diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex index e1120ef0..a529b6a1 100644 --- a/docs/pdf/methods.tex +++ b/docs/pdf/methods.tex @@ -96,7 +96,7 @@ Scope: {\bf global} \\ Type: {\bf optional}.\\ Intent: {\bf in}.\\ Values: 1: use the normwise backward error, 2: use the scaled 2-norm -of the residual. Default: 1. +of the residual. 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q -1 0 0 1 166.9 492.528 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -492.329 cm BT -/F8 9.9626 Tf 169.889 492.329 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 492.329 Td[(get)]TJ ET +1 0 0 1 183.7699 492.329 cm q -1 0 0 1 183.77 492.528 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -492.329 cm BT -/F8 9.9626 Tf 186.759 492.329 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 186.7587 492.329 Td[(lo)-28(cal)]TJ ET +1 0 0 1 207.5585 492.329 cm q -1 0 0 1 207.559 492.528 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -207.5585 -492.329 cm BT -/F8 9.9626 Tf 210.547 492.329 Td [(ro)28(ws)]TJ +/F8 9.9626 Tf 210.5473 492.329 Td[(ro)28(ws)]TJ +ET +1 0 0 1 230.2789 492.329 cm 0 g 0 G - [-385(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -230.2789 -492.329 cm +BT +/F8 9.9626 Tf 234.1123 492.329 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 433.6438 492.329 cm 0 g 0 G - [-1084(14)]TJ +1 0 0 1 -433.6438 -492.329 cm +BT +/F8 9.9626 Tf 433.6438 492.329 Td[(14)]TJ +ET +1 0 0 1 443.6065 492.329 cm 0 g 0 G +1 0 0 1 -305.853 -12.9888 cm 0 0 1 rg 0 0 1 RG - -72.794 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -479.3402 cm +BT +/F8 9.9626 Tf 137.7535 479.3402 Td[(psb)]TJ ET +1 0 0 1 153.3506 479.3402 cm q -1 0 0 1 153.351 479.539 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -479.3402 cm BT -/F8 9.9626 Tf 156.339 479.34 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 479.3402 Td[(cd)]TJ ET +1 0 0 1 166.8998 479.3402 cm q -1 0 0 1 166.9 479.539 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -479.3402 cm BT -/F8 9.9626 Tf 169.889 479.34 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 479.3402 Td[(get)]TJ ET +1 0 0 1 183.7699 479.3402 cm q -1 0 0 1 183.77 479.539 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -479.3402 cm BT -/F8 9.9626 Tf 186.759 479.34 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 186.7587 479.3402 Td[(lo)-28(cal)]TJ ET +1 0 0 1 207.5585 479.3402 cm q -1 0 0 1 207.559 479.539 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -207.5585 -479.3402 cm BT -/F8 9.9626 Tf 210.547 479.34 Td [(cols)]TJ +/F8 9.9626 Tf 210.5473 479.3402 Td[(cols)]TJ +ET +1 0 0 1 226.6536 479.3402 cm 0 g 0 G - [-749(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -226.6536 -479.3402 cm +BT +/F8 9.9626 Tf 234.1123 479.3402 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 433.6438 479.3402 cm 0 g 0 G - [-1084(15)]TJ +1 0 0 1 -433.6438 -479.3402 cm +BT +/F8 9.9626 Tf 433.6438 479.3402 Td[(15)]TJ +ET +1 0 0 1 443.6065 479.3402 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -72.794 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -466.3513 cm +BT +/F8 9.9626 Tf 137.7535 466.3513 Td[(psb)]TJ ET +1 0 0 1 153.3506 466.3513 cm q -1 0 0 1 153.351 466.551 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -466.3513 cm BT -/F8 9.9626 Tf 156.339 466.351 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 466.3513 Td[(cd)]TJ ET +1 0 0 1 166.8998 466.3513 cm q -1 0 0 1 166.9 466.551 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -466.3513 cm BT -/F8 9.9626 Tf 169.889 466.351 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 466.3513 Td[(get)]TJ ET +1 0 0 1 183.7699 466.3513 cm q -1 0 0 1 183.77 466.551 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -466.3513 cm BT -/F8 9.9626 Tf 186.759 466.351 Td [(global)]TJ +/F8 9.9626 Tf 186.7587 466.3513 Td[(glob)1(al)]TJ ET +1 0 0 1 213.3701 466.3513 cm q -1 0 0 1 213.37 466.551 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -213.3701 -466.3513 cm BT -/F8 9.9626 Tf 216.359 466.351 Td [(ro)28(ws)]TJ +/F8 9.9626 Tf 216.3589 466.3513 Td[(ro)28(ws)]TJ +ET +1 0 0 1 236.0905 466.3513 cm 0 g 0 G - [-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -236.0905 -466.3513 cm +BT +/F8 9.9626 Tf 241.8609 466.3513 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 466.3513 cm 0 g 0 G - [-1084(16)]TJ +1 0 0 1 -433.6438 -466.3513 cm +BT +/F8 9.9626 Tf 433.6438 466.3513 Td[(16)]TJ +ET +1 0 0 1 443.6065 466.3513 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -78.605 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -453.3624 cm +BT +/F8 9.9626 Tf 137.7535 453.3624 Td[(psb)]TJ ET +1 0 0 1 153.3506 453.3624 cm q -1 0 0 1 153.351 453.562 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -453.3624 cm BT -/F8 9.9626 Tf 156.339 453.362 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 453.3624 Td[(cd)]TJ ET +1 0 0 1 166.8998 453.3624 cm q -1 0 0 1 166.9 453.562 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -453.3624 cm BT -/F8 9.9626 Tf 169.889 453.362 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 453.3624 Td[(get)]TJ ET +1 0 0 1 183.7699 453.3624 cm q -1 0 0 1 183.77 453.562 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -453.3624 cm BT -/F8 9.9626 Tf 186.759 453.362 Td [(global)]TJ +/F8 9.9626 Tf 186.7587 453.3624 Td[(glob)1(al)]TJ ET +1 0 0 1 213.3701 453.3624 cm q -1 0 0 1 213.37 453.562 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -213.3701 -453.3624 cm BT -/F8 9.9626 Tf 216.359 453.362 Td [(cols)]TJ +/F8 9.9626 Tf 216.3589 453.3624 Td[(cols)]TJ +ET +1 0 0 1 232.4652 453.3624 cm 0 g 0 G - [-943(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +1 0 0 1 -232.4652 -453.3624 cm +BT +/F8 9.9626 Tf 241.8609 453.3624 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 453.3624 cm 0 g 0 G - [-1084(16)]TJ +1 0 0 1 -433.6438 -453.3624 cm +BT +/F8 9.9626 Tf 433.6438 453.3624 Td[(16)]TJ +ET +1 0 0 1 443.6065 453.3624 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -78.605 -12.988 Td [(psb)]TJ +1 0 0 1 -137.7535 -440.3735 cm +BT +/F8 9.9626 Tf 137.7535 440.3735 Td[(psb)]TJ ET +1 0 0 1 153.3506 440.3735 cm q -1 0 0 1 153.351 440.573 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -440.3735 cm BT -/F8 9.9626 Tf 156.339 440.374 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 440.3735 Td[(cd)]TJ ET +1 0 0 1 166.8998 440.3735 cm q -1 0 0 1 166.9 440.573 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -440.3735 cm BT -/F8 9.9626 Tf 169.889 440.374 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 440.3735 Td[(get)]TJ ET +1 0 0 1 183.7699 440.3735 cm q -1 0 0 1 183.77 440.573 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -440.3735 cm BT -/F8 9.9626 Tf 186.759 440.374 Td [(con)28(text)]TJ +/F8 9.9626 Tf 186.7587 440.3735 Td[(con)28(te)-1(x)1(t)]TJ +ET +1 0 0 1 218.8606 440.3735 cm 0 g 0 G - [-753(.)-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 +1 0 0 1 -218.8606 -440.3735 cm +BT +/F8 9.9626 Tf 226.3637 440.3735 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 433.6438 440.3735 cm 0 g 0 G - [-1083(17)]TJ +1 0 0 1 -433.6438 -440.3735 cm +BT +/F8 9.9626 Tf 433.6438 440.3735 Td[(17)]TJ +ET +1 0 0 1 443.6065 440.3735 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -49.005 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -427.3846 cm +BT +/F8 9.9626 Tf 137.7535 427.3846 Td[(psb)]TJ ET +1 0 0 1 153.3506 427.3846 cm q -1 0 0 1 153.351 427.584 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -427.3846 cm BT -/F8 9.9626 Tf 156.339 427.385 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 427.3846 Td[(cd)]TJ ET +1 0 0 1 166.8998 427.3846 cm q -1 0 0 1 166.9 427.584 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -427.3846 cm BT -/F8 9.9626 Tf 169.889 427.385 Td [(get)]TJ +/F8 9.9626 Tf 169.8886 427.3846 Td[(get)]TJ ET +1 0 0 1 183.7699 427.3846 cm q -1 0 0 1 183.77 427.584 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.7699 -427.3846 cm BT -/F8 9.9626 Tf 186.759 427.385 Td [(large)]TJ +/F8 9.9626 Tf 186.7587 427.3846 Td[(lar)1(ge)]TJ ET +1 0 0 1 208.4164 427.3846 cm q -1 0 0 1 208.416 427.584 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -208.4164 -427.3846 cm BT -/F8 9.9626 Tf 211.405 427.385 Td [(threshold)]TJ +/F8 9.9626 Tf 211.4052 427.3846 Td[(th)1(re)-1(shol)1(d)]TJ +ET +1 0 0 1 251.8924 427.3846 cm 0 g 0 G - [-549(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -251.8924 -427.3846 cm +BT +/F8 9.9626 Tf 257.3581 427.3846 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 433.6438 427.3846 cm 0 g 0 G - [-1084(17)]TJ +1 0 0 1 -433.6438 -427.3846 cm +BT +/F8 9.9626 Tf 433.6438 427.3846 Td[(17)]TJ +ET +1 0 0 1 443.6065 427.3846 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -73.652 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -414.3958 cm +BT +/F8 9.9626 Tf 137.7535 414.3958 Td[(psb)]TJ ET +1 0 0 1 153.3506 414.3958 cm q -1 0 0 1 153.351 414.595 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -414.3958 cm BT -/F8 9.9626 Tf 156.339 414.396 Td [(cd)]TJ +/F8 9.9626 Tf 156.3394 414.3958 Td[(cd)]TJ ET +1 0 0 1 166.8998 414.3958 cm q -1 0 0 1 166.9 414.595 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.8998 -414.3958 cm BT -/F8 9.9626 Tf 169.889 414.396 Td [(set)]TJ +/F8 9.9626 Tf 169.8886 414.3958 Td[(se)-1(t)]TJ ET +1 0 0 1 182.7183 414.3958 cm q -1 0 0 1 182.718 414.595 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -182.7183 -414.3958 cm BT -/F8 9.9626 Tf 185.707 414.396 Td [(large)]TJ +/F8 9.9626 Tf 185.7071 414.3958 Td[(lar)1(ge)]TJ ET +1 0 0 1 207.3648 414.3958 cm q -1 0 0 1 207.365 414.595 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -207.3648 -414.3958 cm BT -/F8 9.9626 Tf 210.354 414.396 Td [(threshold)]TJ +/F8 9.9626 Tf 210.3536 414.3958 Td[(th)1(re)-1(shol)1(d)]TJ +ET +1 0 0 1 250.8407 414.3958 cm 0 g 0 G - [-654(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +1 0 0 1 -250.8407 -414.3958 cm +BT +/F8 9.9626 Tf 257.3581 414.3958 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 433.6438 414.3958 cm 0 g 0 G - [-1084(18)]TJ +1 0 0 1 -433.6438 -414.3958 cm +BT +/F8 9.9626 Tf 433.6438 414.3958 Td[(18)]TJ +ET +1 0 0 1 443.6065 414.3958 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -72.601 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -401.4069 cm +BT +/F8 9.9626 Tf 137.7535 401.4069 Td[(psb)]TJ ET +1 0 0 1 153.3506 401.4069 cm q -1 0 0 1 153.351 401.606 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -401.4069 cm BT -/F8 9.9626 Tf 156.339 401.407 Td [(sp)]TJ +/F8 9.9626 Tf 156.3394 401.4069 Td[(sp)]TJ ET +1 0 0 1 166.4017 401.4069 cm q -1 0 0 1 166.402 401.606 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.4017 -401.4069 cm BT -/F8 9.9626 Tf 169.39 401.407 Td [(get)]TJ +/F8 9.9626 Tf 169.3905 401.4069 Td[(get)]TJ ET +1 0 0 1 183.2718 401.4069 cm q -1 0 0 1 183.272 401.606 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.2718 -401.4069 cm BT -/F8 9.9626 Tf 186.261 401.407 Td [(nro)28(ws)]TJ +/F8 9.9626 Tf 186.2606 401.4069 Td[(nr)1(o)28(w)-1(s)]TJ +ET +1 0 0 1 211.527 401.4069 cm 0 g 0 G - [-712(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -211.527 -401.4069 cm +BT +/F8 9.9626 Tf 218.6151 401.4069 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 401.4069 cm 0 g 0 G - [-1084(18)]TJ +1 0 0 1 -433.6438 -401.4069 cm +BT +/F8 9.9626 Tf 433.6438 401.4069 Td[(18)]TJ +ET +1 0 0 1 443.6065 401.4069 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -48.508 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -388.418 cm +BT +/F8 9.9626 Tf 137.7535 388.418 Td[(psb)]TJ ET +1 0 0 1 153.3506 388.418 cm q -1 0 0 1 153.351 388.617 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -388.418 cm BT -/F8 9.9626 Tf 156.339 388.418 Td [(sp)]TJ +/F8 9.9626 Tf 156.3394 388.418 Td[(sp)]TJ ET +1 0 0 1 166.4017 388.418 cm q -1 0 0 1 166.402 388.617 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.4017 -388.418 cm BT -/F8 9.9626 Tf 169.39 388.418 Td [(get)]TJ +/F8 9.9626 Tf 169.3905 388.418 Td[(get)]TJ ET +1 0 0 1 183.2718 388.418 cm q -1 0 0 1 183.272 388.617 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.2718 -388.418 cm BT -/F8 9.9626 Tf 186.261 388.418 Td [(ncols)]TJ +/F8 9.9626 Tf 186.2606 388.418 Td[(ncols)]TJ +ET +1 0 0 1 207.9017 388.418 cm 0 g 0 G - [-298(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -207.9017 -388.418 cm +BT +/F8 9.9626 Tf 210.8665 388.418 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 388.418 cm 0 g 0 G - [-1084(19)]TJ +1 0 0 1 -433.6438 -388.418 cm +BT +/F8 9.9626 Tf 433.6438 388.418 Td[(19)]TJ +ET +1 0 0 1 443.6065 388.418 cm 0 g 0 G +1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG - -48.508 -12.989 Td [(psb)]TJ +1 0 0 1 -137.7535 -375.4291 cm +BT +/F8 9.9626 Tf 137.7535 375.4291 Td[(psb)]TJ ET +1 0 0 1 153.3506 375.4291 cm q -1 0 0 1 153.351 375.628 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -153.3506 -375.4291 cm BT -/F8 9.9626 Tf 156.339 375.429 Td [(sp)]TJ +/F8 9.9626 Tf 156.3394 375.4291 Td[(sp)]TJ ET +1 0 0 1 166.4017 375.4291 cm q -1 0 0 1 166.402 375.628 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -166.4017 -375.4291 cm BT -/F8 9.9626 Tf 169.39 375.429 Td [(get)]TJ +/F8 9.9626 Tf 169.3905 375.4291 Td[(get)]TJ ET +1 0 0 1 183.2718 375.4291 cm q -1 0 0 1 183.272 375.628 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -183.2718 -375.4291 cm BT -/F8 9.9626 Tf 186.261 375.429 Td [(nnzeros)]TJ +/F8 9.9626 Tf 186.2606 375.4291 Td[(nn)1(z)-1(eros)]TJ +ET +1 0 0 1 218.999 375.4291 cm 0 g 0 G - [-739(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +1 0 0 1 -218.999 -375.4291 cm +BT +/F8 9.9626 Tf 226.3637 375.4291 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 433.6438 375.4291 cm 0 g 0 G - [-1084(19)]TJ +1 0 0 1 -433.6438 -375.4291 cm +BT +/F8 9.9626 Tf 433.6438 375.4291 Td[(19)]TJ +ET +1 0 0 1 443.6065 375.4291 cm 0 g 0 G +1 0 0 1 -343.7111 -23.6407 cm 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -86.366 -23.641 Td [(4)-925(Computational)-383(r)-1(ou)1(t)-1(ines)]TJ +1 0 0 1 -99.8954 -351.7884 cm +BT +/F29 9.9626 Tf 99.8954 351.7884 Td[(4)-925(Computati)-1(on)1(al)-384(routines)]TJ +ET +1 0 0 1 234.032 351.7884 cm 0 g 0 G - [-19886(20)]TJ +1 0 0 1 -234.032 -351.7884 cm +BT +/F29 9.9626 Tf 432.1495 351.7884 Td[(20)]TJ +ET +1 0 0 1 114.8394 338.7995 cm 0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -12.988 Td [(psb)]TJ +1 0 0 1 -114.8394 -338.7995 cm +BT +/F8 9.9626 Tf 114.8394 338.7995 Td[(psb)]TJ ET +1 0 0 1 130.4364 338.7995 cm q -1 0 0 1 130.436 338.999 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -338.7995 cm BT -/F8 9.9626 Tf 133.425 338.8 Td [(geaxpb)28(y)]TJ +/F8 9.9626 Tf 133.4253 338.7995 Td[(geaxpb)28(y)]TJ +ET +1 0 0 1 169.1248 338.7995 cm 0 g 0 G - [-301(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -169.1248 -338.7995 cm +BT +/F8 9.9626 Tf 172.1235 338.7995 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 338.7995 cm 0 g 0 G - [-1084(21)]TJ +1 0 0 1 -433.6438 -338.7995 cm +BT +/F8 9.9626 Tf 433.6438 338.7995 Td[(21)]TJ +ET +1 0 0 1 443.6065 338.7995 cm 0 g 0 G +1 0 0 1 -328.7671 -12.9888 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.989 Td [(psb)]TJ +1 0 0 1 -114.8394 -325.8107 cm +BT +/F8 9.9626 Tf 114.8394 325.8107 Td[(psb)]TJ ET +1 0 0 1 130.4364 325.8107 cm q -1 0 0 1 130.436 326.01 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -325.8107 cm BT -/F8 9.9626 Tf 133.425 325.811 Td [(gedot)]TJ +/F8 9.9626 Tf 133.4253 325.8107 Td[(gedot)]TJ +ET +1 0 0 1 157.225 325.8107 cm 0 g 0 G - [-718(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -157.225 -325.8107 cm +BT +/F8 9.9626 Tf 164.3749 325.8107 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 433.6438 325.8107 cm 0 g 0 G - [-1083(23)]TJ +1 0 0 1 -433.6438 -325.8107 cm +BT +/F8 9.9626 Tf 433.6438 325.8107 Td[(23)]TJ +ET +1 0 0 1 443.6065 325.8107 cm 0 g 0 G +1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.989 Td [(psb)]TJ +1 0 0 1 -114.8394 -312.8218 cm +BT +/F8 9.9626 Tf 114.8394 312.8218 Td[(psb)]TJ ET +1 0 0 1 130.4364 312.8218 cm q -1 0 0 1 130.436 313.021 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -312.8218 cm BT -/F8 9.9626 Tf 133.425 312.822 Td [(gedots)]TJ +/F8 9.9626 Tf 133.4253 312.8218 Td[(gedots)]TJ +ET +1 0 0 1 161.1547 312.8218 cm 0 g 0 G - [-323(.)