 390 1752 y(cessor) h(i+1) 438 1856 -y(*) 1002 b(for) 47 b(some) f(i.) 95 b(This) 47 b(should) f(not) h -(occur) f(using) h(the) f(cur-) 390 1959 y(rent) h(algorithms.) 438 -2167 y(*) 811 b(=4:) 47 b(The) g(number) f(of) h(eigenvalues) e(found) h -(in) h(a) h(block) e(of) h(T) h(is) f(bigger) 438 2271 -y(*) 1002 b(then) 46 b(the) h(dimension) f(of) h(the) g(block.) 438 -2582 y(*) 715 b(In) 48 b(theory) e(INFO) g(=) i(2,) f(3,) g(or) g(4) h -(should) e(never) g(occur.) 94 b(If) 47 b(they) g(do) g(occur) 438 -2686 y(*) 715 b(then) 47 b(DSTEBZ3) f(failed) g(to) h(correctly) e -(compute) h(the) h(requested) e(eigenvalues.) 438 2893 -y(*) 715 b(Note) 47 b(that) g(DSTEBZ3) e(is) j(a) f(modification) e(of) -i(LAPACK's) e(DSTEBZ.) 94 b(The) 438 2997 y(*) 715 b(modifications) 45 -b(had) h(to) i(be) f(made) f(to) i(avoid) e(gettings) g(INFOs) g(like) h -(3) g(and) g(4.) 438 3205 y(*/) p Fg 150 3440 a(4.4.6) 63 -b(PSTEIN:) 40 b(eigen) m(v) m(ectors) h(of) g(real) f(symmetric) g -(tridiagonal) h(matrix) p Fs 275 3638 a(Giv) m(en) 23 -b(a) i(real) e(symmetric) g(tridiagonal) g(matrix) p -Fo 23 w(T) p Fs 24 w(and) g(some) i(of) f(its) f(eigen) m(v) -5 -b(alues.) 39 b(The) 23 b(subroutine) p Fo 150 3747 a(PSTEBZ) p -Fs 40 w(computes) 42 b(the) g(sp) s(eci\014ed) e(eigen) m(v) m(ectors) j -(of) p Fo 42 w(T) p Fs(.) f(The) f(syn) m(tax) h(used) f(is) g(not) h -(quit) f(that) h(of) 150 3857 y(curren) m(t) 30 b(LAP) -8 -b(A) m(CK) 31 b(dstein) e(\() i(notice) f(that) h(the) g(e-arra) m(y) g -(is) f(di\013eren) m(t) g(\).) p Fk 390 3991 a(void) 47 -b(pstein) f(\() h(n,) g(dd,) g(ee,) g(meigval,) f(eval,) g(iblock,) g -(nsplit,) g(isplit,) 629 4095 y(mapZ,) g(vecZ,) g(ddwork,) g(iiwork,) g -(ppiwork,) g(info) g(\)) 629 4302 y(Integer) 570 b(*n,) 47 -b(*meigval,) f(*iblock,) f(*nsplit,) h(*isplit,) f(*mapZ,) 1535 -4406 y(*iiwork,) h(*info,) g(**ppiwork;) 629 4510 y(DoublePrecision) 377 -b(*dd,) 47 b(*ee,) g(*eval,) f(**vecZ,) g(*ddwork;) 485 -4717 y(/*) 533 4925 y(*) i(Driver) e(to) h(compute) f(eigenvectors) e -(of) j(a) h(symmetric) d(tridiagonal) g(matrix.) 533 -5029 y(*) j(Basically) d(a) i(parallel) f(version) g(of) h(LAPACK's) e -(DSTEIN.) 533 5236 y(*) 95 b(n) 48 b(.........) d(The) i(dimension) e -(of) i(the) g(matrix.) p 90 rotate dyy eop -%%Page: 48 49 -48 48 bop Fs 150 -116 a(48) 3256 b(P) m(eIGS) p Fk 533 -299 a(*) 95 b(dd) 48 b(........) d(The) i(diagonal) f(of) h(the) g -(matrix.) 533 506 y(*) 95 b(ee) 48 b(........) d(The) i(off-diagonal) d -(of) k(the) f(matrix.) 93 b(ee[0]) 46 b(is) i(junk,) e(the) 533 -610 y(*) 668 b(actual) 46 b(off-diagonal) f(starts) h(at) h(ee[1].) 533 -818 y(*) 95 b(meigval) 46 b(...) h(\(input\)) f(Integer) 533 -922 y(*) 668 b(The) 47 b(number) f(of) h(eigenvalues) e(found) 533 -1129 y(*) 95 b(eval) 47 b(......) f(\(input\)) g(DoublePrecision) e -(array,) i(length) g(\(neigval\)) 533 1233 y(*) 668 b(The) 47 -b(actual) f(eigenvalues.) 92 b(Sorted) 46 b(by) i(split) e(of) h -(block,) 533 1337 y(*) 668 b(and) 47 b(within) f(a) i(block) e(sorted) g -(by) h(value.) 533 1544 y(*) 95 b(iblock) 46 b(....) h(\(input\)) f -(Integer) g(array,) g(length) g(\(neigval\)) 533 1648 -y(*) 668 b(Array) 46 b(from) h(pstebz.) 533 1856 y(*) 95 -b(nsplit) 46 b(....) h(\(input\)) f(Integer) 533 1959 -y(*) 668 b(The) 47 b(number) f(of) h(split) g(points) f(in) h(the) g -(tridiagonal) e(matrix.) 533 2063 y(*) 668 b(From) 47 -b(pstebz.) 533 2271 y(*) 95 b(isplit) 46 b(....) h(\(input\)) f -(Integer) g(array,) g(length) g(\(nsplit\)) 533 2374 -y(*) 668 b(Array) 46 b(from) h(pstebz.) 533 2582 y(*) 95 -b(mapZ) 190 b(\(input/output\)) 44 b(INTEGER) i(array,) g(dimension) f -(\(meigval\)) 533 2686 y(*) 477 b(On) 47 b(entry:) 533 -2893 y(*) 477 b(mapZ\(i\)) 46 b(=) h(the) g(id) h(of) f(a) g(processor) -e(which) i(has) g(room) f(for) h(the) 533 2997 y(*) 954 -b(i-th) 47 b(eigenvector,) e(i) i(=) g(0) h(to) f(meigval-1) 533 -3101 y(*) 477 b(On) 47 b(exit:) 533 3205 y(*) 573 b(mapZ\(i\)) 45 -b(=) j(the) f(id) g(of) g(the) g(processor) e(which) i(actually) e -(owns) i(the) g(i-) 390 3308 y(th) 533 3412 y(*) 1050 -b(eigenvector,) 44 b(i) k(=) f(0) h(to) f(meigval-1.) 533 -3620 y(*) 477 b(The) 47 b(value) f(of) i(mapZ) e(on) h(exit) g(may) g -(be) g(different) e(then) i(on) g(entry.) 533 3827 y(*) 95 -b(vecZ) 190 b(\(output\)) 46 b(array) g(of) h(pointers) f(to) h -(DoublePrecision) d(\(DoublePre-) 390 3931 y(cision) i(**\)) 533 -4035 y(*) 907 b(dimension) 45 b(\() i(nvecsZ) g(\)) 533 -4139 y(*) 477 b(On) 47 b(entry:) 533 4242 y(*) 620 b(vecZ[i],) 46 -b(i) h(=) h(0) f(to) g(nvecsZ-1,) f(should) g(point) g(to) h(an) h -(array) e(of) h(length) f(n.) 533 4450 y(*) 477 b(On) 47 -b(exit:) 533 4658 y(*) 573 b(vecZ[i],) 45 b(i) j(=) f(0) h(to) f -(nvecsZ-1,) e(points) h(to) h(the) g(i-th) g(eigenvector) 533 -4761 y(*) 573 b(\(as) 47 b(determined) e(by) i(the) g(exit) f(values) g -(in) i(mapZ\)) e(owned) g(by) h(this) 533 4865 y(*) 573 -b(processor.) 533 5073 y(*) g(The) 47 b(eigenvectors) d(are) j -(normalized) e(such) i(that:) f(Z'*) h(Z) g(=) h(I.) p -90 rotate dyy eop -%%Page: 49 50 -49 49 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(49) p Fk 533 299 a(*) 95 b(ddwork) 46 -b(....) h(\(workspace\)) e(DoublePrecision) e(array) 533 -403 y(*) 95 b(iiwork) 46 b(....) h(\(workspace\)) e(Integer) h(array,) -533 506 y(*) 95 b(ppiwork) 46 b(...) h(\(workspace\)) e(array) h(of) h -(pointers) f(to) h(Integer,) 533 818 y(*) 95 b(INFO) 47 -b(...) g(\(output\)) e(INTEGER) 533 1025 y(*) 525 b(PSTEIN) 46 -b(attempts) g(to) h(return) f(the) h(same) f(INFO) h(on) g(all) g -(processors) e(in) i(MAPZ.) 533 1129 y(*) 525 b(Currently,) 45 -b(however,) g(if) j(the) f(input) f(data) h(is) g(invalid,) e(-50) i(<) -h(INFO) e(<) i(0,) 533 1233 y(*) 525 b(then) 47 b(INFO) f(will) h(be) g -(different) e(on) i(different) f(processors.) 533 1440 -y(*) 525 b(=) 47 b(0:) 143 b(successful) 45 b(exit) 533 -1648 y(*) 525 b(-50) 47 b(<=) g(INFO) g(<) g(0:) 533 -1752 y(*) 859 b(Then) 47 b(the) g(\(-INFO\)-th) e(argument) g(had) i -(an) g(illegal) f(value) 533 1959 y(*) 525 b(=) 47 b(-51:) g(Then) g -(the) g(input) f(data) h(was) f(not) h(the) g(same) g(on) g(all) g -(proces-) 390 2063 y(sors) g(in) g(MAPZ) 533 2271 y(*) 525 -b(0) 47 b(<) h(INFO) e(<=) i(MEIGVAL:) 533 2374 y(*) 859 -b(Then) 47 b(the) g(INFO-th) e(eigenvector) g(failed) h(to) h -(converge,) f(but) h(all) 533 2478 y(*) 859 b(lower) 46 -b(numbered) g(eigenvectors) e(did) j(converge.) 533 2686 -y(*) 525 b(N) 47 b(<) h(INFO:) 533 2790 y(*) 859 b(Then) 47 -b(the) g(residual,) 533 2893 y(*) 859 b(res) 47 b(==) g(\() h(max_i) e -(|T) h(z_i-lamba_i) e(z_i) i(|) g(/\() g(eps) g(|T|\)) g(\),) 533 -2997 y(*) 859 b(for) 47 b(the) g(tridiagonal) e(eigenproblem) f(was) j -(excessively) e(large.) 533 3101 y(*) 859 b(In) 47 b(particular,) e -(INFO) i(=) g(N) g(+) h(\(Integer\)) d(log10\() h(res) h(\)) 533 -3205 y(*/) p Fg 150 3440 a(4.4.7) 63 b(Residual) 41 b(and) g -(Orthogonalit) m(y) g(c) m(hec) m(ks) p Fs 275 3638 a(This) 35 -b(section) j(describ) s(es) d(routines) i(for) g(computing) f -(residuals) f(for) i(the) h(v) -5 b(arious) 36 b(eigenproblems,) 150 -3748 y(and) 31 b(for) g(testing) h(the) f(orthogonalit) m(y) h(of) g -(computed) f(eigen) m(v) m(ectors.) 46 b(The) 31 b(F) -8 -b(ortran) 32 b(77) g(calling) e(syn) m(tax) 150 3857 -y(is) c(giv) m(en) h(in) e(v) m(ery) i(little) f(detail.) 