diff --git a/README b/README index 35cb420b..bc8503bb 100644 --- a/README +++ b/README @@ -1,13 +1,12 @@ This directory contains the PSBLAS library, version 2.0. -The version 1.0 of the library is described in: + +The version 1.0 of the library was described in: S. Filippone, M. Colajanni PSBLAS: A library for parallel linear algebra computation on sparse matrices ACM Trans. on Math. Software, 26(4), Dec. 2000, pp. 527-550. PLATFORMS: -For the F77 compiler, we assume it supports DOUBLE COMPLEX and DO WHILE/ENDDO. -Practically all compilers do nowadays. The compilation process relies on the choice of an appropriate Make.inc file; we have tested with AIX XLF, Intel ifc/Linux, Lahey F95/Linux, Nag f95/Linux, GNU Fortran/Linux. If you succeed in compiling with @@ -51,13 +50,11 @@ INTERFACE for the dummy argument subroutine PARTS, it wanted an EXTERNAL specification. Again, please move to 7.1. -Testing of NAG f95 versions is still incomplete. - DOCUMENTATION -See userguidef90.ps. +See userguide.pdf Please consult the sample programs, especially TEST/pargen/ppde90.f90. diff --git a/docs/userguide.pdf b/docs/userguide.pdf new file mode 100644 index 00000000..06d3030b --- /dev/null +++ b/docs/userguide.pdf @@ -0,0 +1,26537 @@ +%PDF-1.4 +5 0 obj +<< /S /GoTo /D (title.0) >> +endobj +8 0 obj +(PSBLAS-v2.0 User's Guide) +endobj +9 0 obj +<< /S /GoTo /D (section.1) >> +endobj +12 0 obj +(1 Introduction) +endobj +13 0 obj +<< /S /GoTo /D (section.2) >> +endobj +16 0 obj +(2 General overview) +endobj +17 0 obj +<< /S /GoTo /D (section.3) >> +endobj +20 0 obj +(3 Data Structures) +endobj +21 0 obj +<< /S /GoTo /D (subsection.3.1) >> +endobj +24 0 obj +(3.1 Sparse Matrix data structure) +endobj +25 0 obj +<< /S /GoTo /D (subsection.3.2) >> +endobj +28 0 obj +(3.2 Descriptor data structure) +endobj +29 0 obj +<< /S /GoTo /D (subsection.3.3) >> +endobj +32 0 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Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 494.634 cm +0 g 0 G +1 0 0 1 -458.8 -494.634 cm +BT +/F15 11.955 Tf 458.8 494.634 Td[(18)]TJ +ET +1 0 0 1 470.506 494.634 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -480.14 cm +BT +/F15 11.955 Tf 99.522 480.14 Td[(psb)]TJ +ET +1 0 0 1 117.848 480.14 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -480.14 cm +BT +/F15 11.955 Tf 121.36 480.14 Td[(gea)1(max)]TJ +ET +1 0 0 1 160.055 480.14 cm +0 g 0 G +1 0 0 1 -160.055 -480.14 cm +BT +/F15 11.955 Tf 168.014 480.14 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 480.14 cm +0 g 0 G +1 0 0 1 -458.8 -480.14 cm +BT +/F15 11.955 Tf 458.8 480.14 Td[(20)]TJ +ET +1 0 0 1 470.506 480.14 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -465.647 cm +BT +/F15 11.955 Tf 99.522 465.647 Td[(psb)]TJ +ET +1 0 0 1 117.848 465.647 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -465.647 cm +BT +/F15 11.955 Tf 121.36 465.647 Td[(gea)1(s)-1(um)]TJ +ET +1 0 0 1 159.144 465.647 cm +0 g 0 G +1 0 0 1 -159.144 -465.647 cm +BT +/F15 11.955 Tf 168.014 465.647 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 465.647 cm +0 g 0 G +1 0 0 1 -458.8 -465.647 cm +BT +/F15 11.955 Tf 458.8 465.647 Td[(22)]TJ +ET +1 0 0 1 470.506 465.647 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -451.153 cm +BT +/F15 11.955 Tf 99.522 451.153 Td[(psb)]TJ +ET +1 0 0 1 117.848 451.153 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -451.153 cm +BT +/F15 11.955 Tf 121.36 451.153 Td[(genrm2)]TJ +ET +1 0 0 1 159.079 451.153 cm +0 g 0 G +1 0 0 1 -159.079 -451.153 cm +BT +/F15 11.955 Tf 168.014 451.153 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 451.153 cm +0 g 0 G +1 0 0 1 -458.8 -451.153 cm +BT +/F15 11.955 Tf 458.8 451.153 Td[(24)]TJ +ET +1 0 0 1 470.506 451.153 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -436.66 cm +BT +/F15 11.955 Tf 99.522 436.66 Td[(psb)]TJ +ET +1 0 0 1 117.848 436.66 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -436.66 cm +BT +/F15 11.955 Tf 121.36 436.66 Td[(spnrmi)]TJ +ET +1 0 0 1 156.543 436.66 cm +0 g 0 G +1 0 0 1 -156.543 -436.66 cm +BT +/F15 11.955 Tf 168.014 436.66 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 436.66 cm +0 g 0 G +1 0 0 1 -458.8 -436.66 cm +BT +/F15 11.955 Tf 458.8 436.66 Td[(26)]TJ +ET +1 0 0 1 470.506 436.66 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -422.166 cm +BT +/F15 11.955 Tf 99.522 422.166 Td[(psb)]TJ +ET +1 0 0 1 117.848 422.166 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -422.166 cm +BT +/F15 11.955 Tf 121.36 422.166 Td[(spmm)]TJ +ET +1 0 0 1 151.99 422.166 cm +0 g 0 G +1 0 0 1 -151.99 -422.166 cm +BT +/F15 11.955 Tf 158.785 422.166 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 422.166 cm +0 g 0 G +1 0 0 1 -458.8 -422.166 cm +BT +/F15 11.955 Tf 458.8 422.166 Td[(28)]TJ +ET +1 0 0 1 470.506 422.166 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -407.673 cm +BT +/F15 11.955 Tf 99.522 407.673 Td[(psb)]TJ +ET +1 0 0 1 117.848 407.673 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -407.673 cm +BT +/F15 11.955 Tf 121.36 407.673 Td[(spsm)]TJ +ET +1 0 0 1 146.853 407.673 cm +0 g 0 G +1 0 0 1 -146.853 -407.673 cm +BT +/F15 11.955 Tf 158.785 407.673 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 407.673 cm +0 g 0 G +1 0 0 1 -458.8 -407.673 cm +BT +/F15 11.955 Tf 458.8 407.673 Td[(31)]TJ +ET +1 0 0 1 470.506 407.673 cm +0 g 0 G +1 0 0 1 -388.543 -26.232 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -81.963 -381.441 cm +BT +/F19 11.955 Tf 81.963 381.441 Td[(5)-906(C)1(om)1(m)31(uni)1(cat)1(io)1(n)-375(r)-1(o)1(uti)1(n)-1(es)]TJ +ET +1 0 0 1 244.414 381.441 cm +0 g 0 G +1 0 0 1 -244.414 -381.441 cm +BT +/F19 11.955 Tf 457.056 381.441 Td[(35)]TJ +ET +1 0 0 1 99.522 366.948 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -366.948 cm +BT +/F15 11.955 Tf 99.522 366.948 Td[(psb)]TJ +ET +1 0 0 1 117.848 366.948 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -366.948 cm +BT +/F15 11.955 Tf 121.36 366.948 Td[(halo)]TJ +ET +1 0 0 1 142.821 366.948 cm +0 g 0 G +1 0 0 1 -142.821 -366.948 cm +BT +/F15 11.955 Tf 149.556 366.948 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 366.948 cm +0 g 0 G +1 0 0 1 -458.8 -366.948 cm +BT +/F15 11.955 Tf 458.8 366.948 Td[(36)]TJ +ET +1 0 0 1 470.506 366.948 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -352.454 cm +BT +/F15 11.955 Tf 99.522 352.454 Td[(psb)]TJ +ET +1 0 0 1 117.848 352.454 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -352.454 cm +BT +/F15 11.955 Tf 121.36 352.454 Td[(o)28(vrl)]TJ +ET +1 0 0 1 140.87 352.454 cm +0 g 0 G +1 0 0 1 -140.87 -352.454 cm +BT +/F15 11.955 Tf 149.556 352.454 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 352.454 cm +0 g 0 G +1 0 0 1 -458.8 -352.454 cm +BT +/F15 11.955 Tf 458.8 352.454 Td[(38)]TJ +ET +1 0 0 1 470.506 352.454 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -337.961 cm +BT +/F15 11.955 Tf 99.522 337.961 Td[(psb)]TJ +ET +1 0 0 1 117.848 337.961 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -337.961 cm +BT +/F15 11.955 Tf 121.36 337.961 Td[(ga)1(ther)]TJ +ET +1 0 0 1 153.876 337.961 cm +0 g 0 G +1 0 0 1 -153.876 -337.961 cm +BT +/F15 11.955 Tf 158.785 337.961 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 337.961 cm +0 g 0 G +1 0 0 1 -458.8 -337.961 cm +BT +/F15 11.955 Tf 458.8 337.961 Td[(41)]TJ +ET +1 0 0 1 470.506 337.961 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -323.467 cm +BT +/F15 11.955 Tf 99.522 323.467 Td[(psb)]TJ +ET +1 0 0 1 117.848 323.467 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -323.467 cm +BT +/F15 11.955 Tf 121.36 323.467 Td[(scatter)]TJ +ET +1 0 0 1 155.892 323.467 cm +0 g 0 G +1 0 0 1 -155.892 -323.467 cm +BT +/F15 11.955 Tf 168.014 323.467 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 323.467 cm +0 g 0 G +1 0 0 1 -458.8 -323.467 cm +BT +/F15 11.955 Tf 458.8 323.467 Td[(44)]TJ +ET +1 0 0 1 470.506 323.467 cm +0 g 0 G +1 0 0 1 -388.543 -26.231 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -81.963 -297.236 cm +BT +/F19 11.955 Tf 81.963 297.236 Td[(6)-906(Dat)1(a)-375(manag)1(emen)31(t)-375(a)1(nd)-375(ini)1(ti)1(ali)1(zati)1(on)-375(rout)1(ines)]TJ +ET +1 0 0 1 363.011 297.236 cm +0 g 0 G +1 0 0 1 -363.011 -297.236 cm +BT +/F19 11.955 Tf 457.056 297.236 Td[(47)]TJ +ET +1 0 0 1 99.522 282.743 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -282.743 cm +BT +/F15 11.955 Tf 99.522 282.743 Td[(psb)]TJ +ET +1 0 0 1 117.848 282.743 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -282.743 cm +BT +/F15 11.955 Tf 121.36 282.743 Td[(gea)1(ll)]TJ +ET +1 0 0 1 144.772 282.743 cm +0 g 0 G +1 0 0 1 -144.772 -282.743 cm +BT +/F15 11.955 Tf 149.555 282.743 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 282.743 cm +0 g 0 G +1 0 0 1 -458.8 -282.743 cm +BT +/F15 11.955 Tf 458.8 282.743 Td[(48)]TJ +ET +1 0 0 1 470.506 282.743 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -268.249 cm +BT +/F15 11.955 Tf 99.522 268.249 Td[(psb)]TJ +ET +1 0 0 1 117.848 268.249 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -268.249 cm +BT +/F15 11.955 Tf 121.36 268.249 Td[(gea)1(s)-1(b)]TJ +ET +1 0 0 1 149.389 268.249 cm +0 g 0 G +1 0 0 1 -149.389 -268.249 cm +BT +/F15 11.955 Tf 158.785 268.249 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 268.249 cm +0 g 0 G +1 0 0 1 -458.8 -268.249 cm +BT +/F15 11.955 Tf 458.8 268.249 Td[(49)]TJ +ET +1 0 0 1 470.506 268.249 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -253.756 cm +BT +/F15 11.955 Tf 99.522 253.756 Td[(psb)]TJ +ET +1 0 0 1 117.848 253.756 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -253.756 cm +BT +/F15 11.955 Tf 121.36 253.756 Td[(csrp)]TJ +ET +1 0 0 1 142.235 253.756 cm +0 g 0 G +1 0 0 1 -142.235 -253.756 cm +BT +/F15 11.955 Tf 149.555 253.756 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 253.756 cm +0 g 0 G +1 0 0 1 -458.8 -253.756 cm +BT +/F15 11.955 Tf 458.8 253.756 Td[(50)]TJ +ET +1 0 0 1 470.506 253.756 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -239.262 cm +BT +/F15 11.955 Tf 99.522 239.262 Td[(psb)]TJ +ET +1 0 0 1 117.848 239.262 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -239.262 cm +BT +/F15 11.955 Tf 121.36 239.262 Td[(cdprt)]TJ +ET +1 0 0 1 148.674 239.262 cm +0 g 0 G +1 0 0 1 -148.674 -239.262 cm +BT +/F15 11.955 Tf 158.785 239.262 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 239.262 cm +0 g 0 G +1 0 0 1 -458.8 -239.262 cm +BT +/F15 11.955 Tf 458.8 239.262 Td[(51)]TJ +ET +1 0 0 1 470.506 239.262 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -224.769 cm +BT +/F15 11.955 Tf 99.522 224.769 Td[(psb)]TJ +ET +1 0 0 1 117.848 224.769 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -224.769 cm +BT +/F15 11.955 Tf 121.36 224.769 Td[(gefree)]TJ +ET +1 0 0 1 150.95 224.769 cm +0 g 0 G +1 0 0 1 -150.95 -224.769 cm +BT +/F15 11.955 Tf 158.785 224.769 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 224.769 cm +0 g 0 G +1 0 0 1 -458.8 -224.769 cm +BT +/F15 11.955 Tf 458.8 224.769 Td[(52)]TJ +ET +1 0 0 1 470.506 224.769 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -210.275 cm +BT +/F15 11.955 Tf 99.522 210.275 Td[(psb)]TJ +ET +1 0 0 1 117.848 210.275 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -210.275 cm +BT +/F15 11.955 Tf 121.36 210.275 Td[(gelp)]TJ +ET +1 0 0 1 142.17 210.275 cm +0 g 0 G +1 0 0 1 -142.17 -210.275 cm +BT +/F15 11.955 Tf 149.555 210.275 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 210.275 cm +0 g 0 G +1 0 0 1 -458.8 -210.275 cm +BT +/F15 11.955 Tf 458.8 210.275 Td[(53)]TJ +ET +1 0 0 1 470.506 210.275 cm +0 g 0 G +1 0 0 1 -370.984 -14.493 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -195.782 cm +BT +/F15 11.955 Tf 99.522 195.782 Td[(psb)]TJ +ET +1 0 0 1 117.848 195.782 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -195.782 cm +BT +/F15 11.955 Tf 121.36 195.782 Td[(spins)]TJ +ET +1 0 0 1 146.853 195.782 cm +0 g 0 G +1 0 0 1 -146.853 -195.782 cm +BT +/F15 11.955 Tf 158.785 195.782 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 458.8 195.782 cm +0 g 0 G +1 0 0 1 -458.8 -195.782 cm +BT +/F15 11.955 Tf 458.8 195.782 Td[(54)]TJ +ET +1 0 0 1 470.506 195.782 cm +0 g 0 G +1 0 0 1 -370.984 -14.494 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.522 -181.288 cm +BT +/F15 11.955 Tf 99.522 181.288 Td[(psb)]TJ +ET +1 0 0 1 117.848 181.288 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -117.848 -181.288 cm +BT +/F15 11.955 Tf 121.36 181.288 Td[(cdall)]TJ +ET +1 0 0 1 145.422 181.288 cm +0 g 0 G +1 0 0 1 -145.422 -181.288 cm +BT +/F15 11.955 Tf 149.555 181.288 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Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 628.918 cm +0 g 0 G +1 0 0 1 -500.643 -628.918 cm +BT +/F15 11.955 Tf 500.643 628.918 Td[(68)]TJ +ET +1 0 0 1 512.349 628.918 cm +0 g 0 G +1 0 0 1 -370.984 -14.445 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -614.473 cm +BT +/F15 11.955 Tf 141.365 614.473 Td[(psb)]TJ +ET +1 0 0 1 159.691 614.473 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -614.473 cm +BT +/F15 11.955 Tf 163.203 614.473 Td[(sprn)]TJ +ET +1 0 0 1 185.379 614.473 cm +0 g 0 G +1 0 0 1 -185.379 -614.473 cm +BT +/F15 11.955 Tf 191.399 614.473 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 614.473 cm +0 g 0 G +1 0 0 1 -500.643 -614.473 cm +BT +/F15 11.955 Tf 500.643 614.473 Td[(70)]TJ +ET +1 0 0 1 512.349 614.473 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -600.027 cm +BT +/F15 11.955 Tf 141.365 600.027 Td[(psb)]TJ +ET +1 0 0 1 159.691 600.027 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -600.027 cm +BT +/F15 11.955 Tf 163.203 600.027 Td[(glo)1(b)]TJ +ET +1 0 0 1 185.366 600.027 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -185.366 -600.027 cm +BT +/F15 11.955 Tf 188.878 600.027 Td[(to)]TJ +ET +1 0 0 1 199.986 600.027 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -199.986 -600.027 cm +BT +/F15 11.955 Tf 203.497 600.027 Td[(lo)-27(c)]TJ +ET +1 0 0 1 218.13 600.027 cm +0 g 0 G +1 0 0 1 -218.13 -600.027 cm +BT +/F15 11.955 Tf 228.315 600.027 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 600.027 cm +0 g 0 G +1 0 0 1 -500.643 -600.027 cm +BT +/F15 11.955 Tf 500.643 600.027 Td[(71)]TJ +ET +1 0 0 1 512.349 600.027 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -585.581 cm +BT +/F15 11.955 Tf 141.365 585.581 Td[(psb)]TJ +ET +1 0 0 1 159.691 585.581 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -585.581 cm +BT +/F15 11.955 Tf 163.203 585.581 Td[(lo)-27(c)]TJ +ET +1 0 0 1 178.538 585.581 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -178.538 -585.581 cm +BT +/F15 11.955 Tf 182.049 585.581 Td[(to)]TJ +ET +1 0 0 1 193.157 585.581 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -193.157 -585.581 cm +BT +/F15 11.955 Tf 196.669 585.581 Td[(glo)1(b)]TJ +ET +1 0 0 1 218.13 585.581 cm +0 g 0 G +1 0 0 1 -218.13 -585.581 cm +BT +/F15 11.955 Tf 228.315 585.581 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 585.581 cm +0 g 0 G +1 0 0 1 -500.643 -585.581 cm +BT +/F15 11.955 Tf 500.643 585.581 Td[(72)]TJ +ET +1 0 0 1 512.349 585.581 cm +0 g 0 G +1 0 0 1 -388.543 -26.152 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -123.806 -559.429 cm +BT +/F19 11.955 Tf 123.806 559.429 Td[(7)-906(It)1(e)-1(rat)1(iv)32(e)-376(Metho)-31(ds)]TJ +ET +1 0 0 1 247.555 559.429 cm +0 g 0 G +1 0 0 1 -247.555 -559.429 cm +BT +/F19 11.955 Tf 498.899 559.429 Td[(73)]TJ +ET +1 0 0 1 141.365 544.983 