-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(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -161.1547 -312.8218 cm +BT +/F8 9.9626 Tf 164.3749 312.8218 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 433.6438 312.8218 cm 0 g 0 G - [-1084(25)]TJ +1 0 0 1 -433.6438 -312.8218 cm +BT +/F8 9.9626 Tf 433.6438 312.8218 Td[(25)]TJ +ET +1 0 0 1 443.6065 312.8218 cm 0 g 0 G +1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.989 Td [(psb)]TJ +1 0 0 1 -114.8394 -299.8329 cm +BT +/F8 9.9626 Tf 114.8394 299.8329 Td[(psb)]TJ ET +1 0 0 1 130.4364 299.8329 cm q -1 0 0 1 130.436 300.032 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -299.8329 cm BT -/F8 9.9626 Tf 133.425 299.833 Td [(geamax)]TJ +/F8 9.9626 Tf 133.4253 299.8329 Td[(geam)-1(ax)]TJ +ET +1 0 0 1 166.3574 299.8329 cm 0 g 0 G - [-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -166.3574 -299.8329 cm +BT +/F8 9.9626 Tf 172.1235 299.8329 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 299.8329 cm 0 g 0 G - [-1084(27)]TJ +1 0 0 1 -433.6438 -299.8329 cm +BT +/F8 9.9626 Tf 433.6438 299.8329 Td[(27)]TJ +ET +1 0 0 1 443.6065 299.8329 cm 0 g 0 G +1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.989 Td [(psb)]TJ +1 0 0 1 -114.8394 -286.844 cm +BT +/F8 9.9626 Tf 114.8394 286.844 Td[(psb)]TJ ET +1 0 0 1 130.4364 286.844 cm q -1 0 0 1 130.436 287.043 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -286.844 cm BT -/F8 9.9626 Tf 133.425 286.844 Td [(geamaxs)]TJ +/F8 9.9626 Tf 133.4253 286.844 Td[(geam)-1(axs)]TJ +ET +1 0 0 1 170.2871 286.844 cm 0 g 0 G - [-962(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -170.2871 -286.844 cm +BT +/F8 9.9626 Tf 179.8721 286.844 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 433.6438 286.844 cm 0 g 0 G - [-1084(29)]TJ +1 0 0 1 -433.6438 -286.844 cm +BT +/F8 9.9626 Tf 433.6438 286.844 Td[(29)]TJ +ET +1 0 0 1 443.6065 286.844 cm 0 g 0 G +1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.989 Td [(psb)]TJ +1 0 0 1 -114.8394 -273.8551 cm +BT +/F8 9.9626 Tf 114.8394 273.8551 Td[(psb)]TJ ET +1 0 0 1 130.4364 273.8551 cm q -1 0 0 1 130.436 274.054 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -130.4364 -273.8551 cm BT -/F8 9.9626 Tf 133.425 273.855 Td [(geasum)]TJ +/F8 9.9626 Tf 133.4253 273.8551 Td[(geas)-1(u)1(m)]TJ +ET +1 0 0 1 165.5825 273.8551 cm 0 g 0 G - [-657(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -165.5825 -273.8551 cm +BT +/F8 9.9626 Tf 172.1235 273.8551 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Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 510.1644 cm 0 g 0 G - [-1084(81)]TJ +1 0 0 1 -484.4533 -510.1644 cm +BT +/F8 9.9626 Tf 484.4533 510.1644 Td[(81)]TJ +ET +1 0 0 1 494.4159 510.1644 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -497.9166 cm +BT +/F8 9.9626 Tf 165.6488 497.9166 Td[(psb)]TJ ET +1 0 0 1 181.2459 497.9166 cm q -1 0 0 1 181.246 498.116 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -497.9166 cm BT -/F8 9.9626 Tf 184.235 497.917 Td [(glob)]TJ +/F8 9.9626 Tf 184.2347 497.9166 Td[(glob)]TJ ET +1 0 0 1 203.0974 497.9166 cm q -1 0 0 1 203.097 498.116 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -203.0974 -497.9166 cm BT -/F8 9.9626 Tf 206.086 497.917 Td [(to)]TJ +/F8 9.9626 Tf 206.0862 497.9166 Td[(to)]TJ ET +1 0 0 1 215.5396 497.9166 cm q -1 0 0 1 215.54 498.116 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -215.5396 -497.9166 cm BT -/F8 9.9626 Tf 218.528 497.917 Td [(lo)-28(c)]TJ +/F8 9.9626 Tf 218.5284 497.9166 Td[(lo)-28(c)]TJ +ET +1 0 0 1 230.9818 497.9166 cm 0 g 0 G - [-747(.)-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 +1 0 0 1 -230.9818 -497.9166 cm +BT +/F8 9.9626 Tf 238.4301 497.9166 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 497.9166 cm 0 g 0 G - [-1083(82)]TJ +1 0 0 1 -484.4533 -497.9166 cm +BT +/F8 9.9626 Tf 484.4533 497.9166 Td[(82)]TJ +ET +1 0 0 1 494.4159 497.9166 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -52.879 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -485.6688 cm +BT +/F8 9.9626 Tf 165.6488 485.6688 Td[(psb)]TJ ET +1 0 0 1 181.2459 485.6688 cm q -1 0 0 1 181.246 485.868 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -485.6688 cm BT -/F8 9.9626 Tf 184.235 485.669 Td [(lo)-28(c)]TJ +/F8 9.9626 Tf 184.2347 485.6688 Td[(lo)-28(c)]TJ ET +1 0 0 1 197.2858 485.6688 cm q -1 0 0 1 197.286 485.868 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -197.2858 -485.6688 cm BT -/F8 9.9626 Tf 200.275 485.669 Td [(to)]TJ +/F8 9.9626 Tf 200.2746 485.6688 Td[(to)]TJ ET +1 0 0 1 209.7281 485.6688 cm q -1 0 0 1 209.728 485.868 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -209.7281 -485.6688 cm BT -/F8 9.9626 Tf 212.717 485.669 Td [(glob)]TJ +/F8 9.9626 Tf 212.7169 485.6688 Td[(glob)]TJ +ET +1 0 0 1 230.9818 485.6688 cm 0 g 0 G - [-748(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -230.9818 -485.6688 cm +BT +/F8 9.9626 Tf 238.4301 485.6688 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 485.6688 cm 0 g 0 G - [-1083(84)]TJ +1 0 0 1 -484.4533 -485.6688 cm +BT +/F8 9.9626 Tf 484.4533 485.6688 Td[(84)]TJ +ET +1 0 0 1 494.4159 485.6688 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG - -47.068 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -473.4211 cm +BT +/F8 9.9626 Tf 165.6488 473.4211 Td[(psb)]TJ ET +1 0 0 1 181.2459 473.4211 cm q -1 0 0 1 181.246 473.62 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -473.4211 cm BT -/F8 9.9626 Tf 184.235 473.421 Td [(is)]TJ +/F8 9.9626 Tf 184.2347 473.4211 Td[(is)]TJ ET +1 0 0 1 191.5296 473.4211 cm q -1 0 0 1 191.53 473.62 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -191.5296 -473.4211 cm BT -/F8 9.9626 Tf 194.518 473.421 Td [(o)28(wned)]TJ +/F8 9.9626 Tf 194.5184 473.4211 Td[(o)28(wned)]TJ +ET +1 0 0 1 221.9157 473.4211 cm 0 g 0 G - [-880(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -221.9157 -473.4211 cm +BT +/F8 9.9626 Tf 230.6815 473.4211 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 484.4533 473.4211 cm 0 g 0 G - [-1084(85)]TJ +1 0 0 1 -484.4533 -473.4211 cm +BT +/F8 9.9626 Tf 484.4533 473.4211 Td[(85)]TJ +ET +1 0 0 1 494.4159 473.4211 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -28.869 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -461.1733 cm +BT +/F8 9.9626 Tf 165.6488 461.1733 Td[(psb)]TJ ET +1 0 0 1 181.2459 461.1733 cm q -1 0 0 1 181.246 461.373 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -461.1733 cm BT -/F8 9.9626 Tf 184.235 461.173 Td [(o)28(wned)]TJ +/F8 9.9626 Tf 184.2347 461.1733 Td[(o)28(wned)]TJ ET +1 0 0 1 212.2298 461.1733 cm q -1 0 0 1 212.23 461.373 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -212.2298 -461.1733 cm BT -/F8 9.9626 Tf 215.219 461.173 Td [(index)]TJ +/F8 9.9626 Tf 215.2186 461.1733 Td[(in)1(dex)]TJ +ET +1 0 0 1 238.7416 461.1733 cm 0 g 0 G - [-746(.)-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 +1 0 0 1 -238.7416 -461.1733 cm +BT +/F8 9.9626 Tf 246.1787 461.1733 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 484.4533 461.1733 cm 0 g 0 G - [-1083(86)]TJ +1 0 0 1 -484.4533 -461.1733 cm +BT +/F8 9.9626 Tf 484.4533 461.1733 Td[(86)]TJ +ET +1 0 0 1 494.4159 461.1733 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -49.57 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -448.9255 cm +BT +/F8 9.9626 Tf 165.6488 448.9255 Td[(psb)]TJ ET +1 0 0 1 181.2459 448.9255 cm q -1 0 0 1 181.246 449.125 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -448.9255 cm BT -/F8 9.9626 Tf 184.235 448.926 Td [(is)]TJ +/F8 9.9626 Tf 184.2347 448.9255 Td[(is)]TJ ET +1 0 0 1 191.5296 448.9255 cm q -1 0 0 1 191.53 449.125 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -191.5296 -448.9255 cm BT -/F8 9.9626 Tf 194.518 448.926 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 194.5184 448.9255 Td[(lo)-28(cal)]TJ +ET +1 0 0 1 214.7205 448.9255 cm 0 g 0 G - [-824(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -214.7205 -448.9255 cm +BT +/F8 9.9626 Tf 222.9329 448.9255 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +ET +1 0 0 1 484.4533 448.9255 cm 0 g 0 G - [-1084(87)]TJ +1 0 0 1 -484.4533 -448.9255 cm +BT +/F8 9.9626 Tf 484.4533 448.9255 Td[(87)]TJ +ET +1 0 0 1 494.4159 448.9255 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -28.869 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -436.6777 cm +BT +/F8 9.9626 Tf 165.6488 436.6777 Td[(psb)]TJ ET +1 0 0 1 181.2459 436.6777 cm q -1 0 0 1 181.246 436.877 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -436.6777 cm BT -/F8 9.9626 Tf 184.235 436.678 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 184.2347 436.6777 Td[(lo)-28(cal)]TJ ET +1 0 0 1 205.0345 436.6777 cm q -1 0 0 1 205.035 436.877 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -205.0345 -436.6777 cm BT -/F8 9.9626 Tf 208.023 436.678 Td [(index)]TJ +/F8 9.9626 Tf 208.0234 436.6777 Td[(in)1(dex)]TJ +ET +1 0 0 1 231.5463 436.6777 cm 0 g 0 G - [-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -231.5463 -436.6777 cm +BT +/F8 9.9626 Tf 238.4301 436.6777 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 436.6777 cm 0 g 0 G - [-1084(88)]TJ +1 0 0 1 -484.4533 -436.6777 cm +BT +/F8 9.9626 Tf 484.4533 436.6777 Td[(88)]TJ +ET +1 0 0 1 494.4159 436.6777 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG - -42.374 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -424.43 cm +BT +/F8 9.9626 Tf 165.6488 424.43 Td[(psb)]TJ ET +1 0 0 1 181.2459 424.43 cm q -1 0 0 1 181.246 424.629 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -424.43 cm BT -/F8 9.9626 Tf 184.235 424.43 Td [(get)]TJ +/F8 9.9626 Tf 184.2347 424.43 Td[(get)]TJ ET +1 0 0 1 198.116 424.43 cm q -1 0 0 1 198.116 424.629 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -198.116 -424.43 cm BT -/F8 9.9626 Tf 201.105 424.43 Td [(b)-28(oundary)]TJ +/F8 9.9626 Tf 201.1048 424.43 Td[(b)-27(oun)1(dary)]TJ +ET +1 0 0 1 242.6436 424.43 cm 0 g 0 G - [-354(.)-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 +1 0 0 1 -242.6436 -424.43 cm +BT +/F8 9.9626 Tf 246.1787 424.43 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-412.1822 cm BT -/F8 9.9626 Tf 201.105 412.182 Td [(o)28(v)28(erlap)]TJ +/F8 9.9626 Tf 201.1048 412.1822 Td[(o)28(v)28(e)-1(r)1(lap)]TJ +ET +1 0 0 1 232.4042 412.1822 cm 0 g 0 G - [-605(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -232.4042 -412.1822 cm +BT +/F8 9.9626 Tf 238.4301 412.1822 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 412.1822 cm 0 g 0 G - [-1084(90)]TJ +1 0 0 1 -484.4533 -412.1822 cm +BT +/F8 9.9626 Tf 484.4533 412.1822 Td[(90)]TJ +ET +1 0 0 1 494.4159 412.1822 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -35.456 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -399.9344 cm +BT +/F8 9.9626 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Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ +ET +1 0 0 1 484.4533 399.9344 cm 0 g 0 G - [-1084(91)]TJ +1 0 0 1 -484.4533 -399.9344 cm +BT +/F8 9.9626 Tf 484.4533 399.9344 Td[(91)]TJ +ET +1 0 0 1 494.4159 399.9344 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -31.637 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -387.6866 cm +BT +/F8 9.9626 Tf 165.6488 387.6866 Td[(psb)]TJ ET +1 0 0 1 181.2459 387.6866 cm q -1 0 0 1 181.246 387.886 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -387.6866 cm BT -/F8 9.9626 Tf 184.235 387.687 Td [(sizeof)]TJ +/F8 9.9626 Tf 184.2347 387.6866 Td[(siz)-1(eof)]TJ +ET +1 0 0 1 207.813 387.6866 cm 0 g 0 G - 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+1 0 0 1 -181.2459 -363.1911 cm BT -/F8 9.9626 Tf 184.235 363.191 Td [(msort)]TJ +/F8 9.9626 Tf 184.2347 363.1911 Td[(ms)-1(or)1(t)]TJ +ET +1 0 0 1 209.2244 363.1911 cm 0 g 0 G - [-598(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -209.2244 -363.1911 cm +BT +/F8 9.9626 Tf 215.1843 363.1911 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 484.4533 363.1911 cm 0 g 0 G - [-1084(94)]TJ +1 0 0 1 -484.4533 -363.1911 cm +BT +/F8 9.9626 Tf 484.4533 363.1911 Td[(94)]TJ +ET +1 0 0 1 494.4159 363.1911 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -350.9433 cm +BT +/F8 9.9626 Tf 165.6488 350.9433 Td[(psb)]TJ ET +1 0 0 1 181.2459 350.9433 cm q -1 0 0 1 181.246 351.143 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -350.9433 cm BT -/F8 9.9626 Tf 184.235 350.943 Td [(qsort)]TJ +/F8 9.9626 Tf 184.2347 350.9433 Td[(qsort)]TJ +ET +1 0 0 1 206.1803 350.9433 cm 0 g 0 G - [-904(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -206.1803 -350.9433 cm +BT +/F8 9.9626 Tf 215.1843 350.9433 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 484.4533 350.9433 cm 0 g 0 G - [-1084(94)]TJ +1 0 0 1 -484.4533 -350.9433 cm +BT +/F8 9.9626 Tf 484.4533 350.9433 Td[(94)]TJ +ET +1 0 0 1 494.4159 350.9433 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -338.6955 cm +BT +/F8 9.9626 Tf 165.6488 338.6955 Td[(psb)]TJ ET +1 0 0 1 181.2459 338.6955 cm q -1 0 0 1 181.246 338.895 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -338.6955 cm BT -/F8 9.9626 Tf 184.235 338.696 Td [(hsort)]TJ +/F8 9.9626 Tf 184.2347 338.6955 Td[(hsort)]TJ +ET +1 0 0 1 206.457 338.6955 cm 0 g 0 G - [-876(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +1 0 0 1 -206.457 -338.6955 cm +BT +/F8 9.9626 Tf 215.1843 338.6955 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +ET +1 0 0 1 484.4533 338.6955 cm 0 g 0 G - [-1084(94)]TJ +1 0 0 1 -484.4533 -338.6955 cm +BT +/F8 9.9626 Tf 484.4533 338.6955 Td[(94)]TJ +ET +1 0 0 1 494.4159 338.6955 cm 0 g 0 G +1 0 0 1 -343.7111 -22.4055 cm 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -33.53 -22.406 Td [(7)-925(P)32(arallel)-384(en)32(vironmen)32(t)-383(routines)]TJ +1 0 0 1 -150.7048 -316.29 cm +BT +/F29 9.9626 Tf 150.7048 316.29 Td[(7)-925(P)32(arall)-1(el)-384(en)32(viron)1(m)-1(en)32(t)-383(routi)-1(n)1(e)-1(s)]TJ +ET +1 0 0 1 314.6808 316.29 cm 0 g 0 G - [-16891(96)]TJ +1 0 0 1 -314.6808 -316.29 cm +BT +/F29 9.9626 Tf 482.959 316.29 Td[(96)]TJ +ET +1 0 0 1 165.6488 304.0422 cm 0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -304.0422 cm +BT +/F8 9.9626 Tf 165.6488 304.0422 Td[(psb)]TJ ET +1 0 0 1 181.2459 304.0422 cm q -1 0 0 1 181.246 304.242 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -304.0422 cm BT -/F8 9.9626 Tf 184.235 304.042 Td [(init)]TJ +/F8 9.9626 Tf 184.2347 304.0422 Td[(in)1(it)]TJ +ET +1 0 0 1 199.1787 304.0422 cm 0 g 0 G - [-829(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -199.1787 -304.0422 cm +BT +/F8 9.9626 Tf 207.4357 304.0422 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 304.0422 cm 0 g 0 G - [-1083(97)]TJ +1 0 0 1 -484.4533 -304.0422 cm +BT +/F8 9.9626 Tf 484.4533 304.0422 Td[(97)]TJ +ET +1 0 0 1 494.4159 304.0422 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -291.7945 cm +BT +/F8 9.9626 Tf 165.6488 291.7945 Td[(psb)]TJ ET +1 0 0 1 181.2459 291.7945 cm q -1 0 0 1 181.246 291.994 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -291.7945 cm BT -/F8 9.9626 Tf 184.235 291.795 Td [(info)]TJ +/F8 9.9626 Tf 184.2347 291.7945 Td[(in)1(fo)]TJ +ET +1 0 0 1 200.5625 291.7945 cm 0 g 0 G - [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-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 +1 0 0 1 -200.5625 -291.7945 cm +BT +/F8 9.9626 Tf 207.4357 291.7945 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +ET +1 0 0 1 484.4533 291.7945 cm 0 g 0 G - [-1084(98)]TJ +1 0 0 1 -484.4533 -291.7945 cm +BT +/F8 9.9626 Tf 484.4533 291.7945 Td[(98)]TJ +ET +1 0 0 1 494.4159 291.7945 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.248 Td [(psb)]TJ +1 0 0 1 -165.6488 -279.5467 cm +BT +/F8 9.9626 Tf 165.6488 279.5467 Td[(psb)]TJ ET +1 0 0 1 181.2459 279.5467 cm q -1 0 0 1 181.246 279.746 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -279.5467 cm BT -/F8 9.9626 Tf 184.235 279.547 Td [(exit)]TJ +/F8 9.9626 Tf 184.2347 279.5467 Td[(exit)]TJ +ET +1 0 0 1 200.5624 279.5467 cm 0 g 0 G - 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2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -267.2989 cm BT -/F8 9.9626 Tf 184.235 267.299 Td [(get)]TJ +/F8 9.9626 Tf 184.2347 267.2989 Td[(get)]TJ ET +1 0 0 1 198.116 267.2989 cm q -1 0 0 1 198.116 267.498 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -198.116 -267.2989 cm BT -/F8 9.9626 Tf 201.105 267.299 Td [(mpicomm)]TJ +/F8 9.9626 Tf 201.1048 267.2989 Td[(mpicomm)]TJ +ET +1 0 0 1 243.7229 267.2989 cm 0 g 0 G - [-1024(.)-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 +1 0 0 1 -243.7229 -267.2989 cm +BT +/F8 9.9626 Tf 253.9274 267.2989 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9.9626 Tf 479.4719 242.8034 Td[(102)]TJ +ET +1 0 0 1 494.4159 242.8034 cm 0 g 0 G +1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG - -18.586 -12.247 Td [(psb)]TJ +1 0 0 1 -165.6488 -230.5556 cm +BT +/F8 9.9626 Tf 165.6488 230.5556 Td[(psb)]TJ ET +1 0 0 1 181.2459 230.5556 cm q -1 0 0 1 181.246 230.755 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -181.2459 -230.5556 cm BT -/F8 9.9626 Tf 184.235 230.556 Td [(barrier)]TJ +/F8 9.9626 Tf 184.2347 230.5556 Td[(bar)1(rier)]TJ +ET +1 0 0 1 213.6522 230.5556 cm 0 g 0 G - [-931(.)-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(.)-499(.)-500(.)]TJ +1 0 0 1 -213.6522 -230.5556 cm +BT +/F8 9.9626 Tf 222.9329 230.5556 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-17.3037 Td[(The)-382(PS)1(BL)-1(AS)-381(li)1(brar)1(y)-382(is)-382(in)29(te)-1(rn)1(ally)-381(impleme)-1(n)28(ted)-381(in)-382(t)1(he)-382(F)83(or)1(tran)-381(95)-382([)]TJ +ET +1 0 0 1 409.3334 573.3639 cm 0 1 0 rg 0 1 0 RG - [(14)]TJ +1 0 0 1 -409.3334 -573.3639 cm +BT +/F8 9.9626 Tf 409.3334 573.3639 Td[(14)]TJ +ET +1 0 0 1 419.2961 573.3639 cm 0 g 0 G - [(])-382(pro-)]TJ -14.944 -11.955 Td [(gramming)-345(language,)-348(with)-346(reuse)-345(and/or)-345(adaptation)-345(of)-345(som)-1(e)-345(existing)-345(F)83(ortran)-345(77)]TJ 0 -11.955 Td [(soft)28(w)27(ar)1(e)-1(,)-352(and)-348(a)-349(handful)-348(of)-349(C)-348(routines.)-490(A)-349(similar)-348(approac)28(h)-349(has)-348(b)-28(een)-349(adv)28(o)-28(cated)]TJ 0 -11.956 Td [(b)28(y)-248(a)-248(n)27(um)28(b)-28(er)-248(of)-248(authors,)-265(e.g.)-248([)]TJ +1 0 0 1 -419.2961 -573.3639 cm +BT +/F8 9.9626 Tf 419.2961 573.3639 Td[(])-382(p)1(ro-)]TJ -319.4007 -11.9551 Td[(gramming)-345(lan)1(guage,)-348(w)-1(i)1(th)-345(reuse)-346(an)1(d/or)-345(ad)1(aptation)-344(of)-345(s)-1(ome)-346(existin)1(g)-346(F)84(ortr)1(an)-345(77)]TJ 0 -11.9552 Td[(soft)28(w)27(ar)1(e)-1(,)-352(an)1(d)-348(a)-349(han)1(df)1(ul)-348(of)-348(C)-349(rou)1(tin)1(e)-1(s.)-490(A)-349(similar)-348(app)1(roac)28(h)-349(h)1(as)-349(b)-27(e)-1(en)-348(adv)28(o)-28(cate)-1(d)]TJ 0 -11.9552 Td[(b)28(y)-248(a)-248(n)28(u)1(m)27(b)-27(e)-1(r)-247(of)-248(aut)1(hors,)-265(e)-1(.)1(g.)-248([)]TJ +ET +1 0 0 1 224.5974 537.4984 cm 0 1 0 rg 0 1 0 RG - [(13)]TJ +1 0 0 1 -224.5974 -537.4984 cm +BT +/F8 9.9626 Tf 224.5974 537.4984 Td[(13)]TJ +ET +1 0 0 1 234.5601 537.4984 cm 0 g 0 G - [(].)-416(Moreo)28(v)28(e)-1(r,)-265(the)-248(F)84(ortran)-248(95)-249(facilities)-248(for)-248(dynamic)]TJ 0 -11.955 Td [(memory)-298(managemen)28(t)-297(and)-298(in)28(terface)-298(o)28(v)28(erloading)-298(gr)1(e)-1(atly)-297(enhance)-298(the)-297(usabilit)28(y)-298(of)]TJ 0 -11.955 Td [(the)-457(PSBLAS)-457(subroutines.)-815(In)-457(this)-457(w)28(a)28(y)83(,)-488(th)1(e)-457(library)-457(can)-457(tak)28(e)-457(care)-457(of)-457(run)28(time)]TJ 0 -11.955 Td [(memory)-404(requiremen)28(ts)-403(that)-404(are)-403(quite)-404(di\016cult)-403(or)-404(ev)28(en)-404(imp)-27(os)-1(sibl)1(e)-404(to)-404(predict)-403(at)]TJ 0 -11.955 Td [(implemen)28(tation)-285(or)-285(compilation)-285(time.)