38 -b(Most) 28 b(of) f(the) g(detail) f(and) g(descriptions) f(of) i(the) g -(routines) e(are) j(included) 150 3967 y(with) h(the) i(C) f(calling) e -(syn) m(tax.) 275 4107 y(The) h(F) -8 b(ortran) 31 b(77) h(syn) m(tax) f -(is:) p Fk 629 4241 a(SUBROUTINE) 45 b(tresid\() g(n,) j(m,) f(d,) g -(e,) g(colZ,) g(mapZ,) f(eval,) g(iwork,) g(work,) h(res,) f(info\)) 629 -4345 y(Integer) 427 b(n,) 47 b(m,) h(mapZ\(*\),) d(iwork\(*\),) g(info) -629 4449 y(DoublePrecision) e(d\(*\),) k(e\(*\),) f(colZ\(*\),) g -(eval\(*\),) f(work\(*\),) h(res) 629 4583 y(SUBROUTINE) f(resid\() h -(n,) h(colA,) f(mapA,) h(m,) g(colZ,) f(mapZ,) h(eval,) f(iwork,) g -(work,) 1488 4687 y(res,) g(info\)) 629 4791 y(Integer) 427 -b(n,) 47 b(mapA\(*\),) f(m,) h(mapZ\(*\),) f(iwork\(*\),) f(info) 629 -4894 y(DoublePrecision) e(colA\(*\),) j(colZ\(*\),) f(eval\(*\),) h -(work\(*\),) f(res) 390 5102 y(C) 95 b(Note) 47 b(that) f(the) h(C) h -(routine) e(resid) g(has) h(one) g(more) f(argument,) g(ibuffptr,) f -(than) i(the) 390 5206 y(C) 95 b(Fortran) 46 b(77) h(call) g(syntax) f -(listed) g(here.) 629 5340 y(SUBROUTINE) f(residual\() g(n,) i(colA,) f -(mapA,) h(colB,) f(mapB,) h(m,) g(colZ,) f(mapZ,) g(eval,) p -90 rotate dyy eop -%%Page: 50 51 -50 50 bop Fs 150 -116 a(50) 3256 b(P) m(eIGS) p Fk 1631 -299 a(iwork,) 46 b(work,) g(res,) h(info\)) 629 403 y(Integer) 427 -b(n,) 47 b(mapA\(*\),) f(mapB\(*\),) g(m,) h(mapZ\(*\),) e(iwork\(*\),) -h(info) 629 506 y(DoublePrecision) d(colA\(*\),) j(colB\(*\),) f -(colZ\(*\),) h(eval\(*\),) f(work\(*\),) h(res) 390 714 -y(C) 95 b(Note) 47 b(that) f(the) h(C) h(routine) e(residual) f(has) i -(one) g(more) g(argument,) e(ibuffptr,) g(than) i(the) 390 -818 y(C) 95 b(Fortran) 46 b(77) h(call) g(syntax) f(listed) g(here.) 629 -945 y(SUBROUTINE) f(ortho\() h(n,) h(m,) g(colZ,) f(mapZ,) h(iwork,) f -(work,) g(ort,) h(info\)) 629 1049 y(Integer) e(n,) j(m,) f(mapZ\(*\),) -e(iwork\(*\),) h(info) 629 1153 y(DoublePrecision) d(colZ\(*\),) j -(work\(*\),) 93 b(ort) 390 1360 y(C) i(Note) 47 b(that) f(the) h(C) h -(routine) e(ortho) g(has) h(one) g(more) f(argument,) g(ibuffptr,) f -(than) i(the) 390 1464 y(C) 95 b(Fortran) 46 b(77) h(call) g(syntax) f -(listed) g(here.) 629 1592 y(SUBROUTINE) f(bortho\() g(n,) j(colB,) e -(mapB,) g(m,) i(colZ,) e(mapZ,) g(iwork,) g(work,) h(ort,) f(info\)) 629 -1695 y(Integer) 427 b(n,) 47 b(mapB\(*\),) f(m,) h(mapZ\(*\),) f -(iwork\(*\),) f(info) 629 1799 y(DoublePrecision) e(colB\(*\),) j -(colZ\(*\),) f(work\(*\),) 94 b(ort) 390 2007 y(C) h(Note) 47 -b(that) f(the) h(C) h(routine) e(bortho) g(has) h(one) g(more) f -(argument,) f(ibuffptr,) h(than) g(the) 390 2110 y(C) 95 -b(Fortran) 46 b(77) h(call) g(syntax) f(listed) g(here.) p -Fs 275 2244 a(The) 28 b(input) f(argumen) m(ts) j(for) e(the) i(ab) s -(o) m(v) m(e) g(routines) e(are) h(the) h(same) f(as) g(in) f(the) h(C) -g(co) s(des) g(listed) f(b) s(elo) m(w) 150 2353 y(except) h(that) f -(one) g(c) m(hanges) h(the) f(argumen) m(ts) g(of) g(t) m(yp) s(e) p -Fk 28 w(") p Fs(1-D) h(arra) m(y) g(of) f(p) s(oin) m(ters) e(to) j -(DoublePrecision) p Fk(") p Fs(,) 150 2463 y(i.e.,) k(ro) m(wQ,) f -(colW,) h(etc,) g(to) g(t) m(yp) s(e) p Fk 32 w(") p -Fs(1-D) g(arra) m(y) g(of) f(double) e(precision) h(n) m(um) m(b) s -(ers) p Fk(") p Fs 30 w(and) g(store) i(the) f(data) 150 -2572 y(in) 26 b(these) j(arra) m(ys) f(using) e(the) i(pac) m(k) m(ed) h -(storage) g(format) f(describ) s(ed) e(previously) -8 -b(.) 38 b(The) 27 b(C) h(co) s(de) g(describ) s(es) 150 -2682 y(arra) m(ys) j(of) f(length) g(n) g(with) f(indices) f(of) j(0) g -(to) g(n-1,) g(for) f(fortran) g(usage) h(the) f(indices) f(should) f -(b) s(e) i(1) h(to) g(n.) 275 2815 y(The) d(w) m(ork) h(arra) m(ys) h -(for) e(the) i(F) -8 b(ortran) 29 b(77) h(co) s(des) f(m) m(ust) g(b) s -(e) g(somewhat) g(larger) g(than) f(listed) g(b) s(elo) m(w) g(in) 150 -2925 y(the) i(C) f(calling) f(syn) m(tax.) 41 b(In) 29 -b(particular,) f(let) i(ME,) g(b) s(e) f(the) h(id) e(of) i(a) g(pro) s -(cessor,) f(and) g(let) h(n) m(v) m(ecsX) h(b) s(e) e(the) 150 -3034 y(n) m(um) m(b) s(er) c(of) h(en) m(tries) f(in) g(arra) m(y) h -(mapX) g(equal) f(to) i(ME,) f(where) g(X) g(=) f(Q,W,U,) i(or) f(F.) g -(Then,) h(on) e(pro) s(cessor) 150 3144 y(ME) 31 b(the) f(extra) h -(memory) f(requiremen) m(ts) g(for) g(the) h(F) -8 b(ortran) 31 -b(77) g(routines) e(are:) p Fq 199 3277 a(\000) p Fs -60 w(TRESID:) h(increase) g(size) g(of) h(w) m(ork) f(b) m(y) g(n) m(v) -m(ecsZ) p Fk(+) p Fs(1) p Fq 199 3411 a(\000) p Fs 60 -w(RESID:) g(increase) g(size) h(of) f(w) m(ork) h(b) m(y) f(n) m(v) m -(ecsA) p Fk(+) p Fs(3*n) m(v) m(ecsZ) p Fk(+) p Fs(4) p -Fq 199 3544 a(\000) p Fs 60 w(RESIDUAL:) g(increase) g(size) h(of) f(w) -m(ork) h(b) m(y) f(n) m(v) m(ecsA) p Fk(+) p Fs(n) m(v) m(ecsB) p -Fk(+) p Fs(4*n) m(v) m(ecsZ) p Fk(+) p Fs(6) p Fq 199 -3677 a(\000) p Fs 60 w(OR) -8 b(THO:) 30 b(increase) g(size) h(of) f(w) -m(ork) h(b) m(y) f(2*n) m(v) m(ecsZ) p Fk(+) p Fs(2) p -Fq 199 3810 a(\000) p Fs 60 w(BOR) -8 b(THO:) 31 b(increase) f(size) g -(of) g(w) m(ork) h(b) m(y) f(n) m(v) m(ecsB) p Fk(+) p -Fs(4*n) m(v) m(ecsZ) p Fk(+) p Fs(5) 275 3967 y(The) f(C) h(syn) m(tax) -h(is:) p Fk 390 4095 a(void) 47 b(tresid\() e(n,) j(m,) f(d,) g(e,) g -(colZ,) g(mapZ,) f(eval,) g(iwork,) g(work,) h(res,) f(info\)) 629 -4198 y(Integer) f(*n,) i(*m,) g(*mapZ,) f(*iwork,) g(*info;) 629 -4302 y(DoublePrecision) d(*d,) k(*e,) g(**colZ,) f(*eval,) g(*work,) g -(*res;) 390 4510 y(/*) 724 4614 y(this) h(subroutine) e(computes) g -(the) i(residual) 724 4821 y(res) g(=) g(max_\(i\)) f(|) i(T) f -(z_\(i\)) g(-) g(\\lambda_\(i\)) e(z_\(i\)) h(|/\() h(|) g(T) h(|) f(*) -h(ulp) f(\)) 724 5029 y(where) f(T) i(is) f(an) g(n-by-n) 94 -b(tridiagonal) 45 b(matrix,) 772 5132 y(\() i(\\lambda_\(i\)) e(,) i -(z_\(i\)) g(\)) g(is) g(a) h(standard) d(eigen-pair,) g(and) 724 -5236 y(ULP) i(=) g(\(machine) f(precision\)) f(*) i(\(machine) f -(base\)) p 90 rotate dyy eop -%%Page: 51 52 -51 51 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(51) p Fk 724 299 a(|T|) 47 b(is) g(the) g(1-norm) f -(of) h(T) 724 403 y(|T) g(z_\(i\)) g(....) f(|) i(is) f(the) g -(infinity-norm) 724 506 y(res) g(is) g(reasonable) e(if) i(it) h(is) f -(of) g(order) f(about) h(50) g(or) g(less.) 533 714 y(Arguments) 533 -818 y(---------) 533 922 y(In) g(the) g(following:) 629 -1129 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h(Integer") 629 -1233 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h(DoublePrecision") -629 1440 y(me) 238 b(=) 47 b(this) g(processor's) e(id) i(\(=) g -(mxmynd_\(\)\)) 629 1544 y(nprocs) f(=) h(number) f(of) h(allocated) f -(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 1648 y(nvecsZ) e(=) h -(number) f(of) h(entries) f(in) h(mapZ) g(equal) f(to) i(me) 1249 -1752 y(\(=) f(count_list\() e(me,) i(mapZ,) f(n) i(\)\)) 629 -1856 y(sDP) 190 b(=) 47 b(sizeof\() f(DoublePrecision) e(\)) 533 -2167 y(n.......) i(\(input\)) g(INTEGER) 963 2271 y(dimension) f(of) i -(the) g(matrix) f(T) 533 2478 y(m.......) g(\(input\)) g(INTEGER) 963 -2582 y(number) g(of) h(eigenvalues/eigenvectors) 533 -2790 y(d.......) f(\(input\)) g(DOUBLE) g(PRECISION) f(array,) h -(length) g(\(n\)) 963 2893 y(diagonal) f(of) i(T) 533 -3101 y(e.......) f(\(input\)) g(DOUBLE) g(PRECISION) f(array,) h -(length) g(\(n\)) 963 3205 y(e[0]) g(=) i(junk,) 963 -3308 y(e[1:n-1]) d(=) j(sub-diagonal) c(of) j(T) 1392 -3412 y(=) h(super-diagonal) c(of) j(T) 533 3620 y(colZ) g(...) g -(\(input\)) f(array) g(of) h(pointers) f(to) h(DoublePrecision,) 1345 -3724 y(length) f(\(nvecsZ\)) 963 3827 y(The) h(part) f(of) h(matrix) g -(Z) g(owned) f(by) i(this) e(processer,) f(stored) 963 -3931 y(in) i(packed) f(format,) g(i.e.,) g(colZ[i]) g(points) g(to) h -(the) g(start) 963 4035 y(of) g(the) g(i-th) f(column) h(of) g(matrix) f -(Z) h(owned) g(by) g(this) 963 4139 y(processor,) e(i) i(=) h(0) f(to) g -(nvecsZ-1.) 533 4346 y(mapZ) g(...) g(\(input\)) f(INTEGER) f(array,) h -(length) h(\(m\)) 963 4450 y(The) g(i-th) f(column) g(of) i(matrix) e -(Z) h(is) g(owned) g(by) g(processor) 963 4554 y(mapZ[i],) e(i) j(=) f -(0) h(to) f(m-1.) 533 4761 y(eval....) f(\(input\)) g(DOUBLE) g -(PRECISION) f(array,) h(length) g(\(m\)) 963 4865 y(the) h(eigenvalues) -533 5073 y(iwork...) f(\(workspace\)) e(INTEGER) i(array,) g -(length\(m\)) 533 5280 y(work....) g(\(workspace\)) e(DOUBLE) j -(PRECISION) e(array,) p 90 rotate dyy eop -%%Page: 52 53 -52 52 bop Fs 150 -116 a(52) 3256 b(P) m(eIGS) p Fk 1535 -299 a(length\() 46 b(mxlbuf_\(\)) g(/) h(sDP) g(+) g(1) h(\)) 533 -506 y(res.....) e(\(output\)) f(INTEGER) 963 610 y(the) i(residual) e -(described) g(above.) 