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -544.983 cm +BT +/F15 11.955 Tf 141.365 544.983 Td[(psb)]TJ +ET +1 0 0 1 159.691 544.983 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -544.983 cm +BT +/F15 11.955 Tf 163.203 544.983 Td[(cg)]TJ +ET +1 0 0 1 178.16 544.983 cm +0 g 0 G +1 0 0 1 -178.16 -544.983 cm +BT +/F15 11.955 Tf 182.169 544.983 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 544.983 cm +0 g 0 G +1 0 0 1 -500.643 -544.983 cm +BT +/F15 11.955 Tf 500.643 544.983 Td[(74)]TJ +ET +1 0 0 1 512.349 544.983 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -530.537 cm +BT +/F15 11.955 Tf 141.365 530.537 Td[(psb)]TJ +ET +1 0 0 1 159.691 530.537 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -530.537 cm +BT +/F15 11.955 Tf 163.203 530.537 Td[(cgs)]TJ +ET +1 0 0 1 182.778 530.537 cm +0 g 0 G +1 0 0 1 -182.778 -530.537 cm +BT +/F15 11.955 Tf 191.399 530.537 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 530.537 cm +0 g 0 G +1 0 0 1 -500.643 -530.537 cm +BT +/F15 11.955 Tf 500.643 530.537 Td[(77)]TJ +ET +1 0 0 1 512.349 530.537 cm +0 g 0 G +1 0 0 1 -370.984 -14.445 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -516.092 cm +BT +/F15 11.955 Tf 141.365 516.092 Td[(psb)]TJ +ET +1 0 0 1 159.691 516.092 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -516.092 cm +BT +/F15 11.955 Tf 163.203 516.092 Td[(bicg)]TJ +ET +1 0 0 1 187.915 516.092 cm +0 g 0 G +1 0 0 1 -187.915 -516.092 cm +BT +/F15 11.955 Tf 191.399 516.092 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 516.092 cm +0 g 0 G +1 0 0 1 -500.643 -516.092 cm +BT +/F15 11.955 Tf 500.643 516.092 Td[(80)]TJ +ET +1 0 0 1 512.349 516.092 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -501.646 cm +BT +/F15 11.955 Tf 141.365 501.646 Td[(psb)]TJ +ET +1 0 0 1 159.691 501.646 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -501.646 cm +BT +/F15 11.955 Tf 163.203 501.646 Td[(bicgsta)1(b)]TJ +ET +1 0 0 1 209.441 501.646 cm +0 g 0 G +1 0 0 1 -209.441 -501.646 cm +BT +/F15 11.955 Tf 219.086 501.646 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 501.646 cm +0 g 0 G +1 0 0 1 -500.643 -501.646 cm +BT +/F15 11.955 Tf 500.643 501.646 Td[(83)]TJ +ET +1 0 0 1 512.349 501.646 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -487.2 cm +BT +/F15 11.955 Tf 141.365 487.2 Td[(psb)]TJ +ET +1 0 0 1 159.691 487.2 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -487.2 cm +BT +/F15 11.955 Tf 163.203 487.2 Td[(bicgsta)1(bl)]TJ +ET +1 0 0 1 212.693 487.2 cm +0 g 0 G +1 0 0 1 -212.693 -487.2 cm +BT +/F15 11.955 Tf 219.086 487.2 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 487.2 cm +0 g 0 G +1 0 0 1 -500.643 -487.2 cm +BT +/F15 11.955 Tf 500.643 487.2 Td[(86)]TJ +ET +1 0 0 1 512.349 487.2 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -472.754 cm +BT +/F15 11.955 Tf 141.365 472.754 Td[(psb)]TJ +ET +1 0 0 1 159.691 472.754 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -472.754 cm +BT +/F15 11.955 Tf 163.203 472.754 Td[(gmr)1(e)-1(s)]TJ +ET +1 0 0 1 197.085 472.754 cm +0 g 0 G +1 0 0 1 -197.085 -472.754 cm +BT +/F15 11.955 Tf 200.628 472.754 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 472.754 cm +0 g 0 G +1 0 0 1 -500.643 -472.754 cm +BT +/F15 11.955 Tf 500.643 472.754 Td[(89)]TJ +ET +1 0 0 1 512.349 472.754 cm +0 g 0 G +1 0 0 1 -388.543 -26.152 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -123.806 -446.602 cm +BT +/F19 11.955 Tf 123.806 446.602 Td[(8)-906(P)1(r)-1(econdi)1(ti)1(oner)-375(r)-1(o)1(uti)1(ne)-1(s)]TJ +ET +1 0 0 1 280.411 446.602 cm +0 g 0 G +1 0 0 1 -280.411 -446.602 cm +BT +/F19 11.955 Tf 498.899 446.602 Td[(92)]TJ +ET +1 0 0 1 141.365 432.156 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -432.156 cm +BT +/F15 11.955 Tf 141.365 432.156 Td[(psb)]TJ +ET +1 0 0 1 159.691 432.156 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -432.156 cm +BT +/F15 11.955 Tf 163.203 432.156 Td[(precse)-1(t)]TJ +ET +1 0 0 1 199.036 432.156 cm +0 g 0 G +1 0 0 1 -199.036 -432.156 cm +BT +/F15 11.955 Tf 209.857 432.156 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 432.156 cm +0 g 0 G +1 0 0 1 -500.643 -432.156 cm +BT +/F15 11.955 Tf 500.643 432.156 Td[(93)]TJ +ET +1 0 0 1 512.349 432.156 cm +0 g 0 G +1 0 0 1 -370.984 -14.445 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -417.711 cm +BT +/F15 11.955 Tf 141.365 417.711 Td[(psb)]TJ +ET +1 0 0 1 159.691 417.711 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -417.711 cm +BT +/F15 11.955 Tf 163.203 417.711 Td[(precbld)]TJ +ET +1 0 0 1 200.922 417.711 cm +0 g 0 G +1 0 0 1 -200.922 -417.711 cm +BT +/F15 11.955 Tf 209.857 417.711 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 417.711 cm +0 g 0 G +1 0 0 1 -500.643 -417.711 cm +BT +/F15 11.955 Tf 500.643 417.711 Td[(94)]TJ +ET +1 0 0 1 512.349 417.711 cm +0 g 0 G +1 0 0 1 -370.984 -14.446 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -403.265 cm +BT +/F15 11.955 Tf 141.365 403.265 Td[(psb)]TJ +ET +1 0 0 1 159.691 403.265 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.512 0.199 l +S +Q +1 0 0 1 -159.691 -403.265 cm +BT +/F15 11.955 Tf 163.203 403.265 Td[(precaply)]TJ +ET +1 0 0 1 206.45 403.265 cm +0 g 0 G +1 0 0 1 -206.45 -403.265 cm +BT +/F15 11.955 Tf 209.857 403.265 Td[(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 500.643 403.265 cm +0 g 0 G +1 0 0 1 -500.643 -403.265 cm +BT +/F15 11.955 Tf 500.643 403.265 Td[(95)]TJ +ET +1 0 0 1 512.349 403.265 cm +0 g 0 G +1 0 0 1 -388.543 -26.152 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -123.806 -377.113 cm +BT +/F19 11.955 Tf 123.806 377.113 Td[(9)-906(Er)-1(ror)-375(handli)1(ng)]TJ +ET +1 0 0 1 228.503 377.113 cm +0 g 0 G +1 0 0 1 -228.503 -377.113 cm +BT +/F19 11.955 Tf 498.899 377.113 Td[(97)]TJ +ET +1 0 0 1 141.365 362.667 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -141.365 -362.667 cm +BT +/F15 11.955 Tf 141.365 362.667 Td[(psb)]TJ +ET +1 0 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-(columns)h(in)g(the)1129 5006 y(sparse)i(co)r(e\016cien)n(t)i(matrix.) -36 b(They)28 b(include)g(the)g(halo.)2150 5255 y(4)p -eop -%%Page: 5 5 -5 4 bop 498 523 a Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 -b(p)r(oin)n(ter)g(to)g(in)n(teger)g(arra)n(y)e(of)j(dimension)f(10.)291 -687 y Fm(halo)p 471 687 29 4 v 34 w(index)41 b Fl(A)32 -b(list)g(of)g(the)g(halo)f(and)h(b)r(oundary)f(elemen)n(ts)h(for)f(the) -h(curren)n(t)f(pro)r(cess)498 787 y(to)e(b)r(e)g(exc)n(hanged)e(with)j -(other)e(pro)r(cesses;)g(for)g(eac)n(h)g(pro)r(cesses)f(with)i(whic)n -(h)g(it)g(is)498 887 y(necessary)d(to)h(comm)n(unicate:)575 -1051 y(1.)41 b(Pro)r(cess)26 b(iden)n(ti\014er;)575 1182 -y(2.)41 b(Num)n(b)r(er)28 b(of)f(p)r(oin)n(ts)h(to)f(b)r(e)h(receiv)n -(ed;)575 1313 y(3.)41 b(Indices)27 b(of)h(p)r(oin)n(ts)f(to)h(b)r(e)g -(receiv)n(ed;)575 1445 y(4.)41 b(Num)n(b)r(er)28 b(of)f(p)r(oin)n(ts)h -(to)f(b)r(e)h(sen)n(t;)575 1576 y(5.)41 b(Indices)27 -b(of)h(p)r(oin)n(ts)f(to)h(b)r(e)g(sen)n(t;)498 1740 -y(The)e(list)g(ma)n(y)f(con)n(tain)h(an)f(arbitrary)f(n)n(um)n(b)r(er)i -(of)f(groups;)h(its)g(end)g(is)f(mark)n(ed)g(b)n(y)498 -1840 y(a)i(-1.)498 1939 y(Sp)r(eci\014ed)h(as:)37 b(a)27 -b(p)r(oin)n(ter)g(to)g(an)h(in)n(teger)e(arra)n(y)g(of)h(rank)g(one.) -291 2104 y Fm(o)m(vrlap)p 557 2104 V 35 w(index)41 b -Fl(A)27 b(list)g(of)f(the)h(o)n(v)n(erlap)d(elemen)n(ts)j(for)f(the)g -(curren)n(t)g(pro)r(cess,)g(organized)498 2203 y(in)i(groups)e(lik)n(e) -h(the)h(previous)f(v)n(ector:)575 2368 y(1.)41 b(Pro)r(cess)26 -b(iden)n(ti\014er;)575 2499 y(2.)41 b(Num)n(b)r(er)28 -b(of)f(p)r(oin)n(ts)h(to)f(b)r(e)h(receiv)n(ed;)575 2630 -y(3.)41 b(Indices)27 b(of)h(p)r(oin)n(ts)f(to)h(b)r(e)g(receiv)n(ed;) -575 2761 y(4.)41 b(Num)n(b)r(er)28 b(of)f(p)r(oin)n(ts)h(to)f(b)r(e)h -(sen)n(t;)575 2892 y(5.)41 b(Indices)27 b(of)h(p)r(oin)n(ts)f(to)h(b)r -(e)g(sen)n(t;)498 3057 y(The)e(list)g(ma)n(y)f(con)n(tain)h(an)f -(arbitrary)f(n)n(um)n(b)r(er)i(of)f(groups;)h(its)g(end)g(is)f(mark)n -(ed)g(b)n(y)498 3156 y(a)i(-1.)498 3256 y(Sp)r(eci\014ed)h(as:)37 -b(a)27 b(p)r(oin)n(ter)g(to)g(an)h(in)n(teger)e(arra)n(y)g(of)h(rank)g -(one.)291 3421 y Fm(o)m(vrlap)p 557 3421 V 35 w(index)41 -b Fl(F)-7 b(or)27 b(all)g(o)n(v)n(erlap)f(p)r(oin)n(ts)h(b)r(elonging)g -(to)h(th)g(ecurren)n(t)e(pro)r(cess:)575 3585 y(1.)41 -b(Ov)n(erlap)26 b(p)r(oin)n(t)h(index;)575 3716 y(2.)41 -b(Num)n(b)r(er)28 b(of)f(pro)r(cesses)f(sharing)g(that)i(o)n(v)n(erlap) -e(p)r(oin)n(ts;)498 3880 y(The)g(list)g(ma)n(y)f(con)n(tain)h(an)f -(arbitrary)f(n)n(um)n(b)r(er)i(of)f(groups;)h(its)g(end)g(is)f(mark)n -(ed)g(b)n(y)498 3980 y(a)i(-1.)498 4080 y(Sp)r(eci\014ed)h(as:)37 -b(a)27 b(p)r(oin)n(ter)g(to)g(an)h(in)n(teger)e(arra)n(y)g(of)h(rank)g -(one.)291 4244 y Fm(lo)s(c)p 417 4244 V 33 w(to)p 535 -4244 V 35 w(glob)40 b Fl(eac)n(h)29 b(elemen)n(t)h Fh(i)g -Fl(of)g(this)h(arra)n(y)c(con)n(tains)i(global)g(iden)n(ti\014er)h(of)g -(the)g(lo)r(cal)498 4344 y(v)-5 b(ariable)27 b Fh(i)p -Fl(.)498 4443 y(Sp)r(eci\014ed)h(as:)37 b(a)27 b(p)r(oin)n(ter)g(to)g -(an)h(in)n(teger)e(arra)n(y)g(of)h(rank)g(one.)291 4608 -y Fm(glob)p 473 4608 V 33 w(to)p 591 4608 V 34 w(lo)s(c)41 -b Fl(if)30 b(global)e(v)-5 b(ariable)28 b Fh(i)h Fl(is)g(read)g(b)n(y)g -(curren)n(t)f(pro)r(cess)g(then)i(elemen)n(t)g Fh(i)f -Fl(con-)498 4707 y(tains)c(lo)r(cal)g(index)h(correp)r(onding)e(to)h -(global)f(v)-5 b(ariable)25 b Fh(i)p Fl(;)h(else)f(elemen)n(t)h -Fh(i)f Fl(con)n(tains)498 4807 y Fg(\000)p Fl(\()p Fh(np)12 -b Fl(+)g Fh(p)g Fl(+)g(1\))21 b(where)j Fh(np)g Fl(is)g(the)g(total)g -(n)n(um)n(b)r(er)g(of)g(pro)r(cesses)f(and)h Fh(p)g Fl(is)g(the)h -(index)498 4907 y(of)j(the)g(pro)r(cess)e(o)n(wning)h(global)f(index)i -Fh(i)p Fl(.)498 5006 y(Sp)r(eci\014ed)g(as:)37 b(a)27 -b(p)r(oin)n(ter)g(to)g(an)h(in)n(teger)e(arra)n(y)g(of)h(rank)g(one.) -1702 5255 y(5)p eop -%%Page: 6 6 -6 5 bop 739 523 a Fl(F)n(OR)-7 b(TRAN90)33 b(in)n(terface)g(for)g -Fh(decomp)p 2026 523 25 4 v 30 w(data)h Fl(structures)f(is)g(therefore) 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Fh(dot)p Fl(,)e Fh(X)7 b Fl(,)27 -b Fh(Y)648 b Fm(F)-8 b(unction)p 951 3079 V 1001 3148 -a Fl(Long)27 b(Precision)f(Real)257 b(F90)p 2130 3148 -25 4 v 29 w(PSDOT)1001 3248 y(Long)27 b(Precision)f(Complex)99 -b(F90)p 2130 3248 V 29 w(PSDOT)p 951 3281 1544 4 v 1326 -3513 a(T)-7 b(able)28 b(2.2:)36 b(Data)27 b(t)n(yp)r(es)291 -3782 y Fm(On)k(En)m(try)291 3946 y(x)41 b Fl(the)h(lo)r(cal)e(p)r -(ortion)g(of)g(global)g(dense)h(matrix)f Fh(X)7 b Fl(.)75 -b(This)41 b(function)g(computes)g(the)498 4046 y(lo)r(cation)30 -b(of)h(the)g(\014rst)g(elemen)n(t)g(of)f(lo)r(cal)h(subarra)n(y)d -(used,)k(based)e(on)h Fh(j)5 b(x)31 b Fl(and)g(the)498 -4145 y(\014eld)d Fh(matr)r(ix)p 945 4145 25 4 v 30 w(data)g -Fl(of)g Fh(decomp)p 1532 4145 V 29 w(data)g Fl(.)498 -4245 y(Scop)r(e:)37 b Fm(lo)s(cal)498 4344 y Fl(T)n(yp)r(e:)g -Fm(required)498 4444 y Fl(Sp)r(eci\014ed)28 b(as:)36 -b(a)27 b(p)r(oin)n(ter)g(to)h(arra)n(y)d(of)i(rank)f(one)i(or)e(t)n(w)n -(o)h(con)n(taining)f(n)n(um)n(b)r(ers)h(of)498 4544 y(t)n(yp)r(e)h(sp)r -(eci\014ed)g(in)g(T)-7 b(able)27 b(2.2.)36 b(The)28 b(rank)e(of)i -Fh(x)g Fl(m)n(ust)g(b)r(e)g(the)g(same)f(of)g Fh(y)s -Fl(.)291 4707 y Fm(y)41 b Fl(the)h(lo)r(cal)f(p)r(ortion)g(of)g(global) -f(dense)i(matrix)e Fh(Y)19 b Fl(.)78 b(This)41 b(function)h(computes)g -(the)498 4807 y(lo)r(cation)34 b(of)g(the)g(\014rst)g(elemen)n(t)g(of)g -(lo)r(cal)g(subarra)n(y)e(used,)k(based)d(on)h Fh(iy)s(;)14 -b(j)5 b(y)36 b Fl(and)498 4907 y(the)28 b(\014eld)g Fh(matr)r(ix)p -1088 4907 V 30 w(data)g Fl(of)g Fh(decomp)p 1675 4907 -V 29 w(data)g Fl(.)498 5006 y(Scop)r(e:)37 b Fm(lo)s(cal)1681 -5255 y Fl(11)p eop -%%Page: 12 12 -12 11 bop 946 523 a Fl(T)n(yp)r(e:)37 b Fm(required)946 -623 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(p)r(oin)n(ter)g(to)g(arra) -n(y)e(of)i(rank)g(one)g(or)f(t)n(w)n(o)h(con)n(taining)f(n)n(um)n(b)r -(ers)h(of)946 722 y(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g(T)-7 -b(able)27 b(2.2.)36 b(The)28 b(rank)f(of)g Fh(y)k Fl(m)n(ust)c(b)r(e)h -(the)g(same)f(of)h 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30 w(PSAMAX)g(\()p Ff(x,de)l(c)l(omp)p -2018 2722 26 4 v 32 w(data,)j(jx)p Fl(\))p 474 2947 2497 -4 v 524 3017 a Fh(amax)620 b(X)917 b Fm(F)-8 b(unction)p -474 3050 V 524 3120 a Fl(Long)27 b(Precision)f(Real)99 -b(Long)27 b(Precision)f(Real)257 b(F90)p 2481 3120 25 -4 v 29 w(PSAMAX)524 3220 y(Long)27 b(Precision)f(Real)99 -b(Long)27 b(Precision)f(Complex)99 b(F90)p 2481 3220 -V 29 w(PSZAMAX)p 474 3253 2497 4 v 1326 3485 a(T)-7 b(able)28 -b(2.4:)36 b(Data)27 b(t)n(yp)r(es)291 3768 y Fm(On)k(En)m(try)291 -3939 y(x)41 b Fl(the)h(lo)r(cal)e(p)r(ortion)g(of)g(global)g(dense)h -(matrix)f Fh(X)7 b Fl(.)75 b(This)41 b(function)g(computes)g(the)498 -4039 y(lo)r(cation)30 b(of)h(the)g(\014rst)g(elemen)n(t)g(of)f(lo)r -(cal)h(subarra)n(y)d(used,)k(based)e(on)h Fh(j)5 b(x)31 -b Fl(and)g(the)498 4138 y(\014eld)d Fh(matr)r(ix)p 945 -4138 25 4 v 30 w(data)g Fl(of)g Fh(decomp)p 1532 4138 -V 29 w(data)g Fl(.)498 4238 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -4337 y Fl(T)n(yp)r(e:)g Fm(required)498 4437 y 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-(global)f(dense)h(matrix)g Fh(X)7 b Fl(.)55 b(This)34 -b(subroutine)g(computes)g(the)946 623 y(lo)r(cation)d(of)f(the)i -(\014rst)e(elemen)n(t)h(of)g(lo)r(cal)f(subarra)n(y)e(used,)k(based)e -(on)h Fh(j)5 b(x)31 b Fl(and)g(the)946 722 y(\014eld)d -Fh(matr)r(ix)p 1393 722 25 4 v 31 w(data)f Fl(of)h Fh(decomp)p -1980 722 V 30 w(data)f Fl(.)946 822 y(Scop)r(e:)37 b -Fm(lo)s(cal)946 922 y Fl(T)n(yp)r(e:)g Fm(required)946 -1021 y Fl(Sp)r(eci\014ed)25 b(as:)34 b(a)24 b(rank)f(one)h(or)f(t)n(w)n -(o)g(arra)n(y)e(con)n(taining)i(n)n(um)n(b)r(ers)h(of)g(t)n(yp)r(e)g -(sp)r(eci\014ed)946 1121 y(in)k(T)-7 b(able)28 b(2.9.)36 -b(The)27 b(rank)g(of)h Fh(x)g Fl(m)n(ust)f(b)r(e)h(the)g(same)f(of)h -Fh(y)s Fl(.)739 1277 y Fm(b)s(eta)41 b Fl(the)28 b(scalar)e -Fh(\014)t Fl(.)946 1377 y(Scop)r(e:)37 b Fm(global)946 -1476 y Fl(T)n(yp)r(e:)g Fm(required)946 1576 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(n)n(um)n(b)r(er)g(of)h(the)g(data)f(t)n(yp)r(e)h -(indicated)g(in)f(T)-7 b(able)28 b(2.9.)739 1732 y Fm(y)42 -b Fl(the)35 b(lo)r(cal)f(p)r(ortion)g(of)h(global)f(dense)g(matrix)g -Fh(Y)19 b Fl(.)58 b(This)35 b(subroutine)f(computes)h(the)946 -1831 y(lo)r(cation)c(of)g(the)g(\014rst)g(elemen)n(t)g(of)h(lo)r(cal)e -(subarra)n(y)f(used,)j(based)e(on)h Fh(j)5 b(y)34 b Fl(and)d(the)946 -1931 y(\014eld)d Fh(matr)r(ix)p 1393 1931 V 31 w(data)f -Fl(of)h Fh(decomp)p 1980 1931 V 30 w(data)f Fl(.)946 -2031 y(Scop)r(e:)37 b Fm(lo)s(cal)946 2130 y Fl(T)n(yp)r(e:)g -Fm(required)946 2230 y Fl(Sp)r(eci\014ed)25 b(as:)34 -b(a)24 b(rank)f(one)h(or)f(t)n(w)n(o)g(arra)n(y)e(con)n(taining)i(n)n -(um)n(b)r(ers)h(of)g(t)n(yp)r(e)g(sp)r(eci\014ed)946 -2330 y(in)k(T)-7 b(able)28 b(2.9.)36 b(The)27 b(rank)g(of)h -Fh(y)i Fl(m)n(ust)e(b)r(e)g(the)g(same)f(of)g Fh(x)p -Fl(.)739 2486 y Fm(decomp)p 1066 2486 29 4 v 33 w(data)42 -b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n(unications.)946 -2585 y(Scop)r(e:)37 b Fm(lo)s(cal)946 2685 y Fl(T)n(yp)r(e:)g -Fm(required)946 2785 y Fl(Sp)r(eci\014ed)29 b(as:)36 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41 4 v 48 w(PSSPSM|T)-11 -b(riangular)45 b(System)g(Solv)l(e)739 981 y Fl(This)27 -b(subroutine)h(computes)f(the)h(T)-7 b(riangular)26 b(System)h(Solv)n -(e:)1628 1259 y Fh(Y)101 b Fg( )83 b