-429(In)-285(the)-285(curren)28(t)-285(release)-285(w)28(e)-285(rely)-285(on)-285(the)-286(a)28(v)56(ail-)]TJ 0 -11.955 Td [(abilit)28(y)-405(of)-405(the)-405(so-called)-405(allo)-28(catable)-405(extensions,)-423(sp)-28(eci\014ed)-405(in)-405(TR)-405(15581.)-659(Strictly)]TJ 0 -11.956 Td [(sp)-28(eaking)-329(they)-330(are)-329(outside)-330(the)-329(F)83(ortran)-329(95)-330(standard;)-331(ho)28(w)28(ev)28(er)-330(they)-329(ha)27(v)28(e)-329(b)-28(een)-330(in-)]TJ 0 -11.955 Td [(cluded)-367(in)-368(the)-367(F)83(ortran)-367(2003)-367(language)-368(standard,)-376(and)-367(are)-367(a)27(v)56(ailable)-367(in)-368(practically)]TJ 0 -11.955 Td [(all)-412(F)83(ortran)-412(95)-411(c)-1(ompil)1(e)-1(rs)-412(on)-411(the)-412(mark)27(et,)-431(including)-412(the)-412(GNU)-412(F)83(ortran)-412(compiler)]TJ 0 -11.955 Td [(from)-335(the)-335(F)83(ree)-335(Soft)28(w)28(are)-336(F)84(oundation)-335(\050as)-335(of)-335(v)27(ersion)-335(4.2\051.)-449(The)-336(presen)28(tation)-335(of)-335(the)]TJ 0 -11.955 Td [(PSBLAS)-370(library)-370(follo)28(ws)-371(the)-370(general)-370(structure)-370(of)-370(the)-371(p)1(rop)-28(osal)-370(for)-371(serial)-370(Sparse)]TJ 0 -11.955 Td [(BLAS)-457([)]TJ +1 0 0 1 -234.5601 -537.4984 cm +BT +/F8 9.9626 Tf 234.5601 537.4984 Td[(].)-416(M)1(oreo)27(v)28(er,)-265(th)1(e)-249(F)84(ortr)1(an)-248(95)-248(facilit)1(ie)-1(s)-248(for)-248(d)1(ynamic)]TJ -134.6647 -11.9551 Td[(me)-1(mory)-297(managem)-1(en)28(t)-297(and)-297(in)28(terf)1(ac)-1(e)-298(o)28(v)28(erload)1(ing)-297(greatly)-297(e)-1(n)1(han)1(c)-1(e)-298(th)1(e)-298(usabil)1(it)28(y)-298(of)]TJ 0 -11.9552 Td[(th)1(e)-458(P)1(SBLAS)-457(sub)1(rou)1(tines)-1(.)-815(In)-456(thi)1(s)-458(w)28(a)28(y)83(,)-487(the)-457(lib)1(rary)-456(c)-1(an)-456(tak)28(e)-458(care)-457(of)-457(r)1(un)28(ti)1(m)-1(e)]TJ 0 -11.9552 Td[(me)-1(mory)-403(requi)1(rem)-1(en)28(ts)-404(th)1(at)-404(ar)1(e)-404(quit)1(e)-404(di\016c)-1(u)1(lt)-403(or)-403(e)-1(v)28(en)-403(im)-1(p)-27(oss)-1(ib)1(le)-404(to)-403(predi)1(c)-1(t)-403(at)]TJ 0 -11.9551 Td[(impl)1(e)-1(me)-1(n)29(tation)-285(or)-284(c)-1(ompi)1(lation)-285(t)1(im)-1(e.)-428(In)-285(th)1(e)-286(cur)1(re)-1(n)29(t)-285(rele)-1(ase)-286(w)28(e)-285(re)-1(l)1(y)-285(on)-285(th)1(e)-286(a)28(v)56(ail-)]TJ 0 -11.9552 Td[(abi)1(lit)28(y)-405(of)-404(the)-405(s)-1(o-called)-405(allo)-27(c)-1(atab)1(le)-405(e)-1(xtension)1(s)-1(,)-422(s)-1(p)-27(e)-1(ci\014)1(e)-1(d)-404(in)-405(TR)-405(15581.)-659(Str)1(ic)-1(tl)1(y)]TJ 0 -11.9552 Td[(sp)-28(eakin)1(g)-330(th)1(e)-1(y)-329(are)-330(ou)1(ts)-1(i)1(de)-330(th)1(e)-330(F)83(or)1(tran)-329(95)-330(stand)1(ard)1(;)-331(h)1(o)27(w)28(e)-1(v)28(er)-329(they)-329(ha)28(v)28(e)-330(b)-27(e)-1(en)-329(in-)]TJ 0 -11.9551 Td[(clud)1(e)-1(d)-367(in)-366(the)-368(F)84(ortr)1(an)-367(2003)-368(lan)1(guage)-368(stand)1(ard)1(,)-376(and)-367(ar)1(e)-368(a)28(v)56(ailabl)1(e)-368(in)-367(pr)1(ac)-1(ti)1(c)-1(all)1(y)]TJ 0 -11.9552 Td[(all)-412(F)84(ortr)1(an)-412(95)-412(com)-1(p)1(ilers)-412(on)-412(th)1(e)-413(mark)28(et,)-431(inclu)1(din)1(g)-412(the)-412(GNU)-412(F)84(ortran)-411(c)-1(omp)1(iler)]TJ 0 -11.9552 Td[(fr)1(om)-336(th)1(e)-336(F)84(ree)-336(S)1(oft)28(w)28(are)-336(F)84(oun)1(dation)-334(\050as)-336(of)-334(v)28(e)-1(r)1(s)-1(ion)-334(4.2\051.)-450(Th)1(e)-336(pr)1(e)-1(se)-1(n)29(tation)-335(of)-334(the)]TJ 0 -11.9551 Td[(PS)1(BLAS)-370(lib)1(rary)-370(f)1(ollo)28(ws)-371(th)1(e)-371(general)-370(structur)1(e)-371(of)-370(t)1(he)-371(p)1(rop)-27(os)-1(al)-370(f)1(or)-370(s)-1(eri)1(al)-370(Spar)1(s)-1(e)]TJ 0 -11.9552 Td[(BLAS)-457([)]TJ +ET +1 0 0 1 133.5026 405.9916 cm 0 1 0 rg 0 1 0 RG - [(7)]TJ +1 0 0 1 -133.5026 -405.9916 cm +BT +/F8 9.9626 Tf 133.5026 405.9916 Td[(7)]TJ +ET +1 0 0 1 138.484 405.9916 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -138.484 -405.9916 cm +BT +/F8 9.9626 Tf 138.484 405.9916 Td[(,)]TJ +ET +1 0 0 1 145.8008 405.9916 cm 0 1 0 rg 0 1 0 RG - [-456(8)]TJ +1 0 0 1 -145.8008 -405.9916 cm +BT +/F8 9.9626 Tf 145.8008 405.9916 Td[(8)]TJ +ET +1 0 0 1 150.7822 405.9916 cm 0 g 0 G - [(],)-488(whic)28(h)-457(in)-456(its)-457(turn)-456(is)-457(based)-457(on)-456(the)-457(prop)-28(osal)-456(for)-457(BLAS)-456(on)-457(dense)]TJ 0 -11.956 Td [(matrices)-333([)]TJ +1 0 0 1 -150.7822 -405.9916 cm +BT +/F8 9.9626 Tf 150.7822 405.9916 Td[(],)-487(whic)28(h)-456(in)-456(its)-457(tur)1(n)-457(i)1(s)-457(base)-1(d)-456(on)-456(the)-457(p)1(rop)-27(os)-1(al)-456(for)-456(B)-1(LAS)-456(on)-456(d)1(e)-1(n)1(s)-1(e)]TJ -50.8868 -11.9552 Td[(matrice)-1(s)-333([)]TJ +ET +1 0 0 1 142.5964 394.0364 cm 0 1 0 rg 0 1 0 RG - [(12)]TJ +1 0 0 1 -142.5964 -394.0364 cm +BT +/F8 9.9626 Tf 142.5964 394.0364 Td[(12)]TJ +ET +1 0 0 1 152.5591 394.0364 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -152.5591 -394.0364 cm +BT +/F8 9.9626 Tf 152.5591 394.0364 Td[(,)]TJ +ET +1 0 0 1 158.6474 394.0364 cm 0 1 0 rg 0 1 0 RG - [-334(4)]TJ +1 0 0 1 -158.6474 -394.0364 cm +BT +/F8 9.9626 Tf 158.6474 394.0364 Td[(4)]TJ +ET +1 0 0 1 163.6287 394.0364 cm 0 g 0 G - [(,)]TJ +1 0 0 1 -163.6287 -394.0364 cm +BT +/F8 9.9626 Tf 163.6287 394.0364 Td[(,)]TJ +ET +1 0 0 1 169.717 394.0364 cm 0 1 0 rg 0 1 0 RG - [-333(5)]TJ -0 g 0 G - [(].)]TJ 14.944 -17.303 Td [(The)-403(applicabilit)28(y)-403(of)-403(sparse)-403(iterativ)28(e)-404(solv)28(ers)-403(to)-403(man)28(y)-403(di\013eren)28(t)-403(are)-1(as)-403(causes)]TJ -14.944 -11.956 Td [(some)-317(terminology)-316(problems)-316(b)-28(ecause)-317(th)1(e)-317(same)-316(conce)-1(p)1(t)-317(ma)28(y)-316(b)-28(e)-317(denoted)-316(through)]TJ 0 -11.955 Td [(di\013eren)28(t)-342(names)-342(dep)-28(ending)-342(on)-342(th)1(e)-342(application)-342(area.)-470(The)-342(PSBLAS)-342(features)-342(pre-)]TJ 0 -11.955 Td [(sen)28(ted)-450(in)-450(this)-450(do)-28(cumen)28(t)-450(will)-450(b)-28(e)-450(discussed)-450(referring)-450(to)-450(a)-450(\014nite)-450(di\013erence)-450(dis-)]TJ 0 -11.955 Td [(cretization)-329(of)-329(a)-330(P)28(artial)-329(Di\013eren)28(tial)-329(Equation)-329(\050PDE\051.)-330(Ho)28(w)28(ev)28(er,)-330(the)-330(scop)-27(e)-330(of)-329(the)]TJ 0 -11.955 Td [(library)-345(i)1(s)-345(wider)-345(than)-344(that:)-467(for)-345(example,)-347(it)-345(can)-345(b)-27(e)-345(applied)-344(to)-345(\014nite)-345(elemen)28(t)-345(di)1(s)-1(-)]TJ 0 -11.955 Td [(cretizations)-278(of)-278(PDEs,)-289(and)-278(ev)28(en)-278(to)-278(di\013eren)28(t)-278(c)-1(lasses)-278(of)-278(problems)-278(suc)28(h)-278(as)-278(nonlinear)]TJ 0 -11.956 Td [(optimization,)-333(for)-334(example)-333(in)-333(optimal)-334(con)28(trol)-333(problems.)]TJ 14.944 -17.303 Td [(The)-489(design)-489(of)-489(a)-489(solv)27(er)-489(for)-489(sparse)-489(linear)-489(systems)-489(is)-489(driv)27(en)-489(b)28(y)-489(man)28(y)-489(con-)]TJ -14.944 -11.955 Td [(\015icting)-384(ob)-56(jectiv)28(es,)-398(suc)28(h)-384(as)-385(limiting)-384(o)-28(ccupation)-384(of)-385(storage)-384(res)-1(ou)1(rc)-1(es,)-397(exploiting)]TJ 0 -11.956 Td [(regularities)-433(in)-433(th)1(e)-433(input)-433(data,)-458(expl)1(oiting)-433(hardw)28(are)-433(c)28(haracteristics)-433(of)-433(the)-433(par-)]TJ 0 -11.955 Td [(allel)-370(platform.)-554(T)83(o)-370(ac)28(hiev)28(e)-370(an)-370(optimal)-370(comm)28(unication)-370(to)-370(computation)-370(ratio)-369(on)]TJ 0 -11.955 Td [(distributed)-443(memory)-443(mac)28(hines)-443(it)-443(is)-443(essen)28(tial)-443(to)-443(k)28(eep)-443(the)]TJ/F17 9.9626 Tf 253.961 0 Td [(data)-459(lo)52(c)51(ality)]TJ/F8 9.9626 Tf 57.609 0 Td [(as)-443(high)]TJ -311.57 -11.955 Td [(as)-381(p)-27(os)-1(sible;)-404(this)-381(can)-380(b)-28(e)-381(done)-380(through)-381(an)-380(appropriate)-381(data)-381(allo)-27(cation)-381(strategy)83(.)]TJ 0 -11.955 Td [(The)-389(c)28(hoice)-389(of)-389(the)-389(preconditioner)-389(is)-389(an)1(other)-389(v)27(ery)-388(imp)-28(ortan)28(t)-389(factor)-389(that)-389(a\013ects)]TJ 0 -11.956 Td [(e\016ciency)-415(of)-416(the)-415(implemen)28(ted)-415(application.)-691(Optimal)-415(data)-415(distribution)-415(require-)]TJ 0 -11.955 Td [(men)28(ts)-441(for)-441(a)-440(giv)27(en)-440(preconditioner)-441(ma)28(y)-441(con\015ict)-441(with)-440(distribution)-441(requiremen)28(ts)]TJ 0 -11.955 Td [(of)-427(the)-427(rest)-428(of)-427(the)-427(solv)28(er.)-726(Finding)-427(the)-428(optimal)-427(trade-o\013)-427(ma)28(y)-428(b)-27(e)-428(v)28(ery)-427(di\016cult)]TJ 0 -11.955 Td [(b)-28(ecause)-393(it)-393(is)-393(application)-393(dep)-28(enden)28(t.)-623(P)27(ossible)-393(solutions)-393(to)-393(these)-393(problems)-393(and)]TJ 0 -11.955 Td [(other)-430(imp)-28(ortan)28(t)-430(inputs)-430(to)-430(the)-430(dev)28(elopmen)28(t)-430(of)-430(the)-430(PSBLAS)-430(soft)28(w)27(are)-430(pac)28(k)56(age)]TJ 0 -11.955 Td [(ha)28(v)28(e)-385(come)-385(from)-385(an)-385(established)-385(exp)-28(erience)-384(in)-385(applying)-385(the)-385(PSBLAS)-385(solv)28(ers)-385(to)]TJ 0 -11.956 Td [(computational)-333(\015uid)-333(dynamics)-334(applications.)]TJ +1 0 0 1 -169.717 -394.0364 cm +BT +/F8 9.9626 Tf 169.717 394.0364 Td[(5)]TJ +ET +1 0 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Td[(oth)1(e)-1(r)-261(constrai)1(n)28(ts)-262(on)-260(the)-261(v)56(ariab)1(le)-261(as)-1(signmen)28(t.)-420(T)-1(h)1(is)-261(c)27(hoi)1(c)-1(e)-261(is)-261(c)-1(on)1(s)-1(isten)28(t)-261(with)-261(d)1(ata)]TJ 0 -11.9552 Td[(di)1(s)-1(tr)1(ibu)1(tion)1(s)-310(comm)-1(on)1(ly)-308(use)-1(d)-308(in)-308(ScaLAP)84(A)28(C)-1(K)-308(suc)27(h)-308(as)]TJ/F32 9.9626 Tf 233.5332 0 Td[(CYCLIC\050N\051)]TJ/F8 9.9626 Tf 50.1475 0 Td[(and)]TJ/F32 9.9626 Tf 19.1256 0 Td[(BLOCK)]TJ/F8 9.9626 Tf 26.1517 0 Td[(,)-308(as)]TJ -328.958 -11.9551 Td[(w)28(e)-1(ll)-421(as)-421(c)-1(ompletely)-421(arb)1(itrar)1(y)-422(assignme)-1(n)29(ts)-422(of)-421(equati)1(on)-421(in)1(dice)-1(s)-421(to)-422(p)1(ro)-28(ce)-1(sse)-1(s.)-708(I)-1(n)]TJ 0 -11.9552 Td[(par)1(ticular)-344(it)-345(is)-345(c)-1(on)1(s)-1(i)1(s)-1(ten)28(t)-345(with)-344(the)-345(usage)-345(of)-345(grap)1(h)-345(p)1(arti)1(tionin)1(g)-345(to)-28(ol)1(s)-346(com)-1(monl)1(y)]TJ 0 -11.9552 Td[(a)28(v)56(ailabl)1(e)-396(i)1(n)-395(t)1(he)-395(literatu)1(re,)-410(e)-1(.)1(g.)-629(M)1(ETIS)-395([)]TJ +ET +1 0 0 1 278.9271 574.622 cm 0 1 0 rg 0 1 0 RG - [(11)]TJ +1 0 0 1 -278.9271 -574.622 cm +BT +/F8 9.9626 Tf 278.9271 574.622 Td[(11)]TJ +ET +1 0 0 1 288.8898 574.622 cm 0 g 0 G - [(].)-628(De)-1(n)1(s)-1(e)-394(v)28(e)-1(ctors)-394(conform)-395(to)-395(sparse)]TJ 0 -11.955 Td [(matrices,)-497(that)-464(is,)-497(the)-464(en)27(tr)1(ies)-465(of)-464(a)-464(v)28(ector)-465(fol)1(lo)27(w)-464(the)-464(same)-464(distribution)-464(of)-465(the)]TJ 0 -11.955 Td [(matrix)-333(ro)27(ws.)]TJ 14.944 -11.956 Td [(W)83(e)-413(assume)-413(that)-413(the)-412(s)-1(par)1(s)-1(e)-412(m)-1(atr)1(ix)-413(is)-413(built)-413(in)-413(parallel,)-433(where)-413(eac)28(h)-413(pro)-28(cess)]TJ -14.944 -11.955 Td [(generates)-321(its)-321(o)28(wn)-321(p)-28(ortion.)-440(W)84(e)-321(nev)28(e)-1(r)-320(require)-321(that)-321(the)-321(en)28(tire)-321(matrix)-321(b)-27(e)-321(a)28(v)55(ailable)]TJ 0 -11.955 Td [(on)-279(a)-279(single)-279(no)-28(de.)-426(Ho)27(w)28(ev)28(er,)-290(it)-279(is)-279(p)-28(ossible)-279(to)-279(hold)-279(the)-279(en)28(tire)-279(m)-1(atr)1(ix)-280(in)-279(one)-279(pro)-27(ces)-1(s)]TJ 0 -11.955 Td [(and)-369(distribute)-369(it)-370(expl)1(ic)-1(i)1(tly)]TJ +1 0 0 1 -288.8898 -574.622 cm +BT +/F8 9.9626 Tf 288.8898 574.622 Td[(].)-628(Dense)-396(v)28(ec)-1(t)1(ors)-395(c)-1(on)1(form)-395(t)1(o)-395(s)-1(p)1(arse)]TJ -188.9944 -11.9552 Td[(matrice)-1(s,)-497(th)1(at)-464(is,)-497(the)-464(e)-1(n)29(tries)-465(of)-464(a)-464(v)28(ec)-1(tor)-464(f)1(ollo)28(w)-464(the)-464(s)-1(ame)-465(d)1(is)-1(t)1(rib)1(ution)-463(of)-464(the)]TJ 0 -11.9551 Td[(matrix)-333(r)1(o)27(ws.)]TJ 14.944 -11.9552 Td[(W)84(e)-414(ass)-1(u)1(m)-1(e)-413(th)1(at)-413(the)-413(sparse)-414(matr)1(ix)-413(is)-413(bu)1(ilt)-413(i)1(n)-413(p)1(arallel,)-432(w)-1(h)1(e)-1(r)1(e)-414(eac)27(h)-412(pro)-27(c)-1(es)-1(s)]TJ -14.944 -11.9552 Td[(generates)-322(it)1(s)-322(o)28(wn)-321(p)-27(ort)1(ion.)-440(W)84(e)-322(n)1(e)-1(v)28(er)-320(re)-1(q)1(uir)1(e)-322(th)1(at)-321(th)1(e)-322(en)28(ti)1(re)-321(m)-1(atr)1(ix)-321(b)-27(e)-321(a)27(v)56(ail)1(able)]TJ 0 -11.9551 Td[(on)-279(a)-279(singl)1(e)-280(n)1(o)-28(de.)-426(Ho)27(w)28(ev)28(e)-1(r,)-289(it)-279(is)-279(p)-28(oss)-1(i)1(ble)-279(to)-279(hold)-278(the)-279(e)-1(n)29(tire)-279(m)-1(at)1(rix)-279(in)-278(one)-279(pro)-27(c)-1(es)-1(s)]TJ 0 -11.9552 Td[(and)-368(distri)1(but)1(e)-370(it)-369(e)-1(x)1(pli)1(c)-1(itl)1(y)]TJ +ET +1 0 0 1 215.6221 502.891 cm 0 0 1 rg 0 0 1 RG -/F7 6.9738 Tf 115.727 3.615 Td [(1)]TJ +1 0 0 1 -215.6221 -502.891 cm +BT +/F7 6.9738 Tf 215.6221 506.5064 Td[(1)]TJ +ET +1 0 0 1 220.0914 502.891 cm 0 g 0 G -/F8 9.9626 Tf 4.469 -3.615 Td [(,)-378(ev)28(e)-1(n)-369(though)-369(the)-369(resulting)-369(b)-28(ottlenec)28(k)-369(w)27(ould)-369(mak)28(e)]TJ -120.196 -11.955 Td [(this)-333(option)-334(un)1(a)-1(t)1(trac)-1(t)1(iv)27(e)-333(in)-333(most)-334(cases.)]TJ/F16 11.9552 Tf 0 -27.405 Td [(2.1)-1125(Basic)-375(Nomenclature)]TJ/F8 9.9626 Tf 0 -18.389 Td [(Our)-377(computational)-377(mo)-28(del)-377(implies)-378(that)-377(the)-377(data)-377(allo)-28(cation)-377(on)-378(the)-377(parallel)-377(dis-)]TJ 0 -11.955 Td [(tributed)-303(memory)-302(mac)27(hine)-302(is)-303(guided)-303(b)28(y)-303(the)-302(structure)-303(of)-303(the)-303(p)1(h)27(ysical)-302(mo)-28(del,)-309(and)]TJ 0 -11.956 Td [(sp)-28(eci\014cally)-333(b)28(y)-334(the)-333(discretization)-333(mesh)-334(of)-333(the)-333(PDE.)]TJ 14.944 -11.955 Td [(Eac)28(h)-471(p)-28(oin)28(t)-471(of)-470(the)-471(discretization)-471(mesh)-470(will)-471(ha)28(v)28(e)-471(\050at)-471(least\051)-471(one)-470(asso)-28(ciated)]TJ -14.944 -11.955 Td [(equation/v)56(ariable,)-467(an)1(d)-440(therefore)-440(one)-439(index.)-764(W)84(e)-440(sa)28(y)-440(that)-439(p)-28(oin)28(t)]TJ/F11 9.9626 Tf 286.579 0 Td [(i)]TJ/F17 9.9626 Tf 7.812 0 Td [(dep)51(ends)]TJ/F8 9.9626 Tf 38.804 0 Td [(on)]TJ -333.195 -11.955 Td [(p)-28(oin)28(t)]TJ/F11 9.9626 Tf 26.99 0 Td [(j)]TJ/F8 9.9626 Tf 8.971 0 Td [(if)-431(the)-432(equation)-431(for)-431(a)-431(v)55(ariable)-431(asso)-28(ciated)-431(with)]TJ/F11 9.9626 Tf 205.846 0 Td [(i)]TJ/F8 9.9626 Tf 7.73 0 Td [(con)28(tains)-432(a)-431(term)-431(in)]TJ/F11 9.9626 Tf 86.734 0 Td [(j)]TJ/F8 9.9626 Tf 4.673 0 Td [(,)]TJ -340.944 -11.955 Td [(or)-408(equiv)56(alen)28(tly)-408(if)]TJ/F11 9.9626 Tf 78.912 0 Td [(a)]TJ/F10 6.9738 Tf 5.266 -1.495 Td [(ij)]TJ/F14 9.9626 Tf 11.021 1.495 Td [(6)]TJ/F8 9.9626 Tf 0 0 Td [(=)-402(0.)-668(After)-408(the)-408(partition)-407(of)-408(the)-408(discretization)-408(mesh)-408(in)28(to)]TJ/F17 9.9626 Tf -95.199 -11.955 Td [(sub-domains)]TJ/F8 9.9626 Tf 57.628 0 Td [(assigned)-310(to)-310(the)-310(parallel)-310(pro)-28(cesses,)-315(w)28(e)-310(classify)-310(the)-311(p)-27(oin)28(ts)-311(of)-310(a)-310(giv)28(en)]TJ -57.628 -11.956 Td [(sub-domain)-333(as)-334(follo)28(wing.)]TJ +1 0 0 1 -220.0914 -502.891 cm +BT +/F8 9.9626 Tf 220.0914 502.891 Td[(,)-378(ev)28(e)-1(n)-369(th)1(ough)-368(the)-370(r)1(e)-1(sult)1(ing)-369(b)-27(ottlenec)27(k)-369(w)28(ould)-369(mak)28(e)]TJ -120.196 -11.9552 Td[(th)1(is)-334(opt)1(ion)-333(un)1(attractiv)28(e)-334(i)1(n)-333(m)-1(ost)-333(c)-1(ase)-1(s.)]TJ/F18 11.9552 Tf 0 -27.4046 Td[(2.)-1(1)-1125(Basic)-375(No)-1(mencl)-1(atur)-1(e)]TJ/F8 9.9626 Tf 0 -18.3893 Td[(Ou)1(r)-377(c)-1(ompu)1(tation)1(al)-377(m)-1(o)-27(del)-378(i)1(m)-1(p)1(lies)-378(th)1(at)-378(t)1(he)-378(d)1(ata)-377(allo)-28(cation)-377(on)-377(t)1(he)-378(p)1(arallel)-377(di)1(s)-1(-)]TJ 0 -11.9552 Td[(tri)1(bu)1(te)-1(d)-302(me)-1(mory)-302(m)-1(ac)28(hin)1(e)-303(is)-303(guid)1(e)-1(d)-302(b)28(y)-302(the)-303(structu)1(re)-303(of)-303(t)1(he)-303(ph)29(ys)-1(i)1(c)-1(al)-302(m)-1(o)-28(d)1(e)-1(l)1(,)-309(and)]TJ 0 -11.9552 Td[(sp)-28(ec)-1(i)1(\014cally)-333(b)28(y)-333(th)1(e)-334(discre)-1(t)1(iz)-1(ati)1(on)-333(m)-1(es)-1(h)-332(of)-333(the)-334(P)1(DE.)]TJ 14.944 -11.9551 Td[(Eac)28(h)-470(p)-28(oin)29(t)-471(of)-470(the)-471(d)1(is)-1(cretization)-470(m)-1(esh)-471(will)-470(ha)28(v)28(e)-471(\050at)-470(le)-1(ast\051)-471(on)1(e)-471(as)-1(so)-28(ciate)-1(d)]TJ -14.944 -11.9552 Td[(equati)1(on/v)56(ariab)1(le,)-466(and)-439(therefor)1(e)-441(on)1(e)-440(ind)1(e)-1(x)1(.)-763(W)83(e)-440(sa)27(y)-439(th)1(at)-440(p)-27(oin)28(t)]TJ/F11 9.9626 Tf 286.5782 0 Td[(i)]TJ/F19 9.9626 Tf 7.8121 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 38.8046 0 Td[(on)]TJ -333.1949 -11.9552 Td[(p)-27(oin)28(t)]TJ/F11 9.9626 Tf 26.99 0 Td[(j)]TJ/F8 9.9626 Tf 8.9703 0 Td[(if)-431(th)1(e)-432(equati)1(on)-431(for)-431(a)-431(v)56(ariab)1(le)-432(ass)-1(o)-28(ciated)-431(with)]TJ/F11 9.9626 Tf 205.8468 0 Td[(i)]TJ/F8 9.9626 Tf 7.7295 0 Td[(con)28(tain)1(s)-432(a)-432(t)1(e)-1(rm)-431(in)]TJ/F11 9.9626 Tf 86.7341 0 Td[(j)]TJ/F8 9.9626 Tf 4.673 0 Td[(,)]TJ -340.9437 -11.9551 Td[(or)-408(equ)1(iv)56(ale)-1(n)29(tly)-408(i)1(f)]TJ/F11 9.9626 Tf 78.9119 0 Td[(a)]TJ/F10 6.9738 Tf 5.2662 -1.4944 Td[(ij)]TJ/F14 9.9626 Tf 11.0211 1.4944 Td[(6)]TJ/F8 9.9626 Tf 0 0 Td[(=)-402(0.)-668(Af)1(ter)-408(th)1(e)-409(p)1(artit)1(ion)-408(of)-407(the)-408(d)1(is)-1(cretization)-407(m)-1(es)-1(h)-407(in)28(t)1(o)]TJ/F19 9.9626 Tf -95.1992 -11.9552 Td[(sub-)1(do)-1(m)1(ains)]TJ/F8 9.9626 Tf 57.6275 0 Td[(ass)-1(ign)1(e)-1(d)-309(to)-310(the)-310(paral)1(le)-1(l)-309(pro)-27(c)-1(es)-1(se)-1(s,)-315(w)28(e)-311(class)-1(i)1(fy)-310(th)1(e)-311(p)-27(oin)28(ts)-310(of)-310(a)-310(giv)28(en)]TJ -57.6275 -11.9552 Td[(sub-d)1(om)-1(ain)-332(as)-334(foll)1(o)27(win)1(g.)]TJ +ET +1 0 0 1 94.9141 331.8229 cm 0 g 0 G -/F27 9.9626 Tf 0 -17.677 Td [(In)32(ternal.)]TJ +1 0 0 1 -94.9141 -331.8229 cm +BT +/F29 9.9626 Tf 99.8954 331.8229 Td[(In)32(ternal.)]TJ +ET +1 0 0 1 143.0113 331.8229 cm 0 g 0 G -/F8 9.9626 Tf 48.097 0 Td [(An)-397(in)28(ternal)-397(p)-28(oin)28(t)-397(of)-397(a)-396(giv)27(en)-397(domain)]TJ/F17 9.9626 Tf 164.694 0 Td [(dep)51(ends)]TJ/F8 9.9626 Tf 37.561 0 Td [(only)-397(on)-397(p)-27(oin)27(ts)-397(of)-396(the)]TJ -225.445 -11.955 Td [(same)-288(domain.)