533 818 y(info....) h(\(output\)) f(INTEGER) 963 -922 y(=) i(0,) g(not) g(currently) f(used) 390 1025 y(*/) 390 -1189 y(void) h(resid\() f(n,) h(colA,) f(mapA,) h(m,) g(colZ,) f(mapZ,) -h(eval,) f(ibuffptr,) f(iwork,) h(work,) 963 1293 y(res,) g(info\)) 629 -1396 y(Integer) f(*n,) i(*mapA,) f(*m,) h(*mapZ,) f(*iwork,) g(*info;) -629 1500 y(DoublePrecision) d(**colA,) j(**colZ,) g(*eval,) g -(**ibuffptr,) f(*work,) h(*res;) 390 1708 y(/*) 533 1812 -y(this) h(subroutine) e(computes) g(the) i(residual) 533 -2019 y(res) g(=) h(max_\(i\)) d(|) j(A) f(z_\(i\)) g(-) g -(\\lambda_\(i\)) e(z_\(i\)) h(|/\() h(|) h(A) f(|) g(*) h(ulp) f(\)) 533 -2227 y(where) 533 2330 y(A) h(is) f(an) g(n-by-n) f(symmetric) f -(matrix,) h(in) h(packed) f(storage) g(format,) 533 2434 -y(column) g(\(or) h(equivalently) e(row\)) h(distributed) 533 -2642 y(\(lambda_i,) f(z_i\)) i(is) g(a) g(standard) f(eigen-pair) f(of) -i(A) h(and) 533 2746 y(Z) g(is) f(an) g(n-by-m) f(matrix) g(of) h -(eigenvectors,) e(in) i(packed) f(storage) g(format,) 533 -2849 y(column) g(distributed) 533 3057 y(ULP) h(=) h(\(machine) d -(precision\)) g(*) j(\(machine) d(base\)) 533 3264 y(|A) i(z_\(i\)) g -(...) g(|) g(is) g(the) g(infinity-norm,) 533 3368 y(|A|) g(is) g(the) g -(1-norm) f(of) h(A,) 533 3472 y(res) g(is) g(reasonable) e(if) i(it) h -(is) f(of) g(order) f(about) h(50) g(or) g(less.) 533 -3680 y(Arguments) 533 3783 y(---------) 533 3887 y(In) g(the) g -(following:) 629 4095 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h -(Integer") 629 4198 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h -(DoublePrecision") 629 4406 y(me) 238 b(=) 47 b(this) g(processor's) e -(id) i(\(=) g(mxmynd_\(\)\)) 629 4510 y(nprocs) f(=) h(number) f(of) h -(allocated) f(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 -4614 y(nvecsA) e(=) h(number) f(of) h(entries) f(in) h(mapA) g(equal) f -(to) i(me) 1249 4717 y(\(=) f(count_list\() e(me,) i(mapA,) f(n) i -(\)\)) 629 4821 y(nvecsZ) e(=) h(number) f(of) h(entries) f(in) h(mapZ) -g(equal) f(to) i(me) 1249 4925 y(\(=) f(count_list\() e(me,) i(mapZ,) f -(m) i(\)\)) 629 5029 y(sDP) 190 b(=) 47 b(sizeof\() f(DoublePrecision) e -(\)) 533 5340 y(n.......) i(\(input\)) g(INTEGER) p 90 rotate -dyy eop -%%Page: 53 54 -53 53 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(53) p Fk 963 299 a(dimension) 45 -b(of) i(the) g(matrix) f(A) 533 506 y(colA) h(...) g(\(input\)) f -(array) g(of) h(pointers) f(to) h(DoublePrecision,) 1345 -610 y(length) f(\(nvecsA\)) 963 714 y(The) h(part) f(of) h(matrix) g(A) -g(owned) f(by) i(this) e(processer) f(stored) 963 818 -y(in) i(packed) f(format,) g(i.e.,) g(colA[i]) g(points) g(to) h(the) g -(diagonal) 963 922 y(element) f(of) h(the) g(i-th) f(column) g(\(or) h -(equivalently) e(row\)) h(of) i(A) 963 1025 y(owned) e(by) h(this) g -(processor,) e(i) i(=) h(0) f(to) g(nvecsA-1.) 533 1233 -y(mapA) g(...) g(\(input\)) f(INTEGER) f(array,) h(length) h(\(n\)) 963 -1337 y(The) g(i-th) f(column) g(\(or) h(equivalently) e(row\)) h(of) i -(A) f(is) 963 1440 y(owned) f(by) h(processor) f(mapA[i],) f(i) j(=) f -(0) g(to) h(n-1.) 533 1648 y(m.......) e(\(input\)) g(INTEGER) 963 -1752 y(number) g(of) h(columns) f(of) h(Z,) g(i.e.) g(#) g(of) g -(eigenvalues/eigenvectors) 533 1959 y(colZ) g(...) g(\(input\)) f -(array) g(of) h(pointers) f(to) h(DoublePrecision,) 1345 -2063 y(length) f(\(nvecsZ\)) 963 2167 y(The) h(part) f(of) h(matrix) g -(Z) g(owned) f(by) i(this) e(processer,) f(stored) 963 -2271 y(in) i(packed) f(format,) g(i.e.,) g(colZ[i]) g(points) g(to) h -(the) g(start) 963 2374 y(of) g(the) g(i-th) f(column) h(of) g(matrix) f -(Z) h(owned) g(by) g(this) 963 2478 y(processor,) e(i) i(=) h(0) f(to) g -(nvecsZ-1.) 533 2686 y(mapZ) g(...) g(\(input\)) f(INTEGER) f(array,) h -(length) h(\(m\)) 963 2790 y(The) g(i-th) f(column) g(of) i(matrix) e -(Z) h(is) g(owned) g(by) g(processor) 963 2893 y(mapZ[i],) e(i) j(=) f -(0) h(to) f(m-1.) 533 3101 y(eval....) f(\(input\)) g(DOUBLE) g -(PRECISION) f(array,) h(length) g(\(m\)) 963 3205 y(the) h(eigenvalues) -533 3412 y(ibuffptr) f(\(workspace\)) e(array) j(of) g(pointers) f(to) h -(DoublePrecision,) 1535 3516 y(length) g(\(2) g(*) g(nvecsZ) f(+) i -(1\)) 533 3724 y(iwork...) e(\(workspace\)) e(INTEGER) i(array,) 1535 -3827 y(length\() g(m) i(+) f(maximum\() f(nprocs,) g(n+nvecsA,) f -(i_mxm88) h(\)\)) 1535 3931 y(where) h(i_mxm88) f(=) h -(2*\(n+m\)+nvecsA+nvecsZ) 533 4139 y(work....) f(\(workspace\)) e -(DOUBLE) j(PRECISION) e(array,) 1535 4242 y(length\() h(nvecsZ) g(*) i -(n) f(+) h(maximum\() d(d_mxm88,) 2729 4346 y(n) i(+) h(1) f(+) g -(mxlbuf_\(\)) f(/) h(sDP) g(+) h(1) f(\)) 1535 4450 y(where) g(d_mxm88) -f(=) h(maximum) f(\() h(\(nvecsZ+1\)*n,) 2776 4554 y(mxlbuf_\(\)/sDP) e -(+) i(1) g(\)) 533 4761 y(res.....) f(\(output\)) f(DOUBLE) h -(PRECISION) 963 4865 y(the) h(residual) e(described) g(above.) 533 -5073 y(info....) h(\(output\)) f(INTEGER) 963 5176 y(=) i(0,) g(not) g -(currently) f(used) p 90 rotate dyy eop -%%Page: 54 55 -54 54 bop Fs 150 -116 a(54) 3256 b(P) m(eIGS) p Fk 438 -299 a(*/) 390 462 y(void) 47 b(residual\() e(n,) i(colA,) f(mapA,) h -(colB,) f(mapB,) h(m,) g(colZ,) f(mapZ,) g(eval,) 1154 -566 y(ibuffptr,) f(iwork,) h(work,) g(res,) h(info\)) 629 -670 y(Integer) e(*n,) i(*mapA,) f(*mapB,) h(*m,) f(*mapZ,) h(*iwork,) e -(*info;) 629 774 y(DoublePrecision) e(**colA,) j(**colB,) g(**colZ,) g -(*eval,) g(**ibuffptr,) f(*work,) h(*res;) 390 981 y(/*) 533 -1189 y(This) h(subroutine) e(computes) g(the) i(residual) 533 -1396 y(res) g(=) h(max_\(i\)) d(|) j(A) f(z_\(i\)) g(-) g -(\\lambda_\(i\)) e(B) i(z_\(i\)) g(|/\() g(|) g(A) g(|) h(*) f(ulp) g -(\)) 533 1604 y(where) 533 1812 y(A) h(is) f(an) g(n-by-n) f(symmetric) -f(matrix,) h(in) h(packed) f(storage) g(format,) 533 -1915 y(column) g(\(or) h(equivalently) e(row\)) h(distributed) 533 -2123 y(B) i(is) f(an) g(n-by-n) f(symmetric) f(matrix,) h(in) h(packed) -f(storage) g(format,) 533 2227 y(column) g(\(or) h(equivalently) e -(row\)) h(distributed) 533 2434 y(\(lambda_i,) f(z_i\)) i(is) g(a) g -(generalized) e(eigen-pair) g(and) 533 2538 y(Z) j(is) f(an) g(n-by-m) f -(matrix) g(of) h(eigenvectors,) e(in) i(packed) f(storage) g(format,) -533 2642 y(column) g(distributed) 533 2849 y(ULP) h(=) h(\(machine) d -(precision\)) g(*) j(\(machine) d(base\)) 533 3057 y(|A) i(z_\(i\)) g -(...) g(|) g(is) g(the) g(infinity-norm,) 533 3161 y(|A|) g(is) g(the) g -(1-norm) f(of) h(A,) 533 3368 y(res) g(is) g(reasonable) e(if) i(it) h -(is) f(of) g(order) f(about) h(50) g(or) g(less.) 533 -3576 y(Arguments) 533 3680 y(---------) 533 3783 y(In) g(the) g -(following:) 629 3991 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h -(Integer") 629 4095 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h -(DoublePrecision") 629 4302 y(me) 238 b(=) 47 b(this) g(processor's) e -(id) i(\(=) g(mxmynd_\(\)\)) 629 4406 y(nprocs) f(=) h(number) f(of) h -(allocated) f(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 -4510 y(nvecsA) e(=) h(number) f(of) h(entries) f(in) h(mapA) g(equal) f -(to) i(me) 1058 4614 y(\(=) f(count_list\() e(me,) i(mapA,) f(n) i -(\)\)) 629 4717 y(nvecsB) e(=) h(number) f(of) h(entries) f(in) h(mapB) -g(equal) f(to) i(me) 1058 4821 y(\(=) f(count_list\() e(me,) i(mapB,) f -(n) i(\)\)) 629 4925 y(nvecsZ) e(=) h(number) f(of) h(entries) f(in) h -(mapZ) g(equal) f(to) i(me) 1058 5029 y(\(=) f(count_list\() e(me,) i -(mapZ,) f(m) i(\)\)) 629 5132 y(sDP) 190 b(=) 47 b(sizeof\() f -(DoublePrecision) e(\)) p 90 rotate dyy eop -%%Page: 55 56 -55 55 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(55) p Fk 533 299 a(n.......) 46 -b(\(input\)) g(INTEGER) 963 403 y(size) g(of) i(the) e(symmetric) g -(matrices) f(A) j(and) f(B,) 963 506 y(and) g(the) g(number) f(of) h -(rows) f(in) i(Z.) 533 714 y(colA) f(...) g(\(input\)) f(array) g(of) h -(pointers) f(to) h(DoublePrecision,) 1345 818 y(length) f(\(nvecsA\)) -963 922 y(The) h(part) f(of) h(matrix) g(A) g(owned) f(by) i(this) e -(processer) f(stored) 963 1025 y(in) i(packed) f(format,) g(i.e.,) g -(colA[i]) g(points) g(to) h(the) g(diagonal) 963 1129 -y(element) f(of) h(the) g(i-th) f(column) g(\(or) h(equivalently) e -(row\)) h(of) i(A) 963 1233 y(owned) e(by) h(this) g(processor,) e(i) i -(=) h(0) f(to) g(nvecsA-1.) 533 1440 y(mapA) g(...) g(\(input\)) f -(INTEGER) f(array,) h(length) h(\(n\)) 963 1544 y(The) g(i-th) f -(column) g(\(or) h(equivalently) e(row\)) h(of) i(A) f(is) 963 -1648 y(owned) f(by) h(processor) f(mapA[i],) f(i) j(=) f(0) g(to) h -(n-1.) 533 1856 y(colB) f(...) g(\(input\)) f(array) g(of) h(pointers) f -(to) h(DoublePrecision,) 1345 1959 y(length) f(\(nvecsB\)) 963 -2063 y(The) h(part) f(of) h(matrix) g(B) g(owned) f(by) i(this) e -(processer) f(stored) 963 2167 y(in) i(packed) f(format,) g(i.e.,) g -(colB[i]) g(points) g(to) h(the) g(diagonal) 963 2271 -y(element) f(of) h(the) g(i-th) f(column) g(\(or) h(equivalently) e -(row\)) h(of) i(B) 963 2374 y(owned) e(by) h(this) g(processor,) e(i) i -(=) h(0) f(to) g(nvecsB-1.) 533 2582 y(mapB) g(...) g(\(input\)) f -(INTEGER) f(array,) h(length) h(\(n\)) 963 2686 y(The) g(i-th) f -(column) g(\(or) h(equivalently) e(row\)) h(of) i(B) f(is) 963 -2790 y(owned) f(by) h(processor) f(mapB[i],) f(i) j(=) f(0) g(to) h -(n-1.) 533 2997 y(m.......) e(\(input\)) g(INTEGER) 963 -3101 y(number) g(of) h(columns) f(of) h(Z,) g(i.e.,) g(#) g(of) g -(eigenvalues/eigenvectors) 533 3308 y(colZ) g(...) g(\(input\)) f -(array) g(of) h(pointers) f(to) h(DoublePrecision,) 1345 -3412 y(length) f(\(nvecsZ\)) 963 3516 y(The) h(part) f(of) h(matrix) g -(Z) g(owned) f(by) i(this) e(processer,) f(stored) 963 -3620 y(in) i(packed) f(format,) g(i.e.,) g(colZ[i]) g(points) g(to) h -(the) g(start) 963 3724 y(of) g(the) g(i-th) f(column) h(of) g(matrix) f -(Z) h(owned) g(by) g(this) 963 3827 y(processor,) e(i) i(=) h(0) f(to) g -(nvecsZ-1.) 