Fh(\013P)2049 1271 -y Fc(r)2087 1259 y Fh(T)2148 1224 y Fb(\000)p Fd(1)2236 -1259 y Fh(P)2289 1271 y Fc(c)2323 1259 y Fh(X)25 b Fl(+)18 -b Fh(\014)t(Y)1628 1383 y(Y)101 b Fg( )83 b Fh(\013D)r(P)2120 -1395 y Fc(r)2158 1383 y Fh(T)2219 1349 y Fb(\000)p Fd(1)2307 -1383 y Fh(P)2360 1395 y Fc(c)2394 1383 y Fh(X)25 b Fl(+)18 -b Fh(\014)t(Y)1628 1508 y(Y)101 b Fg( )83 b Fh(\013P)2049 -1520 y Fc(r)2087 1508 y Fh(T)2148 1473 y Fb(\000)p Fd(1)2236 -1508 y Fh(P)2289 1520 y Fc(c)2323 1508 y Fh(D)r(X)25 -b Fl(+)18 b Fh(\014)t(Y)1628 1632 y(Y)101 b Fg( )83 b -Fh(\013P)2049 1644 y Fc(r)2087 1632 y Fh(T)2148 1598 -y Fb(\000)p Fc(T)2251 1632 y Fh(P)2304 1644 y Fc(c)2338 -1632 y Fh(X)25 b Fl(+)18 b Fh(\014)t(Y)1628 1757 y(Y)101 -b Fg( )83 b Fh(\013D)r(P)2120 1769 y Fc(r)2158 1757 y -Fh(T)2219 1723 y Fb(\000)p Fc(T)2322 1757 y Fh(P)2375 -1769 y Fc(c)2409 1757 y Fh(X)25 b Fl(+)18 b Fh(\014)t(Y)1628 -1881 y(Y)101 b Fg( )83 b Fh(\013P)2049 1893 y Fc(r)2087 -1881 y Fh(T)2148 1847 y Fb(\000)p Fc(T)2251 1881 y Fh(P)2304 -1893 y Fc(c)2338 1881 y Fh(D)r(X)25 b Fl(+)18 b Fh(\014)t(Y)1628 -2006 y(Y)101 b Fg( )83 b Fh(\013P)2049 2018 y Fc(r)2087 -2006 y Fh(T)2148 1972 y Fb(\000)p Fc(H)2262 2006 y Fh(P)2315 -2018 y Fc(c)2349 2006 y Fh(X)24 b Fl(+)19 b Fh(\014)t(Y)1628 -2130 y(Y)101 b Fg( )83 b Fh(\013D)r(P)2120 2142 y Fc(r)2158 -2130 y Fh(T)2219 2096 y Fb(\000)p Fc(H)2333 2130 y Fh(P)2386 -2142 y Fc(c)2420 2130 y Fh(X)25 b Fl(+)18 b Fh(\014)t(Y)1628 -2255 y(Y)101 b Fg( )83 b Fh(\013P)2049 2267 y Fc(r)2087 -2255 y Fh(T)2148 2221 y Fb(\000)p Fc(H)2262 2255 y Fh(P)2315 -2267 y Fc(c)2349 2255 y Fh(D)r(X)25 b Fl(+)18 b Fh(\014)t(Y)863 -2558 y Fl(where:)739 2721 y Fh(X)48 b Fl(is)27 b(the)h(global)f(dense)g -(submatrix)g Fh(X)2017 2733 y Fd(:)p Fc(;j)s(x)p Fd(:)p -Fc(j)s(x)p Fd(+)p Fc(n)p Fb(\000)p Fd(1)739 2885 y Fh(Y)60 -b Fl(is)28 b(the)g(global)e(dense)h(submatrix)g Fh(Y)1987 -2897 y Fd(:)p Fc(;j)s(y)r Fd(:)p Fc(j)s(y)r Fd(+)p Fc(n)p -Fb(\000)p Fd(1)739 3050 y Fh(T)52 b Fl(is)28 b(the)g(global)e(sparse)h -(blo)r(c)n(k)g(triangular)f(submatrix)h Fh(T)739 3214 -y(D)43 b Fl(is)28 b(the)g(scaling)f(diagonal)f(matrix.)739 -3378 y Fh(P)792 3390 y Fc(r)829 3378 y Fh(;)14 b(P)919 -3390 y Fc(c)994 3378 y Fl(are)27 b(the)h(p)r(erm)n(utation)f(matrices.) -739 3652 y Fe(Syn)l(tax)1169 3834 y Fl(CALL)h(F90)p 1566 -3834 25 4 v 29 w(PSSPSM)f(\()p Ff(alpha,)32 b(t,)e(x,)g(b)l(eta,)g(y,)g -(de)l(c)l(omp)p 2959 3834 26 4 v 32 w(data)p Fl(\))739 -4033 y(CALL)e(F90)p 1136 4033 25 4 v 29 w(PSSPSM)891 -4133 y(\()p Ff(alpha,)33 b(t,)d(x,)f(b)l(eta,)i(y,)f(de)l(c)l(omp)p -1906 4133 26 4 v 32 w(data,)h(tr)l(ans,)e(unit,)h(choic)l(e,)h(diag,)h -(n,)e(jx,)g(jy,)h(work)p Fl(\))p 1381 4355 1581 4 v 1431 -4424 a Fh(T)12 b Fl(,)27 b Fh(X)7 b Fl(,)27 b Fh(Y)18 -b Fl(,)28 b Fh(D)r Fl(,)g Fh(\013)p Fl(,)g Fh(\014)359 -b Fm(Subroutine)p 1381 4458 V 1431 4527 a Fl(Long)26 -b(Precision)g(Real)258 b(F90)p 2560 4527 25 4 v 29 w(PSSPSM)1431 -4627 y(Long)26 b(Precision)g(Complex)100 b(F90)p 2560 -4627 V 29 w(PSSPSM)p 1381 4660 1581 4 v 1754 4892 a(T)-7 -b(able)27 b(2.10:)36 b(Data)27 b(t)n(yp)r(es)2130 5255 -y(26)p eop -%%Page: 27 27 -27 26 bop 291 523 a Fm(On)31 b(En)m(try)291 692 y(alpha)42 -b Fl(the)27 b(scalar)f Fh(\013)p Fl(.)498 792 y(Scop)r(e:)37 -b Fm(global)498 892 y Fl(T)n(yp)r(e:)g Fm(required)498 -991 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(n)n(um)n(b)r(er)g(of)h -(the)g(data)f(t)n(yp)r(e)h(indicated)f(in)h(T)-7 b(able)27 -b(2.10.)291 1161 y Fm(t)41 b Fl(the)28 b(global)f(p)r(ortion)g(of)g -(the)h(sparse)f(matrix)g Fh(T)12 b Fl(.)498 1260 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 1360 y Fl(T)n(yp)r(e:)g Fm(required)498 -1460 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(structured)g(data)g(t)n -(yp)r(e)h(sp)r(eci\014ed)g(in)g Fg(x)f Fl(1.)291 1629 -y Fm(x)41 b Fl(the)35 b(lo)r(cal)e(p)r(ortion)h(of)g(global)f(dense)h -(matrix)f Fh(X)7 b Fl(.)56 b(This)34 b(subroutine)g(computes)g(the)498 -1729 y(lo)r(cation)c(of)h(the)g(\014rst)g(elemen)n(t)g(of)f(lo)r(cal)h -(subarra)n(y)d(used,)k(based)e(on)h Fh(j)5 b(x)31 b Fl(and)g(the)498 -1828 y(\014eld)d Fh(matr)r(ix)p 945 1828 25 4 v 30 w(data)g -Fl(of)g Fh(decomp)p 1532 1828 V 29 w(data)g Fl(.)498 -1928 y(Scop)r(e:)37 b Fm(lo)s(cal)498 2027 y Fl(T)n(yp)r(e:)g -Fm(required)498 2127 y Fl(Sp)r(eci\014ed)25 b(as:)34 -b(a)24 b(rank)f(one)g(or)g(t)n(w)n(o)h(arra)n(y)d(con)n(taining)i(n)n -(um)n(b)r(ers)h(of)f(t)n(yp)r(e)i(sp)r(eci\014ed)498 -2227 y(in)j(T)-7 b(able)27 b(2.10.)36 b(The)28 b(rank)e(of)i -Fh(x)g Fl(m)n(ust)g(b)r(e)g(the)g(same)f(of)g Fh(y)s -Fl(.)291 2396 y Fm(b)s(eta)41 b Fl(the)28 b(scalar)e -Fh(\014)t Fl(.)498 2496 y(Scop)r(e:)37 b Fm(global)498 -2595 y Fl(T)n(yp)r(e:)g Fm(required)498 2695 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(n)n(um)n(b)r(er)g(of)h(the)g(data)f(t)n(yp)r(e)h -(indicated)f(in)h(T)-7 b(able)27 b(2.10.)291 2864 y Fm(y)41 -b Fl(the)36 b(lo)r(cal)e(p)r(ortion)g(of)h(global)e(dense)i(matrix)f -Fh(Y)19 b Fl(.)58 b(This)35 b(subroutine)f(computes)h(the)498 -2964 y(lo)r(cation)c(of)g(the)g(\014rst)g(elemen)n(t)g(of)g(lo)r(cal)g -(subarra)n(y)d(used,)k(based)f(on)g Fh(j)5 b(y)34 b Fl(and)d(the)498 -3064 y(\014eld)d Fh(matr)r(ix)p 945 3064 V 30 w(data)g -Fl(of)g Fh(decomp)p 1532 3064 V 29 w(data)g Fl(.)498 -3163 y(Scop)r(e:)37 b Fm(lo)s(cal)498 3263 y Fl(T)n(yp)r(e:)g -Fm(required)498 3362 y Fl(Sp)r(eci\014ed)25 b(as:)34 -b(a)24 b(rank)f(one)g(or)g(t)n(w)n(o)h(arra)n(y)d(con)n(taining)i(n)n -(um)n(b)r(ers)h(of)f(t)n(yp)r(e)i(sp)r(eci\014ed)498 -3462 y(in)j(T)-7 b(able)27 b(2.10.)36 b(The)28 b(rank)e(of)i -Fh(y)i Fl(m)n(ust)e(b)r(e)g(the)g(same)f(of)g Fh(x)p -Fl(.)291 3631 y Fm(decomp)p 618 3631 29 4 v 33 w(data)42 -b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n(unications.)498 -3731 y(Scop)r(e:)37 b Fm(lo)s(cal)498 3831 y Fl(T)n(yp)r(e:)g -Fm(required)498 3930 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)291 4100 y Fm(trans)42 b Fl(sp)r(ecify)28 -b(with)g Ff(unitd)f Fl(the)h(op)r(eration)f(to)g(p)r(erform.)498 -4269 y Fm(trans)33 b(=)f('N')40 b Fl(the)28 b(op)r(eration)e(is)i(with) -g(no)f(transp)r(osed)g(matrix)498 4403 y Fm(trans)33 -b(=)f('T')41 b Fl(the)28 b(op)r(eration)e(is)i(with)g(transp)r(osed)e -(matrix.)498 4538 y Fm(trans)33 b(=)f('C')40 b Fl(the)28 -b(op)r(eration)f(is)g(with)h(conjugate)f(transp)r(osed)g(matrix.)498 -4707 y(Scop)r(e:)37 b Fm(global)498 4807 y Fl(T)n(yp)r(e:)g -Fm(optional)498 4907 y Fl(Default:)h Fh(tr)r(ans)23 b -Fl(=)g Fh(N)498 5006 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(c)n(haracter)e(v)-5 b(ariable.)1681 5255 y(27)p -eop -%%Page: 28 28 -28 27 bop 739 523 a Fm(unitd)41 b Fl(sp)r(ecify)28 b(with)g -Ff(tr)l(ans)f Fl(the)h(op)r(eration)f(to)g(p)r(erform.)946 -689 y Fm(unitd)32 b(=)g('U')41 b Fl(the)28 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-(eci\014ed)498 1652 y(in)28 b(T)-7 b(able)27 b(2.11.)1681 -5255 y(31)p eop -%%Page: 32 32 -32 31 bop 739 740 a Fe(F90)p 966 740 41 4 v 48 w(PSO)l(VRL|Ov)l(erlap) -46 b(Up)t(date)739 990 y Fl(These)27 b(subroutines)g(restore)f(a)h -(consisten)n(t)g(status)h(for)f(the)h(o)n(v)n(erlap)d(elemen)n(ts:)1998 -1190 y Fh(X)30 b Fg( )23 b Fh(QX)739 1373 y Fl(where:)739 -1540 y Fh(X)48 b Fl(is)27 b(the)h(global)f(dense)g(submatrix)g -Fh(X)739 1708 y(Q)41 b Fl(is)28 b(the)g(o)n(v)n(erlap)d(op)r(erator;)h -(it)i(is)f(the)h(comp)r(osition)f(of)h(t)n(w)n(o)f(op)r(erators)e -Fh(P)3164 1720 y Fc(a)3233 1708 y Fl(and)i Fh(P)3459 -1678 y Fc(T)3511 1708 y Fl(.)p 1375 1895 1593 4 v 1424 -1964 a Fh(X)917 b Fm(Subroutine)p 1375 1998 V 1424 2067 -a Fl(Long)27 b(Precision)f(Real)257 b(F90)p 2553 2067 -25 4 v 29 w(PSO)n(VRL)1424 2167 y(Long)27 b(Precision)f(Complex)99 -b(F90)p 2553 2167 V 29 w(PSO)n(VRL)p 1375 2200 1593 4 -v 1754 2432 a(T)-7 b(able)27 b(2.12:)36 b(Data)27 b(t)n(yp)r(es)739 -2809 y 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Fg(p)p 2020 1057 94 4 v 64 x Fh(P)2073 1133 y Fc(a)2114 -1121 y Fl(;)498 1287 y(Scop)r(e:)37 b Fm(global)498 1386 -y Fl(Default:)h Fh(update)p 1078 1386 25 4 v 29 w(ty)s(pe)22 -b Fl(=)g Fh(:tr)r(ue:)498 1486 y Fl(Scop)r(e:)37 b Fm(global)498 -1586 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(in)n(teger)f(v)-5 -b(ariable.)291 1752 y Fm(w)m(ork)42 b Fl(the)28 b(w)n(ork)e(arra)n(y)-7 -b(.)498 1851 y(Scop)r(e:)37 b Fm(lo)s(cal)498 1951 y -Fl(T)n(yp)r(e:)g Fm(optional)498 2051 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(one)g(dimensional)g(arra)n(y)e(of)j(the)g(same)f(t)n -(yp)r(e)h(of)f Fh(X)7 b Fl(.)291 2217 y Fm(On)31 b(Return)291 -2383 y(x)41 b Fl(global)27 b(dense)g(result)h(matrix)f -Fh(X)7 b Fl(.)498 2482 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -2582 y Fl(T)n(yp)r(e:)g Fm(required)498 2682 y Fl(Sp)r(eci\014ed)28 -b(as:)36 b(a)27 b(p)r(oin)n(ter)g(to)h(arra)n(y)d(of)i(rank)f(one)i(or) -e(t)n(w)n(o)h(con)n(taining)f(n)n(um)n(b)r(ers)h(of)498 -2781 y(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g(T)-7 b(able)27 -b(2.12.)291 3056 y Fe(Usage)46 b(notes)392 3238 y Fl(1.)41 -b(If)21 b(there)g(is)f(no)h(o)n(v)n(erlap)d(in)j(the)g(data)g -(distribution,)h(no)e(op)r(erations)g(are)f(p)r(erformed;)392 -3404 y(2.)41 b(The)35 b(op)r(erator)f Fh(P)1084 3374 -y Fc(T)1171 3404 y Fl(p)r(erforms)h(the)g(reduction)g(sum)g(of)g(o)n(v) -n(erlap)f(elemen)n(ts;)k(it)e(is)498 3503 y(the)k(in)n(v)n(erse)e(of)h -(a)g(\\stretc)n(h")e(op)r(erator)h Fh(P)51 b Fl(that)40 -b(replicates)e(o)n(v)n(erlap)f(elemen)n(ts,)498 3603 -y(accoun)n(ting)27 b(for)g(the)h(ph)n(ysical)e(replication)h(of)h -(data;)392 3769 y(3.)41 b(The)21 b(op)r(erator)f Fh(P)1044 -3781 y Fc(a)1105 3769 y Fl(p)r(erforms)h(a)g(scaling)f(on)g(the)i(o)n -(v)n(erlap)d(elemen)n(ts)i(b)n(y)g(the)g(amoun)n(t)498 -3869 y(of)j(replication;)g(th)n(us,)h(when)f(com)n(bined)g(with)h(the)f -(reduction)f(op)r(erator,)g(it)i(imple-)498 3968 y(men)n(ts)j(the)g(a)n -(v)n(erage)c(of)k(replicated)f(elemen)n(ts)h(o)n(v)n(er)d(all)j(of)f -(their)h(instances.)392 4134 y(4.)41 b(The)c(square)f(ro)r(ot)h(up)r -(date)h(option)f(mak)n(es)f(it)i(p)r(ossible)f(to)g(applythe)g(follo)n -(wing)498 4234 y(op)r(erator:)1336 4334 y Fh(X)30 b Fg( )1541 -4257 y Fa(p)p 1624 4257 94 4 v 77 x Fh(P)1677 4346 y -Fc(a)1717 4334 y Fh(P)1782 4299 y Fc(T)1834 4334 y Fh(K)1911 -4299 y Fb(\000)p Fd(1)2000 4334 y Fh(P)2065 4257 y Fa(p)p -2148 4257 V 77 x Fh(P)2201 4346 y Fc(a)2241 4334 y Fh(X)498 -4483 y Fl(In)e(the)h(case)e(of)h(a)g(symmetric)g Fh(K)6 -b Fl(,)28 b(this)g(preserv)n(es)e(simmetry)i(of)g(the)h(o)n(v)n(erall)d -(pre-)498 4583 y(conditioner,)h(whic)n(h)h(w)n(ould)f(otherwise)f(b)r -(e)i(destro)n(y)n(ed.)1681 5255 y(33)p eop -%%Page: 34 34 -34 33 bop 739 1146 a Fk(Chapter)65 b(3)739 1561 y Fn(T)-19 -b(o)6 b(ols)77 b(Library)739 1993 y Fl(Routines)34 b(in)h(this)f(c)n -(hapter)f(pro)n(vide)g(a)h(con)n(v)n(enien)n(t)f(in)n(terface)h(to)g -(the)h(k)n(ernels)e(for)g(ini-)739 2092 y(tialize)25 -b(and)g(set)g(comm)n(unication)f(data)h(structures,)g(sparse)e(matrix)i -(and)g(dense)g(matrix;)739 2192 y(they)31 b(hide)g(most)f(of)g(the)h -(details)g(dep)r(ending)g(on)f(the)h(parallel)e(programming)g(en)n -(viron-)739 2291 y(men)n(t.)37 b(Their)27 b(in)n(terfaces)f(are)h -(de\014ned)g(in)h(the)g(mo)r(dule)f Fj(F90TOOLS)d Fl(T)-7 -b(o)27 b(use)g(the)h(TOOLS)739 2391 y(subroutines,)21 -b(the)f(user)f(m)n(ust)h(de\014ne)g(a)f(partition)g(subroutine)h(that)g -(sp)r(eci\014es)f(ho)n(w)g(global)739 2491 y(matrix)27 -b(ro)n(ws)f(are)h(assigned)f(o)n(v)n(er)g(all)h(pro)r(cesses.)2130 -5255 y(34)p eop -%%Page: 35 35 -35 34 bop 291 746 a Fe(P)-11 b(AR)g(TITION|User)43 b(de\014ned)f -(partition)j(subroutine)291 1000 y Fl(De\014nes)35 b(ho)n(w)f(global)g -(matrix)g(ro)n(ws)g(are)g(assigned)f(o)n(v)n(er)g(all)i(pro)r(cesses.) -57 b(This)35 b(routine)291 1100 y(m)n(ust)j(b)r(e)g(implemen)n(ted)h(b) -n(y)e(user)h(and)f(m)n(ust)h(b)r(e)h(passed)e(as)g(argumen)n(t)g(to)h -(all)g(T)-7 b(o)r(ols)291 1200 y(library)26 b(subroutine)h(that)h -(require)e(it.)291 1299 y(It)i(m)n(ust)f(satisfy)g(the)h(follo)n(wing)f -(sp)r(eci\014cation:)291 1472 y Fj(interface)421 1572 -y(subroutine)40 b(partition\(glob_i)o(nd)o(ex,)o(nr)o(ow)o(,np)o(,p)o -(v,n)o(v\))509 1671 y(integer)84 b(glob_index,np,nr)o(ow)o(,nv)509 -1771 y(integer)g(pv\(*\))421 1870 y(end)43 b(subroutine)c(partition)291 -1970 y(end)j(interface)291 2159 y Fm(On)31 b(En)m(try)291 -2332 y(glob)p 473 2332 29 4 v 33 w(index)41 b Fl(global)27 -b(matrix)g(ro)n(w)f(index)498 2432 y(Sp)r(eci\014ed)c(as:)33 -b(an)22 b(in)n(teger)e(v)-5 b(ariable)21 b(0)h Fg(\024)h -Fh(g)s(l)r(ob)p 1958 2432 25 4 v 28 w(index)g Fg(\024)g -Fh(N)9 b(o)p 2421 2432 V 30 w(r)r(ow)r Fl(,)24 b(where)d -Fh(N)9 b(o)p 2988 2432 V 30 w(r)r(ow)498 2531 y Fl(si)28 -b(the)g(total)f(n)n(um)n(b)r(er)g(of)h(global)e(matrix)h(ro)n(ws.)291 -2704 y Fm(pro)s(cs)41 b Fl(F)-7 b(or)27 b(return)g(v)-5 -b(alues)27 b(see)g(\\On)g(Return".)498 2804 y(Sp)r(eci\014ed)h(as:)37 -b(in)n(teger)26 b(arra)n(y)f(of)j(length)g Fh(l)h Fl(with)f -Fh(l)c Fg(\025)f Fh(N)2268 2816 y Fc(p)2306 2804 y Fl(.)291 -3076 y Fm(npro)s(cs)41 b Fl(see)27 b(\\On)g(Return".)291 -3249 y Fm(On)k(Return)291 3422 y(pro)s(cs)41 b Fl(con)n(tains)27 -b(pro)r(cess)f(iden)n(ti\014er)h(to)h(whic)n(h)f(is)h(assigned)e -Fh(g)s(l)r(ob)p 2420 3422 V 29 w(r)r(ow)31 b Fl(matrix)c(ro)n(w.)498 -3521 y(Sp)r(eci\014ed)h(as:)37 b(in)n(teger)26 b(arra)n(y)f(of)j -(length)g Fh(l)h Fl(with)f Fh(l)c Fg(\025)f Fh(N)2268 -3533 y Fc(p)2306 3521 y Fl(.)291 3794 y Fm(npro)s(cs)41 -b Fl(No)27 b(of)h(pro)r(cess)e(to)i(whic)n(h)f(is)h(assigned)e -Fh(g)s(l)r(ob)p 2025 3794 V 29 w(r)r(ow)31 b Fl(matrix)c(ro)n(w.)498 -3893 y(Sp)r(eci\014ed)h(as:)37 b(in)n(teger)26 b(1)d -Fg(\024)f Fh(pr)r(ocs)i Fg(\024)f Fh(N)1782 3905 y Fc(p)1820 -3893 y Fl(.)291 4177 y Fe(Usage)46 b(Notes)392 4362 y -Fl(1.)41 b(Duplicate)28 b(elemen)n(ts)g(are)e(not)i(admitted)g(on)f -(return)g(arra)n(y)f Fh(pr)r(ocs)392 4535 y Fl(2.)41 -b(If)20 b(this)f(subroutine)f(returns)h(for)f(a)h(ro)n(w)f(matrix)g -Fh(r)2035 4547 y Fc(m)2118 4535 y Fl(a)g(n)n(um)n(b)r(er)h(of)g(pro)r -(cesses)e Fh(npr)r(ocs)498 4634 y Fl(greater)25 b(than)i(1,)g(then)g -Fh(r)1289 4646 y Fc(m)1380 4634 y Fl(will)g(b)r(e)h(an)e(o)n(v)n(erlap) -f(ro)n(w)h(b)r(et)n(w)n(een)h(all)f(pro)r(cesses)g(that)498 -4734 y(o)n(wn)h(it.)392 4907 y(3.)41 b(An)21 b(example)e(of)h -(partition)f(subroutine)h(whic)n(h)g(sub)r(divide)g(sparse)f(matrix)g -(in)h(blo)r(c)n(k)498 5006 y(ro)n(ws)26 b(with)i(an)g(one)f(ro)n(w)f(o) -n(v)n(erlap)g(of)h(is:)1681 5255 y(35)p eop -%%Page: 36 36 -36 35 bop 946 523 a Fe(Example)46 b(1)1208 738 y Fj(SUBROUTINE)39 -b(PART_BLOCK\(GLOB_I)o(NDX)o(,P)o(RO)o(CS,)o(NP)o(ROC)o(S\))1208 -838 y(INTEGER)259 b(GLOB_INDX)1208 937 y(INTEGER)g(PROCS\(*\),NPROCS) -946 1236 y(C)218 b(...Common)40 b(area)i(previously)d(initialized)g -(...)1208 1336 y(COMMON)i(/BLOCK_DATA/)e(DIM_BLOCK,)g(NP)1208 -1435 y(INTEGER)i(DIM_BLOCK,)e(NP)1208 1535 y(SAVE)85 -b(/BLOCK_DATA/)946 1635 y(C)218 b(..DIM_BLOCK..is)37 -b(dimension)j(\(number)h(of)i(rows\))e(of)i(each)f(matrix)f(block)946 -1734 y(C)218 b(..NP.........is)37 b(number)k(of)i(processes)d(involved) -g(in)j(computation)1208 1934 y(NPROCS=1)1208 2033 y(PROCS\(1\))d(=)j -(\(GLOB_INDX-1\)/DIM)o(_BL)o(OC)o(K)1208 2133 y(IF)g -(\(\(MOD\(GLOB_INDX,)37 b(DIM_BLOCK\).EQ.0)o(\).A)o(ND)o(.)1164 -2232 y(+)44 b(\(PROCS\(NPROCS\).)o(NE.)o(\(N)o(P-)o(1\)\))o(\))37 -b(THEN)946 2332 y(C)305 b(....this)40 b(is)j(an)g(overlap)e(row....) -1469 2432 y(NPROCS)h(=)h(NPROCS+1)1469 