-429(If)-289(al)1(l)-289(p)-27(oin)28(ts)-289(of)-288(a)-288(domain)-288(are)-288(assigned)-288(to)-288(one)-288(pro)-28(cess,)-297(then)-288(a)]TJ 0 -11.956 Td [(computational)-342(step)-342(\050e.g.,)-344(a)-342(matrix-v)28(ec)-1(tor)-342(pr)1(o)-28(duct\051)-342(of)-342(the)-342(equations)-342(asso-)]TJ 0 -11.955 Td [(ciated)-302(with)-303(t)1(he)-303(in)28(ternal)-302(p)-28(oin)28(ts)-302(requires)-303(no)-302(data)-302(items)-302(from)-303(other)-302(domains)]TJ 0 -11.955 Td [(and)-333(no)-334(comm)28(unications.)]TJ +1 0 0 1 -143.0113 -331.8229 cm +BT +/F8 9.9626 Tf 147.9926 331.8229 Td[(An)-396(in)28(ternal)-396(p)-28(oi)1(n)28(t)-397(of)-396(a)-397(giv)28(e)-1(n)-396(domain)]TJ/F19 9.9626 Tf 164.6933 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 37.5612 0 Td[(onl)1(y)-397(on)-396(p)-28(oin)29(ts)-398(of)-396(the)]TJ -225.4451 -11.9552 Td[(sam)-1(e)-288(domain.)-429(If)-287(all)-288(p)-27(oin)28(ts)-288(of)-288(a)-288(domain)-287(are)-289(assigned)-288(to)-288(on)1(e)-289(p)1(ro)-28(ce)-1(ss)-1(,)-297(t)1(hen)-288(a)]TJ 0 -11.9552 Td[(com)-1(p)1(utati)1(onal)-342(ste)-1(p)-341(\050e)-1(.)1(g.,)-344(a)-342(matrix-v)28(ec)-1(tor)-341(pro)-27(duct\051)-342(of)-341(the)-342(e)-1(qu)1(ation)1(s)-343(ass)-1(o-)]TJ 0 -11.9551 Td[(ciate)-1(d)-301(w)-1(i)1(th)-302(the)-302(in)28(tern)1(al)-302(p)-28(oin)29(ts)-303(requ)1(ires)-303(no)-302(d)1(ata)-303(i)1(te)-1(ms)-303(f)1(rom)-303(ot)1(her)-302(domains)]TJ 0 -11.9552 Td[(and)-332(no)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ +ET +1 0 0 1 94.9141 265.2007 cm 0 g 0 G -/F27 9.9626 Tf -24.907 -18.801 Td [(Boundary)96(.)]TJ +1 0 0 1 -94.9141 -265.2007 cm +BT +/F29 9.9626 Tf 99.8954 265.2007 Td[(Boundar)1(y)96(.)]TJ +ET +1 0 0 1 151.431 265.2007 cm 0 g 0 G -/F8 9.9626 Tf 56.517 0 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[(A)-462(halo)-462(p)-28(oin)28(t)-463(for)-462(a)-462(giv)27(en)-462(domain)-462(is)-463(a)-462(p)-28(oin)28(t)-462(b)-28(elonging)-462(to)-463(an)1(other)-463(do-)]TJ -6.704 -11.955 Td [(main)-313(s)-1(u)1(c)27(h)-313(that)-314(there)-313(is)-314(a)-313(b)-28(oundary)-313(p)-28(oin)28(t)-314(whic)28(h)]TJ/F17 9.9626 Tf 210.37 0 Td [(dep)51(ends)]TJ/F8 9.9626 Tf 37.548 0 Td [(on)-313(it.)-438(Whenev)28(er)]TJ -247.918 -11.955 Td [(p)-28(erforming)-444(a)-444(computational)-444(step,)-472(suc)28(h)-444(as)-444(a)-445(matrix-v)28(ector)-444(pro)-28(duct,)-472(th)1(e)]TJ 0 -11.956 Td [(v)56(alues)-383(asso)-28(ciated)-383(with)-383(halo)-383(p)-27(oin)27(ts)-383(ar)1(e)-383(requested)-383(from)-383(other)-383(domains.)-593(A)]TJ 0 -11.955 Td [(b)-28(oundary)-363(p)-28(oin)28(t)-363(of)-364(a)-363(giv)28(en)-364(domain)-363(is)-364(usually)-363(a)-364(halo)-363(p)-28(oin)28(t)-363(for)-364(some)-363(other)]TJ 0 -11.955 Td [(domain)]TJ +1 0 0 1 -126.5245 -234.4441 cm +BT +/F8 9.9626 Tf 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12.177 -20.203 Td [(1.)]TJ +/F8 9.9626 Tf 150.7049 706.1289 Td[(to)-277(the)-278(ad)1(jace)-1(n)1(c)-1(y)-277(grap)1(h)-277(im)-1(p)-27(ose)-1(d)-277(on)-277(th)1(e)-278(disc)-1(r)1(e)-1(ti)1(z)-1(ation)-277(mes)-1(h)-277(b)28(y)-277(th)1(e)-278(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(ste)-1(n)1(c)-1(il)1(.)]TJ 14.9439 -12.0478 Td[(Th)28(us)-408(the)-409(\014)1(rst)-409(or)1(der)-408(of)-408(bu)1(s)-1(in)1(e)-1(ss)-409(is)-408(to)-409(es)-1(tab)1(lish)-408(an)-408(in)1(dex)-408(s)-1(p)1(ac)-1(e,)-427(and)-408(th)1(is)-409(is)]TJ -14.9439 -11.9552 Td[(don)1(e)-371(w)-1(i)1(th)-371(a)-371(call)-371(to)]TJ/F32 9.9626 Tf 87.1086 0 Td[(psb_cdall)]TJ/F8 9.9626 Tf 50.7685 0 Td[(in)-370(whic)28(h)-371(w)28(e)-372(sp)-28(ecify)-371(t)1(he)-371(s)-1(ize)-371(of)-371(th)1(e)-372(i)1(ndex)-371(space)]TJ/F11 9.9626 Tf -137.8771 -11.9552 Td[(n)]TJ/F8 9.9626 Tf 9.1424 0 Td[(and)-317(t)1(he)-318(all)1(o)-28(c)-1(ati)1(on)-317(of)-317(the)-318(elem)-1(en)28(ts)-318(of)-317(th)1(e)-318(in)1(dex)-318(space)-318(to)-317(the)-318(v)56(ari)1(ous)-318(p)1(ro)-28(ce)-1(ss)-1(es)]TJ -9.1424 -11.9551 Td[(makin)1(g)-334(u)1(p)-333(the)-333(MPI)-333(\050vir)1(tual\051)-333(p)1(arallel)-333(mac)27(hi)1(ne.)]TJ 14.9439 -12.0479 Td[(The)-309(i)1(ndex)-308(s)-1(p)1(ac)-1(e)-308(is)-309(par)1(tition)1(e)-1(d)-308(amon)1(g)-309(p)1(ro)-28(ce)-1(ss)-1(es,)-314(an)1(d)-308(thi)1(s)-309(c)-1(r)1(e)-1(ates)-309(a)-308(m)-1(ap)1(pin)1(g)]TJ -14.9439 -11.9552 Td[(fr)1(om)-250(t)1(he)-250(\134gl)1(obal")-249(n)29(um)27(b)-27(erin)1(g)-249(1)]TJ/F11 9.9626 Tf 132.8519 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 21.7442 0 Td[(to)-249(a)-249(n)28(u)1(m)27(b)-27(e)-1(r)1(ing)-249(\134l)1(o)-28(c)-1(al)1(")-249(to)-249(e)-1(ac)27(h)-248(pr)1(o)-28(c)-1(ess)-1(;)-277(eac)27(h)]TJ -154.5961 -11.9551 Td[(pr)1(o)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 33.7713 0 Td[(i)]TJ/F8 9.9626 Tf 5.7936 0 Td[(will)-237(o)28(wn)-237(a)-237(ce)-1(r)1(tain)-236(s)-1(u)1(bse)-1(t)-237(1)]TJ/F11 9.9626 Tf 113.5085 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 3.6541 2.4907 Td[(,)-256(e)-1(ac)28(h)-237(elem)-1(en)28(t)-237(of)-236(w)-1(h)1(ic)27(h)-236(c)-1(or)1(re)-1(sp)-27(ond)1(s)]TJ -191.7927 -11.9552 Td[(to)-390(a)-389(c)-1(ertai)1(n)-390(elem)-1(en)28(t)-389(of)-389(1)]TJ/F11 9.9626 Tf 111.3133 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 0 Td[(.)-613(The)-390(u)1(s)-1(er)-390(d)1(o)-28(es)-390(not)-390(set)-390(expli)1(c)-1(it)1(ly)-390(t)1(his)-390(mapp)1(ing;)]TJ -130.5766 -11.9552 Td[(when)-392(the)-392(app)1(lication)-392(needs)-393(to)-392(in)1(dicate)-393(to)-392(whi)1(c)27(h)-392(ele)-1(men)28(t)-392(of)-392(the)-392(ind)1(e)-1(x)-392(space)-393(a)]TJ 0 -11.9551 Td[(ce)-1(rt)1(ain)-273(it)1(e)-1(m)-273(is)-273(relate)-1(d)1(,)-285(suc)27(h)-272(as)-273(the)-273(ro)28(w)-273(and)-272(c)-1(olu)1(m)-1(n)-272(in)1(dex)-273(of)-273(a)-273(matr)1(ix)-273(co)-28(e)-1(\016cie)-1(n)29(t,)]TJ 0 -11.9552 Td[(it)-448(do)-28(es)-449(s)-1(o)-448(in)-448(the)-449(\134glob)1(al")-449(n)29(um)28(b)-28(erin)1(g,)-477(and)-448(the)-449(li)1(brar)1(y)-449(wil)1(l)-449(tr)1(anslate)-449(in)28(to)-448(the)]TJ 0 -11.9552 Td[(app)1(rop)1(riate)-333(\134lo)-28(cal")-334(n)29(um)27(b)-27(erin)1(g.)]TJ 14.944 -12.0478 Td[(F)84(or)-274(a)-274(gi)1(v)28(e)-1(n)-273(in)1(dex)-274(space)-274(1)]TJ/F11 9.9626 Tf 109.3313 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 21.9902 0 Td[(th)1(e)-1(re)-274(ar)1(e)-275(man)28(y)-273(p)-28(ossible)-274(ass)-1(o)-27(c)-1(iat)1(e)-1(d)-273(top)-27(ologies)-1(,)]TJ -146.2655 -11.9552 Td[(i.e.)-418(man)28(y)-254(d)1(i\013)-1(eren)28(t)-254(di)1(s)-1(cretization)-254(ste)-1(n)1(c)-1(i)1(ls)-1(;)-280(th)28(u)1(s)-255(th)1(e)-255(d)1(e)-1(sc)-1(r)1(ipti)1(on)-254(of)-254(th)1(e)-255(in)1(dex)-254(s)-1(p)1(ac)-1(e)]TJ 0 -11.9551 Td[(is)-355(not)-355(com)-1(p)1(lete)-1(d)-354(un)28(ti)1(l)-355(the)-355(use)-1(r)-355(h)1(as)-356(d)1(e)-1(\014)1(ned)-355(a)-355(sparsit)28(y)-355(p)1(atte)-1(r)1(n,)-360(e)-1(i)1(ther)-355(e)-1(x)1(pli)1(c)-1(itl)1(y)]TJ 0 -11.9552 Td[(th)1(rough)]TJ/F32 9.9626 Tf 36.9305 0 Td[(psb_cdins)]TJ/F8 9.9626 Tf 49.6601 0 Td[(or)-259(implicitl)1(y)-260(th)1(rough)]TJ/F32 9.9626 Tf 92.2223 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td[(.)-420(Th)1(e)-261(d)1(e)-1(scrip)1(tor)-260(i)1(s)-261(\014)1(nali)1(z)-1(ed)]TJ -225.8859 -11.9552 Td[(with)-354(a)-354(c)-1(al)1(l)-354(to)]TJ/F32 9.9626 Tf 62.2736 0 Td[(psb_cdasb)]TJ/F8 9.9626 Tf 50.6033 0 Td[(and)-353(a)-355(spar)1(s)-1(e)-355(matri)1(x)-355(wit)1(h)-354(a)-355(call)-354(to)]TJ/F32 9.9626 Tf 153.2175 0 Td[(psb_spasb)]TJ/F8 9.9626 Tf 47.0731 0 Td[(.)-507(After)]TJ/F32 9.9626 Tf -313.1675 -11.9551 Td[(psb_cdasb)]TJ/F8 9.9626 Tf 50.4428 0 Td[(eac)27(h)-338(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 57.2447 0 Td[(i)]TJ/F8 9.9626 Tf 6.8021 0 Td[(will)-338(h)1(a)27(v)28(e)-338(de\014n)1(e)-1(d)-338(a)-338(se)-1(t)-338(of)-338(\134h)1(alo")-338(\050or)-338(\134ghost"\051)-338(in)1(dice)-1(s)]TJ/F11 9.9626 Tf -114.4896 -11.9552 Td[(n)]TJ/F8 9.9626 Tf 5.9799 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9962 Td[(i)]TJ/F8 9.9626 Tf 5.9852 2.4906 Td[(+)-234(1)]TJ/F11 9.9626 Tf 16.7216 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -3.4869 Td[(col)]TJ/F9 4.9813 Tf 12.1766 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 3.6541 4.4832 Td[(,)-355(denoti)1(ng)-351(ele)-1(men)28(ts)-352(of)-350(the)-351(in)1(dex)-351(space)-352(th)1(at)-351(are)]TJ/F19 9.9626 Tf 209.5968 0 Td[(not)]TJ/F8 9.9626 Tf 18.4447 0 Td[(ass)-1(ign)1(e)-1(d)]TJ -307.6241 -11.9552 Td[(to)-284(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 45.9205 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-300(ho)28(w)28(e)-1(v)28(er)-284(th)1(e)-284(v)55(ar)1(iabl)1(e)-1(s)-284(as)-1(so)-28(ciated)-284(with)-283(th)1(e)-1(m)-284(are)-284(n)1(e)-1(eded)-284(to)-283(c)-1(omplete)]TJ -49.3528 -11.9551 Td[(com)-1(p)1(utati)1(ons)-410(ass)-1(o)-28(ciated)-409(w)-1(i)1(th)-409(the)-410(spar)1(s)-1(e)-410(matri)1(x)]TJ/F11 9.9626 Tf 216.3159 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(,)-428(and)-409(th)28(u)1(s)-410(they)-409(ha)28(v)28(e)-410(to)-410(b)-27(e)]TJ -223.7879 -11.9552 Td[(fetc)27(h)1(e)-1(d)-463(f)1(rom)-464(\050n)1(e)-1(igh)29(b)-28(ou)1(rin)1(g\051)-464(p)1(ro)-28(ce)-1(ss)-1(es)-1(.)-835(The)-464(d)1(e)-1(sc)-1(r)1(ipt)1(or)-464(of)-463(th)1(e)-465(i)1(nd)1(e)-1(x)-463(s)-1(p)1(ac)-1(e)-464(is)]TJ 0 -11.9552 Td[(bu)1(ilt)-393(e)-1(xactly)-393(for)-394(t)1(he)-394(pu)1(rp)-27(os)-1(e)-394(of)-394(p)1(rop)-27(e)-1(r)1(ly)-394(se)-1(q)1(ue)-1(n)1(c)-1(i)1(ng)-394(th)1(e)-395(comm)27(u)1(nication)-393(s)-1(teps)]TJ 0 -11.9551 Td[(requ)1(ired)-333(to)-333(ac)27(hi)1(e)-1(v)28(e)-334(th)1(is)-334(ob)-55(j)1(e)-1(ctiv)28(e.)]TJ 14.944 -12.0479 Td[(A)-306(simple)-306(app)1(lication)-305(s)-1(tr)1(uctur)1(e)-307(wil)1(l)-306(w)28(alk)-306(th)1(rou)1(gh)-306(th)1(e)-307(i)1(ndex)-306(space)-306(allo)-28(cation)1(,)]TJ -14.944 -11.9551 Td[(matrix)1(/v)28(e)-1(ctor)-333(c)-1(r)1(e)-1(ati)1(on)-333(and)-333(li)1(near)-333(s)-1(ystem)-334(s)-1(ol)1(ution)-332(as)-334(foll)1(o)27(ws:)]TJ +ET +1 0 0 1 150.7049 362.7653 cm 0 g 0 G - [-500(Initialize)-333(parallel)-334(en)28(vironmen)28(t)-333(with)]TJ/F30 9.9626 Tf 169.42 0 Td [(psb_init)]TJ +1 0 0 1 -150.7049 -362.7653 cm +BT +/F8 9.9626 Tf 162.8814 362.7653 Td[(1.)]TJ +ET +1 0 0 1 170.6302 362.7653 cm 0 g 0 G -/F8 9.9626 Tf -169.42 -20.296 Td [(2.)]TJ +1 0 0 1 -170.6302 -362.7653 cm +BT +/F8 9.9626 Tf 175.6115 362.7653 Td[(Ini)1(tialize)-334(p)1(arallel)-333(e)-1(n)29(viron)1(m)-1(en)28(t)-333(with)]TJ/F32 9.9626 Tf 156.6905 0 Td[(psb_init)]TJ +ET +1 0 0 1 150.7049 342.4693 cm 0 g 0 G - [-500(Initialize)-333(index)-334(space)-333(with)]TJ/F30 9.9626 Tf 130.123 0 Td [(psb_cdall)]TJ +1 0 0 1 -150.7049 -342.4693 cm +BT +/F8 9.9626 Tf 162.8814 342.4693 Td[(2.)]TJ +ET +1 0 0 1 170.6302 342.4693 cm 0 g 0 G -/F8 9.9626 Tf -130.123 -20.296 Td [(3.)]TJ +1 0 0 1 -170.6302 -342.4693 cm +BT +/F8 9.9626 Tf 175.6115 342.4693 Td[(Ini)1(tialize)-334(in)1(dex)-333(s)-1(p)1(ac)-1(e)-334(wit)1(h)]TJ/F32 9.9626 Tf 117.3933 0 Td[(psb_cdall)]TJ +ET +1 0 0 1 150.7049 322.1733 cm 0 g 0 G - [-500(Allo)-28(cate)-301(sparse)-302(matrix)-301(and)-302(dense)-302(v)28(ectors)-301(with)]TJ/F30 9.9626 Tf 215.329 0 Td [(psb_spall)]TJ/F8 9.9626 Tf 50.077 0 Td [(and)]TJ/F30 9.9626 Tf 19.055 0 Td [(psb_geall)]TJ +1 0 0 1 -150.7049 -322.1733 cm +BT +/F8 9.9626 Tf 162.8814 322.1733 Td[(3.)]TJ +ET +1 0 0 1 170.6302 322.1733 cm 0 g 0 G -/F8 9.9626 Tf -284.461 -20.296 Td [(4.)]TJ +1 0 0 1 -170.6302 -322.1733 cm +BT +/F8 9.9626 Tf 175.6115 322.1733 Td[(Allo)-27(c)-1(ate)-302(spar)1(s)-1(e)-302(matri)1(x)-302(an)1(d)-301(dense)-302(v)28(e)-1(ctors)-302(with)]TJ/F32 9.9626 Tf 202.5989 0 Td[(psb_spall)]TJ/F8 9.9626 Tf 50.0773 0 Td[(and)]TJ/F32 9.9626 Tf 19.0552 0 Td[(psb_geall)]TJ +ET +1 0 0 1 150.7049 301.8774 cm 0 g 0 G - [-500(Lo)-28(op)-411(o)28(v)28(er)-411(all)-411(lo)-28(cal)-411(ro)27(ws,)-430(generate)-411(matrix)-411(and)-411(v)27(ector)-411(en)28(tries,)-431(an)1(d)-412(in)1(s)-1(ert)]TJ 12.73 -11.955 Td [(them)-333(with)]TJ/F30 9.9626 Tf 48.153 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 50.393 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(psb_geins)]TJ +1 0 0 1 -150.7049 -301.8774 cm +BT +/F8 9.9626 Tf 162.8814 301.8774 Td[(4.)]TJ +ET +1 0 0 1 170.6302 301.8774 cm 0 g 0 G -/F8 9.9626 Tf -130.648 -20.296 Td [(5.)]TJ +1 0 0 1 -170.6302 -301.8774 cm +BT +/F8 9.9626 Tf 175.6115 301.8774 Td[(Lo)-28(op)-410(o)27(v)28(er)-411(all)-411(l)1(o)-28(c)-1(al)-410(ro)28(w)-1(s,)-430(ge)-1(n)1(e)-1(r)1(ate)-412(matrix)-411(an)1(d)-411(v)28(ec)-1(tor)-410(e)-1(n)28(t)1(ries)-1(,)-430(and)-410(inse)-1(r)1(t)]TJ 0 -11.9552 Td[(th)1(e)-1(m)-334(wit)1(h)]TJ/F32 9.9626 Tf 48.1528 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 50.394 0 Td[(and)]TJ/F32 9.9626 Tf 19.3718 0 Td[(psb_geins)]TJ +ET +1 0 0 1 150.7049 269.6262 cm 0 g 0 G - [-500(Assem)28(ble)-334(the)-333(v)56(arious)-334(en)28(tities:)]TJ +1 0 0 1 -150.7049 -269.6262 cm +BT +/F8 9.9626 Tf 162.8814 269.6262 Td[(5.)]TJ +ET +1 0 0 1 170.6302 269.6262 cm 0 g 0 G - 16.936 -20.296 Td [(\050a\051)]TJ +1 0 0 1 -170.6302 -269.6262 cm +BT +/F8 9.9626 Tf 175.6115 269.6262 Td[(Ass)-1(em)27(b)1(le)-334(th)1(e)-334(v)56(ariou)1(s)-334(e)-1(n)29(tities)-1(:)]TJ +ET +1 0 0 1 175.6115 249.3302 cm 0 g 0 G -/F30 9.9626 Tf 17.711 0 Td [(psb_cdasb)]TJ +1 0 0 1 -175.6115 -249.3302 cm +BT +/F8 9.9626 Tf 179.8179 249.3302 Td[(\050a\051)]TJ +ET +1 0 0 1 192.548 249.3302 cm 0 g 0 G -/F8 9.9626 Tf -18.264 -16.126 Td [(\050b\051)]TJ +1 0 0 1 -192.548 -249.3302 cm +BT +/F32 9.9626 Tf 197.5293 249.3302 Td[(psb_cdasb)]TJ +ET +1 0 0 1 175.6115 233.2046 cm 0 g 0 G -/F30 9.9626 Tf 18.264 0 Td [(psb_spasb)]TJ +1 0 0 1 -175.6115 -233.2046 cm +BT +/F8 9.9626 Tf 179.2644 233.2046 Td[(\050b)1(\051)]TJ +ET +1 0 0 1 192.548 233.2046 cm 0 g 0 G -/F8 9.9626 Tf -17.157 -16.125 Td [(\050c\051)]TJ +1 0 0 1 -192.548 -233.2046 cm +BT +/F32 9.9626 Tf 197.5293 233.2046 Td[(psb_spasb)]TJ +ET +1 0 0 1 175.6115 217.0791 cm 0 g 0 G -/F30 9.9626 Tf 17.157 0 Td [(psb_geasb)]TJ +1 0 0 1 -175.6115 -217.0791 cm +BT +/F8 9.9626 Tf 180.3714 217.0791 Td[(\050c\051)]TJ +ET +1 0 0 1 192.548 217.0791 cm 0 g 0 G -/F8 9.9626 Tf -34.647 -20.296 Td [(6.)]TJ +1 0 0 1 -192.548 -217.0791 cm +BT +/F32 9.9626 Tf 197.5293 217.0791 Td[(psb_geasb)]TJ +ET +1 0 0 1 150.7049 196.7831 cm 0 g 0 G - [-500(Cho)-28(ose)-286(the)-287(preconditioner)-287(to)-286(b)-28(e)-287(u)1(s)-1(ed)-286(with)]TJ/F30 9.9626 Tf 198.375 0 Td [(psb_precset)]TJ/F8 9.9626 Tf 60.389 0 Td [(and)-287(b)1(uild)-287(it)-287(with)]TJ/F30 9.9626 Tf -246.034 -11.955 Td [(psb_precbld)]TJ +1 0 0 1 -150.7049 -196.7831 cm +BT +/F8 9.9626 Tf 162.8814 196.7831 Td[(6.)]TJ +ET +1 0 0 1 170.6302 196.7831 cm 0 g 0 G -/F8 9.9626 Tf -12.73 -20.296 Td [(7.)]TJ +1 0 0 1 -170.6302 -196.7831 cm +BT +/F8 9.9626 Tf 175.6115 196.7831 Td[(Cho)-28(ose)-287(the)-287(p)1(rec)-1(on)1(dit)1(ioner)-287(t)1(o)-287(b)-27(e)-287(use)-1(d)-286(with)]TJ/F32 9.9626 Tf 185.645 0 Td[(psb_precset)]TJ/F8 9.9626 Tf 60.3892 0 Td[(and)-286(b)1(uil)1(d)-287(i)1(t)-287(with)]TJ/F32 9.9626 Tf -246.0342 -11.9552 Td[(psb_precbld)]TJ +ET +1 0 0 1 150.7049 164.5319 cm 0 g 0 G - [-500(Call)-333(the)-334(iterativ)28(e)-333(metho)-28(d)-333(of)-334(c)28(hoice,)-333(e.g.)]TJ/F30 9.9626 Tf 189.595 0 Td [(psb_bicgstab)]TJ/F8 9.9626 Tf -201.772 -20.204 Td 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[(Up)-28(date)-398(strategy)-398(based)-398(on)-398(additional)-398(p)-28(erm)28(utation)-398(data)-398(\050s)-1(ee)]TJ -55.311 -11.956 Td [(to)-28(ols)-333(routine)-333(desc)-1(r)1(iption\051.)]TJ/F16 11.9552 Tf -24.906 -28.456 Td [(3.3)-1125(Preconditioner)-375(data)-375(structure)]TJ/F8 9.9626 Tf 0 -18.589 Td [(Our)-383(base)-383(library)-383(o\013ers)-383(supp)-28(ort)-383(for)-383(simple)-383(w)28(ell)-383(kno)27(wn)-383(precondition)1(e)-1(r)1(s)-384(lik)28(e)-383(Di-)]TJ 0 -11.955 Td [(agonal)-333(Scaling)-334(or)-333(Blo)-28(c)28(k)-333(Jacobi)-334(with)-333(incomplete)-333(factorization)-333(ILU\0500\051.)]TJ 14.944 -12.062 Td [(A)-427(preconditioner)-428(is)-427(held)-428(in)-427(the)]TJ/F30 9.9626 Tf 142.723 0 Td [(psb)]TJ +/F8 9.9626 Tf 230.9222 573.8166 Td[(Up)-27(date)-398(s)-1(tr)1(ate)-1(gy)-398(b)1(as)-1(ed)-398(on)-398(ad)1(di)1(tional)-398(p)-27(erm)27(u)1(tation)-397(data)-398(\050se)-1(e)]TJ -55.3107 -11.9551 Td[(to)-28(ol)1(s)-334(rou)1(tine)-333(des)-1(crip)1(tion\051.)]TJ/F18 11.9552 Tf -24.9066 -28.4567 Td[(3.)-1(3)-1125(Pre)-1(condi)-1(ti)-1(one)-1(r)-375(data)-375(st)-1(ruct)-1(ure)]TJ/F8 9.9626 Tf 0 -18.5886 Td[(Ou)1(r)-383(base)-384(l)1(ibr)1(ary)-383(o\013e)-1(r)1(s)-384(sup)1(p)-28(or)1(t)-383(for)-383(simple)-383(w)27(ell)-383(k)1(no)28(wn)-383(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(s)-384(lik)28(e)-383(Di-)]TJ 0 -11.9552 Td[(agonal)-333(S)1(c)-1(al)1(ing)-333(or)-333(Blo)-28(c)27(k)-333(Jacobi)-333(with)-333(i)1(ncom)-1(p)1(le)-1(t)1(e)-334(factorization)-333(ILU\0500\051)1(.)]TJ 14.9439 -12.0623 Td[(A)-427(precondi)1(tioner)-427(is)-428(h)1(e)-1(ld)-427(i)1(n)-428(t)1(he)]TJ/F32 9.9626 Tf 142.7232 0 Td[(psb)]TJ ET +1 0 0 1 324.6906 490.7987 cm q -1 0 0 1 324.691 490.998 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -324.6906 -490.7987 cm BT -/F30 9.9626 Tf 327.829 490.799 Td [(prec)]TJ +/F32 9.9626 Tf 327.8289 490.7987 Td[(prec)]TJ ET +1 0 0 1 349.3778 490.7987 cm q -1 0 0 1 349.378 490.998 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -349.3778 -490.7987 cm BT -/F30 9.9626 Tf 352.516 490.799 Td [(type)]TJ/F8 9.9626 Tf 25.18 0 Td [(data)-427(structure)-428(rep)-28(orted)-427(in)]TJ -226.991 -11.955 Td [(\014gure)]TJ +/F32 9.9626 Tf 352.516 490.7987 Td[(type)]TJ/F8 9.9626 Tf 25.1801 0 Td[(dat)1(a)-428(stru)1(c)-1(tu)1(re)-428(rep)-27(orted)-427(in)]TJ -226.9912 -11.9552 Td[(\014gu)1(re)]TJ +ET +1 0 0 1 178.681 478.8436 cm 0 0 1 rg 0 0 1 RG - [-361(5)]TJ +1 0 0 1 -178.681 -478.8436 cm +BT +/F8 9.9626 Tf 178.681 478.8436 Td[(5)]TJ +ET +1 0 0 1 183.6624 478.8436 cm 0 g 0 G - [(.)