533 4035 y(mapZ) g(...) g(\(input\)) f(INTEGER) f(array,) h -(length) h(\(m\)) 963 4139 y(The) g(i-th) f(column) g(of) i(matrix) e -(Z) h(is) g(owned) g(by) g(processor) 963 4242 y(mapZ[i],) e(i) j(=) f -(0) h(to) f(m-1.) 533 4450 y(eval....) f(\(input\)) g(DOUBLE) g -(PRECISION) f(array,) h(length) g(\(m\)) 963 4554 y(the) h(eigenvalues) -533 4761 y(ibuffptr) f(\(workspace\)) e(array) j(of) g(pointers) f(to) h -(DoublePrecision,) 1535 4865 y(length) g(\(3) g(*) g(nvecsZ) f(+) i -(3\)) 533 5073 y(iwork...) e(\(workspace\)) e(INTEGER) i(array,) 1535 -5176 y(length\() g(m) i(+) f(nvecsA+nvecsB+nvecsZ+) 1917 -5280 y(MAX\() g(i_mxm88,) e(nprocs,) h(nvecsA) g(+) i(n) f(\)) p -90 rotate dyy eop -%%Page: 56 57 -56 56 bop Fs 150 -116 a(56) 3256 b(P) m(eIGS) p Fk 1535 -299 a(where) 47 b(i_mxm88) f(=) h(2*\(n+m\)+nvecsA+nvecsZ+nve) o(csB) -533 506 y(work....) f(\(workspace\)) e(DOUBLE) j(PRECISION) e(array,) -1535 610 y(length\() h(2*nvecsZ) g(*) h(n) h(+) f(maximum\() f -(d_mxm88,) 2681 714 y(n) h(+) h(1) f(+) h(mxlbuf_\(\)) d(/) i(sDP) g(+) -h(1) f(\)) 1535 818 y(where) g(d_mxm88) f(=) h(maximum) f(\() h -(\(nvecsZ+1\)*n,) 2776 922 y(mxlbuf_\(\)/sDP) e(+) i(1) g(\)) 533 -1129 y(res.....) f(\(output\)) f(INTEGER) 963 1233 y(the) i(residual) e -(described) g(above.) 533 1440 y(info....) h(\(output\)) f(INTEGER) 963 -1544 y(=) i(0,) g(not) g(currently) f(used) 438 1752 -y(*/) 390 1915 y(void) h(ortho\() f(n,) h(m,) g(colZ,) f(mapZ,) h -(ibuffptr,) e(iwork,) h(work,) h(ort,) f(info\)) 629 -2019 y(Integer) f(*n,) i(*m,) g(*mapZ,) f(*iwork,) g(*info;) 629 -2123 y(DoublePrecision) d(**colZ,) j(**ibuffptr,) f(*work,) 94 -b(*ort;) 390 2330 y(/*) 533 2538 y(This) 47 b(subroutine) e(computes) g -(the) i(infinity-norm) d(measure:) 533 2746 y(ort) j(=) h(max_i) e(|) h -(\(Z^t.Z\)_i) f(-) h(I_i) g(|) g(/) h(ULP,) 533 2953 -y(for) f(the) g(standard) f(symmetric) f(eigensystem) g(problem) g -(where) 629 3161 y(Z) i(is) g(N-by-M) 629 3264 y(I) g(is) g(M-by-M.) 629 -3368 y(Z_i) g(is) g(an) g(eigenvector,) 629 3472 y(\(Z^t.Z\)_i) e(is) i -(the) g(i-th) g(column) f(of) h(Z^t.Z) 629 3576 y(I_i) g(is) g(the) g -(i-th) f(column) g(of) i(the) e(m-by-m) h(identity) e(matrix) 629 -3680 y(ULP) i(=) g(\(machine) f(precision\)) f(*) i(\(machine) f -(base\)) 629 3783 y(|.|) h(is) g(the) g(infinity-norm.) 533 -3991 y(res) g(is) g(reasonable) e(if) i(it) h(is) f(of) g(order) f -(about) h(50) g(or) g(less.) 533 4302 y(MUST) g(have) f(M) i(<=) f(N.) -95 b(If) 47 b(M) h(>) f(N) h(then) e(program) g(exits.) 533 -4406 y(This) h(is) g(not) g(a) g(limitation) e(of) j(this) e -(subroutine) f(as) i(M) h(>) f(N) 533 4510 y(implies) f(the) h(columns) -f(of) h(Z) g(are) g(linearly) f(dependent,) f(which) 533 -4614 y(implies) h("ort") g(will) h(always) f(be) h(large) g(in) g(this) -f(case.) 533 4821 y(Arguments) 533 4925 y(---------) 533 -5029 y(In) h(the) g(following:) 629 5236 y(INTEGER) 475 -b(=) 47 b("pointer) f(to) h(Integer") 629 5340 y(DOUBLE) f(PRECISION) f -(=) i("pointer) f(to) h(DoublePrecision") p 90 rotate -dyy eop -%%Page: 57 58 -57 57 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(57) p Fk 629 403 a(me) 238 b(=) 47 -b(this) g(processor's) e(id) i(\(=) g(mxmynd_\(\)\)) 629 -506 y(nprocs) f(=) h(number) f(of) h(allocated) f(processors) f(\() i -(=) h(mxnprc_\(\)\)) 629 610 y(nvecsZ) e(=) h(number) f(of) h(entries) f -(in) h(mapZ) g(equal) f(to) i(me) 1249 714 y(\(=) f(count_list\() e -(me,) i(mapZ,) f(m) i(\)\)) 629 818 y(nvecsZ_max) d(=) i(maximum) f -(number) g(of) h(entries) f(in) h(mapZ) g(equal) f(to) h(i,) 1249 -922 y(i) h(=) f(0) g(to) h(nprocs-1) 1249 1025 y(\(=) f(max) g(over) g -(i) g(of) g(count_list\() e(i,) i(mapZ,) g(m) g(\)\)) 629 -1129 y(sDP) 190 b(=) 47 b(sizeof\() f(DoublePrecision) e(\)) 533 -1440 y(n.......) i(\(input\)) g(INTEGER) 963 1544 y(Number) g(of) h -(rows) g(in) g(Z) 533 1752 y(m.......) f(\(input\)) g(INTEGER) 963 -1856 y(number) g(of) h(columns) f(in) h(Z) g(\(i.e.,) g(#) g(of) 963 -1959 y(eigenvalues/eigenvector) o(s\).) 963 2063 y(Must) f(have) h(m) g -(<=) h(n.) 533 2271 y(colZ) f(...) g(\(input\)) f(array) g(of) h -(pointers) f(to) h(DoublePrecision,) 1345 2374 y(length) f(\(nvecsZ\)) -963 2478 y(The) h(part) f(of) h(matrix) g(Z) g(owned) f(by) i(this) e -(processer,) f(stored) 963 2582 y(in) i(packed) f(format,) g(i.e.,) g -(colZ[i]) g(points) g(to) h(the) g(start) 963 2686 y(of) g(the) g(i-th) -f(column) h(of) g(matrix) f(Z) h(owned) g(by) g(this) 963 -2790 y(processor,) e(i) i(=) h(0) f(to) g(nvecsZ-1.) 533 -2997 y(mapZ) g(...) g(\(input\)) f(INTEGER) f(array,) h(length) h -(\(m\)) 963 3101 y(The) g(i-th) f(column) g(of) i(matrix) e(Z) h(is) g -(owned) g(by) g(processor) 963 3205 y(mapZ[i],) e(i) j(=) f(0) h(to) f -(m-1.) 533 3412 y(ibuffptr) f(\(workspace\)) e(array) j(of) g(pointers) -f(to) h(DoublePrecision,) 1535 3516 y(length\(nvecsZ\)) 533 -3724 y(iwork...) f(\(workspace\)) e(INTEGER) i(array,) g(length\() g(7) -i(*) f(m) h(\)) 533 3931 y(work....) e(\(workspace\)) e(DOUBLE) j -(PRECISION) e(array,) 1535 4035 y(length\() h(nvecsZ) g(*) i(n) f(+) h -(maximum\() d(d_mxm25,) 2872 4139 y(mxlbuf_\(\)) g(/) j(sDP) e(+) i(1) f -(\)) 1535 4242 y(where) g(d_mxm25) f(=) h(maximum) f(\() h(2*m,) 2776 -4346 y(\(nvecsZ) f(+) i(2*nvecsZ_max\)*n) 43 b(\)) 533 -4554 y(ort.....) j(\(output\)) f(INTEGER) 963 4658 y(the) i(residual) e -(described) g(above.) 533 4865 y(info....) h(\(output\)) f(INTEGER) 963 -4969 y(=) i(0,) g(not) g(currently) f(used) 438 5176 -y(*/) 390 5340 y(void) h(b_ortho) e(\() j(n,) f(colB,) f(mapB,) h(m,) g -(colZ,) f(mapZ,) h(ibuffptr,) e(iwork,) h(work,) g(ort,) h(info\)) p -90 rotate dyy eop -%%Page: 58 59 -58 58 bop Fs 150 -116 a(58) 3256 b(P) m(eIGS) p Fk 629 -299 a(Integer) 45 b(*n,) i(*mapB,) f(*m,) h(*mapZ,) f(*iwork,) g -(*info;) 629 403 y(DoublePrecision) d(**colB,) j(**colZ,) g -(**ibuffptr,) f(*work,) 93 b(*ort;) 390 610 y(/*) 533 -714 y(This) 47 b(subroutine) e(computes) g(the) 95 b(infinity-norm) 44 -b(measure:) 533 922 y(ort) j(=) h(max_i) e(|) h(\(Z^t.B.Z\)_i) e(-) j -(I_i) e(|) i(/) f(ULP,) 533 1129 y(for) g(the) g(generalized) e -(symmetric) g(eigensystem) g(problem) h(where) 629 1337 -y(Z) h(is) g(N-by-M) f(and) h(distributed) e(by) i(columns) 629 -1440 y(B) g(is) g(N-by-N) f(symmetric) g(and) h(in) g(packed) f -(storage) 629 1544 y(I) h(is) g(M-by-M.) 629 1648 y(Z_i) g(is) g(an) g -(eigenvector,) 629 1752 y(\(Z^t.B.Z\)_i) d(is) k(the) e(i-th) h(column) -f(of) h(Z^t.B.Z) 629 1856 y(I_i) g(is) g(the) g(i-th) f(column) g(of) i -(the) e(m-by-m) h(identity) e(matrix) 629 1959 y(ULP) i(=) g(\(machine) -f(precision\)) f(*) i(\(machine) f(base\)) 629 2063 y(|.|) h(is) g(the) -g(infinity-norm.) 533 2271 y(res) g(is) g(reasonable) e(if) i(it) h(is) -f(of) g(order) f(about) h(50) g(or) g(less.) 533 2478 -y(MUST) g(have) f(M) i(<=) f(N.) 95 b(If) 47 b(M) h(>) f(N) h(then) e -(program) g(exits.) 533 2582 y(This) h(is) g(not) g(a) g(limitation) e -(of) j(this) e(subroutine) f(as) i(M) h(>) f(N) 533 2686 -y(implies) f(the) h(columns) f(of) h(Z) g(are) g(linearly) f -(dependent,) f(which) 533 2790 y(implies) h("ort") g(will) h(always) f -(be) h(large) g(in) g(this) f(case.) 533 2997 y(Arguments) 533 -3101 y(---------) 533 3205 y(In) h(the) g(following:) 629 -3412 y(INTEGER) 475 b(=) 47 b("pointer) f(to) h(Integer") 629 -3516 y(DOUBLE) f(PRECISION) f(=) i("pointer) f(to) h(DoublePrecision") -629 3724 y(me) 238 b(=) 47 b(this) g(processor's) e(id) i(\(=) g -(mxmynd_\(\)\)) 629 3827 y(nprocs) f(=) h(number) f(of) h(allocated) f -(processors) f(\() i(=) h(mxnprc_\(\)\)) 629 3931 y(nvecsZ) e(=) h -(number) f(of) h(entries) f(in) h(mapZ) g(equal) f(to) i(me) 1249 -4035 y(\(=) f(count_list\() e(me,) i(mapZ,) f(n) i(\)\)) 629 -4139 y(nvecsZ_max) d(=) i(maximum) f(number) g(of) h(entries) f(in) h -(mapZ) g(equal) f(to) h(i,) 1249 4242 y(i) h(=) f(0) g(to) h(nprocs-1) -1249 4346 y(\(=) f(max) g(over) g(i) g(of) g(count_list\() e(i,) i -(mapZ,) g(n) g(\)\)) 629 4450 y(sDP) 190 b(=) 47 b(sizeof\() f -(DoublePrecision) e(\)) 533 4761 y(n.......) i(\(input\)) g(INTEGER) 963 -4865 y(Number) g(of) h(rows) g(and) g(columns) e(in) j(B,) f(and) 963 -4969 y(the) g(number) f(of) h(rows) g(in) g(Z) 533 5176 -y(colB) g(...) g(\(input\)) f(array) g(of) h(pointers) f(to) h -(DoublePrecision,) 1345 5280 y(length) f(\(nvecsB\)) p -90 rotate dyy eop -%%Page: 59 60 -59 59 bop Fs 150 -116 a(Chapter) 30 b(4:) 41 b(Calling) 28 -b(Syn) m(tax) 2456 b(59) p Fk 963 299 a(The) 47 b(part) f(of) h(matrix) -g(B) g(owned) f(by) i(this) e(processer) f(stored) 963 -403 y(in) i(packed) f(format,) g(i.e.,) g(colB[i]) g(points) g(to) h -(the) g(diagonal) 963 506 y(element) f(of) h(the) g(i-th) f(column) g -(\(or) h(equivalently) e(row\)) h(of) i(B) 963 610 y(owned) e(by) h -(this) g(processor,) e(i) i(=) h(0) f(to) g(nvecsB-1.) 