2531 y(PROCS\(NPROCS\))c(=)k -(PROCS\(NPROCS-1\)+)o(1)1208 2631 y(ENDIF)1208 2731 y(RETURN)1208 -2930 y(BLOCK)e(DATA)h(BLOCK)1208 3029 y(COMMON)f(/BLOCK_DATA/)e -(DIM_BLOCK,)g(NP)1208 3129 y(INTEGER)i(DIM_BLOCK,)e(NP)1208 -3229 y(SAVE)85 b(/BLOCK_DATA/)2130 5255 y Fl(36)p eop -%%Page: 37 37 -37 36 bop 291 711 a Fe(F90)p 518 711 41 4 v 48 w(PSDSCALL)44 -b(|Allo)t(cate)i(Comm)l(unication)291 861 y(Descriptor)291 -1081 y Fl(This)25 b(subroutine)g(allo)r(cates)g(the)h(comm)n(unication) -f(desciptor)g(for)g(global)f(sparse)g(matrix)291 1181 -y Fh(A)p Fl(.)291 1450 y Fe(Syn)l(tax)577 1631 y Fl(CALL)j(F90)p -973 1631 25 4 v 29 w(PSDSCALL)h(\()p Ff(m,n,p)l(arts,ic)l(ontxt,)j -(ierrv,)g(de)l(c)l(omp)p 2655 1631 26 4 v 32 w(data)p -Fl(\))291 1831 y Fm(On)g(En)m(try)291 1983 y(m)40 b Fl(n)n(um)n(b)r(er) -27 b(of)h(ro)n(ws)e(of)h(global)g(sparse)f(submatrix)h -Fh(A)h Fl(to)f(allo)r(cate.)498 2083 y(Scop)r(e:)37 b -Fm(global)498 2182 y Fl(T)n(yp)r(e:)g Fm(required)498 -2282 y Fl(Sp)r(eci\014ed)20 b(as:)32 b(an)19 b(in)n(teger)f(v)-5 -b(ariable)18 b(0)23 b Fg(\024)f Fh(m)h Fg(\024)g Fh(decomp)p -2258 2282 25 4 v 30 w(data)p Fl(\045)p Fh(matr)r(ix)p -2780 2282 V 30 w(data)p Fl([)p Fh(M)p 3084 2282 V 39 -w Fl(].)291 2434 y Fm(n)41 b Fl(n)n(um)n(b)r(er)27 b(of)h(columns)f(of) -h(global)e(sparse)h(submatrix)g Fh(X)34 b Fl(to)27 b(allo)r(cate.)498 -2534 y(Scop)r(e:)37 b Fm(global)498 2633 y Fl(T)n(yp)r(e:)g -Fm(required)498 2733 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(an)27 b(in)n(teger)g(v)-5 b(ariable)26 b Fh(n)d Fg(\025)g -Fl(0.)291 2885 y Fm(parts)42 b Fl(function)24 b(that)h(sp)r(ecify)f -(the)g(partition)g(of)g(global)f(matrix)g(ro)n(ws)g(o)n(v)n(er)f(all)i -(pro)r(cess.)498 2985 y(See)k(...)37 b(for)27 b(more)g(informations.) -498 3084 y(Scop)r(e:)37 b Fm(global)498 3184 y Fl(T)n(yp)r(e:)g -Fm(required)498 3284 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(pro)r(cedure.)291 3436 y Fm(icon)m(txt)42 b -Fl(BLA)n(CS)27 b(comm)n(unication)g(con)n(text.)498 3536 -y(Scop)r(e:)37 b Fm(global)498 3635 y Fl(T)n(yp)r(e:)g -Fm(required)498 3735 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(an)27 b(in)n(teger)g(v)-5 b(ariable.)291 3887 y Fm(ierrv)41 -b Fl(see)28 b(\\On)e(Return".)291 4039 y Fm(On)31 b(Return)291 -4192 y(ierrv)41 b Fl(error)26 b(v)n(ector)g(used)i(in)g(subroutines)f -(F90)p 1858 4192 V 29 w(PSSPINS)g(and)h(F90)p 2558 4192 -V 29 w(PSSP)-7 b(ASB.)498 4291 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -4391 y Fl(T)n(yp)r(e:)g Fm(required)498 4490 y Fl(Sp)r(eci\014ed)28 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1400 V 29 w(PSSP)-7 b(ALL)p 1363 1433 1617 -4 v 1775 1665 a(T)g(able)27 b(3.1:)36 b(Data)27 b(t)n(yp)r(es)739 -2017 y Fe(Syn)l(tax)1346 2199 y Fl(CALL)g(F90)p 1742 -2199 25 4 v 30 w(PSSP)-7 b(ALL)27 b(\()p Ff(a,)j(ierrv,)h(de)l(c)l(omp) -p 2782 2199 26 4 v 32 w(data)p Fl(\))1255 2398 y(CALL)c(F90)p -1651 2398 25 4 v 29 w(PSSP)-7 b(ALL)27 b(\()p Ff(a,)k(ierrv,)g(de)l(c)l -(omp)p 2691 2398 26 4 v 32 w(data,)g(nnz)p Fl(\))739 -2598 y Fm(On)g(En)m(try)739 2748 y(a)42 b Fl(see)27 b(\\On)g(Return".) -739 2899 y Fm(decomp)p 1066 2899 29 4 v 33 w(data)42 -b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n(unications.)946 -2998 y(Scop)r(e:)37 b Fm(lo)s(cal)946 3098 y Fl(T)n(yp)r(e:)g -Fm(required)946 3197 y Fl(Sp)r(eci\014ed)29 b(as:)36 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)739 3348 y Fm(ierrv)42 b Fl(see)27 b(\\On)g(Return".)739 -3498 y Fm(nnz)42 b Fl(An)28 b(estimate)g(of)f(the)h(n)n(um)n(b)r(er)f -(of)h(non-zero)e(v)-5 b(alues)27 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b(as:)36 b(a)27 b(one)g(dimensional)g(arra) -n(y)f(of)h(in)n(teger.)2130 5255 y(38)p eop -%%Page: 39 39 -39 38 bop 291 745 a Fe(F90)p 518 745 41 4 v 48 w(PSSPINS|Insert)45 -b(Sparse)g(Matrix)291 999 y Fl(This)22 b(subroutine)h(inserts)f(a)h(lo) -r(cal)f(sparse)g(matrix)g Fh(B)t(LC)6 b(K)29 b Fl(in)23 -b(the)g(global)f(sparse)f(matrix)291 1098 y Fh(A)p Fl(.)p -925 1204 1597 4 v 974 1274 a Fh(A;)14 b(B)t(LC)6 b(K)627 -b Fm(Subroutine)p 925 1307 V 974 1377 a Fl(Long)27 b(Precision)f(Real) -257 b(F90)p 2103 1377 25 4 v 29 w(PSSPINS)974 1477 y(Long)27 -b(Precision)f(Complex)99 b(F90)p 2103 1477 V 29 w(PSSPINS)p -925 1510 1597 4 v 1326 1742 a(T)-7 b(able)28 b(3.2:)36 -b(Data)27 b(t)n(yp)r(es)291 2141 y Fe(Syn)l(tax)689 2324 -y Fl(CALL)h(F90)p 1086 2324 25 4 v 29 w(PSSPINS)f(\()p -Ff(a,)k(ia,)g(ja,)g(blck,)g(ierrv,)g(de)l(c)l(omp)p 2542 -2324 26 4 v 32 w(data)p Fl(\))291 2524 y(CALL)c(F90)p -687 2524 25 4 v 29 w(PSSPINS)777 2623 y(\()p Ff(a,)k(ia,)g(ja,)g(blck,) -g(ierrv,)g(de)l(c)l(omp)p 1838 2623 26 4 v 31 w(data,)g(IBLCK=iblck,)h -(JBLCK=jblck)p Fl(\))291 2824 y Fm(On)f(En)m(try)291 -2996 y(a)41 b Fl(the)34 b(lo)r(cal)f(p)r(ortion)g(of)h(global)e(sparse) -g(matrix)h Fh(A)p Fl(.)56 b(This)33 b(subroutine)g(computes)h(the)498 -3096 y(lo)r(cation)j(of)h(the)f(\014rst)h(elemen)n(t)f(of)h(the)g(lo)r -(cal)f(submatrix)g(to)g(insert,)j(based)d(on)498 3195 -y Fh(ia;)14 b(j)5 b(a)27 b Fl(and)g Fh(matr)r(ix)p 1146 -3195 25 4 v 31 w(data)h Fl(\014eld)f(of)h Fh(decomp)p -1913 3195 V 30 w(data)p Fl(.)498 3295 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 3395 y Fl(T)n(yp)r(e:)g Fm(required)498 -3494 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(structured)g(data)g(t)n -(yp)r(e)h(sp)r(eci\014ed)g(in)g Fg(x)f Fl(1.)291 3666 -y Fm(ia)41 b Fl(the)f(ro)n(w)e(index)h(of)g(global)g(sparse)f(matrix)g -Fh(A)p Fl(,)43 b(iden)n(tifying)c(the)h(\014rst)f(ro)n(w)f(of)i(the)498 -3766 y(submatrix)27 b Fh(A)p Fl(.)498 3865 y(Scop)r(e:)37 -b Fm(global)498 3965 y Fl(T)n(yp)r(e:)g Fm(required)498 -4065 y 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b(a)35 -b(structured)f(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)g Fl(1;)j(supp)r(orted)c(storage)946 623 y(formats)27 -b(are)g Fj(CSR)f Fl(and)i Fj(COO)p Fl(..)739 810 y Fm(decomp)p -1066 810 29 4 v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g -(for)g(comm)n(unications.)946 910 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -1009 y Fl(T)n(yp)r(e:)g Fm(required)946 1109 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 1296 y Fm(ierrv)42 b Fl(error)25 b(v)n(ector.)36 -b(It)28 b(m)n(ust)g(b)r(e)g(initialized)f(b)n(y)h(F90)p -2515 1296 25 4 v 29 w(PSSP)-7 b(ALL.)946 1396 y(Scop)r(e:)37 -b Fm(lo)s(cal)946 1495 y Fl(T)n(yp)r(e:)g Fm(required)946 -1595 y Fl(Sp)r(eci\014ed)29 b(as:)36 b(a)27 b(one)g(dimensional)g(arra) -n(y)f(of)h(in)n(teger.)739 1782 y Fm(iblc)m(k)42 b Fl(the)29 -b(ro)n(w)f(index)i(of)f(lo)r(cal)f(sparse)g(matrix)h -Fh(B)t(LC)6 b(K)g Fl(,)29 b(iden)n(tifying)h(the)f(\014rst)g(ro)n(w)f -(of)946 1882 y(the)g(submatrix)f Fh(B)t(LC)6 b(K)g Fl(.)946 -1981 y(Scop)r(e:)37 b Fm(lo)s(cal)946 2081 y Fl(T)n(yp)r(e:)g -Fm(optional)946 2181 y Fl(Default:)h Fh(ibl)r(ck)25 b -Fl(=)d(1.)946 2280 y(Sp)r(eci\014ed)29 b(as:)36 b(an)27 -b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 b(bl)r(ck)25 -b Fg(\025)e Fl(1.)739 2468 y Fm(jblc)m(k)42 b Fl(the)28 -b(column)f(index)h(of)f(the)h(lo)r(cal)f(sparse)f(matrix)g -Fh(B)t(LC)6 b(K)g Fl(,)27 b(iden)n(tifying)h(the)f(\014rst)946 -2567 y(column)h(of)g(the)g(submatrix)f Fh(B)t(LC)6 b(K)g -Fl(.)946 2667 y(Scop)r(e:)37 b Fm(lo)s(cal)946 2766 y -Fl(T)n(yp)r(e:)g Fm(optional)946 2866 y Fl(Default:)h -Fh(j)5 b(bl)r(ck)25 b Fl(=)e(1.)946 2966 y(Sp)r(eci\014ed)29 -b(as:)36 b(an)27 b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 -b(bl)r(ck)25 b Fg(\025)e Fl(1.)739 3153 y Fm(On)31 b(Return)739 -3340 y(a)42 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)g(of)g(global)g(sparse) -f(matrix)h Fh(A)h Fl(up)r(dated)g(with)g(matrix)f Fh(B)t(LC)6 -b(K)g Fl(.)946 3440 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3540 y Fl(T)n(yp)r(e:)g Fm(required)946 3639 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 3826 y Fm(ierrv)42 b Fl(error)24 b(v)n(ector)i(used) -g(in)h(successiv)n(e)e(call)h(to)h(F90)p 2493 3826 V -29 w(PSSPINS)f(and)g(F90)p 3190 3826 V 30 w(PSSP)-7 b(ASB.)946 -3926 y(Scop)r(e:)37 b Fm(lo)s(cal)946 4026 y Fl(T)n(yp)r(e:)g -Fm(required)946 4125 y Fl(Sp)r(eci\014ed)29 b(as:)36 -b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -4428 y Fe(Usage)46 b(Notes)840 4620 y Fl(1.)41 b(Before)28 -b(call)h(this)g(subroutine)f(y)n(ou)g(m)n(ust)h(allo)r(cate)f -Fh(A)h Fl(with)g(F90)p 3033 4620 V 29 w(PSSP)-7 b(ALL)28 -b(sub-)946 4719 y(routine.)840 4907 y(2.)41 b Fh(I)7 -b(A;)14 b(J)8 b(A)38 b Fl(and)e(the)h(indices)g(in)g -Fh(B)t(LC)6 b(K)42 b Fl(are)36 b(written)g(in)h(terms)g(of)f(the)h -(\\global")946 5006 y(n)n(um)n(b)r(ering;)28 b(the)g(mapping)f(to)g(lo) -r(cal)g(storage)f(is)h(handled)h(in)n(ternally)-7 b(.)2130 -5255 y(40)p eop -%%Page: 41 41 -41 40 bop 392 523 a Fl(3.)41 b(The)i(\\insertion")d(in)j(the)g(routine) -f(name)g(means)g(that)h(co)r(e\016cien)n(ts)e(from)i(the)498 -623 y Fh(B)t(LC)6 b(K)46 b Fl(parameter)39 b(are)h(stored)g(in)n(to)g -(the)h(global)f(sparse)f(matrix)h Fh(A)h Fl(starting)498 -722 y(from)22 b Fh(A)p Fl(\()p Fh(I)7 b(A;)14 b(J)8 b(A)p -Fl(\),)25 b(i.e.,)e(elemen)n(t)g Fh(B)t(LC)6 b(K)g Fl(\(1)p -Fh(;)14 b Fl(1\))21 b(\(if)i(it)g(actually)e(exists\),)i(go)r(es)f(on)n -(to)498 822 y Fh(A)p Fl(\()p Fh(I)7 b(A;)14 b(J)8 b(A)p -Fl(\),)35 b(and)e(so)f(on.)51 b(This)32 b(do)r(es)g Ff(not)h -Fl(imply)g(that)f(previously)g(existing)g(co-)498 922 -y(e\016cien)n(ts)g(are)e(o)n(v)n(erwritten;)i(an)n(y)f(clashes)g(are)f -(resolv)n(ed)g(at)h(assem)n(bly)g(time)h(\(see)498 1021 -y(subroutine)27 b(F90)p 1052 1021 25 4 v 29 w(PSSP)-7 -b(ASB\).)392 1187 y(4.)41 b(This)34 b(routine)g(do)r(es)g(not)g(con)n -(tain)g(an)n(y)f(syncronization)g(p)r(oin)n(t;)38 b(th)n(us,)e(it)f -(can)f(b)r(e)498 1287 y(called)28 b(indep)r(enden)n(tly)i(b)n(y)e(eac)n -(h)g(of)h(the)g(participating)f(pro)r(cesses;)f(it)i(is)g(ho)n(w)n(ev)n -(er)498 1386 y(required)e(that)h(all)f(pro)r(cesses)f(execute)i(later)e -(a)i(single)f(call)g(to)g(F90)p 2666 1386 V 30 w(PSSP)-7 -b(ASB.)392 1553 y(5.)41 b(It)26 b(is)f(p)r(erfectly)g(legal)g(to)g -(call)g(this)h(routine)e(m)n(ultiple)i(times)g(with)g(the)f(same)g(v)-5 -b(alue)498 1652 y(of)36 b Fh(I)7 b(A)p Fl(;)41 b(this)36 -b(can)g(b)r(e)g(useful)g(e.g.)62 b(in)36 b(\014nite)h(elemen)n(t)f -(applications,)h(where)f(the)498 1752 y(most)c(natural)f(w)n(a)n(y)f -(to)i(de\014ne)g(the)g(matrix)f(is)h(to)g(lo)r(op)f(o)n(v)n(er)f(the)i -(elemen)n(ts,)h(and)498 1851 y(not)j(o)n(v)n(er)e(the)i(equations.)61 -b(As)36 b(an)f(extreme)h(example,)h(it)f(is)g(p)r(ossible)g(to)f(build) -498 1951 y(a)k(sparse)f(matrix)h(passing)f(just)i(one)f(nonzero)f(en)n -(try)h(to)g(eac)n(h)g(call.)72 b(Ho)n(w)n(ev)n(er)498 -2051 y(it)30 b(is)g(generally)e(con)n(v)n(enien)n(t)h(from)g(a)h(p)r -(erformance)f(p)r(oin)n(t)g(of)h(view)g(to)f(pac)n(k)g(data)498 -2150 y(spanning)18 b(m)n(ultiple)h(ro)n(ws)e(in)n(to)h(a)g(single)g -(call)g(to)g(this)h(subroutine;)i(the)e(optimal)f(size)498 -2250 y(of)k(eac)n(h)f Fh(B)t(LC)6 b(K)28 b Fl(of)22 b(data)f(dep)r -(ends)i(on)f(the)g(underlying)g(pro)r(cessor)d(con\014guration.)1681 -5255 y(41)p eop -%%Page: 42 42 -42 41 bop 739 745 a Fe(F90)p 966 745 41 4 v 48 w(PSSP)-11 -b(ASB|Assem)l(bly)44 b(Sparse)h(Matrix)739 999 y Fl(This)27 -b(subroutine)h(assem)n(blies)e(global)g(sparse)h(matrix)g -Fh(A)p Fl(.)p 1362 1121 1619 4 v 1412 1191 a Fh(A)924 -b Fm(Subroutine)p 1362 1224 V 1412 1293 a Fl(Long)26 -b(Precision)g(Real)258 b(F90)p 2541 1293 25 4 v 29 w(PSSP)-7 -b(ASB)1412 1393 y(Long)26 b(Precision)g(Complex)100 b(F90)p -2541 1393 V 29 w(PSSP)-7 b(ASB)p 1362 1426 1619 4 v 1775 -1658 a(T)g(able)27 b(3.3:)36 b(Data)27 b(t)n(yp)r(es)739 -2042 y Fe(Syn)l(tax)1345 2225 y Fl(CALL)h(F90)p 1742 -2225 25 4 v 29 w(PSSP)-7 b(ASB)27 b(\()p Ff(a,)k(ierrv,)g(de)l(c)l(omp) -p 2783 2225 26 4 v 32 w(data)p Fl(\))739 2424 y(CALL)d(F90)p -1136 2424 25 4 v 29 w(PSSP)-7 b(ASB)751 2524 y(\()p Ff(a,)31 -b(ierrv,)g(de)l(c)l(omp)p 1375 2524 26 4 v 32 w(data,)g(O)n -(VERLAP=overlap,)g(AFMT=afmt,UP=up,DUP=dup)p Fl(\))739 -2724 y Fm(On)g(En)m(try)739 2896 y(a)42 b Fl(the)28 b(lo)r(cal)f(p)r -(ortion)g(of)g(global)g(sparse)f(matrix)h Fh(A)h Fl(to)g(assem)n(bly)-7 -b(.)946 2996 y(Scop)r(e:)37 b Fm(lo)s(cal)946 3096 y -Fl(T)n(yp)r(e:)g Fm(required)946 3195 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 3367 y Fm(decomp)p 1066 3367 29 4 -v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)946 3467 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3566 y Fl(T)n(yp)r(e:)g Fm(required)946 3666 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 3838 y Fm(ierrv)42 b Fl(error)31 b(v)n(ector.)54 -b(It)33 b(m)n(ust)h(b)r(e)g(initialized)g(b)n(y)f(F90)p -2568 3838 25 4 v 29 w(PSSP)-7 b(ALL)33 b(and)g(m)n(ust)h(b)r(e)g(the) -946 3938 y(same)27 b(used)h(in)g(F90)p 1584 3938 V 29 -w(PSSPINS.)946 4037 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -4137 y Fl(T)n(yp)r(e:)g Fm(required)946 4237 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -4408 y Fm(o)m(v)m(erlap)42 b Fl(P)n(ermits)27 b(to)h(impro)n(v)n(e)e -(F90)p 1952 4408 V 29 w(PSSP)-7 b(ASB)28 b(p)r(erformance,)e(if)j -(there)e(isn't)h(o)n(v)n(erlap)946 4508 y(b)r(et)n(w)n(een)37 -b(lo)r(cal)e(p)r(ortions)h(of)g(global)f(sparse)g(matrix)h -Fh(A)h Fl(assigned)e(o)n(v)n(er)f(all)i(pro-)946 4608 -y(cesses.)946 4707 y(Has)28 b(the)g(follo)n(wing)e(meaning:)946 -4807 y(If)j Fh(ov)s(er)r(l)r(ap)24 b Fl(=)f(0,)28 b(there)g(isn't)h(o)n -(v)n(erlap)d(b)r(et)n(w)n(een)i(lo)r(cal)f(p)r(ortions)h(of)g(global)f -(sparse)946 4907 y(matrix)h Fh(A)f Fl(assigned)g(o)n(v)n(er)f(all)h -(pro)r(cesses.)946 5006 y(If)36 b Fh(ov)s(er)r(l)r(ap)h -Fg(6)p Fl(=)f(0,)h(there)e(is)h(o)n(v)n(erlap)d(b)r(et)n(w)n(een)j(lo)r -(cal)f(p)r(ortions)g(of)g(global)g(sparse)2130 5255 y(42)p -eop -%%Page: 43 43 -43 42 bop 498 523 a Fl(matrix)27 b Fh(A)h Fl(assigned)f(o)n(v)n(er)e -(all)j(pro)r(cesses.)498 623 y(Scop)r(e:)37 b Fm(global)498 -722 y Fl(T)n(yp)r(e:)g Fm(optional)498 822 y Fl(Default:)h -Fh(ov)s(er)r(l)r(ap)23 b Fl(=)f(1.)498 922 y(Sp)r(eci\014ed)28 -b(as:)37 b(an)27 b(in)n(teger)g(v)-5 b(ariable.)291 1080 -y Fm(afm)m(t)41 b Fl(Request)29 b(matrix)g Fh(A)g Fl(to)g(b)r(e)h(con)n -(v)n(erted)e(in)n(to)h(a)g(sp)r(ec\014c)g(storage)e(format;)j(it)g(m)n -(ust)498 1180 y(b)r(e)36 b(supp)r(orted)f(b)n(y)g(the)h(underlying)f -(serial)f(sparse)g(BLAS.)i(It)g(is)f(assumed)g(that)498 -1279 y(at)d(least)f Fj(CSR)f Fl(should)i(b)r(e)g(supp)r(orted;)h(the)f -(default)g(is)g Fj(???)p Fl(,)f(whic)n(h)h(requests)f(the)498 -1379 y(default)d(of)g(the)g(underlying)f(serial)f(spares)g(BLAS.)i -(Scop)r(e:)37 b Fm(global)498 1478 y Fl(T)n(yp)r(e:)g -Fm(optional)498 1578 y Fl(Default:)h Fh(ov)s(er)r(l)r(ap)23 -b Fl(=)f Fj(???)o Fl(.)498 1678 y(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b Fj(CHARACTER*5)c Fl(v)-5 b(ariable.)291 1836 -y Fm(UP)42 b Fl(Request)23 b(matrix)g Fh(A)h Fl(to)f(b)r(e)h(prepared)e -(for)h(e\016cien)n(t)g(pattern)g(reuse)g(\(see)g(subroutine)498 -1936 y(F90)p 641 1936 25 4 v 29 w(PSSPUPD\).)g(This)g(en)n(tails)g -(additional)f(storage)g(o)n(v)n(erhead.)33 b(P)n(ossible)21 -b(v)-5 b(alues)498 2035 y(are)27 b Fj(Y)g Fl(and)g Fj(N)p -Fl(.)h(Scop)r(e:)37 b Fm(global)498 2135 y Fl(T)n(yp)r(e:)g -Fm(optional)498 2235 y Fl(Default:)h Fh(U)9 b(P)34 b -Fl(=)23 b Fj(N)p Fl(.)498 2334 y(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b Fj(CHARACTER)d Fl(v)-5 b(ariable.)291 2493 y -Fm(DUP)42 b Fl(Sp)r(eci\014es)30 b(ho)n(w)g(to)f(treat)h(duplicated)g -(matrix)g(en)n(tries;)g(see)g(usage)f(notes)g(b)r(elo)n(w.)498 -2592 y(Scop)r(e:)37 b Fm(global)498 2692 y Fl(T)n(yp)r(e:)g -Fm(optional)498 2792 y Fl(Default:)h Fh(dup)22 b Fl(=)h(1.)498 -2891 y(Sp)r(eci\014ed)28 b(as:)37 b(an)27 b(in)n(teger)g(v)-5 -b(ariable.)291 3050 y Fm(On)31 b(Return)291 3208 y(a)41 -b Fl(the)28 b(lo)r(cal)g(p)r(ortion)f(of)g(global)g(sparse)f(matrix)h -Fh(A)h Fl(assem)n(bled.)498 3308 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -3407 y Fl(T)n(yp)r(e:)g Fm(required)498 3507 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)291 3778 y Fe(Usage)46 b(Notes)392 3960 -y Fl(1.)41 b(Before)28 b(call)g(this)h(subroutine)g(y)n(ou)f(m)n(ust)h -(allo)r(cate)e Fh(A)j Fl(with)f(F90)p 2585 3960 V 29 -w(PSSP)-7 b(ALL)28 b(sub-)498 4060 y(routine)f(and)h(insert)f(all)g(ro) -n(ws)f(of)i(matrix)f Fh(A)h Fl(with)g(F90)p 2271 4060 -V 29 w(PSSPINS.)392 4218 y(2.)41 b(It)35 b(ma)n(y)f(happ)r(en)h(that)g -(calls)f(to)g Fj(F90_PSSPINS)c Fl(ha)n(v)n(e)k(inserted)g(m)n(ultiple)h -(v)-5 b(alues)498 4318 y(with)36 b(the)g(same)f(indices,)i(i.e.)60 -b(y)n(ou)35 b(ma)n(y)f(ha)n(v)n(e)h(duplicated)g(co)r(e\016cien)n(t)h -(en)n(tries.)498 4418 y(This)29 b(subroutine)f(pro)n(vides)f(three)h(w) -n(a)n(ys)f(of)h(coping)g(with)h(duplicated)f(en)n(tries)g(b)n(y)498 -4517 y(sp)r(eci\014yng)f(the)h(relev)-5 b(an)n(t)27 b(v)-5 -b(alue)28 b(in)n(to)f(the)h(DUP)g(v)-5 b(ariable:)598 -4676 y(1)41 b(Raise)27 b(an)g(error,)f(duplicated)i(co)r(e\016cien)n -(ts)f(should)g(not)h(exist;)598 4801 y(2)41 b(Ignore)26 -b(replications,)h(k)n(eep)g(one)g(of)g(the)h(co)r(e\016cien)n(ts)g -(found;)598 4926 y(3)41 b(Sum)28 b(the)g(duplicated)g(en)n(tries)f(to)g -(obtain)g(the)h(\014nal)g(co)r(e\016cien)n(t.)1681 5255 -y(43)p eop -%%Page: 44 44 -44 43 bop 739 719 a Fe(F90)p 966 719 41 4 v 48 w(PSPTINS|Insert)45 -b(P)l(attern)739 947 y Fl(This)29 b(subroutine)f(handles)h(up)r(dates)g -(to)g(a)f(comm)n(unication)g(descriptor)g(based)g(only)h(on)739 -1046 y(the)k(sparsit)n(y)f(pattern.)52 b(This)33 b(is)f(useful)i(in)f -(those)f(cases)g(where)g(w)n(e)h(are)e(only)i(actually)739 -1146 y(using)27 b(a)g(connectivit)n(y)g(graph.)p 1676 -1255 990 4 v 1726 1325 a Fh(B)t(LC)6 b(K)105 b Fm(Subroutine)p -1676 1358 V 2091 1427 a Fl(F90)p 2234 1427 25 4 v 29 -w(PSPTINS)p 1676 1461 990 4 v 1775 1693 a(T)-7 b(able)27 -b(3.4:)36 b(Data)27 b(t)n(yp)r(es)739 2052 y Fe(Syn)l(tax)1179 -2234 y Fl(CALL)h(F90)p 1576 2234 25 4 v 29 w(PSPTINS)f(\()p -Ff(ia,)32 b(ja,)f(blck,)g(ierrv,)g(de)l(c)l(omp)p 2949 -2234 26 4 v 31 w(data)p Fl(\))739 2433 y Fm(On)g(En)m(try)739 -2589 y(ia)41 b Fl(the)29 b(ro)n(w)d(index)i(of)g(global)e(sparse)h -(matrix)g(pattern)h Fh(A)p Fl(,)g(iden)n(tifying)g(the)g(\014rst)g(ro)n -(w)e(of)946 2689 y(the)i(submatrix)f(pattern)h Fh(A)p -Fl(.)946 2789 y(Scop)r(e:)37 b Fm(global)946 2888 y Fl(T)n(yp)r(e:)g -Fm(required)946 2988 y Fl(Sp)r(eci\014ed)20 b(as:)32 -b(an)19 b(in)n(teger)g(v)-5 b(ariable)18 b(1)23 b Fg(\024)f -Fh(ia)h Fg(\024)f Fh(decomp)p 2706 2988 25 4 v 30 w(data)p -Fl(\045)p Fh(matr)r(ix)p 3228 2988 V 31 w(data)p Fl([)p -Fh(M)p 3532 2988 V 38 w Fl(].)739 3144 y Fm(ja)42 b Fl(the)27 -b(column)f(index)g(of)h(the)f(global)f(sparse)g(matrix)h -Fh(A)p Fl(,)h(iden)n(tifying)g(the)f(\014rst)g(column)946 -3243 y(of)i(the)g(submatrix)f Fh(A)p Fl(.)946 3343 y(Scop)r(e:)37 -b Fm(global)946 3443 y Fl(T)n(yp)r(e:)g Fm(required)946 -3542 y Fl(Sp)r(eci\014ed)21 b(as:)33 b(an)19 b(in)n(teger)g(v)-5 -b(ariable)19 b(1)k Fg(\024)g Fh(j)5 b(a)23 b Fg(\024)f -Fh(decomp)p 2720 3542 V 30 w(data)p Fl(\045)p Fh(matr)r(ix)p -3242 3542 V 30 w(data)p Fl([)p Fh(N)p 3532 3542 V 39 -w Fl(].)739 3698 y Fm(blc)m(k)42 b Fl(the)28 b(lo)r(cal)f(submatrix)g -(pattern)h(to)f(insert.)946 3798 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3897 y Fl(T)n(yp)r(e:)g Fm(required)946 3997 y Fl(Sp)r(eci\014ed)f(as:) -50 b(a)35 b(structured)f(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)g Fl(1;)j(supp)r(orted)c(storage)946 4097 y(formats)27 -b(are)g Fj(CSR)f Fl(and)i Fj(COO)p Fl(..)739 4253 y Fm(decomp)p -1066 4253 29 4 v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g -(for)g(comm)n(unications.)946 4352 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -4452 y Fl(T)n(yp)r(e:)g Fm(required)946 4551 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 4707 y Fm(ierrv)42 b Fl(error)25 b(v)n(ector.)36 -b(It)28 b(m)n(ust)g(b)r(e)g(initialized)f(b)n(y)h(F90)p -2515 4707 25 4 v 29 w(PSSP)-7 b(ALL.)946 4807 y(Scop)r(e:)37 -b Fm(lo)s(cal)946 4907 y Fl(T)n(yp)r(e:)g Fm(required)946 -5006 y Fl(Sp)r(eci\014ed)29 b(as:)36 b(a)27 b(one)g(dimensional)g(arra) -n(y)f(of)h(in)n(teger.)2130 5255 y(44)p eop -%%Page: 45 45 -45 44 bop 291 523 a Fm(On)31 b(Return)291 689 y(ierrv)41 -b Fl(error)25 b(v)n(ector)g(used)i(in)g(successiv)n(e)e(call)h(to)g -(F90)p 2044 689 25 4 v 29 w(PSSPINS)h(and)f(F90)p 2742 -689 V 29 w(PSSP)-7 b(ASB.)498 789 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -888 y Fl(T)n(yp)r(e:)g Fm(required)498 988 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(one)g(dimensional)g(arra)n(y)e(of)j(in)n(teger.)291 -1263 y Fe(Usage)46 b(Notes)392 1444 y Fl(1.)41 b(Before)f(call)g(this)h -(subroutine)g(y)n(ou)f(m)n(ust)h(allo)r(cate)f Fh(D)r(E)5 -b(C)h(O)r(M)j(P)p 2672 1444 V 42 w(D)r(AT)j(A)40 b Fl(with)498 -1544 y(F90)p 641 1544 V 29 w(PSDSCALL)28 b(subroutine.)392 -1710 y(2.)41 b Fh(I)7 b(A;)14 b(J)8 b(A)37 b Fl(and)g(the)g(indices)g -(in)f Fh(B)t(LC)6 b(K)43 b Fl(are)35 b(written)i(in)g(terms)f(of)h(the) -g(\\global")498 1810 y(n)n(um)n(b)r(ering;)27 b(the)h(mapping)g(to)f -(lo)r(cal)g(storage)f(is)h(handled)h(in)n(ternally)-7 -b(.)392 1976 y(3.)41 b(This)26 b(routine)f(is)h(v)n(ery)f(similar)g(to) -g(F90)p 1746 1976 V 29 w(PSSPINS,)h(but)g(the)h(co)r(e\016cien)n(t)e(v) --5 b(alues)26 b(in)498 2075 y(the)31 b Fh(B)t(LC)6 b(K)35 -b Fl(parameter)29 b(are)g(completely)h(ignored;)g(only)g(the)g(nonzero) -f(pattern,)498 2175 y(i.e.)37 b(the)28 b(ro)n(w)e(and)i(column)f -(indices,)h(are)f(used)g(to)h(up)r(date)g(DECOMP)p 2783 -2175 V 29 w(D)n(A)-7 b(T)g(A.)392 2341 y(4.)41 b(This)34 -b(routine)g(do)r(es)g(not)g(con)n(tain)g(an)n(y)f(syncronization)g(p)r -(oin)n(t;)38 b(th)n(us,)e(it)f(can)f(b)r(e)498 2441 y(called)28 -b(indep)r(enden)n(tly)i(b)n(y)e(eac)n(h)g(of)h(the)g(participating)f -(pro)r(cesses;)f(it)i(is)g(ho)n(w)n(ev)n(er)498 2540 -y(required)e(that)h(all)f(pro)r(cesses)f(execute)i(later)e(a)i(single)f -(call)g(to)g(F90)p 2666 2540 V 30 w(PSPT)-7 b(ASB.)392 -2706 y(5.)41 b(It)26 b(is)f(p)r(erfectly)g(legal)g(to)g(call)g(this)h -(routine)e(m)n(ultiple)i(times)g(with)g(the)f(same)g(v)-5 -b(alue)498 2806 y(of)21 b Fh(I)7 b(A)p Fl(;)23 b(this)f(can)e(b)r(e)h -(useful)h(e.g.)34 b(in)21 b(\014nite)g(elemen)n(t)g(applications,)h -(where)e(the)h(most)498 2906 y(natural)h(w)n(a)n(y)g(to)g(de\014ne)h -(the)h(matrix)e(is)g(to)h(lo)r(op)f(o)n(v)n(er)f(the)j(elemen)n(ts,)f -(and)g(not)g(o)n(v)n(er)498 3005 y(the)40 b(equations.)72 -b(Ho)n(w)n(ev)n(er)38 b(it)i(is)f(generally)f(con)n(v)n(enien)n(t)h -(from)g(a)g(p)r(erformance)498 3105 y(p)r(oin)n(t)d(of)g(view)g(to)f -(pac)n(k)g(data)g(spanning)h(m)n(ultiple)g(ro)n(ws)e(in)n(to)i(a)f -(single)h(call)f(to)498 3204 y(this)d(subroutine;)h(the)e(optimal)g -(size)g(of)h(eac)n(h)e Fh(B)t(LC)6 b(K)37 b Fl(of)31 -b(data)g(dep)r(ends)h(on)f(the)498 3304 y(underlying)c(pro)r(cessor)f -(con\014guration.)1681 5255 y(45)p eop -%%Page: 46 46 -46 45 bop 739 739 a Fe(F90)p 966 739 41 4 v 48 w(PSPT)-11 -b(ASB|Assem)l(bly)44 b(Sparse)739 888 y(Comm)l(unication)i(P)l(attern) -739 1137 y Fl(This)27 b(subroutine)h(assem)n(blies)e(a)h(comm)n -(unication)g(pattern)g(DECOMP)p 3066 1137 25 4 v 29 w(D)n(A)-7 -b(T)g(A.)p 1798 1256 746 4 v 1948 1325 a Fm(Subroutine)p -1798 1359 V 1948 1428 a Fl(F90)p 2091 1428 25 4 v 29 -w(PSPT)g(ASB)p 1798 1462 746 4 v 1775 1694 a(T)g(able)27 -b(3.5:)36 b(Data)27 b(t)n(yp)r(es)739 2068 y Fe(Syn)l(tax)1387 -2250 y Fl(CALL)h(F90)p 1784 2250 25 4 v 29 w(PSPT)-7 -b(ASB)27 b(\()p Ff(ierrv,)k(de)l(c)l(omp)p 2741 2250 -26 4 v 32 w(data)p Fl(\))739 2449 y Fm(On)g(En)m(try)739 -2615 y(decomp)p 1066 2615 29 4 v 33 w(data)42 b Fl(con)n(tains)27 -b(data)g(structures)g(for)g(comm)n(unications.)946 2715 -y(Scop)r(e:)37 b Fm(lo)s(cal)946 2814 y Fl(T)n(yp)r(e:)g -Fm(required)946 2914 y Fl(Sp)r(eci\014ed)29 b(as:)36 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)739 3080 y Fm(ierrv)42 b Fl(error)31 b(v)n(ector.)54 -b(It)33 b(m)n(ust)h(b)r(e)g(initialized)g(b)n(y)f(F90)p -2568 3080 25 4 v 29 w(PSSP)-7 b(ALL)33 b(and)g(m)n(ust)h(b)r(e)g(the) -946 3179 y(same)27 b(used)h(in)g(F90)p 1584 3179 V 29 -w(PSSPINS.)946 3279 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3379 y Fl(T)n(yp)r(e:)g Fm(required)946 3478 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -3644 y Fm(On)k(Return)739 3810 y(decomp)p 1066 3810 29 -4 v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)946 3910 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -4010 y Fl(T)n(yp)r(e:)g Fm(required)946 4109 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 4384 y Fe(Usage)46 b(Notes)840 4566 -y Fl(1.)41 b(Before)18 b(call)g(this)h(subroutine)f(y)n(ou)f(m)n(ust)i -(allo)r(cate)e(DECOMP)p 2919 4566 25 4 v 29 w(D)n(A)-7 -b(T)g(A)19 b(with)g(F90)p 3516 4566 V 29 w(PSDSCALL)946 -4665 y(subroutine)28 b(and)f(insert)g(all)h(relev)-5 -b(an)n(t)27 b(pattern)g(ro)n(ws)f(with)i(F90)p 2999 4665 -V 29 w(PSPTINS.)2130 5255 y(46)p eop -%%Page: 47 47 -47 46 bop 291 726 a Fe(F90)p 518 726 41 4 v 48 w(PSSPFREE|F)-11 -b(ree)45 b(Sparse)g(Matrix)291 962 y Fl(This)27 b(subroutine)g(deallo)r -(cates)g(sparse)f(matrix's)h(structures.)p 880 1075 1687 -4 v 929 1145 a Fh(A)924 b Fm(Subroutine)p 880 1178 V -929 1248 a Fl(Long)27 b(Precision)f(Real)257 b(F90)p -2058 1248 25 4 v 29 w(PSSPFREE)929 1347 y(Long)27 b(Precision)f -(Complex)99 b(F90)p 2058 1347 V 29 w(PSSPFREE)p 880 1380 -1687 4 v 1326 1612 a(T)-7 b(able)28 b(3.6:)36 b(Data)27 -b(t)n(yp)r(es)291 1978 y Fe(Syn)l(tax)962 2160 y Fl(CALL)g(F90)p -1358 2160 25 4 v 29 w(PSSPFREE)g(\()j Ff(a,)g(de)l(c)l(omp)p -2270 2160 26 4 v 32 w(data)p Fl(\))291 2359 y Fm(On)h(En)m(try)291 -2519 y(a)41 b Fl(the)28 b(lo)r(cal)g(p)r(ortion)f(of)g(global)g(sparse) -f(matrix)h Fh(A)h Fl(to)f(deallo)r(cate.)498 2618 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 2718 y Fl(T)n(yp)r(e:)g Fm(required)498 -2817 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(structured)g(data)g(t)n -(yp)r(e)h(sp)r(eci\014ed)g(in)g Fg(x)f Fl(1.)291 2977 -y Fm(decomp)p 618 2977 29 4 v 33 w(data)42 b Fl(con)n(tains)28 -b(data)h(structures)g(for)g(comm)n(unications)f(referred)g(to)h(sparse) -498 3077 y(matrix)e(to)h(deallo)r(cate.)498 3177 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 3276 y Fl(T)n(yp)r(e:)g Fm(required)498 -3376 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(structured)g(data)g(t)n -(yp)r(e)h(sp)r(eci\014ed)g(in)g Fg(x)f Fl(1.)291 3536 -y Fm(On)k(Return)291 3695 y(a)41 b Fl(deallo)r(cated)27 -b(structure)g(for)h(storing)e(other)h(sparse)f(matrices.)498 -3795 y(Scop)r(e:)37 b Fm(lo)s(cal)498 3895 y Fl(T)n(yp)r(e:)g -Fm(required)498 3994 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)291 4154 y Fm(decomp)p 618 4154 V 33 w(data)42 -b Fl(con)n(tains)27 b(deallo)r(cated)g(data)g(structures)f(for)i(comm)n -(unications.)498 4254 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -4353 y Fl(T)n(yp)r(e:)g Fm(required)498 4453 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)291 4725 y Fe(Usage)46 b(Notes)392 4907 -y Fl(1.)41 b(Before)28 b(call)g(this)h(subroutine)g(y)n(ou)f(m)n(ust)h -(allo)r(cate)e Fh(A)j Fl(with)f(F90)p 2585 4907 25 4 -v 29 w(PSSP)-7 b(ALL)28 b(sub-)498 5006 y(routine.)1681 -5255 y(47)p eop -%%Page: 48 48 -48 47 bop 840 523 a Fl(2.)41 b(After)23 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b(iden)n(tifying)e(the)h(\014rst)e -(ro)n(w)g(of)h(the)498 623 y(submatrix)27 b Fh(X)7 b -Fl(.)498 722 y(Scop)r(e:)37 b Fm(global)498 822 y Fl(T)n(yp)r(e:)g -Fm(required)498 922 y Fl(Sp)r(eci\014ed)22 b(as:)34 b(an)21 -b(in)n(teger)f(v)-5 b(ariable)21 b(1)h Fg(\024)h Fh(ix)g -Fg(\024)g Fh(decomp)p 2272 922 25 4 v 29 w(data)p Fl(\045)p -Fh(matr)r(ix)p 2793 922 V 31 w(data)p Fl([)p Fh(N)p 3084 -922 V 39 w Fl(].)291 1083 y Fm(jx)42 b Fl(the)27 b(column)g(index)g(of) -g(the)g(global)e(dense)i(matrix)g Fh(X)7 b Fl(,)26 b(iden)n(tifying)h -(the)g(\014rst)g(column)498 1183 y(of)h(the)g(submatrix)f -Fh(X)7 b Fl(.)498 1283 y(Scop)r(e:)37 b Fm(global)498 -1382 y Fl(T)n(yp)r(e:)g Fm(required)498 1482 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(an)27 b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 -b(x)24 b Fg(\025)e Fl(1.)291 1644 y Fm(blc)m(k)42 b Fl(the)28 -b(lo)r(cal)f(submatrix)g(to)g(insert.)498 1743 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 1843 y Fl(T)n(yp)r(e:)g Fm(required)498 -1943 y Fl(Sp)r(eci\014ed)42 b(as:)63 b(a)41 b(rank)f(one)h(or)f(rank)g -(t)n(w)n(o)g(con)n(taining)h(n)n(um)n(b)r(ers)f(of)h(the)h(t)n(yp)r(e) -498 2042 y(indicated)28 b(in)g(T)-7 b(able)27 b(3.8.)36 -b(The)28 b(rank)e(of)i Fh(bl)r(ck)h Fl(m)n(ust)f(b)r(e)g(the)g(same)f -(of)h Fh(x)p Fl(.)291 2204 y Fm(decomp)p 618 2204 29 -4 v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)498 2304 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -2403 y Fl(T)n(yp)r(e:)g Fm(required)498 2503 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)291 2665 y Fm(ierrv)41 b Fl(error)26 b(v)n(ector.)36 -b(It)28 b(m)n(ust)f(b)r(e)h(initialized)g(b)n(y)f(F90)p -2066 2665 25 4 v 30 w(PSDSALL.)498 2765 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 2864 y Fl(T)n(yp)r(e:)g Fm(required)498 -2964 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(one)g(dimensional)g(arra) -n(y)e(of)j(in)n(teger.)291 3126 y Fm(iblc)m(k)41 b Fl(the)32 -b(ro)n(w)e(index)h(of)g(lo)r(cal)g(dense)g(matrix)g Fh(B)t(LC)6 -b(K)g Fl(,)31 b(iden)n(tifying)h(the)f(\014rst)g(ro)n(w)f(of)498 -3225 y(the)e(submatrix)f Fh(B)t(LC)6 b(K)g Fl(.)498 3325 -y(Scop)r(e:)37 b Fm(lo)s(cal)498 3425 y Fl(T)n(yp)r(e:)g -Fm(optional)498 3524 y Fl(Default:)h Fh(ibl)r(ck)24 b -Fl(=)f(1.)498 3624 y(Sp)r(eci\014ed)28 b(as:)37 b(an)27 -b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 b(bl)r(ck)25 -b Fg(\025)e Fl(1.)291 3786 y Fm(jblc)m(k)42 b Fl(the)30 -b(column)f(index)h(of)f(the)h(lo)r(cal)f(dense)g(matrix)g -Fh(B)t(LC)6 b(K)g Fl(,)30 b(iden)n(tifying)f(the)h(\014rst)498 -3885 y(column)e(of)f(the)h(submatrix)f Fh(B)t(LC)6 b(K)g -Fl(.)498 3985 y(Scop)r(e:)37 b Fm(lo)s(cal)498 4085 y -Fl(T)n(yp)r(e:)g Fm(optional)498 4184 y Fl(Default:)h -Fh(j)5 b(bl)r(ck)25 b Fl(=)d(1.)498 4284 y(Sp)r(eci\014ed)28 -b(as:)37 b(an)27 b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 -b(bl)r(ck)25 b Fg(\025)e Fl(1.)291 4446 y Fm(On)31 b(Return)291 -4608 y(x)41 b Fl(the)35 b(lo)r(cal)e(p)r(ortion)h(of)g(global)f(dense)h -(matrix)f Fh(X)7 b Fl(.)56 b(This)34 b(subroutine)g(computes)g(the)498 -4707 y(lo)r(cation)23 b(of)g(the)h(\014rst)g(elemen)n(t)f(of)h(the)g -(lo)r(cal)f(subarra)n(y)e(to)i(insert,)h(based)f(on)g -Fh(ix;)14 b(j)5 b(x)498 4807 y Fl(and)28 b Fh(matr)r(ix)p -927 4807 V 30 w(data)g Fl(\014eld)g(of)f Fh(decomp)p -1693 4807 V 30 w(data)p Fl(.)498 4907 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 5006 y Fl(T)n(yp)r(e:)g Fm(required)1681 -5255 y Fl(53)p eop -%%Page: 54 54 -54 53 bop 946 523 a Fl(Sp)r(eci\014ed)41 b(as:)62 b(a)39 -b(t)n(w)n(o)h(dimensional)g(arra)n(y)d(con)n(taining)j(n)n(um)n(b)r -(ers)f(of)h(the)h(t)n(yp)r(e)946 623 y(indicated)28 b(in)g(T)-7 -b(able)27 b(3.8.)739 789 y Fm(ierrv)42 b Fl(error)25 -b(v)n(ector)i(used)g(in)h(successiv)n(e)e(call)h(to)h(F90)p -2500 789 25 4 v 29 w(PSDSINS)g(and)g(F90)p 3207 789 V -29 w(D)n(ASB.)946 888 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -988 y Fl(T)n(yp)r(e:)g Fm(required)946 1088 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -1362 y Fe(Usage)46 b(Notes)840 1544 y Fl(1.)41 b(Before)26 -b(call)f(this)i(subroutine)e(y)n(ou)h(m)n(ust)g(allo)r(cate)f -Fh(X)32 b Fl(with)27 b(F90)p 3022 1544 V 29 w(PSDSALL)f(sub-)946 -1644 y(routine.)2130 5255 y(54)p eop -%%Page: 55 55 -55 54 bop 291 736 a Fe(F90)p 518 736 41 4 v 48 w(PSDSASB|Assem)l(bly)44 -b(Dense)i(Matrix)291 981 y Fl(This)27 b(subroutine)g(assem)n(blies)g -(global)f(dense)i(matrix)f Fh(X)7 b Fl(.)p 907 1099 1632 -4 v 957 1169 a Fh(X)916 b Fm(Subroutine)p 907 1202 V -957 1272 a Fl(In)n(teger)730 b(F90)p 2085 1272 25 4 v -30 w(PSDSASB)957 1371 y(Long)26 b(Precision)g(Real)257 -b(F90)p 2085 1371 V 30 w(PSDSASB)957 1471 y(Long)26 b(Precision)g -(Complex)99 b(F90)p 2085 1471 V 30 w(PSDSASB)p 907 1504 -1632 4 v 1326 1736 a(T)-7 b(able)28 b(3.9:)36 b(Data)27 -b(t)n(yp)r(es)291 2108 y Fe(Syn)l(tax)892 2290 y Fl(CALL)h(F90)p -1289 2290 25 4 v 29 w(PSDSASB)g(\()p Ff(x,)i(ierrv,)h(de)l(c)l(omp)p -2340 2290 26 4 v 31 w(data)p Fl(\))291 2489 y Fm(On)g(En)m(try)291 -2654 y(x)41 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)h(of)f(global)g(dense)g -(matrix)g Fh(X)7 b Fl(.)498 2754 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -2853 y Fl(T)n(yp)r(e:)g Fm(required)498 2953 y Fl(Sp)r(eci\014ed)31 -b(as:)41 b(a)30 b(rank)f(one)g(or)g(t)n(w)n(o)h(arra)n(y)d(with)k(the)f -(POINTER)f(attribute)i(con-)498 3053 y(taining)c(n)n(um)n(b)r(ers)h(of) -f(the)h(t)n(yp)r(e)g(indicated)g(in)g(T)-7 b(able)27 -b(3.9.)291 3217 y Fm(decomp)p 618 3217 29 4 v 33 w(data)42 -b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n(unications.)498 -3317 y(Scop)r(e:)37 b Fm(lo)s(cal)498 3416 y Fl(T)n(yp)r(e:)g -Fm(required)498 3516 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)291 3681 y Fm(ierrv)41 b Fl(error)31 b(v)n(ector.)50 -b(It)33 b(m)n(ust)f(b)r(e)h(initialized)g(b)n(y)f(F90)p -2110 3681 25 4 v 29 w(PSDSALL)h(and)f(m)n(ust)h(b)r(e)g(the)498 -3780 y(same)27 b(used)h(in)g(F90)p 1136 3780 V 29 w(PSDSINS.)498 -3880 y(Scop)r(e:)37 b Fm(lo)s(cal)498 3980 y Fl(T)n(yp)r(e:)g -Fm(required)498 4079 y Fl(Sp)r(eci\014ed)31 b(as:)43 -b(a)30 b(one)g(dimensional)g(arra)n(y)e(of)j(in)n(teger.)45 -b(m)n(ust)31 b(b)r(e)g(the)g(same)f(used)498 4179 y(in)e(F90)p -738 4179 V 29 w(PSDSINS.)498 4278 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -4378 y Fl(T)n(yp)r(e:)g Fm(optional)498 4478 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(one)g(dimensional)g(arra)n(y)e(of)j(in)n(teger.)291 -4642 y Fm(On)j(Return)291 4807 y(x)41 b Fl(the)28 b(lo)r(cal)f(p)r -(ortion)h(of)f(global)g(dense)g(matrix)g Fh(X)7 b Fl(.)498 -4907 y(Scop)r(e:)37 b Fm(lo)s(cal)498 5006 y Fl(T)n(yp)r(e:)g -Fm(required)1681 5255 y Fl(55)p eop -%%Page: 56 56 -56 55 bop 946 523 a Fl(Sp)r(eci\014ed)31 b(as:)41 b(a)30 -b(rank)f(one)h(or)f(t)n(w)n(o)g(arra)n(y)f(with)i(the)h(POINTER)e -(attribute)h(con-)946 623 y(taining)e(n)n(um)n(b)r(ers)f(of)g(the)h(t)n -(yp)r(e)g(indicated)g(in)g(T)-7 b(able)27 b(3.8.)739 -789 y Fm(ierrv)42 b Fl(error)22 b(v)n(ector)h(used)h(in)h(successiv)n -(e)e(call)g(to)i(F90)p 2477 789 25 4 v 29 w(PSDSINS)g(and)f(F90)p -3177 789 V 29 w(PSDSASB.)946 888 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -988 y Fl(T)n(yp)r(e:)g Fm(required)946 1088 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -1362 y Fe(Usage)46 b(Notes)840 1544 y Fl(1.)41 b(Before)26 -b(call)f(this)i(subroutine)e(y)n(ou)h(m)n(ust)g(allo)r(cate)f -Fh(X)32 b Fl(with)27 b(F90)p 3022 1544 V 29 w(PSDSALL)f(sub-)946 -1644 y(routine.)2130 5255 y(56)p eop -%%Page: 57 57 -57 56 bop 291 715 a Fe(F90)p 518 715 41 4 v 48 w(PSDSFREE|F)-11 -b(ree)45 b(Dense)h(Matrix)291 939 y Fl(These)27 b(subroutine)g(deallo)r -(cates)g(dense)g(matrix's)g(structures.)p 876 1030 1694 -4 v 926 1099 a Fh(A)924 b Fm(Subroutine)p 876 1133 V -926 1202 a Fl(In)n(teger)731 b(F90)p 2055 1202 25 4 v -29 w(PSDSFREE)926 1302 y(Long)27 b(Precision)f(Real)257 -b(F90)p 2055 1302 V 29 w(PSDSFREE)926 1402 y(Long)27 -b(Precision)f(Complex)99 b(F90)p 2055 1402 V 29 w(PSDSFREE)p -876 1435 1694 4 v 1306 1667 a(T)-7 b(able)27 b(3.10:)36 -b(Data)27 b(t)n(yp)r(es)291 2040 y Fe(Syn)l(tax)963 2222 -y Fl(CALL)h(F90)p 1360 2222 25 4 v 29 w(PSDSFREE)f(\()p -Ff(X,)j(de)l(c)l(omp)p 2268 2222 26 4 v 32 w(data)p Fl(\))291 -2421 y Fm(On)h(En)m(try)291 2575 y(x)41 b Fl(the)28 b(lo)r(cal)f(p)r -(ortion)h(of)f(global)g(dense)g(matrix)g Fh(X)7 b Fl(.)498 -2675 y(Scop)r(e:)37 b Fm(lo)s(cal)498 2774 y Fl(T)n(yp)r(e:)g -Fm(required)498 2874 y Fl(Sp)r(eci\014ed)31 b(as:)41 -b(a)30 b(rank)f(one)g(or)g(t)n(w)n(o)h(arra)n(y)d(with)k(the)f(POINTER) -f(attribute)i(con-)498 2974 y(taining)c(n)n(um)n(b)r(ers)h(of)f(the)h -(t)n(yp)r(e)g(indicated)g(in)g(T)-7 b(able)27 b(3.9.)291 -3127 y Fm(decomp)p 618 3127 29 4 v 33 w(data)42 b Fl(con)n(tains)27 -b(data)g(structures)g(for)g(comm)n(unications.)498 3227 -y(Scop)r(e:)37 b Fm(lo)s(cal)498 3327 y Fl(T)n(yp)r(e:)g -Fm(required)498 3426 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)291 3580 y Fm(On)k(Return)291 3734 y(x)41 -b Fl(deallo)r(cated)27 b(lo)r(cal)g(p)r(ortion)g(of)h(global)e(dense)i -(matrix)f Fh(X)7 b Fl(.)498 3834 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -3934 y Fl(T)n(yp)r(e:)g Fm(required)498 4033 y Fl(Sp)r(eci\014ed)k(as:) -61 b(a)40 b(t)n(w)n(o)g(dimensional)f(arra)n(y)f(con)n(taining)h(n)n -(um)n(b)r(ers)h(of)g(the)h(t)n(yp)r(e)498 4133 y(indicated)28 -b(in)g(T)-7 b(able)27 b(3.10)291 4402 y Fe(Usage)46 b(Notes)392 -4584 y Fl(1.)41 b(Before)28 b(call)h(this)g(subroutine)f(y)n(ou)g(m)n -(ust)h(allo)r(cate)f Fh(x)i Fl(with)f(F90)p 2571 4584 -25 4 v 29 w(PSDSALL)g(sub-)498 4684 y(routine.)392 4838 -y(2.)41 b(These)31 b(pro)r(cedures)g(cannot)g(b)r(e)h(executed)f(if)h -(related)f(sparse)f(matrix)h(descriptor)498 4937 y(has)c(b)r(een)h -(already)e(deallo)r(cated)h(with)h(F90)p 1903 4937 V -29 w(PSDSCFREE)g(call.)1681 5255 y(57)p eop -%%Page: 58 58 -58 57 bop 739 739 a Fe(F90)p 966 739 41 4 v 48 w(PSSPREINIT)45 -b(|Reinitialize)j(Global)e(Sparse)739 888 y(Matrix)739 -1137 y Fl(This)24 b(subroutine)g(reinitializes)f(global)g(sparse)g -(matrix)h Fh(A)p Fl(;)h(the)g(user)f(planning)f(to)i(regen-)739 -1236 y(erate)k(a)g(matrix)h(with)g(exactly)f(the)i(same)e(nonzero)g -(pattern)g(should)h(call)f(this)i(routine,)739 1336 y(then)d -Fj(F90_PSSPUPD)23 b Fl(instead)28 b(of)f Fj(F90_PSSPINS)p -Fl(.)p 1292 1447 1758 4 v 1342 1516 a Fh(A)924 b Fm(Subroutine)p -1292 1550 V 1342 1619 a Fl(Long)27 b(Precision)f(Real)257 -b(F90)p 2471 1619 25 4 v 29 w(PSSPREINIT)1342 1719 y(Long)27 -b(Precision)f(Complex)99 b(F90)p 2471 1719 V 29 w(PSSPREINIT)p -1292 1752 1758 4 v 1754 1984 a(T)-7 b(able)27 b(3.11:)36 -b(Data)27 b(t)n(yp)r(es)739 2367 y Fe(Syn)l(tax)1275 -2548 y Fl(CALL)h(F90)p 1672 2548 25 4 v 29 w(PSSPREINIT)f(\()p -Ff(a,)k(ierrv,)g(de)l(c)l(omp)p 2853 2548 26 4 v 31 w(data)p -Fl(\))739 2748 y Fm(On)g(En)m(try)739 2914 y(a)42 b Fl(see)27 -b(\\On)g(Return".)739 3080 y Fm(decomp)p 1066 3080 29 -4 v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)946 3179 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3279 y Fl(T)n(yp)r(e:)g Fm(required)946 3379 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 3545 y Fm(ierrv)42 b Fl(see)27 b(\\On)g(Return".)739 -3711 y Fm(On)k(Return)739 3877 y(a)42 b Fl(allo)r(cated)27 -b(lo)r(cal)g(p)r(ortion)g(of)g(global)g(sparse)f(matrix)h -Fh(A)p Fl(.)946 3976 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -4076 y Fl(T)n(yp)r(e:)g Fm(required)946 4176 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 4342 y Fm(ierrv)42 b Fl(error)25 b(v)n(ector)i(used) -g(in)h(subroutines)f(F90)p 2306 4342 25 4 v 29 w(PSSPUPD)g(and)h(F90)p -3050 4342 V 29 w(PSSP)-7 b(ASB.)946 4441 y(Scop)r(e:)37 -b Fm(lo)s(cal)946 4541 y Fl(T)n(yp)r(e:)g Fm(required)946 -4641 y Fl(Sp)r(eci\014ed)29 b(as:)36 b(a)27 b(one)g(dimensional)g(arra) -n(y)f(of)h(in)n(teger.)2130 5255 y(58)p eop -%%Page: 59 59 -59 58 bop 291 754 a Fe(F90)p 518 754 41 4 v 48 w(PSSPUPD|Up)t(date)45 -b(Sparse)g(Matrix)291 1018 y Fl(This)e(subroutine)h(up)r(dates)g(the)g -(sparse)e(matrix)h Fh(A)h Fl(with)h(the)f(lo)r(cal)f(sparse)f(matrix) -291 1117 y Fh(B)t(LC)6 b(K)g Fl(.)61 b(This)36 b(assumes)e(that)j -(there)e(has)h(b)r(een)g(a)f(previous)g(call)g(to)h(F90)p -2765 1117 25 4 v 29 w(PSSP)-7 b(ASB)291 1217 y(with)34 -b(argumen)n(t)e Fh(U)9 b(P)45 b Fl(=)33 b Fh(Y)19 b Fl(.)55 -b(Moreo)n(v)n(er,)33 b(for)g(e\016ciency)g(reasons,)h(it)g(is)g -(assumed)f(that)291 1317 y(the)h(blo)r(c)n(k)g(en)n(tries)g(in)g(BLCK)g -(are)f(generated)h(in)g(exactly)g(the)h(same)e(order)g(as)h(in)h(the) -291 1416 y(previous)26 b(run)h(using)h(F90)p 1134 1416 -V 29 w(PSSPINS.)p 903 1543 1641 4 v 952 1613 a Fh(A;)14 -b(B)t(LC)6 b(K)627 b Fm(Subroutine)p 903 1646 V 952 1716 -a Fl(Long)27 b(Precision)f(Real)257 b(F90)p 2081 1716 -25 4 v 29 w(PSSPUPD)952 1815 y(Long)27 b(Precision)f(Complex)99 -b(F90)p 2081 1815 V 29 w(PSSPUPD)p 903 1849 1641 4 v -1306 2081 a(T)-7 b(able)27 b(3.12:)36 b(Data)27 b(t)n(yp)r(es)291 -2479 y Fe(Syn)l(tax)667 2664 y Fl(CALL)h(F90)p 1064 2664 -25 4 v 29 w(PSSPUPD)f(\()p Ff(a,)k(ia,)g(ja,)g(blck,)g(ierrv,)g(de)l(c) -l(omp)p 2564 2664 26 4 v 32 w(data)p Fl(\))291 2864 y(CALL)c(F90)p -687 2864 25 4 v 29 w(PSSPUPD)777 2963 y(\()p Ff(a,)k(ia,)g(ja,)g(blck,) -g(ierrv,)g(de)l(c)l(omp)p 1838 2963 26 4 v 31 w(data,)g(IBLCK=iblck,)h -(JBLCK=jblck)p Fl(\))291 3166 y Fm(On)f(En)m(try)291 -3348 y(a)41 b Fl(the)34 b(lo)r(cal)f(p)r(ortion)g(of)h(global)e(sparse) -g(matrix)h Fh(A)p Fl(.)56 b(This)33 b(subroutine)g(computes)h(the)498 -3448 y(lo)r(cation)j(of)h(the)f(\014rst)h(elemen)n(t)f(of)h(the)g(lo)r -(cal)f(submatrix)g(to)g(insert,)j(based)d(on)498 3547 -y Fh(ia;)14 b(j)5 b(a)27 b Fl(and)g Fh(matr)r(ix)p 1146 -3547 25 4 v 31 w(data)h Fl(\014eld)f(of)h Fh(decomp)p -1913 3547 V 30 w(data)p Fl(.)498 3647 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 3746 y Fl(T)n(yp)r(e:)g Fm(required)498 -3846 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(structured)g(data)g(t)n -(yp)r(e)h(sp)r(eci\014ed)g(in)g Fg(x)f Fl(1.)291 4028 -y Fm(ia)41 b Fl(the)f(ro)n(w)e(index)h(of)g(global)g(sparse)f(matrix)g -Fh(A)p Fl(,)43 b(iden)n(tifying)c(the)h(\014rst)f(ro)n(w)f(of)i(the)498 -4127 y(submatrix)27 b Fh(A)p Fl(.)498 4227 y(Scop)r(e:)37 -b Fm(global)498 4327 y Fl(T)n(yp)r(e:)g Fm(required)498 -4426 y Fl(Sp)r(eci\014ed)20 b(as:)32 b(an)19 b(in)n(teger)f(v)-5 -b(ariable)19 b(1)j Fg(\024)h Fh(ia)f Fg(\024)h Fh(decomp)p -2258 4426 V 30 w(data)p Fl(\045)p Fh(matr)r(ix)p 2780 -4426 V 30 w(data)p Fl([)p Fh(M)p 3084 4426 V 39 w Fl(].)291 -4608 y Fm(ja)42 b Fl(the)26 b(column)h(index)f(of)g(the)h(global)e -(sparse)g(matrix)h Fh(A)p Fl(,)h(iden)n(tifying)f(the)h(\014rst)f -(column)498 4707 y(of)i(the)g(submatrix)f Fh(A)p Fl(.)498 -4807 y(Scop)r(e:)37 b Fm(global)498 4907 y Fl(T)n(yp)r(e:)g -Fm(required)498 5006 y Fl(Sp)r(eci\014ed)21 b(as:)32 -b(an)20 b(in)n(teger)f(v)-5 b(ariable)19 b(1)k Fg(\024)f -Fh(j)5 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b(bl)r(ck)25 b Fl(=)e(1.)946 3259 y(Sp)r(eci\014ed)29 -b(as:)36 b(an)27 b(in)n(teger)g(v)-5 b(ariable)26 b Fh(j)5 -b(bl)r(ck)25 b Fg(\025)e Fl(1.)739 3445 y Fm(On)31 b(Return)739 -3631 y(a)42 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)g(of)g(global)g(sparse) -f(matrix)h Fh(A)h Fl(up)r(dated)g(with)g(matrix)f Fh(B)t(LC)6 -b(K)g Fl(.)946 3731 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3830 y Fl(T)n(yp)r(e:)g Fm(required)946 3930 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 4116 y Fm(ierrv)42 b Fl(error)24 b(v)n(ector)i(used) -g(in)h(successiv)n(e)e(call)h(to)h(F90)p 2493 4116 V -29 w(PSSPINS)f(and)g(F90)p 3190 4116 V 30 w(PSSP)-7 b(ASB.)946 -4215 y(Scop)r(e:)37 b Fm(lo)s(cal)946 4315 y Fl(T)n(yp)r(e:)g -Fm(required)946 4415 y Fl(Sp)r(eci\014ed)29 b(as:)36 -b(a)27 b(one)g(dimensional)g(arra)n(y)f(of)h(in)n(teger.)739 -4716 y Fe(Usage)46 b(Notes)840 4907 y Fl(1.)41 b(Before)22 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1579 4 v 1431 1624 -a(A)924 b Fm(Subroutine)p 1382 1657 V 1431 1727 a Fl(Long)27 -b(Precision)f(Real)257 b(F90)p 2560 1727 25 4 v 29 w(PSCSRP)1431 -1827 y(Long)27 b(Precision)f(Complex)99 b(F90)p 2560 -1827 V 29 w(PSCSRP)p 1382 1860 1579 4 v 1754 2092 a(T)-7 -b(able)27 b(3.13:)36 b(Data)27 b(t)n(yp)r(es)739 2509 -y Fe(Syn)l(tax)1230 2694 y Fl(CALL)h(F90)p 1627 2694 -25 4 v 29 w(PSCSRP)f(\()p Ff(tr)l(ans,)j(ip)l(erm,)h(a,)f(de)l(c)l(omp) -p 2898 2694 26 4 v 32 w(data)p Fl(\))739 2897 y Fm(On)h(En)m(try)739 -3080 y(trans)42 b Fl(Whether)28 b(the)g(p)r(erm)n(utation)f(or)g(its)h -(transp)r(ose)e(should)h(b)r(e)h(used.)946 3180 y(Scop)r(e:)37 -b Fm(global)946 3279 y Fl(T)n(yp)r(e:)g Fm(required)946 -3379 y Fl(Sp)r(eci\014ed)29 b(as:)36 b(a)27 b(c)n(haracter)f(v)-5 -b(ariable)26 b Fj(N)h Fl(or)g Fj(T)p Fl(.)739 3562 y -Fm(ip)s(erm)39 b Fl(The)28 b(p)r(erm)n(utation)f(to)h(b)r(e)g(applied,) -f(stored)g(in)h(v)n(ector)e(form.)946 3661 y(Scop)r(e:)37 -b Fm(global)946 3761 y Fl(T)n(yp)r(e:)g 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1378 1657 V 1428 -1727 a Fl(Long)27 b(Precision)f(Real)257 b(F90)p 2557 -1727 25 4 v 29 w(PSGELP)1428 1827 y(Long)27 b(Precision)f(Complex)99 -b(F90)p 2557 1827 V 29 w(PSGELP)p 1378 1860 1586 4 v -1754 2092 a(T)-7 b(able)27 b(3.14:)36 b(Data)27 b(t)n(yp)r(es)739 -2509 y Fe(Syn)l(tax)1229 2694 y Fl(CALL)h(F90)p 1626 -2694 25 4 v 29 w(PSGELP)e(\()p Ff(tr)l(ans,)k(ip)l(erm,)h(x,)e(de)l(c)l -(omp)p 2899 2694 26 4 v 32 w(data)p Fl(\))739 2897 y -Fm(On)i(En)m(try)739 3080 y(trans)42 b Fl(Whether)28 -b(the)g(p)r(erm)n(utation)f(or)g(its)h(transp)r(ose)e(should)h(b)r(e)h -(used.)946 3180 y(Scop)r(e:)37 b Fm(global)946 3279 y -Fl(T)n(yp)r(e:)g Fm(required)946 3379 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(c)n(haracter)f(v)-5 b(ariable)26 b -Fj(N)h Fl(or)g Fj(T)p Fl(.)739 3562 y Fm(ip)s(erm)39 -b Fl(The)28 b(p)r(erm)n(utation)f(to)h(b)r(e)g(applied,)f(stored)g(in)h -(v)n(ector)e(form.)946 3661 y(Scop)r(e:)37 b Fm(global)946 -3761 y Fl(T)n(yp)r(e:)g Fm(required)946 3860 y Fl(Sp)r(eci\014ed)29 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Fl(If)30 b Fh(y)i -Fl(is)d(not)g(presen)n(t,)f(then)i Fh(x)f Fl(is)g(o)n(v)n(erwritten)f -(with)h(the)h(translated)e(in)n(teger)g(indices.)498 -4284 y(Scop)r(e:)37 b Fm(global)498 4384 y Fl(T)n(yp)r(e:)g -Fm(required)498 4483 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(rank)f(one)i(in)n(teger)e(arra)n(y)-7 b(.)291 -4691 y Fm(y)41 b Fl(If)30 b Fh(y)i Fl(is)d(not)h(presen)n(t,)f(then)h -Fh(y)i Fl(is)d(o)n(v)n(erwritten)f(with)h(the)h(translated)e(in)n -(teger)h(indices,)498 4791 y(and)f Fh(x)g Fl(is)f(left)h(unc)n(hanged.) -37 b(Scop)r(e:)f Fm(global)498 4890 y Fl(T)n(yp)r(e:)h -Fm(optional)498 4990 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(rank)f(one)i(in)n(teger)e(arra)n(y)-7 b(.)1681 -5255 y(71)p eop -%%Page: 72 72 -72 71 bop 739 523 a Fe(Usage)46 b(Notes)840 705 y Fl(1.)41 -b(The)28 b(descriptors)e(m)n(ust)i(b)r(e)g(assem)n(bled)f(b)r(efore)g -(calls)g(to)g(this)h(subroutine.)840 871 y(2.)41 b(The)26 -b(subroutine)g(will)g(con)n(v)n(ert)e(the)i(in)n(teger)f(v)-5 -b(alues)25 b(con)n(tained)g(in)h(the)h(input)f(v)n(ec-)946 -971 y(tor,)i(mapping)f(from)g(the)h(global)f(n)n(um)n(b)r(ering)g(to)g -(lo)r(cal)g(n)n(um)n(b)r(ering.)840 1137 y(3.)41 b(The)c(v)-5 -b(alue)36 b(of)g Fj(ACT)f Fl(will)h(determine)g(whether)g(an)n(y)g -(range)f(errors)e(in)k(the)f(input)946 1236 y(v)n(ector)23 -b(will)h(b)r(e)h(treated)e(as)h(fatal)g(errors,)e(w)n(arnings)h(or)g -(will)h(b)r(e)g(ignored.)35 b(P)n(ossible)946 1336 y(errors)26 -b(are:)1060 1502 y(-)41 b(V)-7 b(alue)18 b Fh(x)p Fl(\()p -Fh(i)p Fl(\))i(is)e(outside)g(the)h(global)e(n)n(um)n(b)r(ering)h -(range)f(1)d Fh(:)g(:)g(:)f(decomp)p 3295 1502 25 4 v -29 w(data)p Fl(\045)p Fh(matr)r(ix)p 3816 1502 V 31 w(data)p -Fl(\()p Fh(M)p 4130 1502 V 39 w Fl(\))1129 1602 y(for)27 -b(some)g Fh(i)p Fl(;)1060 1734 y(-)41 b(V)-7 b(alue)18 -b Fh(x)p Fl(\()p Fh(i)p Fl(\))i(is)e(within)h(the)g(global)e(n)n(um)n -(b)r(ering)h(range)f(1)d Fh(:)g(:)g(:)f(decomp)p 3267 -1734 V 29 w(data)p Fl(\045)p Fh(matr)r(ix)p 3788 1734 -V 31 w(data)p Fl(\()p Fh(M)p 4102 1734 V 39 w Fl(\),)1129 -1834 y(but)28 b(there)g(is)f(no)g(corresp)r(onding)f(lo)r(cal)h(index)h -(to)f(b)r(e)h(mapp)r(ed)g(on)n(to;)840 2000 y(4.)41 b(A)28 -b(global)f(index)h(will)f(ha)n(v)n(e)g(a)g(corresp)r(onding)f(lo)r(cal) -h(index)g(if)h(either:)982 2166 y(\(a\))41 b(The)23 b(global)g(index)g -(is)g(assigned)f(to)i(the)f(curren)n(t)g(pro)r(cess)f(b)n(y)h(the)h -Fj(PARTS)d Fl(user)1129 2266 y(de\014ned)28 b(routine;)977 -2399 y(\(b\))42 b(The)37 b(global)f(index)h(is)f(in)h(the)h(halo,)g -(i.e.)65 b(there)36 b(is)h(at)g(least)f(one)h(nonzero)1129 -2498 y(en)n(try)21 b(in)g(the)h(lo)r(cal)e(part)h(of)g(the)h(matrix)e -Fh(a)i Fl(corresp)r(onding)d(to)i(the)g(descriptor)1129 -2598 y Fh(decomp)p 1407 2598 V 30 w(data)27 b Fl(with)h(the)g(same)f -(column)h(index.)2130 5255 y(72)p eop -%%Page: 73 73 -73 72 bop 291 781 a Fe(PSLOC)p 745 781 41 4 v 48 w(TO)p -988 781 V 48 w(GLOB|Con)l(v)l(ert)45 b(lo)t(cal)h(to)f(global)291 -930 y(n)l(um)l(b)t(ering)291 1219 y Fl(This)26 b(subroutine)f(accepts)h -(an)f(in)n(teger)g(v)n(ector)g(of)h(arbitrary)e(size)i(con)n(taining)f -(indices)h(in)291 1318 y(the)i(lo)r(cal)f(n)n(um)n(b)r(ering)g(sc)n -(heme,)g(and)g(con)n(v)n(erts)f(them)i(in)n(to)g(global)e(n)n(um)n(b)r -(ering)h(sc)n(heme.)291 1649 y Fe(Syn)l(tax)875 1839 -y Fl(CALL)g(PSLOC)p 1413 1839 25 4 v 29 w(TO)p 1567 1839 -V 30 w(GLOB)g(\()p Ff(x,de)l(c)l(omp)p 2223 1839 26 4 -v 32 w(data,act)p Fl(\))842 2039 y(CALL)h(PSLOC)p 1381 -2039 25 4 v 29 w(TO)p 1535 2039 V 29 w(GLOB)f(\()p Ff(x,y,de)l(c)l(omp) -p 2255 2039 26 4 v 33 w(data,act)p Fl(\))291 2248 y Fm(On)k(En)m(try) -291 2456 y(x)41 b Fl(An)29 b(in)n(teger)d(v)n(ector)h(of)g(indices)h -(to)f(b)r(e)h(con)n(v)n(erted.)498 2556 y(Scop)r(e:)37 -b Fm(lo)s(cal)498 2655 y Fl(T)n(yp)r(e:)g Fm(required)498 -2755 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(rank)f(one)i(in)n(teger)e -(arra)n(y)-7 b(.)291 3063 y Fm(decomp)p 618 3063 29 4 -v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)498 3162 y(Scop)r(e:)37 b Fm(lo)s(cal)498 -3262 y Fl(T)n(yp)r(e:)g Fm(required)498 3362 y Fl(Sp)r(eci\014ed)28 -b(as:)37 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)291 3569 y Fm(act)42 b Fl(sp)r(eci\014es)28 -b(action)f(to)g(b)r(e)h(tak)n(en)f(in)h(case)f(of)g(range)f(errors.)35 -b(Scop)r(e:)i Fm(global)498 3669 y Fl(T)n(yp)r(e:)g Fm(optional)498 -3769 y Fl(Sp)r(eci\014ed)28 b(as:)37 b(a)27 b(c)n(haracter)e(v)-5 -b(ariable)27 b Fj(E)p Fl(,)g Fj(W)g Fl(or)g Fj(A)p Fl(.)291 -3977 y Fm(On)k(Return)291 4184 y(x)41 b Fl(If)30 b Fh(y)i -Fl(is)d(not)g(presen)n(t,)f(then)i Fh(x)f Fl(is)g(o)n(v)n(erwritten)f -(with)h(the)h(translated)e(in)n(teger)g(indices.)498 -4284 y(Scop)r(e:)37 b Fm(global)498 4384 y Fl(T)n(yp)r(e:)g -Fm(required)498 4483 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(rank)f(one)i(in)n(teger)e(arra)n(y)-7 b(.)291 -4691 y Fm(y)41 b Fl(If)30 b Fh(y)i Fl(is)d(not)h(presen)n(t,)f(then)h -Fh(y)i Fl(is)d(o)n(v)n(erwritten)f(with)h(the)h(translated)e(in)n -(teger)h(indices,)498 4791 y(and)f Fh(x)g Fl(is)f(left)h(unc)n(hanged.) -37 b(Scop)r(e:)f Fm(global)498 4890 y Fl(T)n(yp)r(e:)h -Fm(optional)498 4990 y Fl(Sp)r(eci\014ed)28 b(as:)37 -b(a)27 b(rank)f(one)i(in)n(teger)e(arra)n(y)-7 b(.)1681 -5255 y(73)p eop -%%Page: 74 74 -74 73 bop 739 523 a Fe(Usage)46 b(Notes)840 705 y Fl(1.)41 -b(The)28 b(descriptors)e(m)n(ust)i(b)r(e)g(assem)n(bled)f(b)r(efore)g -(calls)g(to)g(this)h(subroutine.)840 871 y(2.)41 b(The)26 -b(subroutine)g(will)g(con)n(v)n(ert)e(the)i(in)n(teger)f(v)-5 -b(alues)25 b(con)n(tained)g(in)h(the)h(input)f(v)n(ec-)946 -971 y(tor,)i(mapping)f(from)g(the)h(lo)r(cal)f(n)n(um)n(b)r(ering)g(to) -h(global)e(n)n(um)n(b)r(ering.)840 1137 y(3.)41 b(The)c(v)-5 -b(alue)36 b(of)g Fj(ACT)f Fl(will)h(determine)g(whether)g(an)n(y)g -(range)f(errors)e(in)k(the)f(input)946 1236 y(v)n(ector)23 -b(will)h(b)r(e)h(treated)e(as)h(fatal)g(errors,)e(w)n(arnings)h(or)g -(will)h(b)r(e)g(ignored.)35 b(P)n(ossible)946 1336 y(errors)26 -b(are:)1060 1502 y(-)41 b(V)-7 b(alue)18 b Fh(x)p Fl(\()p -Fh(i)p Fl(\))i(is)e(outside)g(the)h(lo)r(cal)f(n)n(um)n(b)r(ering)f -(range)g(1)d Fh(:)g(:)g(:)f(decomp)p 3246 1502 25 4 v -30 w(data)p Fl(\045)p Fh(matr)r(ix)p 3768 1502 V 31 w(data)p -Fl(\()p Fh(n)p 4042 1502 V 30 w(col)p 4175 1502 V 31 -w Fl(\))1129 1602 y(for)27 b(some)g Fh(i)p Fl(;)840 1768 -y(4.)41 b(A)28 b(global)f(index)h(will)f(ha)n(v)n(e)g(a)g(corresp)r -(onding)f(lo)r(cal)h(index)g(if)h(either:)982 1934 y(\(a\))41 -b(The)23 b(global)g(index)g(is)g(assigned)f(to)i(the)f(curren)n(t)g -(pro)r(cess)f(b)n(y)h(the)h Fj(PARTS)d Fl(user)1129 2033 -y(de\014ned)28 b(routine;)977 2166 y(\(b\))42 b(The)37 -b(global)f(index)h(is)f(in)h(the)h(halo,)g(i.e.)65 b(there)36 -b(is)h(at)g(least)f(one)h(nonzero)1129 2266 y(en)n(try)21 -b(in)g(the)h(lo)r(cal)e(part)h(of)g(the)h(matrix)e Fh(a)i -Fl(corresp)r(onding)d(to)i(the)g(descriptor)1129 2365 -y Fh(decomp)p 1407 2365 V 30 w(data)27 b Fl(with)h(the)g(same)f(column) -h(index.)2130 5255 y(74)p eop -%%Page: 75 75 -75 74 bop 291 1146 a Fk(Chapter)64 b(4)291 1561 y Fn(Metho)6 -b(d)79 b(Library)291 1993 y Fl(In)31 b(this)g(c)n(hapter)g(w)n(e)f(pro) -n(vide)g(routines)h(for)g(preconditioners)e(and)i(iterativ)n(e)g(metho) -r(ds.)291 2092 y(Their)c(in)n(terfaces)f(are)h(de\014ned)h(in)g(the)g -(mo)r(dule)g Fj(F90METHD)1681 5255 y Fl(75)p eop -%%Page: 76 76 -76 75 bop 739 764 a Fe(PRECONDITIONER)46 b(|Compute)739 -913 y(Preconditioner)739 1185 y Fl(This)27 b(subroutine)h(computes)f(a) -g(preconditioner)g(for)g(sparse)f(matrix)h Fh(A)p Fl(.)739 -1493 y Fe(Syn)l(tax)1003 1680 y Fl(CALL)h(PRECONDITIONER)e(\()p -Ff(ipr)l(e)l(c,a,l,u,vdiag,de)l(c)l(omp)p 2961 1680 26 -4 v 37 w(data,ierr)p Fl(\))739 1885 y Fm(On)31 b(En)m(try)739 -2076 y(iprec)41 b Fl(T)n(yp)r(e)28 b(of)g(preconditioner)e(to)h(b)r(e)h -(computed.)946 2176 y(Scop)r(e:)37 b Fm(global)946 2276 -y Fl(T)n(yp)r(e:)g Fm(required)946 2375 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(an)27 b(in)n(teger)g(v)-5 b(ariable:)946 2566 -y Fm(0)42 b Fl(No)27 b(preconditioner;)946 2711 y Fm(1)42 -b Fl(Diagonal)26 b(scaling;)946 2856 y Fm(2)42 b Fl(Lo)r(cal)27 -b Fh(I)7 b(LU)i Fl(\(0\))27 b(preconditioning;)739 3047 -y Fm(a)42 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)g(of)g(global)g(sparse)f -(matrix)h Fh(A)p Fl(.)946 3147 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3247 y Fl(T)n(yp)r(e:)g Fm(required)946 3346 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 3537 y Fm(decomp)p 1066 3537 29 4 -v 33 w(data)42 b Fl(con)n(tains)27 b(data)g(structures)g(for)g(comm)n -(unications.)946 3637 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -3736 y Fl(T)n(yp)r(e:)g Fm(required)946 3836 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(a)27 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in) -g Fg(x)f Fl(1.)739 4027 y Fm(On)k(Return)739 4218 y(ierr)41 -b Fl(error)26 b(co)r(de.)946 4317 y(Scop)r(e:)37 b Fm(lo)s(cal)946 -4417 y Fl(T)n(yp)r(e:)g Fm(required)946 4516 y Fl(Sp)r(eci\014ed)29 -b(as:)36 b(an)27 b(in)n(teger)g(n)n(um)n(b)r(er.)739 -4707 y Fm(l)41 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)g(of)h(global)e -(sparse)g(matrix)h Fh(L)h Fl(of)f(the)h Fh(I)7 b(LU)i -Fl(\(0\))27 b(factorization)f(of)i Fh(A)946 4807 y Fl(Scop)r(e:)37 -b Fm(lo)s(cal)946 4907 y Fl(T)n(yp)r(e:)g Fm(required)p -Fl(;)28 b(it)g(is)g(only)f(used)g(when)h Fh(ipr)r(ec)23 -b Fl(=)g(2.)946 5006 y(Sp)r(eci\014ed)29 b(as:)36 b(a)27 -b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)f Fl(1.)2130 5255 y(76)p eop -%%Page: 77 77 -77 76 bop 291 523 a Fm(u)41 b Fl(the)28 b(lo)r(cal)f(p)r(ortion)g(of)h -(global)e(sparse)g(matrix)i Fh(U)36 b Fl(of)27 b(the)h -Fh(I)7 b(LU)i Fl(\(0\))27 b(factorization)g(of)g Fh(A)498 -623 y Fl(Scop)r(e:)37 b Fm(lo)s(cal)498 722 y Fl(T)n(yp)r(e:)g -Fm(required)p Fl(;)28 b(it)g(is)f(only)g(used)h(when)g -Fh(ipr)r(ec)23 b Fl(=)f(2.)498 822 y(Sp)r(eci\014ed)41 -b(as:)62 b(a)40 b(structured)g(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)f(in) -h Fg(x)f Fl(1.)75 b(Sp)r(eci\014ed)41 b(as:)62 b(a)498 -922 y(structured)27 b(data)g(t)n(yp)r(e)h(sp)r(eci\014ed)g(in)g -Fg(x)g Fl(1.)291 1088 y Fm(vdiag)41 b Fl(a)27 b(diagonal)f(scaling)h(v) -n(ector.)498 1187 y(Scop)r(e:)37 b Fm(lo)s(cal)498 1287 -y Fl(T)n(yp)r(e:)g Fm(required)p Fl(;)28 b(it)g(is)f(used)h(when)g -Fh(ipr)r(ec)22 b Fl(=)h(2)k(or)g Fh(ipr)r(ec)c Fl(=)f(1.)498 -1386 y(Sp)r(eci\014ed)g(as:)32 b(a)21 b(rank)e(one)i(arra)n(y)d(with)j -(the)h(POINTER)d(attribute;)k(if)f Fh(ipr)r(ec)h Fl(=)f(1)e(it)498 -1486 y(con)n(tains)26 b(the)h(diagonal)f(scaling)g(matrix;)g(if)i -Fh(ipr)r(ec)23 b Fl(=)f(2)27 b(it)g(con)n(tains)f(the)h(diagonal)498 -1586 y(of)h(the)g Fh(I)7 b(LU)i Fl(\(0\))27 b(factorization.)291 -1860 y Fe(Usage)46 b(Notes)392 2042 y Fl(1.)41 b(This)31 -b(routine)f(allo)r(cates)g(the)h(in)n(ternal)g(comp)r(onen)n(ts)f(of)h -Fh(L)f Fl(and)h Fh(U)39 b Fl(as)31 b(necessary;)498 2142 -y(b)r(et)n(w)n(een)h(t)n(w)n(o)f(successiv)n(e)f(calls)h(to)g(this)h -(routine,)h(the)f(user)f(should)g(place)g(a)g(call)498 -2241 y(to)d Fj(F90_PSSPFREE)22 b Fl(for)27 b(b)r(oth)h -Fh(L)g Fl(and)f Fh(U)36 b Fl(to)28 b(a)n(v)n(oid)e(memory)h(leaks.)1681 -5255 y(77)p eop -%%Page: 78 78 -78 77 bop 739 750 a Fe(F90)p 966 750 41 4 v 48 w(CGS)45 -b(|CGS)g(Iterativ)l(e)i(Metho)t(d)739 1008 y Fl(This)36 -b(subroutine)g(implemen)n(ts)h(the)g(CGS)g(metho)r(d)g(with)g -(restarting.)62 b(The)37 b(stopping)739 1108 y(criterion)24 -b(is)i(the)g(norm)n(wise)e(bac)n(kw)n(ard)g(error,)g(in)i(the)g -(in\014nit)n(y)g(norm,)g(i.e.)36 b(the)26 b(iteration)739 -1208 y(is)h(stopp)r(ed)h(when)1995 1302 y Fg(k)p Fh(r)r -Fg(k)p 1776 1340 561 4 v 1776 1416 a Fl(\()p Fg(k)p Fh(A)p -Fg(kk)p Fh(x)p Fg(k)17 b Fl(+)h Fg(k)p Fh(b)p Fg(k)p -Fl(\))2369 1359 y Fh(<)23 b(eps)739 1666 y Fe(Syn)l(tax)1174 -1850 y Fl(CALL)28 b(F90)p 1571 1850 25 4 v 29 w(CGS)g(\()p -Ff(a,ipr)l(e)l(c,l,u,vdiag,b,x,ep)q(s,de)m(c)l(omp)p 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nnr, err, err_act, int_err(5) integer, pointer :: iwork(:) character :: afmt*5, atyp*5 - type(psb_dspmat_type) :: blck + integer, allocatable :: irow(:),icol(:) + real(kind(1.d0)), allocatable :: val(:) integer, parameter :: nb=30 real(kind(1.d0)) :: t0, t1, t2, t3, t4, t5, mpi_wtime external :: mpi_wtime @@ -198,7 +199,7 @@ contains call psb_cdall(nrow,nrow,parts,icontxt,desc_a,info) if(info/=0) then info=4010 - ch_err='psb_psdscall' + ch_err='psb_pscdall' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if @@ -220,17 +221,14 @@ contains isize = max(3*nb,ncol) - blck%m = nb - blck%k = ncol - call psb_sp_all(blck,nb*ncol,info) + allocate(val(nb*ncol),irow(nb*ncol),icol(nb*ncol),stat=info) if(info/=0) then info=4010 - ch_err='spall' + ch_err='Allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - blck%fida = 'CSR' i_count = 1 do while (i_count.le.nrow) @@ -255,21 +253,19 @@ contains if (myprow == root) then do j = i_count, j_count - blck%ia2(j-i_count+1) = a_glob%ia2(j) - & + icol(j-i_count+1) = a_glob%ia2(j) - & & a_glob%ia2(i_count) + 1 enddo k = a_glob%ia2(i_count) do j = k, a_glob%ia2(j_count)-1 - blck%aspk(j-k+1) = a_glob%aspk(j) - blck%ia1(j-k+1) = a_glob%ia1(j) + val(j-k+1) = a_glob%aspk(j) + irow(j-k+1) = a_glob%ia1(j) enddo - ll = blck%ia2(nnr+1) - 1 - blck%m = nnr - blck%k = nrow + ll = icol(nnr+1) - 1 if (iproc == myprow) then - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) + call psb_spins(ll,irow,icol,val,a,desc_a,info) if(info/=0) then info=4010 ch_err='psb_spins' @@ -287,9 +283,9 @@ contains else call igesd2d(icontxt,1,1,nnr,1,iproc,0) call igesd2d(icontxt,1,1,ll,1,iproc,0) - call igesd2d(icontxt,nnr+1,1,blck%ia2,nnr+1,iproc,0) - call igesd2d(icontxt,ll,1,blck%ia1,ll,iproc,0) - call dgesd2d(icontxt,ll,1,blck%aspk,ll,iproc,0) + call igesd2d(icontxt,nnr+1,1,icol,nnr+1,iproc,0) + call igesd2d(icontxt,ll,1,irow,ll,iproc,0) + call dgesd2d(icontxt,ll,1,val,ll,iproc,0) call dgesd2d(icontxt,nnr,1,b_glob(i_count:j_count-1),nnr,iproc,0) call igerv2d(icontxt,1,1,ll,1,iproc,0) endif @@ -298,26 +294,24 @@ contains if (iproc == myprow) then call igerv2d(icontxt,1,1,nnr,1,root,0) call igerv2d(icontxt,1,1,ll,1,root,0) - if (ll > size(blck%ia1)) then + if (ll > size(irow)) then write(0,*) myprow,'need to reallocate ',ll - call psb_sp_reall(blck,ll,info) + deallocate(val,irow,icol) + allocate(val(ll),irow(ll),icol(ll),stat=info) if(info/=0) then info=4010 - ch_err='psb_sp_reall' + ch_err='Allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if endif - call igerv2d(icontxt,ll,1,blck%ia1,ll,root,0) - call igerv2d(icontxt,nnr+1,1,blck%ia2,nnr+1,root,0) - call dgerv2d(icontxt,ll,1,blck%aspk,ll,root,0) + call igerv2d(icontxt,ll,1,irow,ll,root,0) + call igerv2d(icontxt,nnr+1,1,icol,nnr+1,root,0) + call dgerv2d(icontxt,ll,1,val,ll,root,0) call dgerv2d(icontxt,nnr,1,b_glob(i_count:i_count+nnr-1),nnr,root,0) call igesd2d(icontxt,1,1,ll,1,root,0) - blck%m = nnr - blck%k = nrow - blck%infoa(psb_nnz_) = ll - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) + call psb_spins(ll,irow,icol,val,a,desc_a,info) if(info/=0) then info=4010 ch_err='psspins' @@ -343,25 +337,17 @@ contains do j_count = 1, length_row k_count = iwork(j_count) if (myprow == root) then - blck%ia2(1) = 1 - blck%ia2(2) = 1 + icol(1) = 1 + icol(2) = 1 do j = a_glob%ia2(i_count), a_glob%ia2(i_count+1)-1 - blck%aspk(blck%ia2(2)) = a_glob%aspk(j) - blck%ia1(blck%ia2(2)) = a_glob%ia1(j) - blck%ia2(2) =blck%ia2(2) + 1 + val(icol(2)) = a_glob%aspk(j) + irow(icol(2)) = a_glob%ia1(j) + icol(2) =icol(2) + 1 enddo - ll = blck%ia2(2) - 1 + ll = icol(2) - 1 if (k_count == myprow) then - blck%infoa(1) = ll - blck%infoa(2) = ll - blck%infoa(3) = 2 - blck%infoa(4) = 1 - blck%infoa(5) = 1 - blck%infoa(6) = 1 - blck%m = 1 - blck%k = nrow - - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) + + call psb_spins(ll,irow,icol,val,a,desc_a,info) if(info/=0) then info=4010 ch_err='psspins' @@ -378,23 +364,21 @@ contains end if else call igesd2d(icontxt,1,1,ll,1,k_count,0) - call igesd2d(icontxt,ll,1,blck%ia1,ll,k_count,0) - call dgesd2d(icontxt,ll,1,blck%aspk,ll,k_count,0) + call igesd2d(icontxt,ll,1,irow,ll,k_count,0) + call dgesd2d(icontxt,ll,1,val,ll,k_count,0) call dgesd2d(icontxt,1,1,b_glob(i_count),1,k_count,0) call igerv2d(icontxt,1,1,ll,1,k_count,0) endif else if (myprow /= root) then if (k_count == myprow) then call igerv2d(icontxt,1,1,ll,1,root,0) - blck%ia2(1) = 1 - blck%ia2(2) = ll+1 - call igerv2d(icontxt,ll,1,blck%ia1,ll,root,0) - call dgerv2d(icontxt,ll,1,blck%aspk,ll,root,0) + icol(1) = 1 + icol(2) = ll+1 + call igerv2d(icontxt,ll,1,irow,ll,root,0) + call dgerv2d(icontxt,ll,1,val,ll,root,0) call dgerv2d(icontxt,1,1,b_glob(i_count),1,root,0) call igesd2d(icontxt,1,1,ll,1,root,0) - blck%m = 1 - blck%k = nrow - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) + call psb_spins(ll,irow,icol,val,a,desc_a,info) if(info/=0) then info=4010 ch_err='psspins' @@ -470,10 +454,10 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_sp_free(blck,info) + deallocate(val,irow,icol,stat=info) if(info/=0)then info=4010 - ch_err='sp_free' + ch_err='deallocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if @@ -571,7 +555,8 @@ contains & i,j,k, ll, isize, iproc, nnr, err, err_act, int_err(5) integer, pointer :: iwork(:) character :: afmt*5, atyp*5 - type(psb_dspmat_type) :: blck + integer, allocatable :: irow(:),icol(:) + real(kind(1.d0)), allocatable :: val(:) integer, parameter :: nb=30 logical, parameter :: newt=.true. real(kind(1.d0)) :: t0, t1, t2, t3, t4, t5, mpi_wtime @@ -585,198 +570,192 @@ contains ! executable statements if (present(inroot)) then - root = inroot + root = inroot else - root = 0 + root = 0 end if call blacs_gridinfo(icontxt, nprow, npcol, myprow, mypcol) if (myprow == root) then - ! extract information from a_glob - if (a_glob%fida.ne. 