-527(The)]TJ/F30 9.9626 Tf 61.729 0 Td [(psb_prec_type)]TJ/F8 9.9626 Tf 71.59 0 Td [(data)-361(t)28(yp)-28(e)-361(ma)28(y)-361(con)28(tain)-361(a)-361(simple)-361(preconditionin)1(g)]TJ -133.319 -11.956 Td [(matrix)-395(with)-396(the)-395(asso)-28(ciated)-396(comm)28(unication)-395(desc)-1(r)1(iptor.The)-396(v)56(alues)-396(con)28(tained)-395(in)]TJ 0 -11.955 Td [(the)]TJ/F30 9.9626 Tf 16.637 0 Td [(iprcparm)]TJ/F8 9.9626 Tf 44.642 0 Td [(and)]TJ/F30 9.9626 Tf 18.851 0 Td [(rprcparm)]TJ/F8 9.9626 Tf 44.642 0 Td [(de\014ne)-281(tha)-281(t)28(yp)-28(e)-281(of)-281(preconditioner)-281(along)-281(with)-281(all)-281(the)]TJ -124.772 -11.955 Td [(parameters)-420(related)-421(to)-420(it;)-464(th)28(us,)]TJ/F30 9.9626 Tf 139.397 0 Td [(iprcparm)]TJ/F8 9.9626 Tf 46.03 0 Td [(and)]TJ/F30 9.9626 Tf 20.239 0 Td [(rprcparm)]TJ/F8 9.9626 Tf 46.03 0 Td [(de\014ne)-420(ho)28(w)-421(the)-420(other)]TJ -251.696 -11.955 Td [(records)-282(ha)28(v)28(e)-282(to)-282(b)-27(e)-282(in)28(terpreted.)-428(This)-281(data)-282(structure)-282(is)-282(the)-281(basis)-282(of)-282(more)-282(complex)]TJ 0 -11.955 Td [(preconditioning)-333(strategies,)-334(whic)28(h)-333(are)-333(the)-334(sub)-55(ject)-334(of)-333(further)-333(researc)28(h.)]TJ/F16 11.9552 Tf 0 -28.457 Td [(3.4)-1125(Data)-375(structure)-375(query)-375(routines)]TJ +1 0 0 1 -183.6624 -478.8436 cm +BT +/F8 9.9626 Tf 183.6624 478.8436 Td[(.)-527(The)]TJ/F32 9.9626 Tf 28.7717 0 Td[(psb_prec_type)]TJ/F8 9.9626 Tf 71.5898 0 Td[(dat)1(a)-361(t)28(yp)-28(e)-361(ma)28(y)-361(c)-1(on)29(tain)-360(a)-361(s)-1(imp)1(le)-362(p)1(rec)-1(on)1(dit)1(ionin)1(g)]TJ -133.319 -11.9552 Td[(matrix)-395(with)-395(th)1(e)-396(as)-1(so)-28(ciated)-396(comm)27(u)1(nication)-395(d)1(e)-1(sc)-1(r)1(iptor)1(.The)-396(v)56(alu)1(e)-1(s)-396(con)28(tain)1(e)-1(d)-395(in)]TJ 0 -11.9552 Td[(th)1(e)]TJ/F32 9.9626 Tf 16.6367 0 Td[(iprcparm)]TJ/F8 9.9626 Tf 44.6424 0 Td[(and)]TJ/F32 9.9626 Tf 18.8507 0 Td[(rprcparm)]TJ/F8 9.9626 Tf 44.6424 0 Td[(de\014n)1(e)-282(t)1(ha)-281(t)28(yp)-27(e)-282(of)-280(precondi)1(tioner)-281(alon)1(g)-281(with)-281(al)1(l)-281(the)]TJ -124.7722 -11.9551 Td[(par)1(am)-1(eters)-421(r)1(e)-1(lated)-420(to)-420(it;)-463(th)28(us,)]TJ/F32 9.9626 Tf 139.3967 0 Td[(iprcparm)]TJ/F8 9.9626 Tf 46.0303 0 Td[(and)]TJ/F32 9.9626 Tf 20.2386 0 Td[(rprcparm)]TJ/F8 9.9626 Tf 46.0304 0 Td[(de\014n)1(e)-421(h)1(o)27(w)-420(the)-420(other)]TJ -251.696 -11.9552 Td[(rec)-1(or)1(ds)-282(ha)28(v)28(e)-282(to)-282(b)-27(e)-282(in)28(terp)1(rete)-1(d)1(.)-427(T)-1(h)1(is)-282(data)-281(s)-1(tr)1(uctur)1(e)-283(i)1(s)-283(t)1(he)-282(basis)-282(of)-282(more)-282(com)-1(p)1(lex)]TJ 0 -11.9552 Td[(pr)1(e)-1(cond)1(ition)1(ing)-333(strategie)-1(s,)-333(whic)28(h)-333(are)-334(th)1(e)-334(sub)-55(ject)-334(of)-333(f)1(ur)1(ther)-333(res)-1(earc)27(h)1(.)]TJ/F18 11.9552 Tf 0 -28.4566 Td[(3.)-1(4)-1125(D)-1(ata)-375(str)-1(uctur)-1(e)-375(quer)-1(y)-374(r)-1(out)-1(ine)-1(s)]TJ +ET +1 0 0 1 145.7235 355.9751 cm 0 g 0 G 0 g 0 G - 0 -34.636 Td [(psb)]TJ +1 0 0 1 -145.7235 -355.9751 cm +BT +/F18 11.9552 Tf 150.7049 355.9751 Td[(psb)]TJ ET +1 0 0 1 171.7609 355.9751 cm q -1 0 0 1 171.761 356.174 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -171.7609 -355.9751 cm BT -/F16 11.9552 Tf 175.796 355.975 Td [(cd)]TJ +/F18 11.9552 Tf 175.7958 355.9751 Td[(cd)]TJ ET +1 0 0 1 190.0523 355.9751 cm q -1 0 0 1 190.052 356.174 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -190.0523 -355.9751 cm BT -/F16 11.9552 Tf 194.087 355.975 Td [(get)]TJ +/F18 11.9552 Tf 194.0872 355.9751 Td[(ge)-1(t)]TJ ET +1 0 0 1 212.986 355.9751 cm q -1 0 0 1 212.986 356.174 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -212.986 -355.9751 cm BT -/F16 11.9552 Tf 217.021 355.975 Td [(lo)-31(cal)]TJ +/F18 11.9552 Tf 217.0209 355.9751 Td[(lo)-32(cal)]TJ ET +1 0 0 1 244.9138 355.9751 cm q -1 0 0 1 244.914 356.174 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +4.0349 0.1992 l +S Q +1 0 0 1 -244.9138 -355.9751 cm BT -/F16 11.9552 Tf 248.949 355.975 Td [(ro)31(ws|Get)-375(n)32(um)31(b)-31(er)-375(of)-376(lo)-31(cal)-375(ro)32(ws)]TJ/F16 14.3462 Tf -98.244 -32.75 Td [(Syn)31(tax)]TJ/F8 9.9626 Tf 98.979 -21.914 Td [(nr)-333(=)-334(psb)]TJ +/F18 11.9552 Tf 248.9487 355.9751 Td[(ro)30(ws|Ge)-1(t)-375(n)31(um)31(b)-31(e)-1(r)-375(o)-1(f)-374(l)-1(o)-32(ca)1(l)-376(ro)30(ws)]TJ/F18 14.3462 Tf -98.2438 -32.7506 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 98.9788 -21.9131 Td[(nr)-333(=)-333(p)1(s)-1(b)]TJ ET +1 0 0 1 289.1081 301.3114 cm q -1 0 0 1 289.108 301.511 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -289.1081 -301.3114 cm BT -/F8 9.9626 Tf 292.097 301.311 Td [(cd)]TJ +/F8 9.9626 Tf 292.0969 301.3114 Td[(cd)]TJ ET +1 0 0 1 302.6573 301.3114 cm q -1 0 0 1 302.657 301.511 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -302.6573 -301.3114 cm BT -/F8 9.9626 Tf 305.646 301.311 Td [(get)]TJ +/F8 9.9626 Tf 305.6461 301.3114 Td[(get)]TJ ET +1 0 0 1 319.5274 301.3114 cm q -1 0 0 1 319.527 301.511 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -319.5274 -301.3114 cm BT -/F8 9.9626 Tf 322.516 301.311 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 322.5162 301.3114 Td[(lo)-28(cal)]TJ ET +1 0 0 1 343.316 301.3114 cm q -1 0 0 1 343.316 301.511 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -343.316 -301.3114 cm BT -/F8 9.9626 Tf 346.305 301.311 Td [(ro)28(ws)-334(\050)]TJ/F17 9.9626 Tf 26.927 0 Td [(desc)]TJ/F8 9.9626 Tf 18.331 0 Td [(\051)]TJ +/F8 9.9626 Tf 346.3048 301.3114 Td[(ro)28(ws)-334(\050)]TJ/F19 9.9626 Tf 26.9269 0 Td[(desc)]TJ/F8 9.9626 Tf 18.3311 0 Td[(\051)]TJ +ET +1 0 0 1 145.7235 277.2939 cm 0 g 0 G -/F27 9.9626 Tf -240.858 -24.017 Td [(T)32(yp)-32(e:)]TJ +1 0 0 1 -145.7235 -277.2939 cm +BT +/F29 9.9626 Tf 150.7049 277.2939 Td[(T)32(yp)-32(e:)]TJ +ET +1 0 0 1 179.5203 277.2939 cm 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +1 0 0 1 -179.5203 -277.2939 cm +BT +/F8 9.9626 Tf 184.5016 277.2939 Td[(Async)28(hron)1(ous.)]TJ +ET +1 0 0 1 145.7235 256.9403 cm 0 g 0 G -/F27 9.9626 Tf -33.797 -20.354 Td [(On)-383(En)32(try)]TJ +1 0 0 1 -145.7235 -256.9403 cm +BT +/F29 9.9626 Tf 150.7049 256.9403 Td[(On)-383(En)32(tr)1(y)]TJ +ET +1 0 0 1 198.2901 256.9403 cm 0 g 0 G +1 0 0 1 -52.5665 -20.3537 cm 0 g 0 G - 0 -20.353 Td [(desc)]TJ +1 0 0 1 -145.7236 -236.5866 cm +BT +/F29 9.9626 Tf 150.7049 236.5866 Td[(desc)]TJ +ET +1 0 0 1 171.9321 236.5866 cm 0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.301 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -171.9321 -236.5866 cm +BT +/F8 9.9626 Tf 176.9134 236.5866 Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -1.3019 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -55.4517 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -71.5095 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 346.5264 188.7659 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.914 0 Td [(psb)]TJ +1 0 0 1 -346.5264 -188.7659 cm +BT +/F32 9.9626 Tf 346.5264 188.7659 Td[(psb)]TJ ET +1 0 0 1 362.8451 188.7659 cm q -1 0 0 1 362.845 188.965 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -362.8451 -188.7659 cm BT -/F30 9.9626 Tf 365.983 188.766 Td [(desc)]TJ +/F32 9.9626 Tf 365.9833 188.7659 Td[(desc)]TJ ET +1 0 0 1 387.5322 188.7659 cm q -1 0 0 1 387.532 188.965 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -387.5322 -188.7659 cm BT -/F30 9.9626 Tf 390.67 188.766 Td [(type)]TJ +/F32 9.9626 Tf 390.6705 188.7659 Td[(type)]TJ +ET +1 0 0 1 411.5918 188.7659 cm 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +1 0 0 1 -411.5918 -188.7659 cm +BT +/F8 9.9626 Tf 411.5918 188.7659 Td[(.)]TJ +ET +1 0 0 1 145.7235 166.5268 cm 0 g 0 G -/F27 9.9626 Tf -260.887 -22.239 Td [(On)-383(Return)]TJ +1 0 0 1 -145.7235 -166.5268 cm +BT +/F29 9.9626 Tf 150.7049 166.5268 Td[(On)-383(R)-1(etur)1(n)]TJ +ET +1 0 0 1 205.2431 166.5268 cm 0 g 0 G +1 0 0 1 -59.5196 -20.3537 cm 0 g 0 G - 0 -20.354 Td [(F)96(unction)-384(v)64(alue)]TJ +1 0 0 1 -145.7235 -146.1731 cm +BT +/F29 9.9626 Tf 150.7049 146.1731 Td[(F)96(unction)-384(v)64(alue)]TJ +ET +1 0 0 1 224.1097 146.1731 cm 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(The)-460(n)28(um)27(b)-27(er)-461(of)-460(lo)-28(cal)-460(ro)28(ws,)-492(i.e.)-825(the)-460(n)28(um)27(b)-27(er)-461(of)-460(ro)28(ws)-460(o)28(wned)]TJ -53.48 -11.955 Td [(b)28(y)-401(the)-401(curren)27(t)-401(pro)-27(ces)-1(s;)-435(as)-401(explained)-401(in)]TJ +1 0 0 1 -224.1097 -146.1731 cm +BT +/F8 9.9626 Tf 229.0911 146.1731 Td[(The)-460(n)28(um)28(b)-28(er)-460(of)-460(lo)-27(c)-1(al)-460(r)1(o)27(ws,)-492(i.e.)-825(th)1(e)-461(n)28(u)1(m)27(b)-27(e)-1(r)-460(of)-459(ro)28(ws)-461(o)28(w)-1(n)1(e)-1(d)]TJ -53.4796 -11.9551 Td[(b)28(y)-401(th)1(e)-402(cur)1(ren)28(t)-401(pr)1(o)-28(c)-1(es)-1(s;)-435(as)-401(e)-1(xp)1(lain)1(e)-1(d)-400(in)]TJ +ET +1 0 0 1 352.2268 134.218 cm 0 0 1 rg 0 0 1 RG - [-401(1)]TJ -0 g 0 G - 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0 Td [(x,)-358(y,)-357(desc)]TJ +/F8 9.9626 Tf 227.004 512.9899 Td[(gedot)-333(\050)]TJ/F19 9.9626 Tf 30.9949 0 Td[(x,)-357(y,)-357(desc)]TJ ET +1 0 0 1 299.6391 512.9899 cm q -1 0 0 1 299.639 513.189 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -299.6391 -512.9899 cm BT -/F17 9.9626 Tf 302.694 512.99 Td [(a,)-358(info)]TJ/F8 9.9626 Tf 28.515 0 Td [(\051)]TJ +/F19 9.9626 Tf 302.6943 512.9899 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ +ET +1 0 0 1 99.8954 486.9349 cm 0 g 0 G +1 0 0 1 78.7879 -32.9763 cm 0 g 0 G 0 g 0 G -ET +1 0 0 1 4.9813 32.5778 cm q -1 0 0 1 183.665 486.736 cm -[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +176.1727 0.1992 l +S Q +1 0 0 1 -183.6646 -486.5364 cm BT -/F11 9.9626 Tf 189.642 478.168 Td [(dot)]TJ/F8 9.9626 Tf 13.612 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.927 0 Td 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-366.0151 cm +BT +/F8 9.9626 Tf 133.6921 366.0151 Td[(Sy)1(nc)27(h)1(ron)1(ous.)]TJ +ET +1 0 0 1 94.9141 346.4358 cm 0 g 0 G -/F27 9.9626 Tf -33.797 -19.579 Td [(On)-383(En)32(try)]TJ +1 0 0 1 -94.9141 -346.4358 cm +BT +/F29 9.9626 Tf 99.8954 346.4358 Td[(On)-383(En)32(tr)1(y)]TJ +ET +1 0 0 1 147.4806 346.4358 cm 0 g 0 G +1 0 0 1 -52.5665 -19.5793 cm 0 g 0 G - 0 -19.579 Td [(x)]TJ +1 0 0 1 -94.9141 -326.8565 cm +BT +/F29 9.9626 Tf 99.8954 326.8565 Td[(x)]TJ +ET +1 0 0 1 105.9421 326.8565 cm 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +1 0 0 1 -105.9421 -326.8565 cm +BT +/F8 9.9626 Tf 110.9235 326.8565 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -167.9331 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3787 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-474(as:)-727(an)-474(arr)1(a)27(y)-474(of)-474(ran)1(k)-475(on)1(e)-475(or)-474(t)27(w)28(o)-475(con)28(tai)1(nin)1(g)-475(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-474(t)27(y)1(p)-28(e)]TJ 0 -11.9551 Td[(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 204.0051 267.0807 cm 0 0 1 rg 0 0 1 RG - [-333(2)]TJ +1 0 0 1 -204.0051 -267.0807 cm +BT +/F8 9.9626 Tf 204.0051 267.0807 Td[(2)]TJ +ET +1 0 0 1 208.9865 267.0807 cm 0 g 0 G - [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 146.202 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-333(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(y)]TJ/F8 9.9626 Tf 5.241 0 Td [(.)]TJ +1 0 0 1 -208.9865 -267.0807 cm +BT +/F8 9.9626 Tf 208.9865 267.0807 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0175 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(y)]TJ/F8 9.9626 Tf 5.2419 0 Td[(.)]TJ +ET 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110.9235 247.5014 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(y)]TJ/F8 9.9626 Tf 5.2419 0 Td[(.)]TJ -167.4811 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3787 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-474(as:)-727(an)-474(arr)1(a)27(y)-474(of)-474(ran)1(k)-475(on)1(e)-475(or)-474(t)27(w)28(o)-475(con)28(tai)1(nin)1(g)-475(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-474(t)27(y)1(p)-28(e)]TJ 0 -11.9551 Td[(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 204.0051 187.7256 cm 0 0 1 rg 0 0 1 RG - [-333(2)]TJ +1 0 0 1 -204.0051 -187.7256 cm +BT +/F8 9.9626 Tf 204.0051 187.7256 Td[(2)]TJ +ET +1 0 0 1 208.9865 187.7256 cm 0 g 0 G - 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373.544 527.708 Td [(geamaxs)]TJ -240.448 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ +/F8 9.9626 Tf 373.5444 527.7082 Td[(geam)-1(axs)]TJ -240.4488 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1411(Long)-333(Precis)-1(i)1(on)-333(Re)-1(al)-3314(p)1(s)-1(b)]TJ ET +1 0 0 1 370.5556 515.753 cm q -1 0 0 1 370.556 515.952 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -370.5556 -515.753 cm BT -/F8 9.9626 Tf 373.544 515.753 Td [(geamaxs)]TJ -240.448 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Sh)1(ort)-334(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 373.5444 515.753 Td[(geam)-1(axs)]TJ -240.4488 -11.9552 Td[(Sh)1(ort)-333(Pr)1(e)-1(cision)-333(Re)-1(al)-1199(Shor)1(t)-333(Prec)-1(i)1(s)-1(ion)-332(C)-1(ompl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET +1 0 0 1 370.5556 503.7978 cm q -1 0 0 1 370.556 503.997 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 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Td[(con)28(tain)1(s)-334(data)-333(structu)1(re)-1(s)-333(for)-333(com)-1(m)28(un)1(ic)-1(ati)1(ons.)]TJ -10.9958 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3787 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 295.717 268.1883 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -295.717 -268.1883 cm +BT +/F32 9.9626 Tf 295.717 268.1883 Td[(psb)]TJ ET +1 0 0 1 312.0356 268.1883 cm q -1 0 0 1 312.036 268.388 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -312.0356 -268.1883 cm BT -/F30 9.9626 Tf 315.174 268.188 Td [(desc)]TJ +/F32 9.9626 Tf 315.1738 268.1883 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Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-289(as:)-422(a)-289(n)28(um)28(b)-28(er)-289(or)-289(a)-289(ran)1(k-one)-289(arra)27(y)-288(of)-289(long)-289(precision)-289(real)-289(n)28(um)28(b)-28(ers.)]TJ +1 0 0 1 -94.9141 -231.0647 cm +BT +/F29 9.9626 Tf 99.8954 231.0647 Td[(res)]TJ +ET +1 0 0 1 114.3841 231.0647 cm 0 g 0 G -/F27 9.9626 Tf -24.907 -18.562 Td [(info)]TJ +1 0 0 1 -114.3841 -231.0647 cm +BT +/F8 9.9626 Tf 119.3654 231.0647 Td[(is)-334(t)1(he)-334(in)1(\014n)1(it)28(y)-333(nor)1(m)-334(of)-333(th)1(e)-334(c)-1(olu)1(mns)-334(of)]TJ/F11 9.9626 Tf 166.1827 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -166.44 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(out)]TJ/F8 9.9626 Tf 16.5489 0 Td[(.)]TJ -50.0345 -11.9552 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[(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-289(as:)-423(a)-290(rank)-289(one)-290(or)-289(t)27(w)28(o)-289(arra)27(y)-289(con)28(taining)-290(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-28(e)-290(sp)-28(eci\014ed)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ +1 0 0 1 -156.7516 -706.1289 cm +BT +/F8 9.9626 Tf 161.7329 706.1289 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -167.933 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-289(as:)-423(a)-289(ran)1(k)-290(on)1(e)-290(or)-290(t)28(w)28(o)-290(arr)1(a)28(y)-290(con)28(tain)1(ing)-289(n)28(um)28(b)-27(e)-1(rs)-290(of)-289(t)28(yp)-27(e)-290(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9552 Td[(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 214.6319 646.353 cm 0 0 1 rg 0 0 1 RG - [-333(11)]TJ +1 0 0 1 -214.6319 -646.353 cm +BT +/F8 9.9626 Tf 214.6319 646.353 Td[(11)]TJ +ET +1 0 0 1 224.5946 646.353 cm 0 g 0 G - [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 111.001 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-333(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ +1 0 0 1 -224.5946 -646.353 cm +BT +/F8 9.9626 Tf 224.5946 646.353 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0175 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(y)]TJ/F8 9.9626 Tf 5.2419 0 Td[(.)]TJ +ET +1 0 0 1 145.7235 627.1523 cm 0 g 0 G -/F27 9.9626 Tf -241.876 -19.201 Td [(b)-32(eta)]TJ +1 0 0 1 -145.7235 -627.1523 cm +BT +/F29 9.9626 Tf 150.7049 627.1523 Td[(b)-32(eta)]TJ +ET +1 0 0 1 172.664 627.1523 cm 0 g 0 G -/F8 9.9626 Tf 26.94 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.469 0 Td [(\014)]TJ/F8 9.9626 Tf 6.161 0 Td [(.)]TJ -53.664 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)27(yp)-27(e)-334(indicated)-333(in)-333(T)83(able)]TJ +1 0 0 1 -172.664 -627.1523 cm +BT +/F8 9.9626 Tf 177.6454 627.1523 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.9626 Tf 45.4684 0 Td[(\014)]TJ/F8 9.9626 Tf 6.1609 0 Td[(.)]TJ -53.6632 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(n)28(um)28(b)-28(er)-333(of)-333(the)-333(data)-333(t)28(yp)-27(e)-334(in)1(dicate)-1(d)-332(in)-333(T)83(abl)1(e)]TJ +ET +1 0 0 1 433.8934 579.3316 cm 0 0 1 rg 0 0 1 RG - [-333(11)]TJ +1 0 0 1 -433.8934 -579.3316 cm +BT +/F8 9.9626 Tf 433.8934 579.3316 Td[(11)]TJ +ET +1 0 0 1 443.8561 579.3316 cm 0 g 0 G - [(.)]TJ +1 0 0 1 -443.8561 -579.3316 cm +BT +/F8 9.9626 Tf 443.8561 579.3316 Td[(.)]TJ +ET +1 0 0 1 145.7235 560.1309 cm 0 g 0 G -/F27 9.9626 Tf -24.906 -19.201 Td [(y)]TJ +1 0 0 1 -145.7235 -560.1309 cm +BT +/F29 9.9626 Tf 150.7049 560.1309 Td[(y)]TJ +ET +1 0 0 1 156.7516 560.1309 cm 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.482 