533 -818 y(mapB) g(...) g(\(input\)) f(INTEGER) f(array,) h(length) h(\(n\)) -963 922 y(The) g(i-th) f(column) g(\(or) h(equivalently) e(row\)) h(of) -i(B) f(is) 963 1025 y(owned) f(by) h(processor) f(mapB[i],) f(i) j(=) f -(0) g(to) h(n-1.) 533 1233 y(m.......) e(\(input\)) g(INTEGER) 963 -1337 y(number) g(of) h(columns) f(in) h(Z) g(\(i.e.,) g(#) g(of) 963 -1440 y(eigenvalues/eigenvector) o(s\).) 963 1544 y(Must) f(have) h(m) g -(<=) h(n.) 533 1752 y(colZ) f(...) g(\(input\)) f(array) g(of) h -(pointers) f(to) h(DoublePrecision,) 1345 1856 y(length) f(\(nvecsZ\)) -963 1959 y(The) h(part) f(of) h(matrix) g(Z) g(owned) f(by) i(this) e -(processer,) f(stored) 963 2063 y(in) i(packed) f(format,) g(i.e.,) g -(colZ[i]) g(points) g(to) h(the) g(start) 963 2167 y(of) g(the) g(i-th) -f(column) h(of) g(matrix) f(Z) h(owned) g(by) g(this) 963 -2271 y(processor,) e(i) i(=) h(0) f(to) g(nvecsZ-1.) 533 -2478 y(mapZ) g(...) g(\(input\)) f(INTEGER) f(array,) h(length) h -(\(m\)) 963 2582 y(The) g(i-th) f(column) g(of) i(matrix) e(Z) h(is) g -(owned) g(by) g(processor) 963 2686 y(mapZ[i],) e(i) j(=) f(0) h(to) f -(m-1.) 533 2893 y(ibuffptr) f(\(workspace\)) e(array) j(of) g(pointers) -f(to) h(DoublePrecision,) 1535 2997 y(length\() f(3*nvecsZ) g(+) h(1\)) -533 3205 y(iwork...) f(\(workspace\)) e(INTEGER) i(array,) 1535 -3308 y(length\() g(n+m) h(+) h(MAX\(nprocs,) c(3*n+2*m+nvecsB+nvecsZ) e -(\)) 533 3516 y(work....) k(\(workspace\)) e(DOUBLE) j(PRECISION) e -(array,) 1535 3620 y(length\() h(nvecsZ) g(*) i(\(n+m\)) e(+) i -(maximum\() d(d_mxm25,) h(d_mxm88,) 3158 3724 y(mxlbuf_\(\)) f(/) j -(sDP) f(+) g(1) h(\)) 1535 3827 y(where) f(d_mxm25) f(=) h(maximum\() f -(n+m,) 2729 3931 y(\(nvecsZ) f(+) j(2*nvecsZ_max\)*n) c(\)) 1822 -4035 y(d_mxm88) i(=) h(maximum) f(\() h(\(nvecsZ+1\)*n,) 2776 -4139 y(mxlbuf_\(\)/sDP) e(+) i(1) g(\)) 533 4346 y(ort.....) f -(\(output\)) f(INTEGER) 963 4450 y(the) i(residual) e(described) g -(above.) 533 4658 y(info....) h(\(output\)) f(INTEGER) 963 -4761 y(=) i(0,) g(not) g(currently) f(used) 438 4865 -y(*/) p 90 rotate dyy eop -%%Page: 60 61 -60 60 bop Fs 150 -116 a(60) 3256 b(P) m(eIGS) p 90 rotate -dyy eop 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m(w) h -(for) g(the) h(fortran) f(v) m(ersion.) 55 b(The) 35 -b(analogous) h(description) e(applies) f(to) 150 408 -y(the) e(C) f(v) m(ersion.) p Fq 199 548 a(\000) p Fs -60 w(CI) p 434 548 28 4 v 32 w(ENTR) -8 b(Y) 45 b(:returns) f(index) f -(a\(i,j\)) i(in) f(F) -8 b(ortran) 45 b(for) g(a) g(1-D) h(data) f -(arra) m(y) h(storing) e(the) h(lo) m(w) m(er) 330 657 -y(triangular) 29 b(part) h(of) h(a) f(symmetric) g(matrix) p -Fq 199 794 a(\000) p Fs 60 w(CI) p 434 794 V 32 w(SIZE:) 44 -b(returns) f(the) i(total) g(memory) g(required) d(for) p -Fk 45 w(") p Fs(standard) p Fk(") p Fs 43 w(column) h(wrapping) g(of) i -(a) 330 903 y(symmetric) 30 b(matrix) p Fq 199 1040 a(\000) p -Fs 60 w(FIL) p 484 1040 V 33 w(MAPVEC:) 37 b(from) g(map) g(construct) h -(a) f(corresp) s(ondance) g(map) m(v) m(ec:) 56 b(the) 38 -b(real) e(column/ro) m(w) 330 1150 y(index) 29 b(that) i(the) f(matrix) -g(on) g(this) g(pro) s(cessor) g(o) m(wns) p Fg 150 1383 -a(5.2.1) 63 b(CI) p 606 1383 37 5 v 43 w(ENTR) -10 b(Y) 40 -b(and) h(ci) p 1452 1383 V 44 w(en) m(try) p 1780 1383 -V Fk 772 1575 a(integer) 46 b(function) f(ci_entry) h(\(me,) g(n,) i -(i,) f(j,) g(map\)) 772 1678 y(integer) f(me,) h(n,) g(i,) g(j,) g -(map\(*\)) 390 1782 y(c) 390 1886 y(c) 191 b(PeIGS) 46 -b(utility) g(routine) 390 1990 y(c) 390 2093 y(c) 191 -b(this) 46 b(routine) g(returns) g(the) h(F77) g(index) f(of) h(the) g -(a\(i,j\)) 390 2197 y(c) 191 b(for) 47 b(a) g(symmetric) e(matrix) h -(with) h(i) g(>=) h(j) 390 2301 y(c) 191 b(on) 47 b(processor) e(me) i -(stored) f(using) h(a) g(1-D) g(array) 390 2405 y(c) 390 -2509 y(c) 191 b(if) 47 b(\(processor) e(=) i(me\)) 390 -2612 y(c) 191 b(doesn't) 45 b(own) i(this) g(element) f(-1) h(is) g -(returned) 390 2716 y(c) 390 2820 y(c) 191 b(Argument:) 390 -2924 y(c) 390 3027 y(c) g(me) 381 b(=) 47 b(\(input/integer\)) d -(processor) h(id) 390 3131 y(c) 390 3235 y(c) 191 b(n) 477 -b(=) 47 b(\(input/integer\)) d(dimension) h(of) i(the) g(matrix) 390 -3339 y(c) 390 3443 y(c) 191 b(i) 524 b(=) 48 b(\(input/integer\)) 43 -b(the) k(row) g(index) g(of) g(the) g(element) f(a[j][i]) 390 -3546 y(c) 390 3650 y(c) 191 b(j) 524 b(=) 48 b(\(input/integer\)) 43 -b(the) k(column) f(index) h(of) g(the) g(element) f(a[j][i]) 390 -3754 y(c) 390 3858 y(c) 191 b(map) 285 b(=) 48 b(\(input/integer) c -(array) i(\)) h(integer) f(array) h(of) g(length) f(n) 390 -3961 y(c) 191 b(map[j]) 46 b(=) h(the) g(processor) e(id) j(holding) d -(column) h(j) 390 4065 y(c) 390 4198 y(int) h(ci_entry) e(\(me,) i(n,) g -(i,) g(j,) h(map\)) 629 4302 y(int) f(*me,) f(*n,) h(*i,) g(*j,) g -(*map;) 485 4406 y(/*) 581 4510 y(PeIGS) f(utility) g(routine) 581 -4717 y(this) h(routine) e(returns) h(the) h(C) h(index) e(of) h(the) g -(a\(i,j\)) 581 4821 y(for) g(a) g(symmetric) f(matrix) g(with) g(i) i -(>=) f(j) 581 4925 y(on) g(processor) e(me) j(stored) e(using) g(a) h -(1-D) g(array) 581 5132 y(if) g(\(processor) e(=) j(me\)) 581 -5236 y(doesn't) e(own) h(this) f(element) g(-1) h(is) g(returned) p -90 rotate dyy eop -%%Page: 64 65 -64 64 bop Fs 150 -116 a(64) 3256 b(P) m(eIGS) p Fk 581 -299 a(Argument:) 581 506 y(me) 381 b(=) 48 b(\(input/integer\)) 43 -b(processor) j(id) 581 714 y(n) 477 b(=) 47 b(\(input/integer\)) d -(dimension) h(of) i(the) g(matrix) 581 922 y(i) 525 b(=) 47 -b(\(input/integer\)) d(the) j(row) g(index) f(of) h(the) g(element) f -(a[j][i]) 581 1129 y(j) 525 b(=) 47 b(\(input/integer\)) d(the) j -(column) f(index) g(of) h(the) g(element) f(a[j][i]) 581 -1337 y(map) 285 b(=) 48 b(\(input/integer) c(array) i(\)) i(integer) d -(array) i(of) g(length) f(n) 581 1440 y(map[j]) g(=) h(the) g -(processor) f(id) h(holding) f(column) g(j) 581 1648 -y(*/) 772 1782 y(integer) g(function) f(ci_size_) h(\(me,) g(n,) i -(map\)) 772 1885 y(integer) e(me,) h(n,) g(map\(*\)) 390 -1989 y(c) 390 2093 y(c) 191 b(Fortran) 45 b(and) i(C) h(callable) d(\() -j(not) f(very) f(portable) g(\)) 390 2197 y(c) 390 2301 -y(c) 191 b(returns) 45 b(the) i(total) g(number) f(of) h(double) f -(precision) 390 2404 y(c) 191 b(storage) 45 b(location) h(required) g -(for) g(storing) g(the) h(lower) 390 2508 y(c) 191 b(triangular) 45 -b(part) h(of) h(a) h(symmetric) d(matrix) h(distributed) 390 -2612 y(c) 191 b(according) 45 b(the) i(map) 390 2716 -y(c) 390 2819 y(c) 191 b(me) 429 b(=) 47 b(\(input/integer\)) d -(processor) h(id) 390 2923 y(c) 390 3027 y(c) 191 b(n) 524 -b(=) 48 b(\(input/integer\)) 43 b(dimension) j(of) h(the) g(matrix) f -(and) h(also) 390 3131 y(c) 907 b(the) 46 b(length) h(of) g(the) g -(array) f(map) 390 3235 y(c) 390 3338 y(c) 191 b(map\(*\)) 141 -b(=) 48 b(\(input/integer) c(array\)) i(length) g(n) h(array) g(of) g -(processor) e(ids) 390 3442 y(c) 390 3576 y(int) i(ci_size_) e(\(me,) i -(n,) g(map\)) 629 3680 y(int) g(*me,) f(*n,) h(*map;) 485 -3783 y(/*) 581 3887 y(Fortran) f(and) h(C) g(callable) 581 -4095 y(returns) f(the) h(total) f(number) g(of) h(double) f(precision) -581 4198 y(storage) g(location) f(required) h(for) h(storing) f(the) g -(lower) 581 4302 y(triangular) f(part) i(of) g(a) g(symmetric) e -(matrix) i(distributed) 581 4406 y(according) e(the) i(map) 581 -4614 y(me) 429 b(=) 47 b(\(input/integer\)) d(processor) h(id) 581 -4821 y(n) 525 b(=) 47 b(\(input/integer\)) d(dimension) h(of) i(the) g -(matrix) f(and) h(also) 581 4925 y(the) g(length) f(of) h(the) g(array) -f(map) 581 5132 y(map\(*\)) 141 b(=) 48 b(\(input/integer) c(array\)) i -(length) g(n) h(array) g(of) g(processor) e(ids) 581 -5340 y(*/) p 90 rotate dyy eop -%%Page: 65 66 -65 65 bop Fs 150 -116 a(Chapter) 30 b(5:) 41 b(Utilites) 2752 -b(65) p Fk 772 299 a(integer) 46 b(function) f(fil_mapvec) g(\() j(me,) -f(n,) g(map,) f(mapvec\)) 772 403 y(integer) g(me,) h(n,) g(map,) f -(mapvec\(*\)) 390 506 y(c) 390 610 y(c) 191 b(from) 46 -b(the) h(map) g(array) f(construct) g(a) h(shorter) 390 -714 y(c) 191 b(array) 46 b(with) h(information) d(about) j(the) g -(vectors) e(stored) i(on) g(this) f(processor) 390 818 -y(c) 390 922 y(c) 334 b(may) 47 b(be) g(compatibility) d(problems) i -(between) f(C) j(and) f(fortran) 390 1025 