'CSR') then - info=135 - ch_err='CSR' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - endif - - nrow = a_glob%m - ncol = a_glob%k - if (nrow /= ncol) then - write(0,*) 'a rectangular matrix ? ',nrow,ncol - info=-1 - call psb_errpush(info,name) - goto 9999 - endif - - nnzero = size(a_glob%aspk) - nrhs = 1 - ! broadcast informations to other processors - call igebs2d(icontxt, 'a', ' ', 1, 1, nrow, 1) - call igebs2d(icontxt, 'a', ' ', 1, 1, ncol, 1) - call igebs2d(icontxt, 'a', ' ', 1, 1, nnzero, 1) - call igebs2d(icontxt, 'a', ' ', 1, 1, nrhs, 1) + ! extract information from a_glob + if (a_glob%fida.ne. 'CSR') then + info=135 + ch_err='CSR' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + endif + + nrow = a_glob%m + ncol = a_glob%k + if (nrow /= ncol) then + write(0,*) 'a rectangular matrix ? ',nrow,ncol + info=-1 + call psb_errpush(info,name) + goto 9999 + endif + + nnzero = size(a_glob%aspk) + nrhs = 1 + ! broadcast informations to other processors + call igebs2d(icontxt, 'a', ' ', 1, 1, nrow, 1) + call igebs2d(icontxt, 'a', ' ', 1, 1, ncol, 1) + call igebs2d(icontxt, 'a', ' ', 1, 1, nnzero, 1) + call igebs2d(icontxt, 'a', ' ', 1, 1, nrhs, 1) else !(myprow /= root) - ! receive informations - call igebr2d(icontxt, 'a', ' ', 1, 1, nrow, 1, root, 0) - call igebr2d(icontxt, 'a', ' ', 1, 1, ncol, 1, root, 0) - call igebr2d(icontxt, 'a', ' ', 1, 1, nnzero, 1, root, 0) - call igebr2d(icontxt, 'a', ' ', 1, 1, nrhs, 1, root, 0) + ! receive informations + call igebr2d(icontxt, 'a', ' ', 1, 1, nrow, 1, root, 0) + call igebr2d(icontxt, 'a', ' ', 1, 1, ncol, 1, root, 0) + call igebr2d(icontxt, 'a', ' ', 1, 1, nnzero, 1, root, 0) + call igebr2d(icontxt, 'a', ' ', 1, 1, nrhs, 1, root, 0) end if ! allocate integer work area liwork = max(nprow, nrow + ncol) allocate(iwork(liwork), stat = info) if (info /= 0) then - write(0,*) 'matdist allocation failed' - info=2025 - int_err(1)=liwork - call psb_errpush(info,name,i_err=int_err) - goto 9999 + write(0,*) 'matdist allocation failed' + info=2025 + int_err(1)=liwork + call psb_errpush(info,name,i_err=int_err) + goto 9999 endif call psb_cdall(nrow,v,icontxt,desc_a,info) if(info/=0) then - info=4010 - ch_err='psb_cdall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_cdall' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if call psb_spall(a,desc_a,info,nnz=((nnzero+nprow-1)/nprow)) if(info/=0) then - info=4010 - ch_err='psb_psspall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_psspall' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if call psb_geall(nrow,b,desc_a,info) if(info/=0) then - info=4010 - ch_err='psb_psdsall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_psdsall' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if isize = max(3*nb,ncol) - blck%m = nb - blck%k = ncol - call psb_sp_all(blck,nb*ncol,info) + allocate(val(nb*ncol),irow(nb*ncol),icol(nb*ncol),stat=info) if(info/=0) then - info=4010 - ch_err='spall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if - blck%fida = 'COO' i_count = 1 do while (i_count <= nrow) - j_count = i_count - iproc = v(i_count) + j_count = i_count + iproc = v(i_count) + + do + j_count = j_count + 1 + if (j_count-i_count >= nb) exit + if (j_count > nrow) exit + if (v(j_count) /= iproc ) exit + end do + + ! now we should insert rows i_count..j_count-1 + nnr = j_count - i_count + + if (myprow == root) then + ll = a_glob%ia2(j_count)-a_glob%ia2(i_count) + if (ll > size(val)) then + deallocate(val,irow,icol) + allocate(val(ll),irow(ll),icol(ll),stat=info) + if(info/=0) then + info=4010 + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if - do - j_count = j_count + 1 - if (j_count-i_count >= nb) exit - if (j_count > nrow) exit - if (v(j_count) /= iproc ) exit - end do - - ! now we should insert rows i_count..j_count-1 - nnr = j_count - i_count - - if (myprow == root) then - ll = a_glob%ia2(j_count)-a_glob%ia2(i_count) - if (ll > size(blck%aspk)) then - call psb_sp_reall(blck,ll,info) - if(info/=0) then - info=4010 - ch_err='spreall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - endif - k = a_glob%ia2(i_count) - do i= i_count, j_count-1 - do j = a_glob%ia2(i),a_glob%ia2(i+1)-1 - blck%ia1(j-k+1) = i - blck%ia2(j-k+1) = a_glob%ia1(j) - blck%aspk(j-k+1) = a_glob%aspk(j) - end do - enddo - - blck%m = nnr - blck%k = nrow - blck%infoa(psb_nnz_) = ll - if (iproc == myprow) then - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) - if(info/=0) then - info=4010 - ch_err='psb_spins' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& - &desc_a,info) - if(info/=0) then - info=4010 - ch_err='dsins' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - call igesd2d(icontxt,1,1,nnr,1,iproc,0) - call igesd2d(icontxt,1,1,ll,1,iproc,0) - call igesd2d(icontxt,ll,1,blck%ia1,ll,iproc,0) - call igesd2d(icontxt,ll,1,blck%ia2,ll,iproc,0) - call dgesd2d(icontxt,ll,1,blck%aspk,ll,iproc,0) - call dgesd2d(icontxt,nnr,1,b_glob(i_count:j_count-1),nnr,iproc,0) - call igerv2d(icontxt,1,1,ll,1,iproc,0) - endif - else if (myprow /= root) then - - if (iproc == myprow) then - call igerv2d(icontxt,1,1,nnr,1,root,0) - call igerv2d(icontxt,1,1,ll,1,root,0) - if (ll > size(blck%aspk)) then - write(0,*) myprow,'need to reallocate ',ll - call psb_sp_reall(blck,ll,info) - if(info/=0) then - info=4010 - ch_err='spreall' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - endif - call igerv2d(icontxt,ll,1,blck%ia1,ll,root,0) - call igerv2d(icontxt,ll,1,blck%ia2,ll,root,0) - call dgerv2d(icontxt,ll,1,blck%aspk,ll,root,0) - call dgerv2d(icontxt,nnr,1,b_glob(i_count:i_count+nnr-1),nnr,root,0) - call igesd2d(icontxt,1,1,ll,1,root,0) - blck%m = nnr - blck%k = nrow - blck%infoa(psb_nnz_) = ll - call psb_spins(ll,blck%ia1,blck%ia2,blck%aspk,a,desc_a,info) - if(info/=0) then - info=4010 - ch_err='spins' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& - &desc_a,info) - if(info/=0) then - info=4010 - ch_err='psdsins' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + endif + k = a_glob%ia2(i_count) + do i= i_count, j_count-1 + do j = a_glob%ia2(i),a_glob%ia2(i+1)-1 + irow(j-k+1) = i + icol(j-k+1) = a_glob%ia1(j) + val(j-k+1) = a_glob%aspk(j) + end do + enddo + + if (iproc == myprow) then + call psb_spins(ll,irow,icol,val,a,desc_a,info) + if(info/=0) then + info=4010 + ch_err='psb_spins' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& + &desc_a,info) + if(info/=0) then + info=4010 + ch_err='dsins' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + call igesd2d(icontxt,1,1,nnr,1,iproc,0) + call igesd2d(icontxt,1,1,ll,1,iproc,0) + call igesd2d(icontxt,ll,1,irow,ll,iproc,0) + call igesd2d(icontxt,ll,1,icol,ll,iproc,0) + call dgesd2d(icontxt,ll,1,val,ll,iproc,0) + call dgesd2d(icontxt,nnr,1,b_glob(i_count:j_count-1),nnr,iproc,0) + call igerv2d(icontxt,1,1,ll,1,iproc,0) + endif + else if (myprow /= root) then + + if (iproc == myprow) then + call igerv2d(icontxt,1,1,nnr,1,root,0) + call igerv2d(icontxt,1,1,ll,1,root,0) + if (ll > size(val)) then + write(0,*) myprow,'need to reallocate ',ll + deallocate(val,irow,icol) + allocate(val(ll),irow(ll),icol(ll),stat=info) + if(info/=0) then + info=4010 + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if endif - endif - i_count = j_count + call igerv2d(icontxt,ll,1,irow,ll,root,0) + call igerv2d(icontxt,ll,1,icol,ll,root,0) + call dgerv2d(icontxt,ll,1,val,ll,root,0) + call dgerv2d(icontxt,nnr,1,b_glob(i_count:i_count+nnr-1),nnr,root,0) + call igesd2d(icontxt,1,1,ll,1,root,0) + + call psb_spins(ll,irow,icol,val,a,desc_a,info) + if(info/=0) then + info=4010 + ch_err='spins' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& + &desc_a,info) + if(info/=0) then + info=4010 + ch_err='psdsins' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + endif + endif + i_count = j_count end do @@ -784,19 +763,19 @@ contains ! expect duplicated entries. if (present(fmt)) then - afmt=fmt + afmt=fmt else - afmt = 'CSR' + afmt = 'CSR' endif call blacs_barrier(icontxt,'all') t0 = mpi_wtime() call psb_cdasb(desc_a,info) t1 = mpi_wtime() if(info/=0)then - info=4010 - ch_err='psb_cdasb' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_cdasb' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if call blacs_barrier(icontxt,'all') @@ -804,31 +783,31 @@ contains call psb_spasb(a,desc_a,info,dup=1,afmt=afmt) t3 = mpi_wtime() if(info/=0)then - info=4010 - ch_err='psb_spasb' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_spasb' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if call psb_geasb(b,desc_a,info) if (myprow == root) then - write(*,'("Descriptor assembly : ",es10.4)')t1-t0 - write(*,'("Sparse matrix assembly: ",es10.4)')t3-t2 + write(*,'("Descriptor assembly : ",es10.4)')t1-t0 + write(*,'("Sparse matrix assembly: ",es10.4)')t3-t2 end if if(info/=0)then - info=4010 - ch_err='psdsasb' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psdsasb' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if call psb_sp_free(blck,info) if(info/=0)then - info=4010 - ch_err='sp_free' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='sp_free' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if deallocate(iwork) @@ -839,8 +818,8 @@ contains 9999 continue call psb_erractionrestore(err_act) if (err_act.eq.act_abort) then - call psb_error(icontxt) - return + call psb_error(icontxt) + return end if return diff --git a/test/pargen/ppde90.f90 b/test/pargen/ppde90.f90 index 60fbe172..02d9ab6a 100644 --- a/test/pargen/ppde90.f90 +++ b/test/pargen/ppde90.f90 @@ -448,11 +448,12 @@ contains type(psb_dspmat_type) :: a real(kind(1.d0)) :: zt(nbmax),glob_x,glob_y,glob_z integer :: m,n,nnz,glob_row,j - type(psb_dspmat_type) :: row_mat integer :: x,y,z,counter,ia,i,indx_owner integer :: nprow,npcol,myprow,mypcol integer :: element integer :: nv, inv + integer, allocatable :: irow(:),icol(:) + real(kind(1.d0)), allocatable :: val(:) integer, allocatable :: prv(:) integer, pointer :: ierrv(:) real(kind(1.d0)), pointer :: dwork(:) @@ -502,11 +503,8 @@ contains ! time; just a small matrix. might be extended to generate ! a bunch of rows per call. ! - row_mat%descra(1:1) = 'G' - row_mat%fida = 'CSR' -! write(*,*) 'allocating row_mat',20*nbmax - allocate(row_mat%aspk(20*nbmax),row_mat%ia1(20*nbmax),& - &row_mat%ia2(20*nbmax),prv(nprow),stat=info) + allocate(val(20*nbmax),irow(20*nbmax),& + &icol(20*nbmax),prv(nprow),stat=info) if (info.ne.0 ) then info=4000 call psb_errpush(info,name) @@ -520,7 +518,7 @@ contains ! loop over rows belonging to current process in a block ! distribution. -! row_mat%ia2(1)=1 +! icol(1)=1 do glob_row = 1, n call parts(glob_row,n,nprow,prv,nv) do inv = 1, nv @@ -552,116 +550,101 @@ contains ! term depending on (x-1,y,z) ! if (x==1) then - row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z)& + val(element)=-b1(glob_x,glob_y,glob_z)& & -a1(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - zt(1) = exp(-glob_y**2-glob_z**2)*(-row_mat%aspk(element)) + zt(1) = exp(-glob_y**2-glob_z**2)*(-val(element)) else - row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z)& + val(element)=-b1(glob_x,glob_y,glob_z)& & -a1(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-2)*idim*idim+(y-1)*idim+(z) + icol(element)=(x-2)*idim*idim+(y-1)*idim+(z) element=element+1 endif ! term depending on (x,y-1,z) if (y==1) then - row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z)& + val(element)=-b2(glob_x,glob_y,glob_z)& & -a2(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-row_mat%aspk(element)) + zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else - row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z)& + val(element)=-b2(glob_x,glob_y,glob_z)& & -a2(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-1)*idim*idim+(y-2)*idim+(z) + icol(element)=(x-1)*idim*idim+(y-2)*idim+(z) element=element+1 endif ! term depending on (x,y,z-1) if (z==1) then - row_mat%aspk(element)=-b3(glob_x,glob_y,glob_z)& + val(element)=-b3(glob_x,glob_y,glob_z)& & -a3(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-row_mat%aspk(element)) + zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else - row_mat%aspk(element)=-b3(glob_x,glob_y,glob_z)& + val(element)=-b3(glob_x,glob_y,glob_z)& & -a3(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z-1) + icol(element)=(x-1)*idim*idim+(y-1)*idim+(z-1) element=element+1 endif ! term depending on (x,y,z) - row_mat%aspk(element)=2*b1(glob_x,glob_y,glob_z)& + val(element)=2*b1(glob_x,glob_y,glob_z)& & +2*b2(glob_x,glob_y,glob_z)& & +2*b3(glob_x,glob_y,glob_z)& & +a1(glob_x,glob_y,glob_z)& & +a2(glob_x,glob_y,glob_z)& & +a3(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z) + icol(element)=(x-1)*idim*idim+(y-1)*idim+(z) element=element+1 ! term depending on (x,y,z+1) if (z==idim) then - row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element)=-b1(glob_x,glob_y,glob_z) + val(element) = val(element)/(deltah*& & deltah) - zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-row_mat%aspk(element)) + zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else - row_mat%aspk(element)=-b1(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element)=-b1(glob_x,glob_y,glob_z) + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-1)*idim*idim+(y-1)*idim+(z+1) + icol(element)=(x-1)*idim*idim+(y-1)*idim+(z+1) element=element+1 endif ! term depending on (x,y+1,z) if (y==idim) then - row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element)=-b2(glob_x,glob_y,glob_z) + val(element) = val(element)/(deltah*& & deltah) - zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-row_mat%aspk(element)) + zt(1) = exp(-glob_y**2-glob_z**2)*exp(-glob_x)*(-val(element)) else - row_mat%aspk(element)=-b2(glob_x,glob_y,glob_z) - row_mat%aspk(element) = row_mat%aspk(element)/(deltah*& + val(element)=-b2(glob_x,glob_y,glob_z) + val(element) = val(element)/(deltah*& & deltah) - row_mat%ia2(element)=(x-1)*idim*idim+(y)*idim+(z) + icol(element)=(x-1)*idim*idim+(y)*idim+(z) element=element+1 endif ! term depending on (x+1,y,z) if (x