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-289(as:)-423(a)-290(rank)-289(one)-290(or)-289(t)27(w)28(o)-289(arra)27(y)-289(con)28(taining)-290(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-28(e)-290(sp)-28(eci\014ed)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ +1 0 0 1 -156.7516 -560.1309 cm +BT +/F8 9.9626 Tf 161.7329 560.1309 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(y)]TJ/F8 9.9626 Tf 5.242 0 Td[(.)]TJ -167.4811 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ -59.582 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-289(as:)-423(a)-289(ran)1(k)-290(on)1(e)-290(or)-290(t)28(w)28(o)-290(arr)1(a)28(y)-290(con)28(tain)1(ing)-289(n)28(um)28(b)-27(e)-1(rs)-290(of)-289(t)28(yp)-27(e)-290(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9551 Td[(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 214.6319 500.3551 cm 0 0 1 rg 0 0 1 RG - [-333(11)]TJ +1 0 0 1 -214.6319 -500.3551 cm +BT +/F8 9.9626 Tf 214.6319 500.3551 Td[(11)]TJ +ET +1 0 0 1 224.5946 500.3551 cm 0 g 0 G - [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 111.001 0 Td [(y)]TJ/F8 9.9626 Tf 8.563 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-333(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +1 0 0 1 -224.5946 -500.3551 cm +BT +/F8 9.9626 Tf 224.5946 500.3551 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0175 0 Td[(y)]TJ/F8 9.9626 Tf 8.5628 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ +ET +1 0 0 1 145.7235 481.1543 cm 0 g 0 G -/F27 9.9626 Tf -241.876 -19.201 Td [(desc)]TJ +1 0 0 1 -145.7235 -481.1543 cm +BT +/F29 9.9626 Tf 150.7049 481.1543 Td[(desc)]TJ ET +1 0 0 1 172.6195 481.1543 cm q -1 0 0 1 172.619 481.354 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -172.6195 -481.1543 cm BT -/F27 9.9626 Tf 176.057 481.154 Td [(a)]TJ +/F29 9.9626 Tf 176.0566 481.1543 Td[(a)]TJ +ET +1 0 0 1 181.6259 481.1543 cm 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -181.6259 -481.1543 cm +BT +/F8 9.9626 Tf 186.6072 481.1543 Td[(con)28(tain)1(s)-334(data)-333(structu)1(re)-1(s)-333(for)-333(com)-1(m)28(un)1(ic)-1(ati)1(ons.)]TJ -10.9957 -11.9551 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 346.5264 433.3337 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -346.5264 -433.3337 cm +BT +/F32 9.9626 Tf 346.5264 433.3337 Td[(psb)]TJ ET +1 0 0 1 362.8451 433.3337 cm q -1 0 0 1 362.845 433.533 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -362.8451 -433.3337 cm BT -/F30 9.9626 Tf 365.983 433.334 Td [(desc)]TJ +/F32 9.9626 Tf 365.9833 433.3337 Td[(desc)]TJ ET +1 0 0 1 387.5322 433.3337 cm q -1 0 0 1 387.532 433.533 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -387.5322 -433.3337 cm BT -/F30 9.9626 Tf 390.67 433.334 Td [(type)]TJ +/F32 9.9626 Tf 390.6705 433.3337 Td[(type)]TJ +ET +1 0 0 1 411.5918 433.3337 cm 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +1 0 0 1 -411.5918 -433.3337 cm +BT +/F8 9.9626 Tf 411.5918 433.3337 Td[(.)]TJ +ET +1 0 0 1 145.7235 414.1329 cm 0 g 0 G -/F27 9.9626 Tf -260.887 -19.201 Td [(trans)]TJ +1 0 0 1 -145.7235 -414.1329 cm +BT +/F29 9.9626 Tf 150.7049 414.1329 Td[(trans)]TJ +ET +1 0 0 1 176.3322 414.1329 cm 0 g 0 G -/F8 9.9626 Tf 30.609 0 Td [(indicate)-333(what)-334(kin)1(d)-334(of)-333(op)-28(eration)-333(to)-333(p)-28(erform.)]TJ +1 0 0 1 -176.3322 -414.1329 cm +BT +/F8 9.9626 Tf 181.3135 414.1329 Td[(in)1(dicate)-334(what)-333(ki)1(nd)-333(of)-333(op)-27(e)-1(r)1(ation)-333(to)-333(p)-27(e)-1(r)1(form.)]TJ +ET +1 0 0 1 170.6302 394.9322 cm 0 g 0 G -/F27 9.9626 Tf -5.702 -19.201 Td [(trans)-383(=)-384(N)]TJ +1 0 0 1 -170.6302 -394.9322 cm +BT +/F29 9.9626 Tf 175.6115 394.9322 Td[(trans)-383(=)-383(N)]TJ +ET +1 0 0 1 226.7541 394.9322 cm 0 g 0 G -/F8 9.9626 Tf 56.123 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ +1 0 0 1 -226.7541 -394.9322 cm +BT +/F8 9.9626 Tf 231.7355 394.9322 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ +ET +1 0 0 1 398.1949 394.9322 cm 0 0 1 rg 0 0 1 RG - [-334(1)]TJ +1 0 0 1 -398.1949 -394.9322 cm +BT +/F8 9.9626 Tf 398.1949 394.9322 Td[(1)]TJ +ET +1 0 0 1 403.1762 394.9322 cm 0 g 0 G +1 0 0 1 -232.546 -15.2157 cm 0 g 0 G -/F27 9.9626 Tf -56.123 -15.215 Td [(trans)-383(=)-384(T)]TJ +1 0 0 1 -170.6302 -379.7165 cm +BT +/F29 9.9626 Tf 175.6115 379.7165 Td[(trans)-383(=)-383(T)]TJ +ET +1 0 0 1 225.7579 379.7165 cm 0 g 0 G -/F8 9.9626 Tf 55.127 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ +1 0 0 1 -225.7579 -379.7165 cm +BT +/F8 9.9626 Tf 230.7392 379.7165 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(e)-1(q)1(uation)]TJ +ET +1 0 0 1 397.1986 379.7165 cm 0 0 1 rg 0 0 1 RG - [-334(2)]TJ +1 0 0 1 -397.1986 -379.7165 cm +BT +/F8 9.9626 Tf 397.1986 379.7165 Td[(2)]TJ +ET +1 0 0 1 402.1799 379.7165 cm 0 g 0 G +1 0 0 1 -231.5497 -15.2156 cm 0 g 0 G -/F27 9.9626 Tf -55.128 -15.216 Td [(trans)-383(=)-384(C)]TJ +1 0 0 1 -170.6302 -364.5009 cm +BT +/F29 9.9626 Tf 175.6115 364.5009 Td[(trans)-383(=)-383(C)]TJ +ET +1 0 0 1 226.0623 364.5009 cm 0 g 0 G -/F8 9.9626 Tf 55.433 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equation)]TJ +1 0 0 1 -226.0623 -364.5009 cm +BT +/F8 9.9626 Tf 231.0436 364.5009 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(e)-1(q)1(uation)]TJ +ET +1 0 0 1 397.503 364.5009 cm 0 0 1 rg 0 0 1 RG - [-334(3)]TJ +1 0 0 1 -397.503 -364.5009 cm +BT +/F8 9.9626 Tf 397.503 364.5009 Td[(3)]TJ +ET +1 0 0 1 402.4844 364.5009 cm 0 g 0 G - -55.433 -19.201 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(tr)-28(ans)]TJ/F8 9.9626 Tf 27.052 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(N)]TJ/F8 9.9626 Tf -77.005 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-334(v)56(ariable.)]TJ +1 0 0 1 -402.4844 -364.5009 cm +BT +/F8 9.9626 Tf 175.6115 345.3001 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Defau)1(lt:)]TJ/F11 9.9626 Tf 39.4356 0 Td[(tr)-28(ans)]TJ/F8 9.9626 Tf 27.0524 0 Td[(=)]TJ/F11 9.9626 Tf 10.5161 0 Td[(N)]TJ/F8 9.9626 Tf -77.0041 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(c)27(har)1(ac)-1(ter)-333(v)56(ariab)1(le)-1(.)]TJ +ET +1 0 0 1 145.7235 278.2788 cm 0 g 0 G -/F27 9.9626 Tf -24.906 -19.2 Td [(w)32(ork)]TJ +1 0 0 1 -145.7235 -278.2788 cm +BT +/F29 9.9626 Tf 150.7049 278.2788 Td[(w)32(or)1(k)]TJ +ET +1 0 0 1 175.1547 278.2788 cm 0 g 0 G -/F8 9.9626 Tf 29.431 0 Td [(w)28(ork)-334(arr)1(a)27(y)84(.)]TJ -4.525 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-487(as:)-753(a)-487(rank)-488(one)-487(arra)28(y)-488(of)-487(the)-488(same)-487(t)27(yp)-27(e)-488(of)]TJ/F11 9.9626 Tf 239.183 0 Td [(x)]TJ/F8 9.9626 Tf 10.551 0 Td [(and)]TJ/F11 9.9626 Tf 20.907 0 Td [(y)]TJ/F8 9.9626 Tf 10.099 0 Td [(with)-487(the)]TJ -280.74 -11.955 Td [(T)83(AR)28(GET)-333(attribute.)]TJ +1 0 0 1 -175.1547 -278.2788 cm +BT +/F8 9.9626 Tf 180.136 278.2788 Td[(w)28(ork)-333(arra)28(y)84(.)]TJ -4.5245 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 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7.206 4.114 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.114 Td [(P)]TJ/F10 6.9738 Tf 6.396 -1.494 Td [(c)]TJ/F11 9.9626 Tf 4.059 1.494 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.433 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ/F8 9.9626 Tf -206.303 -37.175 Td [(where:)]TJ +/F18 14.3462 Tf 180.8139 679.8081 Td[(spsm|T)93(ri)-1(angul)-1(a)1(r)-376(Sys)1(t)-1(em)-376(Sol)-1(v)32(e)]TJ/F8 9.9626 Tf -30.109 -30.1944 Td[(This)-333(s)-1(u)1(brou)1(tin)1(e)-334(c)-1(omp)1(utes)-334(the)-333(T)83(rian)1(gular)-333(S)1(yste)-1(m)-333(Solv)28(e:)]TJ/F11 9.9626 Tf 111.0608 -34.1864 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F11 9.9626 Tf 4.4693 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -98.5745 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(D)-28(P)]TJ/F10 6.9738 Tf 21.3311 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F11 9.9626 Tf 4.4694 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -107.0995 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F7 6.9738 Tf 6.2267 0 Td[(1)]TJ/F11 9.9626 Tf 4.4693 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(D)-28(x)]TJ/F8 9.9626 Tf 16.4328 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -107.0995 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -100.3812 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(D)-28(P)]TJ/F10 6.9738 Tf 21.3311 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -108.9062 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(D)-28(x)]TJ/F8 9.9626 Tf 16.4328 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -108.9062 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -101.6615 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(D)-28(P)]TJ/F10 6.9738 Tf 21.3311 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -110.1865 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(D)-28(x)]TJ/F8 9.9626 Tf 16.4328 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ/F8 9.9626 Tf -206.3034 -37.1752 Td[(where:)]TJ +ET +1 0 0 1 145.7235 438.4618 cm 0 g 0 G -/F11 9.9626 Tf -14.944 -20.238 Td [(x)]TJ +1 0 0 1 -145.7235 -438.4618 cm +BT +/F11 9.9626 Tf 150.7049 438.4618 Td[(x)]TJ +ET +1 0 0 1 156.3988 438.4618 cm 0 g 0 G -/F8 9.9626 Tf 10.675 0 Td [(is)-333(the)-334(global)-333(dense)-333(submatrix)]TJ/F11 9.9626 Tf 131.092 0 Td [(x)]TJ/F7 6.9738 Tf 5.694 -1.495 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.367 0 Td [(:)]TJ +1 0 0 1 -156.3988 -438.4618 cm +BT +/F8 9.9626 Tf 161.3801 438.4618 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatr)1(ix)]TJ/F11 9.9626 Tf 131.092 0 Td[(x)]TJ/F7 6.9738 Tf 5.6939 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2554 0 Td[(;)]TJ/F7 6.9738 Tf 2.3662 0 Td[(:)]TJ +ET +1 0 0 1 145.7235 418.1186 cm 0 g 0 G -/F11 9.9626 Tf -152.083 -18.849 Td [(y)]TJ +1 0 0 1 -145.7235 -418.1186 cm +BT +/F11 9.9626 Tf 150.7049 418.1186 Td[(y)]TJ +ET +1 0 0 1 155.9468 418.1186 cm 0 g 0 G -/F8 9.9626 Tf 10.223 0 Td [(is)-333(the)-334(global)-333(dense)-333(submatrix)]TJ/F11 9.9626 Tf 131.092 0 Td [(y)]TJ/F7 6.9738 Tf 4.885 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ +1 0 0 1 -155.9468 -418.1186 cm +BT +/F8 9.9626 Tf 160.9281 418.1186 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatri)1(x)]TJ/F11 9.9626 Tf 131.092 0 Td[(y)]TJ/F7 6.9738 Tf 4.8845 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2554 0 Td[(;)]TJ/F7 6.9738 Tf 2.3662 0 Td[(:)]TJ +ET +1 0 0 1 145.7235 397.7755 cm 0 g 0 G -/F11 9.9626 Tf -150.821 -18.849 Td [(T)]TJ +1 0 0 1 -145.7235 -397.7755 cm +BT +/F11 9.9626 Tf 150.7049 397.7755 Td[(T)]TJ +ET +1 0 0 1 157.9105 397.7755 cm 0 g 0 G -/F8 9.9626 Tf 12.187 0 Td [(is)-333(the)-334(global)-333(sparse)-333(blo)-28(c)28(k)-334(triangul)1(ar)-334(submatrix)]TJ/F11 9.9626 Tf 206.78 0 Td [(T)]TJ +1 0 0 1 -157.9105 -397.7755 cm +BT +/F8 9.9626 Tf 162.8918 397.7755 Td[(is)-334(t)1(he)-334(glob)1(al)-333(s)-1(p)1(arse)-334(bl)1(o)-28(c)27(k)-333(tri)1(angul)1(ar)-333(s)-1(u)1(bmatrix)]TJ/F11 9.9626 Tf 206.7805 0 Td[(T)]TJ +ET +1 0 0 1 145.7235 377.4323 cm 0 g 0 G - -218.967 -20.343 Td [(D)]TJ +1 0 0 1 -145.7235 -377.4323 cm +BT +/F11 9.9626 Tf 150.7049 377.4323 Td[(D)]TJ +ET +1 0 0 1 159.2298 377.4323 cm 0 g 0 G -/F8 9.9626 Tf 13.506 0 Td [(is)-333(the)-334(scaling)-333(diagonal)-333(matrix.)]TJ +1 0 0 1 -159.2298 -377.4323 cm +BT +/F8 9.9626 Tf 164.2112 377.4323 Td[(is)-334(t)1(he)-334(sc)-1(al)1(ing)-333(di)1(agonal)-333(matrix.)]TJ +ET +1 0 0 1 145.7235 357.0892 cm 0 g 0 G -/F11 9.9626 Tf -13.506 -20.343 Td [(P)]TJ/F10 6.9738 Tf 6.396 -1.495 Td [(r)]TJ/F11 9.9626 Tf 4.412 1.495 Td [(;)-167(P)]TJ/F10 6.9738 Tf 10.824 -1.495 Td [(c)]TJ +1 0 0 1 -145.7235 -357.0892 cm +BT +/F11 9.9626 Tf 150.7049 357.0892 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(;)-166(P)]TJ/F10 6.9738 Tf 10.824 -1.4944 Td[(c)]TJ +ET +1 0 0 1 176.3952 357.0892 cm 0 g 0 G -/F8 9.9626 Tf 9.039 1.495 Td [(are)-333(the)-334(p)-27(e)-1(r)1(m)27(utation)-333(matrices.)]TJ/F16 14.3462 Tf -30.671 -41.679 Td [(Syn)31(tax)]TJ/F8 9.9626 Tf 68.871 -21.911 Td [(call)-333(psb)]TJ +1 0 0 1 -176.3952 -357.0892 cm +BT +/F8 9.9626 Tf 181.3765 357.0892 Td[(are)-333(the)-334(p)-27(erm)27(u)1(tation)-333(matri)1(c)-1(es)-1(.)]TJ/F18 14.3462 Tf -30.6716 -41.6792 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 68.8715 -21.9109 Td[(call)-333(psb)]TJ ET +1 0 0 1 253.4384 293.4991 cm q -1 0 0 1 253.438 293.698 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -253.4384 -293.4991 cm BT -/F8 9.9626 Tf 256.427 293.499 Td [(spsm)-333(\050)]TJ/F17 9.9626 Tf 28.892 0 Td [(alpha,)-358(t,)-357(x,)-358(b)51(eta,)-358(y,)-358(desc)]TJ +/F8 9.9626 Tf 256.4272 293.4991 Td[(spsm)-334(\050)]TJ/F19 9.9626 Tf 28.8917 0 Td[(alpha,)-357(t)-1(,)-357(x,)-357(b)51(et)-1(a,)-357(y,)-357(desc)]TJ ET +1 0 0 1 390.0996 293.4991 cm q -1 0 0 1 390.1 293.698 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -390.0996 -293.4991 cm BT -/F17 9.9626 Tf 393.155 293.499 Td [(a,)-358(info)]TJ/F8 9.9626 Tf 28.515 0 Td [(\051)]TJ -270.581 -23.91 Td [(call)-333(psb)]TJ +/F19 9.9626 Tf 393.1549 293.4991 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -270.5807 -23.9103 Td[(call)-333(psb)]TJ ET +1 0 0 1 184.9513 269.5888 cm q -1 0 0 1 184.951 269.788 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -184.9513 -269.5888 cm BT -/F8 9.9626 Tf 187.94 269.589 Td [(spsm)-333(\050)]TJ/F17 9.9626 Tf 28.892 0 Td [(alpha,)-358(t,)-357(x,)-358(b)51(eta,)-358(y,)-358(desc)]TJ +/F8 9.9626 Tf 187.9401 269.5888 Td[(spsm)-334(\050)]TJ/F19 9.9626 Tf 28.8917 0 Td[(alpha,)-357(t)-1(,)-357(x,)-357(b)51(et)-1(a,)-357(y,)-357(desc)]TJ ET +1 0 0 1 321.6125 269.5888 cm q -1 0 0 1 321.612 269.788 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -321.6125 -269.5888 cm BT -/F17 9.9626 Tf 324.668 269.589 Td [(a,)-358(info,)-357(tr)51(ans,)-358(unit,)-358(choic)51(e,)-357(diag,)-358(work)]TJ/F8 9.9626 Tf 165.489 0 Td [(\051)]TJ +/F19 9.9626 Tf 324.6677 269.5888 Td[(a,)-358(i)1(nfo,)-358(tr)52(a)-1(ns,)-357(unit,)-357(cho)-1(i)1(c)51(e,)-358(di)1(ag,)-358(work)]TJ/F8 9.9626 Tf 165.4894 0 Td[(\051)]TJ +ET +1 0 0 1 150.7049 242.9788 cm 0 g 0 G +1 0 0 1 73.1112 -32.9763 cm 0 g 0 G 0 g 0 G -ET +1 0 0 1 4.9814 32.5778 cm q -1 0 0 1 228.797 242.78 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +187.5259 0.1992 l +S Q +1 0 0 1 -228.7975 -242.5803 cm BT -/F11 9.9626 Tf 234.775 234.212 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(D)]TJ/F8 9.9626 Tf 8.525 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(\014)]TJ/F27 9.9626 Tf 56.892 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 234.7751 234.2117 Td[(T)]TJ/F8 9.9626 Tf 7.2056 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(y)]TJ/F8 9.9626 Tf 5.2419 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(D)]TJ/F8 9.9626 Tf 8.525 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\013)]TJ/F8 9.9626 Tf 6.41 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\014)]TJ/F29 9.9626 Tf 56.8919 0 Td[(Subr)1(outi)-1(ne)]TJ ET +1 0 0 1 228.7975 230.2267 cm q -1 0 0 1 228.797 230.426 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +187.5259 0.1992 l +S Q +1 0 0 1 -228.7975 -230.2267 cm BT -/F8 9.9626 Tf 234.775 221.858 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ +/F8 9.9626 Tf 234.7751 221.8581 Td[(Sh)1(ort)-333(Pr)1(e)-1(cision)-333(Re)-1(al)-3102(psb)]TJ ET +1 0 0 1 370.7819 221.8581 cm q -1 0 0 1 370.782 222.057 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -370.7819 -221.8581 cm BT -/F8 9.9626 Tf 373.771 221.858 Td [(spsm)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ +/F8 9.9626 Tf 373.7708 221.8581 Td[(spsm)]TJ -138.9957 -11.9552 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-145.7236 -706.1289 cm BT -/F27 9.9626 Tf 150.705 706.129 Td [(vl)]TJ +/F29 9.9626 Tf 150.7049 706.1289 Td[(vl)]TJ +ET +1 0 0 1 159.9341 706.1289 cm 0 g 0 G -/F8 9.9626 Tf 14.21 0 Td [(Data)-408(allo)-28(cation:)-593(the)-408(se)-1(t)-408(of)-407(global)-408(indices)-408(b)-28(elonging)-408(to)-408(the)-408(calling)-408(pro)-28(cess.)]TJ 10.696 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.761 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ +1 0 0 1 -159.9341 -706.1289 cm +BT +/F8 9.9626 Tf 164.9154 706.1289 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[(Data)-223(allo)-28(cation)1(:)-390(in)-222(a)-223(generalized)-223(blo)-28(c)28(k-ro)28(w)-223(distribution)-223(the)-222(n)27(um)28(b)-28(er)-222(of)-223(indices)]TJ 10.377 -11.955 Td [(b)-28(elonging)-333(to)-333(the)-334(curren)28(t)-333(pro)-28(cess.)-445(S)1(c)-1(op)-27(e:)]TJ/F27 9.9626 Tf 175.648 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -198.721 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.761 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)]TJ +1 0 0 1 -160.2523 -638.642 cm +BT +/F8 9.9626 Tf 165.2337 638.642 Td[(Data)-223(al)1(lo)-28(cation:)-389(i)1(n)-223(a)-223(general)1(iz)-1(ed)-222(blo)-28(c)28(k-ro)28(w)-223(distri)1(but)1(ion)-223(t)1(he)-223(n)28(um)28(b)-27(e)-1(r)-222(of)-223(in)1(di)1(c)-1(es)]TJ 10.3778 -11.9552 Td[(b)-27(e)-1(lon)1(gin)1(g)-334(to)-333(th)1(e)-334(c)-1(u)1(rren)28(t)-333(pr)1(o)-28(c)-1(ess)-1(.)-444(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 175.6472 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -198.7203 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf 40.5768 0 Td[(.)]TJ -65.7602 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(v)55(al)1(ue.)]TJ +ET +1 0 0 1 145.7235 571.155 cm 0 g 0 G -/F27 9.9626 Tf -24.906 -19.666 Td [(repl)]TJ +1 0 0 1 -145.7235 -571.155 cm +BT +/F29 9.9626 Tf 150.7049 571.155 Td[(repl)]TJ +ET +1 0 0 1 170.2219 571.155 cm 0 g 0 G -/F8 9.9626 Tf 24.498 0 Td [(Data)-351(allo)-28(cation:)-480(build)-351(a)-351(replicated)-351(index)-351(space)-351(\050i.e.)-498(all)-351(pro)-28(cesses)-351(o)27(wn)-351(all)]TJ 0.408 -11.955 Td [(indices\051.