y(c) 390 1129 -y(c) 191 b(mapvec\(i\)) 45 b(=) i(j) 390 1233 y(c) 191 -b(i) 47 b(=) h(the) e(i-th) h(vector) f(stored) g(on) h(this) g -(processor) 390 1337 y(c) 191 b(j) 47 b(=) h(the) e(real) h(column/row) -e(indx) i(of) g(the) g(i-th) f(vector) 390 1440 y(c) 390 -1544 y(c) 191 b(returns) 45 b(the) i(number) f(of) i(vectors) d(on) j -(this) e(processor) g(given) 390 1648 y(c) 191 b(by) 47 -b(map) g(and) g(also) f(the) h(mapvec) f(list) 390 1752 -y(c) 390 1856 y(c) 191 b(argument:) 390 1959 y(c) 390 -2063 y(c) g(me) 429 b(=) 47 b(\(input/integer\)) d(node) i(id) 390 -2167 y(c) 390 2271 y(c) 191 b(n) 524 b(=) 48 b(\(input/integer\)) 43 -b(dimension) j(of) h(the) g(matrix) 390 2374 y(c) 390 -2478 y(c) 191 b(map) 333 b(=) 47 b(\(input/integer) d(array\)) i -(distribution) f(of) i(the) g(columns) f(of) h(the) g(matrix) 390 -2582 y(c) 1479 b(length) 46 b(n) 390 2686 y(c) 390 2790 -y(c) 191 b(mapvec) 93 b(=) 48 b(\(output/integer) c(array\)) i(length) g -(n) 390 2893 y(c) 390 3057 y(int) h(fil_mapvec_) e(\() i(me,) g(n,) g -(map,) g(mapvec\)) 629 3161 y(int) g(*me,) f(*n,) h(*map,) f(*mapvec;) -485 3264 y(/*) 581 3368 y(from) h(the) f(map) h(array) g(construct) e -(a) i(shorter) 581 3472 y(array) f(with) h(information) e(about) h(the) -h(vectors) f(stored) g(on) h(this) g(processor) 581 3680 -y(mapvec[i]) e(=) j(j) 581 3783 y(i) f(=) h(the) f(i-th) f(vector) g -(stored) h(on) g(this) f(processor) 581 3887 y(j) h(=) h(the) f(real) f -(column/row) f(indx) i(of) g(the) g(i-th) g(vector) 581 -4095 y(returns) f(the) h(number) f(of) h(vectors) f(on) h(this) g -(processor) e(given) 581 4198 y(by) i(map) g(and) g(also) g(the) f -(mapvec) h(list) 581 4406 y(argument:) 581 4614 y(me) 429 -b(=) 47 b(\(input/integer\)) d(node) j(id) 581 4821 y(n) 525 -b(=) 47 b(\(input/integer\)) d(dimension) h(of) i(the) g(matrix) 581 -5029 y(map) 333 b(=) 48 b(\(input/integer) c(array\)) i(distribution) e -(of) j(the) g(columns) f(of) h(the) g(matrix) 1917 5132 -y(length) f(n) 581 5340 y(mapvec) 94 b(=) 47 b(\(output/integer) d -(array\)) i(length) g(n) p 90 rotate dyy eop -%%Page: 66 67 -66 66 bop Fs 150 -116 a(66) 3256 b(P) m(eIGS) p Fk 581 -403 a(*/) 390 635 y(void) 47 b(sfnorm\() e(n,) j(colA,) e(mapA,) g -(norm,) h(iwork,) f(work,) g(info\)) 629 739 y(Integer) f(*n,) i -(*mapA,) f(*iwork,) g(*info;) 629 843 y(DoublePrecision) d(**colA,) j -(*work,) g(*norm;) 485 1050 y(/*) 581 1154 y(computes) f(the) i(F-norm) -f(of) i(a) f(symmetric) e(n-by-n) h(matrix) h(A,) g(where) 581 -1362 y(F-norm\(A\)) e(=) j(sqrt\() e(sum_i,j) g(a_i,j^2) g(\)) 581 -1569 y(n) 334 b(=) 47 b(size) g(of) g(the) g(matrix) 581 -1673 y(colA) 190 b(=) 47 b(DoublePrecision) d(pointer) i(to) h(the) g -(columns) 581 1777 y(mapA) 190 b(=) 47 b(distribution) e(of) i(the) g -(columns) 581 1880 y(iwork) 142 b(=) 47 b(integer) f(scratch) g(space) -581 1984 y(work) 190 b(=) 47 b(DoublePrecision) d(precision) h(scratch) -h(space) 581 2192 y(*/) p 90 rotate dyy eop -%%Page: 67 68 -67 67 bop Fs 150 -116 a(Chapter) 30 b(6:) 41 b(Error) 29 -b(Handling) 2437 b(67) p Fp 150 299 a(6) 80 b(Error) 54 -b(Handling) p Fs 275 533 a(Since) 40 b(the) i(P) m(eIGS) g(routines) e -(are) i(designed) f(to) h(w) m(ork) g(with) e(lists) g(of) i(pro) s -(cessors,) i(and) d(this) f(list) 150 643 y(of) 45 b(pro) s(cessors) e -(ma) m(y) i(not) g(b) s(e) f(all) f(the) i(pro) s(cessors) f(allo) s -(cated) g({) h(there) g(ma) m(y) g(t) m(w) m(o) g(P) m(eIGS) g -(routines) 150 752 y(running) 34 b(on) i(t) m(w) m(o) h(di\013eren) m -(t) f(sets) h(of) f(pro) s(cessors) g(sim) m(ultaneously) e({) j -(global) f(c) m(hec) m(king) h(of) f(data) h(do) s(es) 150 -862 y(not) f(w) m(ork.) 59 b(Instead,) 38 b(the) e(set) h(of) f(pro) s -(cessor) g(ids) f(app) s(earing) f(in) h(mapA,) i(mapB,) f(and/or) g -(mapZ) g(are) 150 971 y(used) 28 b(to) h(determine) f(a) p -Fk 28 w(") p Fs(master) p Fk(") p Fs 29 w(pro) s(cessor) g(list.) 39 -b(P) m(eIGS) 28 b(then) h(tries) f(to) h(ha) m(v) m(e) g(all) f(pro) s -(cessors) g(in) f(this) p Fk 150 1081 a(") p Fs(master) p -Fk(") p Fs 30 w(list) i(return) g(the) i(same) g(INF) m(O) g(whenev) m -(er) f(p) s(ossible.) 275 1215 y(All) 22 b(of) i(the) g(lev) m(el) g(1) -g(and) p Fo 24 w(some) g(of) g(the) g(lev) m(el) i(2) e(routines) p -Fs 25 w(do) g(extensiv) m(e) g(c) m(hec) m(king) h(of) f(the) g(input) e -(data.) 150 1325 y(In) 34 b(particular,) h(they) h(mak) m(e) g(sure) e -(that) i(the) f(input) f(data) h(on) g(a) h(pro) s(cessor) f(is) p -Fk 34 w(") p Fs(v) -5 b(aild) p Fk(") p Fs(.) 53 b(If) 34 -b(an) m(y) i(input) 150 1435 y(data) e(is) f(in) m(v) -5 -b(alid) 31 b(on) i(a) h(pro) s(cessor,) g(then) g(that) g(pro) s -(cessor) f(prin) m(ts) f(a) i(negativ) m(e) h(v) -5 b(alue) 33 -b(of) g(INF) m(O) h(to) h(the) 150 1544 y(standard) 25 -b(error) h(output) f(unit) g(and) g(terminates) h(program) g -(execution.) 39 b(In) 25 b(this) g(case) i(other) f(pro) s(cessors) 150 -1654 y(are) h(not) f(informed) f(of) h(the) h(error) f(and) g(ma) m(y) h -(con) m(tin) m(ue) f(program) h(execution.) 39 b(If) 26 -b(some) h(pro) s(cessors) f(ha) m(v) m(e) 150 1763 y(in) m(v) -5 -b(alid) 32 b(data) k(and) e(some) h(ha) m(v) m(e) h(v) -5 -b(alid) 33 b(data,) j(then) f(some) g(of) g(the) g(pro) s(cessors) f -(will) e(con) m(tin) m(ue) j(running) 150 1873 y(and) 30 -b(will) d(ha) m(v) m(e) 32 b(to) f(b) s(e) f(killed) e(b) m(y) i(the) h -(user.) 275 2007 y(If) i(all) g(of) h(the) g(input) f(data) h(on) g -(eac) m(h) h(pro) s(cessor) f(is) f(v) -5 b(alid,) 34 -b(then) f(the) i(pro) s(cessors) e(in) g(the) p Fk 34 -w(") p Fs(master) p Fk(") p Fs 150 2117 a(pro) s(cessor) d(list) f -(compare) j(their) d(data) i(to) h(mak) m(e) f(sure) f(it) g(is) g -(consisten) m(t) h(across) g(the) g(pro) s(cessors.) 41 -b(If) 30 b(the) 150 2227 y(input) 24 b(data) j(is) f(not) g(consisten) m -(t) h(on) f(all) f(pro) s(cessors,) i(then) f(the) h(pro) s(cessors) f -(with) f(incosisen) m(t) g(data) i(prin) m(t) 150 2336 -y(a) 39 b(negativ) m(e) i(INF) m(O) e(and) f(an) h(error) g(message) h -(to) g(the) f(standard) f(error) h(output) f(unit) g(indicating) f(the) -150 2446 y(nature) 26 b(of) h(the) g(problem) e(to) j(standard) e -(error.) 39 b(With) 26 b(inconsisten) m(t) g(data) h(all) f(pro) s -(cessors) g(in) f(the) p Fk 27 w(") p Fs(mas-) 150 2555 -y(ter) p Fk(") p Fs 32 w(list) 31 b(try) h(to) g(return) f(the) h(same) -h(v) -5 b(alue) 31 b(of) h(INF) m(O) h(and) e(terminate) h(program) g -(execution) g(together.) 150 2665 y(Ho) m(w) m(ev) m(er,) 39 -b(with) c(some) h(t) m(yp) s(es) g(of) g(data) h(inconsistencies) d(it) -h(is) g(not) h(p) s(ossible) d(to) k(exit) f(gracefully) f(and) 150 -2775 y(some) c(pro) s(cessors) f(will) d(con) m(tin) m(ue) k(running.) -38 b(These) 30 b(pro) s(cessors) g(m) m(ust) g(b) s(e) g(killed) e(b) m -(y) i(the) h(user.) 275 2909 y(All) k(P) m(eIGS) i(routines) e(return) h -(a) h(p) s(ositiv) m(e) e(INF) m(O) i(error) g(co) s(de) f(if) g -(something) g(go) s(es) h(wrong) f(in) g(the) 150 3019 -y(computation.) 57 b(The) 35 b(v) -5 b(alue) 35 b(of) h(INF) m(O) g -(should) e(b) s(e) h(the) h(same) g(on) g(all) e(participating) g(pro) s -(cessors) i(and) 150 3128 y(can) 30 b(b) s(e) f(used) g(to) i -(determine) e(what) g(w) m(en) m(t) i(wrong.) 40 b(Program) 30 -b(execution) g(is) f(not) h(stopp) s(ed) e(for) i(p) s(ositiv) m(e) 150 -3238 y(INF) m(Os.) p 90 rotate dyy eop -%%Page: 68 69 -68 68 bop Fs 150 -116 a(68) 3256 b(P) m(eIGS) p 90 rotate -dyy eop -%%Page: 69 70 -69 69 bop Fs 150 -116 a(Chapter) 30 b(7:) 41 b(BUGS) 2790 -b(69) p Fp 150 299 a(7) 80 b(BUGS) p Fs 275 533 a(In) 29 -b(this) f(c) m(hapter) j(w) m(e) f(describ) s(e) e(some) i(p) s -(ossible) d(problems) h(asso) s(ciated) j(with) d(our) h(implemen) m -(tation) 150 643 y(of) i(the) f(P) m(eIGS) h(eigensolv) m(er.) 330 -777 y(1\)) c(If) g(the) g(user) f(wishes) f(to) i(solv) m(e) g(only) f -(for) h(a) g(fraction) f(of) h(the) g(eigen-pairs) f(the) g(curren) m -(t) h(co) s(de) g(asks) 330 887 y(for) g(\() g(but) g(needs) f(only) h -(the) g(minim) m(um) d(memory) j(space) h(\)) f(the) g(same) h(memory) f -(space) h(as) f(for) g(a) g(full) 330 996 y(eigen-system) i(solv) m(e) f -(to) h(satisfy) f(the) g(error) g(c) m(hec) m(king) h(routines) e(and) g -(to) i(prev) m(en) m(t) g(race) g(condition.) 330 1106 -y(W) -8 b(e) 32 b(are) e(w) m(orking) g(on) g(elimanating) f(this) h -(restriction.) 330 1240 y(2\)) k(The) f(in) m(v) m(erse) g(iteration) g -(with) f(mo) s(di\014ed) f(Gram) i(Sc) m(hmidt) f(curren) m(t) h(do) s -(es) g(a) h(\014xed) f(n) m(um) m(b) s(er) f(of) 330 -1350 y(com) m(bined) h(iterations.) 