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 68.411 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -98.167 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.761 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(the)-333(logical)-333(v)55(alue)]TJ/F30 9.9626 Tf 131.784 0 Td [(.true.)]TJ +1 0 0 1 -170.2219 -571.155 cm +BT +/F8 9.9626 Tf 175.2032 571.155 Td[(Data)-351(all)1(o)-28(c)-1(ati)1(on:)-480(b)1(uil)1(d)-351(a)-351(replicated)-351(in)1(dex)-351(s)-1(p)1(ac)-1(e)-351(\050i.e.)-498(all)-351(p)1(ro)-28(ces)-1(se)-1(s)-351(o)27(wn)-351(al)1(l)]TJ 0.4083 -11.9551 Td[(in)1(dice)-1(s\051.)-444(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 68.4103 0 Td[(global)]TJ/F8 9.9626 Tf 29.7563 0 Td[(.)]TJ -98.1666 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf 40.5768 0 Td[(.)]TJ -65.7602 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(the)-333(logical)-334(v)56(alu)1(e)]TJ/F32 9.9626 Tf 131.7838 0 Td[(.true.)]TJ +ET +1 0 0 1 145.7235 502.0642 cm 0 g 0 G -/F27 9.9626 Tf -156.69 -21.27 Td [(On)-383(Return)]TJ +1 0 0 1 -145.7235 -502.0642 cm +BT +/F29 9.9626 Tf 150.7049 502.0642 Td[(On)-383(R)-1(etur)1(n)]TJ +ET +1 0 0 1 205.2431 502.0642 cm 0 g 0 G +1 0 0 1 -59.5196 -19.6662 cm 0 g 0 G - 0 -19.666 Td [(desc)]TJ +1 0 0 1 -145.7235 -482.398 cm +BT +/F29 9.9626 Tf 150.7049 482.398 Td[(desc)]TJ ET +1 0 0 1 172.6195 482.398 cm q -1 0 0 1 172.619 482.597 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -172.6195 -482.398 cm BT -/F27 9.9626 Tf 176.057 482.398 Td [(a)]TJ +/F29 9.9626 Tf 176.0566 482.398 Td[(a)]TJ +ET +1 0 0 1 181.6259 482.398 cm 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -181.6259 -482.398 cm +BT +/F8 9.9626 Tf 186.6072 482.398 Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -10.9957 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(out)]TJ/F8 9.9626 Tf 16.549 0 Td[(.)]TJ -50.0346 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 346.5264 434.5773 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -346.5264 -434.5773 cm +BT +/F32 9.9626 Tf 346.5264 434.5773 Td[(psb)]TJ ET +1 0 0 1 362.8451 434.5773 cm q -1 0 0 1 362.845 434.777 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -362.8451 -434.5773 cm BT -/F30 9.9626 Tf 365.983 434.577 Td [(desc)]TJ +/F32 9.9626 Tf 365.9833 434.5773 Td[(desc)]TJ ET +1 0 0 1 387.5322 434.5773 cm q -1 0 0 1 387.532 434.777 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -387.5322 -434.5773 cm BT -/F30 9.9626 Tf 390.67 434.577 Td [(type)]TJ +/F32 9.9626 Tf 390.6705 434.5773 Td[(type)]TJ +ET +1 0 0 1 411.5918 434.5773 cm 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +1 0 0 1 -411.5918 -434.5773 cm +BT +/F8 9.9626 Tf 411.5918 434.5773 Td[(.)]TJ +ET +1 0 0 1 145.7235 414.9111 cm 0 g 0 G -/F27 9.9626 Tf -260.887 -19.666 Td [(info)]TJ +1 0 0 1 -145.7235 -414.9111 cm +BT +/F29 9.9626 Tf 150.7049 414.9111 Td[(inf)-1(o)]TJ +ET +1 0 0 1 169.4816 414.9111 cm 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 14.3462 Tf -24.906 -32.834 Td [(Notes)]TJ +1 0 0 1 -169.4816 -414.9111 cm +BT +/F8 9.9626 Tf 174.4629 414.9111 Td[(Er)1(ror)-333(co)-28(de.)]TJ 1.1486 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(out)]TJ/F8 9.9626 Tf 16.549 0 Td[(.)]TJ -50.0346 -11.9552 Td[(An)-333(in)29(te)-1(ger)-333(v)56(alue;)-333(0)-334(means)-334(n)1(o)-334(error)-333(h)1(as)-334(b)-27(e)-1(en)-333(detec)-1(ted.)]TJ/F18 14.3462 Tf -24.9066 -32.8343 Td[(Not)-1(es)]TJ +ET +1 0 0 1 150.7049 312.4351 cm 0 g 0 G -/F8 9.9626 Tf 12.176 -21.821 Td [(1.)]TJ +1 0 0 1 -150.7049 -312.4351 cm +BT +/F8 9.9626 Tf 162.8814 312.4351 Td[(1.)]TJ +ET +1 0 0 1 170.6302 312.4351 cm 0 g 0 G - [-500(Exactly)-255(one)-255(of)-255(the)-255(optional)-255(argumen)27(ts)]TJ/F30 9.9626 Tf 178.749 0 Td [(parts)]TJ/F8 9.9626 Tf 26.151 0 Td [(,)]TJ/F30 9.9626 Tf 5.465 0 Td [(vg)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)]TJ/F30 9.9626 Tf 5.465 0 Td [(vl)]TJ/F8 9.9626 Tf 10.46 0 Td [(,)]TJ/F30 9.9626 Tf 5.465 0 Td [(nl)]TJ/F8 9.9626 Tf 13.003 0 Td [(m)28(ust)-255(b)-28(e)-255(sp)-28(eci\014ed,)]TJ -242.489 -11.955 Td [(thereb)28(y)-334(c)28(ho)-28(osing)-333(the)-333(initialization)-333(strategy)-334(as)-333(follo)28(ws:)]TJ +1 0 0 1 -170.6302 -312.4351 cm +BT +/F8 9.9626 Tf 175.6115 312.4351 Td[(Ex)1(ac)-1(tl)1(y)-255(one)-255(of)-255(the)-255(opti)1(onal)-255(argu)1(me)-1(n)28(ts)]TJ/F32 9.9626 Tf 166.0181 0 Td[(parts)]TJ/F8 9.9626 Tf 26.1517 0 Td[(,)]TJ/F32 9.9626 Tf 5.4649 0 Td[(vg)]TJ/F8 9.9626 Tf 10.4607 0 Td[(,)]TJ/F32 9.9626 Tf 5.4649 0 Td[(vl)]TJ/F8 9.9626 Tf 10.4607 0 Td[(,)]TJ/F32 9.9626 Tf 5.4649 0 Td[(nl)]TJ/F8 9.9626 Tf 13.0023 0 Td[(m)27(u)1(s)-1(t)-255(b)-27(e)-255(s)-1(p)-27(e)-1(ci\014)1(e)-1(d)1(,)]TJ -242.4882 -11.9552 Td[(th)1(e)-1(reb)28(y)-333(c)27(h)1(o)-28(osing)-333(th)1(e)-334(ini)1(tialization)-333(strategy)-333(as)-334(f)1(ollo)28(ws)-1(:)]TJ +ET +1 0 0 1 170.6302 280.8137 cm 0 g 0 G -/F27 9.9626 Tf 0 -19.666 Td [(parts)]TJ +1 0 0 1 -170.6302 -280.8137 cm +BT +/F29 9.9626 Tf 175.6115 280.8137 Td[(parts)]TJ +ET +1 0 0 1 201.2388 280.8137 cm 0 g 0 G -/F8 9.9626 Tf 30.609 0 Td [(In)-337(this)-338(case)-338(w)28(e)-337(ha)27(v)28(e)-337(a)-338(subroutine)-337(sp)-28(ecifying)-337(the)-338(mapping)-337(b)-28(et)28(w)28(ee)-1(n)]TJ -8.691 -11.955 Td [(global)-225(indices)-225(and)-225(pro)-28(cess/lo)-28(cal)-225(in)1(dex)-225(pairs.)-409(If)-225(this)-225(optional)-225(argu)1(m)-1(en)28(t)]TJ 0 -11.956 Td [(is)-316(sp)-28(eci\014ed,)-320(then)-316(it)-317(is)-316(mandatory)-316(to)-317(sp)-28(ecify)-316(the)-316(argumen)27(t)]TJ/F30 9.9626 Tf 251.563 0 Td [(mg)]TJ/F8 9.9626 Tf 13.612 0 Td [(as)-316(w)27(ell.)]TJ -265.175 -11.955 Td [(The)-333(subroutine)-334(m)28(ust)-333(conform)-333(to)-334(the)-333(follo)28(wing)-334(in)28(terface:)]TJ +1 0 0 1 -201.2388 -280.8137 cm +BT +/F8 9.9626 Tf 206.2202 280.8137 Td[(In)-337(thi)1(s)-338(c)-1(ase)-338(w)27(e)-338(h)1(a)28(v)28(e)-338(a)-338(sub)1(rou)1(tine)-338(sp)-27(e)-1(cify)1(ing)-337(the)-338(mapp)1(in)1(g)-338(b)-27(e)-1(t)28(w)28(e)-1(en)]TJ -8.6909 -11.9552 Td[(glob)1(al)-225(in)1(dice)-1(s)-225(and)-224(pr)1(o)-28(c)-1(es)-1(s/lo)-28(cal)-225(in)1(dex)-225(p)1(airs.)-408(I)-1(f)-224(thi)1(s)-226(op)1(tional)-224(argumen)28(t)]TJ 0 -11.9551 Td[(is)-317(sp)-27(e)-1(ci\014ed,)-319(then)-316(it)-316(is)-317(mand)1(atory)-316(to)-316(s)-1(p)-27(ec)-1(if)1(y)-316(the)-317(ar)1(gume)-1(n)29(t)]TJ/F32 9.9626 Tf 251.5624 0 Td[(mg)]TJ/F8 9.9626 Tf 13.6127 0 Td[(as)-317(w)28(e)-1(l)1(l.)]TJ -265.1751 -11.9552 Td[(The)-334(sub)1(rou)1(tine)-333(m)27(u)1(s)-1(t)-333(c)-1(on)1(for)1(m)-334(to)-333(the)-334(f)1(ollo)28(win)1(g)-334(in)29(te)-1(r)1(face)-1(:)]TJ +ET +1 0 0 1 192.548 227.2745 cm 0 g 0 G 0 g 0 G -/F30 9.9626 Tf 10.461 -17.674 Td [(interface)]TJ 15.691 -11.955 Td [(subroutine)-525(psb_parts\050glob_index,mg,np,pv,nv\051)]TJ 10.461 -11.955 Td [(integer,)-525(intent)-525(\050in\051)-1050(::)-525(glob_index,np,mg)]TJ 0 -11.955 Td [(integer,)-525(intent)-525(\050out\051)-525(::)-525(nv,)-525(pv\050*\051)]TJ -10.461 -11.955 Td [(end)-525(subroutine)-525(psb_parts)]TJ -15.691 -11.955 Td [(end)-525(interface)]TJ/F8 9.9626 Tf -10.461 -17.674 Td [(The)-333(input)-334(argumen)28(ts)-333(are:)]TJ +1 0 0 1 -192.548 -227.2745 cm +BT +/F32 9.9626 Tf 207.99 227.2745 Td[(interface)]TJ 15.691 -11.9552 Td[(subroutine)-525(psb_parts\050glob_index,mg,np,pv,nv\051)]TJ 10.4607 -11.9551 Td[(integer,)-525(intent)-525(\050in\051)-1050(::)-525(glob_index,np,mg)]TJ 0 -11.9552 Td[(integer,)-525(intent)-525(\050out\051)-525(::)-525(nv,)-525(pv\050*\051)]TJ -10.4607 -11.9552 Td[(end)-525(subroutine)-525(psb_parts)]TJ -15.691 -11.9551 Td[(end)-525(interface)]TJ/F8 9.9626 Tf -10.4607 -17.6737 Td[(The)-334(i)1(np)1(ut)-333(argu)1(m)-1(en)28(ts)-334(ar)1(e)-1(:)]TJ +ET +1 0 0 1 192.548 134.1438 cm 0 g 0 G -/F27 9.9626 Tf 0 -15.681 Td [(glob)]TJ +1 0 0 1 -192.548 -134.1438 cm +BT +/F29 9.9626 Tf 197.5293 134.1438 Td[(glob)]TJ ET +1 0 0 1 219.2211 134.1438 cm q -1 0 0 1 219.221 134.343 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -219.2211 -134.1438 cm BT -/F27 9.9626 Tf 222.658 134.144 Td [(index)]TJ -0 g 0 G -/F8 9.9626 Tf 32.192 0 Td [(The)-333(global)-334(index)-333(to)-333(b)-28(e)-333(mapp)-28(ed;)]TJ +/F29 9.9626 Tf 222.6583 134.1438 Td[(index)]TJ +ET +1 0 0 1 249.8686 134.1438 cm 0 g 0 G -/F27 9.9626 Tf -57.321 -13.818 Td [(np)]TJ +1 0 0 1 -249.8686 -134.1438 cm +BT +/F8 9.9626 Tf 254.8499 134.1438 Td[(The)-334(gl)1(obal)-333(in)1(dex)-333(to)-334(b)-27(e)-334(mapp)-27(e)-1(d)1(;)]TJ +ET +1 0 0 1 192.548 120.3256 cm 0 g 0 G -/F8 9.9626 Tf 17.712 0 Td [(The)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(pro)-28(cesses)-333(in)-334(the)-333(mapping;)]TJ +1 0 0 1 -192.548 -120.3256 cm +BT +/F29 9.9626 Tf 197.5293 120.3256 Td[(np)]TJ +ET +1 0 0 1 210.2593 120.3256 cm 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[(cdbldext|Build)-375(an)-375(extended)]TJ -30.109 -17.933 Td [(comm)31(unication)-375(descriptor)]TJ 0 -36.129 Td [(Syn)31(tax)]TJ/F8 9.9626 Tf 58.316 -21.901 Td [(call)-333(psb)]TJ +/F18 14.3462 Tf 130.0045 679.8522 Td[(cdblde)-1(xt|Buil)-1(d)-375(an)-375(exte)-1(nded)]TJ -30.1091 -17.9327 Td[(com)-1(m)31(uni)-1(cati)-1(on)-375(descr)-1(ipt)-1(or)]TJ 0 -36.1294 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 58.3156 -21.9014 Td[(call)-333(psb)]TJ ET +1 0 0 1 192.0729 603.8887 cm q -1 0 0 1 192.073 604.088 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -192.0729 -603.8887 cm BT -/F8 9.9626 Tf 195.062 603.889 Td [(cdbldext)-333(\050)]TJ/F17 9.9626 Tf 44.555 0 Td [(a,desc)]TJ +/F8 9.9626 Tf 195.0617 603.8887 Td[(cdbl)1(dext)-333(\050)]TJ/F19 9.9626 Tf 44.5553 0 Td[(a,desc)]TJ ET +1 0 0 1 266.7063 603.8887 cm q -1 0 0 1 266.706 604.088 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -266.7063 -603.8887 cm BT -/F17 9.9626 Tf 269.762 603.889 Td [(a,nl,desc)]TJ +/F19 9.9626 Tf 269.7615 603.8887 Td[(a,nl,)1(desc)]TJ ET +1 0 0 1 308.0532 603.8887 cm q -1 0 0 1 308.053 604.088 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -308.0532 -603.8887 cm BT -/F17 9.9626 Tf 311.108 603.889 Td [(out,)-358(info,)-357(extyp)51(e)]TJ/F8 9.9626 Tf 70.309 0 Td [(\051)]TJ -281.522 -24.004 Td [(This)-462(subrout)1(ine)-462(builds)-461(an)-462(extended)-462(comm)28(unication)-461(descriptor,)-494(based)-461(on)-462(the)]TJ 0 -11.955 Td [(input)-389(descriptor)]TJ/F30 9.9626 Tf 74.288 0 Td [(desc_a)]TJ/F8 9.9626 Tf 35.261 0 Td [(and)-389(on)-390(the)-389(stencil)-389(s)-1(p)-27(eci\014ed)-390(through)-389(the)-389(input)-390(sparse)]TJ -109.549 -11.955 Td [(matrix)]TJ/F30 9.9626 Tf 32.407 0 Td [(a)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +/F19 9.9626 Tf 311.1084 603.8887 Td[(out,)-357(info,)-358(ex)1(t)-1(y)1(p)51(e)]TJ/F8 9.9626 Tf 70.3081 0 Td[(\051)]TJ -281.5211 -24.0038 Td[(This)-462(sub)1(rou)1(tine)-462(b)1(ui)1(lds)-462(an)-461(exte)-1(n)1(ded)-461(c)-1(omm)27(u)1(ni)1(c)-1(ation)-461(d)1(e)-1(sc)-1(r)1(ipt)1(or,)-494(b)1(as)-1(ed)-461(on)-461(the)]TJ 0 -11.9551 Td[(in)1(pu)1(t)-390(d)1(e)-1(sc)-1(r)1(iptor)]TJ/F32 9.9626 Tf 74.2872 0 Td[(desc_a)]TJ/F8 9.9626 Tf 35.2614 0 Td[(and)-389(on)-388(the)-390(ste)-1(n)1(c)-1(i)1(l)-389(s)-1(p)-27(e)-1(ci\014ed)-389(th)1(rough)-389(t)1(he)-390(in)1(pu)1(t)-390(spar)1(s)-1(e)]TJ -109.5486 -11.9552 Td[(matrix)]TJ/F32 9.9626 Tf 32.4063 0 Td[(a)]TJ/F8 9.9626 Tf 5.2304 0 Td[(.)]TJ +ET +1 0 0 1 94.9141 535.769 cm 0 g 0 G -/F27 9.9626 Tf -37.637 -20.206 Td [(T)32(yp)-32(e:)]TJ +1 0 0 1 -94.9141 -535.769 cm +BT +/F29 9.9626 Tf 99.8954 535.769 Td[(T)32(yp)-32(e:)]TJ +ET +1 0 0 1 128.7108 535.769 cm 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +1 0 0 1 -128.7108 -535.769 cm +BT +/F8 9.9626 Tf 133.6921 535.769 Td[(Sy)1(nc)27(h)1(ron)1(ous.)]TJ +ET +1 0 0 1 94.9141 515.4699 cm 0 g 0 G -/F27 9.9626 Tf -33.797 -20.299 Td [(On)-383(En)32(try)]TJ +1 0 0 1 -94.9141 -515.4699 cm +BT +/F29 9.9626 Tf 99.8954 515.4699 Td[(On)-383(En)32(tr)1(y)]TJ +ET +1 0 0 1 147.4806 515.4699 cm 0 g 0 G +1 0 0 1 -52.5665 -20.299 cm 0 g 0 G - 0 -20.299 Td [(a)]TJ +1 0 0 1 -94.9141 -495.1709 cm +BT +/F29 9.9626 Tf 99.8954 495.1709 Td[(a)]TJ +ET +1 0 0 1 105.4647 495.1709 cm 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(A)-333(sparse)-334(matrix)-333(Scop)-28(e:)]TJ/F27 9.9626 Tf 101.176 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -109.893 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(t)27(yp)-27(e.)]TJ +1 0 0 1 -105.4647 -495.1709 cm +BT +/F8 9.9626 Tf 110.4461 495.1709 Td[(A)-333(s)-1(p)1(arse)-334(m)-1(at)1(rix)-333(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 101.1763 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -109.8935 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(t)28(yp)-27(e.)]TJ +ET +1 0 0 1 94.9141 439.0064 cm 0 g 0 G -/F27 9.9626 Tf -24.907 -20.299 Td [(desc)]TJ +1 0 0 1 -94.9141 -439.0064 cm +BT +/F29 9.9626 Tf 99.8954 439.0064 Td[(desc)]TJ ET +1 0 0 1 121.81 439.0064 cm q -1 0 0 1 121.81 439.206 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -121.81 -439.0064 cm BT -/F27 9.9626 Tf 125.247 439.006 Td [(a)]TJ +/F29 9.9626 Tf 125.2471 439.0064 Td[(a)]TJ +ET +1 0 0 1 130.8165 439.0064 cm 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -130.8165 -439.0064 cm +BT +/F8 9.9626 Tf 135.7978 439.0064 Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -10.9958 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 295.717 391.1857 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -295.717 -391.1857 cm +BT +/F32 9.9626 Tf 295.717 391.1857 Td[(psb)]TJ ET +1 0 0 1 312.0356 391.1857 cm q -1 0 0 1 312.036 391.385 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -312.0356 -391.1857 cm BT -/F30 9.9626 Tf 315.174 391.186 Td [(spmat)]TJ +/F32 9.9626 Tf 315.1738 391.1857 Td[(spmat)]TJ ET +1 0 0 1 341.9531 391.1857 cm q -1 0 0 1 341.953 391.385 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -341.9531 -391.1857 cm BT -/F30 9.9626 Tf 345.091 391.186 Td [(type)]TJ +/F32 9.9626 Tf 345.0913 391.1857 Td[(type)]TJ +ET +1 0 0 1 366.0127 391.1857 cm 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +1 0 0 1 -366.0127 -391.1857 cm +BT +/F8 9.9626 Tf 366.0127 391.1857 Td[(.)]TJ +ET +1 0 0 1 94.9141 370.8867 cm 0 g 0 G -/F27 9.9626 Tf -266.118 -20.299 Td [(nl)]TJ +1 0 0 1 -94.9141 -370.8867 cm +BT +/F29 9.9626 Tf 99.8954 370.8867 Td[(nl)]TJ +ET +1 0 0 1 109.4429 370.8867 cm 0 g 0 G -/F8 9.9626 Tf 14.529 0 Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(additional)-333(la)28(y)27(ers)-333(desired.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F11 9.9626 Tf 130.428 0 Td [(nl)]TJ/F14 9.9626 Tf 11.916 0 Td [(\025)]TJ/F8 9.9626 Tf 10.516 0 Td [(0.)]TJ +1 0 0 1 -109.4429 -370.8867 cm +BT +/F8 9.9626 Tf 114.4242 370.8867 Td[(th)1(e)-334(n)28(um)28(b)-27(e)-1(r)-333(of)-333(ad)1(diti)1(onal)-333(la)28(y)28(e)-1(r)1(s)-334(desired.)]TJ 10.3778 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(global)]TJ/F8 9.9626 Tf 29.7563 0 Td[(.)]TJ -57.7071 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(v)55(al)1(ue)]TJ/F11 9.9626 Tf 130.4278 0 Td[(nl)]TJ/F14 9.9626 Tf 11.9159 0 Td[(\025)]TJ/F8 9.9626 Tf 10.5161 0 Td[(0.)]TJ +ET +1 0 0 1 94.9141 302.7669 cm 0 g 0 G -/F27 9.9626 Tf -177.767 -20.299 Td [(ext)32(yp)-32(e)]TJ +1 0 0 1 -94.9141 -302.7669 cm +BT +/F29 9.9626 Tf 99.8954 302.7669 Td[(ext)32(yp)-32(e)]TJ +ET +1 0 0 1 133.3116 302.7669 cm 0 g 0 G -/F8 9.9626 Tf 38.398 0 Td [(the)-333(kind)-334(of)-333(estension)-333(required.)]TJ -13.491 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 44.396 0 Td [(.)]TJ -69.579 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-419(as:)-616(an)-420(in)28(teger)-419(v)55(alue)]TJ/F30 9.9626 Tf 135.566 0 Td [(psb_ovt_xhal_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 7.159 0 Td [(psb_ovt_asov_)]TJ/F8 9.9626 Tf 67.995 0 Td [(,)-441(default:)]TJ/F30 9.9626 Tf -278.714 -11.955 Td [(psb_ovt_xhal_)]TJ +1 0 0 1 -133.3116 -302.7669 cm +BT +/F8 9.9626 Tf 138.2929 302.7669 Td[(th)1(e)-334(kin)1(d)-333(of)-333(e)-1(stension)-333(requ)1(ired.)]TJ -13.4909 -11.9551 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(global)]TJ/F8 9.9626 Tf 29.7563 0 Td[(.)]TJ -57.7071 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf 44.3958 0 Td[(.)]TJ -69.5792 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-418(as)-1(:)-616(an)-419(in)29(te)-1(ger)-419(v)56(alue)]TJ/F32 9.9626 Tf 135.566 0 Td[(psb_ovt_xhal_)]TJ/F8 9.9626 Tf 67.9944 0 Td[(,)]TJ/F32 9.9626 Tf 7.1587 0 Td[(psb_ovt_asov_)]TJ/F8 9.9626 Tf 67.9945 0 Td[(,)-441(d)1(e)-1(f)1(aul)1(t:)]TJ/F32 9.9626 Tf -278.7136 -11.9552 Td[(psb_ovt_xhal_)]TJ +ET +1 0 0 1 94.9141 220.6995 cm 0 g 0 G -/F27 9.9626 Tf -24.907 -22.291 Td [(On)-383(Return)]TJ +1 0 0 1 -94.9141 -220.6995 cm +BT +/F29 9.9626 Tf 99.8954 220.6995 Td[(On)-383(R)-1(etur)1(n)]TJ +ET +1 0 0 1 154.4337 220.6995 cm 0 g 0 G +1 0 0 1 -59.5196 -20.299 cm 0 g 0 G - 0 -20.3 Td [(desc)]TJ +1 0 0 1 -94.9141 -200.4005 cm +BT +/F29 9.9626 Tf 99.8954 200.4005 Td[(desc)]TJ ET +1 0 0 1 121.81 200.4005 cm q -1 0 0 1 121.81 200.6 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -121.81 -200.4005 cm BT -/F27 9.9626 Tf 125.247 200.401 Td [(out)]TJ +/F29 9.9626 Tf 125.2471 200.4005 Td[(out)]TJ +ET +1 0 0 1 141.7961 200.4005 cm 0 g 0 G -/F8 9.9626 Tf 21.53 0 Td [(the)-333(extended)-334(comm)28(unication)-333(descriptor.)]TJ -21.975 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -141.7961 -200.4005 cm +BT +/F8 9.9626 Tf 146.7774 200.4005 Td[(th)1(e)-334(e)-1(x)1(te)-1(n)1(ded)-333(c)-1(omm)27(u)1(ni)1(c)-1(ation)-333(d)1(e)-1(scrip)1(tor.)]TJ -21.9754 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ -59.582 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 295.717 152.5798 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -295.717 -152.5798 cm +BT +/F32 9.9626 Tf 295.717 152.5798 Td[(psb)]TJ ET +1 0 0 1 312.0356 152.5798 cm q -1 0 0 1 312.036 152.779 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -312.0356 -152.5798 cm BT -/F30 9.9626 Tf 315.174 152.58 Td [(desc)]TJ +/F32 9.9626 Tf 315.1738 152.5798 Td[(desc)]TJ ET +1 0 0 1 336.7228 152.5798 cm q -1 0 0 1 336.723 152.779 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -336.7228 -152.5798 cm BT -/F30 9.9626 Tf 339.861 152.58 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F32 9.9626 Tf 339.861 152.5798 Td[(type)]TJ +ET +1 0 0 1 360.7824 152.5798 cm 0 g 0 G -/F27 9.9626 Tf -260.887 -20.299 Td [(info)]TJ +1 0 0 1 -360.7824 -152.5798 cm +BT +/F8 9.9626 Tf 360.7824 152.5798 Td[(.)]TJ +ET +1 0 0 1 94.9141 132.2808 cm 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ +1 0 0 1 -94.9141 -132.2808 cm +BT +/F29 9.9626 Tf 99.8954 132.2808 Td[(inf)-1(o)]TJ +ET +1 0 0 1 118.6721 132.2808 cm 0 g 0 G -/F8 9.9626 Tf 109.589 -29.888 Td [(67)]TJ +1 0 0 1 -118.6721 -132.2808 cm +BT +/F8 9.9626 Tf 123.6534 132.2808 Td[(Er)1(ror)-333(co)-28(de.)]TJ 1.1486 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ +ET +1 0 0 1 99.8954 90.4377 cm 0 g 0 G +1 0 0 1 -99.8954 -90.4377 cm +BT +/F8 9.9626 Tf 266.7696 90.4377 Td[(67)]TJ ET +1 0 0 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[(to)]TJ +/F8 9.9626 Tf 280.1824 610.619 Td[(to)]TJ ET +1 0 0 1 289.6359 610.619 cm q -1 0 0 1 289.636 610.818 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -289.6359 -610.619 cm BT -/F8 9.9626 Tf 292.625 610.619 Td [(glob)-333(\050)]TJ/F17 9.9626 Tf 25.46 0 Td [(x,)-358(y,)-357(desc)]TJ +/F8 9.9626 Tf 292.6247 610.619 Td[(glob)-333(\050)]TJ/F19 9.9626 Tf 25.4601 0 Td[(x,)-357(y,)-357(desc)]TJ ET +1 0 0 1 359.725 610.619 cm q -1 0 0 1 359.725 610.818 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -359.725 -610.619 cm BT -/F17 9.9626 Tf 362.78 610.619 Td [(a,)-358(info,)-357(iact)]TJ/F8 9.9626 Tf 51.175 0 Td [(\051)]TJ -180.935 -23.91 Td [(call)-333(psb)]TJ +/F19 9.9626 Tf 362.7802 610.619 Td[(a,)-358(i)1(nfo,)-358(i)1(act)]TJ/F8 9.9626 Tf 51.1745 0 Td[(\051)]TJ -180.9345 -23.9103 Td[(call)-333(psb)]TJ ET +1 0 0 1 266.8822 586.7087 cm q -1 0 0 1 266.882 586.908 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -266.8822 -586.7087 cm BT -/F8 9.9626 Tf 269.871 586.709 Td [(lo)-28(c)]TJ +/F8 9.9626 Tf 269.871 586.7087 Td[(lo)-28(c)]TJ ET +1 0 0 1 282.9221 586.7087 cm q -1 0 0 1 282.922 586.908 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -282.9221 -586.7087 cm BT -/F8 9.9626 Tf 285.911 586.709 Td [(to)]TJ +/F8 9.9626 Tf 285.9109 586.7087 Td[(to)]TJ ET +1 0 0 1 295.3643 586.7087 cm q -1 0 0 1 295.364 586.908 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S Q +1 0 0 1 -295.3643 -586.7087 cm BT -/F8 9.9626 Tf 298.353 586.709 Td [(glob)-333(\050)]TJ/F17 9.9626 Tf 25.46 0 Td [(x,)-358(desc)]TJ +/F8 9.9626 Tf 298.3532 586.7087 Td[(glob)-333(\050)]TJ/F19 9.9626 Tf 25.4601 0 Td[(x,)-357(desc)]TJ ET +1 0 0 1 353.9965 586.7087 cm q -1 0 0 1 353.997 586.908 cm -[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.0552 0.1992 l +S Q +1 0 0 1 -353.9965 -586.7087 cm BT -/F17 9.9626 Tf 357.052 586.709 Td [(a,)-358(info,)-357(iact)]TJ/F8 9.9626 Tf 51.174 0 Td [(\051)]TJ +/F19 9.9626 Tf 357.0518 586.7087 Td[(a,)-358(i)1(nfo,)-358(i)1(act)]TJ/F8 9.9626 Tf 51.1744 0 Td[(\051)]TJ +ET +1 0 0 1 145.7235 562.7983 cm 0 g 0 G -/F27 9.9626 Tf -257.521 -23.911 Td [(T)32(yp)-32(e:)]TJ +1 0 0 1 -145.7235 -562.7983 cm +BT +/F29 9.9626 Tf 150.7049 562.7983 Td[(T)32(yp)-32(e:)]TJ +ET +1 0 0 1 179.5203 562.7983 cm 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +1 0 0 1 -179.5203 -562.7983 cm +BT +/F8 9.9626 Tf 184.5016 562.7983 Td[(Async)28(hron)1(ous.)]TJ +ET +1 0 0 1 145.7235 544.3519 cm 0 g 0 G -/F27 9.9626 Tf -33.797 -18.446 Td [(On)-383(En)32(try)]TJ +1 0 0 1 -145.7235 -544.3519 cm +BT +/F29 9.9626 Tf 150.7049 544.3519 Td[(On)-383(En)32(tr)1(y)]TJ +ET +1 0 0 1 198.2901 544.3519 cm 0 g 0 G +1 0 0 1 -52.5665 -18.4465 cm 0 g 0 G - 0 -18.447 Td [(x)]TJ +1 0 0 1 -145.7236 -525.9054 cm +BT +/F29 9.9626 Tf 150.7049 525.9054 Td[(x)]TJ +ET +1 0 0 1 156.7516 525.9054 cm 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(An)-333(in)28(tege)-1(r)-333(v)28(ector)-333(of)-334(indices)-333(to)-333(b)-28(e)-334(con)28(v)28(erted.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in,)-383(inout)]TJ/F8 9.9626 Tf 42.646 0 Td [(.)]TJ -76.131 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ +1 0 0 1 -156.7516 -525.9054 cm +BT +/F8 9.9626 Tf 161.7329 525.9054 Td[(An)-333(in)29(te)-1(ger)-333(v)28(e)-1(ctor)-333(of)-333(in)1(dice)-1(s)-333(to)-334(b)-27(e)-334(con)28(v)28(erted.)]TJ 13.8786 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in,)-384(i)-1(n)1(out)]TJ/F8 9.9626 Tf 42.6454 0 Td[(.)]TJ -76.131 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(rank)-333(on)1(e)-334(in)28(tege)-1(r)-333(ar)1(ra)28(y)83(.)]TJ +ET +1 0 0 1 145.7235 447.6831 cm 0 g 0 G -/F27 9.9626 Tf -24.907 -30.402 Td [(desc)]TJ +1 0 0 1 -145.7235 -447.6831 cm +BT +/F29 9.9626 Tf 150.7049 447.6831 Td[(desc)]TJ ET +1 0 0 1 172.6195 447.6831 cm q -1 0 0 1 172.619 447.882 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S Q +1 0 0 1 -172.6195 -447.6831 cm BT -/F27 9.9626 Tf 176.057 447.683 Td [(a)]TJ +/F29 9.9626 Tf 176.0566 447.6831 Td[(a)]TJ +ET +1 0 0 1 181.6259 447.6831 cm 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +1 0 0 1 -181.6259 -447.6831 cm +BT +/F8 9.9626 Tf 186.6072 447.6831 Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -10.9957 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +ET +1 0 0 1 346.5264 399.8625 cm 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +1 0 0 1 -346.5264 -399.8625 cm +BT +/F32 9.9626 Tf 346.5264 399.8625 Td[(psb)]TJ ET +1 0 0 1 362.8451 399.8625 cm q -1 0 0 1 362.845 400.062 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -362.8451 -399.8625 cm BT -/F30 9.9626 Tf 365.983 399.862 Td [(desc)]TJ +/F32 9.9626 Tf 365.9833 399.8625 Td[(desc)]TJ ET +1 0 0 1 387.5322 399.8625 cm q -1 0 0 1 387.532 400.062 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +[]0 d +0 J +0.3985 w +0 0.1992 m +3.1382 0.1992 l +S Q +1 0 0 1 -387.5322 -399.8625 cm BT -/F30 9.9626 Tf 390.67 399.862 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F32 9.9626 Tf 390.6705 399.8625 Td[(type)]TJ +ET +1 0 0 1 411.5918 399.8625 cm 0 g 0 G -/F27 9.9626 Tf -260.887 -18.446 Td [(iact)]TJ +1 0 0 1 -411.5918 -399.8625 cm +BT +/F8 9.9626 Tf 411.5918 399.8625 Td[(.)]TJ +ET +1 0 0 1 145.7235 381.416 cm 0 g 0 G -/F8 9.9626 Tf 23.28 0 Td [(sp)-28(eci\014es)-333(action)-334(to)-333(b)-28(e)-333(tak)28(en)-334(in)-333(case)-333(of)-334(range)-333(errors.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 257.148 0 Td [(global)]TJ/F8 9.9626 Tf -255.522 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-256(c)28(haracter)-255(v)56(ariable)]TJ/F30 9.9626 Tf 143.584 0 Td [(I)]TJ/F8 9.9626 Tf 5.231 0 Td [(gnore,)]TJ/F30 9.9626 Tf 29.293 0 Td [(W)]TJ/F8 9.9626 Tf 5.23 0 Td [(arning)-255(or)]TJ/F30 9.9626 Tf 41.67 0 Td [(A)]TJ/F8 9.9626 Tf 5.23 0 Td [(b)-28(ort,)-271(d)1(e)-1(f)1(ault)]TJ/F30 9.9626 Tf 56.742 0 Td [(I)]TJ/F8 9.9626 Tf 5.23 0 Td [(gnore.)]TJ +1 0 0 1 -145.7235 -381.416 cm +BT +/F29 9.9626 Tf 150.7049 381.416 Td[(iac)-1(t)]TJ +ET +1 0 0 1 169.0042 381.416 cm 0 g 0 G -/F27 9.9626 Tf -317.116 -18.22 Td [(On)-383(Return)]TJ +1 0 0 1 -169.0042 -381.416 cm +BT +/F8 9.9626 Tf 173.9855 381.416 Td[(sp)-28(ec)-1(i)1(\014es)-334(ac)-1(ti)1(on)-333(to)-333(b)-28(e)-334(t)1(ak)28(e)-1(n)-333(in)-333(case)-334(of)-333(ran)1(ge)-334(e)-1(r)1(rors.)-444(Scop)-28(e:)]TJ/F29 9.9626 Tf 257.1472 0 Td[(global)]TJ/F8 9.9626 Tf -255.5212 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-254(as)-1(:)-405(a)-255(c)27(h)1(aracte)-1(r)-255(v)56(ari)1(able)]TJ/F32 9.9626 Tf 143.584 0 Td[(I)]TJ/F8 9.9626 Tf 5.2303 0 Td[(gnor)1(e)-1(,)]TJ/F32 9.9626 Tf 29.2928 0 Td[(W)]TJ/F8 9.9626 Tf 5.2304 0 Td[(arn)1(ing)-255(or)]TJ/F32 9.9626 Tf 41.6697 0 Td[(A)]TJ/F8 9.9626 Tf 5.2303 0 Td[(b)-27(ort,)-270(de)-1(f)1(aul)1(t)]TJ/F32 9.9626 Tf 56.7418 0 Td[(I)]TJ/F8 9.9626 Tf 5.2304 0 Td[(gnor)1(e)-1(.)]TJ +ET +1 0 0 1 145.7235 327.3297 cm 0 g 0 G +1 0 0 1 -145.7235 -327.3297 cm +BT +/F29 9.9626 Tf 150.7049 327.3297 Td[(On)-383(R)-1(etur)1(n)]TJ +ET +1 0 0 1 205.2431 327.3297 cm 0 g 0 G - 0 -18.447 Td [(x)]TJ +1 0 0 1 -59.5196 -18.4464 cm 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(If)]TJ/F11 9.9626 Tf 10.132 0 Td [(y)]TJ/F8 9.9626 Tf 8.733 0 Td [(is)-350(not)-351(presen)28(t,)-355(then)]TJ/F11 9.9626 Tf 88.587 0 Td [(x)]TJ/F8 9.9626 Tf 9.185 0 Td [(is)-350(o)27(v)28(erwritten)-350(with)-350(the)-351(translated)-350(in)28(teger)-351(indices.)]TJ -102.759 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(i)1(n)27(teger)-333(arra)28(y)83(.)]TJ +1 0 0 1 -145.7235 -308.8833 cm +BT +/F29 9.9626 Tf 150.7049 308.8833 Td[(x)]TJ +ET +1 0 0 1 156.7516 308.8833 cm 0 g 0 G -/F27 9.9626 Tf -24.906 -18.447 Td [(y)]TJ +1 0 0 1 -156.7516 -308.8833 cm +BT +/F8 9.9626 Tf 161.7329 308.8833 Td[(If)]TJ/F11 9.9626 Tf 10.1325 0 Td[(y)]TJ/F8 9.9626 Tf 8.7327 0 Td[(is)-351(n)1(ot)-350(pres)-1(en)28(t,)-354(then)]TJ/F11 9.9626 Tf 88.5869 0 Td[(x)]TJ/F8 9.9626 Tf 9.1846 0 Td[(is)-351(o)28(v)28(erwritt)1(e)-1(n)-350(with)-350(th)1(e)-351(tr)1(anslate)-1(d)-350(i)1(n)28(tege)-1(r)-350(in)1(dice)-1(s.)]TJ -102.7581 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ -59.582 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(rank)-333(on)1(e)-334(in)28(tege)-1(r)-333(ar)1(ra)28(y)83(.)]TJ +ET +1 0 0 1 145.7235 242.6162 cm 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(If)]TJ/F11 9.9626 Tf 10.166 0 Td [(y)]TJ/F8 9.9626 Tf 8.767 0 Td [(is)-354(not)-354(presen)28(t,)-359(then)]TJ/F11 9.9626 Tf 88.732 0 Td [(y)]TJ/F8 9.9626 Tf 8.767 0 Td [(is)-354(o)28(v)28(erwritten)-354(with)-354(the)-354(translated)-353(in)27(teger)-353(indices,)]TJ -102.554 -11.955 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(left)-334(unc)28(hanged.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 113.242 0 Td [(global)]TJ/F8 9.9626 Tf -141.629 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(i)1(n)27(teger)-333(arra)28(y)83(.)]TJ +1 0 0 1 -145.7235 -242.6162 cm +BT +/F29 9.9626 Tf 150.7049 242.6162 Td[(y)]TJ +ET +1 0 0 1 156.7516 242.6162 cm 0 g 0 G -/F27 9.9626 Tf -24.906 -18.446 Td [(info)]TJ +1 0 0 1 -156.7516 -242.6162 cm +BT +/F8 9.9626 Tf 161.7329 242.6162 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[(a)-448(lev)28(el)-448(of)-447(v)27(erb)-27(osit)27(y)-447(than)-448(can)-448(b)-27(e)-448(c)28(hosen)-448(b)28(y)-448(the)-448(user.)-787(If)-448(the)-448(execution)-447(is)-448(not)]TJ 0 -11.955 Td [(ab)-28(orted,)-328(then,)-329(the)-328(caller)-327(routine)-328(c)28(hec)28(ks)-328(the)-328(v)56(alue)-328(retur)1(ned)-328(in)-328(the)]TJ/F30 9.9626 Tf 285.46 0 Td [(info)]TJ/F8 9.9626 Tf 24.185 0 Td [(v)56(ariable)]TJ -309.645 -11.955 Td [(and,)-359(if)-354(not)-354(zero,)-359(an)-353(e)-1(r)1(ror)-354(condition)-354(is)-354(raised.)-506(This)-354(pro)-28(cess)-354(con)28(tin)28(ues)-354(on)-354(all)-354(the)]TJ 0 -11.955 Td [(lev)28(els)-297(of)-297(nested)-296(calls)-297(un)28(til)-297(the)-296(lev)28(e)-1(l)-296(where)-297(the)-296(user)-297(decides)-297(to)-296(ab)-28(ort)-297(the)-296(program)]TJ 0 -11.955 Td [(execution.)]TJ 14.944 -11.956 Td [(Figure)]TJ +/F18 14.3462 Tf 99.8954 706.1289 Td[(8)-1125(E)-1(rr)-1(or)-376(handli)-1(ng)]TJ/F8 9.9626 Tf 0 -21.821 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/Size 1740 -/Root 1738 0 R -/Info 1739 0 R -/ID [<81D17E18EE0F88B68A52211A4CD6DD81> <81D17E18EE0F88B68A52211A4CD6DD81>] >> +<< +/Size 1653 +/Root 1651 0 R +/Info 1652 0 R +/ID [ ] +>> startxref -953827 +1257375 %%EOF diff --git a/krylov/psb_cbicg.f90 b/krylov/psb_cbicg.f90 index d87433eb..d7feb76d 100644 --- a/krylov/psb_cbicg.f90 +++ b/krylov/psb_cbicg.f90 @@ -149,7 +149,7 @@ subroutine psb_cbicg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! istop_ = 1: normwise backward error, infinity norm diff --git a/krylov/psb_ccg.f90 b/krylov/psb_ccg.f90 index 92862d0f..a9a35098 100644 --- a/krylov/psb_ccg.f90 +++ b/krylov/psb_ccg.f90 @@ -142,7 +142,7 @@ subroutine psb_ccg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_ccgs.f90 b/krylov/psb_ccgs.f90 index ff0d758d..07f96c59 100644 --- a/krylov/psb_ccgs.f90 +++ b/krylov/psb_ccgs.f90 @@ -141,7 +141,7 @@ Subroutine psb_ccgs(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_ccgstab.f90 b/krylov/psb_ccgstab.f90 index 03ea5296..f6b02a21 100644 --- a/krylov/psb_ccgstab.f90 +++ b/krylov/psb_ccgstab.f90 @@ -143,7 +143,7 @@ subroutine psb_ccgstab(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_ccgstabl.f90 b/krylov/psb_ccgstabl.f90 index f36b940b..de225ab3 100644 --- a/krylov/psb_ccgstabl.f90 +++ b/krylov/psb_ccgstabl.f90 @@ -157,7 +157,7 @@ Subroutine psb_ccgstabl(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,is if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif if (present(itmax)) then diff --git a/krylov/psb_crgmres.f90 b/krylov/psb_crgmres.f90 index 2bf65695..18bb817a 100644 --- a/krylov/psb_crgmres.f90 +++ b/krylov/psb_crgmres.f90 @@ -156,7 +156,7 @@ Subroutine psb_crgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,ist if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm diff --git a/krylov/psb_dbicg.f90 b/krylov/psb_dbicg.f90 index 73e7ee85..003f5175 100644 --- a/krylov/psb_dbicg.f90 +++ b/krylov/psb_dbicg.f90 @@ -149,7 +149,7 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! istop_ = 1: normwise backward error, infinity norm diff --git a/krylov/psb_dcg.F90 b/krylov/psb_dcg.F90 index 80fa348f..42c375d1 100644 --- a/krylov/psb_dcg.F90 +++ b/krylov/psb_dcg.F90 @@ -144,7 +144,7 @@ subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop,cond) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_dcgs.f90 b/krylov/psb_dcgs.f90 index 6f6955f8..b3c58642 100644 --- a/krylov/psb_dcgs.f90 +++ b/krylov/psb_dcgs.f90 @@ -142,7 +142,7 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_dcgstab.F90 b/krylov/psb_dcgstab.F90 index 53cf7b56..a569ad1a 100644 --- a/krylov/psb_dcgstab.F90 +++ b/krylov/psb_dcgstab.F90 @@ -164,7 +164,7 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm diff --git a/krylov/psb_dcgstabl.f90 b/krylov/psb_dcgstabl.f90 index 14d7883b..e6c27ece 100644 --- a/krylov/psb_dcgstabl.f90 +++ b/krylov/psb_dcgstabl.f90 @@ -156,7 +156,7 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,is if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif if (present(itmax)) then diff --git a/krylov/psb_drgmres.f90 b/krylov/psb_drgmres.f90 index fc606371..09ae9a03 100644 --- a/krylov/psb_drgmres.f90 +++ b/krylov/psb_drgmres.f90 @@ -157,7 +157,7 @@ subroutine psb_drgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,ist if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm diff --git a/krylov/psb_sbicg.f90 b/krylov/psb_sbicg.f90 index 6dc03228..f87513b7 100644 --- a/krylov/psb_sbicg.f90 +++ b/krylov/psb_sbicg.f90 @@ -150,7 +150,7 @@ subroutine psb_sbicg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! istop_ = 1: normwise backward error, infinity norm diff --git a/krylov/psb_scg.F90 b/krylov/psb_scg.F90 index f6601875..974ca36c 100644 --- a/krylov/psb_scg.F90 +++ b/krylov/psb_scg.F90 @@ -145,7 +145,7 @@ subroutine psb_scg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop,cond) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_scgs.f90 b/krylov/psb_scgs.f90 index bb0ac487..859c0238 100644 --- a/krylov/psb_scgs.f90 +++ b/krylov/psb_scgs.f90 @@ -143,7 +143,7 @@ Subroutine psb_scgs(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_scgstab.F90 b/krylov/psb_scgstab.F90 index 6a6f4fda..53c6e8f5 100644 --- a/krylov/psb_scgstab.F90 +++ b/krylov/psb_scgstab.F90 @@ -166,7 +166,7 @@ Subroutine psb_scgstab(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm diff --git a/krylov/psb_scgstabl.f90 b/krylov/psb_scgstabl.f90 index ffaa4303..1b172d8d 100644 --- a/krylov/psb_scgstabl.f90 +++ b/krylov/psb_scgstabl.f90 @@ -157,7 +157,7 @@ Subroutine psb_scgstabl(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,is if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif if (present(itmax)) then diff --git a/krylov/psb_srgmres.f90 b/krylov/psb_srgmres.f90 index 978cc39c..d446fa49 100644 --- a/krylov/psb_srgmres.f90 +++ b/krylov/psb_srgmres.f90 @@ -156,7 +156,7 @@ subroutine psb_srgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,ist if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm diff --git a/krylov/psb_zbicg.f90 b/krylov/psb_zbicg.f90 index f5648635..eed7147a 100644 --- a/krylov/psb_zbicg.f90 +++ b/krylov/psb_zbicg.f90 @@ -148,7 +148,7 @@ subroutine psb_zbicg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! istop_ = 1: normwise backward error, infinity norm diff --git a/krylov/psb_zcg.F90 b/krylov/psb_zcg.F90 index f2b3362c..5d85c057 100644 --- a/krylov/psb_zcg.F90 +++ b/krylov/psb_zcg.F90 @@ -141,7 +141,7 @@ subroutine psb_zcg(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_zcgs.f90 b/krylov/psb_zcgs.f90 index 94143d74..34f6c199 100644 --- a/krylov/psb_zcgs.f90 +++ b/krylov/psb_zcgs.f90 @@ -140,7 +140,7 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_zcgstab.f90 b/krylov/psb_zcgstab.f90 index 15101cac..de00c0c1 100644 --- a/krylov/psb_zcgstab.f90 +++ b/krylov/psb_zcgstab.f90 @@ -142,7 +142,7 @@ subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,istop) If (Present(istop)) Then istop_ = istop Else - istop_ = 1 + istop_ = 2 Endif call psb_chkvect(mglob,1,size(x,1),1,1,desc_a,info) diff --git a/krylov/psb_zcgstabl.f90 b/krylov/psb_zcgstabl.f90 index 8fa47f42..3d8c14be 100644 --- a/krylov/psb_zcgstabl.f90 +++ b/krylov/psb_zcgstabl.f90 @@ -156,7 +156,7 @@ Subroutine psb_zcgstabl(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,is if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif if (present(itmax)) then diff --git a/krylov/psb_zrgmres.f90 b/krylov/psb_zrgmres.f90 index 2c4bd64f..a9c45a10 100644 --- a/krylov/psb_zrgmres.f90 +++ b/krylov/psb_zrgmres.f90 @@ -157,7 +157,7 @@ Subroutine psb_zrgmres(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,irst,ist if (present(istop)) then istop_ = istop else - istop_ = 1 + istop_ = 2 endif ! ! ISTOP_ = 1: Normwise backward error, infinity norm