50 b(This) 32 b(pro) s(cess) h(can) -h(theoretically) f(fail) g(to) h(con) m(v) m(erge) i(to) e(an) g(eigen) -m(v) m(ector) 330 1460 y(on) c(a) h(degenerate) h(eigen-sub-space.) 330 -1594 y(3\)) c(The) f(error) g(rep) s(orting) f(is) h(b) s(eing) f(done) -h(on) h(all) e(pro) s(cessors.) 39 b(One) 27 b(should) f(just) h(mak) m -(e) h(pro) s(cessor) 330 1704 y(0) j(rep) s(ort) f(errors.) 330 -1838 y(4\)) f(The) f(C) g(co) s(des) h(calling) e(C) h(co) s(de) g -(needs) g(a) h(fortran) f(driv) m(er) f(so) i(that) g(the) g -(mxsubs.cpp) d(co) s(des) j(get) 330 1948 y(initialized) e(correctly) -8 -b(...SUN) 32 b(common) f(blo) s(c) m(k) f(is) f(...) 330 -2082 y(5\)) 37 b(When) f(solving) f(a) h(tridiagonal) f(problem) f -(with) h(n) g(=) h(2053) i(on) e(four) f(pro) s(cessors) h(of) g(an) g -(In) m(tel) 330 2192 y(P) -8 b(ARA) m(GON) 34 b(w) m(e) e(sp) s -(oradically) e(get) j(large) g(residuals.) 44 b(The) 32 -b(problem) e(is) i(in) f(mxm25,) i(the) g(eigen-) 330 -2301 y(v) m(ector) 43 b(bac) m(k-transformation.) 75 -b(W) -8 b(e) 43 b(ha) m(v) m(e) g(not) f(b) s(een) f(able) g(to) h -(\014nd) e(an) m(y) i(problems) e(with) h(the) 330 2411 -y(P) m(eIGS) 29 b(co) s(de,) g(and) f(b) s(eliev) m(e) g(that) h(the) g -(errors) f(o) s(ccuring) f(here) i(are) g(caused) f(b) m(y) h(a) g -(system) g(problem) 330 2521 y(ha) m(ving) f(to) g(do) g(with) f(the) i -(use) e(of) p Fk 29 w(") p Fs(virtual) p Fk(") p Fs 25 -w(memory) h(on) g(the) h(no) s(des) e(\(this) g(problem) g(exceeds) i -(the) 330 2630 y(ph) m(ysical) g(memory) h(a) m(v) -5 -b(ailable) 30 b(on) g(a) h(no) s(de\).) 330 2765 y(W) -8 -b(e) 36 b(appreciate) f(an) m(y) g(advice) f(and) g(rep) s(orts) g(of) h -(bugs.) 53 b(W) -8 b(e) 35 b(ask) g(the) g(user) f(to) h(mail) f(us) f -(all) h(of) h(the) 330 2874 y(input) i(parameters) j(and) e(the) h -(parallel) f(\() h(or) g(serial) f(\)) h(en) m(vironmen) m(t) g(\() g -(as) h(w) m(ell) e(as) h(\)) g(op) s(erating) 330 2984 -y(system) 31 b(v) m(ersion) e(n) m(um) m(b) s(er.) 330 -3118 y(There) 40 b(are) h(lik) m(ely) e(to) i(b) s(e) f(unkno) m(wn) f -(bugs) h(in) g(the) g(co) s(de) h(and) f(w) m(e) h(strongly) f -(recommend) g(that) 330 3228 y(the) d(user) f(run) f(the) h(residual) f -(and) h(orthogonalit) m(y) h(c) m(hec) m(king) g(routines) e(to) j(c) m -(hec) m(k) g(the) e(results) g(of) 330 3337 y(computations) 30 -b(whenev) m(er) g(practical.) p 90 rotate dyy eop -%%Page: 70 71 -70 70 bop Fs 150 -116 a(70) 3256 b(P) m(eIGS) p 90 rotate -dyy eop -%%Page: 71 72 -71 71 bop Fs 150 -116 a(Index) 3286 b(71) p Fp 330 299 -a(Index) p Fr 150 614 a(B) p Fj 330 736 a(BUGS) p Fc -21 w(.) 12 b(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) p Fj 46 w(69) p Fr 150 980 -a(C) p Fj 330 1102 a(C) 26 b(co) r(de:) 35 b(b) p 666 -1102 24 4 v 27 w(ortho) p Fc 23 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) g(.) h(.) p Fj 48 w(57) 330 1193 y(C) 26 b(co) r(de:) 35 -b(c) n(holeski) p Fc 17 w(.) 13 b(.) g(.) f(.) g(.) h(.) f(.) g(.) g(.) -h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) p Fj 43 w(34) 330 1285 y(C) 26 b(co) r(de:) 35 b(ci) p -678 1285 V 28 w(en) n(try) p Fc 18 w(.) 12 b(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f -(.) g(.) h(.) f(.) p Fj 44 w(63) 330 1376 y(C) 26 b(co) r(de:) 35 -b(ci) p 678 1376 V 28 w(size) p 825 1376 V Fc 43 w(.) 12 -b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) p Fj -40 w(64) 330 1468 y(C) 26 b(co) r(de:) 35 b(\014l) p -687 1468 V 28 w(map) n(v) n(ec) p 966 1468 V Fc 43 w(.) 13 -b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) p Fj 43 w(65) 330 1559 y(C) 26 -b(co) r(de:) 35 b(in) n(v) n(erseL) p Fc 9 w(.) 12 b(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) p Fj 35 w(36) 330 1650 y(C) 26 -b(co) r(de:) 35 b(memreq) p 892 1650 V Fc 44 w(.) 12 -b(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p Fj 44 w(62) 330 -1742 y(C) 26 b(co) r(de:) 35 b(mxm25) p Fc 7 w(.) 10 -b(.) j(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) p Fj -32 w(37) 330 1833 y(C) 26 b(co) r(de:) 35 b(mxm5x) p -Fc 21 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) p -Fj 49 w(39) 330 1925 y(C) 26 b(co) r(de:) 35 b(mxm88) p -Fc 7 w(.) 10 b(.) j(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) p -Fj 32 w(41) 330 2016 y(C) 26 b(co) r(de:) 35 b(ortho) p -Fc 22 w(.) 12 b(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 47 w(56) 330 2107 y(C) 26 b(co) r(de:) 35 b(p) r(dsp) r(ev) p -Fc 21 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p Fj 48 w(18,) 26 -b(20) 330 2199 y(C) g(co) r(de:) 35 b(p) r(dsp) r(evx) p -Fc 9 w(.) 11 b(.) h(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 34 w(24) 330 2290 y(C) 26 b(co) r(de:) 35 b(p) r(dspgv) p -Fc 10 w(.) 11 b(.) i(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) p -Fj 35 w(30) 330 2382 y(C) 26 b(co) r(de:) 35 b(pstebz) p -Fc 22 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 48 w(44) 330 2473 y(C) 26 b(co) r(de:) 35 b(pstein) p -Fc 11 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) p -Fj 36 w(47) 330 2564 y(C) 26 b(co) r(de:) 35 b(resid) p -Fc 14 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) p Fj 39 w(52) 330 2656 y(C) 26 b(co) r(de:) 35 b(residual) p -Fc 17 w(.) 13 b(.) g(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 43 w(54) 330 2747 y(C) 26 b(co) r(de:) 35 b(sfnorm) p -Fc 15 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) p -Fj 40 w(66) 330 2839 y(C) 26 b(co) r(de:) 35 b(tred2) p -Fc 24 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 49 w(42) 330 2930 y(C) 26 b(co) r(de:) 35 b(tresid) p -Fc 17 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) p -Fj 43 w(50) 330 3021 y(C) 26 b(input) p Fc 16 w(.) 12 -b(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) p Fj 42 w(11) 330 3113 y(C) 26 b(routine) g(c) n(holeski) -p Fc 6 w(.) 13 b(.) g(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 32 w(34) 330 3204 y(c) n(holeski) 26 b(factorization) p -Fc 11 w(.) 15 b(.) d(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) p Fj 36 w(34) p -Fr 150 3449 a(E) p Fj 330 3570 a(eigensystem:regular) 27 -b(symmetric) p Fc 13 w(.) 10 b(.) i(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) p Fj 38 w(18) 330 3662 y(error) 26 b(handling) p -Fc 16 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) p -Fj 42 w(67) p Fr 150 3919 a(F) p Fj 330 4040 a(F77) 27 -b(co) r(de:) 34 b(b) r(ortho) p Fc 18 w(.) 13 b(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) p Fj 43 w(50) 330 4132 y(F77) 27 b(co) r(de:) 34 -b(CI) p 777 4132 V 28 w(ENTR) -6 b(Y) p Fc 11 w(.) 11 -b(.) i(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) g(.) h(.) p Fj 36 w(63) 330 4223 y(F77) 27 b(co) r(de:) 34 -b(ci) p 749 4223 V 29 w(size) p Fc 10 w(.) 13 b(.) f(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) p Fj 36 w(64) 330 4315 y(F77) 27 b(co) r(de:) 34 -b(FIL) p 820 4315 V 28 w(MAPVEC) p Fc 8 w(.) 12 b(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 33 w(64) 330 4406 y(F77) 27 b(co) r(de:) 34 b(FMEMREQ) p -Fc 15 w(.) 13 b(.) g(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) p Fj 40 w(61) 330 4497 y(F77) 27 -b(co) r(de:) 34 b(mxm25) p Fc 7 w(.) 11 b(.) i(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) p Fj 33 w(37) 330 4589 y(F77) 27 b(co) r(de:) 34 -b(mxm5x) p Fc 6 w(.) 10 b(.) j(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 32 w(37) 330 4680 y(F77) 27 b(co) r(de:) 34 b(mxm88) p -Fc 7 w(.) 11 b(.) i(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 33 w(37) 2205 614 y(F77) 26 b(co) r(de:) 35 b(ortho) p -Fc 23 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 48 w(50) 2205 707 y(F77) 26 b(co) r(de:) 35 b(PDSPEV) p -Fc 8 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) p Fj 34 w(18) 2205 -799 y(F77) 26 b(co) r(de:) 35 b(p) r(dsp) r(evx) p Fc -9 w(.) 12 b(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p Fj 35 w(18) 2205 -891 y(F77) 26 b(co) r(de:) 35 b(p) r(dspgv) p Fc 10 w(.) 12 -b(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p Fj 36 w(29) 2205 -983 y(F77) 26 b(co) r(de:) 35 b(PDSPGVX) p Fc 12 w(.) 12 -b(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) p Fj 38 w(29) 2205 1075 y(F77) 26 -b(co) r(de:) 35 b(PSTEBZ) p Fc 14 w(.) 14 b(.) e(.) g(.) h(.) f(.) g(.) -h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 40 w(43) 2205 1167 y(F77) 26 b(co) r(de:) 35 b(resid) p -Fc 14 w(.) 13 b(.) g(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 40 w(49) 2205 1260 y(F77) 26 b(co) r(de:) 35 b(residual) p -Fc 18 w(.) 13 b(.) f(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) p Fj -43 w(49) 2205 1352 y(F77) 26 b(co) r(de:) 35 b(tresid) p -Fc 18 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) p -Fj 43 w(49) 2205 1444 y(fortran) 26 b(input) p Fc 18 -w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 44 w(10) p Fr 2025 1705 a(G) p Fj 2205 1829 a(generalized) 27 -b(symmetrix) c(eigensolv) n(er) p Fc 12 w(.) 14 b(.) e(.) g(.) h(.) f -(.) g(.) h(.) p Fj 37 w(29) p Fr 2025 2090 a(I) p Fj -2205 2213 a(in) n(v) n(erse) 25 b(of) i(lo) n(w) n(er) f(triangular) h -(matrix) p Fc 19 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 45 w(36) p Fr 2025 2475 a(M) p Fj 2205 2598 a(matrix) 25 -b(m) n(ultiplication) p Fc 24 w(.) 12 b(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 50 w(37) 2205 2690 y(MPI) 26 b(Use) p Fc 15 w(.) 13 -b(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) p Fj 41 w(13) p Fr 2025 2939 a(O) p Fj 2205 -3062 a(o) n(v) n(erview) p Fc 20 w(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) p -Fj 47 w(3) p Fr 2025 3311 a(P) p Fj 2205 3434 a(pstebz) p -Fc 21 w(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) p Fj 47 w(43) 2205 3526 -y(pstein) p Fc 9 w(.) h(.) f(.) g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) -h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g -(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p Fj 35 w(47) p -Fr 2025 3788 a(R) p Fj 2205 3911 a(residual) 26 b(and) g(orthogonalit) n -(y) g(c) n(hec) n(ks) p Fc 21 w(.) 13 b(.) f(.) g(.) h(.) f(.) g(.) h -(.) p Fj 47 w(49) p Fr 2025 4172 a(S) p Fj 2205 4296 -a(symmetric) 24 b(input) p Fc 15 w(.) 11 b(.) i(.) f(.) g(.) g(.) h(.) f -(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) p Fj 41 w(11) p Fr 2025 4557 a(T) p Fj -2205 4680 a(tred2) p Fc 22 w(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) -g(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h -(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) g(.) h(.) f(.) p -Fj 48 w(42) p 90 rotate dyy eop -%%Page: 72 73 -72 72 bop Fs 150 -116 a(72) 3256 b(P) m(eIGS) p 90 rotate -dyy eop -%%Page: -1 74 --1 73 bop Fs 3725 -116 a(i) p Fp 330 299 a(T) -13 b(able) 54 -b(of) g(Con) l(ten) l(ts) p Fr 330 641 a(1) 135 b(P) l(eIGS:) 45 -b(an) g(o) l(v) l(erview) p Fb 27 w(.) 21 b(.) f(.) f(.) h(.) f(.) g(.) -h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) p -Fr 72 w(3) p Fs 449 778 a(1.1) 92 b(Problems) 29 b(that) i(P) m(eIGS) g -(can) f(Solv) m(e) p Fa 8 w(.) 15 b(.) g(.) h(.) f(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) p Fs 38 w(3) 449 888 y(1.2) 92 -b(Computers) 29 b(for) h(whic) m(h) g(P) m(eIGS) g(is) g(Suitable) p -Fa 24 w(.) 15 b(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) p Fs 56 w(3) 449 997 -y(1.3) 92 b(BLAS) 30 b(and) g(Floating) g(P) m(oin) m(t) h -(Computations) p Fa 23 w(.) 14 b(.) h(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p Fs 53 w(3) 449 -1107 y(1.4) 92 b(Algorithms) p Fa 26 w(.) 15 b(.) g(.) g(.) g(.) g(.) g -(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) p -Fs 57 w(4) 449 1216 y(1.5) 92 b(P) m(ortabilit) m(y) p -Fa 13 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) p Fs 43 w(4) 449 1326 y(1.6) 92 -b(Supp) s(ort) p Fa 22 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 54 w(5) 449 1435 y(1.7) 92 b(Thanks) p Fa 15 w(.) 14 -b(.) h(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) p Fs 45 w(5) p Fr 330 1678 -a(2) 135 b(Installation) p Fb 24 w(.) 22 b(.) d(.) h(.) f(.) g(.) h(.) f -(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f -(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) p Fr 69 w(7) 330 -1948 y(3) 135 b(Con) l(ten) l(t:) 61 b(Co) t(de) 45 b(F) -11 -b(unctionalities) 46 b(and) f(Data) 599 2081 y(Structure) p -Fb 13 w(.) 19 b(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f -(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f -(.) h(.) f(.) g(.) p Fr 58 w(9) p Fs 449 2218 a(3.1) 92 -b(Summary) p Fa 15 w(.) 14 b(.) h(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) -g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p Fs 45 w(9) 449 -2327 y(3.2) 92 b(Data) 32 b(La) m(y) m(out) p Fa 18 w(.) 17 -b(.) e(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 47 w(10) 748 2437 y(3.2.1) 93 b(F) -8 b(ortran) 31 -b(Data) h(Structure) p Fa 27 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) -g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g -(.) g(.) p Fs 57 w(10) 748 2546 y(3.2.2) 93 b(C) 29 b(Data) k -(Structure) p Fa 16 w(.) 14 b(.) h(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h -(.) f(.) g(.) g(.) g(.) g(.) g(.) p Fs 45 w(11) 748 2656 -y(3.2.3) 93 b(MPI) 30 b(Use) p Fa 16 w(.) 15 b(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) p Fs 45 w(13) p Fr 330 2898 a(4) 135 -b(Calling) 46 b(Syn) l(tax) p Fb 16 w(.) 20 b(.) f(.) g(.) h(.) f(.) h -(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h -(.) f(.) h(.) f(.) h(.) p Fr 60 w(15) p Fs 449 3035 a(4.1) 92 -b(Lev) m(el) 31 b(I) f(Subroutines) p Fa 12 w(.) 12 b(.) j(.) h(.) f(.) -g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) h(.) p Fs 41 w(15) 449 3145 y(4.2) 92 b(PDSPEV:) 30 -b(Real) h(Symmetric) e(Eigensystem) h(Solv) m(er) p Fa -26 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 56 w(18) 449 3254 y(4.3) 92 b(PDSPGV) 30 b(and) g(PDSPGVX:) h -(Generalized) f(Symmetric) 631 3364 y(Eigensystem) g(Solv) m(er) p -Fa 27 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) p -Fs 56 w(29) 449 3474 y(4.4) 92 b(Lev) m(el) 31 b(I) s(I) e(Subroutines) -p Fa 16 w(.) 13 b(.) i(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) p Fs -45 w(34) 748 3583 y(4.4.1) 93 b(Choleski) 28 b(F) -8 -b(actorization) 32 b(of) f(P) m(ositiv) m(e) f(De\014nite) 930 -3693 y(Symmetric) f(Matrix) p Fa 25 w(.) 15 b(.) g(.) g(.) g(.) h(.) f -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 55 w(34) 748 3802 y(4.4.2) 93 b(In) m(v) m(erse) 30 -b(of) h(Lo) m(w) m(er) g(T) -8 b(riangular) 29 b(Matrix) p -Fa 28 w(.) 16 b(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) p Fs 58 w(36) 748 3912 y(4.4.3) 93 b(Matrix) 30 b(Multiplication) p -Fa 17 w(.) 12 b(.) j(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 46 w(37) 748 4022 y(4.4.4) 93 b(TRED2:) 41 b(Householder) 29 -b(reduction) g(of) i(a) g(symmetric) 930 4131 y(matrix) e(to) i -(tridiagonal) e(form) p Fa 16 w(.) 14 b(.) i(.) f(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) p Fs 45 w(42) 748 4241 y(4.4.5) 93 b(PSTEBZ) 29 -b(eigen) m(v) -5 b(alues) 30 b(of) g(real) g(symmetric) g(tridiagonal) -930 4350 y(matrix) p Fa 21 w(.) 14 b(.) h(.) g(.) g(.) g(.) g(.) g(.) g -(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) p Fs 51 w(43) 748 4460 y(4.4.6) 93 -b(PSTEIN:) 29 b(eigen) m(v) m(ectors) j(of) f(real) f(symmetric) g -(tridiagonal) 930 4570 y(matrix) p Fa 21 w(.) 14 b(.) h(.) g(.) g(.) g -(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p Fs 51 w(47) 748 -4679 y(4.4.7) 93 b(Residual) 28 b(and) i(Orthogonalit) m(y) g(c) m(hec) -m(ks) p Fa 16 w(.) 17 b(.) e(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) -g(.) g(.) g(.) p Fs 46 w(49) p Fr 330 4922 a(5) 135 b(Utilites) p -Fb 13 w(.) 22 b(.) d(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h -(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h -(.) f(.) h(.) f(.) g(.) h(.) p Fr 58 w(61) p Fs 449 5059 -a(5.1) 92 b(FMEMREQ) 31 b(and) e(memreq) p 1671 5059 -28 4 v 33 w(:) 41 b(Scratc) m(h) 31 b(Memory) g(Size) p -Fa 25 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 55 w(61) 449 5168 y(5.2) 92 b(General) 30 b(Utilities) p -Fa 26 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 57 w(62) 748 5278 y(5.2.1) 93 b(CI) p 1130 5278 V -32 w(ENTR) -8 b(Y) 30 b(and) g(ci) p 1758 5278 V 32 w(en) m(try) p -1997 5278 V Fa 48 w(.) 15 b(.) g(.) g(.) g(.) g(.) g(.) h(.) f(.) g(.) g -(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) g(.) p -Fs 44 w(63) p 90 rotate dyy eop -%%Page: -2 75 --2 74 bop Fs 150 -116 a(ii) 3294 b(P) m(eIGS) p Fr 330 -83 a(6) 135 b(Error) 45 b(Handling) p Fb 29 w(.) 20 b(.) g(.) f(.) h(.) -f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f -(.) h(.) f(.) g(.) h(.) p Fr 74 w(67) 330 353 y(7) 135 -b(BUGS) p Fb 40 w(.) 19 b(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f -(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) h(.) f(.) g -(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) p Fr 86 w(69) 330 -623 y(Index) p Fb 41 w(.) g(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h -(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) f(.) g(.) h -(.) f(.) h(.) f(.) h(.) f(.) g(.) h(.) f(.) h(.) f(.) h(.) p -Fr 85 w(71) p 90 rotate dyy eop -%%Trailer -end -userdict /end-hook known{end-hook}if -%%EOF